CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27

CGER-REPORTISSN 1341-4356
CGER-I153-2021

CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27

Numerical studies on the variety of climates of exoplanets
using idealistic configurations

Masaki Ishiwatari, Kensuke Nakajima, Shin-ichi Takehiro,
Yuta Kawai, Yoshiyuki O. Takahashi, George L. Hashimoto,
Youhei Sasaki and Yoshi-Yuki Hayashi

Center for Global Environmental Research

CGER-I153-2021

National Institute for Environmental Studies, Japan

CGER-REPORTISSN 1341-4356
CGER-I153-2021

CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27

Numerical studies on the variety of climates of exoplanets
using idealistic configurations

Masaki Ishiwatari, Kensuke Nakajima, Shin-ichi Takehiro,
Yuta Kawai, Yoshiyuki O. Takahashi, George L. Hashimoto,
Youhei Sasaki and Yoshi-Yuki Hayashi

Center for Global Environmental Research

National Institute for Environmental Studies, Japan

CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27

Numerical studies on the variety of climates of exoplanets using idealistic configurations
Masaki Ishiwatari, Kensuke Nakajima, Shin-ichi Takehiro,
Yuta Kawai, Yoshiyuki O. Takahashi, George L. Hashimoto,
Youhei Sasaki and Yoshi-Yuki Hayashi
Edited by:Center for Global Environmental Research (CGER)
National Institute for Environmental Studies (NIES)

Coordination for Resource Allocation of the Supercomputer:
Center for Global Environmental Research (CGER)
National Institute for Environmental Studies (NIES)

Supercomputer Steering Committee (FY2020):

Masayoshi Ishii (Meteorological Research Institute, Japan Meteorological Agency)
Masaki Satoh (Atmosphere and Ocean Research Institute, The University of Tokyo)
Seiya Nishizawa (Computational Climate Science Research Team, RIKEN AICS)
Akinori Takami (Center for Regional Environmental Research, NIES)
Nobuaki Yoshiguchi (Planning Department, NIES)
Hisashi Yashiro (Center for Global Environmental Research, NIES)
Hideharu Akiyoshi (Center for Global Environmental Research, NIES)
Seita Emori (Center for Global Environmental Research, NIES)

Maintenance of the Supercomputer System:

Environmental Information Department (EID)
National Institute for Environmental Studies (NIES)

Operation of the Supercomputer System:
NEC Corporation

Copies of this report can be obtained from:Center for Global Environmental Research (CGER)
National Institute for Environmental Studies (NIES)
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Fax: +81-29-858-2645
E-mail: www-cger@nies.go.jp
This report is also available as a PDF file.
See: http://www.cger.nies.go.jp/ja/activities/supporting/publications/report/index.html

Copyright 2021:

NIES: National Institute for Environmental Studies
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ISSN 1341-4356 (printed version), ISSN 2434-5679 (online version), CGER-I153-2021

Foreword
The Center for Global Environmental Research (CGER) at the National Institute forEnvironmental Studies (NIES) was established in October 1990, with the main objectives ofcontributing to the scientific understanding of global environmental change and identifying
solutions to critical environmental problems. CGER conducts environmental research from aninterdisciplinary, multi-agency, and international perspective, and provides an intellectual
infrastructure for research activities in the form of databases and a supercomputer system.
CGER also ensures that data from its long-term monitoring of the global environment is madeavailable to the public.
CGER installed its first supercomputer system (NEC SX-3, Model 14) in March 1992, andthis was subsequently upgraded to an NEC Model SX-4/32 in 1997, an NEC Model SX-6 in
2002, an NEC Model SX-8R/128M16 in 2007, an NEC Model SX-9/A(ECO) in June 2013,
and an NEC Model SX-ACE in June 2015. In March 2020, the system was further upgradedwith the inclusion of an NEC Model SX-Aurora TSUBASA A511-64 to provide an increased
capacity for speed and storage.
The supercomputer system is available for use by researchers from NIES and other researchorganizations and universities in Japan. The Supercomputer Steering Committee consists ofleading Japanese scientists in climate modeling, atmospheric chemistry, ocean environment,
computer science, and other areas concerned with global environmental research, and one of its
functions is to evaluate proposals of any research requiring the use of the supercomputer system.
To promote the dissemination of results, we publish both Annual Reports and occasional
Monograph Reports. Annual Reports deliver the results of all research projects that have madeuse of the supercomputer system in a given year, while Monograph Reports present the
integrated results of a particular research program.
This Monograph presents the results obtained in numerical studies performed by a researchgroup of GFD Dennou Club. The contents are based mainly on two papers: Ishiwatari et al.
(2002) and Noda et al. (2017). In these studies, a variety of climates of aquaplanets with grayatmosphere are investigated by changing the values of solar constant and the horizontal
distribution of incoming solar radiation flux. Since simple physical schemes and idealized
model configurations are used in these studies, the results obtained by experiments are more
understandable compared to results obtained by sophisticated models and are expected toprovide a theoretical framework for acquiring a general understanding of the maintenancemechanism and existence conditions of various climates. The results will contribute toinvestigations of the variety of climates of exoplanets and the stability of Earth's climate.
In the years to come, we intend to continue our support for environmental research byenabling the use of our supercomputer resources and continue to disseminate practicalinformation based on our results.
March 2021

