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\journal{Icarus}

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\begin{document}

\begin{frontmatter}

\title{
 The circulation pattern and day-night heat transport
 in an atmosphere of a synchronously rotating aquaplanet: 
 dependence on planetary rotation rate
}

\author[kyoto-u,mri]{S.~Noda}
\ead{noda@gfd-dennou.org}
\author[hokudai,cps]{M.~Ishiwatari}
\author[kyushu]{K.~Nakajima}
\author[kobe,cps]{Y.O.~Takahashi}
\author[kurims]{S.~Takehiro}
\author[kobe,cps]{M.~Onishi}
\author[okayama]{G.L.~Hashimoto}
\author[hokudai,cps]{K.~Kuramoto}
\author[kobe,cps]{Y.-Y.~Hayashi}

\cortext[cor1]{Corresponding author} 

\address[kyoto-u]{
 Division of Earth and Planetary Sciences, Kyoto University,
 Kyoto 606-8502, Japan
}
\address[mri]{
 Climate Research Department, Meteorological Research Institute,
 Tsukuba 305-0052, Japan
}
\address[hokudai]{
 Division of Earth and Planetary Sciences, Hokkaido University,
 Sapporo 060-0810, Japan
}
\address[cps]{
 Center for Planetary Science, Kobe University,
 Kobe 650-0047, Japan
}
\address[kyushu]{
 Department of Earth and Planetary Sciences, Kyushu University,
 Fukuoka 812-8581, Japan
}
\address[kobe]{
 Department of Earth and Planetary Sciences, Kobe University,
 Kobe 657-8501, Japan
}
\address[kurims]{
 Research Institute for Mathematical Sciences, Kyoto University,
 Kyoto 606-8502, Japan
}
\address[okayama]{
 Department of Earth Sciences, Okayama University,
 Okayama 700-8530, Japan
}


\begin{abstract}
A parameter experiment on planetary rotation rate dependence
   is performed by the use of an atmospheric general circulation model (GCM)
   with simplified hydrological and radiative processes
   to investigate a possible variety of 
   atmospheric states realized on a synchronously rotating aquaplanet. 
The entire planetary surface is covered by the swamp ocean.
The value of planetary rotation rate is varied from zero 
   to the Earth's,
   while other parameters such as planetary radius,
   mean molecular weight and total mass of atmospheric dry 
   components, and solar constant 
   are set to the present Earth's values.
The integration results show that 
   the atmosphere reaches statistically equilibrium states
   for all runs;
   none of the calculated cases exemplifies the runaway greenhouse state. 
The obtained circulation patterns are classified 
   into the four types:
Type-I characterized by the dominance of a day-night thermally direct circulation,
Type-II characterized by a zonal wave number one resonant Rossby wave
   over a meridionally broad westerly jet on the equator,
Type-III characterized by a 
   long time scale
   north-south asymmetric variation,
   and
Type-IV characterized by a pair of 
  mid-latitude westerly jets.
With the increase of planetary rotation rate,
the circulation evolves from Type-I to Type-II and then to Type-III 
   gradually and smoothly,
   whereas the change from Types-III to Type-IV is abrupt and discontinuous.
Over a finite range of planetary rotation rate,
   both Types-III and -IV emerge as statistically steady states,
   constituting multiple equilibria.
In spite of the substantial change of
   the characteristics of circulation patterns,
   the net energy transport from the day side to the night side
   remains almost insensitive to planetary rotation rate,
   although
   the partition into dry static energy and latent heat energy 
   transports changes.
The reason for this notable insensitivity
   is that 
   the outgoing longwave radiation in the broad area of the day side 
   is constrained by the radiation limit of moist atmospheres, 
   so that the transport to the night side,
   which is determined as the difference between the incoming solar radiation
   and the radiation limit, cannot change greatly. 
\end{abstract}

\begin{keyword}
 Astrobiology;
 Atmospheres, dynamics;
 Atmospheres, structure;
 Extra-solar planets;
 Meteorology
\end{keyword}

\end{frontmatter}

\linenumbers

\section{Introduction}

A number of recent systematic surveys
  have made discoveries of earth-sized exoplanets quite common
  (e.g., Torres et al, 2015).
Many of those planets exist inside of the tidal lock radius of 
  their central stars,
  and are considered to be synchronously rotating 
  \citep{vonbloh}.
 Even when the global mean incoming heat flux from the central star
   is comparable to that of the present Earth's,
 the
  incident flux in the 
  perpetual
  day side of a synchronously rotating planet
  can easily exceed the radiation limit of moist atmosphere,
  which
  is an upper limit of 
  outgoing longwave (infrared) radiation at the top of atmosphere (OLR)
  defined by a one-dimensional radiative-convective 
  equilibrium model of an atmosphere with a plenty amount 
  of liquid water on its bottom surface \citep{nakajima}. 
So, a synchronously rotating planet may easily
   go into the runaway greenhouse state  
   if the amount of day to night energy transport
   is insufficient.

However, in the previous studies 
  on atmospheres of synchronously rotating planets
  by using general circulation models (GCMs),
  the runaway greenhouse state does not emerge
  for several different values of planetary rotation rate
  with the present value of Earth's solar constant 
  \citep[][etc.]{joshi03,merlis,edson}.
Even with the value of solar constant 1.9 times as much as the Earth's,
  \citet{Yang} obtains statistically equilibrium states
  by an aquaplanet GCM experiment, 
  in which high cloud albedo in the regions around the subsolar point
  presumably prevents the realization of runaway greenhouse state.
After the results of those works, we feel
  the mechanism that determines the amount of day-night energy transport
  still remains to be understood 
  and its dependence on planetary rotation rate to be revealed. 
These issues may be crucial in considering the so-called habitability
  of synchronously rotating exoplanets.

Actually, the atmospheric circulation structure, 
  which should be related to day-night energy transport, 
  has been shown to change according to 
  planetary rotation rate (e.g., \citet{showman-etal-CCTP}),
  which is, in this paper, represented by $\Omega^*$,
  the value devided by that of the present Earth:
  $7.272 \times 10^{-5}$ s$^{-1}$.
Merlis and Schneider (2010) obtains, 
  by the use of a GCM with a slab ocean,
  a day-night thermally direct circulation emerges
  in the case with $\Omega^*=1/365$, 
  whereas high-latitudinal westerlies emerge in the case with $\Omega^*=1$.
The latter circulation pattern is similar to that obtained 
  earlier by \citet{joshi03} with $\Omega^*$=1.
\citet{merlis} names the two circulation regimes as
  ``slowly rotating regime'' and ``rapidly rotating regime'',
  respectively.
However,
  there is little description on 
  the transition between those two regimes.
\citet{edson} explores $\Omega^*$ dependence of 
  the atmospheric circulation structures
  both of dry and moist planets,
  and shows that, 
  in addition to the two regimes similar to those identified by 
  \citet{merlis},
  a regime with a strong westerly zonal wind 
  in the low-latitudes
  appears with the intermediate values of $\Omega^*$.
It is also shown that, for the dry planet condition,
  an abrupt change of zonal wind velocity occurs 
  and
  multiple equilibria with hysteretic behavior exist
  between $\Omega^*$=0.109 and $\Omega^*$=0.25.
However, 
  corresponding multiple equilibria for the aquaplanet condition
  have not been described clearly.

As for day-night energy transport, 
  \citet{merlis} shows that 
  the amounts of moist static energy transport
  are almost the same
  between the two cases with $\Omega^*=1/365$ and $\Omega^*=1$,
  but
  there is no description on energy transport 
  for the intermediate values of $\Omega^*$.
\citet{edson} describes
  $\Omega^*$ dependence of surface temperature averaged over the hemisphere,
  but does not present that of energy transport. 
The dependence of day-night energy transport on $\Omega^*$,
  together with what possibly constrains it, 
  remains to be explored. 

Recently,
  GCM experiments are also performed in order to examine possible climates
  on the synchronously rotating terrestrial exoplanets 
  with the particular parameter setups estimated from observations
  \citep{heng,wordsworth}.
Naturally, 
  detailed parameter dependence is not examined in these works, 
  since they focus on exploration of climates under 
  the particular parameters of exoplanets.

In this paper, 
  an experiment with a series of GCM runs with $\Omega^*$ changed finely 
  is performed 
  under a simple setup considering a moist planet that rotates synchronously.
We will attempt to confirm that, for the same value of incoming solar flux 
  as that of the present Earth's, 
  statistically equilibrium states are obtained 
  and the atmosphere does not go into the runaway greenhouse state 
  for various values of $\Omega^*$ 
  including those which are not well examined in the previous studies. 
We also examine
  how $\Omega^*$ affects
  atmospheric circulation structures and day-night energy transport,
  and consider what determine the amount of day-night energy transport.
The same simple model configuration as 
  those of Ishiwatari et al., (2002) and Ishiwatari et al., (2007), 
  namely cloud-free condition, gray radiation, 
  swamp ocean and so on, are adopted.
This choice allows us
  to compare the results of the experiment
  directly with those previous studies of ours
  that show
  the three-dimensional moist atmosphere evolves
  into the runaway greenhouse state 
  when the global mean insolation exceeds the radiation limit.
The use of swamp condition,
  with which the system can reach a statistically equilibrium state
  within a time shorter than that with a slab ocean, 
  is convenient for execution of a large number of runs with various 
  $\Omega^*$ and initial conditions,
  the latter of which is necessary to search for 
  possible multiple equilibrium solutions.

The specification of the GCM and the experimental setups are described
  in Section 2.
The realization of statistically equilibrium states is confirmed,
  and an overview of the dependence of the atmospheric circulation structure
  on $\Omega^*$ are given in Section 3.
Four typical cases with different values of  $\Omega^*$ are 
  chosen and the structures of atmospheric circulation are described
  in Section 4.
The dependence of day-night energy transport on $\Omega^*$ is
  analyzed,
  and it is argued that day-night energy transport is constrained
  by the radiation limit of moist atmosphere in Section 5.
Discussions and conclusions are given in Section 6. 


\section{Model and experimental setup}

The GCM utilized in this study is 
  DCPAM5 (Dennou-Club Planetary Atmospheric Model, 
  \url{http://www.gfd-dennou.org/library/dcpam/index.htm.en}),
  which is reconstructed from 
  GFD-Dennou-Club AGCM5 
  used in \citet{ishiwatari02} and \citet{ishiwatari07}
  with the same basic design
  for  numerical experiments on various planetary atmospheres.
With DCPAM5, 
  it is confirmed that 
  the runaway greenhouse state emerges 
  with the same conditions as those of \citet{ishiwatari02}.
  Here in this study, we use the same model configuration as that of 
  \citet{ishiwatari02}.
The governing equations for dynamical processes are
  the primitive equations.
As for physical processes, 
  simple parameterization schemes are adopted.
The atmosphere consists of water vapor and dry air.
Both of dry air and water vapor are transparent to 
  shortwave radiation, 
  and only water vapor absorbs longwave radiation
  with constant absorption coefficient (0.01 m$^2$ kg$^{-1}$).
The moist convective adjustment scheme \citep{manabe}
  is used as a cumulus parameterization.
  Condensed water is immediately removed from the
  atmosphere as rain. 
There is no cloud; absorption and scattering of radiation by clouds
  are not incorporated.
The surface of planet is entirely covered with the swamp ocean, 
  an ocean with zero heat capacity.
It is assumed that 
  the ocean does not transport heat horizontally
  and does not freeze.
The surface albedo is set to be zero.
A bulk formula \citep{louis}
  is used for surface flux calculation.

