地下熱伝導モデルを用いた場合の陰解法による時間積分

Time integration by using implicit scheme in case using subsurface thermal diffusion model

Note that Japanese and English are described in parallel.

Procedures List

PhyImplSDHTendency :	時間変化率の計算
PhyImplSDHSetMethodFromMatthews :	SurfType から計算法インデクスの作成
PhyImplSDHInit :	初期化
——————————- :	————
PhyImplSDHTendency :	Calculate tendency
PhyImplSDHSetMethodFromMatthews :	Set index for calculation method
PhyImplSDHInit :	Initialization

Methods

FlagBucketModel FlagMajCompPhaseChange FlagSeaIce FlagSlabOcean FlagSnow FlagSublimation IndexLand IndexLandWithPresTs IndexPresTs IndexSeaIce IndexSlabOcean IndexSlabOceanSeaIce IndexSpcH2O IndexSpcMajComp NumMaxItr PhyImplSDHV5ChkConservation PhyImplSDHV5ChkConservationTQ PhyImplSDHV5CorSOTempBySnowMelt PhyImplSDHV5IceSnowPhaseChgCor PhyImplSDHV5Init PhyImplSDHV5SOSeaIceCorrection PhyImplSDHV5SeaIceCorrection PhyImplSDHV5SetMethodMatthews PhyImplSDHV5Tendency PhyImplSDHV5TendencyHeatCore PhyImplSDHV5TendencyHeatTQCore PhyImplSDHV5TendencyMomCore ResidualMessageThreshold SOHeatCapacity TempItrCrit module_name phy_implicit_sdh_V5_inited version

Included Modules

gridset composition dc_types dc_message constants_snowseaice snowice_frac timeset constants mpi_wrapper axesset saturate Bucket_Model surface_flux_util phy_implicit_utils sosi_utils gtool_historyauto saturate_major_comp namelist_util dc_iounit dc_string constants0

Public Instance methods

PhyImplSDHV5CorSOTempBySnowMelt( xy_IndexCalcMethod, xy_SurfSnowFlux, xy_SurfTemp )

Subroutine :

xy_IndexCalcMethod(0:imax-1, 1:jmax) :

integer , intent(in )

:	Index for calculation method

xy_SurfSnowFlux(0:imax-1, 1:jmax) : real(DP), intent(in )

xy_SurfTemp(0:imax-1, 1:jmax) : real(DP), intent(inout)

Set index for calculation method from Matthews’ index

[Source]

  subroutine PhyImplSDHV5CorSOTempBySnowMelt( xy_IndexCalcMethod, xy_SurfSnowFlux, xy_SurfTemp )
    !
    !
    !
    ! Set index for calculation method from Matthews' index
    !

    ! モジュール引用 ; USE statements
    !

    ! 時刻管理
    ! Time control
    !
    use timeset, only: DelTime               ! $ \Delta t $ [s]

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: LatentHeatFusion
                              ! $ L $ [J kg-1] . 
                              ! 融解の潜熱. 
                              ! Latent heat of fusion

    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: SeaIceVolHeatCap, SeaIceThickness


    ! 宣言文 ; Declaration statements
    !
    integer , intent(in   ) :: xy_IndexCalcMethod(0:imax-1, 1:jmax)
                              ! 
                              ! Index for calculation method
    real(DP), intent(in   ) :: xy_SurfSnowFlux   (0:imax-1, 1:jmax)
    real(DP), intent(inout) :: xy_SurfTemp       (0:imax-1, 1:jmax)


    ! 作業変数
    ! Work variables
    !
    real(DP) :: xy_SeaIceThickness(0:imax-1, 1:jmax)

    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitude
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude


    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. phy_implicit_sdh_V5_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


!!$    if ( .not. FlagSSModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagSSModel has to be true.' )
!!$    end if

    ! FlagBucketModel は関係ないよね?
    ! SSModel 強制にした時点で, 水蒸気は地面と分離したから. 
!!$    if ( .not. FlagBucketModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagBucketModel has to be true.' )
!!$    end if


    !
    ! Set sea ice thickness
    !
    xy_SeaIceThickness = SeaIceThickness

    !
    ! Set index for calculation method
    !
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
        case ( IndexSeaIce )
          xy_SurfTemp(i,j) = xy_SurfTemp(i,j) + LatentHeatFusion * xy_SurfSnowFlux(i,j) * 2.0_DP * DelTime / ( SeaIceVolHeatCap * xy_SeaIceThickness(i,j) )
        case ( IndexSlabOcean )
          xy_SurfTemp(i,j) = xy_SurfTemp(i,j) + LatentHeatFusion * xy_SurfSnowFlux(i,j) * 2.0_DP * DelTime / SOHeatCapacity
        case ( IndexPresTs )
        case default
          call MessageNotify( 'E', module_name, 'This index is inappropriate.' )
        end select
      end do
    end do


  end subroutine PhyImplSDHV5CorSOTempBySnowMelt

PhyImplSDHV5Init( ArgFlagBucketModel, ArgFlagSnow, ArgFlagSlabOcean, ArgFlagMajCompPhaseChange, CondMajCompName )

Subroutine :

ArgFlagBucketModel :

logical , intent(in )

:	flag for use of bucket model

ArgFlagSnow :

logical , intent(in )

:	flag for treating snow

ArgFlagSlabOcean :

logical , intent(in )

:	flag for use of slab ocean

ArgFlagMajCompPhaseChange :

logical , intent(in )

:	flag for use of major component phase change

CondMajCompName : character(*), intent(in )

This procedure input/output NAMELIST#phy_implicit_sdh_V5_nml .

[Source]

  subroutine PhyImplSDHV5Init( ArgFlagBucketModel, ArgFlagSnow, ArgFlagSlabOcean, ArgFlagMajCompPhaseChange, CondMajCompName )

    !
    ! phy_implicit モジュールの初期化を行います. 
    ! NAMELIST#phy_implicit_nml の読み込みはこの手続きで行われます. 
    !
    ! "phy_implicit" module is initialized. 
    ! "NAMELIST#phy_implicit_nml" is loaded in this procedure. 
    !

    ! モジュール引用 ; USE statements
    !

    ! NAMELIST ファイル入力に関するユーティリティ
    ! Utilities for NAMELIST file input
    !
    use namelist_util, only: namelist_filename, NmlutilMsg, NmlutilAryValid

    ! ファイル入出力補助
    ! File I/O support
    !
    use dc_iounit, only: FileOpen

    ! 種別型パラメタ
    ! Kind type parameter
    !
    use dc_types, only: STDOUT ! 標準出力の装置番号. Unit number of standard output

    ! 文字列操作
    ! Character handling
    !
    use dc_string, only: StoA

    ! 物理・数学定数設定
    ! Physical and mathematical constants settings
    !
    use constants0, only: WaterHeatCap
                               ! Water heat capacity (J K-1 kg-1)

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: LatentHeatFusion
                              ! $ L $ [J kg-1] . 
                              ! 融解の潜熱. 
                              ! Latent heat of fusion

    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: TempCondWater, SeaIceHeatCap, TempBelowSeaIce

    ! 飽和比湿の算出
    ! Evaluate saturation specific humidity
    !
    use saturate, only: SaturateInit

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: SOMass
                              ! Slab ocean mass

    ! 主成分相変化
    ! Phase change of atmospheric major component
    !
    use saturate_major_comp, only : SaturateMajorCompInit

    ! 地表面フラックスユーティリティ
    ! Surface flux utility routines
    !
    use surface_flux_util, only : SurfaceFluxUtilInit

    !
    ! Slab ocean sea ice utility module
    !
    use sosi_utils, only : SOSIUtilsInit


    ! 宣言文 ; Declaration statements
    !

    logical     , intent(in ) :: ArgFlagBucketModel
                              ! flag for use of bucket model
    logical     , intent(in ) :: ArgFlagSnow
                              ! flag for treating snow
    logical     , intent(in ) :: ArgFlagSlabOcean
                              ! flag for use of slab ocean
    logical     , intent(in ) :: ArgFlagMajCompPhaseChange
                              ! flag for use of major component phase change
    character(*), intent(in ) :: CondMajCompName


    ! 作業変数
    ! Work variables
    !
    integer:: unit_nml        ! NAMELIST ファイルオープン用装置番号. 
                              ! Unit number for NAMELIST file open
    integer:: iostat_nml      ! NAMELIST 読み込み時の IOSTAT. 
                              ! IOSTAT of NAMELIST read

    ! NAMELIST 変数群
    ! NAMELIST group name
    !
    namelist /phy_implicit_sdh_V5_nml/ NumMaxItr, TempItrCrit, FlagSublimation, FlagSeaIce, ResidualMessageThreshold
          !
          ! デフォルト値については初期化手続 "phy_implicit#PhyImplInit" 
          ! のソースコードを参照のこと. 
          !
          ! Refer to source codes in the initialization procedure
          ! "phy_implicit#PhyImplInit" for the default values. 
          !

    ! 実行文 ; Executable statement
    !

    if ( phy_implicit_sdh_V5_inited ) return


    ! Set flag for bucket model
    FlagBucketModel = ArgFlagBucketModel

    ! Set flag for treating snow
    FlagSnow = ArgFlagSnow

    ! Set flag for slab ocean
    FlagSlabOcean = ArgFlagSlabOcean

    ! Set flag for major component phase change
    FlagMajCompPhaseChange = ArgFlagMajCompPhaseChange

    ! デフォルト値の設定
    ! Default values settings
    !

    NumMaxItr   = 50
    TempItrCrit = 0.05_DP

    FlagSublimation = .false.

    ! Flag for sea ice calculation
    !
!!$    FlagSeaIce = .true.
    FlagSeaIce = .false.

    ! Threshold for residual for message output
    ResidualMessageThreshold = 1.0e-10_DP


    ! NAMELIST の読み込み
    ! NAMELIST is input
    !
    if ( trim(namelist_filename) /= '' ) then
      call FileOpen( unit_nml, namelist_filename, mode = 'r' ) ! (in)

      rewind( unit_nml )
      read( unit_nml, nml = phy_implicit_sdh_V5_nml, iostat = iostat_nml )             ! (out)
      close( unit_nml )

      call NmlutilMsg( iostat_nml, module_name ) ! (in)
    end if


!!$    SOHeatCapacity = 4.187e3_DP * 1.0e3_DP * 60.0_DP
!    SOHeatCapacity = 4.187e3_DP * SOMass
    SOHeatCapacity = WaterHeatCap * SOMass
                         ! 4.187d3 (J (kg K)-1) * 1.0d3 (kg m-3) * 60.0d0 (m)


    ! Initialization of modules used in this model
    !

    ! 飽和比湿の算出
    ! Evaluate saturation specific humidity
    !
    call SaturateInit

    if ( FlagMajCompPhaseChange ) then
      ! 主成分相変化
      ! Phase change of atmospheric major component
      !
      call SaturateMajorCompInit( CondMajCompName )
    end if

    ! 地表面フラックスユーティリティ
    ! Surface flux utility routines
    !
    call SurfaceFluxUtilInit

    !
    ! Slab ocean sea ice utility module
    !
    call SOSIUtilsInit


    ! 印字 ; Print
    !
    call MessageNotify( 'M', module_name, '----- Initialization Messages -----' )
    call MessageNotify( 'M', module_name, '  SOHeatCapacity           = %f', d = (/ SOHeatCapacity /) )
    call MessageNotify( 'M', module_name, '  NumMaxItr                = %d', i = (/ NumMaxItr /) )
    call MessageNotify( 'M', module_name, '  TempItrCrit              = %f', d = (/ TempItrCrit /) )
    call MessageNotify( 'M', module_name, '  FlagSublimation          = %b', l = (/ FlagSublimation /) )
    call MessageNotify( 'M', module_name, '  FlagSeaIce               = %b', l = (/ FlagSeaIce /) )
    call MessageNotify( 'M', module_name, '  ResidualMessageThreshold = %f', d = (/ ResidualMessageThreshold /) )
    call MessageNotify( 'M', module_name, '-- version = %c', c1 = trim(version) )


    phy_implicit_sdh_V5_inited = .true.

  end subroutine PhyImplSDHV5Init

PhyImplSDHV5SetMethodMatthews( xy_SurfCond, xy_SurfType, xy_SeaIceConc, xy_SOSeaIceMass, xy_IndexCalcMethod )

Subroutine :

xy_SurfCond(0:imax-1, 1:jmax) :

integer , intent(in )

:	Surface condition

xy_SurfType(0:imax-1, 1:jmax) :

integer , intent(in )

:	土地利用. Surface index

xy_SeaIceConc(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	海氷密度 (0 <= xy_SeaIceConc <= 1) Sea ice concentration (0 <= xy_SeaIceConc <= 1)

xy_SOSeaIceMass(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	$ M_si (t-1) $ . 海氷質量 (kg m-2) Slab ocean sea ice mass (kg m-2)

xy_IndexCalcMethod(0:imax-1, 1:jmax) :

integer , intent(out)

:	Index for calculation method

Set index for calculation method from Matthews’ index

[Source]

  subroutine PhyImplSDHV5SetMethodMatthews( xy_SurfCond, xy_SurfType, xy_SeaIceConc, xy_SOSeaIceMass, xy_IndexCalcMethod )
    !
    !
    !
    ! Set index for calculation method from Matthews' index
    !

    ! モジュール引用 ; USE statements
    !

    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: SOSeaIceThresholdMass

    ! 雪, 氷の割合
    ! snow/ice fraction
    !
    use snowice_frac, only : SeaIceAboveThreshold


    ! 宣言文 ; Declaration statements
    !

    integer , intent(in ) :: xy_SurfCond       (0:imax-1, 1:jmax)
                              ! 
                              ! Surface condition
    integer , intent(in ) :: xy_SurfType       (0:imax-1, 1:jmax)
                              ! 土地利用.
                              ! Surface index
    real(DP), intent(in ) :: xy_SeaIceConc     (0:imax-1, 1:jmax)
                              ! 海氷密度 (0 <= xy_SeaIceConc <= 1)
                              ! Sea ice concentration (0 <= xy_SeaIceConc <= 1)
    real(DP), intent(in) :: xy_SOSeaIceMass    (0:imax-1, 1:jmax)
                              ! $ M_si (t-1) $ . 海氷質量 (kg m-2)
                              ! Slab ocean sea ice mass (kg m-2)
    integer , intent(out) :: xy_IndexCalcMethod(0:imax-1, 1:jmax)
                              ! 
                              ! Index for calculation method


    ! 作業変数
    ! Work variables
    !

    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitude
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude


    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. phy_implicit_sdh_V5_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


!!$    if ( .not. FlagSSModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagSSModel has to be true.' )
!!$    end if

    ! FlagBucketModel は関係ないよね?
    ! SSModel 強制にした時点で, 水蒸気は地面と分離したから. 
!!$    if ( .not. FlagBucketModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagBucketModel has to be true.' )
!!$    end if


    !
    ! Set index for calculation method
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_SurfCond(i,j) == 0 ) then
          if ( xy_SurfType(i,j) >= 1 ) then
            ! land
            xy_IndexCalcMethod(i,j) = IndexLandWithPresTs
          else
            ! prescribed surface temperature
            xy_IndexCalcMethod(i,j) = IndexPresTs
          end if
        else
          if ( xy_SurfType(i,j) >= 1 ) then
            ! land
            xy_IndexCalcMethod(i,j) = IndexLand
          else
            if ( SeaIceAboveThreshold( xy_SeaIceConc(i,j) ) ) then
              ! sea ice
              xy_IndexCalcMethod(i,j) = IndexSeaIce
            else if ( FlagSlabOcean ) then
              ! slab ocean
              if ( xy_SOSeaIceMass(i,j) < SOSeaIceThresholdMass ) then
                xy_IndexCalcMethod(i,j) = IndexSlabOcean
              else
                if ( FlagSeaIce ) then
                  xy_IndexCalcMethod(i,j) = IndexSlabOceanSeaIce
                else
                  xy_IndexCalcMethod(i,j) = IndexSlabOcean
                end if
              end if
            else
              ! prescribed surface temperature
!!$              xy_IndexCalcMethod(i,j) = IndexPresTs
              call MessageNotify( 'E', module_name, 'Unexpected behavior.' )
            end if
          end if
        end if
      end do
    end do


  end subroutine PhyImplSDHV5SetMethodMatthews

PhyImplSDHV5Tendency( xy_IndexCalcMethod, xy_BucketFlagOceanGrid, xy_SnowFrac, xyr_MomFluxX, xyr_MomFluxY, xyr_HeatFlux, xyrf_QMixFlux, xy_SurfH2OVapFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xyz_TempB, xy_SurfTemp, xyz_SoilTemp, xyzf_QMixB, xy_SurfHumidCoef, xy_SoilHeatCap, xy_SoilHeatDiffCoef, xyra_DelRadLFlux, xyr_Press, xyz_Exner, xyr_Exner, xyr_VirTemp, xyz_Height, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef, xy_SurfVelTransCoef, xy_SurfTempTransCoef, xy_SurfQVapTransCoef, xyr_SoilTempTransCoef, xy_SurfMajCompIceB, xy_SoilMoistB, xy_SurfSnowB, xy_SOSeaIceMassB, xyz_SOSeaIceTemp, xyz_DUDt, xyz_DVDt, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DPsDt, xy_DSurfMajCompIceDt, xy_DSoilMoistDt, xy_DSurfSnowDt, xy_DSOSeaIceMassDtTop, xy_DSOSeaIceMassDtBot, xyz_DSOSeaIceTempDt )

Subroutine :

xy_IndexCalcMethod(0:imax-1, 1:jmax) :

integer , intent(in)

:	Index for calculation method

xy_BucketFlagOceanGrid(0:imax-1, 1:jmax) :

logical , intent(in)

:	Flag for ocean grid point used in bucket model

xy_SnowFrac(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Snow fraction

xyr_MomFluxX(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	東西方向運動量フラックス. Eastward momentum flux

xyr_MomFluxY(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	南北方向運動量フラックス. Northward momentum flux

xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	熱フラックス. Heat flux

xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax) :

real(DP), intent(in)

:	比湿フラックス. Specific humidity flux

xy_SurfH2OVapFlux(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	惑星表面水蒸気フラックス. Water vapor flux at the surface

xy_SurfLatentHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	惑星表面潜熱フラックス. Latent heat flux at the surface

xyr_SoilHeatFlux(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	土壌中の熱フラックス (W m-2) Heat flux in sub-surface soil (W m-2)

xyr_RadSFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	短波 (日射) フラックス. Shortwave (insolation) flux

xyr_RadLFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	長波フラックス. Longwave flux

xy_DeepSubSurfHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地中熱フラックス. "Deep subsurface heat flux" Heat flux at the bottom of surface/soil layer.

xyz_TempB(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in)

:	温度. Temperature

xy_SurfTemp(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表面温度. Surface temperature

xyz_SoilTemp(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(in)

:	土壌温度 (K) Soil temperature (K)

xyzf_QMixB(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) : real(DP), intent(in)

xy_SurfHumidCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表湿潤度. Surface humidity coefficient

xy_SoilHeatCap(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	土壌熱容量 (J K-1 m-3) Specific heat of soil (J K-1 m-3)

xy_SoilHeatDiffCoef(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	土壌熱伝導係数 (J m-3 K-1) Heat conduction coefficient of soil (J m-3 K-1)

xyra_DelRadLFlux(0:imax-1, 1:jmax, 0:kmax, 0:1) :

real(DP), intent(in)

:	長波地表温度変化. Surface temperature tendency with longwave

xyr_Press(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	$ hat{p} $ . 気圧 (半整数レベル). Air pressure (half level)

xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in)

:	Exner 関数 (整数レベル). Exner function (full level)

xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	Exner 関数 (半整数レベル). Exner function (half level)

xyr_VirTemp(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	$ hat{T}_v $ . 仮温度 (半整数レベル). Virtual temperature (half level)

xyz_Height(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in)

:	高度 (整数レベル). Height (full level)

xyr_VelDiffCoef(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	拡散係数：運動量. Diffusion coefficient: velocity

xyr_TempDiffCoef(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	拡散係数：温度. Transfer coefficient: temperature

xyr_QMixDiffCoef(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	拡散係数：比湿. Diffusion coefficient: specific humidity

xy_SurfVelTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：運動量. Diffusion coefficient: velocity

xy_SurfTempTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：温度. Transfer coefficient: temperature

xy_SurfQVapTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：比湿. Transfer coefficient: specific humidity

xyr_SoilTempTransCoef(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	輸送係数：土壌温度. Transfer coefficient: soil temperature

xy_SurfMajCompIceB(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Surface major component ice amount.

xy_SoilMoistB(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	土壌水分. Soil moisture.

xy_SurfSnowB(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	積雪量. Surface snow amount.

xy_SOSeaIceMassB(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	$ M_si (t) $ . 海氷質量 (kg m-2) Slab ocean sea ice mass (kg m-2)

xyz_SOSeaIceTemp(0:imax-1, 1:jmax, 1:ksimax) :

real(DP), intent(in)

:	海氷温度 (K) Slab ocean sea ice temperature (K)

xyz_DUDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(out)

:	$ DP{u}{t} $ . 東西風速変化. Eastward wind tendency

xyz_DVDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(out)

:	$ DP{v}{t} $ . 南北風速変化. Northward wind tendency

xyz_DTempDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(out)

:	$ DP{T}{t} $ . 温度変化. Temperature tendency

xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :

real(DP), intent(out)

:	$ DP{q}{t} $ . 質量混合比変化. Mass mixing ratio tendency

xy_DSurfTempDt(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	地表面温度変化率 (K s-1) Surface temperature tendency (K s-1)

xyz_DSoilTempDt(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(out)

:	$ DP{Tg}{t} $ . 土壌温度変化 (K s-1) Temperature tendency (K s-1)

xy_DPsDt(0:imax-1, 1:jmax) : real(DP), intent(out)

xy_DSurfMajCompIceDt(0:imax-1, 1:jmax) : real(DP), intent(out)

xy_DSoilMoistDt(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	土壌温度時間変化率 (kg m-2 s-1) Soil temperature tendency (kg m-2 s-1)

xy_DSurfSnowDt(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	積雪率時間変化率 (kg m-2 s-1) Surface snow amount tendency (kg m-2 s-1)

xy_DSOSeaIceMassDtTop(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	海氷質量時間変化率 (kg m-2 s-1) Slab ocean sea ice mass tendency (kg m-2)

xy_DSOSeaIceMassDtBot(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	海氷質量時間変化率 (kg m-2 s-1) Slab ocean sea ice mass tendency (kg m-2)

xyz_DSOSeaIceTempDt(0:imax-1, 1:jmax, 1:ksimax) :

real(DP), intent(out)

:	$ DP{TSI}{t} $ . 海氷温度変化 (K s-1) Sea ice temperature tendency (K s-1)

時間変化率の計算を行います.

Calculate tendencies.

[Source]

  subroutine PhyImplSDHV5Tendency( xy_IndexCalcMethod, xy_BucketFlagOceanGrid, xy_SnowFrac, xyr_MomFluxX, xyr_MomFluxY, xyr_HeatFlux, xyrf_QMixFlux, xy_SurfH2OVapFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xyz_TempB, xy_SurfTemp, xyz_SoilTemp, xyzf_QMixB, xy_SurfHumidCoef, xy_SoilHeatCap, xy_SoilHeatDiffCoef, xyra_DelRadLFlux, xyr_Press, xyz_Exner, xyr_Exner, xyr_VirTemp, xyz_Height, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef, xy_SurfVelTransCoef, xy_SurfTempTransCoef, xy_SurfQVapTransCoef, xyr_SoilTempTransCoef, xy_SurfMajCompIceB, xy_SoilMoistB, xy_SurfSnowB, xy_SOSeaIceMassB, xyz_SOSeaIceTemp, xyz_DUDt, xyz_DVDt, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DPsDt, xy_DSurfMajCompIceDt, xy_DSoilMoistDt, xy_DSurfSnowDt, xy_DSOSeaIceMassDtTop, xy_DSOSeaIceMassDtBot, xyz_DSOSeaIceTempDt )
    !
    ! 時間変化率の計算を行います. 
    !
    ! Calculate tendencies. 
    !

    ! モジュール引用 ; USE statements
    !

    ! MPI 関連ルーチン
    ! MPI related routines
    !
    use mpi_wrapper, only: myrank, MPIWrapperFindMaxVal

    ! 座標データ設定
    ! Axes data settings
    !
    use axesset, only: r_SSDepth, z_SSDepth, r_SIDepth         ! sea ice grid on interface of layer

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: Grav, CpDry, GasRDry, LatentHeat

    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: TempCondWater, SnowVolHeatCap, SnowDens, SnowMaxThermDepth, SeaIceVolHeatCap   , SeaIceDen          , SeaIceThermCondCoef, SeaIceThickness, TempBelowSeaIce

    ! 飽和比湿の算出
    ! Evaluation of saturation specific humidity
    !
    use saturate, only: xy_CalcQVapSatOnLiq, xy_CalcQVapSatOnSol, xy_CalcDQVapSatDTempOnLiq, xy_CalcDQVapSatDTempOnSol

    ! 時刻管理
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop

    ! バケツモデル
    ! Bucket model
    !
    use Bucket_Model, only : BucketModEvapAndLatentHeatFlux

    ! 地表面フラックスユーティリティ
    ! Surface flux utility routines
    !
    use surface_flux_util, only : SurfaceFluxUtilLimitFlux

    ! 陰解法による時間積分のためのルーチン
    ! Routines for time integration with implicit scheme
    !
    use phy_implicit_utils, only : PhyImplLUDecomp3, PhyImplLUSolve3

    !
    ! Slab ocean sea ice utility module
    !
    use sosi_utils, only : SOSIUtilsSetSOSeaIceLevels

    ! 宣言文 ; Declaration statements
    !

    integer , intent(in):: xy_IndexCalcMethod(0:imax-1, 1:jmax) 
                              ! 
                              ! Index for calculation method
    logical , intent(in):: xy_BucketFlagOceanGrid(0:imax-1, 1:jmax)
                              !
                              ! Flag for ocean grid point used in bucket model
    real(DP), intent(in):: xy_SnowFrac  (0:imax-1, 1:jmax)
                              !
                              ! Snow fraction
    real(DP), intent(in):: xyr_MomFluxX (0:imax-1, 1:jmax, 0:kmax)
                              ! 東西方向運動量フラックス. 
                              ! Eastward momentum flux
    real(DP), intent(in):: xyr_MomFluxY (0:imax-1, 1:jmax, 0:kmax)
                              ! 南北方向運動量フラックス. 
                              ! Northward momentum flux
    real(DP), intent(in):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 熱フラックス. 
                              ! Heat flux
    real(DP), intent(in):: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! 比湿フラックス. 
                              ! Specific humidity flux

    real(DP), intent(out):: xy_SurfH2OVapFlux(0:imax-1, 1:jmax)
                              ! 惑星表面水蒸気フラックス.
                              ! Water vapor flux at the surface
    real(DP), intent(out):: xy_SurfLatentHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面潜熱フラックス.
                              ! Latent heat flux at the surface

    real(DP), intent(in):: xyr_SoilHeatFlux (0:imax-1, 1:jmax, 0:kslmax)
                              ! 土壌中の熱フラックス (W m-2)
                              ! Heat flux in sub-surface soil (W m-2)

    real(DP), intent(in):: xyr_RadSFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 短波 (日射) フラックス. 
                              ! Shortwave (insolation) flux
    real(DP), intent(in):: xyr_RadLFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Longwave flux

    real(DP), intent(in):: xy_DeepSubSurfHeatFlux (0:imax-1, 1:jmax)
                              ! 地中熱フラックス. 
                              ! "Deep subsurface heat flux"
                              ! Heat flux at the bottom of surface/soil layer.
    real(DP), intent(in):: xyz_TempB(0:imax-1, 1:jmax, 1:kmax)
                              ! 温度. 
                              ! Temperature
    real(DP), intent(in):: xy_SurfTemp (0:imax-1, 1:jmax)
                              ! 地表面温度. 
                              ! Surface temperature
    real(DP), intent(in):: xyz_SoilTemp (0:imax-1, 1:jmax, 1:kslmax)
                              ! 土壌温度 (K)
                              ! Soil temperature (K)
    real(DP), intent(in):: xyzf_QMixB(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! 
                              ! 
    real(DP), intent(in):: xy_SurfHumidCoef (0:imax-1, 1:jmax)
                              ! 地表湿潤度. 
                              ! Surface humidity coefficient
    real(DP), intent(in ):: xy_SoilHeatCap (0:imax-1, 1:jmax)
                              ! 土壌熱容量 (J K-1 m-3)
                              ! Specific heat of soil (J K-1 m-3)
    real(DP), intent(in ):: xy_SoilHeatDiffCoef (0:imax-1, 1:jmax)
                              ! 土壌熱伝導係数 (J m-3 K-1)
                              ! Heat conduction coefficient of soil (J m-3 K-1)

    real(DP), intent(in):: xyra_DelRadLFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Surface temperature tendency with longwave

    real(DP), intent(in):: xyr_Press (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . 気圧 (半整数レベル). 
                              ! Air pressure (half level)
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner 関数 (整数レベル). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner 関数 (半整数レベル). 
                              ! Exner function (half level)
    real(DP), intent(in):: xyr_VirTemp (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T}_v $ . 仮温度 (半整数レベル). 
                              ! Virtual temperature (half level)
    real(DP), intent(in):: xyz_Height (0:imax-1, 1:jmax, 1:kmax)
                              ! 高度 (整数レベル). 
                              ! Height (full level)

    real(DP), intent(in):: xyr_VelDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 拡散係数：運動量. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(in):: xyr_TempDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 拡散係数：温度. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xyr_QMixDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 拡散係数：比湿. 
                              ! Diffusion coefficient: specific humidity

    real(DP), intent(in):: xy_SurfVelTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：運動量. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(in):: xy_SurfTempTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：温度. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xy_SurfQVapTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：比湿. 
                              ! Transfer coefficient: specific humidity

    real(DP), intent(in):: xyr_SoilTempTransCoef (0:imax-1, 1:jmax, 0:kslmax)
                              ! 輸送係数：土壌温度.
                              ! Transfer coefficient: soil temperature

    real(DP), intent(in):: xy_SurfMajCompIceB  (0:imax-1, 1:jmax)
                              !
                              ! Surface major component ice amount.

    real(DP), intent(in):: xy_SoilMoistB (0:imax-1, 1:jmax)
                              ! 土壌水分.
                              ! Soil moisture.
    real(DP), intent(in):: xy_SurfSnowB (0:imax-1, 1:jmax)
                              ! 積雪量.
                              ! Surface snow amount.

    real(DP), intent(in):: xy_SOSeaIceMassB(0:imax-1, 1:jmax)
                              ! $ M_si (t) $ . 海氷質量 (kg m-2)
                              ! Slab ocean sea ice mass (kg m-2)
    real(DP), intent(in):: xyz_SOSeaIceTemp(0:imax-1, 1:jmax, 1:ksimax)
                              ! 海氷温度 (K)
                              ! Slab ocean sea ice temperature (K)

    real(DP), intent(out):: xyz_DUDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{u}{t} $ . 東西風速変化. 
                              ! Eastward wind tendency
    real(DP), intent(out):: xyz_DVDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{v}{t} $ . 南北風速変化. 
                              ! Northward wind tendency
    real(DP), intent(out):: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . 温度変化. 
                              ! Temperature tendency
    real(DP), intent(out):: xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ \DP{q}{t} $ . 質量混合比変化. 
                              ! Mass mixing ratio tendency
    real(DP), intent(out):: xy_DSurfTempDt (0:imax-1, 1:jmax)
                              ! 地表面温度変化率 (K s-1)
                              ! Surface temperature tendency (K s-1)
    real(DP), intent(out):: xyz_DSoilTempDt (0:imax-1, 1:jmax, 1:kslmax)
                              ! $ \DP{Tg}{t} $ . 土壌温度変化 (K s-1)
                              ! Temperature tendency (K s-1)

    real(DP), intent(out):: xy_DPsDt            (0:imax-1, 1:jmax)
    real(DP), intent(out):: xy_DSurfMajCompIceDt(0:imax-1, 1:jmax)

    real(DP), intent(out):: xy_DSoilMoistDt (0:imax-1, 1:jmax)
                              ! 土壌温度時間変化率 (kg m-2 s-1)
                              ! Soil temperature tendency (kg m-2 s-1)
    real(DP), intent(out):: xy_DSurfSnowDt (0:imax-1, 1:jmax)
                              ! 積雪率時間変化率 (kg m-2 s-1)
                              ! Surface snow amount tendency (kg m-2 s-1)

    real(DP), intent(out):: xy_DSOSeaIceMassDtTop(0:imax-1, 1:jmax)
                              ! 海氷質量時間変化率 (kg m-2 s-1)
                              ! Slab ocean sea ice mass tendency (kg m-2)
    real(DP), intent(out):: xy_DSOSeaIceMassDtBot(0:imax-1, 1:jmax)
                              ! 海氷質量時間変化率 (kg m-2 s-1)
                              ! Slab ocean sea ice mass tendency (kg m-2)
    real(DP), intent(out):: xyz_DSOSeaIceTempDt(0:imax-1, 1:jmax, 1:ksimax)
                              ! $ \DP{TSI}{t} $ . 海氷温度変化 (K s-1)
                              ! Sea ice temperature tendency (K s-1)

    ! 作業変数
    ! Work variables
    !
    real(DP) :: xy_SurfHeatCapacity (0:imax-1, 1:jmax)
                              ! 地表熱容量. 
                              ! Surface heat capacity

    real(DP) :: xy_SeaIceThickness(0:imax-1, 1:jmax)
                              !
                              ! Sea ice thickness

    real(DP) :: xyr_VelTransCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 輸送係数：運動量. 
                              ! Transfer coefficient: velocity
    real(DP) :: xyr_TempTransCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 輸送係数：温度. 
                              ! Transfer coefficient: temperature
    real(DP) :: xyr_QMixTransCoef(0:imax-1, 1:jmax, 0:kmax)
                              ! 輸送係数：質量. 
                              ! Transfer coefficient: mass of constituents

    real(DP):: xyza_UVMtx (0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 速度陰解行列. 
                              ! Implicit matrix about velocity 
    real(DP):: xyz_UVec (0:imax-1, 1:jmax, 1:kmax)
                              ! 速度陰解ベクトル. 
                              ! Implicit vector about velocity 
    real(DP):: xyz_VVec (0:imax-1, 1:jmax, 1:kmax)
                              ! 速度陰解ベクトル. 
                              ! Implicit vector about velocity 
    real(DP):: xyza_TempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 温度陰解行列. 
                              ! Implicit matrix about temperature
    real(DP):: xyz_TempVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 温度陰解ベクトル. 
                              ! Implicit vector about temperature
    real(DP):: xyza_QMixMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 質量混合比陰解行列. 
                              ! Implicit matrix about mass mixing ratio
    real(DP):: xyzf_QMixVec(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! 質量混合比陰解ベクトル. 
                              ! Implicit vector about mass mixing ratio
    real(DP):: xyaa_SurfMtx(0:imax-1, 1:jmax, 0:0, -1:1)
                              ! 惑星表面エネルギー収支用陰解行列
                              ! Implicit matrix for surface energy balance

    real(DP):: xy_SurfRH(0:imax-1,1:jmax)

    real(DP):: xyza_UVLUMtx (0:imax-1, 1:jmax, 1:kmax,-1:1)
                              ! LU 行列. 
                              ! LU matrix