Nobuko Saigusa
Director
Center for Global Environmental Research
National Institute for Environmental Studies-i-Preface
This volume of the CGER’S SUPERCOMPUTER MONOGRAPH REPORT series is the27th publication of research outcomes achieved by users of the supercomputer facilities at theCenter for Global Environmental Research (CGER) at the National Institute for Environmental
Studies (NIES).
The authors have investigated a variety of climates of aquaplanets with gray atmospheretaking exoplanets into consideration using atmospheric general circulation models. Exoplanets
are planets that exist around stars outside our solar system and are considered to have a climate
different from the climate of Earth. The authors have focused on extreme climates of planetswith amounts and a horizontal distribution of incident solar flux different from those of the
Earth, since solar flux is one of the most important parameters for determining climate. In theexperiments, the runaway greenhouse state emerged when the amount of solar flux (solar
constant) increased by several tens of percent. The runaway greenhouse state is thenonequilibrium atmospheric state in which temperature and atmospheric water vapor keepincreasing. In the runaway greenhouse state, liquid water disappears from the planetary surface,
thus the surface environment would not be suitable for harboring life. As for the extreme
horizontal distribution of solar flux, the authors investigated the climates of synchronously
rotating planets. A synchronously rotating planet has the same rotation period as the orbital
period due to strong tidal force and is a possible type of exoplanet. Since such planets have apeculiar distribution of incoming flux with a perpetual dayside and a nightside, the climate
would be severe for life.
This monograph is a summary of two papers that consider extreme climates: Ishiwatari etal. (2002) that examined the occurrence conditions of the runaway greenhouse state, and Noda
et al. (2017) that examined the climates of synchronously rotating planets. These papers provide
knowledge about the various climates from mild to extreme of aquaplanets with grayatmosphere. Although the models used in these studies are simple, the results can be describedby simpler conceptual models such as one-dimensional models and can be used as a theoreticalframework for considering the variety of planetary climates. We believe that the publication ofthis monograph will be valuable as a summary of such a theoretical framework. It is expectedthat the consideration of the occurrence conditions of the drastic change in climate will becomea basis for the examination of the stability of Earth's climate. This monograph will also
contribute to assessing the habitability of terrestrial-type exoplanets that have been discovered
and will be discovered in the future.
March 2021

Masaki Ishiwatari
Professor
Graduate School of Science
Hokkaido University- ii -

Contents
Foreword .....................................................................................................................................i
Preface ....................................................................................................................................... ii
Contents .................................................................................................................................... iii
List of Figures ...........................................................................................................................vi
List of Tables .............................................................................................................................. x

Numerical studies on the variety of climates of exoplanets
using idealistic configurations ................................................................................................. 1
Abstract ..................................................................................................................................... 3
Chapter 1
Introduction .............................................................................................................................. 5
1.1 Drastic climate change caused by the change of the solar constant: occurrence ofthe runaway greenhouse state ............................................................................................... 7
1.2 Circulation structures of planets with a peculiar distribution of solar flux .......................... 8
1.3 Contents of this monograph ................................................................................................. 9
Chapter 2
Model description ................................................................................................................... 11
2.1 Basic assumptions .............................................................................................................. 12
2.2 An overview of GCMs ....................................................................................................... 12
2.3 Discretization ..................................................................................................................... 12
2.4 Atmospheric constituents and radiation processes ............................................................. 12
2.5 Physical processes other than radiation processes ............................................................. 13
2.6 Surface conditions .............................................................................................................. 13
2.7 Model modification for experiments with increased solar constant .................................. 14
2.7.1 𝑝𝑝� change due to evaporation and condensation .................................................... 14
2.7.2 Upper damping layer ................................................................................................ 14
2.7.3 Vertical filter ............................................................................................................ 15
Chapter 3
Occurrence condition of the runaway greenhouse state
in a three-dimensional system ............................................................................................... 17
3.1 Introduction ........................................................................................................................ 18
3.2 Model configuration ........................................................................................................... 18- iii -

3.3 Emergence of thermally runaway states............................................................................. 22
3.4 Comparison with a one-dimensional system ...................................................................... 23
3.5 Circulation structure toward the runaway greenhouse state............................................... 27
3.6 Remarks .............................................................................................................................. 35
3.7 Summary ............................................................................................................................ 35
Chapter 4
Circulation structure of planets with a peculiar distribution ofincoming solar radiation flux: climate of synchronously rotating planets ....................... 37
4.1 Introduction ........................................................................................................................ 38
4.2 Model configuration ........................................................................................................... 38
4.3 Dependence of the atmospheric circulation characteristics on the planetary rotation
rate ...................................................................................................................................... 40
4.4 Typical atmospheric circulation structures ........................................................................ 43
4.4.1 Type-I: Day-night convection (Case Ω0.0) .............................................................. 44
4.4.2 Type-II: Stationary Rossby wave on broad equatorial westerly jet (Case Ω0.15) ... 46
4.4.3 Type-III: Long time scale north-south asymmetric variability (Case Ω0.75) .......... 50
4.4.4 Type-IV: Mid-latitude westerly jets (Case Ω1.0) ..................................................... 54
4.5 Day-night energy transport................................................................................................. 57
4.5.1 Dependence on Ω* ................................................................................................... 57
4.5.2 Moist atmosphere radiation limit constraint ............................................................ 59
4.6 Dependence on resolution .................................................................................................. 60
4.7 Summary ............................................................................................................................ 63
Chapter 5
Preliminary results obtained for cloudy atmosphere with non-gray radiation................ 65
5.1 Introduction ........................................................................................................................ 66
5.2 Model configuration ........................................................................................................... 66
5.3 Results ................................................................................................................................ 67
5.4 Summary ............................................................................................................................ 68
Chapter 6
Conclusion and discussion ..................................................................................................... 69
6.1 Summary ............................................................................................................................ 70
6.2 Ongoing problem and future plans ..................................................................................... 70
Acknowledgements .................................................................................................................. 73
References ................................................................................................................................ 73
Contact person .......................................................................................................................... 75- iv -CGER’S SUPERCOMPUTER ACTIVITY REPORT (previously published) ....................... 77
NIES Supercomputer Annual Report (previously published) .................................................. 77
CGER’S SUPERCOMPUTER MONOGRAPH REPORT (previously published) ................ 77-v-

