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C.b. Finite difference equations of the 1D model, simulation setup and results
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The space differencing is evaluated by the second order centered
scheme.
The time integration is performed by the forward scheme for the
radiative heating term and the Crank-Nicolson scheme for the
vertical diffusion term.
Detail expressions of finite difference form of the radiative
transfer equation and the vertical diffusion term are same as those
shown in appendix B.d.i,
appendix B.d.ii and appendix B.e
The arrangement of vertical grid and its interval are same as those of
the 2D model (section 2.b).
The time interval is 30 seconds.
The solar flux at the top of model atmosphere diurnally changes
under the condition of Ls = 100° at 20°N.
The initial atmospheric and grand surface temperature is constant
(220 K and 210 K respectively).
The numerical integration time is 30 days.
The vertical profiles of the atmospheric and the grand surface
temperature at LT = 6:00 are shown in Figure C1
and Figure C2 .
These profiles are used for the initial condition of the 2D model simulation
(section 2.b).
Even if the initial atmospheric temperature is 160 K, the result is
similar to that obtained in the case that the initial atmospheric
temperature is 220 K (Figure C3, Figure C4).
The diurnal changes of the atmospheric and the grand surface
temperature at 30 days are shown in Figure
C5 and Figure C6, respectively.
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Figure C1:
Vertical profile of the atmospheric temperature at LT = 6:00 on 30
days calculated by the 1D model.
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Figure C2:
Vertical profile of the grand surface temperature at LT = 6:00 on
30th day calculated by the 1D model.
The unit of vertical axis is the diurnal skin depth.
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Figure C3:
Time development of the vertical profile of atmospheric temperature at
LT = 6:00 every 10 days calculated by the 1D model.
The initial atmospheric temperature is 220 K.
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Figure C4:
Time development of the vertical profile of atmospheric temperature at
LT = 6:00 every 10 days calculated by the 1D model.
The initial atmospheric temperature is 160 K.
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Figure C5:
Time development of the vertical profile of atmospheric temperature
every 4 hours on 30th day calculated by the 1D model.
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Figure C6:
(left panel) Time development of vertical profile of the grand
temperature from LT = 8:00 to 4:00 every 4 hours on 30th day.
The numbers on each line show local time.
The unit of vertical axis is the diurnal skin depth.
(right panel) Time evolution of horizontal mean surface temperature (red
line) and atmospheric temperature at about 1.5 m hight (blue line).
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