In order to obtain advantage from 
  experiences on the present Earth's atmosphere, 
  the values of parameters used in our experiment
  are basically adopted from the values of Earth's 
  except for planetary rotation rate and obliquity.
The values of molecular weight and specific heat of dry air 
  are set to 
  $28.964 \times 10^{-3}$ kg mol$^{-1}$ and 1004.6 J K$^{-1}$ kg$^{-1}$, 
  respectively.
The values of molecular weight and specific heat of water vapor
  are set to 
  $18.0 \times 10^{-3}$ kg mol$^{-1}$ 1810.0 J K$^{-1}$ kg$^{-1}$, 
  respectively. 
The planetary radius $R_p$ is set to be $6.371 \times 10^3$ km.
The acceleration of gravity is 9.80665 m s$^{-2}$, and 
  global mean surface pressure is $10^{5}$ Pa.  
As for the synchronously rotating planet configuration,
  the obliquity is set to be zero, and
  distribution  of solar
  incident flux is fixed to the planetary surface
  (Fig. \ref{fig:OSR})
  as given by 
\begin{eqnarray}
   S_{TOA} = S_0 {\rm max} [0, \cos \phi \cos (\lambda - \lambda_0)], 
    \label{eq:insol_pattern}
\end{eqnarray} 
  where $\phi$ is latitude and $\lambda$ is longitude, 
  with subsolar longitude $\lambda_0 = 90^{\circ}$
  and solar constant $S_0 = 1380$ W m$^{-2}$,
  which is about 88\% of the threshold value of $S_0$ for 
  the non-synchronously rotating aquaplanet 
  to enter to the runaway greenhouse state, 1570 W m$^{-2}$
  \citep{ishiwatari02}.
We use 16 values of $\Omega^*$:
   $\Omega^*$ = 0, 0.05, 0.1,
   0.15, 0.2, 0.25, 0.33, 
  0.5, 0.6, 0.67, 0.7, 0.75, 0.8, 0.85, 0.9, and 1.0.
Hereafter each case will be referred to as 
  character $\Omega$ followed by the value of $\Omega^*$. 
For example, 
  $\Omega0.05$ is the case with its orbital period of 20 Earth days. 
Note that changing $\Omega^*$ with fixed solar constant 
  means changing luminosity of the central star. 
Although a planet with $\Omega^* = 0$ does not exist in reality,
  we examine the circulation structure of this idealized non-rotating planet
  as the limiting case of small $\Omega^*$.


\begin{figure}[ht]
  \centering
  \includegraphics[width=100mm]{./fig/OSR_S1380_sr_Omega0.0.eps}
  \caption{
 Horizontal distribution of the incident solar flux [W m$^{-2}$]
 given by Eq. \ref{eq:insol_pattern}.
  Contour interval is 300 W m$^{-2}$.
  }
  \label{fig:OSR}
\end{figure}


As for the horizontal discretization,
  T21, the triangular truncation at the total wavenumber 21, 
  is adopted in the spherical spectral transform method:
  64 grid-points for the longitudinal axis
  and 32 grid-points for the latitudinal axis. 
As the vertical coordinate,
  $\sigma \equiv p/p_s$ is adopted, 
  where $p_s$ is surface pressure. 
The number of vertical levels is set to be 16.
The model top level is set to be $\sigma=0.02$.
We performed test runs for several values of $\Omega^*$ 
  employing 32 vertical levels with
  the top level of $\sigma = 9.2 \times 10^{-5}$,
  whose results show
  no qualitative change appears
  either in the atmospheric circulation characteristics
  or in the energy budget 
  compared with those with the 16 vertical levels;
  the change of the day side averaged OLR
  is at most 10 W m$^{-2}$ (figures not shown),
  which is negligibly small compared to the value of OLR itself.
We also conducted a high resolution test experiment 
  up to T341 with $\Omega^* = 1$,
  and confirmed that 
  the large scale circulation and the surface temperature
  patterns are mostly unchanged.
These sensitivity tests assure that
  vertical and horizontal resolutions are adequate
  for the present purpose.
Some aspects of the resolution dependence are demonstrated
  later in Appendix A.

For each $\Omega^*$, we perform 10 runs.
As will be mentioned in the following sections,
   we have recognized initial condition dependence
   appears for a certain values of $\Omega^*$;
   different types of circulation patterns are 
   realized from slightly different initial conditions.
The initial condition for each run is an isothermal (280K) resting
  atmosphere perturbed by a small temperature disturbance,
  which is random noise with the amplitude of 0.1 K added 
  to all grid-points;
  we prepare ten different disturbance fields for the ten runs.
Each run is integrated for 2000 Earth days,
  and the data in the later 1000 days are used for analyses.


\section{Dependence of
         atmospheric circulation characteristics 
         on planetary rotation rate}

In all runs, 
   the atmospheres reach statistically equilibrium states; 
   the runaway greenhouse state does not emerge.
Fig. \ref{fig:timeseries} shows
  temporal changes of the global mean values of surface temperature
  and OLR obtained in typical four runs with different values of $\Omega^{*}$.
  In every case,
  the atmosphere settles down to a statistically equilibrium state in which 
  both of global mean surface temperature
  and OLR
  fluctuate around their equilibrium values after about 300 days.
The temporal mean values of global mean surface temperature
  and the magnitudes of temperature fluctuation differ among runs.

The structure of the atmospheric circulation varies with $\Omega^*$.
Fig. \ref{fig:tg_series} overviews the variety 
of the global distributions of time mean surface temperature 
for various values of $\Omega^*$. 
For each value of $\Omega^*$, plotted is the result of a single run 
arbitrary chosen from the ten runs. 
In Fig. \ref{fig:tg_series}, 
we can identify at least three features that characterize 
the variety of surface temperature.
First, an equatorial warm belt in the night hemisphere is present
in $\Omega0.05-\Omega0.8$ (Fig. \ref{fig:tg_series}(b)-(m)), 
while it is absent in the other cases.
Second, the equatorial region in generally warmer in 
$\Omega0.0-\Omega0.8$ (Fig. \ref{fig:tg_series}(a)-(m)), 
while the mid-latitude regions are warmer in the other cases.
These two features above reflect the meridional structures of zonal mean
zonal wind, as will be shown later.
Third, a north-south asymmetry is evident in $\Omega0.6-\Omega0.8$
(Fig. \ref{fig:tg_series}(i)-(m)), 
while it is absent or weak in the other cases.
This last feature reflects the presence of north-south asymmetric 
variability with long time scales,
as will be described in Section 4.3.

\begin{figure}[ht]
 \centering
  \begin{minipage}{13cm}
  \subcaption{Ts} \label{fig:SurfTemp_timeseries}
  \centering \includegraphics[width=130mm]{./fig/SurfTemp_timeseries_all_006.eps}
  \end{minipage}
  \begin{minipage}{13cm}
  \subcaption{OLR} \label{fig:OLRA_timeseries}
  \centering \includegraphics[width=130mm]{./fig/OLRA_timeseries_all_006.eps}
  \end{minipage}
  \caption{
   Time series of global mean quantities.
   (a) Surface temperature [K] and
     (b) OLR [W m$^{-2}$].
    Green line, light-blue line, black line, and red line
     indicate the cases $\Omega0.0$, $\Omega0.15$, 
     $\Omega0.5$, and $\Omega1.0$, respectively.
  }
  \label{fig:timeseries}
\end{figure}

\clearpage

\begin{figure}[hbtp]
 \centering
  \begin{tabular}{llll}
    \hspace{-8.5mm} (a) $\Omega$0.0 
  & \hspace{-8.5mm} (b) $\Omega$0.05 
  & \hspace{-8.5mm} (c) $\Omega$0.1 
  & \hspace{-8.5mm} (d) $\Omega$0.15 \\
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.0E_Tg_xy.eps} &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.05E_Tg_xy.eps} &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.1E_Tg_xy.eps} &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.15E_Tg_xy.eps}
 \\
    \hspace{-8.5mm} (e) $\Omega$0.2 
  & \hspace{-8.5mm} (f) $\Omega$0.25 
  & \hspace{-8.5mm} (g) $\Omega$0.33 
  & \hspace{-8.5mm} (h) $\Omega$0.5 \\
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.2E_Tg_xy.eps}
  &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.25E_Tg_xy.eps}
  &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.33E_Tg_xy.eps}
  &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.5E_Tg_xy.eps}
 \\
    \hspace{-8.5mm} (i) $\Omega$0.6 
  & \hspace{-8.5mm} (j) $\Omega$0.67 
  & \hspace{-8.5mm} (k) $\Omega$0.7 
  & \hspace{-8.5mm} (l) $\Omega$0.75 \\
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.6E_Tg_xy.eps}
  &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.67E_Tg_xy.eps}
  &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.7E_Tg_xy.eps}
  &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.75E_Tg_xy.eps}
 \\
    \hspace{-8.5mm} (m) $\Omega$0.8 
  & \hspace{-8.5mm} (n) $\Omega$0.85 
  & \hspace{-8.5mm} (o) $\Omega$0.9 
  & \hspace{-8.5mm} (p) $\Omega$1.0 \\
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.8E_Tg_xy_006.eps}
  &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.85E_Tg_xy_009.eps}
  &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega0.9E_Tg_xy.eps}
  &
    \hspace{-20.5mm}
    \includegraphics[width=50.0mm,height=30mm]{./fig/Omega1.0E_Tg_xy.eps}
 \\
  \end{tabular}
  \caption{
    Horizontal distributions of 1000-day mean surface temperature
    for all of the computed values of $\Omega^*$. 
    Contour interval is 5 K.
  }
 \label{fig:tg_series}
\end{figure}

\clearpage


In order to describe the general dependence of the
  atmospheric circulation structure on $\Omega^{*}$
  more quantitatively,
  bearing the three features of surface temperature 
  fields identified above in mind,
  we examine the $\Omega^*$-dependences of 
  the values of
  the following four quantities:
  surface temperature at the subsolar point, 
  and that at the antisolar point,  
  upper tropospheric zonal mean zonal wind at the equator,
  and,
  a measure of north-south asymmetry in the surface temperature
  with short time scale transients filtered out.
  The last one is defined as
\begin{eqnarray}
  \Delta_{NS}[T_s]  \equiv
  \frac{1}{2 \pi} \int_{0}^{\pi/2} \int_{0}^{2 \pi}
        \overline{\left| \tilde{T_s} (\lambda, \phi) - 
                         \tilde{T_s} (\lambda, - \phi)\right| }
                  d \lambda \cos \phi d \phi, 
  \label{eq:Ts_equator_antisym_compo}
\end{eqnarray}
where 
  $\tilde{T_s}$ is 50 day running average of 
  surface temperature,
  and
  overbar means temporal average over 1000 days. 
Fig. \ref{fig:omega_dependence_ensemble} shows 
the $\Omega^{*}$ dependences of these quantities.
Note that all of the ten runs for each value of $\Omega^{*}$ 
  are plotted separately.
Now we can identify two separate branches of atmospheric states:
  one continues from  $\Omega^*=0.0$ to  $\Omega^*=0.8$
  (hereafter, referred to as the small-$\Omega$ branch), 
  and the other continues from $\Omega^*=0.7$ to  $\Omega^*=1.0$
  (hereafter, referred to as the large-$\Omega$ branch).
Between  $\Omega^*=0.7$ and $\Omega^*=0.8$,
  these two branches coexist, 
  constituting multiple equilibria.
The preference between the two branches 
  in the range of the multiple equilibria
  seems to depend on the value of $\Omega^*$;
  the ratio of runs on large-$\Omega$ branch increases 
  from 10\% for $\Omega^* = 0.7$ to 80\% for $\Omega^* = 0.8$.
Into which of the two branches a particular run evolves
  depends on the small difference in the initial condition;
each run sets in to either of the two branches in $\sim$ 500 days
  from the start of the model integration,
  and,
  after that,
  does not switch to the other branch.
Note that
  those shown in Fig. \ref{fig:tg_series} (k)-(m) 
  belong to the small-$\Omega$ branch by chance; 
  there are also runs belonging to the large-$\Omega$ branch
  for this range of $\Omega^{*}$, 
  whose surface temperature structure is similar to 
  those shown in Fig. \ref{fig:tg_series} (n)-(p).

In Fig. \ref{fig:omega_dependence_ensemble}
   we can observe 
   the atmospheric circulation characteristics change 
   continuously but distinctly on the small-$\Omega$ branch.
When $\Omega^*=0$, 
  both zonal mean zonal wind 
  and north-south asymmetry are nearly absent.
As $\Omega^*$ increases,
  westerly wind rapidly intensifies,
  and 
  night side surface temperature rapidly rises, 
  both of which are tied to the appearance of the equatorial warm belt
  identified in Fig. \ref{fig:tg_series}(b)-(m).
The temperature at the subsolar point
  falls at first, then rises.
The north-south asymmetry remains to be small.
Around $\Omega^*$=0.5, 
  the north-south asymmetry rises, 
  and increases further as the increase of $\Omega^{*}$.
The asymmetry has been identified in Fig. \ref{fig:tg_series}(i)-(m),
  but has not been evident in cases $\Omega0.2-\Omega0.5$
  (Fig. \ref{fig:tg_series}(e)-(h)),
  where, as will be shown later,
  the temporal scale of the variability is short 
  compared to the averaging period of 1000-days.
Until the end of the small-$\Omega$ branch at $\Omega^*$=0.8,
  the values of temperature at the subsolar and the antisolar points
  are maintained to be 
  high, 
  and the zonal mean wind at the equator 
  keeps its strength.
On the large-$\Omega$ branch,
  the upper tropospheric zonal mean wind is easterly.
Temperature is lower than that of the small-$\Omega$ branch
  at both of the subsolar and the antisolar points,
  and north-south asymmetry is weak.
The changes of the four circulation characteristics are rather small
  over the entire range ($0.7 < \Omega^* < 1$) of the large-$\Omega$ branch.