!!$    real(DP):: xyza_TempQVapLUMtx (0:imax-1, 1:jmax, -kmax:kmax, -1:1)
!!$                              ! LU 行列. 
!!$                              ! LU matrix
!!$    real(DP):: xyz_DelTempQVap (0:imax-1, 1:jmax, -kmax:kmax)
!!$                              ! $ T q $ の時間変化. 
!!$                              ! Tendency of $ T q $ 
!!$
!!$    real(DP):: xyza_TempLUMtx (0:imax-1, 1:jmax, 0:kmax, -1:1)
!!$                              ! LU 行列.
!!$                              ! LU matrix
!!$    real(DP):: xyz_DelTempLUVec (0:imax-1, 1:jmax, 0:kmax)
!!$                              ! $ T q $ の時間変化.
!!$                              ! Tendency of $ T q $
    real(DP):: xyza_QMixLUMtx (0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! LU 行列.
                              ! LU matrix
    real(DP):: xyz_DelQMixLUVec (0:imax-1, 1:jmax, 1:kmax)
                              ! $ q $ の時間変化.
                              ! Tendency of $ q $

    real(DP):: xyaa_SoilTempMtx (0:imax-1, 1:jmax, 1:kslmax,-1:1)
                              ! 土壌温度拡散方程式の行列
                              ! Matrix for diffusion equation of soil temperature
    real(DP):: xya_SoilTempVec (0:imax-1, 1:jmax, 1:kslmax)
                              ! 土壌温度拡散方程式のベクトル
                              ! Vector for diffusion equation of soil temperature
    real(DP):: xyaa_TempSoilTempLUMtx (0:imax-1, 1:jmax, -kslmax:kmax, -1:1)
                              ! LU 行列.
                              ! LU matrix
    real(DP):: xya_DelTempSoilTempLUVec (0:imax-1, 1:jmax, -kslmax:kmax)
                              ! $ T, Tg $ の時間変化.
                              ! Tendency of $ T $ and $ Tg |

    real(DP):: SurfSnowATentative
                              ! 積雪量の仮の値 (kg m-2)
                              ! pseudo value of surface snow amount (kg m-2)

    real(DP):: xy_LatHeatFluxByMajCompIceSubl(0:imax-1, 1:jmax)
                              !
                              ! Latent heat flux by major component ice sublimation
                              ! (variable only for debug)
    real(DP):: xy_LatHeatFluxBySnowMelt(0:imax-1, 1:jmax)
                              !
                              ! Latent heat flux by melt
                              ! (variable only for debug)
    real(DP):: xy_LatHeatFluxBySeaIceMelt(0:imax-1, 1:jmax)
                              !
                              ! Latent heat flux by sea ice melt
                              ! (variable only for debug)

    real(DP):: xy_LatHeatFluxByOtherSpc(0:imax-1, 1:jmax)

    real(DP):: xy_DAtmMassDt(0:imax-1, 1:jmax)

    real(DP):: xy_SurfQVapSatOnLiq(0:imax-1, 1:jmax)
                              ! 地表飽和比湿. 
                              ! Saturated specific humidity on surface
    real(DP):: xy_SurfQVapSatOnSol (0:imax-1, 1:jmax)
                              ! 地表飽和比湿. 
                              ! Saturated specific humidity on surface
    real(DP):: xy_SurfQVapSat (0:imax-1, 1:jmax)
                              ! 地表飽和比湿. 
                              ! Saturated specific humidity on surface
    real(DP):: xy_SurfDQVapSatDTempOnLiq (0:imax-1, 1:jmax)
                              ! 地表飽和比湿変化. 
                              ! Saturated specific humidity tendency on surface
    real(DP):: xy_SurfDQVapSatDTempOnSol (0:imax-1, 1:jmax)
                              ! 地表飽和比湿変化. 
                              ! Saturated specific humidity tendency on surface
    real(DP):: xy_SurfDQVapSatDTemp (0:imax-1, 1:jmax)
                              ! 地表飽和比湿変化. 
                              ! Saturated specific humidity tendency on surface

    real(DP):: xy_SurfSoilHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面土壌熱伝導フラックス.
                              ! Soil heat conduction flux at the surface
    real(DP):: xy_SurfSOSIHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面海氷熱伝導フラックス.
                              ! Sea ice heat conduction flux at the surface

    real(DP):: xy_SurfSoilHeatFluxTentative(0:imax-1, 1:jmax)
                              ! 惑星表面土壌熱伝導フラックス.
                              ! Soil heat conduction flux at the surface
    real(DP):: xy_SurfSOSIHeatFluxTentative(0:imax-1, 1:jmax)
                              ! 惑星表面海氷熱伝導フラックス.
                              ! Sea ice heat conduction flux at the surface

    integer  :: xy_SOSILocalKMax(0:imax-1, 1:jmax)
    real(DP) :: xyr_SOSILocalDepth(0:imax-1, 1:jmax, 0:ksimax)
    real(DP) :: xyz_SOSILocalDepth(0:imax-1, 1:jmax, 1:ksimax)

    real(DP) :: xyr_SOSIThermCondCoef(0:imax-1, 1:jmax, 0:ksimax)
    real(DP) :: xyr_SOSIHeatTransCoef(0:imax-1, 1:jmax, 0:ksimax)
    real(DP) :: xyr_SOSIHeatFlux     (0:imax-1, 1:jmax, 0:ksimax)

    real(DP):: xyz_TempSave   (0:imax-1, 1:jmax, 1:kmax)
    real(DP):: xyz_TempA      (0:imax-1, 1:jmax, 1:kmax)
    real(DP):: MaxTempInc
    real(DP):: xy_SurfTempSave(0:imax-1, 1:jmax)
    real(DP):: xy_SurfTempA   (0:imax-1, 1:jmax)
    real(DP):: MaxSurfTempInc

    real(DP):: a_LocalMax (2)
    real(DP):: a_GlobalMax(2)

    integer:: iitr

    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitude
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude
    integer:: k               ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction
    integer:: l               ! 行列用 DO ループ用作業変数
                              ! Work variables for DO loop of matrices
    integer:: n               ! 組成方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in dimension of constituents

    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. phy_implicit_sdh_V5_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! 計算時間計測開始
    ! Start measurement of computation time
    !
    call TimesetClockStart( module_name )


    ! Check kskmax
    !
    if ( kslmax < 1 ) then
      call MessageNotify( 'E', module_name, 'kslmax is less than 1.' )
    end if
    if ( FlagSlabOcean .and. ( ksimax < 1 ) ) then
      if ( FlagSeaIce ) then
        call MessageNotify( 'E', module_name, 'ksimax is less than 1.' )
      end if
    end if

    if ( kslmax < ksimax ) then
      call MessageNotify( 'E', module_name, 'kslmax is less than ksimax.' )
    end if

!!$    if ( .not. FlagSSModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagSSModel has to be true.' )
!!$    end if

    ! FlagBucketModel は関係ないよね?
    ! SSModel 強制にした時点で, 水蒸気は地面と分離したから. 
!!$    if ( .not. FlagBucketModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagBucketModel has to be true.' )
!!$    end if

    ! Set heat capacity
    !
    xy_SurfHeatCapacity = 0.0_DP
    !
    !   Below was a test version. 
!!$    do j = 1, jmax
!!$      do i = 0, imax-1
!!$        select case ( xy_IndexCalcMethod(i,j) )
!!$        case ( IndexLand )
!!$          !   J K-1 m-3 kg m-2 (kg m-3)-1 = J K-1 m-5 m3 = J K-1 m-2
!!$          xy_SurfHeatCapacity(i,j) = &
!!$            & SnowVolHeatCap &
!!$            & * min( max( xy_SurfSnowB(i,j) / SnowDens, 0.0_DP ), SnowMaxThermDepth )
!!$        case default
!!$          xy_SurfHeatCapacity(i,j) = 0.0_DP
!!$        end select
!!$      end do
!!$    end do

    !
    ! Set sea ice thickness
    !
    do i = 0, imax-1
      do j = 1, jmax
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexSlabOceanSeaIce )
          xy_SeaIceThickness(i,j) = xy_SOSeaIceMassB(i,j) / SeaIceDen
        case default
          xy_SeaIceThickness(i,j) = SeaIceThickness
        end select
      end do
    end do
    !
    ! Set sea ice levels
    !
    call SOSIUtilsSetSOSeaIceLevels( xy_SeaIceThickness, xy_SOSILocalKMax, xyr_SOSILocalDepth, xyz_SOSILocalDepth )
!!$    do i = 0, imax-1
!!$      do j = 1, jmax
!!$        select case ( xy_IndexCalcMethod(i,j) )
!!$        case ( IndexSlabOceanSeaIce )
!!$          if ( xy_SeaIceThickness(i,j) == 0.0_DP ) then
!!$            xy_SOSILocalKMax(i,j) = 0
!!$          else if ( - xy_SeaIceThickness(i,j) < r_SIDepth(ksimax) ) then
!!$            xy_SOSILocalKMax(i,j) = ksimax
!!$          else
!!$            xy_SOSILocalKMax(i,j) = 0
!!$            search_ksimax : do k = 0+1, ksimax
!!$              if ( - xy_SeaIceThickness(i,j) >= r_SIDepth(k) ) then
!!$                xy_SOSILocalKMax(i,j) = k
!!$                exit search_ksimax
!!$              end if
!!$            end do search_ksimax
!!$          end if
!!$        case default
!!$          xy_SOSILocalKMax(i,j) = 0
!!$        end select
!!$      end do
!!$    end do
!!$    do j = 1, jmax
!!$      do i = 0, imax-1
!!$        do k = 0, xy_SOSILocalKMax(i,j)-1
!!$          xyr_SOSILocalDepth(i,j,k) = r_SIDepth(k)
!!$        end do
!!$        k = xy_SOSILocalKMax(i,j)
!!$        xyr_SOSILocalDepth(i,j,k) = - xy_SeaIceThickness(i,j)
!!$        do k = xy_SOSILocalKMax(i,j)+1, ksimax
!!$          xyr_SOSILocalDepth(i,j,k) = -1.0e100_DP
!!$        end do
!!$        !
!!$        do k = 1, xy_SOSILocalKMax(i,j)
!!$          xyz_SOSILocalDepth(i,j,k) = &
!!$            & ( xyr_SOSILocalDepth(i,j,k-1) + xyr_SOSILocalDepth(i,j,k) ) / 2.0_DP
!!$        end do
!!$        do k = xy_SOSILocalKMax(i,j)+1, ksimax
!!$          xyz_SOSILocalDepth(i,j,k) = -1.0e100_DP
!!$        end do
!!$      end do
!!$    end do


    ! Set coefficients for soil heat flux
    !
!!$    xyr_SoilTempTransCoef = xyr_BareSoilTempTransCoef
!!$    do j = 1, jmax
!!$      do i = 0, imax-1
!!$        if ( xy_SurfSnowB(i,j) > 
!!$    xyr_SoilTempTransCoef = xyr_BareSoilTempTransCoef


    ! 輸送係数の計算
    ! Calculate transfer coefficient
    !
    xyr_VelTransCoef (:,:,0)    = 0.0_DP
    xyr_VelTransCoef (:,:,kmax) = 0.0_DP
    xyr_TempTransCoef(:,:,0)    = 0.0_DP
    xyr_TempTransCoef(:,:,kmax) = 0.0_DP
    xyr_QMixTransCoef(:,:,0)    = 0.0_DP
    xyr_QMixTransCoef(:,:,kmax) = 0.0_DP

    do k = 1, kmax-1
      xyr_VelTransCoef(:,:,k) = xyr_VelDiffCoef(:,:,k) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )

      xyr_TempTransCoef(:,:,k) = xyr_TempDiffCoef(:,:,k) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )

      xyr_QMixTransCoef(:,:,k) = xyr_QMixDiffCoef(:,:,k) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )
    end do


    xyr_SOSIThermCondCoef = SeaIceThermCondCoef
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_SOSILocalKMax(i,j) == 0 ) then
          do k = 0, ksimax
            xyr_SOSIHeatTransCoef(i,j,k) = -1.0e100_DP
          end do
        else
          k = 0
          xyr_SOSIHeatTransCoef(i,j,k) = xyr_SOSIThermCondCoef(i,j,k) / ( xyz_SOSILocalDepth(i,j,k+1) - 0.0_DP )
          do k = 1, xy_SOSILocalKMax(i,j)-1
            xyr_SOSIHeatTransCoef(i,j,k) = xyr_SOSIThermCondCoef(i,j,k) / ( xyz_SOSILocalDepth(i,j,k+1) - xyz_SOSILocalDepth(i,j,k) )
          end do
          k = xy_SOSILocalKMax(i,j)
          xyr_SOSIHeatTransCoef(i,j,k) = xyr_SOSIThermCondCoef(i,j,k) / ( xyr_SOSILocalDepth(i,j,k) - xyz_SOSILocalDepth(i,j,k) )
          do k = xy_SOSILocalKMax(i,j)+1, ksimax
            xyr_SOSIHeatTransCoef(i,j,k) = 0.0_DP
          end do
        end if
      end do
    end do
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_SOSILocalKMax(i,j) == 0 ) then
          do k = 0, ksimax
            xyr_SOSIHeatFlux(i,j,k) = -1.0e100_DP
          end do
        else
          k = 0
          xyr_SOSIHeatFlux(i,j,k) = - xyr_SOSIHeatTransCoef(i,j,k) * ( xyz_SOSeaIceTemp(i,j,k+1) - xy_SurfTemp(i,j) )
          do k = 1, xy_SOSILocalKMax(i,j)-1
            xyr_SOSIHeatFlux(i,j,k) = - xyr_SOSIHeatTransCoef(i,j,k) * ( xyz_SOSeaIceTemp(i,j,k+1) - xyz_SOSeaIceTemp(i,j,k) )
          end do
          k = xy_SOSILocalKMax(i,j)
          xyr_SOSIHeatFlux(i,j,k) = - xyr_SOSIHeatTransCoef(i,j,k) * ( TempBelowSeaIce - xyz_SOSeaIceTemp(i,j,k) )
          do k = xy_SOSILocalKMax(i,j)+1, ksimax
            xyr_SOSIHeatFlux(i,j,k) = 0.0_DP
          end do
        end if
      end do
    end do

    ! Calculation for momentum diffusion
    !
    call PhyImplSDHV5TendencyMomCore( xyr_MomFluxX, xyr_MomFluxY, xyr_Press, xyr_VelTransCoef, xy_SurfVelTransCoef, xyz_DUDt, xyz_DVDt )


    ! Calculation for thermal diffusion
    !

    ! 飽和比湿の計算
    ! Calculate saturated specific humidity
    !
    xy_SurfQVapSatOnLiq       = xy_CalcQVapSatOnLiq      ( xy_SurfTemp, xyr_Press(:,:,0) )
    xy_SurfQVapSatOnSol       = xy_CalcQVapSatOnSol      ( xy_SurfTemp, xyr_Press(:,:,0) )
    xy_SurfQVapSat       = ( 1.0_DP - xy_SnowFrac ) * xy_SurfQVapSatOnLiq + xy_SnowFrac              * xy_SurfQVapSatOnSol
    xy_SurfDQVapSatDTempOnLiq = xy_CalcDQVapSatDTempOnLiq( xy_SurfTemp, xy_SurfQVapSatOnLiq )
    xy_SurfDQVapSatDTempOnSol = xy_CalcDQVapSatDTempOnSol( xy_SurfTemp, xy_SurfQVapSatOnSol )
    xy_SurfDQVapSatDTemp = ( 1.0_DP - xy_SnowFrac ) * xy_SurfDQVapSatDTempOnLiq + xy_SnowFrac              * xy_SurfDQVapSatDTempOnSol



    ! Initialization
    !
    xyzf_DQMixDt        = 0.0_DP
    xy_DSurfTempDt      = 0.0_DP
    xyz_DSoilTempDt     = 0.0_DP
    xyz_DSOSeaIceTempDt = 0.0_DP


    xyz_TempSave    = xyz_TempB
    xy_SurfTempSave = xy_SurfTemp

    ! iteration
    iitr = 1
    loop_itr : do

      ! Tendencies of atmospheric and surface temperatures, and atmospheric 
      ! water vapor are solved with a fixed surface heat conduction flux at the surface. 
      ! Obtained tendencies of surface temperature and atmospheric water vapor will be 
      ! used below to estimate surface water vapor flux. 
      !
!!$      xy_SurfSoilHeatFlux = xyr_SoilHeatFlux(:,:,0)                              &
!!$        & - xyr_SoilTempTransCoef(:,:,0)                                         &
!!$        &   * ( xyz_DSoilTempDt(:,:,1) - xy_DSurfTempDt ) * ( 2.0_DP * DelTime )
      xy_SurfSoilHeatFluxTentative = xyr_SoilHeatFlux(:,:,0) - xyr_SoilTempTransCoef(:,:,0) * ( xyz_DSoilTempDt(:,:,1)                  ) * ( 2.0_DP * DelTime )
      !
      do j = 1, jmax
        do i = 0, imax-1
!!$          if ( xy_SOSILocalKMax(i,j) == 0 ) then
!!$            xy_SurfSOSIHeatFlux(i,j) = -1.0e100_DP
!!$          else
!!$            k = 0
!!$            xy_SurfSOSIHeatFlux(i,j) = xyr_SOSIHeatFlux(i,j,k)       &
!!$              & - xyr_SOSIHeatTransCoef(i,j,k)                       &
!!$              &     * ( xyz_DSOSeaIceTempDt(i,j,k+1) - xy_DSurfTempDt(i,j) ) * ( 2.0_DP * DelTime )
!!$          end if
          if ( xy_SOSILocalKMax(i,j) == 0 ) then
            xy_SurfSOSIHeatFluxTentative(i,j) = -1.0e100_DP
          else
            k = 0
            xy_SurfSOSIHeatFluxTentative(i,j) = xyr_SOSIHeatFlux(i,j,k) - xyr_SOSIHeatTransCoef(i,j,k) * ( xyz_DSOSeaIceTempDt(i,j,k+1)                       ) * ( 2.0_DP * DelTime )
          end if
        end do
      end do
      !
      call PhyImplSDHV5TendencyHeatTQCore( xy_IndexCalcMethod, xy_SOSILocalKMax, xy_SeaIceThickness, xy_SnowFrac, xyr_HeatFlux, xyrf_QMixFlux, xy_SurfSoilHeatFluxTentative, xy_SurfSOSIHeatFluxTentative, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xy_SurfTemp, xy_SurfHumidCoef, xy_SurfHeatCapacity, xyra_DelRadLFlux, xyr_Press, xyz_Exner, xyr_Exner, xyr_VelTransCoef, xyr_TempTransCoef, xyr_QMixTransCoef, xyr_SoilTempTransCoef, xyr_SOSIHeatTransCoef, xy_SurfVelTransCoef, xy_SurfTempTransCoef, xy_SurfQVapTransCoef, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt, xy_SurfSoilHeatFlux, xy_SurfSOSIHeatFlux )


      ! Tendencies of atmospheric, surface, and subsurface temperatures, and 
      ! atmospheric water vapor are solved with a fixed surface water vapor flux. 
      !
      n = IndexH2OVap
      xy_SurfH2OVapFlux = xyrf_QMixFlux(:,:,0,n) - xy_SurfHumidCoef * xy_SurfQVapTransCoef * ( xyzf_DQMixDt(:,:,1,n) - xy_SurfDQVapSatDTemp * xy_DSurfTempDt ) * 2.0_DP * DelTime
      ! Limit surface flux not to be negative atmospheric content
      ! IMPORTANT : Now, only the water vapor flux is restricted.
      call SurfaceFluxUtilLimitFlux( ( 2.0_DP * DelTime ), xyzf_QMixB, xyr_Press, xy_SurfH2OVapFlux )
      ! Calculation of latent heat flux
      xy_SurfLatentHeatFlux = LatentHeat * xy_SurfH2OVapFlux
      !
      if ( FlagBucketModel ) then
        ! バケツモデルのための地表面フラックス修正
        ! Modification of surface flux for bucket model
        !
        call BucketModEvapAndLatentHeatFlux( xy_BucketFlagOceanGrid, xy_SoilMoistB, xy_SurfSnowB, xy_SurfH2OVapFlux, xy_SurfLatentHeatFlux )
      end if
      !
      call PhyImplSDHV5TendencyHeatCore( xy_IndexCalcMethod, xy_SeaIceThickness, xy_SOSeaIceMassB, xyr_HeatFlux, xyrf_QMixFlux, xy_SurfH2OVapFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xy_SurfTemp, xyz_SoilTemp, xyz_SOSeaIceTemp, xy_SurfHumidCoef, xy_SurfHeatCapacity, xy_SoilHeatCap, xy_SoilHeatDiffCoef, xyra_DelRadLFlux, xyr_Press, xyz_Exner, xyr_Exner, xyr_VelTransCoef, xyr_TempTransCoef, xyr_QMixTransCoef, xy_SurfVelTransCoef, xy_SurfTempTransCoef, xy_SurfQVapTransCoef, xyr_SoilTempTransCoef, xy_SOSILocalKMax, xyr_SOSILocalDepth, xyz_SOSILocalDepth, xyr_SOSIHeatTransCoef, xyr_SOSIHeatFlux, xy_SurfMajCompIceB, xy_SoilMoistB, xy_SurfSnowB, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DPsDt, xy_DSurfMajCompIceDt, xy_DSoilMoistDt, xy_DSurfSnowDt, xy_DSOSeaIceMassDtTop, xy_DSOSeaIceMassDtBot, xyz_DSOSeaIceTempDt )


      ! Check

      xyz_TempA    = xyz_TempB   + xyz_DTempDt    * 2.0_DP * DelTime
      xy_SurfTempA = xy_SurfTemp + xy_DSurfTempDt *          DelTime

      MaxTempInc     = maxval( abs( xyz_TempA    - xyz_TempSave    ) )
      MaxSurfTempInc = maxval( abs( xy_SurfTempA - xy_SurfTempSave ) )

      a_LocalMax(1) = MaxTempInc
      a_LocalMax(2) = MaxSurfTempInc
      call MPIWrapperFindMaxVal( 2, a_LocalMax, a_GlobalMax )
      MaxTempInc     = a_GlobalMax(1)
      MaxSurfTempInc = a_GlobalMax(2)

!!$      if ( myrank == 0 ) then
!!$        call MessageNotify( 'M', module_name, &
!!$          & 'Itr: %d : dT = %f, dTs = %f',    &
!!$          & i = (/iitr/), d = (/ MaxTempInc, MaxSurfTempInc /) )
!!$      end if

      if ( ( MaxTempInc <= TempItrCrit ) .and. ( MaxSurfTempInc <= TempItrCrit ) ) then
        exit loop_itr
      end if

      xyz_TempSave    = xyz_TempA
      xy_SurfTempSave = xy_SurfTempA

      iitr = iitr + 1
      if ( iitr > NumMaxItr ) then
        if ( NumMaxItr > 2 ) then
          if ( myrank == 0 ) then
            call MessageNotify( 'M', module_name, 'Too many iterations, Itr: %d : dT = %f, dTs = %f', i = (/iitr/), d = (/ MaxTempInc, MaxSurfTempInc /) )
          end if
        end if
        exit loop_itr
      end if
    end do loop_itr

!!$    if ( myrank == 0 ) then
!!$      call MessageNotify( 'M', module_name, &
!!$        & 'Itr: %d : dT = %f, dTs = %f', &
!!$        & i = (/iitr/), d = (/ MaxTempInc, MaxSurfTempInc /) )
!!$    end if


    ! 計算時間計測一時停止
    ! Pause measurement of computation time
    !
    call TimesetClockStop( module_name )


  end subroutine PhyImplSDHV5Tendency

Private Instance methods

FlagBucketModel

Variable :

FlagBucketModel :

logical, save

:	flag for use of bucket model

FlagMajCompPhaseChange

Variable :

FlagMajCompPhaseChange :

logical, save

:	flag for use of slab ocean

FlagSeaIce

Variable :

FlagSeaIce :

logical, save

:	flag for sea ice

FlagSlabOcean

Variable :

FlagSlabOcean :

logical, save

:	flag for use of slab ocean

FlagSnow

Variable :

FlagSnow :

logical, save

:	flag for treating snow

FlagSublimation

Variable :

FlagSublimation :

logical, save

:	flag for treating sublimation

IndexLand

Constant :

IndexLand = 13 :

integer, parameter

Land

IndexLandWithPresTs

Constant :

IndexLandWithPresTs = 14 :

integer, parameter

:	Land with prescribed surface temperature

IndexPresTs

Constant :

IndexPresTs = 10 :

integer, parameter

:	Prescribed surface temperature

IndexSeaIce

Constant :

IndexSeaIce = 12 :

integer, parameter

Sea ice

IndexSlabOcean

Constant :

IndexSlabOcean = 11 :

integer, parameter

:	Slab ocean

IndexSlabOceanSeaIce

Constant :

IndexSlabOceanSeaIce = 15 :

integer, parameter

:	Sea ice on slab ocean

IndexSpcH2O

*Constant* :
`IndexSpcH2O` `= 1` :	`integer, parameter`

IndexSpcMajComp

*Constant* :
`IndexSpcMajComp` `= 0` :	`integer, parameter`

NumMaxItr

*Variable* :
`NumMaxItr` :	`integer, save`

PhyImplSDHV5ChkConservation( xy_IndexCalcMethod, xy_FlagSOSeaIceAllMelt, xy_FlagSOSIWoSIOceanAllFreeze, xy_FlagSOSIWSIOceanAllFreeze, xy_SeaIceThickness, xy_SOSeaIceMassB, xyr_Press, xyz_Exner, xyr_Exner, xy_SurfTemp, xy_SurfHeatCapacity, xy_SoilHeatCap, xyr_HeatFlux, xy_SurfH2OVapFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xy_SurfTempTransCoef, xyr_SoilTempTransCoef, xyr_SOSIHeatTransCoef, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_LatHeatFluxByMajCompIceSubl, xy_LatHeatFluxBySnowMelt, xy_LatHeatFluxBySeaIceMelt, xy_DeepSubSurfHeatFlux, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DSoilMoistDt, xy_DSurfSnowDt, xy_DPsDt, xy_DSurfMajCompIceDt, xy_SOSILocalKMax, xyr_SOSILocalDepth, xyz_SOSeaIceTemp, xyz_DSOSeaIceTempDt, xy_DSOSeaIceMassDtTop, xy_DSOSeaIceMassDtBot )

Subroutine :

xy_IndexCalcMethod(0:imax-1, 1:jmax) :

integer , intent(in)

:	Index for calculation method

xy_FlagSOSeaIceAllMelt(0:imax-1, 1:jmax) : logical , intent(in)

xy_FlagSOSIWoSIOceanAllFreeze(0:imax-1, 1:jmax) : logical , intent(in)

xy_FlagSOSIWSIOceanAllFreeze(0:imax-1, 1:jmax) : logical , intent(in)

xy_SeaIceThickness(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Sea ice thickness

xy_SOSeaIceMassB(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	$ M_si (t-1) $ . 海氷質量 (kg m-2) Slab ocean sea ice mass (kg m-2)

xyr_Press(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	$ hat{p} $ . 気圧 (半整数レベル). Air pressure (half level)

xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in)

:	Exner 関数 (整数レベル). Exner function (full level)

xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	Exner 関数 (半整数レベル). Exner function (half level)

xy_SurfTemp(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表面温度. Surface temperature

xy_SurfHeatCapacity(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表熱容量. Surface heat capacity

xy_SoilHeatCap(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	土壌熱容量 (J K-1 m-3) Specific heat of soil (J K-1 m-3)

xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

熱フラックス. Heat flux

!$ real(DP), intent(in):

xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)

!$ ! 比湿フラックス. !$ ! Specific humidity flux

xy_SurfH2OVapFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	惑星表面水蒸気フラックス. Water vapor flux at the surface

xy_SurfLatentHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	惑星表面潜熱フラックス. Latent heat flux at the surface

xyr_SoilHeatFlux(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	土壌中の熱フラックス (W m-2) Heat flux in sub-surface soil (W m-2)

xy_SurfTempTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：温度. Transfer coefficient: temperature

xyr_SoilTempTransCoef(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	輸送係数：土壌温度. Transfer coefficient: soil temperature

xyr_SOSIHeatTransCoef(0:imax-1, 1:jmax, 0:ksimax) : real(DP), intent(in)

xyr_RadSFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	短波 (日射) フラックス. Shortwave (insolation) flux

xyr_RadLFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	長波フラックス. Longwave flux

xyra_DelRadLFlux(0:imax-1, 1:jmax, 0:kmax, 0:1) :

real(DP), intent(in)

:	長波地表温度変化. Surface temperature tendency with longwave

xy_LatHeatFluxByMajCompIceSubl(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	Latent heat flux by major component ice sublimation (variable only for debug)

xy_LatHeatFluxBySnowMelt(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	Latent heat flux by melt (variable only for debug)

xy_LatHeatFluxBySeaIceMelt(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	Latent heat flux by sea ice melt (variable only for debug)

xy_DeepSubSurfHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地中熱フラックス. "Deep subsurface heat flux" Heat flux at the bottom of surface/soil layer.

xyz_DTempDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in )

:	$ DP{T}{t} $ . 温度変化. Temperature tendency

xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :

real(DP), intent(in )

:	$ DP{q}{t} $ . 質量混合比変化. Mass mixing ratio tendency

xy_DSurfTempDt(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	地表面温度変化率 (K s-1) Surface temperature tendency (K s-1)

xyz_DSoilTempDt(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(in )

:	$ DP{Tg}{t} $ . 土壌温度変化 (K s-1) Temperature tendency (K s-1)

xy_DSoilMoistDt(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	土壌温度時間変化率 (kg m-2 s-1) Soil temperature tendency (kg m-2 s-1)

xy_DSurfSnowDt(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	積雪率時間変化率 (kg m-2 s-1) Surface snow amount tendency (kg m-2 s-1)

xy_DPsDt(0:imax-1, 1:jmax) : real(DP), intent(in )

xy_DSurfMajCompIceDt(0:imax-1, 1:jmax) : real(DP), intent(in )

xy_SOSILocalKMax(0:imax-1, 1:jmax) : integer , intent(in )

xyr_SOSILocalDepth(0:imax-1, 1:jmax, 0:ksimax) : real(DP), intent(in )

xyz_SOSeaIceTemp(0:imax-1, 1:jmax, 1:ksimax) : real(DP), intent(in )

xyz_DSOSeaIceTempDt(0:imax-1, 1:jmax, 1:ksimax) :

real(DP), intent(in )

:	$ DP{TSI}{t} $ . 海氷温度変化 (K s-1) Sea ice temperature tendency (K s-1)

xy_DSOSeaIceMassDtTop(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	海氷質量時間変化率 (kg m-2 s-1) Slab ocean sea ice mass tendency (kg m-2)

xy_DSOSeaIceMassDtBot(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	海氷質量時間変化率 (kg m-2 s-1) Slab ocean sea ice mass tendency (kg m-2)

A part of conservation of energy is checked.

[Source]

  subroutine PhyImplSDHV5ChkConservation( xy_IndexCalcMethod, xy_FlagSOSeaIceAllMelt, xy_FlagSOSIWoSIOceanAllFreeze, xy_FlagSOSIWSIOceanAllFreeze, xy_SeaIceThickness, xy_SOSeaIceMassB, xyr_Press, xyz_Exner, xyr_Exner, xy_SurfTemp, xy_SurfHeatCapacity, xy_SoilHeatCap, xyr_HeatFlux, xy_SurfH2OVapFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xy_SurfTempTransCoef, xyr_SoilTempTransCoef, xyr_SOSIHeatTransCoef, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_LatHeatFluxByMajCompIceSubl, xy_LatHeatFluxBySnowMelt, xy_LatHeatFluxBySeaIceMelt, xy_DeepSubSurfHeatFlux, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DSoilMoistDt, xy_DSurfSnowDt, xy_DPsDt, xy_DSurfMajCompIceDt, xy_SOSILocalKMax, xyr_SOSILocalDepth, xyz_SOSeaIceTemp, xyz_DSOSeaIceTempDt, xy_DSOSeaIceMassDtTop, xy_DSOSeaIceMassDtBot )
    !
    ! 
    !
    ! A part of conservation of energy is checked.
    !

    ! モジュール引用 ; USE statements
    !

    ! 座標データ設定
    ! Axes data settings
    !
    use axesset, only: r_SSDepth, z_SSDepth         ! subsurface grid at midpoint of layer

    ! 時刻管理
    ! Time control
    !
    use timeset, only: DelTime               ! $ \Delta t $ [s]

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: Grav, CpDry, GasRDry, LatentHeatFusion
                              ! $ L $ [J kg-1] . 
                              ! 融解の潜熱. 
                              ! Latent heat of fusion

    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: TempCondWater, SeaIceVolHeatCap   , SeaIceThermCondCoef, TempBelowSeaIce    , SeaIceDen          , LatentHeatFusionBelowSeaIce
                              ! Latant heat for fusion below sea ice

    ! 宣言文 ; Declaration statements
    !

    integer , intent(in):: xy_IndexCalcMethod (0:imax-1, 1:jmax)
                              ! 
                              ! Index for calculation method

    logical , intent(in):: xy_FlagSOSeaIceAllMelt     (0:imax-1, 1:jmax)
    logical , intent(in):: xy_FlagSOSIWoSIOceanAllFreeze(0:imax-1, 1:jmax)
    logical , intent(in):: xy_FlagSOSIWSIOceanAllFreeze (0:imax-1, 1:jmax)

    real(DP), intent(in):: xy_SeaIceThickness(0:imax-1, 1:jmax)
                              !
                              ! Sea ice thickness
    real(DP), intent(in):: xy_SOSeaIceMassB(0:imax-1, 1:jmax)
                              ! $ M_si (t-1) $ . 海氷質量 (kg m-2)
                              ! Slab ocean sea ice mass (kg m-2)
    real(DP), intent(in):: xyr_Press (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . 気圧 (半整数レベル). 
                              ! Air pressure (half level)
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner 関数 (整数レベル). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner 関数 (半整数レベル). 
                              ! Exner function (half level)

    real(DP), intent(in):: xy_SurfTemp (0:imax-1, 1:jmax)
                              ! 地表面温度. 
                              ! Surface temperature

    real(DP), intent(in):: xy_SurfHeatCapacity (0:imax-1, 1:jmax)
                              ! 地表熱容量. 
                              ! Surface heat capacity
    real(DP), intent(in):: xy_SoilHeatCap (0:imax-1, 1:jmax)
                              ! 土壌熱容量 (J K-1 m-3)
                              ! Specific heat of soil (J K-1 m-3)

    real(DP), intent(in):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 熱フラックス. 
                              ! Heat flux
!!$    real(DP), intent(in):: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
!!$                              ! 比湿フラックス. 
!!$                              ! Specific humidity flux
    real(DP), intent(in):: xy_SurfH2OVapFlux(0:imax-1, 1:jmax)
                              ! 惑星表面水蒸気フラックス.
                              ! Water vapor flux at the surface
    real(DP), intent(in):: xy_SurfLatentHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面潜熱フラックス.
                              ! Latent heat flux at the surface
    real(DP), intent(in):: xyr_SoilHeatFlux (0:imax-1, 1:jmax, 0:kslmax)
                              ! 土壌中の熱フラックス (W m-2)
                              ! Heat flux in sub-surface soil (W m-2)
    real(DP), intent(in):: xy_SurfTempTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：温度. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xyr_SoilTempTransCoef (0:imax-1, 1:jmax, 0:kslmax)
                              ! 輸送係数：土壌温度.
                              ! Transfer coefficient: soil temperature
    real(DP), intent(in):: xyr_SOSIHeatTransCoef(0:imax-1, 1:jmax, 0:ksimax)

    real(DP), intent(in):: xyr_RadSFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 短波 (日射) フラックス. 
                              ! Shortwave (insolation) flux
    real(DP), intent(in):: xyr_RadLFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Longwave flux
    real(DP), intent(in):: xyra_DelRadLFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Surface temperature tendency with longwave

    real(DP), intent(in ):: xy_LatHeatFluxByMajCompIceSubl(0:imax-1, 1:jmax)
                              !
                              ! Latent heat flux by major component ice sublimation
                              ! (variable only for debug)
    real(DP), intent(in ):: xy_LatHeatFluxBySnowMelt      (0:imax-1, 1:jmax)
                              !
                              ! Latent heat flux by melt (variable only for debug)
    real(DP), intent(in ):: xy_LatHeatFluxBySeaIceMelt    (0:imax-1, 1:jmax)
                              !
                              ! Latent heat flux by sea ice melt (variable only for debug)
    real(DP), intent(in):: xy_DeepSubSurfHeatFlux (0:imax-1, 1:jmax)
                              ! 地中熱フラックス. 
                              ! "Deep subsurface heat flux"
                              ! Heat flux at the bottom of surface/soil layer.

    real(DP), intent(in ):: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . 温度変化. 
                              ! Temperature tendency
    real(DP), intent(in ):: xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ \DP{q}{t} $ . 質量混合比変化. 
                              ! Mass mixing ratio tendency
    real(DP), intent(in ):: xy_DSurfTempDt (0:imax-1, 1:jmax)
                              ! 地表面温度変化率 (K s-1)
                              ! Surface temperature tendency (K s-1)
    real(DP), intent(in ):: xyz_DSoilTempDt (0:imax-1, 1:jmax, 1:kslmax)
                              ! $ \DP{Tg}{t} $ . 土壌温度変化 (K s-1)
                              ! Temperature tendency (K s-1)
    real(DP), intent(in ):: xy_DSoilMoistDt (0:imax-1, 1:jmax)
                              ! 土壌温度時間変化率 (kg m-2 s-1)
                              ! Soil temperature tendency (kg m-2 s-1)
    real(DP), intent(in ):: xy_DSurfSnowDt (0:imax-1, 1:jmax)
                              ! 積雪率時間変化率 (kg m-2 s-1)
                              ! Surface snow amount tendency (kg m-2 s-1)

    real(DP), intent(in ):: xy_DPsDt            (0:imax-1, 1:jmax)
    real(DP), intent(in ):: xy_DSurfMajCompIceDt(0:imax-1, 1:jmax)

    integer , intent(in ):: xy_SOSILocalKMax   (0:imax-1, 1:jmax)
    real(DP), intent(in ):: xyr_SOSILocalDepth   (0:imax-1, 1:jmax, 0:ksimax)
    real(DP), intent(in ):: xyz_SOSeaIceTemp   (0:imax-1, 1:jmax, 1:ksimax)
    real(DP), intent(in ):: xyz_DSOSeaIceTempDt(0:imax-1, 1:jmax, 1:ksimax)
                              ! $ \DP{TSI}{t} $ . 海氷温度変化 (K s-1)
                              ! Sea ice temperature tendency (K s-1)
    real(DP), intent(in ):: xy_DSOSeaIceMassDtTop(0:imax-1, 1:jmax)
                              ! 海氷質量時間変化率 (kg m-2 s-1)
                              ! Slab ocean sea ice mass tendency (kg m-2)
    real(DP), intent(in ):: xy_DSOSeaIceMassDtBot(0:imax-1, 1:jmax)
                              ! 海氷質量時間変化率 (kg m-2 s-1)
                              ! Slab ocean sea ice mass tendency (kg m-2)

    ! 作業変数
    ! Work variables
    !

    real(DP) :: xy_SurfRadSFlux        (0:imax-1, 1:jmax)
    real(DP) :: xy_SurfRadLFlux        (0:imax-1, 1:jmax)
    real(DP) :: xy_SurfSensHeatFlux(0:imax-1, 1:jmax)
    real(DP) :: xy_SurfSoilHeatCondFlux(0:imax-1, 1:jmax)
    real(DP) :: xy_SeaIceHeatCondFlux  (0:imax-1, 1:jmax)
    real(DP) :: xy_BottomSeaIceHeatCondFlux(0:imax-1, 1:jmax)
    real(DP) :: xy_BottomHeating           (0:imax-1, 1:jmax)

    real(DP) :: xy_Residual            (0:imax-1, 1:jmax)
    real(DP) :: xy_SumAtmRate          (0:imax-1, 1:jmax)

    real(DP) :: xy_TempCond            (0:imax-1, 1:jmax)

    real(DP) :: SOSeaIceTempA1Tentative
    real(DP) :: SOSeaIceTempALowLevTentative
    real(DP) :: SurfTempATentative

    real(DP) :: MaxResidual

    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitude
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude
    integer:: k               ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction


    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. phy_implicit_sdh_V5_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    xy_SurfRadSFlux = xyr_RadSFlux(:,:,0)
    xy_SurfRadLFlux = xyr_RadLFlux(:,:,0) + xyra_DelRadLFlux(:,:,0,0) * xy_DSurfTempDt * ( 2.0_DP * DelTime ) + xyra_DelRadLFlux(:,:,0,1) * xyz_DTempDt(:,:,1) * ( 2.0_DP * DelTime )
    xy_SurfSoilHeatCondFlux = xyr_SoilHeatFlux(:,:,0) - xyr_SoilTempTransCoef(:,:,0) * ( xyz_DSoilTempDt(:,:,1) - xy_DSurfTempDt ) * ( 2.0_DP * DelTime )
    xy_SurfSensHeatFlux = xyr_HeatFlux(:,:,0) - CpDry * xyr_Exner(:,:,0) * xy_SurfTempTransCoef * ( xyz_DTempDt(:,:,1) / xyz_Exner(:,:,1) - xy_DSurfTempDt / xyr_Exner(:,:,0) ) * ( 2.0_DP * DelTime )
    xy_SeaIceHeatCondFlux = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexSeaIce )
          xy_SeaIceHeatCondFlux(i,j) = - SeaIceThermCondCoef * (   xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime ) - TempBelowSeaIce ) / xy_SeaIceThickness(i,j)
        case ( IndexSlabOcean )
!!$          xy_SeaIceHeatCondFlux(i,j) =                                              &
!!$            & - SeaIceThermCondCoef                                                 &
!!$            &   * (   xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime ) &
!!$            &       - TempBelowSeaIce ) &
!!$            &   / xy_SeaIceThickness(i,j)
          xy_SeaIceHeatCondFlux(i,j) = 0.0_DP
        case ( IndexSlabOceanSeaIce )
          ! slab sea ice
          if ( .not. xy_FlagSOSeaIceAllMelt(i,j) ) then
            SurfTempATentative = xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime )
            k = 1
            SOSeaIceTempA1Tentative = xyz_SOSeaIceTemp(i,j,k) + xyz_DSOSeaIceTempDt(i,j,k) * ( 2.0_DP * DelTime )
            k = 0
            xy_SeaIceHeatCondFlux(i,j) = - xyr_SOSIHeatTransCoef(i,j,k) * ( SOSeaIceTempA1Tentative - SurfTempATentative )
          end if
        end select
      end do
    end do
    !
    xy_BottomSeaIceHeatCondFlux = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexSlabOceanSeaIce )
          ! slab sea ice
          if ( ( .not. xy_FlagSOSeaIceAllMelt(i,j)       ) .and. ( .not. xy_FlagSOSIWSIOceanAllFreeze(i,j) ) ) then
            k = xy_SOSILocalKMax(i,j)
            SOSeaIceTempALowLevTentative = xyz_SOSeaIceTemp(i,j,k) + xyz_DSOSeaIceTempDt(i,j,k) * ( 2.0_DP * DelTime )
            xy_BottomSeaIceHeatCondFlux(i,j) = - xyr_SOSIHeatTransCoef(i,j,k) * ( TempBelowSeaIce - SOSeaIceTempALowLevTentative )
          else
            xy_BottomSeaIceHeatCondFlux(i,j) = 0.0_DP
          end if
        end select
      end do
    end do


    !-----
    ! Atmospheric heating
    !
    xy_SumAtmRate = 0.0_DP
    do k = kmax, 1, -1
      xy_SumAtmRate = xy_SumAtmRate + CpDry * ( xyr_Press(:,:,k-1) - xyr_Press(:,:,k) ) / Grav * xyz_DTempDt(:,:,k)
    end do
    !
    xy_Residual = - ( 0.0_DP - xy_SurfSensHeatFlux ) - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )

!!$        select case ( xy_IndexCalcMethod(i,j) )
!!$        case ( IndexSeaIce )
!!$        case default
!!$          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
!!$        end select

      end do
    end do
    if ( MaxResidual > 1.0d-10 ) then
      call MessageNotify( 'M', module_name, 'Atm. sensible heating res. : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Land surface
    !
    xy_SumAtmRate = xy_SurfHeatCapacity * xy_DSurfTempDt
    !
    xy_Residual = xy_SurfRadSFlux + xy_SurfRadLFlux + xy_SurfSensHeatFlux + xy_SurfLatentHeatFlux - xy_SurfSoilHeatCondFlux + xy_LatHeatFluxByMajCompIceSubl + xy_LatHeatFluxBySnowMelt + xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
        case ( IndexSeaIce, IndexSlabOceanSeaIce )
          ! sea ice
        case ( IndexSlabOcean )
          ! slab ocean
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error when checking land surf. heating.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'Land surf. heat budget res.: %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Soil heating
    !
    xy_SumAtmRate = 0.0_DP
    do k = 1, kslmax
      xy_SumAtmRate = xy_SumAtmRate + xy_SoilHeatCap * ( r_SSDepth(k-1) - r_SSDepth(k) ) * xyz_DSoilTempDt(:,:,k)
    end do
    !
    xy_Residual = - ( xy_SurfSoilHeatCondFlux - xy_DeepSubSurfHeatFlux ) - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
        case ( IndexSeaIce, IndexSlabOceanSeaIce )
          ! sea ice
        case ( IndexSlabOcean )
          ! slab ocean
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error when checking soil heating.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'Soil heating res.          : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Slab ocean heating (not all freeze)
    !
    xy_SumAtmRate = SOHeatCapacity * xy_DSurfTempDt
    !
    xy_Residual = - ( xy_SurfRadSFlux + xy_SurfRadLFlux + xy_SurfSensHeatFlux + xy_SurfLatentHeatFlux ) - xy_LatHeatFluxBySeaIceMelt - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
        case ( IndexSeaIce, IndexSlabOceanSeaIce )
          ! sea ice
        case ( IndexSlabOcean )
          ! slab ocean
          if ( .not. xy_FlagSOSIWoSIOceanAllFreeze(i,j) ) then
              MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
          end if
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error when checking slab ocean heating.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'Slab ocean heating res. (not all freeze) : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Slab ocean heating (all freeze)
    !
!!$    xy_SumAtmRate = SeaIceVolHeatCap * xy_SeaIceThickness * xy_DSurfTempDt
    xy_SumAtmRate = SeaIceVolHeatCap * xy_SOSeaIceMassB / SeaIceDen * xy_DSurfTempDt
    !
    xy_Residual = - ( ( xy_SurfRadSFlux + xy_SurfRadLFlux + xy_SurfSensHeatFlux + xy_SurfLatentHeatFlux ) ) - xy_LatHeatFluxBySeaIceMelt - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
        case ( IndexSeaIce )
          ! sea ice
        case ( IndexSlabOceanSeaIce )
          ! slab sea ice
        case ( IndexSlabOcean )
          ! slab ocean
          if ( xy_FlagSOSIWoSIOceanAllFreeze(i,j) ) then
            MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
          end if
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error when checking sea ice heating.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'Slab ocean heating res. (all freeze) : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Sea ice heating
    !
    xy_SumAtmRate = SeaIceVolHeatCap * xy_SeaIceThickness * xy_DSurfTempDt
    !
    xy_Residual = - ( ( xy_SurfRadSFlux + xy_SurfRadLFlux + xy_SurfSensHeatFlux + xy_SurfLatentHeatFlux ) - xy_SeaIceHeatCondFlux ) - xy_LatHeatFluxBySeaIceMelt - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
        case ( IndexSeaIce )
          ! sea ice
          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
        case ( IndexSlabOceanSeaIce )
          ! slab sea ice
        case ( IndexSlabOcean )
          ! slab ocean
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error when checking sea ice heating.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'Sea ice heating res. : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Slab ocean sea ice surface heat budget (all sea ice does not melt)
    !
!!$    xy_SumAtmRate = SeaIceVolHeatCap * xy_SeaIceThickness * xy_DSurfTempDt
    xy_SumAtmRate = xy_SurfHeatCapacity * xy_DSurfTempDt
    !
    xy_Residual = - ( ( xy_SurfRadSFlux + xy_SurfRadLFlux + xy_SurfSensHeatFlux + xy_SurfLatentHeatFlux ) - xy_SeaIceHeatCondFlux ) - xy_LatHeatFluxBySeaIceMelt - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
        case ( IndexSeaIce )
          ! sea ice
        case ( IndexSlabOceanSeaIce )
          ! slab sea ice
          if ( .not. xy_FlagSOSeaIceAllMelt(i,j) ) then
            MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
          end if
        case ( IndexSlabOcean )
          ! slab ocean
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error when checking slab sea ice heating.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'Slab ocean sea ice surface budget res. (all sea ice does not melt) : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Slab ocean (sea ice) heating (all sea ice melt)
    !
    xy_TempCond = TempCondWater
    xy_SumAtmRate = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        do k = 1, xy_SOSILocalKMax(i,j)
          xy_SumAtmRate(i,j) = xy_SumAtmRate(i,j) + SeaIceVolHeatCap * ( xyr_SOSILocalDepth(i,j,k-1) - xyr_SOSILocalDepth(i,j,k) ) * ( xy_TempCond(i,j) - xyz_SOSeaIceTemp(i,j,k) ) / ( 2.0_DP * DelTime )
        end do
      end do
    end do
    xy_SumAtmRate = xy_SumAtmRate + SOHeatCapacity * ( xy_SurfTemp + xy_DSurfTempDt * ( 2.0_DP * DelTime ) - xy_TempCond ) / ( 2.0_DP * DelTime )
    !
    xy_Residual = - ( ( xy_SurfRadSFlux + xy_SurfRadLFlux + xy_SurfSensHeatFlux + xy_SurfLatentHeatFlux ) ) + LatentHeatFusion * xy_DSOSeaIceMassDtTop - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
        case ( IndexSeaIce )
          ! sea ice
        case ( IndexSlabOceanSeaIce )
          ! slab sea ice
          if ( xy_FlagSOSeaIceAllMelt(i,j) ) then
            MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
          end if
        case ( IndexSlabOcean )
          ! slab ocean
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error when checking slab sea ice heating.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'Slab ocean (sea ice) heat budget res. (all sea ice melt) : %f.', d = (/ MaxResidual /) )
    end if



    !-----
    ! Slab ocean sea ice heating
    !
    xy_SumAtmRate = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        do k = 1, xy_SOSILocalKMax(i,j)
          xy_SumAtmRate(i,j) = xy_SumAtmRate(i,j) + SeaIceVolHeatCap * ( xyr_SOSILocalDepth(i,j,k-1) - xyr_SOSILocalDepth(i,j,k) ) * xyz_DSOSeaIceTempDt(i,j,k)
        end do
      end do
    end do
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagSOSIWSIOceanAllFreeze(i,j) ) then
          if ( xy_SOSILocalKMax(i,j) > 0 ) then
            k = xy_SOSILocalKMax(i,j)
            SOSeaIceTempALowLevTentative = xyz_SOSeaIceTemp(i,j,k) + xyz_DSOSeaIceTempDt(i,j,k) * ( 2.0_DP * DelTime )
            xy_BottomHeating(i,j) = + xy_DSOSeaIceMassDtBot(i,j) * SeaIceVolHeatCap / SeaIceDen * ( TempBelowSeaIce - SOSeaIceTempALowLevTentative ) + xy_DSOSeaIceMassDtBot(i,j) * LatentHeatFusionBelowSeaIce
          else
            xy_BottomHeating(i,j) = 0.0_DP
          end if
        else
          xy_BottomHeating(i,j) = 0.0_DP
        end if
      end do
    end do
    !
    xy_Residual = - ( xy_SeaIceHeatCondFlux - xy_BottomSeaIceHeatCondFlux ) + xy_BottomHeating - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexSlabOceanSeaIce )
          ! slab sea ice
!!$          if ( ( .not. xy_FlagSOSeaIceAllMelt(i,j)      ) .and. &
!!$            &  ( .not. xy_FlagSOSlabOceanAllFreeze(i,j) ) ) then
          if ( .not. xy_FlagSOSeaIceAllMelt(i,j) ) then
            MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
          end if
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'Slab ocean sea ice heating res. : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Land water budget
    !
    xy_SumAtmRate = 0.0_DP
    do k = kmax, 1, -1
      xy_SumAtmRate = xy_SumAtmRate + ( xyr_Press(:,:,k-1) - xyr_Press(:,:,k) ) / Grav * xyzf_DQMixDt(:,:,k,IndexH2OVap)
    end do
    !
    xy_Residual = xy_DSoilMoistDt + xy_DSurfSnowDt + xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
        case ( IndexSeaIce )
          ! sea ice
        case ( IndexSlabOceanSeaIce )
          ! slab sea ice
        case ( IndexSlabOcean )
          ! slab ocean
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error when checking land water.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'Land water budget res.     : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Atmospheric mass budget
    !
    xy_Residual = xy_DPsDt / Grav + xy_DSurfMajCompIceDt
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'Atm. mass budget res.      : %f.', d = (/ MaxResidual /) )
    end if


  end subroutine PhyImplSDHV5ChkConservation

PhyImplSDHV5ChkConservationTQ( xy_IndexCalcMethod, xy_SeaIceThickness, xy_SnowFrac, xyr_Press, xyz_Exner, xyr_Exner, xy_SurfTemp, xyr_HeatFlux, xyrf_QMixFlux, xy_SurfSoilHeatFlux, xy_SurfSOSIHeatFlux, xy_SurfTempTransCoef, xy_SurfQVapTransCoef, xy_SurfHumidCoef, xy_SurfHeatCapacity, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_DeepSubSurfHeatFlux, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt )

Subroutine :

xy_IndexCalcMethod(0:imax-1, 1:jmax) :

integer , intent(in)

:	Index for calculation method

xy_SeaIceThickness(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Sea ice thickness

xy_SnowFrac(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Snow fraction

xyr_Press(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	$ hat{p} $ . 気圧 (半整数レベル). Air pressure (half level)

xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in)

:	Exner 関数 (整数レベル). Exner function (full level)

xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	Exner 関数 (半整数レベル). Exner function (half level)

xy_SurfTemp(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表面温度. Surface temperature

xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	熱フラックス. Heat flux

xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax) :

real(DP), intent(in)

:	比湿フラックス. Specific humidity flux

xy_SurfSoilHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	惑星表面土壌熱伝導フラックス. Soil heat conduction flux at the surface

xy_SurfSOSIHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	惑星表面海氷熱伝導フラックス. Sea ice heat conduction flux at the surface

xy_SurfTempTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：温度. Transfer coefficient: temperature

xy_SurfQVapTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：比湿. Transfer coefficient: specific humidity

xy_SurfHumidCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表湿潤度. Surface humidity coefficient

xy_SurfHeatCapacity(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表熱容量. Surface heat capacity

xyr_RadSFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	短波 (日射) フラックス. Shortwave (insolation) flux

xyr_RadLFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	長波フラックス. Longwave flux

xyra_DelRadLFlux(0:imax-1, 1:jmax, 0:kmax, 0:1) :

real(DP), intent(in)

:	長波地表温度変化. Surface temperature tendency with longwave

xy_DeepSubSurfHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地中熱フラックス. "Deep subsurface heat flux" Heat flux at the bottom of surface/soil layer.

xyz_DTempDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in )

:	$ DP{T}{t} $ . 温度変化. Temperature tendency

xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :

real(DP), intent(in )

:	$ DP{q}{t} $ . 質量混合比変化. Mass mixing ratio tendency

xy_DSurfTempDt(0:imax-1, 1:jmax) :

real(DP), intent(in )

地表面温度変化率 (K s-1) Surface temperature tendency (K s-1)

!$ real(DP), intent(in ):

xy_DSOSeaIceMassDt(0:imax-1, 1:jmax)

A part of conservation of energy is checked.

[Source]

  subroutine PhyImplSDHV5ChkConservationTQ( xy_IndexCalcMethod, xy_SeaIceThickness, xy_SnowFrac, xyr_Press, xyz_Exner, xyr_Exner, xy_SurfTemp, xyr_HeatFlux, xyrf_QMixFlux, xy_SurfSoilHeatFlux, xy_SurfSOSIHeatFlux, xy_SurfTempTransCoef, xy_SurfQVapTransCoef, xy_SurfHumidCoef, xy_SurfHeatCapacity, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_DeepSubSurfHeatFlux, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt )
    !
    ! 
    !
    ! A part of conservation of energy is checked.
    !

    ! モジュール引用 ; USE statements
    !

    ! 座標データ設定
    ! Axes data settings
    !
    use axesset, only: r_SSDepth, z_SSDepth         ! subsurface grid at midpoint of layer

    ! 時刻管理
    ! Time control
    !
    use timeset, only: DelTime               ! $ \Delta t $ [s]

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: Grav, CpDry, GasRDry, LatentHeat, LatentHeatFusion
                              ! $ L $ [J kg-1] . 
                              ! 融解の潜熱. 
                              ! Latent heat of fusion

    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: TempCondWater, SeaIceVolHeatCap   , SeaIceThermCondCoef, TempBelowSeaIce

    ! 飽和比湿の算出
    ! Evaluation of saturation specific humidity
    !
    use saturate, only: xy_CalcQVapSatOnLiq, xy_CalcQVapSatOnSol, xy_CalcDQVapSatDTempOnLiq, xy_CalcDQVapSatDTempOnSol

    ! 宣言文 ; Declaration statements
    !

    integer , intent(in):: xy_IndexCalcMethod (0:imax-1, 1:jmax)
                              ! 
                              ! Index for calculation method
    real(DP), intent(in):: xy_SeaIceThickness(0:imax-1, 1:jmax)
                              !
                              ! Sea ice thickness
    real(DP), intent(in):: xy_SnowFrac(0:imax-1, 1:jmax)
                              !
                              ! Snow fraction
    real(DP), intent(in):: xyr_Press (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . 気圧 (半整数レベル). 
                              ! Air pressure (half level)
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner 関数 (整数レベル). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner 関数 (半整数レベル). 
                              ! Exner function (half level)

    real(DP), intent(in):: xy_SurfTemp (0:imax-1, 1:jmax)
                              ! 地表面温度. 
                              ! Surface temperature

    real(DP), intent(in):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 熱フラックス. 
                              ! Heat flux
    real(DP), intent(in):: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! 比湿フラックス. 
                              ! Specific humidity flux
    real(DP), intent(in):: xy_SurfSoilHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面土壌熱伝導フラックス.
                              ! Soil heat conduction flux at the surface
    real(DP), intent(in):: xy_SurfSOSIHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面海氷熱伝導フラックス.
                              ! Sea ice heat conduction flux at the surface
    real(DP), intent(in):: xy_SurfTempTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：温度. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xy_SurfQVapTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：比湿. 
                              ! Transfer coefficient: specific humidity
    real(DP), intent(in):: xy_SurfHumidCoef (0:imax-1, 1:jmax)
                              ! 地表湿潤度. 
                              ! Surface humidity coefficient
    real(DP), intent(in):: xy_SurfHeatCapacity (0:imax-1, 1:jmax)
                              ! 地表熱容量. 
                              ! Surface heat capacity

    real(DP), intent(in):: xyr_RadSFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 短波 (日射) フラックス. 
                              ! Shortwave (insolation) flux
    real(DP), intent(in):: xyr_RadLFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Longwave flux
    real(DP), intent(in):: xyra_DelRadLFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Surface temperature tendency with longwave

    real(DP), intent(in):: xy_DeepSubSurfHeatFlux (0:imax-1, 1:jmax)
                              ! 地中熱フラックス. 
                              ! "Deep subsurface heat flux"
                              ! Heat flux at the bottom of surface/soil layer.

    real(DP), intent(in ):: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . 温度変化. 
                              ! Temperature tendency
    real(DP), intent(in ):: xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ \DP{q}{t} $ . 質量混合比変化. 
                              ! Mass mixing ratio tendency
    real(DP), intent(in ):: xy_DSurfTempDt (0:imax-1, 1:jmax)
                              ! 地表面温度変化率 (K s-1)
                              ! Surface temperature tendency (K s-1)
!!$    real(DP), intent(in ):: xy_DSOSeaIceMassDt(0:imax-1, 1:jmax)


    ! 作業変数
    ! Work variables
    !
    real(DP):: xy_SurfQVapSatOnLiq(0:imax-1, 1:jmax)
                              ! 地表飽和比湿. 
                              ! Saturated specific humidity on surface
    real(DP):: xy_SurfQVapSatOnSol (0:imax-1, 1:jmax)
                              ! 地表飽和比湿. 
                              ! Saturated specific humidity on surface
    real(DP):: xy_SurfQVapSat (0:imax-1, 1:jmax)
                              ! 地表飽和比湿. 
                              ! Saturated specific humidity on surface
    real(DP):: xy_SurfDQVapSatDTempOnLiq (0:imax-1, 1:jmax)
                              ! 地表飽和比湿変化. 
                              ! Saturated specific humidity tendency on surface
    real(DP):: xy_SurfDQVapSatDTempOnSol (0:imax-1, 1:jmax)
                              ! 地表飽和比湿変化. 
                              ! Saturated specific humidity tendency on surface
    real(DP):: xy_SurfDQVapSatDTemp (0:imax-1, 1:jmax)
                              ! 地表飽和比湿変化. 
                              ! Saturated specific humidity tendency on surface

    real(DP) :: xy_SurfRadSFlux        (0:imax-1, 1:jmax)
    real(DP) :: xy_SurfRadLFlux        (0:imax-1, 1:jmax)
    real(DP) :: xy_SurfSensHeatFlux    (0:imax-1, 1:jmax)
    real(DP) :: xy_SurfH2OVapFlux      (0:imax-1, 1:jmax)
    real(DP) :: xy_SurfLatentHeatFlux  (0:imax-1, 1:jmax)
    real(DP) :: xy_SurfSoilHeatCondFlux(0:imax-1, 1:jmax)
    real(DP) :: xy_SeaIceHeatCondFlux  (0:imax-1, 1:jmax)

    real(DP) :: xy_Residual            (0:imax-1, 1:jmax)
    real(DP) :: xy_SumAtmRate          (0:imax-1, 1:jmax)

    real(DP) :: MaxResidual

    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitude
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude
    integer:: k               ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction
    integer:: n


    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. phy_implicit_sdh_V5_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! 飽和比湿の計算
    ! Calculate saturated specific humidity
    !
    xy_SurfQVapSatOnLiq       = xy_CalcQVapSatOnLiq      ( xy_SurfTemp, xyr_Press(:,:,0) )
    xy_SurfQVapSatOnSol       = xy_CalcQVapSatOnSol      ( xy_SurfTemp, xyr_Press(:,:,0) )
    xy_SurfQVapSat       = ( 1.0_DP - xy_SnowFrac ) * xy_SurfQVapSatOnLiq + xy_SnowFrac              * xy_SurfQVapSatOnSol
    xy_SurfDQVapSatDTempOnLiq = xy_CalcDQVapSatDTempOnLiq( xy_SurfTemp, xy_SurfQVapSatOnLiq )
    xy_SurfDQVapSatDTempOnSol = xy_CalcDQVapSatDTempOnSol( xy_SurfTemp, xy_SurfQVapSatOnSol )
    xy_SurfDQVapSatDTemp = ( 1.0_DP - xy_SnowFrac ) * xy_SurfDQVapSatDTempOnLiq + xy_SnowFrac              * xy_SurfDQVapSatDTempOnSol


    xy_SurfRadSFlux = xyr_RadSFlux(:,:,0)
    xy_SurfRadLFlux = xyr_RadLFlux(:,:,0) + xyra_DelRadLFlux(:,:,0,0) * xy_DSurfTempDt * ( 2.0_DP * DelTime ) + xyra_DelRadLFlux(:,:,0,1) * xyz_DTempDt(:,:,1) * ( 2.0_DP * DelTime )
    xy_SurfSoilHeatCondFlux = xy_SurfSoilHeatFlux
    xy_SurfSensHeatFlux = xyr_HeatFlux(:,:,0) - CpDry * xyr_Exner(:,:,0) * xy_SurfTempTransCoef * ( xyz_DTempDt(:,:,1) / xyz_Exner(:,:,1) - xy_DSurfTempDt / xyr_Exner(:,:,0) ) * ( 2.0_DP * DelTime )
    xy_SeaIceHeatCondFlux = - SeaIceThermCondCoef * ( xy_SurfTemp + xy_DSurfTempDt * ( 2.0_DP * DelTime ) - TempBelowSeaIce ) / xy_SeaIceThickness

    n = IndexH2OVap
    xy_SurfH2OVapFlux = xyrf_QMixFlux(:,:,0,n) - xy_SurfHumidCoef * xy_SurfQVapTransCoef * ( xyzf_DQMixDt(:,:,1,n) - xy_SurfDQVapSatDTemp * xy_DSurfTempDt ) * 2.0_DP * DelTime
    xy_SurfLatentHeatFlux = LatentHeat * xy_SurfH2OVapFlux


    !-----
    ! Atmospheric heating
    !
    xy_SumAtmRate = 0.0_DP
    do k = kmax, 1, -1
      xy_SumAtmRate = xy_SumAtmRate + CpDry * ( xyr_Press(:,:,k-1) - xyr_Press(:,:,k) ) / Grav * xyz_DTempDt(:,:,k)
    end do
    !
    xy_Residual = - ( 0.0_DP - xy_SurfSensHeatFlux ) - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )

!!$        select case ( xy_IndexCalcMethod(i,j) )
!!$        case ( IndexSeaIce )
!!$        case default
!!$          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
!!$        end select

      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'TQ: Atm. sensible heating res. : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Land surface
    !
    xy_SumAtmRate = xy_SurfHeatCapacity * xy_DSurfTempDt
    !
    xy_Residual = xy_SurfRadSFlux + xy_SurfRadLFlux + xy_SurfSensHeatFlux + xy_SurfLatentHeatFlux - xy_SurfSoilHeatCondFlux + xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
        case ( IndexSeaIce, IndexSlabOceanSeaIce )
          ! sea ice
        case ( IndexSlabOcean )
          ! slab ocean
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'TQ: Land surf. heat budget res.: %f.', d = (/ MaxResidual /) )
    end if


!!$    !-----
!!$    ! Soil heating
!!$    !
!!$    xy_SumAtmRate = 0.0_DP
!!$    do k = 1, kslmax
!!$      xy_SumAtmRate = xy_SumAtmRate                            &
!!$        & + xy_SoilHeatCap * ( r_SSDepth(k-1) - r_SSDepth(k) ) &
!!$        &     * xyz_DSoilTempDt(:,:,k)
!!$    end do
!!$    !
!!$    xy_Residual =                                               &
!!$      & - ( xy_SurfSoilHeatCondFlux - xy_DeepSubSurfHeatFlux )  &
!!$      & - xy_SumAtmRate
!!$    !
!!$    MaxResidual = 0.0_DP
!!$    do j = 1, jmax
!!$      do i = 0, imax-1
!!$        select case ( xy_IndexCalcMethod(i,j) )
!!$        case ( IndexLand )
!!$          ! land
!!$          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
!!$        case ( IndexSeaIce )
!!$          ! sea ice
!!$        case ( IndexSlabOcean )
!!$          ! slab ocean
!!$        case ( IndexOceanPresSST )
!!$          ! open ocean
!!$        case default
!!$          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
!!$        end select
!!$      end do
!!$    end do
!!$    if ( MaxResidual > 1.0d-10 ) then
!!$      call MessageNotify( 'M', module_name, &
!!$        & 'Soil heating res.          : %f.', d = (/ MaxResidual /) )
!!$    end if



    !-----
    ! Slab ocean heating
    !
    xy_SumAtmRate = SOHeatCapacity * xy_DSurfTempDt
    !
    xy_Residual = - ( xy_SurfRadSFlux + xy_SurfRadLFlux + xy_SurfSensHeatFlux + xy_SurfLatentHeatFlux ) - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
        case ( IndexSeaIce, IndexSlabOceanSeaIce )
          ! sea ice
        case ( IndexSlabOcean )
          ! slab ocean
          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'TQ: Slab ocean heating res.    : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Sea ice heating
    !
    xy_SumAtmRate = SeaIceVolHeatCap * xy_SeaIceThickness * xy_DSurfTempDt
    !
    xy_Residual = - ( ( xy_SurfRadSFlux + xy_SurfRadLFlux + xy_SurfSensHeatFlux + xy_SurfLatentHeatFlux ) - xy_SeaIceHeatCondFlux ) - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
        case ( IndexSeaIce )
          ! sea ice
          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
        case ( IndexSlabOceanSeaIce )
          ! sea ice
        case ( IndexSlabOcean )
          ! slab ocean
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'TQ: Sea ice heating res.       : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Slab ocean sea ice heating
    !
    xy_SumAtmRate = SeaIceVolHeatCap * xy_SeaIceThickness * xy_DSurfTempDt
    !
    xy_Residual = - ( ( xy_SurfRadSFlux + xy_SurfRadLFlux + xy_SurfSensHeatFlux + xy_SurfLatentHeatFlux ) - xy_SurfSOSIHeatFlux ) - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
        case ( IndexSeaIce )
          ! sea ice
        case ( IndexSlabOceanSeaIce )
          ! sea ice
          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
        case ( IndexSlabOcean )
          ! slab ocean
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'TQ: Slab ocean sea ice heating res. : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Atmospheric moistening
    !
    xy_SumAtmRate = 0.0_DP
    do k = kmax, 1, -1
      xy_SumAtmRate = xy_SumAtmRate + ( xyr_Press(:,:,k-1) - xyr_Press(:,:,k) ) / Grav * xyzf_DQMixDt(:,:,k,IndexH2OVap)
    end do
    !
    xy_Residual = - ( 0.0_DP - xy_SurfH2OVapFlux ) - xy_SumAtmRate
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'TQ: Atm. moistening res.       : %f.', d = (/ MaxResidual /) )
    end if


    !-----
    ! Land water budget
    !
    xy_SumAtmRate = 0.0_DP
    do k = kmax, 1, -1
      xy_SumAtmRate = xy_SumAtmRate + ( xyr_Press(:,:,k-1) - xyr_Press(:,:,k) ) / Grav * xyzf_DQMixDt(:,:,k,IndexH2OVap)
    end do
    !
!!$    xy_Residual = xy_DSoilMoistDt + xy_DSurfSnowDt + xy_SumAtmRate
    xy_Residual = xy_SumAtmRate - xy_SurfH2OVapFlux
    !
    MaxResidual = 0.0_DP
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
          MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
        case ( IndexSeaIce, IndexSlabOceanSeaIce )
          ! sea ice
        case ( IndexSlabOcean )
          ! slab ocean
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
        end select
      end do
    end do
    if ( MaxResidual > ResidualMessageThreshold ) then
      call MessageNotify( 'M', module_name, 'TQ: Land water budget res.     : %f.', d = (/ MaxResidual /) )
    end if


!!$    !-----
!!$    ! Atmospheric mass budget
!!$    !
!!$    xy_Residual = xy_DPsDt / Grav + xy_DSurfMajCompIceDt
!!$    !
!!$    MaxResidual = 0.0_DP
!!$    do j = 1, jmax
!!$      do i = 0, imax-1
!!$        MaxResidual = max( MaxResidual, abs( xy_Residual(i,j) ) )
!!$      end do
!!$    end do
!!$    if ( MaxResidual > 1.0d-10 ) then
!!$      call MessageNotify( 'M', module_name, &
!!$        & 'Atm. mass budget res.      : %f.', d = (/ MaxResidual /) )
!!$    end if


  end subroutine PhyImplSDHV5ChkConservationTQ

PhyImplSDHV5IceSnowPhaseChgCor( IndexSpc, xy_Ps, xyr_HeatFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xyr_SoilTempTransCoef, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xy_SurfTemp, xyz_SoilTemp, xy_SurfLiqB, xy_SurfSolB, xy_SurfHeatCapacity, xy_SoilHeatCap, xy_SoilHeatDiffCoef, xy_IndexCalcMethod, xyra_DelRadLFlux, xyz_Exner, xyr_Exner, xy_SurfTempTransCoef, xy_LatHeatFluxByOtherSpc, xyza_ArgTempMtx, xyz_ArgTempVec, xyaa_ArgSurfMtx, xy_ArgSurfRH, xyaa_ArgSoilTempMtx, xya_ArgSoilTempVec, xyz_DTempDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DSurfLiqDt, xy_DSurfSolDt, xy_LatHeatFluxBySnowMelt )

Subroutine :

IndexSpc : integer , intent(in)

xy_Ps(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Surface pressure

xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	熱フラックス. Heat flux

xy_SurfLatentHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	惑星表面潜熱フラックス. Latent heat flux at the surface

xyr_SoilHeatFlux(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	土壌中の熱フラックス (W m-2) Heat flux in sub-surface soil (W m-2)

xyr_SoilTempTransCoef(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	輸送係数：土壌温度. Transfer coefficient: soil temperature

xyr_RadSFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	短波 (日射) フラックス. Shortwave (insolation) flux

xyr_RadLFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	長波フラックス. Longwave flux

xy_DeepSubSurfHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地中熱フラックス. "Deep subsurface heat flux" Heat flux at the bottom of surface/soil layer.

xy_SurfTemp(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表面温度. Surface temperature

xyz_SoilTemp(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(in)

:	土壌温度 (K) Soil temperature (K)

xy_SurfLiqB(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Surface liquid amount

xy_SurfSolB(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	積雪量. Surface snow amount.

xy_SurfHeatCapacity(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表熱容量. Surface heat capacity

xy_SoilHeatCap(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	土壌熱容量 (J K-1 m-3) Specific heat of soil (J K-1 m-3)

xy_SoilHeatDiffCoef(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	土壌熱伝導係数 (J m-3 K-1) Heat conduction coefficient of soil (J m-3 K-1)

xy_IndexCalcMethod(0:imax-1, 1:jmax) :

integer , intent(in )

:	Index for calculation method

xyra_DelRadLFlux(0:imax-1, 1:jmax, 0:kmax, 0:1) :

real(DP), intent(in)

:	長波地表温度変化. Surface temperature tendency with longwave

xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in)

:	Exner 関数 (整数レベル). Exner function (full level)

xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	Exner 関数 (半整数レベル). Exner function (half level)

xy_SurfTempTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：温度. Transfer coefficient: temperature

xy_LatHeatFluxByOtherSpc(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	Latent heat flux by other specie

xyza_ArgTempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1) :

real(DP), intent(in )

:	温度陰解行列. Implicit matrix about temperature

xyz_ArgTempVec(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in )

:	温度陰解ベクトル. Implicit vector about temperature

xyaa_ArgSurfMtx(0:imax-1, 1:jmax, 0:0, -1:1) :

real(DP), intent(in )

:	惑星表面エネルギー収支用陰解行列 Implicit matrix for surface energy balance

xy_ArgSurfRH(0:imax-1,1:jmax) : real(DP), intent(in )

xyaa_ArgSoilTempMtx(0:imax-1, 1:jmax, 1:kslmax,-1:1) :

real(DP), intent(in )

:	土壌温度拡散方程式の行列 Matrix for diffusion equation of soil temperature

xya_ArgSoilTempVec(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(in )

:	土壌温度拡散方程式のベクトル Vector for diffusion equation of soil temperature

xyz_DTempDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(inout)

:	$ DP{T}{t} $ . 温度変化. Temperature tendency

xy_DSurfTempDt(0:imax-1, 1:jmax) :

real(DP), intent(inout)

:	地表面温度変化率 (K s-1) Surface temperature tendency (K s-1)

xyz_DSoilTempDt(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(inout)

:	$ DP{Tg}{t} $ . 土壌温度変化 (K s-1) Temperature tendency (K s-1)

xy_DSurfLiqDt(0:imax-1, 1:jmax) :

real(DP), intent(inout)

:	土壌温度時間変化率 (kg m-2 s-1) Soil temperature tendency (kg m-2 s-1)

xy_DSurfSolDt(0:imax-1, 1:jmax) :

real(DP), intent(inout)

:	積雪率時間変化率 (kg m-2 s-1) Surface snow amount tendency (kg m-2 s-1)

xy_LatHeatFluxBySnowMelt(0:imax-1, 1:jmax) :

real(DP), intent(out )

:	Latent heat flux by melt (variable only for debug)

融雪による時間変化率の修正を行います.

Correction of tendencies due to melt of snow.

[Source]

  subroutine PhyImplSDHV5IceSnowPhaseChgCor( IndexSpc, xy_Ps, xyr_HeatFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xyr_SoilTempTransCoef, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xy_SurfTemp, xyz_SoilTemp, xy_SurfLiqB, xy_SurfSolB, xy_SurfHeatCapacity, xy_SoilHeatCap, xy_SoilHeatDiffCoef, xy_IndexCalcMethod, xyra_DelRadLFlux, xyz_Exner, xyr_Exner, xy_SurfTempTransCoef, xy_LatHeatFluxByOtherSpc, xyza_ArgTempMtx, xyz_ArgTempVec, xyaa_ArgSurfMtx, xy_ArgSurfRH, xyaa_ArgSoilTempMtx, xya_ArgSoilTempVec, xyz_DTempDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DSurfLiqDt, xy_DSurfSolDt, xy_LatHeatFluxBySnowMelt )
    !
    ! 融雪による時間変化率の修正を行います. 
    !
    ! Correction of tendencies due to melt of snow. 
    !

    ! モジュール引用 ; USE statements
    !