List of Figures
Chapter 1
1.1

1.2

Relationships between surface temperature and OLR for gray atmosphere. The blacksolid line shows 𝜎𝜎 𝑇𝑇�� . Other solid lines represent equilibrium solutions obtained by
the vertical one-dimensional radiative-convective model. The green, red, orange, andblue lines represent the results for 𝑝𝑝�� =106, 105, 104, 0 Pa, respectively. 𝑝𝑝�� is thepartial pressure of dry air at the surface. The solid dashed-line represents the
Komabayashi-Ingersoll limit obtained by the stratosphere model. Modified from
Ishiwatari (2014), Fig. 1.......................................................................................................... 7
Small-mass exoplanets discovered by astronomical missions. The ordinate is the massof the central host star and the abscissa is the semi-major axis. Red crosses represent
exoplanets discovered until 2014 with a mass smaller than ten times of Earth's mass.
The data were obtained at http://exoplanet.eu. Large black dots represent planets in thesolar system. Orange lines represent 10.0, 1.0. and 0.1 times of Earth's solar constant.
Thin blue lines represent 1 day, 10 days, and 100 days of the orbital period. The thickblue line represents the tidal lock radius inside which planets are considered to besynchronously rotating planets. .............................................................................................. 8

Chapter 3
3.1

3.2

3.3

3.4

3.5

3.6

Meridional distributions of incoming solar radiation flux. Unit is W m-2. Thick solidline, dashed line and dotted line are for S=1380 W m-2, S=1200 W m-2 and S=1800
W m - 2 , respectively. Dotted-dashed line indicates the Komabayashi-Ingersoll limit(385.2 Wm-2), and thin solid line indicates the upper-limit value of OLR (355.0
W m - 2 ) obtained by the NHA92 model. Both of them are calculated with theparameters of the present study. From Ishiwatari et al. (2002), Fig. 1. ................................ 20
Time evolutions of (a) global mean OLR (W m-2) and (b) global mean surface
temperature (K). Dashed line, solid line, dotted line and dashed-dotted line indicate
experiments S1200, S1380, S1570 and S1800, respectively. From Ishiwatari et al.
(2002), Fig. 2. ....................................................................................................................... 22
The relationship between global mean SSR and global mean OLR. The values of OLR
at day 1000 are plotted except for S1600 where the value is at day 2000. White circles
represent the cases where the atmosphere reaches an equilibrium state, while crossmarks represent the cases where the atmosphere is in a thermally runaway state. Notethat the values of OLR for thermally runaway states are continuously decreasing. From
Ishiwatari et al. (2002), Fig. 3. .............................................................................................. 23
The meridional distributions of (a) zonal mean OLR (W m-2) and (b) zonal meansurface temperature (K) of the cases in which the system reaches equilibrium states.
Thick solid line, dotted line, dotted-dashed line, dashed line, and thin solid line indicate
experiments S1570, S1550, S1500, S1380, and S1200, respectively. The data aretemporally averaged between days 950 and 1000. From Ishiwatari et al. (2002), Fig. 4.
.............................................................................................................................................. 24
Vertical distributions of temperature obtained by one-dimensional model with relative
humidity of 60% for the radiation scheme. The profiles are plotted by specifying thevalues of temperature at the bottom of atmosphere as those obtained by the experiments.
Ordinates are (a) pressure (Pa) and (b) optical depth. Cross marks indicate surface
temperature. From Ishiwatari et al. (2002), Fig. 5. ............................................................... 25
Vertical distributions of zonally averaged temperature at the equator for various valuesof solar constant. Ordinates are (a) pressure (Pa) and (b) optical depth. The profiles
obtained in the experiments S1800, S1700, S1600, S1570, S1550, S1500, S1380,- vi -

3.7

3.8

3.9
3.10
3.11

3.12

3.13

S1200 are plotted. Cross marks indicate surface temperature. From Ishiwatari et al.
(2002), Fig. 6. ....................................................................................................................... 25
The relationship between surface temperature (K) and OLR (Wm-2). Curves represent
surface temperature--OLR relationship obtained by the one-dimensional radiativeconvective equilibrium model with various values of relative humidity for the radiation
scheme. Thin solid line, dotted line, thick solid line and dashed line indicate 100% of
relative humidity (the same as the results of NHA92), 80%, 60% and 40%, respectively.
Marks represent the relationship between equatorial zonal mean values of surface
temperature and OLR obtained by GCM. White circles and cross marks represent theresults where the system reaches an equilibrium state and where the system cannot,
respectively. From Ishiwatari et al. (2002), Fig. 7. ............................................................... 26
Meridional structures of the zonal mean circulation fields of the experiment S1380: (a)temperature, (b) condensation heating, (c) specific humidity, (d) relative humidity, (e)mass stream function, and (f) zonal wind. Contour intervals are (a) 5 K, (b) 5 × 10��K day-1, (c) 2 × 10�� , (d) 0.05, (e) 5 m s-1, (f) 1.0 × 10�� kg s-1, respectively. Timemean fields between t=950 to 1000 days are plotted. From Ishiwatari et al. (2002),
Fig.8.. .................................................................................................................................... 28
Same as in Fig. 3.8 but for the experiment S1570. Contour intervals are the same as inFig. 3.8 except for (c) 1.0 × 10�� . From Ishiwatari et al. (2002), Fig.9. .......................... 29
Same as in Fig. 3.8 but for the experiment S1800. Time-mean fields between t=870 to
920 days are plotted. Contour intervals are the same as in Fig. 3.8 except for (b)1.0 × 10�� K day-1 and (c) 0.1. From Ishiwatari et al. (2002), Fig.10. ............................... 30
Meridional structure of zonal mean optical depth in the experiments (a) S1380, (b)S1570, and (c) S1800. Here, 𝜎𝜎 is used as the vertical coordinate. The contour intervals
are (a) 0.05, (b) 0.2, and (c) 5.0, respectively. The shaded areas in (c) represent the areawith optical depth less than 1. From Ishiwatari et al. (2002), Fig.11. .................................. 32
Meridional structure of temperature with the optical depth as the vertical coordinate in
the experiments (a) S1380, (b) S1570, and (c) S1800. The areas without data
correspond to the regions below the ground surface. The contour intervals are (a) 2.5K,(b) 2.5K, and (c) 5.0K, respectively. From Ishiwatari et al. (2002), Fig.12. ........................ 33
The meridional distributions of vertical energy fluxes in experiments (a) S1380, (b)S1570, and (c) S1800. Thick solid line, dashed line, dotted line, dashed–dotted line,
and thin solid line indicate condensation heating (RAIN), evaporation flux (EVAP),
OLR, net longwave radiation at the surface (SLR), and sensible heat flux (SENS),
respectively. Unit is W m-2. The condensation heating of (c) has its maximum value of
920 W m-2 at the equator. From Ishiwatari et al. (2002), Fig.13. ......................................... 34