\clearpage

\begin{figure}[ht]
  \centering
  \begin{tabular}{cc}
  \begin{minipage}{0.49\textwidth}
   \centering
  \subcaption{$T_s (\lambda=90^{\circ}, \phi=0^{\circ})$}
  \label{fig:omega_SurfTemp_mean-t_x90_y0_ensemble}
  \includegraphics[width=75mm]{./fig/omega_SurfTemp_mean-t_x90_y0_ensemble_with-mean_nostd.eps}
  \end{minipage}
  &
  \begin{minipage}{0.49\textwidth}
  \subcaption{$T_s (\lambda=270^{\circ}, \phi=0^{\circ})$}
  \label{fig:omega_SurfTemp_mean-t_x270_y0_ensemble}
  \includegraphics[width=75mm]{./fig/omega_SurfTemp_mean-t_x270_y0_ensemble_with-mean_nostd.eps}
  \end{minipage}
  \\
  \begin{minipage}{0.49\textwidth}
  \subcaption{$\overline{u} (\phi=0^{\circ}, \sigma=0.17)$}
  \label{fig:omega_U_mean-xt_y0_sig0.2_ensemble}
  \includegraphics[width=75mm]{./fig/omega_U_mean-xt_y0_sig0.2_ensemble_with-mean_nostd.eps}
  \end{minipage}
  &
  \begin{minipage}{0.49\textwidth}
  \subcaption{$ \Delta_{NS}[T_s] $ }
  \label{fig:omega_SurfTemp_asym_mean-xt_ensemble}
    \includegraphics[width=57mm,angle=-90,trim=114 180 190 55,clip]{./fig_new/omega_SurfTemp_asym_mean-xt_ensemble_with-mean_nostd_running-mean50_T21.pdf}
  \end{minipage}
  \end{tabular}
 \caption{
   $\Omega^*$ dependences of
   (a) surface temperature [K] at the subsolar point,
   (b) surface temperature [K] at the antisolar point,
   (c) zonal mean equatorial zonal wind [m s$^{-1}$] at $\sigma=0.17$,
   and
   (d) degree of north-south asymmetry of surface temperature 
       defined by Eq. \ref{eq:Ts_equator_antisym_compo} in the text [K].
   The values are temporal averages between 1000 day and 2000 day.
   All of the 10 runs for each $\Omega^*$ case are plotted.
   Red lines and blue lines are ensemble averages
     for the small-$\Omega$ and the large-$\Omega$ branches, respectively.
 }
 \label{fig:omega_dependence_ensemble}
\end{figure}

\clearpage


\section{Typical atmospheric circulation structures}

In order to understand the atmospheric circulation
  and its dependence on $\Omega^{*}$ on the synchronously rotating planet,
  here we examine spatial structures and temporal variation of
  the solutions in detail.
Although the circulation structure changes more or less continuously 
  as the change of $\Omega^{*}$ on the small-$\Omega$ branch as
  is implied
  in Fig. \ref{fig:tg_series} and Fig. \ref{fig:omega_dependence_ensemble},
  we can classify the realized circulation structures into three types
  according to the zonal wind structure and the temporal variability.
They are, 
  in the order of planetary rotation rate where they appear, 
  Type-I characterized with day-night convection,
  Type-II characterized with a broad equatorial westerly jet
  and north-south symmetric stationary wavy
  pattern which turns out to be a stationary Rossby wave,
  and,
  Type-III characterized with long time scale
  north-south asymmetric variability.
As for the large-$\Omega$ branch, 
  we can classify the circulation structure as 
  Type-IV characterized with a pair of 
  mid-latitude deep westerly jets.
For each of the four types, 
   we choose one case and examine it in detail below.



\subsection{Type-I: Day-night convection (Case $\Omega$0.0)}

The Type-I circulation 
   appears in cases with very small values of $\Omega^*$,
   and is characterized with day-night convection,
   being similar to those obtained
   with small $\Omega^*$ in the earlier studies 
   \citep{merlis,edson}.
As a representative case of Type-I, 
  we examine Case $\Omega0.0$. 

The time mean structure of the atmospheric circulation in case $\Omega0.0$ 
  is shown in Fig. \ref{fig:omega0.0E}.
Upper tropospheric horizontal flow diverges toward the night side
  (Fig. \ref{fig:Omega0.0E_wind_vector_geopot_sigma0.2})
  from the concentrated upward motion at the subsolar point,
  where an intense precipitation develops
  (Fig. \ref{fig:Omega0.0E_Rain_xy}).
The 
  outflow is strong not only in the upper troposphere 
  ($\sigma \sim 0.23$) but also at the middle levels around $ \sigma \sim 0.55$
  (Fig. \ref{fig:Omega0.0E_wind-u-sigdot_temp_lat0}).
In the middle troposphere,
  the entire planet except at the subsolar point is covered with
  a widespread, weak, and almost homogeneous downward flow
  (Fig. \ref{fig:Omega0.0E_wind-u-sigdot_temp_lat0}).
In the lower troposphere ($\sigma \sim 0.9$),
  the air flow diverges from the antisolar point and returns to 
  the day side,
  connected to the flow in the heat low converging to
  the subsolar point.

The surface temperature distribution
  (Fig. \ref{fig:Omega0.0E_Tg_xy})
  closely follows the incident solar flux distribution
  (Fig. \ref{fig:OSR}).
The night side surface temperature is almost homogeneous;
  its variation is as small as 10 K,
  being by far the smallest among all of the experiments.
The surface pressure distribution  (Fig. \ref{fig:Omega0.0E_Ps_xy})
  can be interpreted as a direct response to
  the surface temperature distribution;
  a notable feature is the heat low
  in the lower troposphere of the day side
  (Fig. \ref{fig:Omega0.0E_Ps_xy} and 
  Fig. \ref{fig:Omega0.0E_wind-u-sigdot_temp_lat0}).
Temperature in the night side is generally the highest 
   in the middle levels ($\sigma\sim0.6$) 
   and is the lower nearer the surface
   (Fig. \ref{fig:Omega0.0E_wind-u-sigdot_temp_lat0}).
In contrast, 
   temperature in the heat low
   around the subsolar point ($20^{\circ} \leq \lambda \leq 160^{\circ}$),
   increases as the altitude decreases to the ground surface.

The hydrological cycle is governed by the direct day-night circulation.
Surface evaporation flux has its maximum at the subsolar point, 
  and is very small on the whole night side
  (Fig. \ref{fig:Omega0.0E_Evap_xy}).
Rainfall occurs almost exclusively around the subsolar point 
  (Fig. \ref{fig:Omega0.0E_Rain_xy}).
The middle level outflow from the subsolar point
  (Fig. \ref{fig:Omega0.0E_wind-u-sigdot_temp_lat0})
  advects moist air into the night side,
  producing relatively moist tongues 
  ( $0.45 \leq \sigma \leq 0.65$, $\lambda < 210^{\circ}$ and $\lambda > 320^{\circ}$)
  (Fig. \ref{fig:Omega0.0E_QVap_xz-y0}).
However, the magnitude of vertically integrated water vapor flux
  (Fig. \ref{fig:Omega0.0_qvap-column_trnsprt_q_all})
  is fairly small compared to those for the other types. 

\clearpage

\begin{figure}[hbt]
 \centering
  \vspace*{-10mm}
  \begin{tabular}{cc}
  \begin{minipage}{65mm}
  \subcaption{Ps \& $(u,v)$ at $\sigma=0.99$}\label{fig:Omega0.0E_Ps_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.0E_wind_vector_sigma0.99_ps_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{$\Phi$ \& $(u,v)$ at $\sigma=0.17$}
  \label{fig:Omega0.0E_wind_vector_geopot_sigma0.2}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.0E_wind_vector_geopot_sigma0.17_t1000-2000_006.eps}
  \end{minipage}
  \vspace*{-5mm}
  \\
  \vspace*{-5mm}
  \begin{minipage}{65mm}
  \subcaption{T \& $(u,\dot{\sigma})$ at eq.}\label{fig:Omega0.0E_wind-u-sigdot_temp_lat0}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.0E_wind-u-sigdot_temp_lat0_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{$q$ at eq.}\label{fig:Omega0.0E_QVap_xz-y0}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.0E_QVap_xz-y0_t1000-2000_006.eps}
  \end{minipage}
  \\
  \vspace*{-5mm}
  \begin{minipage}{65mm}
  \subcaption{Rain}\label{fig:Omega0.0E_Rain_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.0E_Rain_xy_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{Evap}
  \label{fig:Omega0.0E_Evap_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.0E_Evap_xy_t1000-2000_006.eps}
  \end{minipage}
  \\
  \vspace*{-5mm}
  \begin{minipage}{65mm}
  \subcaption{$\int q d \sigma$ \& $\int q \boldmath{v} d \sigma$}
  \label{fig:Omega0.0_qvap-column_trnsprt_q_all}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.0_qvap-column_trnsprt_q_all_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{Ts}\label{fig:Omega0.0E_Tg_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.0E_Tg_xy_t1000-2000_006.eps}
 \end{minipage}
  \end{tabular}
 \caption{
  \setlength{\baselineskip}{12pt}
  {\footnotesize
  Temporal mean fields between 1000 day and 2000 day 
    of case $\Omega$0.
  (a) Surface pressure [Pa] and horizontal wind vector [m s$^{-1}$] 
      at the lowest level. 
      Contour interval is $5 \times 10^4$ Pa.
  (b) Horizontal wind vector [m s$^{-1}$] and geopotential [J kg$^{-1}$] 
      at $\sigma=0.17$.
      Unit vector indicates 25 m s$^{-1}$.
      Contour interval of geopotential is 500 J kg$^{-1}$.
  (c) Vertical wind $-\dot{\sigma}$ [s$^{-1}$]
      and zonal wind [m s$^{-1}$] (vector), 
      and temperature [K] (color) in the equatorial vertical section.
      Unit vectors of vertical wind and zonal wind are
      $1.67 \times 10^{-5}$ s$^{-1}$ and 
      50 m s$^{-1}$, respectively.
      Contour interval of temperature is 5 K.
  (d) Specific humidity at the equator.
      Contour interval is  $2 \times 10^{-3}$.
  (e) Condensation heating [W m$^{-2}$].
      Color interval is 50 W m$^{-2}$. 
      White area represents heating over 2000 W m$^{-2}$.
  (f) Horizontal distribution of surface evaporation flux [W m$^{-2}$]. 
      Color interval is 50 W m$^{-2}$. 
  (g) Vertically integrated water vapor flux [m s$^{-1}$]
      and vertically integrated water vapor mass [kg m$^{-2}$].
      Unit vector is 0.3 m s$^{-1}$.
      Contour interval is 10 kg m$^{-2}$. 
  (h) Surface temperature [K]. Contour interval is 5 K.
 } 
 }
 \label{fig:omega0.0E}
\end{figure}


\clearpage


\subsection{Type-II: 
  Stationary Rossby wave on broad equatorial westerly jet (Case $\Omega$0.15)}

The atmospheric circulation structure of Type-II
   appears in $0.05 \leq \Omega^* \leq 0.2$
   and is characterized with a warm region in the night side 
   (Fig. \ref{fig:tg_series}b-d)
   below an intense broad equatorial westerly wind
   as is indicated in Fig. \ref{fig:omega_dependence_ensemble}c,
   and large amplitude 
   wavenumber one stationary
   waves in the higher latitudes.
These features are also seen in the circulations obtained
   in an intermediate range of $\Omega^*$ in \citet{edson}.
As a representative case of Type-II, we examine Case $\Omega0.15$.

The time mean structure of the atmospheric circulation in case $\Omega0.15$ 
  is shown in Fig. \ref{fig:omega0.15E}.
The most notable feature is the emergence of a broad and deep 
   westerly wind which covers almost whole depth of the troposphere 
  (Fig. \ref{fig:Omega0.15E_wind-u-sigdot_temp_lat0})
   of the low-latitudinal region
  (Fig. \ref{fig:Omega0.15E_wind_vector_geopot_sigma0.2}).
In the bottom layer near the surface, 
  a trace signature of day-night circulation 
  can still be noted (Fig. \ref{fig:Omega0.15E_Ps_xy}). 
The location of maximum rainfall and the associated deep updraft 
  are
  shifted eastward from the subsolar point by about $20^{\circ}$ 
  (Fig. \ref{fig:Omega0.15E_wind-u-sigdot_temp_lat0} and
  Fig. \ref{fig:Omega0.15E_Rain_xy}), 
  possibly due to moisture advection by the deep westerly wind.
The surface temperature peak is also shifted eastward
  from the subsolar point by $25^{\circ}$ (Fig. \ref{fig:Omega0.15E_Tg_xy}). 
Similar eastward shift emerges also in the other cases on 
  the small $\Omega$ branch, 
  explaining the drop of subsolar point surface temperature
  at $\Omega^\ast \sim 0$ (Fig.\ref{fig:omega_dependence_ensemble}a).
 The peak of evaporation 
   remains at the subsolar point (Fig. \ref{fig:Omega0.15E_Evap_xy}). 
In fact, 
   the latent heat flux around the equator in the day side 
   changes little 
   over the range of $\Omega^\ast$ examined in this study.
The insensitivity to $\Omega^\ast$ 
   results from the employment of 
   swamp surface condition and cloud free condition;
   the ground surface is given the energy of
   the shortwave incoming radiation with fixed geographical distribution,
   to which the energy loss by latent heat of evaporation 
   must approximately balance.
The surface pressure minima are located at $(\lambda,\phi) \sim (120^{\circ},\pm 15^{\circ})$,
  being not only to the east of the subsolar point,
  but also off the equator (Fig. \ref{fig:Omega0.15E_Ps_xy}).
The higher latitude regions are characterized with
  intense wavenumber one stationary waves
  manifested as the ridge around $\lambda \sim 150^{\circ}$
  and the cyclones around $(\lambda,\phi) \sim (330^{\circ}, \pm 60^{\circ})$
  (Fig. \ref{fig:Omega0.15E_wind_vector_geopot_sigma0.2}).
The pressure signatures are generally geostrophic, 
  and have an equivalent barotropic vertical structure
  suggested by the low surface pressure signatures 
  below the upper level low pressure area 
  (Fig. \ref{fig:Omega0.15E_Ps_xy}).