    ! 座標データ設定
    ! Axes data settings
    !
    use axesset, only: r_SSDepth, z_SSDepth         ! subsurface grid at midpoint of layer

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: Grav, CpDry, LatentHeatFusion
                              ! $ L $ [J kg-1] . 
                              ! 融解の潜熱. 
                              ! Latent heat of fusion

    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: TempCondWater

    ! 時刻管理
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop


    ! ヒストリデータ出力
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! 陰解法による時間積分のためのルーチン
    ! Routines for time integration with implicit scheme
    !
    use phy_implicit_utils, only : PhyImplLUDecomp3, PhyImplLUSolve3

    ! 主成分相変化
    ! Phase change of atmospheric major component
    !
    use saturate_major_comp, only : SaturateMajorCompCondTemp, SaturateMajorCompPressSat, SaturateMajorCompDPressSatDT, SaturateMajorCompInqLatentHeat


    ! 宣言文 ; Declaration statements
    !

    integer , intent(in):: IndexSpc
    real(DP), intent(in):: xy_Ps(0:imax-1, 1:jmax)
                              ! 
                              ! Surface pressure

    real(DP), intent(in):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 熱フラックス. 
                              ! Heat flux

    real(DP), intent(in):: xy_SurfLatentHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面潜熱フラックス.
                              ! Latent heat flux at the surface

    real(DP), intent(in):: xyr_SoilHeatFlux (0:imax-1, 1:jmax, 0:kslmax)
                              ! 土壌中の熱フラックス (W m-2)
                              ! Heat flux in sub-surface soil (W m-2)
    real(DP), intent(in):: xyr_SoilTempTransCoef (0:imax-1, 1:jmax, 0:kslmax)
                              ! 輸送係数：土壌温度.
                              ! Transfer coefficient: soil temperature


    real(DP), intent(in):: xyr_RadSFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 短波 (日射) フラックス. 
                              ! Shortwave (insolation) flux
    real(DP), intent(in):: xyr_RadLFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Longwave flux

    real(DP), intent(in):: xy_DeepSubSurfHeatFlux (0:imax-1, 1:jmax)
                              ! 地中熱フラックス. 
                              ! "Deep subsurface heat flux"
                              ! Heat flux at the bottom of surface/soil layer.
    real(DP), intent(in):: xy_SurfTemp (0:imax-1, 1:jmax)
                              ! 地表面温度. 
                              ! Surface temperature
    real(DP), intent(in):: xyz_SoilTemp (0:imax-1, 1:jmax, 1:kslmax)
                              ! 土壌温度 (K)
                              ! Soil temperature (K)

    real(DP), intent(in):: xy_SurfLiqB (0:imax-1, 1:jmax)
                              ! 
                              ! Surface liquid amount
    real(DP), intent(in):: xy_SurfSolB (0:imax-1, 1:jmax)
                              ! 積雪量.
                              ! Surface snow amount.

    real(DP), intent(in):: xy_SurfHeatCapacity (0:imax-1, 1:jmax)
                              ! 地表熱容量. 
                              ! Surface heat capacity
    real(DP), intent(in ):: xy_SoilHeatCap (0:imax-1, 1:jmax)
                              ! 土壌熱容量 (J K-1 m-3)
                              ! Specific heat of soil (J K-1 m-3)
    real(DP), intent(in ):: xy_SoilHeatDiffCoef (0:imax-1, 1:jmax)
                              ! 土壌熱伝導係数 (J m-3 K-1)
                              ! Heat conduction coefficient of soil (J m-3 K-1)

    integer , intent(in ) :: xy_IndexCalcMethod(0:imax-1, 1:jmax)
                              ! 
                              ! Index for calculation method

    real(DP), intent(in):: xyra_DelRadLFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Surface temperature tendency with longwave

    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner 関数 (整数レベル). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner 関数 (半整数レベル). 
                              ! Exner function (half level)

    real(DP), intent(in):: xy_SurfTempTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：温度. 
                              ! Transfer coefficient: temperature

    real(DP), intent(in   ):: xyza_ArgTempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 温度陰解行列. 
                              ! Implicit matrix about temperature
    real(DP), intent(in   ):: xyz_ArgTempVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 温度陰解ベクトル. 
                              ! Implicit vector about temperature
    real(DP), intent(in   ):: xyaa_ArgSurfMtx(0:imax-1, 1:jmax, 0:0, -1:1)
                              ! 惑星表面エネルギー収支用陰解行列
                              ! Implicit matrix for surface energy balance
    real(DP), intent(in   ):: xy_ArgSurfRH(0:imax-1,1:jmax)


    real(DP), intent(in   ):: xyaa_ArgSoilTempMtx (0:imax-1, 1:jmax, 1:kslmax,-1:1)
                              ! 土壌温度拡散方程式の行列
                              ! Matrix for diffusion equation of soil temperature
    real(DP), intent(in   ):: xya_ArgSoilTempVec (0:imax-1, 1:jmax, 1:kslmax)
                              ! 土壌温度拡散方程式のベクトル
                              ! Vector for diffusion equation of soil temperature

    real(DP), intent(in   ):: xy_LatHeatFluxByOtherSpc(0:imax-1, 1:jmax)
                              !
                              ! Latent heat flux by other specie

    real(DP), intent(inout):: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . 温度変化. 
                              ! Temperature tendency
    real(DP), intent(inout):: xy_DSurfTempDt (0:imax-1, 1:jmax)
                              ! 地表面温度変化率 (K s-1)
                              ! Surface temperature tendency (K s-1)
    real(DP), intent(inout):: xyz_DSoilTempDt (0:imax-1, 1:jmax, 1:kslmax)
                              ! $ \DP{Tg}{t} $ . 土壌温度変化 (K s-1)
                              ! Temperature tendency (K s-1)

    real(DP), intent(inout):: xy_DSurfLiqDt (0:imax-1, 1:jmax)
                              ! 土壌温度時間変化率 (kg m-2 s-1)
                              ! Soil temperature tendency (kg m-2 s-1)
    real(DP), intent(inout):: xy_DSurfSolDt (0:imax-1, 1:jmax)
                              ! 積雪率時間変化率 (kg m-2 s-1)
                              ! Surface snow amount tendency (kg m-2 s-1)
    real(DP), intent(out  ):: xy_LatHeatFluxBySnowMelt(0:imax-1, 1:jmax)
                              !
                              ! Latent heat flux by melt (variable only for debug)

    ! 作業変数
    ! Work variables
    !
    real(DP):: xy_DSurfLiqDtSave(0:imax-1, 1:jmax)
    real(DP):: xy_DSurfSolDtSave (0:imax-1, 1:jmax)

    real(DP):: xy_TempCond          (0:imax-1, 1:jmax)
    real(DP):: xy_MajCompPressSatB  (0:imax-1, 1:jmax)
    real(DP):: xy_DMajCompPressSatDT(0:imax-1, 1:jmax)

    logical :: xy_FlagCalc(0:imax-1, 1:jmax)
    integer :: xy_IndexMeltOrFreeze(0:imax-1, 1:jmax)
    integer, parameter :: IndexOthers = 0
    integer, parameter :: IndexMelt   = 1
    integer, parameter :: IndexFreeze = 2

    real(DP):: xyza_TempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 温度陰解行列. 
                              ! Implicit matrix about temperature
    real(DP):: xyz_TempVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 温度陰解ベクトル. 
                              ! Implicit vector about temperature
    real(DP):: xyaa_SurfMtx(0:imax-1, 1:jmax, 0:0, -1:1)
                              ! 惑星表面エネルギー収支用陰解行列
                              ! Implicit matrix for surface energy balance
    real(DP):: xy_SurfRH(0:imax-1,1:jmax)


    real(DP):: xyaa_SoilTempMtx (0:imax-1, 1:jmax, 1:kslmax,-1:1)
                              ! 土壌温度拡散方程式の行列
                              ! Matrix for diffusion equation of soil temperature
    real(DP):: xya_SoilTempVec (0:imax-1, 1:jmax, 1:kslmax)
                              ! 土壌温度拡散方程式のベクトル
                              ! Vector for diffusion equation of soil temperature

    real(DP):: xyaa_TempSoilTempLUMtx (0:imax-1, 1:jmax, -kslmax:kmax, -1:1)
                              ! LU 行列.
                              ! LU matrix
    real(DP):: xya_DelTempSoilTempLUVec (0:imax-1, 1:jmax, -kslmax:kmax)
                              ! $ T, Tg $ の時間変化.
                              ! Tendency of $ T $ and $ Tg |

    real(DP):: LatentHeatLocal
    real(DP):: LatentHeatFluxByMelt
    real(DP):: SenHeatFluxA
    real(DP):: LatHeatFluxA
    real(DP):: CondHeatFluxA
    real(DP):: ValueAlpha
    real(DP):: SurfTempATentative
    real(DP):: SoilTempATentative
    real(DP):: SurfLiqATentative
    real(DP):: xy_SurfLiqATentativeSave(0:imax-1, 1:jmax)
    real(DP):: SurfSolATentative
    real(DP):: xy_SurfSolATentativeSave(0:imax-1, 1:jmax)
    real(DP):: DelSurfSol

    real(DP) :: xy_TempMajCompCond(0:imax-1, 1:jmax)
    real(DP) :: SurfMajCompIceATentative

    real(DP) :: xy_SurfRadSFlux        (0:imax-1, 1:jmax)
    real(DP) :: xy_SurfRadLFlux        (0:imax-1, 1:jmax)
    real(DP) :: xy_SurfSoilHeatCondFlux(0:imax-1, 1:jmax)
    real(DP) :: xy_SurfSensHeatFlux    (0:imax-1, 1:jmax)
    real(DP) :: xy_SeaIceHeatCondFlux  (0:imax-1, 1:jmax)
    real(DP) :: xy_HeatingTendency     (0:imax-1, 1:jmax)

    real(DP) :: LatHeatFluxBySnowMelt

    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitude
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude
    integer:: k               ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction
    integer:: l


    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. phy_implicit_sdh_V5_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if

!!$    ! 計算時間計測開始
!!$    ! Start measurement of computation time
!!$    !
!!$    call TimesetClockStart( module_name )


    !
    ! check flag of snow melt
    !
    if ( ( .not. FlagBucketModel ) .or. ( .not. FlagSnow ) ) then
      xy_LatHeatFluxBySnowMelt = 0.0_DP
      return
    end if


    if ( kslmax == 0 ) then

      call MessageNotify( 'E', module_name, 'kslmax <= 0 in PhyImplSDHV5IceSnowPhaseChgCor.' )

    else

      xy_DSurfLiqDtSave = xy_DSurfLiqDt
      xy_DSurfSolDtSave = xy_DSurfSolDt


      select case ( IndexSpc )
      case ( IndexSpcMajComp )
        call SaturateMajorCompCondTemp( xy_Ps, xy_TempCond )
        call SaturateMajorCompPressSat( xy_SurfTemp, xy_MajCompPressSatB )
        call SaturateMajorCompDPressSatDT( xy_SurfTemp, xy_DMajCompPressSatDT )
        LatentHeatLocal = SaturateMajorCompInqLatentHeat()
      case ( IndexSpcH2O )
        xy_TempCond     = TempCondWater
        LatentHeatLocal = LatentHeatFusion
      case default
        call MessageNotify( 'E', module_name, 'Undefined IndexSpc, %d.', i = (/ IndexSpc /) )
      end select


      xy_SurfLiqATentativeSave = xy_SurfLiqB + xy_DSurfLiqDt * ( 2.0_DP * DelTime )
      xy_SurfSolATentativeSave = xy_SurfSolB + xy_DSurfSolDt * ( 2.0_DP * DelTime )

      !----------
      ! A case that a part of snow/ice melt or soil moisture freeze
      !----------

      ! Melt
      do j = 1, jmax
        do i = 0, imax-1

          select case ( xy_IndexCalcMethod(i,j) )
          case ( IndexLand )

            SurfTempATentative = xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * 2.0_DP * DelTime
            SurfSolATentative = xy_SurfSolATentativeSave(i,j)

            if ( ( SurfSolATentative  > 0.0_DP           ) .and. ( SurfTempATentative > xy_TempCond(i,j) ) ) then
              xy_FlagCalc         (i,j) = .true.
            else
              xy_FlagCalc         (i,j) = .false.
            end if

          case default
            xy_FlagCalc         (i,j) = .false.
          end select

        end do
      end do

      ! Freeze
      select case ( IndexSpc )
      case ( IndexSpcMajComp )

        do j = 1, jmax
          do i = 0, imax-1
            select case ( xy_IndexCalcMethod(i,j) )
            case ( IndexLand )
              SurfTempATentative = xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * 2.0_DP * DelTime
              if ( SurfTempATentative < xy_TempCond(i,j) ) then
                xy_FlagCalc         (i,j) = .true.
              end if
            end select
          end do
        end do

!!$      case ( IndexSpcH2O )
!!$
!!$        do j = 1, jmax
!!$          do i = 0, imax-1
!!$            select case ( xy_IndexCalcMethod(i,j) )
!!$            case ( IndexLand )
!!$              SurfTempATentative = xy_SurfTemp(i,j)          &
!!$                & + xy_DSurfTempDt(i,j) * 2.0_DP * DelTime
!!$              SurfLiqATentative = xy_SurfLiqATentativeSave(i,j)
!!$              if ( &
!!$                & ( SurfLiqATentative  > 0.0_DP           ) .and. &
!!$                & ( SurfTempATentative < xy_TempCond(i,j) )       &
!!$                & ) then
!!$                xy_FlagCalc         (i,j) = .true.
!!$              end if
!!$            end select
!!$
!!$          end do
!!$        end do
!!$
      end select


      xyza_TempMtx     = xyza_ArgTempMtx
      xyz_TempVec = xyz_ArgTempVec
      !
      xyaa_SurfMtx     = xyaa_ArgSurfMtx
      xy_SurfRH        = xy_ArgSurfRH
      !
      select case ( IndexSpc )
      case ( IndexSpcMajComp )
        do j = 1, jmax
          do i = 0, imax-1
            if ( xy_FlagCalc(i,j) ) then
              xyaa_SurfMtx(i,j,0, 0) = xyaa_SurfMtx(i,j,0, 0) + LatentHeatLocal / Grav * xy_DMajCompPressSatDT(i,j) / ( 2.0_DP * DelTime )
              xy_SurfRH   (i,j)      = xy_SurfRH(i,j) - LatentHeatLocal / Grav * ( xy_MajCompPressSatB(i,j) - xy_Ps(i,j) ) / ( 2.0_DP * DelTime )
            end if
          end do
        end do
      case ( IndexSpcH2O )
        do j = 1, jmax
          do i = 0, imax-1
            if ( xy_FlagCalc(i,j) ) then
              xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
              xyaa_SurfMtx(i,j,0, 0) = 1.0_DP
              xyaa_SurfMtx(i,j,0, 1) = 0.0_DP
              xy_SurfRH   (i,j)      = xy_TempCond(i,j) - xy_SurfTemp(i,j)
            end if
          end do
        end do
      end select
      !
      xyaa_SoilTempMtx = xyaa_ArgSoilTempMtx
      xya_SoilTempVec = xya_ArgSoilTempVec


      ! 温度の計算
      ! Calculate temperature and specific humidity
      !
      do l = -1, 1
        do k = 1, kslmax
          xyaa_TempSoilTempLUMtx(:,:,-k,-l) = xyaa_SoilTempMtx(:,:,k,l)
        end do
        k = 0
        xyaa_TempSoilTempLUMtx(:,:, k, l) = xyaa_SurfMtx(:,:,0,l)
        do k = 1, kmax
          xyaa_TempSoilTempLUMtx(:,:, k, l) = xyza_TempMtx(:,:,k,l)
        end do
      end do

      call PhyImplLUDecomp3( xyaa_TempSoilTempLUMtx, imax * jmax, kmax + 1 + kslmax )

      do k = 1, kslmax
        xya_DelTempSoilTempLUVec(:,:,-k) = xya_SoilTempVec(:,:,k)
      end do
      k = 0
      xya_DelTempSoilTempLUVec(:,:,k) = xy_SurfRH
      do k = 1, kmax
        xya_DelTempSoilTempLUVec(:,:,k) = xyz_TempVec(:,:,k)
      end do

      call PhyImplLUSolve3( xya_DelTempSoilTempLUVec, xyaa_TempSoilTempLUMtx, 1, imax * jmax , kmax + 1 + kslmax )


      do k = 1, kslmax
        do j = 1, jmax
          do i = 0, imax-1
            if ( xy_FlagCalc(i,j) ) then
              select case ( xy_IndexCalcMethod(i,j) )
              case ( IndexLand )
                xyz_DSoilTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,-k) / ( 2.0_DP * DelTime )
              case default
                xyz_DSoilTempDt(i,j,k) = 0.0_DP
              end select
            end if
          end do
        end do
      end do
      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_FlagCalc(i,j) ) then
            select case ( xy_IndexCalcMethod(i,j) )
            case ( IndexLand )
              ! land
              xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
!!$            case ( IndexSeaIce )
!!$              ! sea ice
!!$              xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
!!$            case ( IndexSlabOcean )
!!$              ! slab ocean
!!$              xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
!!$            case ( IndexOceanPresSST )
!!$              ! open ocean
!!$              xy_DSurfTempDt(i,j) = 0.0_DP
            case default
              call MessageNotify( 'E', module_name, 'Unexpected Error.' )
            end select
          end if
        end do
      end do
      do k = 1, kmax
        do j = 1, jmax
          do i = 0, imax-1
            if ( xy_FlagCalc(i,j) ) then
              xyz_DTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,k) / ( 2.0_DP * DelTime )
            end if
          end do
        end do
      end do


      !----------
      ! Surface fluxes used below
      !----------
      xy_SurfRadSFlux = xyr_RadSFlux(:,:,0)
      xy_SurfRadLFlux = xyr_RadLFlux(:,:,0) + xyra_DelRadLFlux(:,:,0,0) * xy_DSurfTempDt * ( 2.0_DP * DelTime ) + xyra_DelRadLFlux(:,:,0,1) * xyz_DTempDt(:,:,1) * ( 2.0_DP * DelTime )
      xy_SurfSoilHeatCondFlux = xyr_SoilHeatFlux(:,:,0) - xyr_SoilTempTransCoef(:,:,0) * ( xyz_DSoilTempDt(:,:,1) - xy_DSurfTempDt ) * ( 2.0d0 * DelTime )
      xy_SurfSensHeatFlux = xyr_HeatFlux(:,:,0) - CpDry * xyr_Exner(:,:,0) * xy_SurfTempTransCoef * ( xyz_DTempDt(:,:,1) / xyz_Exner(:,:,1) - xy_DSurfTempDt / xyr_Exner(:,:,0) ) * ( 2.0_DP * DelTime )

      do j = 1, jmax
        do i = 0, imax-1

          if ( xy_FlagCalc(i,j) ) then

            xy_LatHeatFluxBySnowMelt(i,j) = - xy_SurfRadSFlux(i,j) - xy_SurfRadLFlux(i,j) - xy_SurfSensHeatFlux(i,j) - xy_SurfLatentHeatFlux(i,j) + xy_SurfSoilHeatCondFlux(i,j) - xy_LatHeatFluxByOtherSpc(i,j) - xy_SurfHeatCapacity(i,j) * xy_DSurfTempDt(i,j)

            xy_DSurfSolDt(i,j) = xy_DSurfSolDtSave(i,j) - xy_LatHeatFluxBySnowMelt(i,j) / LatentHeatLocal
            xy_DSurfLiqDt(i,j) = xy_DSurfLiqDtSave(i,j) + xy_LatHeatFluxBySnowMelt(i,j) / LatentHeatLocal

!!$            if ( xy_SurfSnowB(i,j) + xy_DSurfSnowDt(i,j) * ( 2.0_DP * DelTime ) < 0.0_DP ) then
!!$              call MessageNotify( 'M', module_name, &
!!$                & 'Surface snow amount is negative %f, %f.', &
!!$                & d = (/ xy_SurfSnowB(i,j) + xy_DSurfSnowDt(i,j) * ( 2.0_DP * DelTime ), xy_SurfSnowB(i,j) /) )
!!$            end if

          else
            xy_LatHeatFluxBySnowMelt(i,j) = 0.0_DP
          end if

        end do
      end do

      !----------
      ! A case that all snow melt or soil moisture freeze
      !----------

      do j = 1, jmax
        do i = 0, imax-1

          select case ( xy_IndexCalcMethod(i,j) )
          case ( IndexLand )

            if ( xy_FlagCalc(i,j) ) then
              SurfSolATentative = xy_SurfSolB(i,j) + xy_DSurfSolDt(i,j) * 2.0_DP * DelTime
              if ( SurfSolATentative < 0.0_DP ) then
                xy_FlagCalc(i,j) = .true.
                xy_IndexMeltOrFreeze(i,j) = IndexMelt
              else
                xy_FlagCalc(i,j) = .false.
                xy_IndexMeltOrFreeze(i,j) = IndexOthers
              end if

!!$              select case ( IndexSpc )
!!$              case ( IndexSpcH2O )
!!$                SurfLiqATentative = xy_SurfLiqB(i,j) &
!!$                  & + xy_DSurfLiqDt(i,j) * 2.0_DP * DelTime
!!$                if ( SurfLiqATentative < 0.0_DP ) then
!!$                  xy_FlagCalc(i,j) = .true.
!!$                  xy_IndexMeltOrFreeze(i,j) = IndexFreeze
!!$                end if
!!$              end select

            else
              xy_FlagCalc(i,j) = .false.
              xy_IndexMeltOrFreeze(i,j) = IndexOthers
            end if

          case default
            xy_FlagCalc(i,j) = .false.
            xy_IndexMeltOrFreeze(i,j) = IndexOthers
          end select

        end do
      end do


      xyza_TempMtx     = xyza_ArgTempMtx
      xyz_TempVec      = xyz_ArgTempVec
      !
      xyaa_SurfMtx     = xyaa_ArgSurfMtx
      xy_SurfRH        = xy_ArgSurfRH
      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_FlagCalc(i,j) ) then
!!$            SurfSnowATentative = xy_SurfSnowB(i,j)         &
!!$              & + xy_DSurfSnowDt(i,j) * 2.0d0 * DelTime
            select case ( xy_IndexMeltOrFreeze(i,j) )
            case ( IndexMelt )
              ! all ice/snow melt
              DelSurfSol =   xy_SurfSolATentativeSave(i,j)
            case ( IndexFreeze )
              ! all soil moisture freeze (= negative melt of ice/snow)
              DelSurfSol = - xy_SurfLiqATentativeSave(i,j)
            end select

            xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - xy_SurfLatentHeatFlux(i,j) + xyr_SoilHeatFlux(i,j,0) - xy_LatHeatFluxByOtherSpc(i,j) - LatentHeatLocal * DelSurfSol / ( 2.0_DP * DelTime )

          end if
        end do
      end do
      !
      xyaa_SoilTempMtx = xyaa_ArgSoilTempMtx
      xya_SoilTempVec = xya_ArgSoilTempVec


      ! 温度の計算
      ! Calculate temperature and specific humidity
      !
      do l = -1, 1
        do k = 1, kslmax
          xyaa_TempSoilTempLUMtx(:,:,-k,-l) = xyaa_SoilTempMtx(:,:,k,l)
        end do
        k = 0
        xyaa_TempSoilTempLUMtx(:,:, k, l) = xyaa_SurfMtx(:,:,0,l)
        do k = 1, kmax
          xyaa_TempSoilTempLUMtx(:,:, k, l) = xyza_TempMtx(:,:,k,l)
        end do
      end do
      !
      call PhyImplLUDecomp3( xyaa_TempSoilTempLUMtx, imax * jmax, kmax + 1 + kslmax )
      !
      do k = 1, kslmax
        xya_DelTempSoilTempLUVec(:,:,-k) = xya_SoilTempVec(:,:,k)
      end do
      k = 0
      xya_DelTempSoilTempLUVec(:,:,k) = xy_SurfRH
      do k = 1, kmax
        xya_DelTempSoilTempLUVec(:,:,k) = xyz_TempVec(:,:,k)
      end do
      !
      call PhyImplLUSolve3( xya_DelTempSoilTempLUVec, xyaa_TempSoilTempLUMtx, 1, imax * jmax , kmax + 1 + kslmax )

      do k = 1, kslmax
        do j = 1, jmax
          do i = 0, imax-1

            if ( xy_FlagCalc(i,j) ) then

              select case ( xy_IndexCalcMethod(i,j) )
              case ( IndexLand )
                xyz_DSoilTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,-k) / ( 2.0_DP * DelTime )
              case default
                xyz_DSoilTempDt(i,j,k) = 0.0_DP
              end select

            end if

          end do
        end do
      end do
      do j = 1, jmax
        do i = 0, imax-1

          if ( xy_FlagCalc(i,j) ) then

            select case ( xy_IndexCalcMethod(i,j) )
            case ( IndexLand )
              ! land
              xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
!!$            case ( IndexSeaIce )
!!$              ! sea ice
!!$              xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
!!$            case ( IndexSlabOcean )
!!$              ! slab ocean
!!$              xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
!!$            case ( IndexOceanPresSST )
!!$              ! open ocean
!!$              xy_DSurfTempDt(i,j) = 0.0_DP
            case default
              call MessageNotify( 'E', module_name, 'Unexpected Error.' )
            end select

          end if

        end do
      end do
      do k = 1, kmax
        do j = 1, jmax
          do i = 0, imax-1
            if ( xy_FlagCalc(i,j) ) then
              xyz_DTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,k) / ( 2.0_DP * DelTime )
            end if
          end do
        end do
      end do
      !
      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_FlagCalc(i,j) ) then
!!$            SurfSnowATentative = xy_SurfSnowB(i,j)         &
!!$              & + xy_DSurfSnowDt(i,j) * 2.0d0 * DelTime

            select case ( xy_IndexMeltOrFreeze(i,j) )
            case ( IndexMelt )
              ! all ice/snow melt
              DelSurfSol =   xy_SurfSolATentativeSave(i,j)
            case ( IndexFreeze )
              ! all soil moisture freeze (= negative melt of ice/snow)
              DelSurfSol = - xy_SurfLiqATentativeSave(i,j)
            end select

            xy_LatHeatFluxBySnowMelt(i,j) = LatentHeatLocal * DelSurfSol / ( 2.0_DP * DelTime )
            xy_DSurfSolDt(i,j) = xy_DSurfSolDtSave(i,j) - xy_LatHeatFluxBySnowMelt(i,j) / LatentHeatLocal
            xy_DSurfLiqDt(i,j) = xy_DSurfLiqDtSave(i,j) + xy_LatHeatFluxBySnowMelt(i,j) / LatentHeatLocal
          end if
        end do
      end do


!!$      do j = 1, jmax
!!$        do i = 0, imax-1
!!$          if ( xy_FlagCalc(i,j) ) then
!!$            if ( xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime ) < xy_TempCond(i,j) ) then
!!$              call MessageNotify( 'M', module_name, &
!!$                & 'Surface temperature is lower than condensation temperature, %f < %f.', &
!!$                & d = (/ xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime ), xy_TempCond(i,j) /) )
!!$            end if
!!$          end if
!!$        end do
!!$      end do


      !----------


      ! Calculation for a land point with prescribed temperature
      !
      !----------
      ! Surface fluxes used below
      !----------
!!$      xy_SurfRadSFlux = xyr_RadSFlux(:,:,0)
!!$      xy_SurfRadLFlux = xyr_RadLFlux(:,:,0)                                           &
!!$        &   + xyra_DelRadLFlux(:,:,0,0) * xy_DSurfTempDt * ( 2.0_DP * DelTime )        &
!!$        &   + xyra_DelRadLFlux(:,:,0,1) * xyz_DTempDt(:,:,1) * ( 2.0_DP * DelTime )
!!$      xy_SurfSoilHeatCondFlux = xyr_SoilHeatFlux(:,:,0)                                &
!!$        & - xyr_SoilTempTransCoef(:,:,0)                                               &
!!$        &   * ( xyz_DSoilTempDt(:,:,1) - xy_DSurfTempDt ) * ( 2.0d0 * DelTime )
!!$      xy_SurfSensHeatFlux =                                                       &
!!$        & xyr_HeatFlux(:,:,0)                                                     &
!!$        &   - CpDry * xyr_Exner(:,:,0) * xy_SurfTempTransCoef                     &
!!$        &     * ( xyz_DTempDt(:,:,1) / xyz_Exner(:,:,1)                           &
!!$        &       - xy_DSurfTempDt / xyr_Exner(:,:,0) ) * ( 2.0_DP * DelTime )
!!$      !
!!$      xy_LatHeatFluxBySnowMelt =           &
!!$        & - xy_SurfRadSFlux                &
!!$        & - xy_SurfRadLFlux                &
!!$        & - xy_SurfSensHeatFlux            &
!!$        & - xy_SurfLatentHeatFlux          &
!!$        & + xy_SurfSoilHeatCondFlux        &
!!$        & - xy_LatHeatFluxByOtherSpc       &
!!$        & - xy_SurfHeatCapacity * xy_DSurfTempDt
      !
      do j = 1, jmax
        do i = 0, imax-1
          select case ( xy_IndexCalcMethod(i,j) )
          case ( IndexLandWithPresTs )
            SurfSolATentative = xy_SurfSolATentativeSave(i,j)
            LatHeatFluxBySnowMelt = - xy_SurfRadSFlux(i,j) - xy_SurfRadLFlux(i,j) - xy_SurfSensHeatFlux(i,j) - xy_SurfLatentHeatFlux(i,j) - xy_LatHeatFluxByOtherSpc(i,j) - xy_SurfHeatCapacity(i,j) * xy_DSurfTempDt(i,j)

            if ( SurfSolATentative > 0.0_DP ) then
              ! Ice exists on the ground.
              !   Calculation is performed only when freezing and melting
              xy_FlagCalc(i,j) = .true.
              xy_LatHeatFluxBySnowMelt(i,j) = LatHeatFluxBySnowMelt
!!$            else if ( xy_LatHeatFluxBySnowMelt(i,j) < 0.0_DP ) then
            else if ( LatHeatFluxBySnowMelt < 0.0_DP ) then
              ! Ice does not exist on the ground.
              !   Calculation is performed only when freezing
              xy_FlagCalc(i,j) = .true.
              xy_LatHeatFluxBySnowMelt(i,j) = LatHeatFluxBySnowMelt
            else
              xy_FlagCalc(i,j) = .false.
            end if
          case default
            xy_FlagCalc(i,j) = .false.
          end select
        end do
      end do
      !
      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_FlagCalc(i,j) ) then
            SurfSolATentative = xy_SurfSolATentativeSave(i,j) - xy_LatHeatFluxBySnowMelt(i,j) / LatentHeatLocal * ( 2.0_DP * DelTime )
            if ( SurfSolATentative < 0.0_DP ) then
              xy_LatHeatFluxBySnowMelt(i,j) = LatentHeatLocal * SurfSolATentative / ( 2.0_DP * DelTime )
            end if
!!$              xy_DSurfSolDt(i,j) = xy_DSurfSolDtSave(i,j) &
!!$                & - SurfSolATentative / ( 2.0_DP * DelTime )
!!$              xy_DSurfLiqDt(i,j) = xy_DSurfLiqDtSave(i,j) &
!!$                & + SurfSolATentative / ( 2.0_DP * DelTime )
            xy_DSurfSolDt(i,j) = xy_DSurfSolDtSave(i,j) - xy_LatHeatFluxBySnowMelt(i,j) / LatentHeatLocal
            xy_DSurfLiqDt(i,j) = xy_DSurfLiqDtSave(i,j) + xy_LatHeatFluxBySnowMelt(i,j) / LatentHeatLocal
          end if
        end do
      end do


    end if




!!$    ! 計算時間計測一時停止
!!$    ! Pause measurement of computation time
!!$    !
!!$    call TimesetClockStop( module_name )

  end subroutine PhyImplSDHV5IceSnowPhaseChgCor

PhyImplSDHV5SOSeaIceCorrection( xy_IndexCalcMethod, xy_SurfHeatCapacity, xy_SOSeaIceMassB, xy_SeaIceThickness, xyz_Exner, xyr_Exner, xy_SurfTemp, xyz_SOSeaIceTemp, xyr_HeatFlux, xyr_SoilHeatFlux, xy_SurfTempTransCoef, xyr_SoilTempTransCoef, xy_SOSILocalKMax, xyr_SOSILocalDepth, xyr_SOSIHeatTransCoef, xyr_SOSIHeatFlux, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_SurfLatentHeatFlux, xyza_ArgTempMtx, xyz_ArgTempVec, xyaa_ArgSurfMtx, xy_ArgSurfRH, xyaa_ArgSoilTempMtx, xya_ArgSoilTempVec, xyaa_ArgSOSITempMtx, xya_ArgSOSITempVec, xyz_DTempDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DSOSeaIceMassDtTop, xy_DSOSeaIceMassDtBot, xyz_DSOSeaIceTempDt, xy_LatHeatFluxBySeaIceMelt, xy_FlagSOSeaIceAllMelt, xy_FlagSOSIWoSIOceanAllFreeze, xy_FlagSOSIWSIOceanAllFreeze )

Subroutine :

xy_IndexCalcMethod(0:imax-1, 1:jmax) :

integer , intent(in )

:	Index for calculation method

xy_SurfHeatCapacity(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	地表熱容量. Surface heat capacity

xy_SOSeaIceMassB(0:imax-1, 1:jmax) : real(DP), intent(in )

xy_SeaIceThickness(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Sea ice thickness

xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in)

:	Exner 関数 (整数レベル). Exner function (full level)

xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	Exner 関数 (半整数レベル). Exner function (half level)

xy_SurfTemp(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表面温度. Surface temperature

xyz_SOSeaIceTemp(0:imax-1, 1:jmax, 1:ksimax) :

real(DP), intent(in)

:	海氷温度 (K) Slab ocean sea ice temperature (K)

xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	熱フラックス. Heat flux

xyr_SoilHeatFlux(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	土壌中の熱フラックス (W m-2) Heat flux in sub-surface soil (W m-2)

xy_SurfTempTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：温度. Transfer coefficient: temperature

xyr_SoilTempTransCoef(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	輸送係数：土壌温度. Transfer coefficient: soil temperature

xy_SOSILocalKMax(0:imax-1, 1:jmax) : integer , intent(in)

xyr_SOSILocalDepth(0:imax-1, 1:jmax, 0:ksimax) : real(DP), intent(in)

xyr_SOSIHeatTransCoef(0:imax-1, 1:jmax, 0:ksimax) : real(DP), intent(in)

xyr_SOSIHeatFlux(0:imax-1, 1:jmax, 0:ksimax) : real(DP), intent(in)

xyr_RadSFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in )

:	短波 (日射) フラックス. Shortwave (insolation) flux

xyr_RadLFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in )

:	長波フラックス. Longwave flux

xyra_DelRadLFlux(0:imax-1, 1:jmax, 0:kmax, 0:1) :

real(DP), intent(in )

:	長波地表温度変化. Surface temperature tendency with longwave

xy_SurfLatentHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	惑星表面潜熱フラックス. Latent heat flux at the surface

xyza_ArgTempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1) :

real(DP), intent(in )

:	温度陰解行列. Implicit matrix about temperature

xyz_ArgTempVec(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in )

:	温度陰解ベクトル. Implicit vector about temperature

xyaa_ArgSurfMtx(0:imax-1, 1:jmax, 0:0, -1:1) :

real(DP), intent(in )

:	惑星表面エネルギー収支用陰解行列 Implicit matrix for surface energy balance

xy_ArgSurfRH(0:imax-1,1:jmax) : real(DP), intent(in )

xyaa_ArgSoilTempMtx(0:imax-1, 1:jmax, 1:kslmax,-1:1) :

real(DP), intent(in )

:	土壌温度拡散方程式の行列 Matrix for diffusion equation of soil temperature

xya_ArgSoilTempVec(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(in )

:	土壌温度拡散方程式のベクトル Vector for diffusion equation of soil temperature

xyaa_ArgSOSITempMtx(0:imax-1, 1:jmax, 1:ksimax, -1:1) :

real(DP), intent(in )

:	海氷温度拡散方程式の行列 Matrix for diffusion equation of soil temperature

xya_ArgSOSITempVec(0:imax-1, 1:jmax, 1:ksimax) :

real(DP), intent(in )

:	海氷温度拡散方程式のベクトル Vector for diffusion equation of soil temperature

xyz_DTempDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(inout)

:	$ DP{T}{t} $ . 温度変化. Temperature tendency

xy_DSurfTempDt(0:imax-1, 1:jmax) :

real(DP), intent(inout)

:	地表面温度変化率 (K s-1) Surface temperature tendency (K s-1)

xyz_DSoilTempDt(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(inout)

:	$ DP{Tg}{t} $ . 土壌温度変化 (K s-1) Temperature tendency (K s-1)

xy_DSOSeaIceMassDtTop(0:imax-1, 1:jmax) : real(DP), intent(out )

xy_DSOSeaIceMassDtBot(0:imax-1, 1:jmax) : real(DP), intent(out )

xyz_DSOSeaIceTempDt(0:imax-1, 1:jmax, 1:ksimax) : real(DP), intent(inout)

xy_LatHeatFluxBySeaIceMelt(0:imax-1, 1:jmax) : real(DP), intent(inout)

xy_FlagSOSeaIceAllMelt(0:imax-1, 1:jmax) : logical , intent(out )

xy_FlagSOSIWoSIOceanAllFreeze(0:imax-1, 1:jmax) : logical , intent(out )

xy_FlagSOSIWSIOceanAllFreeze(0:imax-1, 1:jmax) : logical , intent(out )

融雪による時間変化率の修正を行います.

Correction of tendencies due to melt of snow.

[Source]

  subroutine PhyImplSDHV5SOSeaIceCorrection( xy_IndexCalcMethod, xy_SurfHeatCapacity, xy_SOSeaIceMassB, xy_SeaIceThickness, xyz_Exner, xyr_Exner, xy_SurfTemp, xyz_SOSeaIceTemp, xyr_HeatFlux, xyr_SoilHeatFlux, xy_SurfTempTransCoef, xyr_SoilTempTransCoef, xy_SOSILocalKMax, xyr_SOSILocalDepth, xyr_SOSIHeatTransCoef, xyr_SOSIHeatFlux, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_SurfLatentHeatFlux, xyza_ArgTempMtx, xyz_ArgTempVec, xyaa_ArgSurfMtx, xy_ArgSurfRH, xyaa_ArgSoilTempMtx, xya_ArgSoilTempVec, xyaa_ArgSOSITempMtx, xya_ArgSOSITempVec, xyz_DTempDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DSOSeaIceMassDtTop, xy_DSOSeaIceMassDtBot, xyz_DSOSeaIceTempDt, xy_LatHeatFluxBySeaIceMelt, xy_FlagSOSeaIceAllMelt, xy_FlagSOSIWoSIOceanAllFreeze, xy_FlagSOSIWSIOceanAllFreeze )
    !
    ! 融雪による時間変化率の修正を行います. 
    !
    ! Correction of tendencies due to melt of snow. 
    !

    ! モジュール引用 ; USE statements
    !