Chapter 4
4.1

4.2
4.3
4.4

Horizontal distribution of the incoming solar flux [W m-2] given by Eq. (4.1). Contour
interval is 300 Wm-2. From Noda et al. (2017), Fig. 1.......................................................... 39
Time series of global mean quantities. (a) Surface temperature [K] and (b) OLR [Wm-2].
Green, light-blue, black, and red lines indicate Ω0.0, Ω0.15, Ω0.75, and Ω1.0,
respectively. From Noda et al. (2017), Fig. 2. ...................................................................... 40
Horizontal distributions of 1000-day mean surface temperature for all of the computed
values of Ω*. Contour interval is 5 K. From Noda et al. (2017), Fig. 3. .............................. 41
Ω* 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
𝜎𝜎 =0.17, and (d) degree of north-south asymmetry of surface temperature defined by
Eq. (4.2) in the text [K]. The values are temporal averages between day 1000 and day
2000. All 10 runs for each Ω* case are plotted. Red and blue lines are ensemble- vii -

4.5

4.6
4.7

4.8
4.9
4.10
4.11
4.12

4.13

4.14
4.15

averages for the small-Ω and the large-Ω branches, respectively. From Noda et al.
(2017), Fig. 4. ....................................................................................................................... 43
Day 1000 to day 2000 temporal mean fields for case Ω0.0. (a) Surface pressure (color
shading) [Pa] and horizontal wind vectors [m s-1] at the lowest level. Contour intervalof surface pressure is 5×102 Pa, and the unit vectors of zonal and meridional wind are
20 m s-1. (b) Horizontal wind vector [m s-1] and geopotential [J kg-1] at 𝜎𝜎 =0.17. Unit
vector indicates 25 m s-1. Contour interval of geopotential is 500 J kg-1. (c) Verticalwind -𝜎𝜎� ̇ [s-1] and zonal wind [m s-1] (vector), and temperature [K] (color) in theequatorial vertical section. Unit vectors of vertical wind and zonal wind are 1.67×10-5 s-1
and 50 m s-1, respectively. Contour interval of temperature is 5 K. (d) Specific humidity
at the equator. Contour interval is 2×10-3. (e) Condensation heating [W m-2]. Colorinterval is 50 W m-2. White area represents heating over 2000 W m-2. (f) Horizontal
distribution of surface evaporation [W m-2]. Color interval is 50 W m-2. (g) Verticallyintegrated 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. From Noda et al. (2017), Fig. 5................................................ 45-46
Same as Fig. 4.5 but for case Ω0.15, except that the unit vector in (b) is 50 m s-1 andthe unit vector of vertical wind in (c) is 2.5 × 10-6 s-1. From Noda et al. (2017), Fig 6.. ...... 48
Mass weighted global mean zonal wind velocity for cases with Ω* from 0.0 to 0.33
(circles). Absolute value of westward phase velocity of the zonal wavenumber one
gravest Rossby normal mode is indicated by the thin line for comparison. From Noda
et al. (2017), Fig. 7. ............................................................................................................... 50
Latitude--time distribution of zonal mean surface pressure [Pa] for (a) Ω0.2, (b) Ω0.5,(c) Ω0.67, and (d) Ω0.75. From Noda et al. (2017), Fig. 8. .................................................. 51
Same as Fig. 4.6 but for case Ω0.75, except that the unit vector of vertical wind in (c)is 1.3×10-6 s-1. From Noda et al. (2017), Fig. 9. .................................................................... 53
Structure of the atmosphere averaged from day 1000 to day 2000 for case Ω0.75: (a)zonal mean zonal wind, and (b) eddy stream function at 𝜎𝜎 =0.17. From Noda et al.
(2017), Fig. 10. ..................................................................................................................... 54
Same as Fig. 4.9 but for case Ω1.0 except that unit vector of the vertical wind in (c) is
2.5×10-6 s-1. From Noda et al. (2017), Fig. 11. ..................................................................... 56(a) Ω* dependences of outgoing longwave radiation on the night side, 𝐹𝐹��� (∘), daynight dry static energy transport per unit area, 𝑇𝑇���� /(2 𝜋𝜋 𝑅𝑅�� ) (black triangle), andday-night latent energy transport per unit area, 𝑇𝑇��� /(2 𝜋𝜋 𝑅𝑅�� ) (×). Units are [W m-2].
All 10 runs for each Ω* case are plotted. Blue and red lines represent ensemble averages
for the small-Ω and the large-Ω branches, respectively. (b) Same as (a) but for global
mean (∘), day side mean (×), and night side mean (Box) of surface temperature [K].
From Noda et al. (2017), Fig. 12. ......................................................................................... 58
Relationships between surface temperature and OLR obtained by the GCM and by the
one-dimensional (vertical) radiative-convective equilibrium model. The GCM results
are shown as colored dots: purple, light blue, green, and pink dots indicate runs Ω0.0,
0.15, 0.75, and 1.0, respectively. Data are from the grid points in the 120°
× 120°
rectangular region centered on the subsolar point. Crosses in black circles indicate thevalues at the subsolar point. Black lines are the one-dimensional model results withtropospheric relative humidity of (in order from the top) 50, 60, 70, 80, 90, and 100 %,respectively. From Noda et al. (2017), Fig. 13. .................................................................... 60
Same as Fig.4.7, but showing values for horizontal resolutions of T42 (squares) andT85 (triangles) in addition to those for T21 (circles). From Noda et al. (2017), Fig. A.2.
.............................................................................................................................................. 61(a), (b) Same as Fig. 4.4c but for the T42 model (a) and T85 model (b), and (c), (d)same as Fig. 4.4d but for the T42 model (c) and T85 model (d). From Noda et al. (2017),
Fig. A.1. ................................................................................................................................ 62- viii -4.16