The deep, broad equatorial westerly wind transports 
  a large amount of sensible and latent heat to the night side,
  which is manifested as the warm and moist tongue in the lower to
  the middle troposphere extending eastward crossing the 
  terminator at $\lambda=180^{\circ}$ 
  (Fig. \ref{fig:Omega0.15E_wind-u-sigdot_temp_lat0} and
   Fig. \ref{fig:Omega0.15E_QVap_xz-y0}).
Considerable portion of water vapor 
  transported to the night side at $\lambda=180^{\circ}$
  returns to the day side at $\lambda=360^{\circ}$;
  the amount of the latter is about one fourth 
  of the former (figure not shown).
  At $\lambda=180^{\circ}$,
  water vapor transport to the night side is 
  more intense in the high-latitudinal regions
  than in the equatorial region,
  resulting from the meandering of eastward wind
  associated with
  the intense wavenumber one stationary waves
  and near surface westward wind near the equator.
Supplied by the moisture transport, 
  rainfall is no longer focused at the subsolar point, 
  and 
  some amount of rainfall occurs even in the night hemisphere 
  (Fig. \ref{fig:Omega0.15E_Rain_xy})
  despite the negligibly small amount of surface evaporation.
Also due to the enhanced water vapor transport,
  column integrated moisture content around the antisolar point 
  reaches to about three times that in Case $\Omega0.0$
  (Fig. \ref{fig:Omega0.15_qvap-column_trnsprt_q_all}).
Actually,
  column integrated moisture content increases considerably
  also in the day side; 
  the peak value near the subsolar point in Case $\Omega0.15$ is
  about 1.5 times the value of that in Case $\Omega0.0$,
  whose greenhouse effect results in the rise of surface 
  temperature following the drop near $\Omega^\ast \sim 0$
  (Fig. \ref{fig:omega_dependence_ensemble}a).


It is notable that
  the horizontal distribution of surface temperature closely follows 
  that of column moisture content on the night side 
  (Fig. \ref{fig:Omega0.15_qvap-column_trnsprt_q_all}
  and Fig. \ref{fig:Omega0.15E_Tg_xy});
  in an extensive region of high column water 
  vapor content in the low latitudes,
  surface temperature is high,
  whereas it is very low 
  in the dry regions located around the low pressure centers 
  of wavenumber one structure in the higher latitudes.
Energy budget at the ground surface
  explains the above close relationship;
  because incident solar flux is absent and 
  both latent ($\sim$ 2 W m$^{-2}$) and 
  sensible ($\sim$ -4 W m$^{-2}$) heat fluxes 
  are negligibly small in the night side,
  the upward thermal radiation flux ($\sim$ 230 W m$^{-2}$)
  at the surface almost balances
  with the downward longwave radiation from the atmosphere
  that is exclusively emitted by water vapor, 
  the only radiatively active component in this model. 

All cases in Type-II compared,
  the broad equatorial jet is stronger for the cases with
  larger value of $\Omega^\ast$ as is indicated 
  in Fig. \ref{fig:u_mass_cos_mean_T21},
  where the values of mass weighted global mean zonal wind 
  velocity in Type-II are shown.
Moreover,
  for $\Omega^\ast \gtrsim 0.2$,
  the wind speed is close to the absolute values of the 
  phase speed of the intrinsic phase speed of the normal 
  mode Rossby wave of \citet{Longuet-Higgins}.
The thin line in Fig. \ref{fig:u_mass_cos_mean_T21}
  shows the intrinsic phase speed of 
  meridionally gravest normal mode Rossby wave
  with wave number one,
  which we calculate with the spectral method by \citet{kasahara};
  the equivalent depth of 10000 m, the value for the barotropic mode 
  in an isothermal atmosphere of 245 K is employed
  considering the vertical structure of the waves appearing in Type-II.
The rough coincidence of the speed of the broad eastward 
  equatorial jet and that of the intrinsically westward propagating
  normal mode Rossby wave for each $\Omega^\ast$ suggests that
  the wavenumber one planetary scale stationary wave in Type-II
  is resonantly excited on the broad westerly jet.
Another supporting evidence for the resonant excitation
  is the $\Omega^\ast$-dependence of the amplitude and phase of
  the stationary wavenumber one waves.
The cyclonic regions associated with the waves are implied
  as the north-south symmetric cold regions in the night side 
  mid- to high-latitudes (Fig. \ref{fig:tg_series}).
For $\Omega^\ast$ from 0.05 to 0.2,
  the amplitude of the cyclonic regions is generally large.
The longitudinal phase difference
  between the precipitation maximum and the cyclonic centers
  is about $270^\circ$ for $\Omega^\ast=$ 0.05.
It is the largest eastward phase shift of the upper Rossby wave response
  to a wavenumber one thermal forcing in a westerly flow
  faster than the resonant speed. 
As the increase of $\Omega^\ast$, 
  the phase difference decreases and 
  becomes below $180^\circ$ for $\Omega^\ast=$ 0.25 and 0.33.
Possible mechanism of the acceleration of the broad westerly wind 
  and its resonant relation to the normal mode Rossby waves
  will be discussed in more detail in Section 6.2,
  referring to earlier studies.

For $\Omega^\ast \gtrsim 0.25$,
  the westerly wind  does not catch up to 
  the normal mode Rossby wave speed.
Our preliminary analysis reveals that,
  in these cases,  mid-latitude transient disturbances,
  which originate possibly from baroclinic instability
  considering the development of meridional temperature gradient (not shown),
  transports westerly momentum poleward and 
  decelerates the broad westerly jet.
Detailed analysis on the nature of the transient disturbances
  and their possible role as the ``governor'' of the equatorial jet
  remain to be performed.

\clearpage

\begin{figure}[ht]
 \centering
  \begin{tabular}{cc}
  \begin{minipage}{65mm}
  \subcaption{Ps \& $(u,v)$ at $\sigma=0.99$}
  \label{fig:Omega0.15E_Ps_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.15E_wind_vector_sigma0.99_ps_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{$\Phi$ \& $(u,v)$ at $\sigma=0.17$}
  \label{fig:Omega0.15E_wind_vector_geopot_sigma0.2}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.15E_wind_vector_geopot_sigma0.17_t1000-2000_006.eps}
 \end{minipage}
  \\
  \begin{minipage}{65mm}
  \subcaption{T \& $(u,\dot{\sigma})$ at eq.}\label{fig:Omega0.15E_wind-u-sigdot_temp_lat0}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.15E_wind-u-sigdot_temp_lat0_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{$q$ at eq.}\label{fig:Omega0.15E_QVap_xz-y0}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.15E_QVap_xz-y0_t1000-2000_006.eps}
 \end{minipage}
  \\
  \begin{minipage}{65mm}
  \subcaption{Rain}
  \label{fig:Omega0.15E_Rain_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.15E_Rain_xy_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{Evap}
  \label{fig:Omega0.15E_Evap_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.15E_Evap_xy_t1000-2000_006.eps}
  \end{minipage}
  \\
  \begin{minipage}{65mm}
  \subcaption{$\int q d \sigma$ \& $\int q \boldmath{v} d \sigma$}
  \label{fig:Omega0.15_qvap-column_trnsprt_q_all}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.15_qvap-column_trnsprt_q_all_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{Ts}
  \label{fig:Omega0.15E_Tg_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega0.15E_Tg_xy_t1000-2000_006.eps}
  \end{minipage}
  \end{tabular}
 \caption{
   Same as Fig. \ref{fig:omega0.0E} but for case $\Omega0.15$, 
   except that unit vector in (b) indicates 50 m s$^{-1}$ and
   unit vectors of vertical wind in (c) is
      $2.5 \times 10^{-6}$ s$^{-1}$.
 }
 \label{fig:omega0.15E}
\end{figure}

\clearpage

\begin{figure}[hbtp]
 \centering
  \begin{minipage}{65mm}
  \includegraphics[width=70mm]{fig_new/u_mass_cos_mean_T21.eps}
  \vspace{10mm}
  \end{minipage}
 \\
 \caption{
 Mass-weighted global mean zonal wind velocity for cases with $\Omega^\ast$
 from 0.0 to 0.33 (circles). 
 Absolute value of westward phase velocity of zonal wavenumber one,
 gravest Rossby normal mode is indicated by the thin line for comparison.
 }
 \label{fig:u_mass_cos_mean_T21}
\end{figure}

\clearpage

\subsection{Type-III: 
Long time scale north-south asymmetric variability (Case $\Omega$0.75)
}

The atmospheric circulation structure of Type-III appears 
  on the small-$\Omega$ branch for  $0.5 \lesssim \Omega^* \lesssim 0.8$.
In temporal average, 
  the characteristics of Type-III is similar 
  to that in Type-II in having 
  a strong eastward equatorial jet,
  but, 
  as shown in Fig. \ref{fig:omega_dependence_ensemble}d,
  is different in the presence of 
  significant north-south asymmetric long time scale variabilities.

Before showing the circulation structure of Type-III in detail,
  we overview the $\Omega^{*}$ dependences of 
  the amplitude and the typical oscillation period of 
  the north-south asymmetric variability.
Fig.\ref{fig:Ps_timeseries-xmean}
  compares the time series of zonal mean surface pressure 
  in four cases with different values of $\Omega^{*}$.
In Case $\Omega0.2$, where Type-II structure appears,
  a quasi periodic oscillation with 
  an amplitudes are $\sim$20 hPa and a temporal scale 
  of $\sim$10 days is notable.
In Case $\Omega0.5$,
  in addition to an oscillation with $\sim$20 day period,
  a slower, north-south asymmetric variability is clearly notable;
  its period and amplitude are $\sim$40-100 days and $\sim$45 hPa,
  respectively.
In cases with larger $\Omega^{*}$,
  the slow, north-south asymmetric variability is more intense
  and its characteristic period is longer;
  in Case $\Omega0.67$,
  the amplitude is $\sim$80hPa, and 
  the period is  $\sim$ 1,000 days.
In Case $\Omega0.75$,
  the amplitude is as large as $\sim$160hPa, and,
  looks almost perpetually lasting in Fig.\ref{fig:Ps_timeseries-xmean}d.
However,
  by conducting several extended experiments,
  we have confirmed 
  that the asymmetry does change its sign in a long time;
  the pressure deviation reverses at around t=25,000 days
  for the run shown in Fig.\ref{fig:Ps_timeseries-xmean}d.
Furthermore,
  the sign of the asymmetry is determined by chance;
  in the ten runs conducted for $\Omega0.75$,
  Type-III structure appears in four runs (not shown),
  and, during the period shown in Fig.\ref{fig:Ps_timeseries-xmean}d,
  two of them have positive pressure anomaly in the northern high latitudes, 
  and the remaining two have negative.
We can conclude that,
  despite the development of the distinct long time scale north-south 
  asymmetric variation,
  the obtained structure of the atmospheric circulation is, 
  in statistical sense, north-south symmetric,
  being consistent with the symmetry of the applied solar influx.

Considering the characteristics of the north-south variation,
  we examine Case $\Omega0.75$
  as a representative case of Type-III, 
  where the north-south asymmetry appears as a quasi stationary structure
  lasting the entire duration of the 1000 day for which 
  temporal average is taken.
Throughout the averaging period,
  as shown in Fig.\ref{fig:Ps_timeseries-xmean}d,
  northern(southern) high latitudes is occupied with high(low) pressure.
The north-south asymmetric features discussed below are,
  of course, 
  all reversed at the time period when the surface pressure 
  in northern(southern) hemisphere is low(high).
We also note that,
  the structure of the north-south asymmetric
  atmospheric circulation features develops also in GCM experiments
  with higher horizontal resolution (T42 and T85),
  although it appears in slightly different ranges of $\Omega^\ast$
  (see Appendix A).
So we believe their emergence itself is
  insensitive to model resolution.