    ! ヒストリデータ出力
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! 時刻管理
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: CpDry, LatentHeatFusion, SOMass
                              ! Slab ocean mass


    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: TempCondWater      , SeaIceThermCondCoef, SeaIceVolHeatCap   , SeaIceDen          , TempBelowSeaIce    , LatentHeatFusionBelowSeaIce
                              ! Latant heat for fusion below sea ice

    ! 陰解法による時間積分のためのルーチン
    ! Routines for time integration with implicit scheme
    !
    use phy_implicit_utils, only : PhyImplLUDecomp3, PhyImplLUSolve3

    ! 宣言文 ; Declaration statements
    !

    integer , intent(in   ) :: xy_IndexCalcMethod(0:imax-1, 1:jmax)
                              ! 
                              ! Index for calculation method
    real(DP), intent(in   ):: xy_SurfHeatCapacity (0:imax-1, 1:jmax)
                              ! 地表熱容量. 
                              ! Surface heat capacity
    real(DP), intent(in   ) :: xy_SOSeaIceMassB(0:imax-1, 1:jmax)

    real(DP), intent(in):: xy_SeaIceThickness(0:imax-1, 1:jmax)
                              !
                              ! Sea ice thickness
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner 関数 (整数レベル). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner 関数 (半整数レベル). 
                              ! Exner function (half level)

    real(DP), intent(in) :: xy_SurfTemp (0:imax-1, 1:jmax)
                              ! 地表面温度. 
                              ! Surface temperature

    real(DP), intent(in):: xyz_SOSeaIceTemp(0:imax-1, 1:jmax, 1:ksimax)
                              ! 海氷温度 (K)
                              ! Slab ocean sea ice temperature (K)
    real(DP), intent(in):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 熱フラックス. 
                              ! Heat flux
    real(DP), intent(in):: xyr_SoilHeatFlux (0:imax-1, 1:jmax, 0:kslmax)
                              ! 土壌中の熱フラックス (W m-2)
                              ! Heat flux in sub-surface soil (W m-2)

    real(DP), intent(in):: xy_SurfTempTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：温度. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xyr_SoilTempTransCoef (0:imax-1, 1:jmax, 0:kslmax)
                              ! 輸送係数：土壌温度.
                              ! Transfer coefficient: soil temperature

    integer , intent(in):: xy_SOSILocalKMax     (0:imax-1, 1:jmax)
    real(DP), intent(in):: xyr_SOSILocalDepth   (0:imax-1, 1:jmax, 0:ksimax)
    real(DP), intent(in):: xyr_SOSIHeatTransCoef(0:imax-1, 1:jmax, 0:ksimax)
    real(DP), intent(in):: xyr_SOSIHeatFlux     (0:imax-1, 1:jmax, 0:ksimax)

    real(DP), intent(in   ):: xyr_RadSFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 短波 (日射) フラックス. 
                              ! Shortwave (insolation) flux
    real(DP), intent(in   ):: xyr_RadLFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Longwave flux
    real(DP), intent(in   ):: xyra_DelRadLFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Surface temperature tendency with longwave

    real(DP), intent(in   ):: xy_SurfLatentHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面潜熱フラックス.
                              ! Latent heat flux at the surface

    real(DP), intent(in   ):: xyza_ArgTempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 温度陰解行列. 
                              ! Implicit matrix about temperature
    real(DP), intent(in   ):: xyz_ArgTempVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 温度陰解ベクトル. 
                              ! Implicit vector about temperature
    real(DP), intent(in   ):: xyaa_ArgSurfMtx(0:imax-1, 1:jmax, 0:0, -1:1)
                              ! 惑星表面エネルギー収支用陰解行列
                              ! Implicit matrix for surface energy balance
    real(DP), intent(in   ):: xy_ArgSurfRH(0:imax-1,1:jmax)


    real(DP), intent(in   ):: xyaa_ArgSoilTempMtx (0:imax-1, 1:jmax, 1:kslmax,-1:1)
                              ! 土壌温度拡散方程式の行列
                              ! Matrix for diffusion equation of soil temperature
    real(DP), intent(in   ):: xya_ArgSoilTempVec (0:imax-1, 1:jmax, 1:kslmax)
                              ! 土壌温度拡散方程式のベクトル
                              ! Vector for diffusion equation of soil temperature
    real(DP), intent(in   ):: xyaa_ArgSOSITempMtx(0:imax-1, 1:jmax, 1:ksimax, -1:1)
                              ! 海氷温度拡散方程式の行列
                              ! Matrix for diffusion equation of soil temperature
    real(DP), intent(in   ):: xya_ArgSOSITempVec (0:imax-1, 1:jmax, 1:ksimax)
                              ! 海氷温度拡散方程式のベクトル
                              ! Vector for diffusion equation of soil temperature

    real(DP), intent(inout):: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . 温度変化. 
                              ! Temperature tendency
    real(DP), intent(inout) :: xy_DSurfTempDt (0:imax-1, 1:jmax)
                              ! 地表面温度変化率 (K s-1)
                              ! Surface temperature tendency (K s-1)
    real(DP), intent(inout):: xyz_DSoilTempDt (0:imax-1, 1:jmax, 1:kslmax)
                              ! $ \DP{Tg}{t} $ . 土壌温度変化 (K s-1)
                              ! Temperature tendency (K s-1)
    real(DP), intent(out  ) :: xy_DSOSeaIceMassDtTop      (0:imax-1, 1:jmax)
    real(DP), intent(out  ) :: xy_DSOSeaIceMassDtBot      (0:imax-1, 1:jmax)
    real(DP), intent(inout) :: xyz_DSOSeaIceTempDt        (0:imax-1, 1:jmax, 1:ksimax)
    real(DP), intent(inout) :: xy_LatHeatFluxBySeaIceMelt (0:imax-1, 1:jmax)
    logical , intent(out  ) :: xy_FlagSOSeaIceAllMelt     (0:imax-1, 1:jmax)
    logical , intent(out  ) :: xy_FlagSOSIWoSIOceanAllFreeze(0:imax-1, 1:jmax)
    logical , intent(out  ) :: xy_FlagSOSIWSIOceanAllFreeze (0:imax-1, 1:jmax)


    ! 作業変数
    ! Work variables
    !

    real(DP):: xyza_TempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 温度陰解行列. 
                              ! Implicit matrix about temperature
    real(DP):: xyz_TempVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 温度陰解ベクトル. 
                              ! Implicit vector about temperature
    real(DP):: xyaa_SurfMtx(0:imax-1, 1:jmax, 0:0, -1:1)
                              ! 惑星表面エネルギー収支用陰解行列
                              ! Implicit matrix for surface energy balance
    real(DP):: xy_SurfRH(0:imax-1,1:jmax)


    real(DP):: xyaa_SoilTempMtx (0:imax-1, 1:jmax, 1:kslmax,-1:1)
                              ! 土壌温度拡散方程式の行列
                              ! Matrix for diffusion equation of soil temperature
    real(DP):: xya_SoilTempVec (0:imax-1, 1:jmax, 1:kslmax)
                              ! 土壌温度拡散方程式のベクトル
                              ! Vector for diffusion equation of soil temperature
    real(DP):: xyaa_TempSoilTempLUMtx (0:imax-1, 1:jmax, -kslmax:kmax, -1:1)
                              ! LU 行列.
                              ! LU matrix
    real(DP):: xya_DelTempSoilTempLUVec (0:imax-1, 1:jmax, -kslmax:kmax)
                              ! $ T, Tg $ の時間変化.
                              ! Tendency of $ T $ and $ Tg |

    real(DP):: xyaa_SOSITempMtx(0:imax-1, 1:jmax, 1:ksimax, -1:1)
                              ! 海氷温度拡散方程式の行列
                              ! Matrix for diffusion equation of soil temperature
    real(DP):: xya_SOSITempVec (0:imax-1, 1:jmax, 1:ksimax)
                              ! 海氷温度拡散方程式のベクトル
                              ! Vector for diffusion equation of soil temperature

!!$    logical :: xy_FlagSeaIceMelt(0:imax-1, 1:jmax)

    real(DP) :: xy_TempCond(0:imax-1, 1:jmax)

    integer            :: xy_IDSOSI(0:imax-1, 1:jmax)
    integer, parameter :: IDSOSIDoNothing    = 0
    integer, parameter :: IDSOSIWoSIIncrease = 1
    integer, parameter :: IDSOSIWoSIDecrease = 2
    integer, parameter :: IDSOSIWSIIncrease  = 3
    integer, parameter :: IDSOSIWSIDecrease  = 4


    real(DP) :: xy_SurfTempATentative  (0:imax-1, 1:jmax)
    real(DP) :: SurfTempATentative

    real(DP) :: xy_DSurfTempDtTentative     (0:imax-1, 1:jmax)
    real(DP) :: xyz_DTempDtTentative        (0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_DSOSeaIceTempDtTentative(0:imax-1, 1:jmax, 1:kslmax)

!!$    real(DP) :: xy_SurfRadSFlux        (0:imax-1, 1:jmax)
!!$    real(DP) :: xy_SurfRadLFlux        (0:imax-1, 1:jmax)
!!$    real(DP) :: xy_SurfSoilHeatCondFlux(0:imax-1, 1:jmax)
!!$    real(DP) :: xy_SurfSensHeatFlux    (0:imax-1, 1:jmax)
!!$    real(DP) :: xy_SeaIceHeatCondFlux  (0:imax-1, 1:jmax)
!!$    real(DP) :: xy_HeatingTendency     (0:imax-1, 1:jmax)

    real(DP) :: SurfRadSFlux
    real(DP) :: SurfRadLFlux
!!$    real(DP) :: SurfSoilHeatCondFlux
    real(DP) :: SurfSensHeatFlux
    real(DP) :: SeaIceHeatCondFlux
    real(DP) :: HeatingTendency

    logical  :: xy_FlagAllSIMelt       (0:imax-1, 1:jmax)
    logical  :: xy_FlagFixTempCondTop  (0:imax-1, 1:jmax)
    logical  :: xy_FlagFixTempCondBot  (0:imax-1, 1:jmax)
    logical  :: xy_FlagAllSOFreeze     (0:imax-1, 1:jmax)
    real(DP) :: SOSeaIceMassATentative
    real(DP) :: LatHeatFluxBySOSeaIce

    real(DP) :: SOSeaIceTempA1Tentative
    real(DP) :: SOSeaIceTempALowLevTentative

    real(DP) :: DSOSeaIceMassDt

    real(DP) :: Sum

!!$    logical  :: FlagReturn

    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitude
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude
    integer:: k               ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction
    integer:: l


    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. phy_implicit_sdh_V5_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


!!$    ! 計算時間計測開始
!!$    ! Start measurement of computation time
!!$    !
!!$    call TimesetClockStart( module_name )


    xy_DSOSeaIceMassDtTop         = 0.0_DP
    xy_DSOSeaIceMassDtBot         = 0.0_DP
    xy_FlagSOSeaIceAllMelt        = .false.
    xy_FlagSOSIWoSIOceanAllFreeze = .false.
    xy_FlagSOSIWSIOceanAllFreeze  = .false.

!!$      xy_LatHeatFluxBySeaIceMelt = 0.0_DP


    !
    ! check flag of snow melt
    !
    if ( .not. FlagSlabOcean ) then
      return
    end if

    !
    ! check flag of snow melt
    !
    if ( ( .not. FlagBucketModel ) .or. ( .not. FlagSnow ) ) then
      return
    end if

    !
    ! check flag of sea ice
    !
    if ( .not. FlagSeaIce ) then
      return
    end if


    xy_TempCond = TempCondWater

    do j = 1, jmax
      do i = 0, imax-1
        xy_SurfTempATentative(i,j) = xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime )
      end do
    end do
    do j = 1, jmax
      do i = 0, imax-1

        SurfTempATentative = xy_SurfTempATentative(i,j)

        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexSlabOcean )
!          if ( SurfTempATentative < xy_TempCond(i,j) ) then
          if ( SurfTempATentative < TempBelowSeaIce ) then
            xy_IDSOSI(i,j) = IDSOSIWoSIIncrease
          else
            if ( xy_SOSeaIceMassB(i,j) > 0.0_DP ) then
              xy_IDSOSI(i,j) = IDSOSIWoSIDecrease
            else
              xy_IDSOSI(i,j) = IDSOSIDoNothing
            end if
          end if
        case ( IndexSlabOceanSeaIce )
          if ( SurfTempATentative > xy_TempCond(i,j) ) then
            xy_IDSOSI(i,j) = IDSOSIWSIDecrease
          else
            xy_IDSOSI(i,j) = IDSOSIWSIIncrease
          end if
        case default
          xy_IDSOSI(i,j) = IDSOSIDoNothing
        end select

      end do
    end do

    if ( all( xy_IDSOSI == IDSOSIDoNothing ) ) then
      return
    end if
!!$    FlagReturn = .true.
!!$    do j = 1, jmax
!!$      do i = 0, imax-1
!!$        if ( xy_IDSOSI(i,j) /= IDSOSIDoNothing ) then
!!$          FlagReturn = .false.
!!$        end if
!!$      end do
!!$    end do
!!$    if ( FlagReturn ) then
!!$      xy_DSOSeaIceMassDt          = 0.0_DP
!!$      xy_FlagSOSeaIceAllMelt      = .false.
!!$      xy_FlagSOSlabOceanAllFreeze = .false.
!!$      return
!!$    end if


    !##################
    !##################
    !##################
!!$    i = 0
!!$    j = 1
!!$    select case ( xy_IDSOSI(i,j) )
!!$    case ( IDSOSIDoNothing )
!!$      write( 6, * ) 'Nothing'
!!$    case ( IDSOSIWoSIIncrease )
!!$      write( 6, * ) 'WoSIIncrease'
!!$    case ( IDSOSIWoSIDecrease )
!!$      write( 6, * ) 'WoSIDecrease'
!!$    case ( IDSOSIWSIIncrease )
!!$      write( 6, * ) 'WSIIncrease'
!!$    case ( IDSOSIWSIDecrease )
!!$      write( 6, * ) 'WSIDecrease'
!!$    end select
!!$!    write( 6, * ) xy_IDSOSI(i,j)
    !##################
    !##################
    !##################


    !
    ! Grid points where not slab ocean
    !

    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IDSOSI(i,j) )
        case ( IDSOSIDoNothing )
!!$          xy_SeaIceHeatCondFlux(i,j) = 0.0_DP
!!$          xy_LatHeatFluxBySeaIceMelt(i,j) = 0.0_DP
          xy_DSOSeaIceMassDtTop     (i,j) = 0.0_DP
          xy_DSOSeaIceMassDtBot     (i,j) = 0.0_DP
        end select
      end do
    end do


    !
    ! Grid points where sea ice is not present and it increases/decreases
    !

    xy_FlagFixTempCondTop = .false.
    xy_FlagFixTempCondBot = .false.
    do j = 1, jmax
      do i = 0, imax-1

        select case ( xy_IDSOSI(i,j) )
        case ( IDSOSIWoSIIncrease )
          xy_FlagFixTempCondBot(i,j) = .true.
        case ( IDSOSIWoSIDecrease )
          xy_FlagFixTempCondTop(i,j) = .true.
        end select

      end do
    end do
    !
    !
    xyza_TempMtx     = xyza_ArgTempMtx
    xyz_TempVec      = xyz_ArgTempVec
    !
    xyaa_SurfMtx     = xyaa_ArgSurfMtx
    xy_SurfRH        = xy_ArgSurfRH
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagFixTempCondTop(i,j) .or. xy_FlagFixTempCondBot(i,j) ) then
          xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
          xyaa_SurfMtx(i,j,0, 0) = 1.0_DP
          xyaa_SurfMtx(i,j,0, 1) = 0.0_DP
!!$          xy_SurfRH   (i,j)      = xy_TempCond(i,j) - xy_SurfTemp(i,j)
          if ( xy_FlagFixTempCondTop(i,j) ) then
            xy_SurfRH   (i,j)      = xy_TempCond(i,j) - xy_SurfTemp(i,j)
          else if ( xy_FlagFixTempCondBot(i,j) ) then
            xy_SurfRH   (i,j)      = TempBelowSeaIce - xy_SurfTemp(i,j)
          end if
        end if
      end do
    end do
    !
    xyaa_SoilTempMtx = xyaa_ArgSoilTempMtx
    xya_SoilTempVec = xya_ArgSoilTempVec
    !
    do l = -1, 1
      do k = 1, kslmax
        xyaa_TempSoilTempLUMtx(:,:,-k,-l) = xyaa_SoilTempMtx(:,:,k,l)
      end do
      k = 0
      xyaa_TempSoilTempLUMtx(:,:, k, l) = xyaa_SurfMtx(:,:,0,l)
      do k = 1, kmax
        xyaa_TempSoilTempLUMtx(:,:, k, l) = xyza_TempMtx(:,:,k,l)
      end do
    end do
    !
    call PhyImplLUDecomp3( xyaa_TempSoilTempLUMtx, imax * jmax, kmax + 1 + kslmax )
    !
    do k = 1, kslmax
      xya_DelTempSoilTempLUVec(:,:,-k) = xya_SoilTempVec(:,:,k)
    end do
    k = 0
    xya_DelTempSoilTempLUVec(:,:,k) = xy_SurfRH
    do k = 1, kmax
      xya_DelTempSoilTempLUVec(:,:,k) = xyz_TempVec(:,:,k)
    end do
    !
    call PhyImplLUSolve3( xya_DelTempSoilTempLUVec, xyaa_TempSoilTempLUMtx, 1, imax * jmax , kmax + 1 + kslmax )
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagFixTempCondTop(i,j) .or. xy_FlagFixTempCondBot(i,j) ) then
          ! sea ice
          xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
        end if
      end do
    end do
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_FlagFixTempCondTop(i,j) .or. xy_FlagFixTempCondBot(i,j) ) then
            xyz_DTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,k) / ( 2.0_DP * DelTime )
          end if
        end do
      end do
    end do
    !
    do j = 1, jmax
      do i = 0, imax-1

        if ( xy_FlagFixTempCondTop(i,j) .or. xy_FlagFixTempCondBot(i,j) ) then
          SurfRadSFlux = xyr_RadSFlux(i,j,0)
          SurfRadLFlux = xyr_RadLFlux(i,j,0) + xyra_DelRadLFlux(i,j,0,0) * xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime ) + xyra_DelRadLFlux(i,j,0,1) * xyz_DTempDt(i,j,1) * ( 2.0_DP * DelTime )
          SurfSensHeatFlux = xyr_HeatFlux(i,j,0) - CpDry * xyr_Exner(i,j,0) * xy_SurfTempTransCoef(i,j) * ( xyz_DTempDt(i,j,1) / xyz_Exner(i,j,1) - xy_DSurfTempDt(i,j) / xyr_Exner(i,j,0) ) * ( 2.0_DP * DelTime )
          HeatingTendency = SOHeatCapacity * xy_DSurfTempDt(i,j)
          !
          xy_LatHeatFluxBySeaIceMelt(i,j) = - ( ( SurfRadSFlux + SurfRadLFlux + SurfSensHeatFlux + xy_SurfLatentHeatFlux(i,j) ) ) - HeatingTendency
          if ( xy_FlagFixTempCondTop(i,j) ) then
            DSOSeaIceMassDt = - xy_LatHeatFluxBySeaIceMelt(i,j) / LatentHeatFusion
            xy_DSOSeaIceMassDtTop(i,j) = DSOSeaIceMassDt
            xy_DSOSeaIceMassDtBot(i,j) = 0.0_DP
          else if ( xy_FlagFixTempCondBot(i,j) ) then
            DSOSeaIceMassDt = - xy_LatHeatFluxBySeaIceMelt(i,j) / LatentHeatFusionBelowSeaIce
            xy_DSOSeaIceMassDtTop(i,j) = 0.0_DP
            xy_DSOSeaIceMassDtBot(i,j) = DSOSeaIceMassDt
          end if
        end if

      end do
    end do
    !   Grid points where sea ice is not present and it decreases
    xy_FlagAllSIMelt   = .false.
    xy_FlagAllSOFreeze = .false.
    do j = 1, jmax
      do i = 0, imax-1

        select case ( xy_IDSOSI(i,j) )
        case ( IDSOSIWoSIDecrease, IDSOSIWoSIIncrease )
          SOSeaIceMassATentative = xy_SOSeaIceMassB(i,j) + ( xy_DSOSeaIceMassDtTop(i,j) + xy_DSOSeaIceMassDtBot(i,j) ) * ( 2.0_DP * DelTime )
          if ( SOSeaIceMassATentative < 0.0_DP ) then
            ! All sea ice melt.
            xy_FlagAllSIMelt  (i,j) = .true.
            xy_DSOSeaIceMassDtTop(i,j) = - xy_SOSeaIceMassB(i,j) / ( 2.0_DP * DelTime )
            xy_DSOSeaIceMassDtBot(i,j) = 0.0_DP
          else if ( SOSeaIceMassATentative > SOMass ) then
            ! All slab ocean freeze. 
            xy_FlagAllSOFreeze(i,j) = .true.
            xy_DSOSeaIceMassDtTop(i,j) = 0.0_DP
            xy_DSOSeaIceMassDtBot(i,j) = ( SOMass - xy_SOSeaIceMassB(i,j) ) / ( 2.0_DP * DelTime )
          end if
        end select

      end do
    end do
    !
    !   All sea ice melts when sea ice is not present.
    !
    xyza_TempMtx     = xyza_ArgTempMtx
    xyz_TempVec      = xyz_ArgTempVec
    !
    xyaa_SurfMtx     = xyaa_ArgSurfMtx
    xy_SurfRH        = xy_ArgSurfRH
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSIMelt(i,j) ) then
          ! slab ocean
!          xyaa_SurfMtx(i,j,0, 0) =                                          &
!            &   SOHeatCapacity / ( 2.0_DP * DelTime )                       &
!            & + CpDry * xy_SurfTempTransCoef(i,j)                           &
!            & + xyra_DelRadLFlux(i,j,0,0)

          ! slab ocean
          !   add cooling by latent heat by melting sea ice
          xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - xy_SurfLatentHeatFlux(i,j) + LatentHeatFusion * xy_DSOSeaIceMassDtTop(i,j)

!            & - SeaIceThermCondCoef                             &
!            &   * ( xy_SurfTemp(i,j) - TempBelowSeaIce ) / xy_SeaIceThickness(i,j)

        end if
      end do
    end do
    !
    xyaa_SoilTempMtx = xyaa_ArgSoilTempMtx
    xya_SoilTempVec = xya_ArgSoilTempVec
    !
    do l = -1, 1
      do k = 1, kslmax
        xyaa_TempSoilTempLUMtx(:,:,-k,-l) = xyaa_SoilTempMtx(:,:,k,l)
      end do
      k = 0
      xyaa_TempSoilTempLUMtx(:,:, k, l) = xyaa_SurfMtx(:,:,0,l)
      do k = 1, kmax
        xyaa_TempSoilTempLUMtx(:,:, k, l) = xyza_TempMtx(:,:,k,l)
      end do
    end do
    !
    call PhyImplLUDecomp3( xyaa_TempSoilTempLUMtx, imax * jmax, kmax + 1 + kslmax )
    !
    do k = 1, kslmax
      xya_DelTempSoilTempLUVec(:,:,-k) = xya_SoilTempVec(:,:,k)
    end do
    k = 0
    xya_DelTempSoilTempLUVec(:,:,k) = xy_SurfRH
    do k = 1, kmax
      xya_DelTempSoilTempLUVec(:,:,k) = xyz_TempVec(:,:,k)
    end do
    !
    call PhyImplLUSolve3( xya_DelTempSoilTempLUVec, xyaa_TempSoilTempLUMtx, 1, imax * jmax , kmax + 1 + kslmax )
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSIMelt(i,j) ) then
          xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
        end if
      end do
    end do
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_FlagAllSIMelt(i,j) ) then
            xyz_DTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,k) / ( 2.0_DP * DelTime )
          end if
        end do
      end do
    end do
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSIMelt(i,j) ) then
!!$          xy_LatHeatFluxBySeaIceMelt(i,j) = &
!!$!            & LatentHeatFusion * xy_SOSeaIceMassB(i,j) / ( 2.0_DP * DelTime )
!!$            & - LatentHeatFusion * xy_DSOSeaIceMassDtTop(i,j)
!!$          xy_LatHeatFluxBySeaIceMelt(i,j) = 0.0_DP
          xy_LatHeatFluxBySeaIceMelt(i,j) = - LatentHeatFusion * xy_DSOSeaIceMassDtTop(i,j)
        end if
      end do
    end do
    !
    !   All slab ocean freeze when sea ice is not present.
    !
    xyza_TempMtx     = xyza_ArgTempMtx
    xyz_TempVec      = xyz_ArgTempVec
    !
    xyaa_SurfMtx     = xyaa_ArgSurfMtx
    xy_SurfRH        = xy_ArgSurfRH
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSOFreeze(i,j) ) then

!!$          xyaa_SurfMtx(i,j,0,-1) =                                             &
!!$            & 0.0_DP
!!$          xyaa_SurfMtx(i,j,0, 0) =                                             &
!!$            &   SOHeatCapacity / ( 2.0_DP * DelTime )                          &
!!$            & + CpDry * xy_SurfTempTransCoef(i,j)                              &
!!$            & + xyra_DelRadLFlux(i,j,0,0)
!!$          xyaa_SurfMtx(i,j,0, 1) =                                             &
!!$            & - CpDry * xyr_Exner(i,j,0) / xyz_Exner(i,j,1)                    &
!!$            &   * xy_SurfTempTransCoef(i,j)                                    &
!!$            & + xyra_DelRadLFlux(i,j,0,1)


          ! sea ice
          xyaa_SurfMtx(i,j,0, 0) = SeaIceVolHeatCap * xy_SOSeaIceMassB(i,j) / SeaIceDen / ( 2.0_DP * DelTime ) + CpDry * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,0) + SeaIceVolHeatCap * xy_DSOSeaIceMassDtBot(i,j) / SeaIceDen

          ! sea ice
          xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - xy_SurfLatentHeatFlux(i,j) + xy_DSOSeaIceMassDtBot(i,j) * (   LatentHeatFusionBelowSeaIce + SeaIceVolHeatCap / SeaIceDen * ( TempBelowSeaIce - xy_SurfTemp(i,j) ) ) - SOHeatCapacity * ( TempBelowSeaIce - xy_SurfTemp(i,j) ) / ( 2.0_DP * DelTime )
        end if
      end do
    end do
    !
    xyaa_SoilTempMtx = xyaa_ArgSoilTempMtx
    xya_SoilTempVec = xya_ArgSoilTempVec
    !
    do l = -1, 1
      do k = 1, kslmax
        xyaa_TempSoilTempLUMtx(:,:,-k,-l) = xyaa_SoilTempMtx(:,:,k,l)
      end do
      k = 0
      xyaa_TempSoilTempLUMtx(:,:, k, l) = xyaa_SurfMtx(:,:,0,l)
      do k = 1, kmax
        xyaa_TempSoilTempLUMtx(:,:, k, l) = xyza_TempMtx(:,:,k,l)
      end do
    end do
    !
    call PhyImplLUDecomp3( xyaa_TempSoilTempLUMtx, imax * jmax, kmax + 1 + kslmax )
    !
    do k = 1, kslmax
      xya_DelTempSoilTempLUVec(:,:,-k) = xya_SoilTempVec(:,:,k)
    end do
    k = 0
    xya_DelTempSoilTempLUVec(:,:,k) = xy_SurfRH
    do k = 1, kmax
      xya_DelTempSoilTempLUVec(:,:,k) = xyz_TempVec(:,:,k)
    end do
    !
    call PhyImplLUSolve3( xya_DelTempSoilTempLUVec, xyaa_TempSoilTempLUMtx, 1, imax * jmax , kmax + 1 + kslmax )
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSOFreeze(i,j) ) then
          xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
        end if
      end do
    end do
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_FlagAllSOFreeze(i,j) ) then
            xyz_DTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,k) / ( 2.0_DP * DelTime )
          end if
        end do
      end do
    end do
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSOFreeze(i,j) ) then
          SurfTempATentative = xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime )
          ! xy_LatHeatFluxBySeaIceMelt(i,j) is calculated for check routine.
          xy_LatHeatFluxBySeaIceMelt(i,j) = - ( xy_DSOSeaIceMassDtBot(i,j) * (   LatentHeatFusionBelowSeaIce + SeaIceVolHeatCap / SeaIceDen * ( TempBelowSeaIce - SurfTempATentative ) ) - SOHeatCapacity * ( TempBelowSeaIce - xy_SurfTemp(i,j) ) / ( 2.0_DP * DelTime ) )
          ! xy_DSOSeaIceMassDtBot(i,j) is calculated above.
        end if
      end do
    end do

    xy_FlagSOSIWoSIOceanAllFreeze = xy_FlagAllSOFreeze



    !--------------------------------------------
    !----- Case in which sea ice is present -----
    !--------------------------------------------


    !
    ! Grid points where sea ice is present and it decreases (melts at top)
    !

    xyza_TempMtx     = xyza_ArgTempMtx
    xyz_TempVec      = xyz_ArgTempVec
    !
    xyaa_SurfMtx     = xyaa_ArgSurfMtx
    xy_SurfRH        = xy_ArgSurfRH
    !
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IDSOSI(i,j) )
        case ( IDSOSIWSIDecrease )
          xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
          xyaa_SurfMtx(i,j,0, 0) = 1.0_DP
          xyaa_SurfMtx(i,j,0, 1) = 0.0_DP
          xy_SurfRH   (i,j)      = xy_TempCond(i,j) - xy_SurfTemp(i,j)
        end select
      end do
    end do
    !
    xyaa_SoilTempMtx = xyaa_ArgSoilTempMtx
    xya_SoilTempVec = xya_ArgSoilTempVec
    !
    do l = -1, 1
      do k = 1, kslmax
        xyaa_TempSoilTempLUMtx(:,:,-k,-l) = xyaa_SoilTempMtx(:,:,k,l)
      end do
      k = 0
      xyaa_TempSoilTempLUMtx(:,:, k, l) = xyaa_SurfMtx(:,:,0,l)
      do k = 1, kmax
        xyaa_TempSoilTempLUMtx(:,:, k, l) = xyza_TempMtx(:,:,k,l)
      end do
    end do
    !
    call PhyImplLUDecomp3( xyaa_TempSoilTempLUMtx, imax * jmax, kmax + 1 + kslmax )
    !
    do k = 1, kslmax
      xya_DelTempSoilTempLUVec(:,:,-k) = xya_SoilTempVec(:,:,k)
    end do
    k = 0
    xya_DelTempSoilTempLUVec(:,:,k) = xy_SurfRH
    do k = 1, kmax
      xya_DelTempSoilTempLUVec(:,:,k) = xyz_TempVec(:,:,k)
    end do
    !
    call PhyImplLUSolve3( xya_DelTempSoilTempLUVec, xyaa_TempSoilTempLUMtx, 1, imax * jmax , kmax + 1 + kslmax )
    !
    do k = 1, ksimax
      do j = 1, jmax
        do i = 0, imax-1
          select case ( xy_IDSOSI(i,j) )
          case ( IDSOSIWSIDecrease )
            ! sea ice
            xyz_DSOSeaIceTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,-k) / ( 2.0_DP * DelTime )
          end select
        end do
      end do
    end do
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IDSOSI(i,j) )
        case ( IDSOSIWSIDecrease )
          ! sea ice
          xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
        end select
      end do
    end do
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          select case ( xy_IDSOSI(i,j) )
          case ( IDSOSIWSIDecrease )
            xyz_DTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,k) / ( 2.0_DP * DelTime )
          end select
        end do
      end do
    end do
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IDSOSI(i,j) )
        case ( IDSOSIWSIDecrease )
          SurfRadSFlux = xyr_RadSFlux(i,j,0)
          SurfRadLFlux = xyr_RadLFlux(i,j,0) + xyra_DelRadLFlux(i,j,0,0) * xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime ) + xyra_DelRadLFlux(i,j,0,1) * xyz_DTempDt(i,j,1) * ( 2.0_DP * DelTime )
          SurfSensHeatFlux = xyr_HeatFlux(i,j,0) - CpDry * xyr_Exner(i,j,0) * xy_SurfTempTransCoef(i,j) * ( xyz_DTempDt(i,j,1) / xyz_Exner(i,j,1) - xy_DSurfTempDt(i,j) / xyr_Exner(i,j,0) ) * ( 2.0_DP * DelTime )
          SurfTempATentative = xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime )
          k = 1
          SOSeaIceTempA1Tentative = xyz_SOSeaIceTemp(i,j,k) + xyz_DSOSeaIceTempDt(i,j,k) * ( 2.0_DP * DelTime )
          k = 0
          SeaIceHeatCondFlux = - xyr_SOSIHeatTransCoef(i,j,k) * ( SOSeaIceTempA1Tentative - SurfTempATentative )
          HeatingTendency = xy_SurfHeatCapacity(i,j) * xy_DSurfTempDt(i,j)
          !
          xy_LatHeatFluxBySeaIceMelt(i,j) = - ( ( SurfRadSFlux + SurfRadLFlux + SurfSensHeatFlux + xy_SurfLatentHeatFlux(i,j) ) - SeaIceHeatCondFlux ) - HeatingTendency

          xy_DSOSeaIceMassDtTop(i,j) = - xy_LatHeatFluxBySeaIceMelt(i,j) / LatentHeatFusion
        end select
      end do
    end do


    !
    ! Grid points where sea ice is present and it increases (the underlying ocean freezes)
    !

    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IDSOSI(i,j) )
        case ( IDSOSIWSIDecrease, IDSOSIWSIIncrease )
!!$          SurfTempATentative = xy_SurfTempATentative(i,j)
          k = xy_SOSILocalKMax(i,j)
          SOSeaIceTempALowLevTentative = xyz_SOSeaIceTemp(i,j,k) + xyz_DSOSeaIceTempDt(i,j,k) * ( 2.0_DP * DelTime )
          SeaIceHeatCondFlux = - xyr_SOSIHeatTransCoef(i,j,k) * ( TempBelowSeaIce - SOSeaIceTempALowLevTentative )
          !
!!$          ! In this case, energy budget is closed without latent heat flux by sea ice melt.
!!$          ! Instead, downward heat flux is posed on underlying sea and produces sea ice.
!!$          xy_LatHeatFluxBySeaIceMelt(i,j) = 0.0_DP
!!$          xy_DSOSeaIceMassDt(i,j) = SeaIceHeatCondFlux / LatentHeatFusion
          xy_DSOSeaIceMassDtBot(i,j) = SeaIceHeatCondFlux / (   LatentHeatFusionBelowSeaIce + SeaIceVolHeatCap / SeaIceDen * ( TempBelowSeaIce - SOSeaIceTempALowLevTentative ) )
        end select
      end do
    end do
    !
    !   Check whether all sea ice melt or freeze
    !
    xy_FlagAllSIMelt   = .false.
    xy_FlagAllSOFreeze = .false.
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IDSOSI(i,j) )
        case ( IDSOSIWSIDecrease, IDSOSIWSIIncrease )
          SOSeaIceMassATentative = xy_SOSeaIceMassB(i,j) + ( xy_DSOSeaIceMassDtTop(i,j) + xy_DSOSeaIceMassDtBot(i,j) ) * ( 2.0_DP * DelTime )
          if ( SOSeaIceMassATentative < 0.0_DP ) then
            ! All sea ice melt
            xy_FlagAllSIMelt  (i,j) = .true.
            xy_DSOSeaIceMassDtTop(i,j) = - xy_SOSeaIceMassB(i,j) / ( 2.0_DP * DelTime )
            xy_DSOSeaIceMassDtBot(i,j) = 0.0_DP
          else if ( SOSeaIceMassATentative > SOMass ) then
            ! All slab ocean freeze
            xy_FlagAllSOFreeze(i,j) = .true.
            xy_DSOSeaIceMassDtTop(i,j) = 0.0_DP
            xy_DSOSeaIceMassDtBot(i,j) = ( SOMass - xy_SOSeaIceMassB(i,j) ) / ( 2.0_DP * DelTime )
          end if
        end select
      end do
    end do
    !
    !   All sea ice melts when sea ice is present.
    !
    xyza_TempMtx     = xyza_ArgTempMtx
    xyz_TempVec      = xyz_ArgTempVec
    !
    xyaa_SurfMtx     = xyaa_ArgSurfMtx
    xy_SurfRH        = xy_ArgSurfRH
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSIMelt(i,j) ) then
          ! slab ocean
          xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
          xyaa_SurfMtx(i,j,0, 0) = SOHeatCapacity / ( 2.0_DP * DelTime ) + CpDry * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,0)

          ! slab ocean
          !   add cooling by latent heat by melting sea ice
          !   and cooling by increasing sea ice temperature up to freezing temperature
          !   and part of slab ocean temperature tendency
          xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - xy_SurfLatentHeatFlux(i,j) + LatentHeatFusion * xy_DSOSeaIceMassDtTop(i,j) - SOHeatCapacity * ( xy_SurfTemp(i,j) - xy_TempCond(i,j) ) / ( 2.0_DP * DelTime )
            !      a term below is part of tendency of sea ice
            !        from temperature at previous step to condensation temperature
!!$            & - SeaIceVolHeatCap * xy_SeaIceThickness(i,j)       &
!!$            &     * ( xy_TempCond(i,j) - xy_SurfTemp(i,j) )      &
!!$            &     / ( 2.0_DP * DelTime )
          Sum = 0.0_DP
          do k = 1, xy_SOSILocalKMax(i,j)
            Sum = Sum - SeaIceVolHeatCap * ( xyr_SOSILocalDepth(i,j,k-1) - xyr_SOSILocalDepth(i,j,k) ) * ( xy_TempCond(i,j) - xyz_SOSeaIceTemp(i,j,k) ) / ( 2.0_DP * DelTime )
          end do
          xy_SurfRH(i,j) = xy_SurfRH(i,j) + Sum

!            & - SeaIceThermCondCoef                             &
!            &   * ( xy_SurfTemp(i,j) - TempBelowSeaIce ) / xy_SeaIceThickness(i,j)

        end if
      end do
    end do
    !
    xyaa_SoilTempMtx = xyaa_ArgSoilTempMtx
    xya_SoilTempVec = xya_ArgSoilTempVec
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSIMelt(i,j) ) then
          do k = 1, xy_SOSILocalKMax(i,j)
            xyaa_SoilTempMtx(i,j,k,-1) = 0.0_DP
            xyaa_SoilTempMtx(i,j,k, 0) = 1.0_DP
            xyaa_SoilTempMtx(i,j,k, 1) = 0.0_DP
!!$            xya_SoilTempVec (i,j,k)    = 0.0_DP
            xya_SoilTempVec (i,j,k)    = xy_TempCond(i,j) - xyz_SOSeaIceTemp(i,j,k)
          end do
          do k = xy_SOSILocalKMax(i,j)+1, kslmax
            xyaa_SoilTempMtx(i,j,k,-1) = 0.0_DP
            xyaa_SoilTempMtx(i,j,k, 0) = 1.0_DP
            xyaa_SoilTempMtx(i,j,k, 1) = 0.0_DP
            xya_SoilTempVec (i,j,k)    = 0.0_DP
          end do
        end if
      end do
    end do
    !
    do l = -1, 1
      do k = 1, kslmax
        xyaa_TempSoilTempLUMtx(:,:,-k,-l) = xyaa_SoilTempMtx(:,:,k,l)
      end do
      k = 0
      xyaa_TempSoilTempLUMtx(:,:, k, l) = xyaa_SurfMtx(:,:,0,l)
      do k = 1, kmax
        xyaa_TempSoilTempLUMtx(:,:, k, l) = xyza_TempMtx(:,:,k,l)
      end do
    end do
    !
    call PhyImplLUDecomp3( xyaa_TempSoilTempLUMtx, imax * jmax, kmax + 1 + kslmax )
    !
    do k = 1, kslmax
      xya_DelTempSoilTempLUVec(:,:,-k) = xya_SoilTempVec(:,:,k)
    end do
    k = 0
    xya_DelTempSoilTempLUVec(:,:,k) = xy_SurfRH
    do k = 1, kmax
      xya_DelTempSoilTempLUVec(:,:,k) = xyz_TempVec(:,:,k)
    end do
    !
    call PhyImplLUSolve3( xya_DelTempSoilTempLUVec, xyaa_TempSoilTempLUMtx, 1, imax * jmax , kmax + 1 + kslmax )
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSIMelt(i,j) ) then
          do k = 1, kslmax
            xyz_DSOSeaIceTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,-k) / ( 2.0_DP * DelTime )
          end do
        end if
      end do
    end do
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSIMelt(i,j) ) then
          xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
        end if
      end do
    end do
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_FlagAllSIMelt(i,j) ) then
            xyz_DTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,k) / ( 2.0_DP * DelTime )
          end if
        end do
      end do
    end do