Mean surface pressure distributions for Ω0.6 in the T42 model (a) and T85 model (b)for 500 days during which high (low) pressure occupies the north (south) pole. From
Noda et al. (2017), Fig. A.3. ................................................................................................. 63

Chapter 5
5.1(a) Relationship between Ω* and global mean OLR, (b) Relationship between Ω* andsolar constant divided by 4.0. The squares and circles represent the cases in which
equilibrium states were obtained. The crosses represent the case in which the runaway
greenhouse state emerged. The red marks represent the cloudy case with synchronously
rotating planet distribution of solar flux. The blue marks represent the cloudy case with
Earth-like distribution of solar flux. The yellow marks represent the cloud-free casewith synchronously rotating planet distribution of solar flux. The green marks represent
the cloudy case with Earth-like distribution of solar flux. .................................................... 68- ix -

List of Tables
Chapter 3
3.1
3.2

3.3

Values of the parameters used in this section. ....................................................................... 19
The list of experiments and the values of the solar constant. SSR is the shortwave
radiation flux incoming on the surface. White circles indicate the case where the model
atmosphere reaches a thermally equilibrium state, while cross marks indicate the cases
where it does not. For details, see the description in Section 3.3. From Ishiwatari et al.
(2002), Table 3. ..................................................................................................................... 20
Position of the vertical grid points used in section: k is the index of vertical level; σ_kand σ_(k+1/2) indicate integer and semi-integer grids, respectively. Horizontal wind,temperature and specific humidity are evaluated at the integer grids, while vertical windis evaluated at the semi-integer grids. From Ishiwatari et al. (2002), Table 2. ..................... 21-x-

CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27
CGER-I153-2021, CGER/NIES

Numerical studies on the variety of climates of exoplanets
using idealistic configurations

Masaki Ishiwatari 1, Kensuke Nakajima 2, Shin-ichi Takehiro 3,
Yuta Kawai 4, Yoshiyuki O. Takahashi 5, George L. Hashimoto 6,
Youhei Sasaki 7 and Yoshi-Yuki Hayashi 5

1Graduate School of Science, Hokkaido University,
Graduate School of Science, Kyushu University,
3
Research Institute for Mathematical Studies, Kyoto University,
4
Computational Climate Science Research Team, RIKEN AICS,
5
Graduate School of Science, Kobe University,
6
Graduate School of Natural Science and Technology, Okayama University,
7
Faculty of Science and Engineering, Setsunan University
2-1-

CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27
CGER-I153-2021, CGER/NIES

Abstract-3-3-

Abstract

This monograph summarizes the results of our numerical works so far on the variety ofclimates caused by changes in the value of solar constant and the horizontal distribution ofincoming solar radiation flux. Our aim was to examine the mechanisms causing drastic changes
in climate, such as the disappearance of oceans. For this aim, the following two studies were
performed using the CGER supercomputer system.
One of our studies is an investigation of the dependence of the climate on the solar constant.
Numerical experiments using a general circulation model (GCM) adopting a gray radiation
scheme, aquaplanet condition, and cloud-free condition, were performed. The results imply that
there exists an upper limit of the outgoing longwave radiation (OLR) even in a threedimensional system, including the effects of spherical geometry and atmospheric motion, justlike in vertical one-dimensional systems. The value of the upper limit of OLR corresponded to
the radiation limit calculated by the one-dimensional radiative-convective equilibrium modelwith the relative humidity considered. In the three-dimensional system, the runaway greenhousestate appeared when the global mean incoming flux exceeded the upper limit of OLR.
The other of our studies is an investigation of the circulation structure of synchronously
rotating planets that have a peculiar distribution of incoming solar radiation flux, i.e., a
distribution with a perpetual dayside and nightside. A numerical experiment using a GCM
adopting a gray radiation scheme, aquaplanet condition, and cloud-free condition was
performed with the value of planetary rotation rate varied from zero to that of the Earth. The
value of solar constant was set to be Earth's value. The results showed that the atmospherereached statistically equilibrium states for all runs; none of the calculated cases exemplified the
runaway greenhouse state. The circulation patterns obtained were classified into four types:
Type-I characterized by the dominance of a day-night thermally direct circulation, Type-II
characterized by a zonal wavenumber one resonant Rossby wave over a meridionally broad
westerly jet on the equator, Type-III characterized by a long time scale north-south asymmetricvariation, and Type-IV characterized by a pair of mid-latitude westerly jets. Despite thesubstantial changes in circulation, the net energy transport from the dayside to the nightside
remained almost insensitive to the planetary rotation rate. The reason for this notable
insensitivity is that the outgoing longwave radiation over a broad area of the dayside wasconstrained by the radiation limit of a moist atmosphere, so that the transport to the nightside,which was determined as the difference between the incoming solar radiation and the radiation
limit, could not change greatly.
The common conclusion obtained from the above two investigations is that the existenceof an upper limit of OLR is an important factor in determining the climate state. The existenceof an upper limit of OLR is also shown in a preliminary experiment using GCM including a
non-gray radiation scheme and a simple cloud model. The results obtained in our studies will
be a basic concept for considering the variety of planetary climates.
Keywords:
exoplanets; synchronously rotating planets; runaway greenhouse state; globally ice-covered
state; radiation limit; aquaplanet; general circulation model-4-4-

CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27
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Chapter 1
Introduction-5-5-Chapter 1