The time mean structure of the atmospheric circulation in case $\Omega0.75$ 
  is shown in Fig. \ref{fig:omega0.75E}.
The deep westerly flow along the equator (Fig. \ref{fig:omega0.75E}b and c), 
  and the associated eastward advection of water vapor 
  (Fig. \ref{fig:omega0.75E}d and g)
  resulting in a warm belt along the equator 
  in the night hemisphere (Fig. \ref{fig:omega0.75E}h),
  are features similar to those in Type-II (Fig. \ref{fig:omega0.15E}).
However,
  except the distribution of evaporation,
  which is strongly constrained by insolation 
  as was discussed before concerning Type-II,
  most of the off equatorial features exhibit north-south asymmetry
  in contrast to the north-south symmetry in Type-II.
Northern (southern) high latitudes are covered with surface 
  high (low) pressure area (Fig. \ref{fig:omega0.75E}a).
The low pressure area 
  in the day hemisphere also exhibits north-south asymmetry
   (Fig. \ref{fig:omega0.75E}e);
  the low pressure center in the southern hemisphere is much
  more intense than the counterpart in the northern hemisphere.
Being in geostrophic balance with the gradient around 
  the polar pressure anomalies,
  northern (southern) mid latitude is prevailed by 
  surface north-easterly (north-westerly) wind 
  (arrows in Fig. \ref{fig:omega0.75E}a),
  which brings dry (moist) air into the mid latitudes
  of day (night) hemisphere (Fig. \ref{fig:omega0.75E}g)
  crossing the day-night boundary at $\lambda=180^\circ$,
  inducing 
  the north-westward (south-eastward) development of 
  mid latitude precipitation zone (Fig. \ref{fig:omega0.75E}e) 
  and the north-south asymmetry of surface temperature 
  in both of the day and night hemispheres (Fig. \ref{fig:omega0.75E}h)
  by the anomaly of downward thermal radiation.

Two additional features can be noted 
  that characterize the north-south asymmetry.
First, 
  the westerly region extends further poleward in southern hemisphere
  than in northern hemisphere (Fig. \ref{fig:omega0.75E_suppl}a),
  where intense baroclinic disturbances are developing 
  (not shown here),
  presumably transporting westerly momentum downward.
Second,
  there is a baroclinic zonal wavenumber one feature
  (Fig. \ref{fig:omega0.75E}b and c)
  which has highly north-south asymmetric meridional phase tilt
  (Fig. \ref{fig:omega0.75E_suppl}b);
  the phase lines tilt
  from northwest to southeast in a wide latitudinal zone
  covering from northern high latitudes ($\phi \sim +70^{\circ}$) 
  to southern mid latitudes ($\phi \sim -40^{\circ}$),
  crossing the equator.
The phase tilt of the zonal wavenumber one feature,
  which implies southward transport of westerly momentum
  from northern to southern hemisphere,
  is presumably contributing to drive the mid-latitude
  westerly jet in southern hemisphere noted above.

According to our preliminary analysis (not shown here) on 
  vorticity source following the formulation of \citet{sardeshmukh},
  the meridionally tilted wavenumber one feature seems to be forced 
  jointly by tropical and extratropical precipitation
  (Fig. \ref{fig:omega0.75E}e);
  the heating near the subsolar point, which is distributed 
  mainly in the northern tropics around at 
  $(\phi,\lambda)=(+12^\circ, 120^\circ)$,
  can be regarded as a excitation source of a Rossby wave 
  that contributes northern half of the wavenumber one structure,
  and, the latent heating associated with 
  the precipitation band in southern mid latitudes
  distributed around 
  at $(\phi,\lambda)=(-30^\circ, 180^\circ)$,
  can be regarded as a excitation source of a Rossby wave 
  that contributes southern half.
Upward cascade of baroclinic eddies developing
  in the westerly jet could also contribute the southern half. 
The distribution of midlatitude precipitation seems to be, 
  in turn,
  induced by the north-south asymmetry of moisture flux
  associated with surface pressure
  as is described in the previous paragraph.
All of these features combined,
  the north-south asymmetry may possibly be maintained 
  through a positive feedback loop,
  so that the asymmetry tends to have long life time.
Quantitative examination of the dynamics of the possible
  feedback loop implied above remains for future studies.

\begin{figure}[hbtp]
 \centering
  \begin{minipage}{60mm}
  \subcaption{$\Omega=0.2$}\label{fig:Omega0.2E_Ps_timeseries-xmean}
  \includegraphics[width=60mm]{./fig/Omega0.2E_Ps_timeseries-xmean_006.eps}
  \end{minipage}
  \begin{minipage}{60mm}
  \subcaption{$\Omega=0.5$}\label{fig:Omega0.5E_Ps_timeseries-xmean}
  \includegraphics[width=60mm]{./fig/Omega0.5E_Ps_timeseries-xmean_006.eps}
  \end{minipage}
  \begin{minipage}{60mm}
  \subcaption{$\Omega=0.67$}\label{fig:Omega0.67E_Ps_timeseries-xmean}
  \includegraphics[width=60mm]{./fig/Omega0.67E_Ps_timeseries-xmean_006.eps}
  \end{minipage}
  \begin{minipage}{60mm}
  \subcaption{$\Omega=0.75$}\label{fig:Omega0.75E_Ps_timeseries-xmean}
  \includegraphics[trim = 20mm 27mm 29mm 3mm,clip,width=60mm]{./fig/Omega0.75E_Ps_timeseries-xmean_003.eps}
  \end{minipage}
  \caption{
    Time series of the latitudinal distributions of 
    zonal mean surface pressure [Pa]
    for 
    (a) $\Omega^*=0.2$,
    (b) $\Omega^*=0.5$,
    (c) $\Omega^*=0.67$,
    and
    (d) $\Omega^*=0.75$.
  }
  \label{fig:Ps_timeseries-xmean}
\end{figure}

\clearpage

\begin{figure}[hbtp]
 \centering
 \begin{tabular}{cc}
 \begin{minipage}{65mm}
 \subcaption{Ps \& $(u,v)$ at $\sigma=0.99$}\label{fig:Omega0.75E_Ps_xy}
 \includegraphics[trim = 65mm 25mm 45mm 90mm,clip,width=65mm,height=40mm]{./fig/Omega0.75E_wind_vector_sigma0.99_ps_t1000-2000_003.eps}
 \end{minipage}
 &
 \begin{minipage}{65mm}
 \subcaption{$\Phi$ \& $(u,v)$ at $\sigma=0.17$}
 \label{fig:Omega0.75E_wind_vector_geopot_sigma0.2}
 \includegraphics[trim = 65mm 25mm 45mm 90mm,clip,width=65mm,height=40mm]{./fig/Omega0.75E_wind_vector_geopot_sigma0.17_t1000-2000_003.eps}
 \end{minipage}
  \\
 \begin{minipage}{65mm}
 \subcaption{T \& $(u,\dot{\sigma})$ at eq.}
 \label{fig:Omega0.75E_wind-u-sigdot_temp_lat0}
 \includegraphics[trim = 65mm 25mm 45mm 90mm,clip,width=65mm,height=40mm]{./fig/Omega0.75E_wind-u-sigdot_temp_lat0_t1000-2000_003.eps}
 \end{minipage}
 &
 \begin{minipage}{65mm}
 \subcaption{$q$ at eq.}
 \label{fig:Omega0.75E_QVap_xz-y0}
 \includegraphics[trim = 0mm 30mm 20mm 30mm,clip,width=65mm,height=40mm]{./fig/Omega0.75E_QVap_xz-y0_t1000-2000_003.eps}
 \end{minipage}
 \\
 \begin{minipage}{65mm}
 \subcaption{Rain}
 \label{fig:Omega0.75E_Rain_xy}
 \includegraphics[trim = 0mm 30mm 20mm 30mm,clip,width=65mm,height=40mm]{./fig/Omega0.75E_Rain_xy_t1000-2000_003.eps}
 \end{minipage}
 &
 \begin{minipage}{65mm}
 \subcaption{Evap}
 \label{fig:Omega0.75E_Evap_xy}
 \includegraphics[trim = 0mm 30mm 20mm 30mm,clip,width=65mm,height=40mm]{./fig/Omega0.75E_Evap_xy_t1000-2000_003.eps}
 \end{minipage}
 \\
 \begin{minipage}{65mm}
 \subcaption{$\int q d \sigma$ \& $\int q \boldmath{v} d \sigma$}
 \label{fig:Omega0.75_qvap-column_trnsprt_q_all}
 \includegraphics[trim = 65mm 25mm 45mm 90mm,clip,width=65mm,height=40mm]{./fig/Omega0.75_qvap-column_trnsprt_q_all_t1000-2000_003.eps}
 \end{minipage} 
 &
 \begin{minipage}{65mm}
 \subcaption{Ts}\label{fig:Omega0.75E_Tg_xy}
 \includegraphics[trim = 0mm 30mm 20mm 30mm,clip,width=65mm,height=40mm]{./fig/Omega0.75E_Tg_xy_t1000-2000_003.eps}
 \end{minipage}
 \end{tabular}
 \caption{
 Same as Fig. \ref{fig:omega0.15E} but for 
 case $\Omega$0.75, 
 except that unit vector of vertical wind in (c) is
      $1.3 \times 10^{-6}$ s$^{-1}$.
 }
 \label{fig:omega0.75E}
\end{figure}

\clearpage

\begin{figure}[hbtp]
 \centering
 \begin{tabular}{cc}
 \begin{minipage}{65mm}
 \subcaption{Zonal mean zonal wind }\label{fig:Omega0.75E_Umean}
  \includegraphics[width=60mm,angle=-90]{fig_new/Umean_Omega0.75_3.pdf}
 \label{fig:Omegaa0.75E_umean}
 \end{minipage}
 &
 \begin{minipage}{65mm}
 \subcaption{Eddy Stream Function at $\sigma=0.17$}
  \includegraphics[width=60mm,angle=-90]{fig_new/psi017_Omega0.75_3.pdf}
 \label{fig:Omega0.75E_psi_sigma0.2}
 \end{minipage}
  \\
 \end{tabular}
 \caption{
 Temporally averaged structure of the atmosphere for case $\Omega$0.75:
 (a) zonal mean zonal wind, and (b) eddy stream function at $\sigma$=0.17
 averaged from 1000 day to 2000 day.
 }
 \label{fig:omega0.75E_suppl}
\end{figure}

\clearpage

\subsection{Type-IV : mid-latitude westerly jets (Case $\Omega$1.0)}

The atmospheric circulation structure of Type-IV appears
  on the entire large-$\Omega$ branch for  $\Omega^* > 0.7$.
The characteristics of this type
  is a somewhat Earth-like
  the mid- to high- latitudes westerly jets.
This characteristics is similar to those 
  obtained by \citet{merlis} and \citet{edson} 
  with $\Omega^* = 1$,
  although several points of difference can be noted (See Section 6.1).
As a representative case of Type-IV, we examine Case $\Omega1.0$.

The time mean structure of the atmospheric circulation in case $\Omega1.0$
  is shown in Fig. \ref{fig:omega1.0E}.
The mid latitudes are occupied by 
  westerly wind extending whole depth of the troposphere
  (Fig. \ref{fig:Omega1.0E_Ps_xy} and 
   Fig. \ref{fig:Omega1.0E_wind_vector_geopot_sigma0.2}).
The low latitudes are occupied by easterly wind,
  but it covers only upper troposphere. 
The lower tropospheric circulation along the equator
  (Fig. \ref{fig:Omega1.0E_wind-u-sigdot_temp_lat0})
  is more strongly controlled by the day-night contrast;
  longitudinal wind near the surface converges to form the upward motion
  at the subsolar point,
  and diverges around the antisolar point
  compensated by the broad downward motion. 
In the off-equatorial latitudes, 
  latitudinal tilting of zonal wavenumber one wave
  features are notable, 
  whose vertical structure is generally baroclinic,
  in contrast to the barotropic Rossby wave in Type-II.
Polar regions are covered with deep low pressure areas. 

The precipitation and water vapor distributions 
  are more complicated than those 
  of the cases on the small-$\Omega$ branch.
Precipitation (Fig. \ref{fig:Omega1.0E_Rain_xy}) is most intense 
  in a sideway-toppled V-shaped region 
  extending from the equatorial point $(\lambda,\phi) \sim (110^{\circ},0^{\circ})$ to 
  $(\lambda,\phi) \sim (30^{\circ}, \pm25^{\circ})$,
  loosely overlapping the low pressure area in the western part of 
  the day hemisphere
  (contours in Fig. \ref{fig:Omega1.0E_Ps_xy}).
The wings of the V-shaped precipitation region intrude into the night side 
  from the regions around $\phi=\pm 25^{\circ}$
  at $\lambda=360^{\circ}$.
There are also a pair of zonally elongated precipitation zone
  in the higher latitudes,
  which starts at $(\lambda,\phi) \sim (45^{\circ}, \pm45^{\circ})$ 
  to points $(\lambda,\phi) \sim (330^{\circ}, \pm80^{\circ})$ in the night side.
The distribution of column integrated water vapor content
  roughly follows that of precipitation 
  (Fig. \ref{fig:Omega1.0_qvap-column_trnsprt_q_all}),
  but largest moisture content areas are located
  around the high latitude parts of the equatorial V-shaped strong
  precipitation area at $(\lambda,\phi) \sim (50^{\circ}, \pm30^{\circ})$,
  being far from the equator.