!!$    do j = 1, jmax
!!$      do i = 0, imax-1
!!$        if ( xy_FlagAllSIMelt(i,j) ) then
!!$          xy_LatHeatFluxBySeaIceMelt(i,j) = &
!!$!            & + LatentHeatFusion * xy_SOSeaIceMassB(i,j)         &
!!$!            &     / ( 2.0_DP * DelTime )                         &
!!$            & - LatentHeatFusion * xy_DSOSeaIceMassDtTop(i,j)    &
!!$            & - SOHeatCapacity                                   &
!!$            &     * ( xy_TempCond(i,j) - xy_SurfTemp(i,j) )      &
!!$            &     / ( 2.0_DP * DelTime )
!!$!          &
!!$!            & + SeaIceVolHeatCap * xy_SeaIceThickness(i,j)       &
!!$!            &     * ( xy_TempCond(i,j) - xy_SurfTemp(i,j) )      &
!!$!            &     / ( 2.0_DP * DelTime )
!!$          Sum = 0.0_DP
!!$          do k = 1, xy_SOSILocalKMax(i,j)
!!$            Sum = Sum &
!!$            & - SeaIceVolHeatCap                                                &
!!$            &     * ( xyr_SOSILocalDepth(i,j,k-1) - xyr_SOSILocalDepth(i,j,k) ) &
!!$            &     * ( xy_TempCond(i,j) - xyz_SOSeaIceTemp(i,j,k) )              &
!!$            &     / ( 2.0_DP * DelTime )
!!$          end do
!!$          xy_LatHeatFluxBySeaIceMelt(i,j) = &
!!$            & xy_LatHeatFluxBySeaIceMelt(i,j) + Sum
!!$        end if
!!$      end do
!!$    end do

    ! xy_FlagSOSeaIceAllMelt will be used in checking routine, PhyImplSDHV5ChkConservation
    xy_FlagSOSeaIceAllMelt = xy_FlagAllSIMelt


    !
    !   case in which all slab ocean freeze
    !
    xyza_TempMtx     = xyza_ArgTempMtx
    xyz_TempVec      = xyz_ArgTempVec
    !
    xyaa_SurfMtx     = xyaa_ArgSurfMtx
    xy_SurfRH        = xy_ArgSurfRH
    !
    xyaa_SoilTempMtx = xyaa_ArgSoilTempMtx
    xya_SoilTempVec = xya_ArgSoilTempVec
    !
    xyaa_SOSITempMtx = xyaa_ArgSOSITempMtx
    xya_SOSITempVec = xya_ArgSOSITempVec
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSOFreeze(i,j) ) then
          select case ( xy_IDSOSI(i,j) )
          case ( IDSOSIWSIDecrease )
            xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
            xyaa_SurfMtx(i,j,0, 0) = 1.0_DP
            xyaa_SurfMtx(i,j,0, 1) = 0.0_DP
            xy_SurfRH   (i,j)      = xy_TempCond(i,j) - xy_SurfTemp(i,j)
          end select
        end if
      end do
    end do
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSOFreeze(i,j) ) then
          k = xy_SOSILocalKMax(i,j)

!!$          xyaa_SOSITempMtx(i,j,k,-1) =                                   &
!!$            & - xyr_SOSIHeatTransCoef(i,j,k-1)
!!$          xyaa_SOSITempMtx(i,j,k, 0) =                                   &
!!$            &   SeaIceVolHeatCap                                         &
!!$            &     * ( xyr_SOSILocalDepth(i,j,k) - xyr_SOSILocalDepth(i,j,k-1) )  &
!!$            &     / ( 2.0_DP * DelTime )                                 &
!!$            & + xyr_SOSIHeatTransCoef(i,j,k-1)                           &
!!$!            & + xyr_SOSIHeatTransCoef(i,j,k  )
!!$!            & + xy_DSOSeaIceMassDt(i,j) * SeaIceVolHeatCap / SeaIceDen
!!$            ! the sign is minus because
!!$            ! ( xyr_SOSILocalDepth(i,j,k) - xyr_SOSILocalDepth(i,j,k-1) ) is
!!$            ! negative
!!$            & - xy_DSOSeaIceMassDtBot(i,j) * SeaIceVolHeatCap / SeaIceDen
!!$          xyaa_SOSITempMtx(i,j,k, 1) = 0.0_DP
!!$
!!$          xya_SOSITempVec (i,j,k) = &
!!$!            & - ( xyr_SOSIHeatFlux(i,j,k) - xyr_SOSIHeatFlux(i,j,k-1) ) &
!!$            & - ( 0.0_DP - xyr_SOSIHeatFlux(i,j,k-1) ) &
!!$!            & + xy_DSOSeaIceMassDt(i,j)                           &
!!$            ! the sign is minus because
!!$            ! ( xyr_SOSILocalDepth(i,j,k) - xyr_SOSILocalDepth(i,j,k-1) ) is
!!$            ! negative
!!$            & - xy_DSOSeaIceMassDtBot(i,j)                        &
!!$            &   * (   LatentHeatFusion                            &
!!$            &       + SeaIceVolHeatCap / SeaIceDen                &
!!$!            &         * ( xy_TempCond(i,j) - xy_SurfTemp(i,j) ) )
!!$!            &         * ( TempBelowSeaIce - xy_SurfTemp(i,j) ) )
!!$            &         * ( TempBelowSeaIce - xyz_SOSeaIceTemp(i,j,k) ) )


!!$              xyaa_SOSITempMtx(i,j,k,-1) =                                   &
!!$                & - xyr_SOSIHeatTransCoef(i,j,k-1)
              xyaa_SOSITempMtx(i,j,k, 0) = SeaIceVolHeatCap * ( xyr_SOSILocalDepth(i,j,k) - xyr_SOSILocalDepth(i,j,k-1) ) / ( 2.0_DP * DelTime ) + xyr_SOSIHeatTransCoef(i,j,k-1) - xy_DSOSeaIceMassDtBot(i,j) * SeaIceVolHeatCap / SeaIceDen
!!$              xyaa_SOSITempMtx(i,j,k, 1) = 0.0_DP
!!$              xya_SOSITempVec (i,j,k) = - ( xyr_SOSIHeatFlux(i,j,k) - xyr_SOSIHeatFlux(i,j,k-1) )
              xya_SOSITempVec (i,j,k) = - ( 0.0_DP - xyr_SOSIHeatFlux(i,j,k-1) ) - xy_DSOSeaIceMassDtBot(i,j) * (   LatentHeatFusionBelowSeaIce + SeaIceVolHeatCap / SeaIceDen * ( TempBelowSeaIce - xyz_SOSeaIceTemp(i,j,k) ) )

          xyaa_SoilTempMtx(i,j,k,-1) = xyaa_SOSITempMtx(i,j,k,-1)
          xyaa_SoilTempMtx(i,j,k, 0) = xyaa_SOSITempMtx(i,j,k, 0)
          xyaa_SoilTempMtx(i,j,k, 1) = xyaa_SOSITempMtx(i,j,k, 1)
          xya_SoilTempVec (i,j,k)    = xya_SOSITempVec (i,j,k)

        end if
      end do
    end do
    !
    do l = -1, 1
      do k = 1, kslmax
        xyaa_TempSoilTempLUMtx(:,:,-k,-l) = xyaa_SoilTempMtx(:,:,k,l)
      end do
      k = 0
      xyaa_TempSoilTempLUMtx(:,:, k, l) = xyaa_SurfMtx(:,:,0,l)
      do k = 1, kmax
        xyaa_TempSoilTempLUMtx(:,:, k, l) = xyza_TempMtx(:,:,k,l)
      end do
    end do
    !
    call PhyImplLUDecomp3( xyaa_TempSoilTempLUMtx, imax * jmax, kmax + 1 + kslmax )
    !
    do k = 1, kslmax
      xya_DelTempSoilTempLUVec(:,:,-k) = xya_SoilTempVec(:,:,k)
    end do
    k = 0
    xya_DelTempSoilTempLUVec(:,:,k) = xy_SurfRH
    do k = 1, kmax
      xya_DelTempSoilTempLUVec(:,:,k) = xyz_TempVec(:,:,k)
    end do
    !
    call PhyImplLUSolve3( xya_DelTempSoilTempLUVec, xyaa_TempSoilTempLUMtx, 1, imax * jmax , kmax + 1 + kslmax )
    !
    do k = 1, ksimax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_FlagAllSOFreeze(i,j) ) then
            xyz_DSOSeaIceTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,-k) / ( 2.0_DP * DelTime )
          end if
        end do
      end do
    end do
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSOFreeze(i,j) ) then
          xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
        end if
      end do
    end do
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_FlagAllSOFreeze(i,j) ) then
            xyz_DTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,k) / ( 2.0_DP * DelTime )
          end if
        end do
      end do
    end do
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagAllSOFreeze(i,j) ) then

          select case ( xy_IDSOSI(i,j) )
          case ( IDSOSIWSIDecrease )
            SurfRadSFlux = xyr_RadSFlux(i,j,0)
            SurfRadLFlux = xyr_RadLFlux(i,j,0) + xyra_DelRadLFlux(i,j,0,0) * xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime ) + xyra_DelRadLFlux(i,j,0,1) * xyz_DTempDt(i,j,1) * ( 2.0_DP * DelTime )
            SurfSensHeatFlux = xyr_HeatFlux(i,j,0) - CpDry * xyr_Exner(i,j,0) * xy_SurfTempTransCoef(i,j) * ( xyz_DTempDt(i,j,1) / xyz_Exner(i,j,1) - xy_DSurfTempDt(i,j) / xyr_Exner(i,j,0) ) * ( 2.0_DP * DelTime )
            SurfTempATentative = xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime )
            k = 1
            SOSeaIceTempA1Tentative = xyz_SOSeaIceTemp(i,j,k) + xyz_DSOSeaIceTempDt(i,j,k) * ( 2.0_DP * DelTime )
            k = 0
            SeaIceHeatCondFlux = - xyr_SOSIHeatTransCoef(i,j,k) * ( SOSeaIceTempA1Tentative - SurfTempATentative )
            HeatingTendency = xy_SurfHeatCapacity(i,j) * xy_DSurfTempDt(i,j)
            !
            xy_LatHeatFluxBySeaIceMelt(i,j) = - ( ( SurfRadSFlux + SurfRadLFlux + SurfSensHeatFlux + xy_SurfLatentHeatFlux(i,j) ) - SeaIceHeatCondFlux ) - HeatingTendency

            xy_DSOSeaIceMassDtTop(i,j) = - xy_LatHeatFluxBySeaIceMelt(i,j) / LatentHeatFusion
          end select

        end if
      end do
    end do

!!$    do j = 1, jmax
!!$      do i = 0, imax-1
!!$        if ( xy_FlagAllSOFreeze(i,j) ) then
!!$          SurfTempATentative = xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * ( 2.0_DP * DelTime )
!!$          k = 1
!!$          SOSeaIceTempA1Tentative = xyz_SOSeaIceTemp(i,j,k) &
!!$            & + xyz_DSOSeaIceTempDt(i,j,k) * ( 2.0_DP * DelTime )
!!$          ! xy_LatHeatFluxBySeaIceMelt(i,j) is calculated for check routine.
!!$          !   A term below seems confusing because heat conduction term is included.
!!$          !   This term cancel a corresponding heat conduction term in check routine. 
!!$          xy_LatHeatFluxBySeaIceMelt(i,j) = &
!!$            & - SeaIceThermCondCoef                        &
!!$            &   * ( SurfTempATentative - TempBelowSeaIce ) &
!!$            &   / xy_SeaIceThickness(i,j)                  &
!!$            & - (                                                      &
!!$            &      xy_DSOSeaIceMassDt(i,j)                             &
!!$            &      * (   LatentHeatFusion                              &
!!$            &          + SeaIceVolHeatCap / SeaIceDen                  &
!!$!            &            * ( xy_TempCond(i,j) - SurfTempATentative ) ) &
!!$            &            * ( TempBelowSeaIce - SurfTempATentative ) ) &
!!$            &   )
!!$          ! xy_DSOSeaIceMassDt(i,j) is calculated above.
!!$        end if
!!$      end do
!!$    end do


    xy_FlagSOSIWSIOceanAllFreeze  = xy_FlagAllSOFreeze




!!$    xy_SurfRadSFlux = xyr_RadSFlux(:,:,0)
!!$    xy_SurfRadLFlux = xyr_RadLFlux(:,:,0)                                           &
!!$      &   + xyra_DelRadLFlux(:,:,0,0) * xy_DSurfTempDt * ( 2.0_DP * DelTime )        &
!!$      &   + xyra_DelRadLFlux(:,:,0,1) * xyz_DTempDt(:,:,1) * ( 2.0_DP * DelTime )
!!$    xy_SurfSoilHeatCondFlux = xyr_SoilHeatFlux(:,:,0)                                &
!!$      & - xyr_SoilTempTransCoef(:,:,0)                                               &
!!$      &   * ( xyz_DSoilTempDt(:,:,1) - xy_DSurfTempDt ) * ( 2.0_DP * DelTime )
!!$    xy_SurfSensHeatFlux =                                                       &
!!$      & xyr_HeatFlux(:,:,0)                                                     &
!!$      &   - CpDry * xyr_Exner(:,:,0) * xy_SurfTempTransCoef                     &
!!$      &     * ( xyz_DTempDt(:,:,1) / xyz_Exner(:,:,1)                           &
!!$      &       - xy_DSurfTempDt / xyr_Exner(:,:,0) ) * ( 2.0_DP * DelTime )
!!$    xy_SeaIceHeatCondFlux =                                                           &
!!$      & - SeaIceThermCondCoef                                                         &
!!$      &   * ( xy_SurfTemp + xy_DSurfTempDt * ( 2.0_DP * DelTime ) - TempBelowSeaIce ) &
!!$      &   / xy_SeaIceThickness
!!$    xy_HeatingTendency = SeaIceVolHeatCap * xy_SeaIceThickness * xy_DSurfTempDt
!!$
!!$    do j = 1, jmax
!!$      do i = 0, imax-1
!!$
!!$        if ( xy_FlagSeaIceMelt(i,j) ) then
!!$          xy_LatHeatFluxBySeaIceMelt(i,j) =          &
!!$            & - (                                    &
!!$            &     (                                  &
!!$            &         xy_SurfRadSFlux(i,j)           &
!!$            &       + xy_SurfRadLFlux(i,j)           &
!!$            &       + xy_SurfSensHeatFlux(i,j)       &
!!$            &       + xy_SurfLatentHeatFlux(i,j)     &
!!$            &     )                                  &
!!$            &     - xy_SeaIceHeatCondFlux(i,j)       &
!!$            &   )                                    &
!!$            & - xy_HeatingTendency(i,j)
!!$        else
!!$          xy_LatHeatFluxBySeaIceMelt(i,j) = 0.0_DP
!!$        end if
!!$
!!$      end do
!!$    end do




!!$    ! 計算時間計測一時停止
!!$    ! Pause measurement of computation time
!!$    !
!!$    call TimesetClockStop( module_name )


  end subroutine PhyImplSDHV5SOSeaIceCorrection

PhyImplSDHV5SeaIceCorrection( xy_IndexCalcMethod, xy_SeaIceThickness, xyz_Exner, xyr_Exner, xy_SurfTemp, xyr_HeatFlux, xyr_SoilHeatFlux, xy_SurfTempTransCoef, xyr_SoilTempTransCoef, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_SurfLatentHeatFlux, xyza_ArgTempMtx, xyz_ArgTempVec, xyaa_ArgSurfMtx, xy_ArgSurfRH, xyaa_ArgSoilTempMtx, xya_ArgSoilTempVec, xyz_DTempDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_LatHeatFluxBySeaIceMelt )

Subroutine :

xy_IndexCalcMethod(0:imax-1, 1:jmax) :

integer , intent(in )

:	Index for calculation method

xy_SeaIceThickness(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Sea ice thickness

xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in)

:	Exner 関数 (整数レベル). Exner function (full level)

xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	Exner 関数 (半整数レベル). Exner function (half level)

xy_SurfTemp(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	地表面温度. Surface temperature

xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	熱フラックス. Heat flux

xyr_SoilHeatFlux(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	土壌中の熱フラックス (W m-2) Heat flux in sub-surface soil (W m-2)

xy_SurfTempTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：温度. Transfer coefficient: temperature

xyr_SoilTempTransCoef(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	輸送係数：土壌温度. Transfer coefficient: soil temperature

xyr_RadSFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in )

:	短波 (日射) フラックス. Shortwave (insolation) flux

xyr_RadLFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in )

:	長波フラックス. Longwave flux

xyra_DelRadLFlux(0:imax-1, 1:jmax, 0:kmax, 0:1) :

real(DP), intent(in )

:	長波地表温度変化. Surface temperature tendency with longwave

xy_SurfLatentHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	惑星表面潜熱フラックス. Latent heat flux at the surface

xyza_ArgTempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1) :

real(DP), intent(in )

:	温度陰解行列. Implicit matrix about temperature

xyz_ArgTempVec(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in )

:	温度陰解ベクトル. Implicit vector about temperature

xyaa_ArgSurfMtx(0:imax-1, 1:jmax, 0:0, -1:1) :

real(DP), intent(in )

:	惑星表面エネルギー収支用陰解行列 Implicit matrix for surface energy balance

xy_ArgSurfRH(0:imax-1,1:jmax) : real(DP), intent(in )

xyaa_ArgSoilTempMtx(0:imax-1, 1:jmax, 1:kslmax,-1:1) :

real(DP), intent(in )

:	土壌温度拡散方程式の行列 Matrix for diffusion equation of soil temperature

xya_ArgSoilTempVec(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(in )

:	土壌温度拡散方程式のベクトル Vector for diffusion equation of soil temperature

xyz_DTempDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(inout)

:	$ DP{T}{t} $ . 温度変化. Temperature tendency

xy_DSurfTempDt(0:imax-1, 1:jmax) :

real(DP), intent(inout)

:	地表面温度変化率 (K s-1) Surface temperature tendency (K s-1)

xyz_DSoilTempDt(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(inout)

:	$ DP{Tg}{t} $ . 土壌温度変化 (K s-1) Temperature tendency (K s-1)

xy_LatHeatFluxBySeaIceMelt(0:imax-1, 1:jmax) : real(DP), intent(inout)

融雪による時間変化率の修正を行います.

Correction of tendencies due to melt of snow.

[Source]

  subroutine PhyImplSDHV5SeaIceCorrection( xy_IndexCalcMethod, xy_SeaIceThickness, xyz_Exner, xyr_Exner, xy_SurfTemp, xyr_HeatFlux, xyr_SoilHeatFlux, xy_SurfTempTransCoef, xyr_SoilTempTransCoef, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_SurfLatentHeatFlux, xyza_ArgTempMtx, xyz_ArgTempVec, xyaa_ArgSurfMtx, xy_ArgSurfRH, xyaa_ArgSoilTempMtx, xya_ArgSoilTempVec, xyz_DTempDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_LatHeatFluxBySeaIceMelt )
    !
    ! 融雪による時間変化率の修正を行います. 
    !
    ! Correction of tendencies due to melt of snow. 
    !

    ! モジュール引用 ; USE statements
    !

    ! ヒストリデータ出力
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! 時刻管理
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: CpDry
                              ! $ C_p $ [J kg-1 K-1]. 
                              ! 乾燥大気の定圧比熱. 
                              ! Specific heat of air at constant pressure

    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: TempCondWater      , SeaIceThermCondCoef, SeaIceVolHeatCap   , TempBelowSeaIce

    ! 陰解法による時間積分のためのルーチン
    ! Routines for time integration with implicit scheme
    !
    use phy_implicit_utils, only : PhyImplLUDecomp3, PhyImplLUSolve3

    ! 宣言文 ; Declaration statements
    !

    integer , intent(in   ) :: xy_IndexCalcMethod(0:imax-1, 1:jmax)
                              ! 
                              ! Index for calculation method
    real(DP), intent(in):: xy_SeaIceThickness(0:imax-1, 1:jmax)
                              !
                              ! Sea ice thickness
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner 関数 (整数レベル). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner 関数 (半整数レベル). 
                              ! Exner function (half level)

    real(DP), intent(in   ) :: xy_SurfTemp (0:imax-1, 1:jmax)
                              ! 地表面温度. 
                              ! Surface temperature

    real(DP), intent(in):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 熱フラックス. 
                              ! Heat flux
    real(DP), intent(in):: xyr_SoilHeatFlux (0:imax-1, 1:jmax, 0:kslmax)
                              ! 土壌中の熱フラックス (W m-2)
                              ! Heat flux in sub-surface soil (W m-2)

    real(DP), intent(in):: xy_SurfTempTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：温度. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xyr_SoilTempTransCoef (0:imax-1, 1:jmax, 0:kslmax)
                              ! 輸送係数：土壌温度.
                              ! Transfer coefficient: soil temperature

    real(DP), intent(in   ):: xyr_RadSFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 短波 (日射) フラックス. 
                              ! Shortwave (insolation) flux
    real(DP), intent(in   ):: xyr_RadLFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Longwave flux
    real(DP), intent(in   ):: xyra_DelRadLFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Surface temperature tendency with longwave

    real(DP), intent(in   ):: xy_SurfLatentHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面潜熱フラックス.
                              ! Latent heat flux at the surface

    real(DP), intent(in   ):: xyza_ArgTempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 温度陰解行列. 
                              ! Implicit matrix about temperature
    real(DP), intent(in   ):: xyz_ArgTempVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 温度陰解ベクトル. 
                              ! Implicit vector about temperature
    real(DP), intent(in   ):: xyaa_ArgSurfMtx(0:imax-1, 1:jmax, 0:0, -1:1)
                              ! 惑星表面エネルギー収支用陰解行列
                              ! Implicit matrix for surface energy balance
    real(DP), intent(in   ):: xy_ArgSurfRH(0:imax-1,1:jmax)


    real(DP), intent(in   ):: xyaa_ArgSoilTempMtx (0:imax-1, 1:jmax, 1:kslmax,-1:1)
                              ! 土壌温度拡散方程式の行列
                              ! Matrix for diffusion equation of soil temperature
    real(DP), intent(in   ):: xya_ArgSoilTempVec (0:imax-1, 1:jmax, 1:kslmax)
                              ! 土壌温度拡散方程式のベクトル
                              ! Vector for diffusion equation of soil temperature

    real(DP), intent(inout):: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . 温度変化. 
                              ! Temperature tendency
    real(DP), intent(inout) :: xy_DSurfTempDt (0:imax-1, 1:jmax)
                              ! 地表面温度変化率 (K s-1)
                              ! Surface temperature tendency (K s-1)
    real(DP), intent(inout):: xyz_DSoilTempDt (0:imax-1, 1:jmax, 1:kslmax)
                              ! $ \DP{Tg}{t} $ . 土壌温度変化 (K s-1)
                              ! Temperature tendency (K s-1)
    real(DP), intent(inout) :: xy_LatHeatFluxBySeaIceMelt(0:imax-1, 1:jmax)


    ! 作業変数
    ! Work variables
    !

    real(DP):: xyza_TempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 温度陰解行列. 
                              ! Implicit matrix about temperature
    real(DP):: xyz_TempVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 温度陰解ベクトル. 
                              ! Implicit vector about temperature
    real(DP):: xyaa_SurfMtx(0:imax-1, 1:jmax, 0:0, -1:1)
                              ! 惑星表面エネルギー収支用陰解行列
                              ! Implicit matrix for surface energy balance
    real(DP):: xy_SurfRH(0:imax-1,1:jmax)


    real(DP):: xyaa_SoilTempMtx (0:imax-1, 1:jmax, 1:kslmax,-1:1)
                              ! 土壌温度拡散方程式の行列
                              ! Matrix for diffusion equation of soil temperature
    real(DP):: xya_SoilTempVec (0:imax-1, 1:jmax, 1:kslmax)
                              ! 土壌温度拡散方程式のベクトル
                              ! Vector for diffusion equation of soil temperature
    real(DP):: xyaa_TempSoilTempLUMtx (0:imax-1, 1:jmax, -kslmax:kmax, -1:1)
                              ! LU 行列.
                              ! LU matrix
    real(DP):: xya_DelTempSoilTempLUVec (0:imax-1, 1:jmax, -kslmax:kmax)
                              ! $ T, Tg $ の時間変化.
                              ! Tendency of $ T $ and $ Tg |


    logical :: xy_FlagSeaIceMelt(0:imax-1, 1:jmax)

    real(DP) :: xy_TempCond(0:imax-1, 1:jmax)

    real(DP) :: SurfTempATentative

    real(DP) :: xy_SurfRadSFlux        (0:imax-1, 1:jmax)
    real(DP) :: xy_SurfRadLFlux        (0:imax-1, 1:jmax)
    real(DP) :: xy_SurfSoilHeatCondFlux(0:imax-1, 1:jmax)
    real(DP) :: xy_SurfSensHeatFlux    (0:imax-1, 1:jmax)
    real(DP) :: xy_SeaIceHeatCondFlux  (0:imax-1, 1:jmax)
    real(DP) :: xy_HeatingTendency     (0:imax-1, 1:jmax)


    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitude
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude
    integer:: k               ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction
    integer:: l


    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. phy_implicit_sdh_V5_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


!!$    ! 計算時間計測開始
!!$    ! Start measurement of computation time
!!$    !
!!$    call TimesetClockStart( module_name )


    !
    ! check flag of snow melt
    !
    if ( ( .not. FlagBucketModel ) .or. ( .not. FlagSnow ) ) then
!!$      xy_LatHeatFluxBySeaIceMelt = 0.0_DP
      return
    end if


    xy_TempCond = TempCondWater

    do j = 1, jmax
      do i = 0, imax-1

        SurfTempATentative = xy_SurfTemp(i,j) + xy_DSurfTempDt(i,j) * 2.0_DP * DelTime
        if ( ( xy_IndexCalcMethod(i,j) == IndexSeaIce ) .and. ( SurfTempATentative > xy_TempCond(i,j) ) ) then
          xy_FlagSeaIceMelt(i,j) = .true.
        else
          xy_FlagSeaIceMelt(i,j) = .false.
        end if

      end do
    end do


    xyza_TempMtx     = xyza_ArgTempMtx
    xyz_TempVec      = xyz_ArgTempVec
    !
    xyaa_SurfMtx     = xyaa_ArgSurfMtx
    xy_SurfRH        = xy_ArgSurfRH
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagSeaIceMelt(i,j) ) then
          xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
          xyaa_SurfMtx(i,j,0, 0) = 1.0_DP
          xyaa_SurfMtx(i,j,0, 1) = 0.0_DP
          xy_SurfRH   (i,j)      = xy_TempCond(i,j) - xy_SurfTemp(i,j)
        end if
      end do
    end do
    !
    xyaa_SoilTempMtx = xyaa_ArgSoilTempMtx
    xya_SoilTempVec = xya_ArgSoilTempVec



    ! 温度の計算
    ! Calculate temperature and specific humidity
    !
    do l = -1, 1
      do k = 1, kslmax
        xyaa_TempSoilTempLUMtx(:,:,-k,-l) = xyaa_SoilTempMtx(:,:,k,l)
      end do
      k = 0
      xyaa_TempSoilTempLUMtx(:,:, k, l) = xyaa_SurfMtx(:,:,0,l)
      do k = 1, kmax
        xyaa_TempSoilTempLUMtx(:,:, k, l) = xyza_TempMtx(:,:,k,l)
      end do
    end do

    call PhyImplLUDecomp3( xyaa_TempSoilTempLUMtx, imax * jmax, kmax + 1 + kslmax )

    do k = 1, kslmax
      xya_DelTempSoilTempLUVec(:,:,-k) = xya_SoilTempVec(:,:,k)
    end do
    k = 0
    xya_DelTempSoilTempLUVec(:,:,k) = xy_SurfRH
    do k = 1, kmax
      xya_DelTempSoilTempLUVec(:,:,k) = xyz_TempVec(:,:,k)
    end do

    call PhyImplLUSolve3( xya_DelTempSoilTempLUVec, xyaa_TempSoilTempLUMtx, 1, imax * jmax , kmax + 1 + kslmax )



    do k = 1, kslmax
      do j = 1, jmax
        do i = 0, imax-1

          if ( xy_FlagSeaIceMelt(i,j) ) then

            select case ( xy_IndexCalcMethod(i,j) )
!!$            case ( IndexLand )
!!$              xyz_DSoilTempDt(i,j,k) = &
!!$                & xya_DelTempSoilTempLUVec(i,j,-k) / ( 2.0_DP * DelTime )
            case default
              xyz_DSoilTempDt(i,j,k) = 0.0_DP
            end select

          end if

        end do
      end do
    end do
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_FlagSeaIceMelt(i,j) ) then
          select case ( xy_IndexCalcMethod(i,j) )
!!$          case ( IndexLand )
!!$            ! land
!!$            xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
          case ( IndexSeaIce )
            ! sea ice
            xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
!!$          case ( IndexSlabOcean )
!!$            ! slab ocean
!!$            xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
!!$          case ( IndexOceanPresSST )
!!$            ! open ocean
!!$            xy_DSurfTempDt(i,j) = 0.0_DP
          case default
            call MessageNotify( 'E', module_name, 'Unexpected Error.' )
          end select
        end if
      end do
    end do
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1

          if ( xy_FlagSeaIceMelt(i,j) ) then
            xyz_DTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,k) / ( 2.0_DP * DelTime )
          end if

        end do
      end do
    end do


    xy_SurfRadSFlux = xyr_RadSFlux(:,:,0)
    xy_SurfRadLFlux = xyr_RadLFlux(:,:,0) + xyra_DelRadLFlux(:,:,0,0) * xy_DSurfTempDt * ( 2.0_DP * DelTime ) + xyra_DelRadLFlux(:,:,0,1) * xyz_DTempDt(:,:,1) * ( 2.0_DP * DelTime )
    xy_SurfSoilHeatCondFlux = xyr_SoilHeatFlux(:,:,0) - xyr_SoilTempTransCoef(:,:,0) * ( xyz_DSoilTempDt(:,:,1) - xy_DSurfTempDt ) * ( 2.0_DP * DelTime )
    xy_SurfSensHeatFlux = xyr_HeatFlux(:,:,0) - CpDry * xyr_Exner(:,:,0) * xy_SurfTempTransCoef * ( xyz_DTempDt(:,:,1) / xyz_Exner(:,:,1) - xy_DSurfTempDt / xyr_Exner(:,:,0) ) * ( 2.0_DP * DelTime )
    xy_SeaIceHeatCondFlux = - SeaIceThermCondCoef * ( xy_SurfTemp + xy_DSurfTempDt * ( 2.0_DP * DelTime ) - TempBelowSeaIce ) / xy_SeaIceThickness
    xy_HeatingTendency = SeaIceVolHeatCap * xy_SeaIceThickness * xy_DSurfTempDt

    do j = 1, jmax
      do i = 0, imax-1

        if ( xy_FlagSeaIceMelt(i,j) ) then
          xy_LatHeatFluxBySeaIceMelt(i,j) = - ( ( xy_SurfRadSFlux(i,j) + xy_SurfRadLFlux(i,j) + xy_SurfSensHeatFlux(i,j) + xy_SurfLatentHeatFlux(i,j) ) - xy_SeaIceHeatCondFlux(i,j) ) - xy_HeatingTendency(i,j)
        end if

      end do
    end do


!!$    ! 計算時間計測一時停止
!!$    ! Pause measurement of computation time
!!$    !
!!$    call TimesetClockStop( module_name )


  end subroutine PhyImplSDHV5SeaIceCorrection

PhyImplSDHV5TendencyHeatCore( xy_IndexCalcMethod, xy_SeaIceThickness, xy_SOSeaIceMassB, xyr_HeatFlux, xyrf_QMixFlux, xy_SurfH2OVapFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xy_SurfTemp, xyz_SoilTemp, xyz_SOSeaIceTemp, xy_SurfHumidCoef, xy_SurfHeatCapacity, xy_SoilHeatCap, xy_SoilHeatDiffCoef, xyra_DelRadLFlux, xyr_Press, xyz_Exner, xyr_Exner, xyr_VelTransCoef, xyr_TempTransCoef, xyr_QMixTransCoef, xy_SurfVelTransCoef, xy_SurfTempTransCoef, xy_SurfQVapTransCoef, xyr_SoilTempTransCoef, xy_SOSILocalKMax, xyr_SOSILocalDepth, xyz_SOSILocalDepth, xyr_SOSIHeatTransCoef, xyr_SOSIHeatFlux, xy_SurfMajCompIceB, xy_SoilMoistB, xy_SurfSnowB, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DPsDt, xy_DSurfMajCompIceDt, xy_DSoilMoistDt, xy_DSurfSnowDt, xy_DSOSeaIceMassDtTop, xy_DSOSeaIceMassDtBot, xyz_DSOSeaIceTempDt )

Subroutine :

xy_IndexCalcMethod(0:imax-1, 1:jmax) :

integer , intent(in)

:	Index for calculation method

xy_SeaIceThickness(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Sea ice thickness

xy_SOSeaIceMassB(0:imax-1, 1:jmax) : real(DP), intent(in)

xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	熱フラックス. Heat flux

xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax) :

real(DP), intent(in)

:	比湿フラックス. Specific humidity flux

xy_SurfH2OVapFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	惑星表面水蒸気フラックス. Water vapor flux at the surface

xy_SurfLatentHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	惑星表面潜熱フラックス. Latent heat flux at the surface

xyr_SoilHeatFlux(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	土壌中の熱フラックス (W m-2) Heat flux in sub-surface soil (W m-2)

xyr_RadSFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	短波 (日射) フラックス. Shortwave (insolation) flux

xyr_RadLFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	長波フラックス. Longwave flux

xy_DeepSubSurfHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地中熱フラックス. "Deep subsurface heat flux" Heat flux at the bottom of surface/soil layer.

xy_SurfTemp(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表面温度. Surface temperature

xyz_SoilTemp(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(in)

:	土壌温度 (K) Soil temperature (K)

xyz_SOSeaIceTemp(0:imax-1, 1:jmax, 1:ksimax) :

real(DP), intent(in)

:	海氷温度 (K) Slab ocean sea ice temperature (K)

xy_SurfHumidCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表湿潤度. Surface humidity coefficient

xy_SurfHeatCapacity(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表熱容量. Surface heat capacity

xy_SoilHeatCap(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	土壌熱容量 (J K-1 m-3) Specific heat of soil (J K-1 m-3)

xy_SoilHeatDiffCoef(0:imax-1, 1:jmax) :

real(DP), intent(in )

:	土壌熱伝導係数 (J m-3 K-1) Heat conduction coefficient of soil (J m-3 K-1)

xyra_DelRadLFlux(0:imax-1, 1:jmax, 0:kmax, 0:1) :

real(DP), intent(in)

:	長波地表温度変化. Surface temperature tendency with longwave

xyr_Press(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	$ hat{p} $ . 気圧 (半整数レベル). Air pressure (half level)

xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in)

:	Exner 関数 (整数レベル). Exner function (full level)

xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	Exner 関数 (半整数レベル). Exner function (half level)

xyr_VelTransCoef(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	輸送係数：運動量. Transfer coefficient: velocity

xyr_TempTransCoef(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	輸送係数：温度. Transfer coefficient: temperature

xyr_QMixTransCoef(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	輸送係数：質量. Transfer coefficient: mass of constituents

xy_SurfVelTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：運動量. Diffusion coefficient: velocity

xy_SurfTempTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：温度. Transfer coefficient: temperature

xy_SurfQVapTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：比湿. Transfer coefficient: specific humidity

xyr_SoilTempTransCoef(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	輸送係数：土壌温度. Transfer coefficient: soil temperature

xy_SOSILocalKMax(0:imax-1, 1:jmax) : integer , intent(in)

xyr_SOSILocalDepth(0:imax-1, 1:jmax, 0:ksimax) : real(DP), intent(in)

xyz_SOSILocalDepth(0:imax-1, 1:jmax, 1:ksimax) : real(DP), intent(in)

xyr_SOSIHeatTransCoef(0:imax-1, 1:jmax, 0:ksimax) : real(DP), intent(in)

xyr_SOSIHeatFlux(0:imax-1, 1:jmax, 0:ksimax) : real(DP), intent(in)

xy_SurfMajCompIceB(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Surface major component ice amount.

xy_SoilMoistB(0:imax-1, 1:jmax) : real(DP), intent(in)

xy_SurfSnowB(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	積雪量. Surface snow amount.

xyz_DTempDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(out)

:	$ DP{T}{t} $ . 温度変化. Temperature tendency

xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :

real(DP), intent(out)

:	$ DP{q}{t} $ . 質量混合比変化. Mass mixing ratio tendency

xy_DSurfTempDt(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	地表面温度変化率 (K s-1) Surface temperature tendency (K s-1)

xyz_DSoilTempDt(0:imax-1, 1:jmax, 1:kslmax) :

real(DP), intent(out)

:	$ DP{Tg}{t} $ . 土壌温度変化 (K s-1) Temperature tendency (K s-1)

xy_DPsDt(0:imax-1, 1:jmax) : real(DP), intent(out)

xy_DSurfMajCompIceDt(0:imax-1, 1:jmax) : real(DP), intent(out)

xy_DSoilMoistDt(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	土壌温度時間変化率 (kg m-2 s-1) Soil temperature tendency (kg m-2 s-1)

xy_DSurfSnowDt(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	積雪率時間変化率 (kg m-2 s-1) Surface snow amount tendency (kg m-2 s-1)

xy_DSOSeaIceMassDtTop(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	海氷質量時間変化率 (kg m-2 s-1) Slab ocean sea ice mass tendency (kg m-2)

xy_DSOSeaIceMassDtBot(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	海氷質量時間変化率 (kg m-2 s-1) Slab ocean sea ice mass tendency (kg m-2)

xyz_DSOSeaIceTempDt(0:imax-1, 1:jmax, 1:ksimax) :

real(DP), intent(out)

:	$ DP{TSI}{t} $ . 海氷温度変化 (K s-1) Sea ice temperature tendency (K s-1)

時間変化率の計算を行います.