Introduction

This monograph summarizes the results of our works so far on the variety of climates using
idealistic model configurations including those assuming exoplanets. Exoplanets are planetsthat exist around stars outside our solar system. Astronomical exploring observations so far
have discovered over 4000 exoplanets1. The observational results show that exoplanets areunder different conditions from those of the planets in our solar system: for example, the hoststar has a luminosity different from Sun’s value, and the semi-major axes of planets are muchsmaller than those of the planets of our solar system, and so on. Observations with spacetelescopes have found over 20 exoplanets that are considered to have liquid water on theirsurfaces and to be able to harbor life. Such planets are called habitable planets. Future
observational missions such as the James Webb Space Telescope (https://jwst.nasa.gov) are
expected to discover many habitable exoplanets. Based on this background, many climate
predictions of terrestrial-type exoplanets have been performed (e.x., Heng and Vogt, 2011;
Wordsworth et al., 2011). Especially, the existence conditions of liquid water on planet surfaces
are focused. Such studies are not only expected to be extended to examinations of thehabitability of exoplanets but are also expected to give new knowledge on the behavior of theatmosphere of planets under conditions different from Earth's. Thus, research on exoplanet
climates poses new problems for climate research.
In recent years, numerical simulations of the climates of exoplanets that were discoveredby astronomical observations have been attempted by some research groups using sophisticatedmodels. When more possible climates are considered due to the increase in discoveries ofterrestrial exoplanets by future missions, it will be desirable to acquire a general understandingof the maintenance mechanism and existence condition of each climate state in addition tosimulations of the climate of particular exoplanets. Based on a general understanding, it will bepossible to discuss the stability of each climate to the changes in external conditions, such as
orbital parameters and stellar flux, and thus, the possibility of the long-term existence of liquidwater on planet surfaces. As a basic theoretical framework for acquiring a general
understanding, simple models that include necessary processes represented roughly can be
useful. They enable us to perform parameter experiments covering a wide parameter range andcan provide basic concepts for considering various climates.
We attempted to construct a possible basic theoretical framework for the general
understanding of the variety of climates by examining the variety of climates of aquaplanetswith grey atmosphere. A model with a gray radiation scheme cannot provide correct radiation
fields like a sophisticated model but can numerically explore climates under various conditions
by including the greenhouse effect and atmospheric circulation. Using an aquaplanet GCM witha gray radiation scheme, we have examined the variety of climates of aquaplanets with grey
atmosphere and the mechanisms causing drastic changes in climate, such as the disappearanceof oceans, using model configurations different from Earth's conditions (Supercomputer
Annual Report since 2000 to 2020). Our studies are related to two problems described in thefollowing subsections 1.1 and 1.2. In these studies, we have examined the dependencies ofclimate on the solar constant and horizontal distribution of incoming solar radiation flux.
Although a part of the results was obtained from a paper published about twenty years ago, it
provides a theoretical framework necessary for the investigation of the climate of exoplanets.
We believe that it is valuable to summarize these results as a monograph.

1

https://exoplanetarchive.ipac.caltech.edu-6-6-

CGER-I153-2021, CGER/NIES

1.1 Drastic climate change caused by the change of the solar constant: occurrence ofthe runaway greenhouse state
The solar constant is one of the most important parameters that determine the climate of
terrestrial planets. A state with oceans on the planetary surface like that of the present Earthvanishes when the value of solar constant changes by several tens of percent and the runaway
greenhouse state emerges with an increased solar constant (Ishiwatari et al., 2002).
The runaway greenhouse state is the nonequilibrium atmospheric state which occurs when
the incoming solar flux exceeds the limit value of outgoing longwave (infrared) radiation (OLR)
of an atmosphere with a sufficient amount of liquid water on its bottom surface, as shown in
Fig. 1.1 (Nakajima et al., 1992, hereafter referred to as NHA92). There are two different typesof OLR limit. NHA92 clarifies them using a one-dimensional radiative-convective equilibrium
model in which the atmosphere is transparent to shortwave radiation and gray to longwave
radiation. One of the OLR limits is the limit constrained by the radiation flux going through thestratosphere. This limit is referred to as the Komabayashi-Ingersoll limit, since it is the key
mechanism that causes runaway greenhouse states in the stratospheric models of Komabayashi(1967) and Ingersoll (1969). The other is the limit constrained by the emissivity of thetroposphere. The limit of OLR that appears in a radiative-convective equilibrium model is thelower of these two. When the incoming flux exceeds the lower OLR limit, the atmospherictemperature will continue to rise until all the oceans evaporate. The runaway greenhouse stateis often discussed in studies on the atmospheric evolution of Earth and Venus (Pollack, 1971;
Abe and Matsui, 1988; Kasting, 1988).

Figure 1.1 Relationships between surface temperature and OLR for gray atmosphere. The blacksolid line shows 𝝈𝝈 𝑻𝑻𝟒𝟒𝒔𝒔 . Other solid lines represent equilibrium solutions obtained by
the vertical one-dimensional radiative-convective model. The green, red, orange, andblue lines represent the results for 𝒑𝒑𝒏𝒏𝒏𝒏 =106, 105, 104, 0 Pa, respectively. 𝒑𝒑𝒏𝒏𝒏𝒏 is thepartial pressure of dry air at the surface. The solid dashed-line represents the
Komabayashi-Ingersoll limit obtained by the stratosphere model. Modified from
Ishiwatari (2014), Fig. 1.

-7-7-

Chapter 1

Introduction

As described above, the runaway greenhouse state had been discussed only by vertical onedimensional models until around the year 2000. Ishiwatari et al. (1998, 2002) examined, for the
first time, the occurrence condition of the runaway greenhouse state in a three-dimensional
system. In Chapter 3, we describe the results of Ishiwatari et al. (2002).
1.2 Circulation structures of planets with a peculiar distribution of solar flux
Synchronously rotating planets are planets that exist near a central host star and have thesame rotation period as the orbital period due to strong tidal force. Since a particular hemisphere
always faces the central star, they have a peculiar distribution of incoming flux with a perpetual
dayside and nightside. Some potentially habitable exoplanets that have been discovered aresynchronously rotating planets (Fig. 1.2: Von Bloh et al., 2007). Much more exoplanets are
expected to be discovered by future missions. Therefore, synchronously rotating planets are an
important scientific target for considering the habitability of exoplanets.