The distribution of night side surface temperature 
  (Fig. \ref{fig:Omega1.0E_Tg_xy})
  closely follows that of the atmospheric water vapor content 
  (Fig. \ref{fig:Omega1.0_qvap-column_trnsprt_q_all})
  as in the cases on the small-$\Omega$ branch. 
However, reflecting the complex structure of humidity,
  temperature varies longitudinally;
  it is warmer to the east along $\phi\sim\pm30^{\circ}$, 
  whereas it is warmer to the west
  along $\phi\sim\pm50^{\circ}$. 
Also the distribution of surface temperature in the day side 
  is affected by the distribution of water vapor content;
  the highest surface temperature appears 
  at $(\lambda,\phi) \sim (80^{\circ}, \pm 40^{\circ})$,
  which are the locations quite far from the subsolar point
  and below the belts of large water content
  (deep blue colors of Fig. \ref{fig:Omega1.0_qvap-column_trnsprt_q_all}).
The values of surface temperature at the subsolar and the antisolar points
  are lower than the respective values in Type-II or III
  (Fig. \ref{fig:omega_SurfTemp_mean-t_x90_y0_ensemble} 
  and Fig. \ref{fig:omega_SurfTemp_mean-t_x270_y0_ensemble}), 
  resulting from the reduction of atmospheric 
  water content compared to those cases. 

\begin{figure}[hbtp]
 \centering
  \begin{tabular}{cc}
  \begin{minipage}{65mm}
  \subcaption{Ps \& $(u,v)$ at $\sigma=0.99$}
  \label{fig:Omega1.0E_Ps_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega1.0E_wind_vector_sigma0.99_ps_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{$\Phi$ \& $(u,v)$ at $\sigma=0.17$}
  \label{fig:Omega1.0E_wind_vector_geopot_sigma0.2}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega1.0E_wind_vector_geopot_sigma0.17_t1000-2000_006.eps}
  \end{minipage}
  \\
  \begin{minipage}{65mm}
  \subcaption{T \& $(u,\dot{\sigma})$ at eq.}
  \label{fig:Omega1.0E_wind-u-sigdot_temp_lat0}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega1.0E_wind-u-sigdot_temp_lat0_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{$q$ at eq.}
  \label{fig:Omega1.0E_QVap_xz-y0}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega1.0E_QVap_xz-y0_t1000-2000_006.eps}
  \end{minipage}
  \\
  \begin{minipage}{65mm}
  \subcaption{Rain}
  \label{fig:Omega1.0E_Rain_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega1.0E_Rain_xy_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{Evap}
  \label{fig:Omega1.0E_Evap_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega1.0E_Evap_xy_t1000-2000_006.eps}
  \end{minipage}
  \\
  \begin{minipage}{65mm}
  \subcaption{$\int q d \sigma$ \& $\int q \boldmath{v} d \sigma$}
  \label{fig:Omega1.0_qvap-column_trnsprt_q_all}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega1.0_qvap-column_trnsprt_q_all_t1000-2000_006.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{Ts}
  \label{fig:Omega1.0E_Tg_xy}
  \includegraphics[width=65mm,height=40mm]{./fig/Omega1.0E_Tg_xy_t1600-1650_006.eps}
  \end{minipage}
  \end{tabular}
 \caption{
  Same as Fig. \ref{fig:omega0.75E} but for case $\Omega$1.0.
 }
 \label{fig:omega1.0E}
\end{figure}

\clearpage

\section{Day-night energy transport}

\subsection{Dependence on $\Omega^*$}

In this section,
   we examine
   how day-night energy transport changes with $\Omega^*$,
   responding to the considerable change of the atmospheric circulation structure
   described in the previous section.
We analyze 
  outgoing longwave radiation of the night side, $F_{OLR}$, 
  day-night dry static energy transport, $\mathcal{T}_{sens}$, 
  and day-night latent energy transport, $\mathcal{T}_{lat}$,
  which, 
  in equilibrium states, 
  satisfy the energy balance of the night side:
\begin{eqnarray}
  \mathcal{T}_{sens} + \mathcal{T}_{lat} - 2 \pi R_p^2 F_{OLR} = 0.
  \label{eq:OLR_AllHeatTransport}
\end{eqnarray}
$\mathcal{T}_{sens}$ and $\mathcal{T}_{lat}$ are
  calculated assuming 
  the approximate balances of 
  heat and moisture budgets in the night side atmosphere, 
  which are
\begin{eqnarray}
   2 \pi R_p^2 ( F_{SLR} + F_{sens} - F_{OLR} + L P ) + \mathcal{T}_{sens}  &=& 0,  \\
   2 \pi R_p^2 ( F_{evap} - P ) + \mathcal{T}_{lat}/L  &=& 0, 
\end{eqnarray}
where
  $F_{evap}$ is surface evaporation flux, 
  $F_{SLR}$ is net upward longwave radiation flux at the surface, 
  $F_{sens}$ is surface sensible heat flux, 
  $P$ is precipitation, and
  $L$ is latent heat of water vapor,
  all of which 
  are the 1000-day mean spatially averaged values 
  over the night side.

Fig. \ref{fig:Omega-dep-LatSensFlux} shows 
  $\Omega^*$ dependences of 
  $F_{OLR}$, $\mathcal{T}_{sens}/ (2\pi R_p^2)$, 
  and $\mathcal{T}_{lat}/ (2\pi R_p^2)$.
All of the 10 runs are plotted for each value of $\Omega^*$. 
The most remarkable feature is that
  total energy transport is almost unchanged
  regardless of the branches of solutions and the value of $\Omega^*$,
  while
  the partition into 
  $\mathcal{T}_{sens}$ and $\mathcal{T}_{lat}$ changes.
For $\Omega^* \sim 0$, 
  where Type-I structure appears,
  $\mathcal{T}_{lat}$ is negligibly small,
  as atmospheric water vapor content is very small 
  (Fig. \ref{fig:Omega0.0_qvap-column_trnsprt_q_all}).
As $\Omega^*$ increases 
  and Type-II structure appears,
  $\mathcal{T}_{lat}$ rapidly increases, 
  but $\mathcal{T}_{sens}$ decreases as much,
  keeping the sum of the two ($F_{OLR}$) almost unchanged.
The increase of $\mathcal{T}_{lat}$ 
  results from the development of the deep broad 
  westerly wind
  (Fig. \ref{fig:Omega0.15E_wind_vector_geopot_sigma0.2}
  and
  Fig. \ref{fig:Omega0.15E_wind-u-sigdot_temp_lat0})
  together with the increase of moisture in the day hemisphere
  (Fig. \ref{fig:Omega0.15E_QVap_xz-y0}).
Further increase of $\mathcal{T}_{lat}$
  and decrease of  $\mathcal{T}_{sens}$
  continue for larger $\Omega^{*}$
  for which Type-III with north-south asymmetric variabilities appear.
$\mathcal{T}_{lat}$ exceeds $\mathcal{T}_{sens}$ at $\Omega^* = 0.33$, 
  and, 
  $\mathcal{T}_{lat}$ reaches about twice $\mathcal{T}_{sens}$ 
  at the large-$\Omega$ end of the small-$\Omega$ branch ($\Omega^* = 0.8$).
Still, the sum of the two ($F_{OLR}$) is kept almost constant.
At the transition 
  from the small-$\Omega$ branch to the large-$\Omega$ branch
  around $\Omega^*\sim0.75$,
  $\mathcal{T}_{lat}$ suddenly reduce by about half.
Nevertheless,
  compensated by the equally abrupt increase of $\mathcal{T}_{sens}$, 
  total heat transport changes only a little. 
The decline of $\mathcal{T}_{lat}$ 
  at the transition 
  results from 
  the associated disappearance of broad westerly wind in the low latitudes.
Type-IV structure has a pair of deep mid-latitude 
  westerly jets blowing through the day and the night sides
  (Fig. \ref{fig:Omega1.0E_wind_vector_geopot_sigma0.2}),
  but they can not transport as much water vapor
  as the broad equatorial westerly wind in Type-II or Type-III does,
  because the water vapor mixing ratio in the mid latitudes 
  is smaller than in the lower latitudes.
The variation of total day-night energy transport is 
  less than 2 \%
  over the wide range of $\Omega^{*}$, 
  while the atmospheric circulation structure varies considerably. 
Day-night total energy transport scarcely depends on 
  the atmospheric circulation structure. 

We have already seen in Fig. \ref{fig:omega_SurfTemp_mean-t_x270_y0_ensemble}
  that surface temperature at the antisolar point changes greatly with
  the change of $\Omega^*$. 
One might feel curious about this result, since
  day-night total energy transport is almost constant. 
However, 
  if we examine the hemispherically averaged temperature,
  the change become only modest.
Fig. \ref{fig:Omega-dep-MeanSurfTemp} shows $\Omega^\ast$ dependences 
   of surface temperature averaged
   over the night side, the day side, and the whole globe.
The range of the variation of night side average temperature
   is around 10 K,
   which is much smaller than 
   the variation at the antisolar point, i.e., almost 50 K
   (Fig. \ref{fig:omega_dependence_ensemble}b).
This results from
  the compensation between the temperature variations
  in the lower and the higher latitudes;
  in Type-II and Type-III, surface temperature in the low latitudes 
  including the antisolar point is high,
  while 
  the regions of low surface temperature appear in the higher latitudes 
  associated with the large amplitude Rossby waves
  (Fig. \ref{fig:tg_series}(b)-(m)). 
The remaining modest changes of averaged temperatures
  can be accounted mainly by 
  the change of mean column water vapor content.

\subsection{Constraint by the radiation limit of moist atmosphere}

As described in the previous subsection,
  the total amount of day-night energy transport is found to be 
  insensitive to the change of $\Omega^*$
  and to the associated change of atmospheric circulation structure. 
The invariance of day-night total energy transport
  is equivalent to
  the invariance of day side OLR,
  because the day-night total energy transport equals to 
  the difference between the day side OLR and 
  the incident solar flux;
  the latter is constant in the present study.
It has been recognized that, in the framework of 
  one-dimensional radiative convective equilibrium model, 
  the value of OLR from the atmosphere on a water covered planet
  can not exceed the radiation limit. 
In the following, 
  we attempt to understand the invariance of 
  day-night energy transport
  as being related to the constraint on the day side OLR
  by the radiation limit of moist atmosphere. 

Fig. \ref{fig:tg_olr} shows
  the relationship between surface temperature and OLR in the day side
  obtained by the present GCM calculations
  superposed on
  the relations obtained by the one-dimensional radiative convective 
  equilibrium model which is the same as that described in section 4 
  of \citet{ishiwatari02} 
  with several specified values of tropospheric relative humidity. 
The relationship between surface temperature and OLR are sampled
   at the grid points within
   the 120 degree $\times$ 120 degree rectangular region
   centered at the subsolar point
   from the run for each $\Omega^{*}$
   described in the previous section.

In all of the GCM runs,
  the maximum values of OLR are between 400 and 430 W/m$^2$,
  which reside under the values of the radiation limits  
  in the one-dimensional calculation,
  considering that the values of relative humidity
  averaged over the troposphere in the day side of the GCM runs 
  are within the range of 60$\sim$80 \%.
Moreover, 
  in each of the GCM results,
  the relationship between surface temperature and OLR
  roughly follows those obtained in the one-dimensional calculations.
These results imply
  that the day side OLR in the present GCM calculations
  are determined as being constrained by the radiation limit
  of moist atmosphere on a water covered planet. 
Now recalling that the system is in a statistically equilibrium state, 
  the amount of day-night total energy transport 
  should be equal to the difference between
  the incident solar flux and the radiation limit of moist atmosphere.
The results of our GCM calculations indicate that 
  the change of the atmospheric circulation structure associated with
  the change of $\Omega^*$
  does not modify drastically the mean value of atmospheric humidity,
  and hence does not affect
  the value of the radiation limit. 
This explains the general insensitivity of day-night energy 
  transport to $\Omega^*$ obtained in the present GCM calculations. 