Calculate tendencies.

[Source]

  subroutine PhyImplSDHV5TendencyHeatCore( xy_IndexCalcMethod, xy_SeaIceThickness, xy_SOSeaIceMassB, xyr_HeatFlux, xyrf_QMixFlux, xy_SurfH2OVapFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xy_SurfTemp, xyz_SoilTemp, xyz_SOSeaIceTemp, xy_SurfHumidCoef, xy_SurfHeatCapacity, xy_SoilHeatCap, xy_SoilHeatDiffCoef, xyra_DelRadLFlux, xyr_Press, xyz_Exner, xyr_Exner, xyr_VelTransCoef, xyr_TempTransCoef, xyr_QMixTransCoef, xy_SurfVelTransCoef, xy_SurfTempTransCoef, xy_SurfQVapTransCoef, xyr_SoilTempTransCoef, xy_SOSILocalKMax, xyr_SOSILocalDepth, xyz_SOSILocalDepth, xyr_SOSIHeatTransCoef, xyr_SOSIHeatFlux, xy_SurfMajCompIceB, xy_SoilMoistB, xy_SurfSnowB, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DPsDt, xy_DSurfMajCompIceDt, xy_DSoilMoistDt, xy_DSurfSnowDt, xy_DSOSeaIceMassDtTop, xy_DSOSeaIceMassDtBot, xyz_DSOSeaIceTempDt )
    !
    ! 時間変化率の計算を行います. 
    !
    ! Calculate tendencies. 
    !

    ! モジュール引用 ; USE statements
    !

    ! 座標データ設定
    ! Axes data settings
    !
    use axesset, only: r_SSDepth, z_SSDepth         ! subsurface grid at midpoint of layer

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: Grav, CpDry, GasRDry
                              ! $ R $ [J kg-1 K-1]. 
                              ! 乾燥大気の気体定数. 
                              ! Gas constant of air

    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: TempCondWater, SeaIceVolHeatCap   , SeaIceThermCondCoef, TempBelowSeaIce

    ! 時刻管理
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop

    ! 陰解法による時間積分のためのルーチン
    ! Routines for time integration with implicit scheme
    !
    use phy_implicit_utils, only : PhyImplLUDecomp3, PhyImplLUSolve3

    ! 宣言文 ; Declaration statements
    !

    integer , intent(in):: xy_IndexCalcMethod (0:imax-1, 1:jmax)
                              ! 
                              ! Index for calculation method

    real(DP), intent(in):: xy_SeaIceThickness(0:imax-1, 1:jmax)
                              !
                              ! Sea ice thickness

    real(DP), intent(in) :: xy_SOSeaIceMassB(0:imax-1, 1:jmax)

    real(DP), intent(in):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 熱フラックス. 
                              ! Heat flux
    real(DP), intent(in):: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! 比湿フラックス. 
                              ! Specific humidity flux

    real(DP), intent(in):: xy_SurfH2OVapFlux(0:imax-1, 1:jmax)
                              ! 惑星表面水蒸気フラックス.
                              ! Water vapor flux at the surface
    real(DP), intent(in):: xy_SurfLatentHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面潜熱フラックス.
                              ! Latent heat flux at the surface

    real(DP), intent(in):: xyr_SoilHeatFlux (0:imax-1, 1:jmax, 0:kslmax)
                              ! 土壌中の熱フラックス (W m-2)
                              ! Heat flux in sub-surface soil (W m-2)

    real(DP), intent(in):: xyr_RadSFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 短波 (日射) フラックス. 
                              ! Shortwave (insolation) flux
    real(DP), intent(in):: xyr_RadLFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Longwave flux

    real(DP), intent(in):: xy_DeepSubSurfHeatFlux (0:imax-1, 1:jmax)
                              ! 地中熱フラックス. 
                              ! "Deep subsurface heat flux"
                              ! Heat flux at the bottom of surface/soil layer.
    real(DP), intent(in):: xy_SurfTemp (0:imax-1, 1:jmax)
                              ! 地表面温度. 
                              ! Surface temperature
    real(DP), intent(in):: xyz_SoilTemp (0:imax-1, 1:jmax, 1:kslmax)
                              ! 土壌温度 (K)
                              ! Soil temperature (K)
    real(DP), intent(in):: xyz_SOSeaIceTemp(0:imax-1, 1:jmax, 1:ksimax)
                              ! 海氷温度 (K)
                              ! Slab ocean sea ice temperature (K)
    real(DP), intent(in):: xy_SurfHumidCoef (0:imax-1, 1:jmax)
                              ! 地表湿潤度. 
                              ! Surface humidity coefficient
    real(DP), intent(in):: xy_SurfHeatCapacity (0:imax-1, 1:jmax)
                              ! 地表熱容量. 
                              ! Surface heat capacity
    real(DP), intent(in ):: xy_SoilHeatCap (0:imax-1, 1:jmax)
                              ! 土壌熱容量 (J K-1 m-3)
                              ! Specific heat of soil (J K-1 m-3)
    real(DP), intent(in ):: xy_SoilHeatDiffCoef (0:imax-1, 1:jmax)
                              ! 土壌熱伝導係数 (J m-3 K-1)
                              ! Heat conduction coefficient of soil (J m-3 K-1)

    real(DP), intent(in):: xyra_DelRadLFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Surface temperature tendency with longwave

    real(DP), intent(in):: xyr_Press (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . 気圧 (半整数レベル). 
                              ! Air pressure (half level)
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner 関数 (整数レベル). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner 関数 (半整数レベル). 
                              ! Exner function (half level)

    real(DP), intent(in):: xyr_VelTransCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 輸送係数：運動量. 
                              ! Transfer coefficient: velocity
    real(DP), intent(in):: xyr_TempTransCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 輸送係数：温度. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xyr_QMixTransCoef(0:imax-1, 1:jmax, 0:kmax)
                              ! 輸送係数：質量. 
                              ! Transfer coefficient: mass of constituents

    real(DP), intent(in):: xy_SurfVelTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：運動量. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(in):: xy_SurfTempTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：温度. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xy_SurfQVapTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：比湿. 
                              ! Transfer coefficient: specific humidity

    real(DP), intent(in):: xyr_SoilTempTransCoef (0:imax-1, 1:jmax, 0:kslmax)
                              ! 輸送係数：土壌温度.
                              ! Transfer coefficient: soil temperature

    integer , intent(in):: xy_SOSILocalKMax     (0:imax-1, 1:jmax)
    real(DP), intent(in):: xyr_SOSILocalDepth   (0:imax-1, 1:jmax, 0:ksimax)
    real(DP), intent(in):: xyz_SOSILocalDepth   (0:imax-1, 1:jmax, 1:ksimax)
    real(DP), intent(in):: xyr_SOSIHeatTransCoef(0:imax-1, 1:jmax, 0:ksimax)
    real(DP), intent(in):: xyr_SOSIHeatFlux     (0:imax-1, 1:jmax, 0:ksimax)

    real(DP), intent(in):: xy_SurfMajCompIceB  (0:imax-1, 1:jmax)
                              !
                              ! Surface major component ice amount.

    real(DP), intent(in):: xy_SoilMoistB(0:imax-1, 1:jmax)
    real(DP), intent(in):: xy_SurfSnowB (0:imax-1, 1:jmax)
                              ! 積雪量.
                              ! Surface snow amount.

    real(DP), intent(out):: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . 温度変化. 
                              ! Temperature tendency
    real(DP), intent(out):: xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ \DP{q}{t} $ . 質量混合比変化. 
                              ! Mass mixing ratio tendency
    real(DP), intent(out):: xy_DSurfTempDt (0:imax-1, 1:jmax)
                              ! 地表面温度変化率 (K s-1)
                              ! Surface temperature tendency (K s-1)
    real(DP), intent(out):: xyz_DSoilTempDt (0:imax-1, 1:jmax, 1:kslmax)
                              ! $ \DP{Tg}{t} $ . 土壌温度変化 (K s-1)
                              ! Temperature tendency (K s-1)

    real(DP), intent(out):: xy_DPsDt            (0:imax-1, 1:jmax)
    real(DP), intent(out):: xy_DSurfMajCompIceDt(0:imax-1, 1:jmax)

    real(DP), intent(out):: xy_DSoilMoistDt (0:imax-1, 1:jmax)
                              ! 土壌温度時間変化率 (kg m-2 s-1)
                              ! Soil temperature tendency (kg m-2 s-1)
    real(DP), intent(out):: xy_DSurfSnowDt (0:imax-1, 1:jmax)
                              ! 積雪率時間変化率 (kg m-2 s-1)
                              ! Surface snow amount tendency (kg m-2 s-1)
    real(DP), intent(out):: xy_DSOSeaIceMassDtTop(0:imax-1, 1:jmax)
                              ! 海氷質量時間変化率 (kg m-2 s-1)
                              ! Slab ocean sea ice mass tendency (kg m-2)
    real(DP), intent(out):: xy_DSOSeaIceMassDtBot(0:imax-1, 1:jmax)
                              ! 海氷質量時間変化率 (kg m-2 s-1)
                              ! Slab ocean sea ice mass tendency (kg m-2)
    real(DP), intent(out):: xyz_DSOSeaIceTempDt(0:imax-1, 1:jmax, 1:ksimax)
                              ! $ \DP{TSI}{t} $ . 海氷温度変化 (K s-1)
                              ! Sea ice temperature tendency (K s-1)

    ! 作業変数
    ! Work variables
    !
    real(DP):: xyza_TempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 温度陰解行列. 
                              ! Implicit matrix about temperature
    real(DP):: xyz_TempVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 温度陰解ベクトル. 
                              ! Implicit vector about temperature
    real(DP):: xyza_QMixMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 質量混合比陰解行列. 
                              ! Implicit matrix about mass mixing ratio
    real(DP):: xyzf_QMixVec(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! 質量混合比陰解ベクトル. 
                              ! Implicit vector about mass mixing ratio
    real(DP):: xyaa_SurfMtx(0:imax-1, 1:jmax, 0:0, -1:1)
                              ! 惑星表面エネルギー収支用陰解行列
                              ! Implicit matrix for surface energy balance

    real(DP):: xy_SurfRH(0:imax-1,1:jmax)


!!$    real(DP):: xyza_TempQVapLUMtx (0:imax-1, 1:jmax, -kmax:kmax, -1:1)
!!$                              ! LU 行列. 
!!$                              ! LU matrix
!!$    real(DP):: xyz_DelTempQVap (0:imax-1, 1:jmax, -kmax:kmax)
!!$                              ! $ T q $ の時間変化. 
!!$                              ! Tendency of $ T q $ 
!!$
!!$    real(DP):: xyza_TempLUMtx (0:imax-1, 1:jmax, 0:kmax, -1:1)
!!$                              ! LU 行列.
!!$                              ! LU matrix
!!$    real(DP):: xyz_DelTempLUVec (0:imax-1, 1:jmax, 0:kmax)
!!$                              ! $ T q $ の時間変化.
!!$                              ! Tendency of $ T q $
    real(DP):: xyza_QMixLUMtx (0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! LU 行列.
                              ! LU matrix
    real(DP):: xyz_DelQMixLUVec (0:imax-1, 1:jmax, 1:kmax)
                              ! $ q $ の時間変化.
                              ! Tendency of $ q $

    real(DP):: xyaa_SoilTempMtx (0:imax-1, 1:jmax, 1:kslmax, -1:1)
                              ! 土壌温度拡散方程式の行列
                              ! Matrix for diffusion equation of soil temperature
    real(DP):: xya_SoilTempVec (0:imax-1, 1:jmax, 1:kslmax)
                              ! 土壌温度拡散方程式のベクトル
                              ! Vector for diffusion equation of soil temperature
    real(DP):: xyaa_SOSITempMtx(0:imax-1, 1:jmax, 1:ksimax, -1:1)
                              ! 海氷温度拡散方程式の行列
                              ! Matrix for diffusion equation of soil temperature
    real(DP):: xya_SOSITempVec (0:imax-1, 1:jmax, 1:ksimax)
                              ! 海氷温度拡散方程式のベクトル
                              ! Vector for diffusion equation of soil temperature
    real(DP):: xyaa_TempSoilTempLUMtx (0:imax-1, 1:jmax, -kslmax:kmax, -1:1)
                              ! LU 行列.
                              ! LU matrix
    real(DP):: xya_DelTempSoilTempLUVec (0:imax-1, 1:jmax, -kslmax:kmax)
                              ! $ T, Tg $ の時間変化.
                              ! Tendency of $ T $ and $ Tg |


    real(DP):: SurfSnowATentative
                              ! 積雪量の仮の値 (kg m-2)
                              ! pseudo value of surface snow amount (kg m-2)

    real(DP):: xy_LatHeatFluxByMajCompIceSubl(0:imax-1, 1:jmax)
                              !
                              ! Latent heat flux by major component ice sublimation
                              ! (variable only for debug)
    real(DP):: xy_LatHeatFluxBySnowMelt(0:imax-1, 1:jmax)
                              !
                              ! Latent heat flux by melt
                              ! (variable only for debug)
    real(DP):: xy_LatHeatFluxBySeaIceMelt(0:imax-1, 1:jmax)
                              !
                              ! Latent heat flux by sea ice melt
                              ! (variable only for debug)

    real(DP):: xy_SurfMajCompLiqB      (0:imax-1, 1:jmax)
    real(DP):: xy_LatHeatFluxByOtherSpc(0:imax-1, 1:jmax)

    real(DP):: xy_DAtmMassDt(0:imax-1, 1:jmax)

    logical:: xy_FlagSOSeaIceAllMelt     (0:imax-1, 1:jmax)
    logical:: xy_FlagSOSIWoSIOceanAllFreeze(0:imax-1, 1:jmax)
    logical:: xy_FlagSOSIWSIOceanAllFreeze (0:imax-1, 1:jmax)

    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitude
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude
    integer:: k               ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction
    integer:: l               ! 行列用 DO ループ用作業変数
                              ! Work variables for DO loop of matrices
    integer:: n               ! 組成方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in dimension of constituents

    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. phy_implicit_sdh_V5_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


!!$    ! 計算時間計測開始
!!$    ! Start measurement of computation time
!!$    !
!!$    call TimesetClockStart( module_name )



!!$    if ( .not. FlagSSModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagSSModel has to be true.' )
!!$    end if

    ! FlagBucketModel は関係ないよね?
    ! SSModel 強制にした時点で, 水蒸気は地面と分離したから. 
!!$    if ( .not. FlagBucketModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagBucketModel has to be true.' )
!!$    end if



    ! 陰解法のための行列作成
    ! Create matrices for implicit scheme
    !

    ! 鉛直拡散スキームの輸送係数から陰解行列の計算 (温度)
    ! Calculate implicit matrices from transfer coefficient of vertical diffusion scheme (temperature)
    !
    k = 1
    xyza_TempMtx(:,:,k,-1) = - CpDry * xy_SurfTempTransCoef(:,:)
    xyza_TempMtx(:,:,k, 0) = - CpDry * ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + CpDry * xyr_Exner(:,:,k-1) / xyz_Exner(:,:,k  ) * xy_SurfTempTransCoef(:,:) + CpDry * xyr_Exner(:,:,k  ) / xyz_Exner(:,:,k  ) * xyr_TempTransCoef(:,:,k  )
    xyza_TempMtx(:,:,k, 1) = - CpDry * xyr_Exner(:,:,k  ) / xyz_Exner(:,:,k+1) * xyr_TempTransCoef(:,:,k  )

    do k = 2, kmax-1
      xyza_TempMtx(:,:,k,-1) = - CpDry * xyr_Exner(:,:,k-1) / xyz_Exner(:,:,k-1) * xyr_TempTransCoef(:,:,k-1)
      xyza_TempMtx(:,:,k, 0) = - CpDry * ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + CpDry * xyr_Exner(:,:,k-1) / xyz_Exner(:,:,k  ) * xyr_TempTransCoef(:,:,k-1) + CpDry * xyr_Exner(:,:,k  ) / xyz_Exner(:,:,k  ) * xyr_TempTransCoef(:,:,k  )
      xyza_TempMtx(:,:,k, 1) = - CpDry * xyr_Exner(:,:,k  ) / xyz_Exner(:,:,k+1) * xyr_TempTransCoef(:,:,k  )
    end do

    k = kmax
    xyza_TempMtx(:,:,k,-1) = - CpDry * xyr_Exner(:,:,k-1) / xyz_Exner(:,:,k-1) * xyr_TempTransCoef(:,:,k-1)
    xyza_TempMtx(:,:,k, 0) = - CpDry * ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + CpDry * xyr_Exner(:,:,k-1) / xyz_Exner(:,:,k  ) * xyr_TempTransCoef(:,:,k-1)
    xyza_TempMtx(:,:,k, 1) = 0.0_DP

    do k = 1, kmax
      xyz_TempVec(:,:,k) = - ( xyr_HeatFlux(:,:,k) - xyr_HeatFlux(:,:,k-1) )
    end do


    ! 鉛直拡散スキームの輸送係数から陰解行列の計算 (比湿)
    ! Calculate implicit matrices from transfer coefficient of vertical diffusion scheme (specific humidity)
    !

    k = 1
    xyza_QMixMtx(:,:,k,-1) = 0.0_DP
    xyza_QMixMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_QMixTransCoef(:,:,k  )
    xyza_QMixMtx(:,:,k, 1) = - xyr_QMixTransCoef(:,:,k  )

    do k = 2, kmax-1
      xyza_QMixMtx(:,:,k,-1) = - xyr_QMixTransCoef(:,:,k-1)
      xyza_QMixMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_QMixTransCoef(:,:,k-1) + xyr_QMixTransCoef(:,:,k  )
      xyza_QMixMtx(:,:,k, 1) = - xyr_QMixTransCoef(:,:,k  )
    end do

    k = kmax
    xyza_QMixMtx(:,:,k,-1) = - xyr_QMixTransCoef(:,:,k-1)
    xyza_QMixMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_QMixTransCoef(:,:,k-1)
    xyza_QMixMtx(:,:,k, 1) = 0.0_DP

    do n = 1, ncmax
      if ( n == IndexH2OVap ) then
        do k = 1, 1
          xyzf_QMixVec(:,:,k,n) = - ( xyrf_QMixFlux(:,:,k,n) - xy_SurfH2OVapFlux )
        end do
        do k = 1+1, kmax
          xyzf_QMixVec(:,:,k,n) = - ( xyrf_QMixFlux(:,:,k,n) - xyrf_QMixFlux(:,:,k-1,n) )
        end do
      else
        do k = 1, kmax
          xyzf_QMixVec(:,:,k,n) = - ( xyrf_QMixFlux(:,:,k,n) - xyrf_QMixFlux(:,:,k-1,n) )
        end do
      end if
    end do



    ! 土壌温度計算用の輸送係数から陰解行列の計算 (土壌温度)
    ! Calculate implicit matrices by using transfer coefficient (soil temperature)
    !
    if ( kslmax /= 0 ) then ! xyr_SoilTempMtx is not used when kslmax = 0.

      do k = 1, kslmax-1
        xyaa_SoilTempMtx(:,:,k,-1) = - xyr_SoilTempTransCoef(:,:,k-1)
        xyaa_SoilTempMtx(:,:,k, 0) = xy_SoilHeatCap(:,:) * ( r_SSDepth(k) - r_SSDepth(k-1) ) / ( 2.0_DP * DelTime ) + xyr_SoilTempTransCoef(:,:,k-1) + xyr_SoilTempTransCoef(:,:,k  )
        xyaa_SoilTempMtx(:,:,k, 1) = - xyr_SoilTempTransCoef(:,:,k  )
      end do

      k = kslmax
      xyaa_SoilTempMtx(:,:,k,-1) = - xyr_SoilTempTransCoef(:,:,k-1)
      xyaa_SoilTempMtx(:,:,k, 0) = xy_SoilheatCap(:,:) * ( r_SSDepth(k) - r_SSDepth(k-1) ) / ( 2.0_DP * DelTime ) + xyr_SoilTempTransCoef(:,:,k-1)
      xyaa_SoilTempMtx(:,:,k, 1) = 0.0_DP

    end if

    do k = 1, kslmax
      xya_SoilTempVec (:,:,k) = - ( xyr_SoilHeatFlux(:,:,k) - xyr_SoilHeatFlux(:,:,k-1) )
    end do


    ! Matrix and vector for sea ice on a slab ocean
    if ( ksimax /= 0 ) then ! xyr_SOSITempMtx is not used when ksimax = 0.

      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_SOSILocalKMax(i,j) == 0 ) then
            do k = 1, ksimax
              xyaa_SOSITempMtx(i,j,k,-1) = -1.0e100_DP
              xyaa_SOSITempMtx(i,j,k, 0) = -1.0e100_DP
              xyaa_SOSITempMtx(i,j,k, 1) = -1.0e100_DP
            end do
          else
            do k = 1, xy_SOSILocalKMax(i,j)-1
              xyaa_SOSITempMtx(i,j,k,-1) = - xyr_SOSIHeatTransCoef(i,j,k-1)
              xyaa_SOSITempMtx(i,j,k, 0) = SeaIceVolHeatCap * ( xyr_SOSILocalDepth(i,j,k) - xyr_SOSILocalDepth(i,j,k-1) ) / ( 2.0_DP * DelTime ) + xyr_SOSIHeatTransCoef(i,j,k-1) + xyr_SOSIHeatTransCoef(i,j,k  )
              xyaa_SOSITempMtx(i,j,k, 1) = - xyr_SOSIHeatTransCoef(i,j,k  )
            end do
            do k = xy_SOSILocalKMax(i,j), xy_SOSILocalKMax(i,j)
              xyaa_SOSITempMtx(i,j,k,-1) = - xyr_SOSIHeatTransCoef(i,j,k-1)
              xyaa_SOSITempMtx(i,j,k, 0) = SeaIceVolHeatCap * ( xyr_SOSILocalDepth(i,j,k) - xyr_SOSILocalDepth(i,j,k-1) ) / ( 2.0_DP * DelTime ) + xyr_SOSIHeatTransCoef(i,j,k-1) + xyr_SOSIHeatTransCoef(i,j,k  )
              xyaa_SOSITempMtx(i,j,k, 1) = 0.0_DP
            end do
            do k = xy_SOSILocalKMax(i,j)+1, ksimax
              xyaa_SOSITempMtx(i,j,k,-1) = 0.0_DP
              xyaa_SOSITempMtx(i,j,k, 0) = 1.0_DP
              xyaa_SOSITempMtx(i,j,k, 1) = 0.0_DP
            end do
          end if
        end do
      end do
      do j = 1, jmax
        do i = 0, imax-1
          if ( xy_SOSILocalKMax(i,j) == 0 ) then
            do k = 1, ksimax
              xya_SOSITempVec (i,j,k) = -1.0e100_DP
            end do
          else
            do k = 1, xy_SOSILocalKMax(i,j)
              xya_SOSITempVec (i,j,k) = - ( xyr_SOSIHeatFlux(i,j,k) - xyr_SOSIHeatFlux(i,j,k-1) )
            end do
            do k = xy_SOSILocalKMax(i,j)+1, ksimax
              xya_SOSITempVec (i,j,k) = 0.0_DP
            end do
          end if
        end do
      end do

    end if

    ! Pack matrix and vector
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexSlabOceanSeaIce )
          do k = 1, xy_SOSILocalKMax(i,j)
            xyaa_SoilTempMtx(i,j,k,-1) = xyaa_SOSITempMtx(i,j,k,-1)
            xyaa_SoilTempMtx(i,j,k, 0) = xyaa_SOSITempMtx(i,j,k, 0)
            xyaa_SoilTempMtx(i,j,k, 1) = xyaa_SOSITempMtx(i,j,k, 1)
            xya_SoilTempVec (i,j,k)    = xya_SOSITempVec (i,j,k)
          end do
          do k = xy_SOSILocalKMax(i,j)+1, kslmax
            xyaa_SoilTempMtx(i,j,k,-1) = 0.0_DP
            xyaa_SoilTempMtx(i,j,k, 0) = 1.0_DP
            xyaa_SoilTempMtx(i,j,k, 1) = 0.0_DP
            xya_SoilTempVec (i,j,k)    = 0.0_DP
          end do
        end select
      end do
    end do


    ! 地表面過程の輸送係数から陰解行列の計算
    ! Calculate implicit matrices from transfer coefficient of surface process
    !
    do i = 0, imax-1
      do j = 1, jmax
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
          xyaa_SurfMtx(i,j,0,-1) = xyr_SoilTempTransCoef(i,j,0)
          xyaa_SurfMtx(i,j,0, 0) = xy_SurfHeatCapacity(i,j) / ( 2.0_DP * DelTime ) + CpDry * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,0) - xyr_SoilTempTransCoef(i,j,0)
          xyaa_SurfMtx(i,j,0, 1) = - CpDry * xyr_Exner(i,j,0) / xyz_Exner(i,j,1) * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,1)
        case ( IndexSeaIce )
          ! sea ice
          xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
          xyaa_SurfMtx(i,j,0, 0) = SeaIceVolHeatCap * xy_SeaIceThickness(i,j) / ( 2.0_DP * DelTime ) + CpDry * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,0) + SeaIceThermCondCoef / xy_SeaIceThickness(i,j)
          xyaa_SurfMtx(i,j,0, 1) = - CpDry * xyr_Exner(i,j,0) / xyz_Exner(i,j,1) * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,1)
        case ( IndexSlabOcean )
          ! slab ocean
          xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
          xyaa_SurfMtx(i,j,0, 0) = SOHeatCapacity / ( 2.0_DP * DelTime ) + CpDry * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,0)
          xyaa_SurfMtx(i,j,0, 1) = - CpDry * xyr_Exner(i,j,0) / xyz_Exner(i,j,1) * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,1)
        case ( IndexSlabOceanSeaIce )
          ! sea ice on a slab ocean
          xyaa_SurfMtx(i,j,0,-1) = xyr_SOSIHeatTransCoef(i,j,0)
          xyaa_SurfMtx(i,j,0, 0) = xy_SurfHeatCapacity(i,j) / ( 2.0_DP * DelTime ) + CpDry * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,0) - xyr_SOSIHeatTransCoef(i,j,0)
          xyaa_SurfMtx(i,j,0, 1) = - CpDry * xyr_Exner(i,j,0) / xyz_Exner(i,j,1) * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,1)
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
          xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
          xyaa_SurfMtx(i,j,0, 0) = 1.0_DP
          xyaa_SurfMtx(i,j,0, 1) = 0.0_DP
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
        end select

      end do
    end do

    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
          xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - xy_SurfLatentHeatFlux(i,j) + xyr_SoilHeatFlux(i,j,0)
        case ( IndexSeaIce )
          ! sea ice
          xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - xy_SurfLatentHeatFlux(i,j) - SeaIceThermCondCoef * ( xy_SurfTemp(i,j) - TempBelowSeaIce ) / xy_SeaIceThickness(i,j)
        case ( IndexSlabOcean )
          ! slab ocean
          xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - xy_SurfLatentHeatFlux(i,j)                       !&
!              & + xy_DeepSubSurfHeatFlux(i,j)
        case ( IndexSlabOceanSeaIce )
          ! sea ice on a slab ocean
          xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - xy_SurfLatentHeatFlux(i,j) + xyr_SOSIHeatFlux(i,j,0)
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
          xy_SurfRH(i,j) = 0.0_DP
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
        end select
      end do
    end do


    ! 温度と比湿の計算
    ! Calculate temperature and specific humidity
    !

    do l = -1, 1
      do k = 1, kslmax
        xyaa_TempSoilTempLUMtx(:,:,-k,-l) = xyaa_SoilTempMtx(:,:,k,l)
      end do
      k = 0
      xyaa_TempSoilTempLUMtx(:,:, k, l) = xyaa_SurfMtx(:,:,0,l)
      do k = 1, kmax
        xyaa_TempSoilTempLUMtx(:,:, k, l) = xyza_TempMtx(:,:,k,l)
      end do
    end do

    call PhyImplLUDecomp3( xyaa_TempSoilTempLUMtx, imax * jmax, kmax + 1 + kslmax )

    do k = 1, kslmax
      xya_DelTempSoilTempLUVec(:,:,-k) = xya_SoilTempVec(:,:,k)
    end do
    k = 0
    xya_DelTempSoilTempLUVec(:,:,k) = xy_SurfRH
    do k = 1, kmax
      xya_DelTempSoilTempLUVec(:,:,k) = xyz_TempVec(:,:,k)
    end do

    call PhyImplLUSolve3( xya_DelTempSoilTempLUVec, xyaa_TempSoilTempLUMtx, 1, imax * jmax , kmax + 1 + kslmax )

    do k = 1, kslmax
      do j = 1, jmax
        do i = 0, imax-1
          select case ( xy_IndexCalcMethod(i,j) )
          case ( IndexLand )
            xyz_DSoilTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,-k) / ( 2.0_DP * DelTime )
          case default
            xyz_DSoilTempDt(i,j,k) = 0.0_DP
          end select
        end do
      end do
    end do
    do k = 1, ksimax
      do j = 1, jmax
        do i = 0, imax-1
          select case ( xy_IndexCalcMethod(i,j) )
          case ( IndexSlabOceanSeaIce )
            xyz_DSOSeaIceTempDt(i,j,k) = xya_DelTempSoilTempLUVec(i,j,-k) / ( 2.0_DP * DelTime )
          case default
            xyz_DSOSeaIceTempDt(i,j,k) = 0.0_DP
          end select
        end do
      end do
    end do
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
          xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
        case ( IndexSeaIce )
          ! sea ice
          xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
        case ( IndexSlabOcean )
          ! slab ocean
          xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
        case ( IndexSlabOceanSeaIce )
          ! sea ice on a slab ocean
          xy_DSurfTempDt(i,j) = xya_DelTempSoilTempLUVec(i,j,0) / ( 2.0_DP * DelTime )
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
          xy_DSurfTempDt(i,j) = 0.0_DP
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
        end select
      end do
    end do
    do k = 1, kmax
      xyz_DTempDt(:,:,k) = xya_DelTempSoilTempLUVec(:,:,k) / ( 2.0_DP * DelTime )
    end do


    !
    ! Calculation of tendencies of soil moisture and surface snow amount
    !
    if ( FlagBucketModel ) then
      if ( FlagSnow ) then
        ! Evaporation is subtracted from surface snow and soil moisture
        !
        do j = 1, jmax
          do i = 0, imax-1

!!$            if ( xyrf_QMixFlux(i,j,0,IndexH2OVap) >= 0.0_DP ) then
            if ( xy_SurfH2OVapFlux(i,j) >= 0.0_DP ) then

!!$              xy_DSurfSnowDt(i,j) = - xyrf_QMixFlux(i,j,0,IndexH2OVap)
              xy_DSurfSnowDt(i,j) = - xy_SurfH2OVapFlux(i,j)
              SurfSnowATentative = xy_SurfSnowB(i,j) + xy_DSurfSnowDt(i,j) * 2.0_DP * DelTime
              if ( SurfSnowATentative < 0.0_DP ) then
                xy_DSoilMoistDt(i,j) = SurfSnowATentative / ( 2.0_DP * DelTime )
                xy_DSurfSnowDt (i,j) = - xy_SurfSnowB(i,j) / ( 2.0_DP * DelTime )
              else
                xy_DSoilMoistDt(i,j) = 0.0_DP
              end if

            else

              if ( xy_SurfSnowB(i,j) > 0.0_DP ) then
!!$                xy_DSurfSnowDt (i,j) = - xyrf_QMixFlux(i,j,0,IndexH2OVap)
                xy_DSurfSnowDt (i,j) = - xy_SurfH2OVapFlux(i,j)
                xy_DSoilMoistDt(i,j) = 0.0_DP
              else
                xy_DSurfSnowDt (i,j) = 0.0_DP
!!$                xy_DSoilMoistDt(i,j) = - xyrf_QMixFlux(i,j,0,IndexH2OVap)
                xy_DSoilMoistDt(i,j) = - xy_SurfH2OVapFlux(i,j)
              end if

            end if

          end do
        end do
      else
        ! Evaporation is subtracted from soil moisture
        !
!!$        xy_DSoilMoistDt = - xyrf_QMixFlux(:,:,0,IndexH2OVap)
        xy_DSoilMoistDt = - xy_SurfH2OVapFlux
        xy_DSurfSnowDt  = 0.0_DP
      end if
    else
      xy_DSoilMoistDt = 0.0_DP
      xy_DSurfSnowDt  = 0.0_DP
    end if


    ! Temporarily set
    !
    xy_DSurfMajCompIceDt = 0.0_DP



    if ( FlagMajCompPhaseChange ) then

      xy_DAtmMassDt        = 0.0_DP
      xy_DSurfMajCompIceDt = 0.0_DP
      ! Dummy values
      !
      xy_SurfMajCompLiqB       = 0.0_DP
      xy_LatHeatFluxByOtherSpc = 0.0_DP

      call PhyImplSDHV5IceSnowPhaseChgCor( IndexSpcMajComp, xyr_Press(:,:,0), xyr_HeatFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xyr_SoilTempTransCoef, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xy_SurfTemp, xyz_SoilTemp, xy_SurfMajCompLiqB, xy_SurfMajCompIceB, xy_SurfHeatCapacity, xy_SoilHeatCap, xy_SoilHeatDiffCoef, xy_IndexCalcMethod, xyra_DelRadLFlux, xyz_Exner, xyr_Exner, xy_SurfTempTransCoef, xy_LatHeatFluxByOtherSpc, xyza_TempMtx, xyz_TempVec, xyaa_SurfMtx, xy_SurfRH, xyaa_SoilTempMtx, xya_SoilTempVec, xyz_DTempDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DAtmMassDt, xy_DSurfMajCompIceDt, xy_LatHeatFluxByMajCompIceSubl )

    else
      xy_DAtmMassDt                  = 0.0_DP
      xy_LatHeatFluxByMajCompIceSubl = 0.0_DP
    end if

    xy_DPsDt = xy_DAtmMassDt * Grav

    xy_LatHeatFluxByOtherSpc = xy_LatHeatFluxByMajCompIceSubl

    if ( FlagSublimation ) then
      ! If sublimation is considered, the melt of snow/ice is not calculated.
      xy_LatHeatFluxBySnowMelt = 0.0_DP
    else
      ! Else, the melt of snow/ice is calculated.
      call PhyImplSDHV5IceSnowPhaseChgCor( IndexSpcH2O, xyr_Press(:,:,0), xyr_HeatFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xyr_SoilTempTransCoef, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xy_SurfTemp, xyz_SoilTemp, xy_SoilMoistB, xy_SurfSnowB, xy_SurfHeatCapacity, xy_SoilHeatCap, xy_SoilHeatDiffCoef, xy_IndexCalcMethod, xyra_DelRadLFlux, xyz_Exner, xyr_Exner, xy_SurfTempTransCoef, xy_LatHeatFluxByOtherSpc, xyza_TempMtx, xyz_TempVec, xyaa_SurfMtx, xy_SurfRH, xyaa_SoilTempMtx, xya_SoilTempVec, xyz_DTempDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DSoilMoistDt, xy_DSurfSnowDt, xy_LatHeatFluxBySnowMelt )
    end if


    xy_LatHeatFluxBySeaIceMelt = 0.0_DP
    !
    ! Correction of temperature when prescribed sea ice is present.
    !
    call PhyImplSDHV5SeaIceCorrection( xy_IndexCalcMethod, xy_SeaIceThickness, xyz_Exner, xyr_Exner, xy_SurfTemp, xyr_HeatFlux, xyr_SoilHeatFlux, xy_SurfTempTransCoef, xyr_SoilTempTransCoef, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_SurfLatentHeatFlux, xyza_TempMtx, xyz_TempVec, xyaa_SurfMtx, xy_SurfRH, xyaa_SoilTempMtx, xya_SoilTempVec, xyz_DTempDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_LatHeatFluxBySeaIceMelt )
    !
    ! Correction of temperature when slab sea ice and/or slab ocean are present
    !
    call PhyImplSDHV5SOSeaIceCorrection( xy_IndexCalcMethod, xy_SurfHeatCapacity, xy_SOSeaIceMassB, xy_SeaIceThickness, xyz_Exner, xyr_Exner, xy_SurfTemp, xyz_SOSeaIceTemp, xyr_HeatFlux, xyr_SoilHeatFlux, xy_SurfTempTransCoef, xyr_SoilTempTransCoef, xy_SOSILocalKMax, xyr_SOSILocalDepth, xyr_SOSIHeatTransCoef, xyr_SOSIHeatFlux, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_SurfLatentHeatFlux, xyza_TempMtx, xyz_TempVec, xyaa_SurfMtx, xy_SurfRH, xyaa_SoilTempMtx, xya_SoilTempVec, xyaa_SOSITempMtx, xya_SOSITempVec, xyz_DTempDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DSOSeaIceMassDtTop, xy_DSOSeaIceMassDtBot, xyz_DSOSeaIceTempDt, xy_LatHeatFluxBySeaIceMelt, xy_FlagSOSeaIceAllMelt, xy_FlagSOSIWoSIOceanAllFreeze, xy_FlagSOSIWSIOceanAllFreeze )


    do l = -1, 1
      do k = 1, kmax
        xyza_QMixLUMtx(:,:,k,l) = xyza_QMixMtx(:,:,k,l)
      end do
    end do

    call PhyImplLUDecomp3( xyza_QMixLUMtx, imax * jmax, kmax )

    do n = 1, ncmax
      do k = 1, kmax
        xyz_DelQMixLUVec(:,:,k) = xyzf_QMixVec(:,:,k,n)
      end do

      call PhyImplLUSolve3( xyz_DelQMixLUVec, xyza_QMixLUMtx, 1, imax * jmax , kmax )

      do k = 1, kmax
        xyzf_DQMixDt(:,:,k,n) = xyz_DelQMixLUVec(:,:,k) / ( 2.0_DP * DelTime )
      end do
    end do



    ! Debug routine
    !
    call PhyImplSDHV5ChkConservation( xy_IndexCalcMethod, xy_FlagSOSeaIceAllMelt, xy_FlagSOSIWoSIOceanAllFreeze, xy_FlagSOSIWSIOceanAllFreeze, xy_SeaIceThickness, xy_SOSeaIceMassB, xyr_Press, xyz_Exner, xyr_Exner, xy_SurfTemp, xy_SurfHeatCapacity, xy_SoilHeatCap, xyr_HeatFlux, xy_SurfH2OVapFlux, xy_SurfLatentHeatFlux, xyr_SoilHeatFlux, xy_SurfTempTransCoef, xyr_SoilTempTransCoef, xyr_SOSIHeatTransCoef, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_LatHeatFluxByMajCompIceSubl, xy_LatHeatFluxBySnowMelt, xy_LatHeatFluxBySeaIceMelt, xy_DeepSubSurfHeatFlux, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt, xyz_DSoilTempDt, xy_DSoilMoistDt, xy_DSurfSnowDt, xy_DPsDt, xy_DSurfMajCompIceDt, xy_SOSILocalKMax, xyr_SOSILocalDepth, xyz_SOSeaIceTemp, xyz_DSOSeaIceTempDt, xy_DSOSeaIceMassDtTop, xy_DSOSeaIceMassDtBot )


!!$    ! 計算時間計測一時停止
!!$    ! Pause measurement of computation time
!!$    !
!!$    call TimesetClockStop( module_name )

  end subroutine PhyImplSDHV5TendencyHeatCore

PhyImplSDHV5TendencyHeatTQCore( xy_IndexCalcMethod, xy_SOSILocalKMax, xy_SeaIceThickness, xy_SnowFrac, xyr_HeatFlux, xyrf_QMixFlux, xy_SurfSoilHeatFluxTentative, xy_SurfSOSIHeatFluxTentative, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xy_SurfTemp, xy_SurfHumidCoef, xy_SurfHeatCapacity, xyra_DelRadLFlux, xyr_Press, xyz_Exner, xyr_Exner, xyr_VelTransCoef, xyr_TempTransCoef, xyr_QMixTransCoef, xyr_SoilTempTransCoef, xyr_SOSIHeatTransCoef, xy_SurfVelTransCoef, xy_SurfTempTransCoef, xy_SurfQVapTransCoef, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt, xy_SurfSoilHeatFlux, xy_SurfSOSIHeatFlux )

Subroutine :

xy_IndexCalcMethod(0:imax-1, 1:jmax) :

integer , intent(in)

:	Index for calculation method

xy_SOSILocalKMax(0:imax-1, 1:jmax) : integer , intent(in)

xy_SeaIceThickness(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Sea ice thickness

xy_SnowFrac(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	Snow fraction

xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	熱フラックス. Heat flux

xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax) :

real(DP), intent(in)

:	比湿フラックス. Specific humidity flux

xy_SurfSoilHeatFluxTentative(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	惑星表面土壌熱伝導フラックス. Soil heat conduction flux at the surface

xy_SurfSOSIHeatFluxTentative(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	惑星表面海氷熱伝導フラックス. Sea ice heat conduction flux at the surface

xyr_RadSFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	短波 (日射) フラックス. Shortwave (insolation) flux

xyr_RadLFlux(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	長波フラックス. Longwave flux

xy_DeepSubSurfHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地中熱フラックス. "Deep subsurface heat flux" Heat flux at the bottom of surface/soil layer.

xy_SurfTemp(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表面温度. Surface temperature

xy_SurfHumidCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表湿潤度. Surface humidity coefficient

xy_SurfHeatCapacity(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	地表熱容量. Surface heat capacity

xyra_DelRadLFlux(0:imax-1, 1:jmax, 0:kmax, 0:1) :

real(DP), intent(in)

:	長波地表温度変化. Surface temperature tendency with longwave

xyr_Press(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	$ hat{p} $ . 気圧 (半整数レベル). Air pressure (half level)

xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(in)

:	Exner 関数 (整数レベル). Exner function (full level)

xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	Exner 関数 (半整数レベル). Exner function (half level)

xyr_VelTransCoef(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	輸送係数：運動量. Transfer coefficient: velocity

xyr_TempTransCoef(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	輸送係数：温度. Transfer coefficient: temperature

xyr_QMixTransCoef(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	輸送係数：質量. Transfer coefficient: mass of constituents

xyr_SoilTempTransCoef(0:imax-1, 1:jmax, 0:kslmax) :

real(DP), intent(in)

:	輸送係数：土壌温度. Transfer coefficient: soil temperature

xyr_SOSIHeatTransCoef(0:imax-1, 1:jmax, 0:ksimax) :

real(DP), intent(in)

:	輸送係数： Transfer coefficient: slab ocean sea ice

xy_SurfVelTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：運動量. Diffusion coefficient: velocity

xy_SurfTempTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：温度. Transfer coefficient: temperature

xy_SurfQVapTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：比湿. Transfer coefficient: specific humidity

xyz_DTempDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(out)

:	$ DP{T}{t} $ . 温度変化. Temperature tendency

xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :

real(DP), intent(out)

:	$ DP{q}{t} $ . 質量混合比変化. Mass mixing ratio tendency

xy_DSurfTempDt(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	地表面温度変化率 (K s-1) Surface temperature tendency (K s-1)

xy_SurfSoilHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	惑星表面土壌熱伝導フラックス. Soil heat conduction flux at the surface

xy_SurfSOSIHeatFlux(0:imax-1, 1:jmax) :

real(DP), intent(out)

:	惑星表面海氷熱伝導フラックス. Sea ice heat conduction flux at the surface

時間変化率の計算を行います.