Figure 1.2 Small-mass exoplanets discovered by astronomical missions. The ordinate is the massof the central host star and the abscissa is the semi-major axis. Red crosses represent
exoplanets discovered until 2014 with a mass smaller than ten times of Earth's mass.
The data were obtained at http://exoplanet.eu. Large black dots represent planets inthe solar system. Orange lines represent 10.0, 1.0. and 0.1 times of Earth's solar
constant. Thin blue lines represent 1 day, 10 days, and 100 days of the orbital period.
The thick blue line represents the tidal lock radius inside which planets are considered
to be synchronously rotating planets.

-8-8-

CGER-I153-2021, CGER/NIES

Even when the global mean incoming heat flux from the central star is comparable to thatof the present Earth, the incoming flux on the perpetual dayside of a synchronously rotating
planet can easily exceed the upper limit of OLR that a moist atmosphere can emit (NHA92).
So, a synchronously rotating planet may easily enter the runaway greenhouse state if the dayside
to nightside (hereafter, day-night) energy transport is insufficient. Contrary to the above naive
speculation, in previous studies on atmospheres of synchronously rotating planets using generalcirculation models (GCMs), the runaway greenhouse state did not emerge for several different
values of planetary rotation rate with the present value of the Earth's solar constant (e.g., Joshi
et al., 1997; Joshi, 2003; Merlis and Schneider, 2010; Edson et al., 2011). However, in theseprevious studies, the mechanism that determines the amount of day-night energy transportremains to be understood and its dependence on the planetary rotation rate to be revealed. To
consider these problems, Noda et al. (2017) investigated atmospheric circulation structures andday-night energy transports by performing parameter experiments for various values ofplanetary rotation rate. The results are presented in Chapter 4.
1.3 Contents of this monograph

The contents of this monograph are organized as follows. In Chapter 2, we briefly describe
our general circulation models. In Chapter 3, we show that the occurrence condition of the
runaway greenhouse state in cloud-free gray atmosphere can be described by the results
obtained by a vertical one-dimensional model. In Chapter 4, we discuss the circulation structureof synchronously rotating planets. Chapter 5 presents the preliminary results of experiments inwhich a non-gray radiation scheme and a simple cloud model were used. The summary of thismonograph is found in Chapter 6.

-9-9-Chapter 1

Introduction- 10 - 10 -

CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27
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Chapter 2
Model description- 11 - 11 -

Chapter 2

Model discription

2.1 Basic assumptions
In order to examine the variety of climates of aquaplanets whose entire surface is covered
with the ocean, we used a simple setup. In our studies, moist atmospheres were considered.
Based on this configuration, we used atmospheric general circulation models (AGCMs).
2.2 An overview of GCMs
In the following chapters, two GCMs are used. The GCM utilized in Chapter 3 is AGCM5.3
of GFD DENNOU CLUB1. As described in Section 3.6, a model bug was found in AGCM5.3
in the year 2019. We are now planning to perform a re-experiment with DCAPM5 described
below and the results will be updated. In this monograph, we describe the results anddiscussions obtained by using AGCM5.3, including the model bug. We expect that the results
will be qualitatively unchanged in our future re-experiment. The GCM utilized in Chapters 4
and 5 is DCPAM5 of GFD DENNOU CLUB (Dennou-Club Planetary Atmospheric Model)2.
It has been developed by reconstructing AGCM5.3 to investigate the possible variety of generalcirculations of atmospheres of terrestrial planets in general.
Both GCMs are three-dimensional primitive systems on a sphere. The following arecommon descriptions of AGCM5.3 and DCPAM unless either of the two models is specified.
2.3 Discretization
The equations were discretized horizontally by using a non-alias latitude-longitude grid andintegrated using the spherical spectral transform method. We used 𝜎𝜎 as the vertical coordinate,
which was discretized by following the method of Arakawa and Suarez (1983). The time
integration was performed by using a leap-frog scheme for the terms of dynamical processes
other than dissipative processes, a backward scheme for the terms of physical processes, and an
Euler scheme for the horizontal diffusion terms. The time filter of Asselin (1972) was used toremove the computational mode caused by the leap-frog scheme. In Chapter 5, the advectionof water vapor and cloud water was calculated with the semi-Lagrangian scheme of Kashimura
et al. (2013).
2.4 Atmospheric constituents and radiation processes
The following two types of atmospheric constituents and related radiation processes wereassumed. In all cases, atmospheric gases behaved as ideal gases.
(1) The atmosphere consists of a condensable component (water vapor) and a non-condensable
component (dry air).
As for longwave radiation, we included only the absorption and emission of waterwith a constant absorption coefficient (0.01 m2 kg-1). The effect of scattering was notincluded. Dry air was assumed to be transparent; radiatively active non-condensable gases
1
2

https://www.gfd-dennou.org/library/agcm5/index.htm.en
https://www.gfd-dennou.org/library/dcpam/index.htm.en- 12 - 12 -