\clearpage

\begin{figure}[hbtp]
 \centering
  \begin{tabular}{cc}
  \begin{minipage}{65mm}
  \subcaption{Day-to-Night Heat Fluxes}
  \label{fig:Omega-dep-LatSensFlux}
  \includegraphics[width=75mm]{./fig/atmos_heat_east_unit-watt_nostd.eps}
  \end{minipage}
  &
  \begin{minipage}{65mm}
  \subcaption{Mean Surface Temperature}
  \label{fig:Omega-dep-MeanSurfTemp}
  \includegraphics[width=75mm]{./fig/SurfTemp_ensemble_nostd.eps}
  \end{minipage}
  \\
  \end{tabular}
 \caption{
   (a) $\Omega^\ast$ dependences of 
   outgoing longwave radiation of the night side, $F_{OLR}$
     ($\bigcirc$), 
   day-night dry static energy transport per unit area, 
     $\mathcal{T}_{sens}/ (2 \pi R^2)$ ($\blacktriangledown$), 
     and 
   day-night latent energy transport per unit area,
   $\mathcal{T}_{lat}/ (2 \pi R^2)$ ($\times$).
   Unit is [W m$^{-2}$].
   All of the 10 runs for each $\Omega^\ast$ case are plotted.
   Blue and red lines represent ensemble averages 
   for 
   the small-$\Omega$ and the large-$\Omega$ branches, respectively.
   (b) Same as (a) but for 
     global mean ($\bigcirc$), 
     day side mean ($\times$), and
     night side mean ($\Box$) of surface temperature [K].
 }
 \label{fig:Omega-dep-Flux-Ts}
\end{figure}

\begin{figure}[ht]
 \centering
  \includegraphics[width=110mm]{./fig/Tg_OLR_120x120region_withSubSolar.eps}
 \caption{
  Relationships between surface temperature and OLR
    obtained by the GCM and by the vertically one-dimensional
    radiative-convective equilibrium model.
  Scatter plots show the GCM results. 
  Data are from the grid points in the 120 degree $\times$ 120 degree 
    rectangular region whose center is the subsolar point.
  Purple, light blue, green, and pink dots indicate
    runs $\Omega$0.0, 0.15, 0.5, and 1.0, respectively.
  Crosses in black circles indicate the values at the subsolar point.
  Black solid lines are the one-dimensional model results
  with 50, 60, 70, 80, 90, and 100 \% for the value
  of tropospheric relative humidity
  in order from the uppermost, respectively. 
  }
 \label{fig:tg_olr}
\end{figure}

\clearpage



\section{Concluding remarks}

\subsection{Summary of Results and Comparison with Previous Studies} 

A numerical experiment is performed 
  by the use of a cloud-free, swamp aquaplanet GCM 
  with a gray absorption coefficient for longwave radiation 
  and with Earth's solar constant. 
The values of planetary rotation rate
  normalized by the Earth's value, $\Omega^*$,
  is varied from 0 to 1. 
For all $\Omega^*$ cases, 
  statistical equilibrium states are obtained;
  the runaway greenhouse state does not emerge. 
The obtained circulation structures are classified 
   into the four types;
Type-I characterized with day-night convection,
Type-II characterized with a broad equatorial westerly jet
  and a stationary Rossby wave,
  and,
Type-III characterized by a long time scale north-south asymmetric 
  variability, and
Type-IV characterized by a pair of mid-latitudinal westerly jets.
Type-I, II, and III evolve continuously from one to another 
  as $\Omega^*$ increases, constituting one branch of solution 
  referred to as the small-$\Omega$ branch, 
  whereas Type-IV belongs to different branch
  referred to as the large-$\Omega$ branch
  (Fig. \ref{fig:omega_dependence_ensemble}).
For $0.7 \leq \Omega^* \leq 0.8$, multiple equilibrium states emerge; 
  both Types-III and Type-IV are allowed.
The dependence of the amount of day-night energy transport 
  on $\Omega^*$ is analyzed.
It is confirmed that the amount is large enough to prevent
  the day side atmosphere from entering to a runaway greenhouse state.
Moreover, 
  the amount is found to be almost insensitive to $\Omega^*$
  despite the drastic change of the atmospheric circulation structure,
  although the partition into latent and sensible energy transports varies.
Day side OLR in the experiments are analyzed and compared
  with the values obtained by the one-dimensional radiative convective model.
The result strongly suggests
  that day side OLR is constrained by the radiation limit of moist
  atmosphere;
  the details of the circulation structure does not greatly change 
  atmospheric humidity,
  so that the value of the radiation limit is unchanged. 
This explains the invariance of 
  day to night energy transport.
It equals to the difference between 
  incoming solar flux and day side OLR. 
The former is a constant prescribed amount in this study,
  and the latter is constrained to be the radiation limit. 

It should be useful to re-examine
  the circulation characteristics obtained in previous studies
  from the present viewpoint,
  since this study has performed more complete investigation
  on its sensitivity to $\Omega^*$
  than have been done in the previous studies.
The ``slowly rotating regime'' and the ``rapidly rotating regime'',
  identified by \citet{merlis} may presumably
  correspond to the small-$\Omega$ branch 
  and the large-$\Omega$ branch in the present study, respectively.
However,
  the correspondence is not certain
  because they present
  the horizontal distributions of atmospheric variables for only 
  two values of $\Omega^*$.
The circulation structures similar to those of Type-I and Type-IV
  are obtained for those two values of $\Omega^*$, 
  but it remains unclear
  whether they have obtained atmospheric structures similar
  to Type-II and Type-III.
The dependence of the circulation structure on $\Omega^*$
  obtained by \citet{edson} 
  can be compared with the results of the present study with more confidence. 
They observed two separate branches of 
  solutions with multiple equilibria,
  and solutions
  with planetary waves of zonal wavenumber one
  superposed on broad westerly wind in the low latitudes
  for intermediate values of $\Omega^*$. 
These features are similar to those obtained in the present study.

However, more careful comparison suggests  a few differences.
One is the difference of the directions of the zonal mean equatorial 
  upper tropospheric wind obtained on the large-$\Omega$ branch.
It is easterly in the present study, 
  whereas it is westerly in \citet{edson},
  at least in their ``dry'' experiment;
  the structure of the low to mid-latitude Rossby response
  in the upper troposphere implies that 
  it is also westerly in their ``aquaplanet'' case,
  although its intensity and structure is unclear.
  \footnote{\citet{edson} presents the maximum values of zonal wind
  in each of the aquaplanet experiments in Table 3, 
  but does not mention whether it occurs at the equator or not.}
This difference may originate from the difference 
  in the precipitation distribution:
  the maximum of rainfall seems to be located at the equator
  in the case of $\Omega^\ast=1$ of \citet{edson}, 
  judged from the figures showing the distribution of 
  cloud cover and the meridionally averaged latent heat 
  flux convergence,
  whereas 
  it is located in subtropics in the present study,
  driving equatorward flow in the upper troposphere (not shown).
The difference of precipitation distribution may arise from 
  the differences in the GCM setups used 
  in theirs and in the present studies,
  namely the treatment of oceanic heat transport:
  \citet{edson} includes linear oceanic heat transport,
  whereas we do not.
The fact that \citet{merlis}, where no oceanic heat transport
  is included, obtains subtropical maxima of day side precipitation
  and easterly upper tropospheric zonal mean wind similar to ours
  supports the speculation.
Another difference
  is that in the ranges of planetary 
  rotation rates allowing the multiple equilibria;
  it is around $\Omega^\ast = 0.2$ in \citet{edson},
  whereas
  it is around $\Omega^\ast = 0.75$ in the present study.
Part of the difference originates from the use of rather low
  horizontal resolution, T21, with which we conducted the experiments;
  with T42 and T85, 
  the range shifts to smaller value of $\Omega$
  (Fig.\ref{fig:omega_dep_resolution}).
Such difference could be an important issue when considering 
  whether the multiple equilibrium solutions is possible 
  in the habitable zones around M type red dwarf stars,
  for which $\Omega^\ast < 0.5$.
Possible sensitivity of the realizability of multiple equilibria
  to model physics, e.g., treatment of cloud, surface albedo,
  or oceans, will be a focus of future studies.

One of the most novel features in the present experiments
  could be the global-scale north-south asymmetric variability
  (Type-III) appearing for a fairly wide range of $\Omega^*$,
  whose origin remains to be examined in detail.
Both \citet{merlis} and \citet{edson} do not mention such
  north-south asymmetric oscillating structures,
which suggests that
  the occurrence of oscillation may depend on the physical 
  configurations of the experimental design.
Both \citet{merlis} and \citet{edson}
  employ a slab ocean with finite heat storage as the surface condition,
  whereas the swamp condition with zero heat storage is used 
  in the present study.
However,
  oceanic
  heat storage 
  does not seems to be a critical factor;
  we repeated several runs of $\Omega0.75$ employing a slab ocean,
  and still obtained north-south asymmetric variation
  essentially similar to that described in Section 4.3.
Oceanic heat transport,
  which \citet{edson} considered, could be more important.
Including possible importance of ocean discussed above,
  the clarification of the conditions for the emergence of 
  the global-scale, north-south asymmetric variability 
  is left for future studies,
  together with more convincing understandings on 
  the nature and dynamics of the north-south 
  asymmetric variability.

Provided that the north-south asymmetric variability of 
  Type-III in the present study is theoretically permitted,
  an interesting question would be 
  whether such a variability is 
  observationally detectable on exoplanets or not. 
Actually, around M9 type red dwarf stars, 
  synchronously rotating habitable planets
  should have $\Omega^{*}\sim0.5$ 
  (Kaltenegger and Traub, 2009),
  which is in the range for Type-III structure. 
Typical difference between the northern and the southern
  averaged OLRs obtained in our GCM calculations
  reaches about 30 W m$^{-2}$, 
  which is as large as about 10 \% of OLR averaged over the entire day side. 
Since this difference of OLR is the same order of magnitude 
  as the error in the observation of secondary eclipses of hot-Neptune
  \citep[e.g.]{deming},
  it might be detectable if the observational accuracy 
  improves by another order of magnitude.

\subsection{Mechanism of the Broad Equatorial Jet in Type-II}

The latitudinally broad equatorial eastward jet in Type-II is similar to 
  those of the synchronously rotating terrestrial planet of \citet{edson} 
  and of the hot Jupiters of 
  \citet{showman-guillot}, \citet{dobbs-dixon}, and others.
This universal appearance of equatorial prograde jets
  in synchronously rotating planetary atmospheres
  implies an existence of common mechanism underneath.
\citet[2011]{showman-polvani10} argues that
  the equatorward eddy transport of westerly momentum arising
  from the superposition of equatorial Kelvin and Rossby waves 
  excited by the day-night contrast of heating
  is responsible to the appearance of equatorial jets.
Preliminary analysis of the present experiments also indicates
  the importance of the equatorward westerly momentum transport 
  due to stationary eddies,
  which can be interpreted to be caused by 
  Rossby and Kelvin responses to the equatorial thermal forcing
  as described by \citet{showman-polvani}.

A novel observation in the present study is 
  that
  the broad equatorial eastward jet is accelerated
  for a relatively wide range 
  of $\Omega^\ast$ to
  up to or exceeding the speed of wavenumber one
  normal mode Rossby wave (Fig. \ref{fig:u_mass_cos_mean_T21}).
Appearance of the large amplitude normal mode Rossby wave 
  as a near resonance with the zonal mean wind
  is also noted by \citet{edson} for the case 
  for $\Omega^\ast \sim 0.2$ of
  the dry atmosphere of a synchronously rotating planet.
Our novel point is that
  resonant-like behavior is established over much 
  wider range of $\Omega^\ast$ starting from very small value 
  of $\Omega^\ast$.

\citet{arnold} obtains, 
  in an three-dimensional atmospheric model of the Earth's setup
  forced by planetary scale wavy tropical heat source,
  an abrupt transition of equatorial zonal wind 
  to a westerly speed exceeding that of the propagation of 
  the Rossby wave.
\citet{tsai} describes the equatorial acceleration
  due to combination of the equatorial Kelvin and the Rossby wave
  responses forced by thermal forcing,
  and demonstrates that 
  the longitudinal phase of the Rossby wave is shifted eastward
  as the increase of the background westerly and, eventually,
  the direction of westerly momentum flux caused by
  the combined effect with the Kelvin response is reversed
  when the background westerly exceeds the resonant speed.
The shift of the Rossby response phase is also observed 
  as the circulation pattern difference between
  the spin-up and the mature periods of the broad equatorial 
  jet formation
  in the simulation of hot Jupiters by \citet{showman-polvani}. 
A notable difference between the results of present study
  and those for the hot Jupiters of previous studies is that
  the excited wave here is vertically barotropic 
  while those are vertically propagating.
The excitation of barotropic wave by latent heating
  can be understood by considering 
  the vertical shear of the broad equatorial
  westerly jet \citep{wang}
  and also 
  the presence of the rigid lower boundary. 