Calculate tendencies.

[Source]

  subroutine PhyImplSDHV5TendencyHeatTQCore( xy_IndexCalcMethod, xy_SOSILocalKMax, xy_SeaIceThickness, xy_SnowFrac, xyr_HeatFlux, xyrf_QMixFlux, xy_SurfSoilHeatFluxTentative, xy_SurfSOSIHeatFluxTentative, xyr_RadSFlux, xyr_RadLFlux, xy_DeepSubSurfHeatFlux, xy_SurfTemp, xy_SurfHumidCoef, xy_SurfHeatCapacity, xyra_DelRadLFlux, xyr_Press, xyz_Exner, xyr_Exner, xyr_VelTransCoef, xyr_TempTransCoef, xyr_QMixTransCoef, xyr_SoilTempTransCoef, xyr_SOSIHeatTransCoef, xy_SurfVelTransCoef, xy_SurfTempTransCoef, xy_SurfQVapTransCoef, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt, xy_SurfSoilHeatFlux, xy_SurfSOSIHeatFlux )
    !
    ! 時間変化率の計算を行います. 
    !
    ! Calculate tendencies. 
    !

    ! モジュール引用 ; USE statements
    !

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: Grav, CpDry, GasRDry, LatentHeat

    ! 雪と海氷の定数の設定
    ! Setting constants of snow and sea ice
    !
    use constants_snowseaice, only: SeaIceVolHeatCap   , SeaIceThermCondCoef, TempBelowSeaIce

    ! 時刻管理
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop

    ! 飽和比湿の算出
    ! Evaluation of saturation specific humidity
    !
    use saturate, only: xy_CalcQVapSatOnLiq, xy_CalcQVapSatOnSol, xy_CalcDQVapSatDTempOnLiq, xy_CalcDQVapSatDTempOnSol

    ! 陰解法による時間積分のためのルーチン
    ! Routines for time integration with implicit scheme
    !
    use phy_implicit_utils, only : PhyImplLUDecomp3, PhyImplLUSolve3

    ! 宣言文 ; Declaration statements
    !

    integer , intent(in):: xy_IndexCalcMethod (0:imax-1, 1:jmax)
                              ! 
                              ! Index for calculation method
    integer , intent(in):: xy_SOSILocalKMax(0:imax-1, 1:jmax)
                              !
                              !
    real(DP), intent(in):: xy_SeaIceThickness(0:imax-1, 1:jmax)
                              !
                              ! Sea ice thickness
    real(DP), intent(in):: xy_SnowFrac  (0:imax-1, 1:jmax)
                              !
                              ! Snow fraction
    real(DP), intent(in):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 熱フラックス. 
                              ! Heat flux
    real(DP), intent(in):: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! 比湿フラックス. 
                              ! Specific humidity flux

!!$    real(DP), intent(in):: xy_SurfSoilHeatFlux(0:imax-1, 1:jmax)
!!$                              ! 惑星表面土壌熱伝導フラックス.
!!$                              ! Soil heat conduction flux at the surface
!!$    real(DP), intent(in):: xy_SurfSOSIHeatFlux(0:imax-1, 1:jmax)
!!$                              ! 惑星表面海氷熱伝導フラックス.
!!$                              ! Sea ice heat conduction flux at the surface
    real(DP), intent(in):: xy_SurfSoilHeatFluxTentative(0:imax-1, 1:jmax)
                              ! 惑星表面土壌熱伝導フラックス.
                              ! Soil heat conduction flux at the surface
    real(DP), intent(in):: xy_SurfSOSIHeatFluxTentative(0:imax-1, 1:jmax)
                              ! 惑星表面海氷熱伝導フラックス.
                              ! Sea ice heat conduction flux at the surface

    real(DP), intent(in):: xyr_RadSFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 短波 (日射) フラックス. 
                              ! Shortwave (insolation) flux
    real(DP), intent(in):: xyr_RadLFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! 長波フラックス. 
                              ! Longwave flux

    real(DP), intent(in):: xy_DeepSubSurfHeatFlux (0:imax-1, 1:jmax)
                              ! 地中熱フラックス. 
                              ! "Deep subsurface heat flux"
                              ! Heat flux at the bottom of surface/soil layer.
    real(DP), intent(in):: xy_SurfTemp (0:imax-1, 1:jmax)
                              ! 地表面温度. 
                              ! Surface temperature
    real(DP), intent(in):: xy_SurfHumidCoef (0:imax-1, 1:jmax)
                              ! 地表湿潤度. 
                              ! Surface humidity coefficient
    real(DP), intent(in):: xy_SurfHeatCapacity (0:imax-1, 1:jmax)
                              ! 地表熱容量. 
                              ! Surface heat capacity

    real(DP), intent(in):: xyra_DelRadLFlux (0:imax-1, 1:jmax, 0:kmax, 0:1)
                              ! 長波地表温度変化. 
                              ! Surface temperature tendency with longwave

    real(DP), intent(in):: xyr_Press (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . 気圧 (半整数レベル). 
                              ! Air pressure (half level)
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner 関数 (整数レベル). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner 関数 (半整数レベル). 
                              ! Exner function (half level)

    real(DP), intent(in):: xyr_VelTransCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 輸送係数：運動量. 
                              ! Transfer coefficient: velocity
    real(DP), intent(in):: xyr_TempTransCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 輸送係数：温度. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xyr_QMixTransCoef(0:imax-1, 1:jmax, 0:kmax)
                              ! 輸送係数：質量. 
                              ! Transfer coefficient: mass of constituents

    real(DP), intent(in):: xyr_SoilTempTransCoef (0:imax-1, 1:jmax, 0:kslmax)
                              ! 輸送係数：土壌温度.
                              ! Transfer coefficient: soil temperature
    real(DP), intent(in):: xyr_SOSIHeatTransCoef(0:imax-1, 1:jmax, 0:ksimax)
                              ! 輸送係数：
                              ! Transfer coefficient: slab ocean sea ice

    real(DP), intent(in):: xy_SurfVelTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：運動量. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(in):: xy_SurfTempTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：温度. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xy_SurfQVapTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：比湿. 
                              ! Transfer coefficient: specific humidity

    real(DP), intent(out):: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . 温度変化. 
                              ! Temperature tendency
    real(DP), intent(out):: xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ \DP{q}{t} $ . 質量混合比変化. 
                              ! Mass mixing ratio tendency
    real(DP), intent(out):: xy_DSurfTempDt (0:imax-1, 1:jmax)
                              ! 地表面温度変化率 (K s-1)
                              ! Surface temperature tendency (K s-1)

    real(DP), intent(out):: xy_SurfSoilHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面土壌熱伝導フラックス.
                              ! Soil heat conduction flux at the surface
    real(DP), intent(out):: xy_SurfSOSIHeatFlux(0:imax-1, 1:jmax)
                              ! 惑星表面海氷熱伝導フラックス.
                              ! Sea ice heat conduction flux at the surface

    ! 作業変数
    ! Work variables
    !
    real(DP):: xyza_TempMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 温度陰解行列. 
                              ! Implicit matrix about temperature
    real(DP):: xyz_TempVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 温度陰解ベクトル. 
                              ! Implicit vector about temperature
    real(DP):: xyza_QMixMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 質量混合比陰解行列. 
                              ! Implicit matrix about mass mixing ratio
    real(DP):: xyz_QMixVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 質量混合比陰解ベクトル. 
                              ! Implicit vector about mass mixing ratio
    real(DP):: xyaa_SurfMtx(0:imax-1, 1:jmax, 0:0, -1:1)
                              ! 惑星表面エネルギー収支用陰解行列
                              ! Implicit matrix for surface energy balance
    real(DP):: xy_SurfRH(0:imax-1,1:jmax)


    real(DP):: xy_SurfQVapSatOnLiq(0:imax-1, 1:jmax)
                              ! 地表飽和比湿. 
                              ! Saturated specific humidity on surface
    real(DP):: xy_SurfQVapSatOnSol (0:imax-1, 1:jmax)
                              ! 地表飽和比湿. 
                              ! Saturated specific humidity on surface
    real(DP):: xy_SurfQVapSat (0:imax-1, 1:jmax)
                              ! 地表飽和比湿. 
                              ! Saturated specific humidity on surface
    real(DP):: xy_SurfDQVapSatDTempOnLiq (0:imax-1, 1:jmax)
                              ! 地表飽和比湿変化. 
                              ! Saturated specific humidity tendency on surface
    real(DP):: xy_SurfDQVapSatDTempOnSol (0:imax-1, 1:jmax)
                              ! 地表飽和比湿変化. 
                              ! Saturated specific humidity tendency on surface
    real(DP):: xy_SurfDQVapSatDTemp (0:imax-1, 1:jmax)
                              ! 地表飽和比湿変化. 
                              ! Saturated specific humidity tendency on surface

    real(DP):: xyaa_TempQVapLUMtx (0:imax-1, 1:jmax, -kmax:kmax, -1:1)
                              ! LU 行列.
                              ! LU matrix
    real(DP):: xya_DelTempQVapLUVec (0:imax-1, 1:jmax, -kmax:kmax)
                              ! $ T, Qv $ の時間変化.
                              ! Tendency of $ T $ and $ Qv $

    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitude
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude
    integer:: k               ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction
    integer:: l               ! 行列用 DO ループ用作業変数
                              ! Work variables for DO loop of matrices
    integer:: n               ! 組成方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in dimension of constituents

    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. phy_implicit_sdh_V5_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


!!$    ! 計算時間計測開始
!!$    ! Start measurement of computation time
!!$    !
!!$    call TimesetClockStart( module_name )



!!$    if ( .not. FlagSSModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagSSModel has to be true.' )
!!$    end if

    ! FlagBucketModel は関係ないよね?
    ! SSModel 強制にした時点で, 水蒸気は地面と分離したから. 
!!$    if ( .not. FlagBucketModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagBucketModel has to be true.' )
!!$    end if


    ! 飽和比湿の計算
    ! Calculate saturated specific humidity
    !
    xy_SurfQVapSatOnLiq       = xy_CalcQVapSatOnLiq      ( xy_SurfTemp, xyr_Press(:,:,0) )
    xy_SurfQVapSatOnSol       = xy_CalcQVapSatOnSol      ( xy_SurfTemp, xyr_Press(:,:,0) )
    xy_SurfQVapSat       = ( 1.0_DP - xy_SnowFrac ) * xy_SurfQVapSatOnLiq + xy_SnowFrac              * xy_SurfQVapSatOnSol
    xy_SurfDQVapSatDTempOnLiq = xy_CalcDQVapSatDTempOnLiq( xy_SurfTemp, xy_SurfQVapSatOnLiq )
    xy_SurfDQVapSatDTempOnSol = xy_CalcDQVapSatDTempOnSol( xy_SurfTemp, xy_SurfQVapSatOnSol )
    xy_SurfDQVapSatDTemp = ( 1.0_DP - xy_SnowFrac ) * xy_SurfDQVapSatDTempOnLiq + xy_SnowFrac              * xy_SurfDQVapSatDTempOnSol


    ! 陰解法のための行列作成
    ! Create matrices for implicit scheme
    !

    ! 鉛直拡散スキームの輸送係数から陰解行列の計算 (温度)
    ! Calculate implicit matrices from transfer coefficient of vertical diffusion scheme (temperature)
    !
    k = 1
    xyza_TempMtx(:,:,k,-1) = - CpDry * xy_SurfTempTransCoef(:,:)
    xyza_TempMtx(:,:,k, 0) = - CpDry * ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + CpDry * xyr_Exner(:,:,k-1) / xyz_Exner(:,:,k  ) * xy_SurfTempTransCoef(:,:) + CpDry * xyr_Exner(:,:,k  ) / xyz_Exner(:,:,k  ) * xyr_TempTransCoef(:,:,k  )
    xyza_TempMtx(:,:,k, 1) = - CpDry * xyr_Exner(:,:,k  ) / xyz_Exner(:,:,k+1) * xyr_TempTransCoef(:,:,k  )

    do k = 2, kmax-1
      xyza_TempMtx(:,:,k,-1) = - CpDry * xyr_Exner(:,:,k-1) / xyz_Exner(:,:,k-1) * xyr_TempTransCoef(:,:,k-1)
      xyza_TempMtx(:,:,k, 0) = - CpDry * ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + CpDry * xyr_Exner(:,:,k-1) / xyz_Exner(:,:,k  ) * xyr_TempTransCoef(:,:,k-1) + CpDry * xyr_Exner(:,:,k  ) / xyz_Exner(:,:,k  ) * xyr_TempTransCoef(:,:,k  )
      xyza_TempMtx(:,:,k, 1) = - CpDry * xyr_Exner(:,:,k  ) / xyz_Exner(:,:,k+1) * xyr_TempTransCoef(:,:,k  )
    end do

    k = kmax
    xyza_TempMtx(:,:,k,-1) = - CpDry * xyr_Exner(:,:,k-1) / xyz_Exner(:,:,k-1) * xyr_TempTransCoef(:,:,k-1)
    xyza_TempMtx(:,:,k, 0) = - CpDry * ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + CpDry * xyr_Exner(:,:,k-1) / xyz_Exner(:,:,k  ) * xyr_TempTransCoef(:,:,k-1)
    xyza_TempMtx(:,:,k, 1) = 0.0_DP

    do k = 1, kmax
      xyz_TempVec(:,:,k) = - ( xyr_HeatFlux(:,:,k) - xyr_HeatFlux(:,:,k-1) )
    end do


    ! 鉛直拡散スキームの輸送係数から陰解行列の計算 (比湿)
    ! Calculate implicit matrices from transfer coefficient of vertical diffusion scheme (specific humidity)
    !

    k = 1
    xyza_QMixMtx(:,:,k,-1) = - xy_SurfHumidCoef(:,:) * xy_SurfQVapTransCoef(:,:) * xy_SurfDQVapSatDTemp(:,:)
    xyza_QMixMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xy_SurfHumidCoef(:,:) * xy_SurfQVapTransCoef(:,:) + xyr_QMixTransCoef(:,:,k  )
    xyza_QMixMtx(:,:,k, 1) = - xyr_QMixTransCoef(:,:,k  )

    do k = 2, kmax-1
      xyza_QMixMtx(:,:,k,-1) = - xyr_QMixTransCoef(:,:,k-1)
      xyza_QMixMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_QMixTransCoef(:,:,k-1) + xyr_QMixTransCoef(:,:,k  )
      xyza_QMixMtx(:,:,k, 1) = - xyr_QMixTransCoef(:,:,k  )
    end do

    k = kmax
    xyza_QMixMtx(:,:,k,-1) = - xyr_QMixTransCoef(:,:,k-1)
    xyza_QMixMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_QMixTransCoef(:,:,k-1)
    xyza_QMixMtx(:,:,k, 1) = 0.0_DP

    n = IndexH2OVap
    do k = 1, kmax
      xyz_QMixVec(:,:,k) = - ( xyrf_QMixFlux(:,:,k,n) - xyrf_QMixFlux(:,:,k-1,n) )
    end do



    ! 地表面過程の輸送係数から陰解行列の計算
    ! Calculate implicit matrices from transfer coefficient of surface process
    !
    do i = 0, imax-1
      do j = 1, jmax
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
          !    for thermal diffusion in soil
!!$          xyaa_SurfMtx(i,j,0,-1) =                                             &
!!$            &   xyr_SoilTempTransCoef(i,j,0)
          !    for water vapor diffusion in atmosphere
          xyaa_SurfMtx(i,j,0,-1) = - LatentHeat * xy_SurfHumidCoef(i,j) * xy_SurfQVapTransCoef(i,j)
          xyaa_SurfMtx(i,j,0, 0) = xy_SurfHeatCapacity(i,j) / ( 2.0_DP * DelTime ) + CpDry * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,0) + LatentHeat * xy_SurfHumidCoef(i,j) * xy_SurfQVapTransCoef(i,j) * xy_SurfDQVapSatDTemp(i,j) - xyr_SoilTempTransCoef(i,j,0)
          xyaa_SurfMtx(i,j,0, 1) = - CpDry * xyr_Exner(i,j,0) / xyz_Exner(i,j,1) * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,1)
        case ( IndexSeaIce )
          ! sea ice
!!$          xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
          !    for water vapor diffusion in atmosphere
          xyaa_SurfMtx(i,j,0,-1) = - LatentHeat * xy_SurfHumidCoef(i,j) * xy_SurfQVapTransCoef(i,j)
          xyaa_SurfMtx(i,j,0, 0) = SeaIceVolHeatCap * xy_SeaIceThickness(i,j) / ( 2.0_DP * DelTime ) + CpDry * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,0) + SeaIceThermCondCoef / xy_SeaIceThickness(i,j) + LatentHeat * xy_SurfHumidCoef(i,j) * xy_SurfQVapTransCoef(i,j) * xy_SurfDQVapSatDTemp(i,j)
          xyaa_SurfMtx(i,j,0, 1) = - CpDry * xyr_Exner(i,j,0) / xyz_Exner(i,j,1) * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,1)
        case ( IndexSlabOceanSeaIce )
          ! sea ice
!!$          xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
          !    for water vapor diffusion in atmosphere
          xyaa_SurfMtx(i,j,0,-1) = - LatentHeat * xy_SurfHumidCoef(i,j) * xy_SurfQVapTransCoef(i,j)
          xyaa_SurfMtx(i,j,0, 0) = SeaIceVolHeatCap * xy_SeaIceThickness(i,j) / ( 2.0_DP * DelTime ) + CpDry * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,0) + LatentHeat * xy_SurfHumidCoef(i,j) * xy_SurfQVapTransCoef(i,j) * xy_SurfDQVapSatDTemp(i,j)

          if ( xy_SOSILocalKMax(i,j) == 0 ) then
          else
            xyaa_SurfMtx(i,j,0, 0) = xyaa_SurfMtx(i,j,0, 0) - xyr_SOSIHeatTransCoef(i,j,0)
          end if

          xyaa_SurfMtx(i,j,0, 1) = - CpDry * xyr_Exner(i,j,0) / xyz_Exner(i,j,1) * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,1)
        case ( IndexSlabOcean )
          ! slab ocean
!!$          xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
          !    for water vapor diffusion in atmosphere
          xyaa_SurfMtx(i,j,0,-1) = - LatentHeat * xy_SurfHumidCoef(i,j) * xy_SurfQVapTransCoef(i,j)
          xyaa_SurfMtx(i,j,0, 0) = SOHeatCapacity / ( 2.0_DP * DelTime ) + CpDry * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,0) + LatentHeat * xy_SurfHumidCoef(i,j) * xy_SurfQVapTransCoef(i,j) * xy_SurfDQVapSatDTemp(i,j)
          xyaa_SurfMtx(i,j,0, 1) = - CpDry * xyr_Exner(i,j,0) / xyz_Exner(i,j,1) * xy_SurfTempTransCoef(i,j) + xyra_DelRadLFlux(i,j,0,1)
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
          xyaa_SurfMtx(i,j,0,-1) = 0.0_DP
          xyaa_SurfMtx(i,j,0, 0) = 1.0_DP
          xyaa_SurfMtx(i,j,0, 1) = 0.0_DP
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
        end select

      end do
    end do

    n = IndexH2OVap
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
          xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - LatentHeat * xyrf_QMixFlux(i,j,0,n) + xy_SurfSoilHeatFluxTentative(i,j)
        case ( IndexSeaIce )
          ! sea ice
          xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - LatentHeat * xyrf_QMixFlux(i,j,0,n) - SeaIceThermCondCoef * ( xy_SurfTemp(i,j) - TempBelowSeaIce ) / xy_SeaIceThickness(i,j)
        case ( IndexSlabOceanSeaIce )
          ! sea ice
          xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - LatentHeat * xyrf_QMixFlux(i,j,0,n) + xy_SurfSOSIHeatFluxTentative(i,j)
        case ( IndexSlabOcean )
          ! slab ocean
          xy_SurfRH(i,j) = - xyr_RadSFlux(i,j,0) - xyr_RadLFlux(i,j,0) - xyr_HeatFlux(i,j,0) - LatentHeat * xyrf_QMixFlux(i,j,0,n)              !&
!              & + xy_DeepSubSurfHeatFlux(i,j)
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
          xy_SurfRH(i,j) = 0.0_DP
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
        end select
      end do
    end do


    ! 温度と比湿の計算
    ! Calculate temperature and specific humidity
    !

    do l = -1, 1
      do k = 1, kmax
        xyaa_TempQVapLUMtx(:,:,-k,-l) = xyza_QMixMtx(:,:,k,l)
      end do
      k = 0
      xyaa_TempQVapLUMtx(:,:, k, l) = xyaa_SurfMtx(:,:,0,l)
      do k = 1, kmax
        xyaa_TempQVapLUMtx(:,:, k, l) = xyza_TempMtx(:,:,k,l)
      end do
    end do

    call PhyImplLUDecomp3( xyaa_TempQVapLUMtx, imax * jmax, kmax + 1 + kmax )

    do k = 1, kmax
      xya_DelTempQVapLUVec(:,:,-k) = xyz_QMixVec(:,:,k)
    end do
    k = 0
    xya_DelTempQVapLUVec(:,:,k) = xy_SurfRH
    do k = 1, kmax
      xya_DelTempQVapLUVec(:,:,k) = xyz_TempVec(:,:,k)
    end do

    call PhyImplLUSolve3( xya_DelTempQVapLUVec, xyaa_TempQVapLUMtx, 1, imax * jmax , kmax + 1 + kmax )

    n = IndexH2OVap
    do k = 1, kmax
      xyzf_DQMixDt(:,:,k,n) = xya_DelTempQVapLUVec(:,:,-k) / ( 2.0_DP * DelTime )
    end do
    do j = 1, jmax
      do i = 0, imax-1
        select case ( xy_IndexCalcMethod(i,j) )
        case ( IndexLand )
          ! land
          xy_DSurfTempDt(i,j) = xya_DelTempQVapLUVec(i,j,0) / ( 2.0_DP * DelTime )
        case ( IndexSeaIce, IndexSlabOceanSeaIce )
          ! sea ice
          xy_DSurfTempDt(i,j) = xya_DelTempQVapLUVec(i,j,0) / ( 2.0_DP * DelTime )
        case ( IndexSlabOcean )
          ! slab ocean
          xy_DSurfTempDt(i,j) = xya_DelTempQVapLUVec(i,j,0) / ( 2.0_DP * DelTime )
        case ( IndexPresTs, IndexLandWithPresTs )
          ! prescribed surface temperature
          xy_DSurfTempDt(i,j) = 0.
        case default
          call MessageNotify( 'E', module_name, 'Unexpected Error.' )
        end select
      end do
    end do
    do k = 1, kmax
      xyz_DTempDt(:,:,k) = xya_DelTempQVapLUVec(:,:,k) / ( 2.0_DP * DelTime )
    end do


    ! Update soil heat flux and slab ocean sea ice heat flux
    !
    xy_SurfSoilHeatFlux = xy_SurfSoilHeatFluxTentative - xyr_SoilTempTransCoef(:,:,0) * ( - xy_DSurfTempDt ) * ( 2.0_DP * DelTime )
    !
    do j = 1, jmax
      do i = 0, imax-1
        if ( xy_SOSILocalKMax(i,j) == 0 ) then
          xy_SurfSOSIHeatFlux(i,j) = -1.0e100_DP
        else
          k = 0
          xy_SurfSOSIHeatFlux(i,j) = xy_SurfSOSIHeatFluxTentative(i,j) - xyr_SOSIHeatTransCoef(i,j,k) * ( - xy_DSurfTempDt(i,j) ) * ( 2.0_DP * DelTime )
        end if
      end do
    end do


    call PhyImplSDHV5ChkConservationTQ( xy_IndexCalcMethod, xy_SeaIceThickness, xy_SnowFrac, xyr_Press, xyz_Exner, xyr_Exner, xy_SurfTemp, xyr_HeatFlux, xyrf_QMixFlux, xy_SurfSoilHeatFlux, xy_SurfSOSIHeatFlux, xy_SurfTempTransCoef, xy_SurfQVapTransCoef, xy_SurfHumidCoef, xy_SurfHeatCapacity, xyr_RadSFlux, xyr_RadLFlux, xyra_DelRadLFlux, xy_DeepSubSurfHeatFlux, xyz_DTempDt, xyzf_DQMixDt, xy_DSurfTempDt )


!!$    ! 計算時間計測一時停止
!!$    ! Pause measurement of computation time
!!$    !
!!$    call TimesetClockStop( module_name )

  end subroutine PhyImplSDHV5TendencyHeatTQCore

PhyImplSDHV5TendencyMomCore( xyr_MomFluxX, xyr_MomFluxY, xyr_Press, xyr_VelTransCoef, xy_SurfVelTransCoef, xyz_DUDt, xyz_DVDt )

Subroutine :

xyr_MomFluxX(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	東西方向運動量フラックス. Eastward momentum flux

xyr_MomFluxY(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	南北方向運動量フラックス. Northward momentum flux

xyr_Press(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	$ hat{p} $ . 気圧 (半整数レベル). Air pressure (half level)

xyr_VelTransCoef(0:imax-1, 1:jmax, 0:kmax) :

real(DP), intent(in)

:	輸送係数：運動量. Transfer coefficient: velocity

xy_SurfVelTransCoef(0:imax-1, 1:jmax) :

real(DP), intent(in)

:	輸送係数：運動量. Diffusion coefficient: velocity

xyz_DUDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(out)

:	$ DP{u}{t} $ . 東西風速変化. Eastward wind tendency

xyz_DVDt(0:imax-1, 1:jmax, 1:kmax) :

real(DP), intent(out)

:	$ DP{v}{t} $ . 南北風速変化. Northward wind tendency

時間変化率の計算を行います.

Calculate tendencies.

[Source]

  subroutine PhyImplSDHV5TendencyMomCore( xyr_MomFluxX, xyr_MomFluxY, xyr_Press, xyr_VelTransCoef, xy_SurfVelTransCoef, xyz_DUDt, xyz_DVDt )
    !
    ! 時間変化率の計算を行います. 
    !
    ! Calculate tendencies. 
    !

    ! モジュール引用 ; USE statements
    !

    ! 物理定数設定
    ! Physical constants settings
    !
    use constants, only: Grav, CpDry, GasRDry
                              ! $ R $ [J kg-1 K-1]. 
                              ! 乾燥大気の気体定数. 
                              ! Gas constant of air

    ! 時刻管理
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop

    ! 陰解法による時間積分のためのルーチン
    ! Routines for time integration with implicit scheme
    !
    use phy_implicit_utils, only : PhyImplLUDecomp3, PhyImplLUSolve3

    ! 宣言文 ; Declaration statements
    !

    real(DP), intent(in):: xyr_MomFluxX (0:imax-1, 1:jmax, 0:kmax)
                              ! 東西方向運動量フラックス. 
                              ! Eastward momentum flux
    real(DP), intent(in):: xyr_MomFluxY (0:imax-1, 1:jmax, 0:kmax)
                              ! 南北方向運動量フラックス. 
                              ! Northward momentum flux

    real(DP), intent(in):: xyr_Press (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . 気圧 (半整数レベル). 
                              ! Air pressure (half level)

    real(DP), intent(in):: xyr_VelTransCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 輸送係数：運動量. 
                              ! Transfer coefficient: velocity
    real(DP), intent(in):: xy_SurfVelTransCoef (0:imax-1, 1:jmax)
                              ! 輸送係数：運動量. 
                              ! Diffusion coefficient: velocity

    real(DP), intent(out):: xyz_DUDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{u}{t} $ . 東西風速変化. 
                              ! Eastward wind tendency
    real(DP), intent(out):: xyz_DVDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{v}{t} $ . 南北風速変化. 
                              ! Northward wind tendency


    ! 作業変数
    ! Work variables
    !
    real(DP):: xyza_UVMtx (0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 速度陰解行列. 
                              ! Implicit matrix about velocity 
    real(DP):: xyz_UVec (0:imax-1, 1:jmax, 1:kmax)
                              ! 速度陰解ベクトル. 
                              ! Implicit vector about velocity 
    real(DP):: xyz_VVec (0:imax-1, 1:jmax, 1:kmax)
                              ! 速度陰解ベクトル. 
                              ! Implicit vector about velocity 

    real(DP):: xyza_UVLUMtx (0:imax-1, 1:jmax, 1:kmax,-1:1)
                              ! LU 行列. 
                              ! LU matrix


    integer:: i               ! 経度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in longitude
    integer:: j               ! 緯度方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in latitude
    integer:: k               ! 鉛直方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in vertical direction
    integer:: l               ! 行列用 DO ループ用作業変数
                              ! Work variables for DO loop of matrices
    integer:: n               ! 組成方向に回る DO ループ用作業変数
                              ! Work variables for DO loop in dimension of constituents

    ! 実行文 ; Executable statement
    !

    ! 初期化確認
    ! Initialization check
    !
    if ( .not. phy_implicit_sdh_V5_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


!!$    ! 計算時間計測開始
!!$    ! Start measurement of computation time
!!$    !
!!$    call TimesetClockStart( module_name )



!!$    if ( .not. FlagSSModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagSSModel has to be true.' )
!!$    end if

    ! FlagBucketModel は関係ないよね?
    ! SSModel 強制にした時点で, 水蒸気は地面と分離したから. 
!!$    if ( .not. FlagBucketModel ) then
!!$      call MessageNotify( 'E', module_name, 'FlagBucketModel has to be true.' )
!!$    end if



    ! 陰解法のための行列作成
    ! Create matrices for implicit scheme
    !

    ! 鉛直拡散スキームの輸送係数から陰解行列の計算 (速度)
    ! Calculate implicit matrices from transfer coefficient of vertical diffusion scheme (velocity)
    !
    k = 1
    xyza_UVMtx  (:,:,k,-1) = 0.0_DP
    xyza_UVMtx  (:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xy_SurfVelTransCoef(:,:) + xyr_VelTransCoef(:,:,k  )
    xyza_UVMtx  (:,:,k, 1) = - xyr_VelTransCoef(:,:,k)

    do k = 2, kmax-1
      xyza_UVMtx  (:,:,k,-1) = - xyr_VelTransCoef(:,:,k-1)
      xyza_UVMtx  (:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_VelTransCoef(:,:,k-1) + xyr_VelTransCoef(:,:,k  )
      xyza_UVMtx  (:,:,k, 1) = - xyr_VelTransCoef(:,:,k)
    end do

    k = kmax
    xyza_UVMtx  (:,:,k,-1) = - xyr_VelTransCoef(:,:,k-1)
    xyza_UVMtx  (:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_VelTransCoef(:,:,k-1)
    xyza_UVMtx  (:,:,k, 1) = 0.0_DP

    do k = 1, kmax
      xyz_UVec(:,:,k) = - ( xyr_MomFluxX(:,:,k) - xyr_MomFluxX(:,:,k-1) )
      xyz_VVec(:,:,k) = - ( xyr_MomFluxY(:,:,k) - xyr_MomFluxY(:,:,k-1) )
    end do

    ! 東西風速, 南北風速の計算
    ! Calculate eastward and northward wind
    !
    xyza_UVLUMtx = xyza_UVMtx

    call PhyImplLUDecomp3( xyza_UVLUMtx, imax * jmax, kmax ) ! (in)

    do k = 1, kmax
      xyz_DUDt(:,:,k) = xyz_UVec(:,:,k)
      xyz_DVDt(:,:,k) = xyz_VVec(:,:,k)
    end do

    call PhyImplLUSolve3( xyz_DUDt, xyza_UVLUMtx, 1, imax * jmax, kmax ) ! (in)

    call PhyImplLUSolve3( xyz_DVDt, xyza_UVLUMtx, 1, imax * jmax, kmax ) ! (in)

    do k = 1, kmax
      xyz_DUDt(:,:,k) = xyz_DUDt(:,:,k) / ( 2. * DelTime )
      xyz_DVDt(:,:,k) = xyz_DVDt(:,:,k) / ( 2. * DelTime )
    end do


!!$    ! 計算時間計測一時停止
!!$    ! Pause measurement of computation time
!!$    !
!!$    call TimesetClockStop( module_name )

  end subroutine PhyImplSDHV5TendencyMomCore

ResidualMessageThreshold

*Variable* :
`ResidualMessageThreshold` :	`real(DP), save`

SOHeatCapacity

Variable :

SOHeatCapacity :

real(DP), save

:	Slab ocean heat capacity (J m-2 K-1)

TempItrCrit

*Variable* :
`TempItrCrit` :	`real(DP), save`

module_name

Constant :

module_name = ‘phy_implicit_sdh_V5‘ :

character(*), parameter

:	モジュールの名称. Module name

phy_implicit_sdh_V5_inited

Variable :

phy_implicit_sdh_V5_inited = .false. :

logical, save

:	初期設定フラグ. Initialization flag

version

Constant :

version = ’$Name: $’ // ’$Id: phy_implicit_sdh_V3.f90,v 1.1 2015/01/29 12:05:01 yot Exp $’ :

character(*), parameter

:	モジュールのバージョン Module version