It should be kept in mind, however,
  that equatorial Kelvin and Rossby responses can only
  re-distribute westerly momentum within radius of deformation,
  and, by itself,
  can not explain the development of the broad
  equatorial westerly jet.
As the equatorial radius of deformation associated with 
  the barotropic mode concerned is comparable to or 
  larger than the planetary radius,
  the dominant excitation of barotropic wave is 
  favorable to driving a meridionally broad equatorial jet.
Still,
  some other mechanisms has to cancel
  the easterly acceleration in high latitudes,
  which should compensate for the westerly acceleration 
  around the equator,
  so as to realize the wind structure of Type-II 
  in the present study
  whose zonal mean zonal wind is westerly almost everywhere 
  in the middle and upper troposphere (not shown).
Downward motion in high latitudes associated with
  Hadley circulation
  may be contributing to remove the easterly momentum.
Detailed investigation of the driving mechanism of 
  the broad equatorial jet 
  including the effects of various types of transient 
  disturbances is left for future studies.

\subsection{Implications and Remaining Issues}

The insensitivity of the day to night energy transport 
  to the variety of circulation structures
  demonstrated in the present study has an important implication
  in consideration of habitability of a synchronously rotating planet. 
Since it assures a certain amount of energy to be transported 
  from the day side to the night side, 
  relatively warm regions will be maintained at some locations
  on the night side regardless of $\Omega^*$. 
In fact,
  regions with surface temperature warmer than freezing point 
  appear in the night side in the present calculation.
The location of warm regions in the night side
  changes with $\Omega^*$;
  a warm region appears in the equatorial region to the east of
  the trailing terminator for the cases on the small-$\Omega$ branch,
  whereas it appears in the mid-latitudes to the west of 
  leading terminator for the cases on the large-$\Omega$ branch.
Based on the location of possible habitable zone 
  for a planetary system discussed by 
  \citet{kaltenegger},
  $\Omega^*$ should be generally less than and not very close to 1 
  for synchronously rotating habitable exoplanets,
  which means that the cases on the small-$\Omega^*$ branch 
  is more applicable.

It should be emphasized, however, that 
  the insensitivity of day-night energy transport to $\Omega^*$
  found in the present study hold with several conditions.
We may list a few cases below for examples 
  where the insensitivity could be broken. 
First, when incident solar flux is small and
  the day side temperature is not warm enough 
  to raise OLR to the radiation limit of moist atmosphere,
  the value of the day side OLR, and therefore day night 
  energy transport, shall not be constrained 
  by the radiation limit.
Second, to the contrary, 
  when incident solar flux is so large that the anticipated amount  
  of day night energy transport exceeds the amount that can 
  escape from the night hemisphere to space 
  at the radiation limit of moist atmosphere, 
  day night energy transport will differ from that 
  determined by the values of incident solar flux and OLR 
  constrained by the radiation limit in the day side. 
In this situation,
  the atmosphere is expected to proceed to the runaway greenhouse state,
  where day night energy transport is also regulated 
  by the radiation limit but increase of atmospheric temperature
  should be taken into account.
Third,
  when the amount of water on planetary surface is so small that
  the radiation limit of moist atmosphere is hard to be 
  established, 
  energy transport may depend considerably on $\Omega^*$. 
In such situation, i.e., ``a land planet'',
  the change of circulation pattern influences 
  even the existence condition of statistically equilibrium state
  \citep{abe}.

Cloud, which is not considered in the present study, 
   may well modify the thermal and dynamical aspects of the present
   results. 
\citet{Yang} performed 
  a GCM experiment with cloud effects on synchronously rotating planets
  with increased solar constant. 
They show that equilibrium states can be obtained with the larger values 
  of solar constant 
  compared to those of the not-tidally locked case.
However,
  they do not investigate 
  possible relationship between the emergence of the runaway greenhouse 
  and the radiation limit. 
We have been performing a numerical study concerning the latter point,
  and will report the results in a near future.

Finally,
  the dynamics of the ocean is undoubtedly one of the important element
  to be examined in considering the habitability of synchronously
  rotating exoplanets.
\citet{hu} has performed
  a series of climate simulation using a coupled atmosphere-ocean model
  with the setting of Gliese 581g,
  and has found that 
  the ocean can contribute largely to the day to night hemisphere energy 
  transport and the partition of the heat transport into the atmospheric
  and oceanic transports varies much depending on the atmospheric CO$_2$
  concentration and the incident short wave flux from the central star.
The inclusion of dynamically active ocean may possibly affect
  the insensitivity of day-night energy transport to $\Omega^*$.
This issue remains to be a focus of future studies.


\appendix

\section{Resolution dependence}

\setcounter{figure}{0}

Because of the large number of experiments required to examine
  the $\Omega^\ast$ dependence of circulation structures
  including the possibility of multiple equilibrium solutions,
  the horizontal resolution of the GCM used in this study
  is limited T21.
In this appendix,
  we check the resolution dependence of the results,
  by briefly describing the results obtained in 
  higher resolution models, T42 and T85,
  focusing on some of the possibly resolution sensitive features.
For T42,
  we have performed 10 runs for several selected values of $\Omega^\ast$.
For T85,
  only one run was performed for each values of $\Omega^\ast$.
As show below,
  in a qualitative sense,
  main results, namely the existence of the four types of solutions,
  are not sensitive to the model's resolution.
Figs.\ref{fig:omega_dep_resolution}a and \ref{fig:omega_dep_resolution}b
  show
  upper tropospheric zonal mean zonal wind at the equator
  for various values of $\Omega^\ast$ in the T42 and T85 models, respectively;
  for T42, those in all runs for each $\Omega^\ast$ are plotted.
Compared to the corresponding figure for T21 resolution
  (Fig.\ref{fig:omega_dependence_ensemble}c),
  the gross feature is common:
  there are two branches of solutions,
  and the equatorial zonal wind velocity for each $\Omega^\ast$
  is insensitive to the resolution.
And,
  at least in the T42 model,
  the two branches coexist in a range of $\Omega^\ast$ 
  constituting multiple equilibria,
  although the value of $\Omega^\ast$ for the multiple equilibria
  is smaller than that in the T21 model by about 0.1.
In the case of T85 model,
  as we can not perform more than one runs for each $\Omega^\ast$,
  the existence of multiple equilibria can not be confirmed.
However,
  the gross behavior is not inconsistent with that in T42;
  the value of $\Omega^\ast$ for the upper end of the small
  $\Omega$ branch is the same.



Fig. \ref{fig:u_mass_cos_mean_T21-85} shows 
  the values of mass weighted zonal mean wind speed for
  different values of $\Omega^\ast$ obtained in the runs
  with T21, T42 and T85 resolutions,
  comparing with the intrinsic phase speed of the 
  Rossby wave normal mode.
In a qualitative sense,
  we can confirm the main feature described in Section 4.2,
  i.e., the mass weighted zonal mean wind speed closely follows
  or slightly exceeds the Rossby wave phase speed
  for $0.0 \lesssim \Omega^\ast \lesssim 0.2$,
  and levels off for larger $\Omega^\ast$.
Only mild exception is $\Omega0.15$ in T85,
  where the zonal mean wind is decelerated by transient disturbance
  whose nature is unclear.



In Figs.\ref{fig:omega_dep_resolution}c and \ref{fig:omega_dep_resolution}d,
  a measure of north-south asymmetry of surface temperature
  for various values of $\Omega^\ast$ in the T42 and T85 models are shown,
  respectively;
  for T42, those in all runs for each $\Omega^\ast$ are plotted.
Compared to the corresponding figure for T21 resolution
  (Fig.\ref{fig:omega_dependence_ensemble}d),
  the degree of north-south asymmetry seems to be weaker 
  in higher resolution models.
Still,
  we can identify features grossly free from resolution dependence;
  monotonic increase of the degree of north-south asymmetry
  on the small-$\Omega$ branch,
  and the smaller degree of north-south asymmetry on 
  the large-$\Omega$ branch.
The temporal scales of the north-south asymmetric variability
  is common in the order of magnitude for all model resolutions
  (not shown here).
The spatial structure of the north-south asymmetric variability
  in Type III, i.e., toward the large-$\Omega^\ast$ end
  of the small-$\Omega$ branch,
  is also common in all model resolution.
Fig. \ref{fig:Ps_Omega0.6_resolution}
  the horizontal structures of surface pressure in T42 and T85 models
  for $\Omega^\ast = 0.6$ averaged for 500 days 
  during which north(south) pole is occupied with high(low) pressure.
Compared to the Fig.\ref{fig:omega0.75E}a showing the structure of
  the variability for $\Omega^\ast = 0.75$ in T21 model,
  all of major features, such as the longitudes of the low pressure area
  in the southern day hemisphere and 
  the high pressure area in the southern night hemisphere,
  are common.


\section*{Acknowledgments}

Two anonymous reviewers are deeply acknowledged for carefully reading 
  the original manuscript and providing many helpful comments.
This study was supported by MEXT KAKENHI Grant Number JP23103003,
  and JSPS KAKENHI Grant Numbers JP20540223, JP24340016,
  JP25400219, JP25800264, and global COE program
  ``Foundation of international center for planetary science''
  of the Japan Society for the Promotion of Science.
A part of calculations were performed by SX8R of
  the Institute of Space and Astronautical Science supercomputer system, 
  Japan Aerospace Exploration Agency.
  Resolution tests of numerical integrations
  were realized by the use of
  the SX series of
  Center for Global Environmental Research, 
  National Institute of Environmental Studies.
We used the software 
  developed by Dennou Ruby Project for simulations, analyses, and drawings.

\clearpage

\begin{figure}[hbtp]
 \centering
 \begin{tabular}{cc}
 \begin{minipage}{65mm}
  \subcaption{$\overline{u} (\phi=0, \sigma=0.17)$ in T42}
  \label{fig:omega_U_mean-xt_y0_sig0.2_T42}
  \includegraphics[height=65mm,angle=-90,trim = 50mm 50mm 70mm 110mm,clip]{./fig_new/omega_U_mean-xt_y0_sig0.2_T42.pdf}
 \end{minipage}
 &
 \begin{minipage}{65mm}
  \subcaption{$\overline{u} (\phi=0, \sigma=0.17)$ in T85}
  \label{fig:omega_U_mean-xt_y0_sig0.2_T85}
  \includegraphics[height=65mm,angle=-90,trim = 50mm 50mm 70mm 110mm,clip]{./fig_new/omega_U_mean-xt_y0_sig0.2_T85.pdf}
 \end{minipage}
 \\
 \begin{minipage}{65mm}
  \subcaption{$ \Delta_{NS}[T_s]$ in T42}
  \label{fig:omega_SurfTemp_asym_mean-xt_T42}
  \includegraphics[height=65mm,angle=-90,trim = 50mm 50mm 70mm 110mm,clip]{./fig_new/omega_SurfTemp_asym_mean-xt_ensemble_with-mean_nostd_running-mean50_T42.pdf}
 \end{minipage}
 &
 \begin{minipage}{65mm}
  \subcaption{$ \Delta_{NS}[T_s]$ in T85 }
  \label{fig:omega_SurfTemp_asym_mean-xt_T85}
  \includegraphics[height=65mm,angle=-90,trim = 50mm 50mm 70mm 110mm,clip]{./fig_new/omega_SurfTemp_asym_mean-xt_running-mean50_T85.pdf}
 \end{minipage}
 \\
 \end{tabular}
 \caption{
 Same as Fig. \ref{fig:omega_dependence_ensemble} c but for 
 in T42 model (a) and T85 model (b),
 and same as Fig. \ref{fig:omega_dependence_ensemble} d but for 
 in T42 model (c) and T85 model (d).
 }
 \label{fig:omega_dep_resolution}
\end{figure}

\begin{figure}[hbtp]
 \centering
  \begin{minipage}{65mm}
  \includegraphics[width=70mm]{fig_new/u_mass_cos_mean_T21-85.eps}
  \vspace{10mm}
  \end{minipage}
 \\
 \caption{
 Same as Fig.\ref{fig:u_mass_cos_mean_T21},
 but for including the those for horizontal resolutions of T42 (squares)
 and T85 (triangles) in addition to those for T21(circles).
 }
 \label{fig:u_mass_cos_mean_T21-85}
\end{figure}

\begin{figure}[hbtp]
 \centering
 \begin{tabular}{cc}
 \begin{minipage}{65mm}
 \subcaption{Ps Omega0.6 T42}
 \label{fig:Ps_Omega0.6_T42}
 \includegraphics[height=65mm,angle=-90]{./fig_new/T42_0.6_Ps_tave.pdf}
 \end{minipage}
 &
 \begin{minipage}{65mm}
 \subcaption{Ps Omega0.6 T85}
 \label{fig:Ps_Omega0.6_T85}
 \includegraphics[height=65mm,angle=-90]{./fig_new/T85_0.6_Ps_tave.pdf}
 \end{minipage}
  \\
 \end{tabular}
 \caption{
 Mean surface pressure distributions for $\Omega$0.6
 in T42 model (a) and T85 model (b) for 500 days
 during which north(south)
 pole is occupied with high(low) pressure.
 }
 \label{fig:Ps_Omega0.6_resolution}
\end{figure}

\newpage

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\end{thebibliography}



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