CGER-I153-2021, CGER/NIES

such as ozone or carbon dioxide were excluded.
(2) The atmosphere consists of CO2, water vapor, and N2, which are constituents of Earth's
atmosphere.
As for the radiation processes, the schemes of Chou and Lee (1996) and Chou et al.
(2001) were used. In these schemes, the absorption of longwave radiation and shortwave
radiation by water vapor, CO2, and clouds were considered. For evaluating the scattering of
shortwave radiation, Rayleigh scattering was assumed.
2.5 Physical processes other than radiation processes● Cumulus parameterization
For case (1) described in Section 2.4 (case for gray radiation), the moist convective
adjustment scheme of Manabe et al. (1965) was used. Condensed water was immediately
removed from the atmosphere as rain.
For case (2) described in Section 2.4 (case for Earth radiation), the relaxed ArakawaSchubert scheme (Moorthy and Suarez, 1992) was used.
● Cloud water
For case (1) described in Section 2.4 (case for gray radiation), absorption and scatteringof radiation by clouds were not incorporated.
For case (2) described in Section 2.4 (case for Earth radiation), the amount of cloud water
was calculated by solving the time-dependent equation including the terms of cloud water
generation calculated from the cumulus scheme, advection, turbulent diffusion, andextinction, which was assumed to be proportional to the amount of cloud water and was given
an extinction time.
● Vertical mixing
Vertical turbulent mixing was represented by the level II scheme of Mellor and Yamada(1974).
● Surface flux
For case (1) described in Section 2.4 (gray radiation case), the surface fluxes ofmomentum, sensible heat, and latent heat were evaluated with bulk formulas, the bulk
coefficients of which were evaluated by following Louis (1979).
For case (2) described in Section 2.4 (case for Earth radiation), the surface fluxes were
evaluated by using the method of Beljaars and Holtslag (1991).
2.6 Surface conditions
The entire surface was assumed to be a “swamp ocean”; heat capacity was zero and thewetness was uniform (Delworth and Manabe, 1988). Heat transport by the ocean was excluded.
The value of surface albedo was fixed to a constant value regardless of the value of surface
temperature.

- 13 - 13 -Chapter 2

Model discription

2.7 Model modification for experiments with increased solar constant
The atmospheric structure expected to be realized in the runaway greenhouse state required
the following modifications of the model. The change in the total atmospheric mass had to betaken into account. A significant increase in water vapor amount was anticipated in the stateswith an increased solar constant. The change in the total atmospheric mass was evaluated witha surface pressure correction by the amount corresponding to the difference between
evaporation and precipitation. Moreover, the model top had to be taken to a higher level, since
the tropopause goes up to a higher level in experiments with an increased solar constant. Inmodels with a higher top level, a numerical instability problem related to internal gravity waves
occurs. In order to suppress the numerical instability, an upper damping layer and a verticalfilter had to be introduced for some runs. The following is a detailed description of each model
modification for the experiments with an increased solar constant.
2.7.1 𝒑𝒑𝒔𝒔 change due to evaporation and condensation

The atmospheric mass varies with the evaporation and condensation (precipitation) of
water vapor. We have considered only the total variation of the mass of the vertical column ateach grid point and evaluated the correction of surface pressure 𝑝𝑝� and specific humidity 𝑞𝑞
after the integration of each time step.
The correction of surface pressure ∆𝑝𝑝� for each time step was calculated as follows(Ishiwatari et al., 2002):∆ 𝑝𝑝� = 𝐹𝐹������∆𝑡𝑡 + 𝑝𝑝�� � 𝑆𝑆����� ∆𝑡𝑡 𝑑𝑑𝑑𝑑

(1)

The first term on the right-hand side describes the water vapor increase by evaporation and thesecond term describes the water vapor decrease by condensation. The value 𝐹𝐹���� is theevaporative latent energy flux at the surface, ∆𝑡𝑡 is the time step, 𝑆𝑆����� is the tendency ofspecific humidity due to condensation, and 𝑝𝑝�� is the surface pressure before correction.
The correction of the specific humidity was calculated by using the conservation of themass of water vapor. The mass of water vapor should be conserved through the correction of
𝑞𝑞 as follows,𝜌𝜌�𝑞𝑞� = 𝜌𝜌𝜌𝜌

(2)

��
�

𝑞𝑞�

where 𝜌𝜌�, �𝑞𝑞 are density and specific humidity, respectively, before correction, and 𝜌𝜌, 𝑞𝑞 are
those after correction. From this equation, the corrected specific humidity 𝑞𝑞 is
𝑞𝑞 = ��� � ∆��(3)

2.7.2 Upper damping layer
For cases with an increased solar constant and a higher model top level, we encountered anumerical instability problem due to the amplification of internal gravity waves in the- 14 - 14 -

CGER-I153-2021, CGER/NIES

uppermost region. In some runs described in the next chapters, we introduced a strong artificial
dissipation to suppress the internal gravity waves in the upper levels. The artificial dissipationconsisted of Newtonian cooling, Rayleigh damping, and a vertical filter. The vertical filter is
described in section 2.7.3 below.
The Newtonian cooling adjusts temperature T to its zonal mean value. The Rayleighfriction damps the horizontal wind (u, v) toward 0. It was introduced to the seven levels fromthe top level of the model. The time constants of the Newtonian cooling and Rayleigh damping
were set to be 10800 s at the uppermost level. The time constants increased downwards; thevalue at the seventh level from the top was 75600 s.
2.7.3 Vertical filter
In addition to the damping layer described in the previous section, a vertical filter was
introduced for T to suppress the growth of the 2-grid noise. The filter utilized was similar tothat of Shapiro (1971). Since the original form of the Shapiro filter does not conserve the totalenergy, we modified the filter in the following way to satisfy energy conservation. This
modification was especially important in the experiments where the runaway greenhouse state
emerged (Ishiwatari et al., 2002).
We determined a reference state first by using the values at half-integer grid points 𝑇𝑇��� ,�which were calculated in the model for the use of the radiation process.

𝑇𝑇�,� ≡�� �� �
��
��
�
�

(4)

�

The temperature profile was then smoothed toward this reference state. From the bottom (k=2)
to the top (k=31), the following scheme was applied.
�𝑇𝑇��� = 𝑇𝑇
��� + 𝐹𝐹� �𝑇𝑇�,��� − 𝑇𝑇��� � −�� + 𝐹𝐹� �𝑇𝑇�,� − 𝑇𝑇� � −𝑇𝑇� = 𝑇𝑇

�

�

����
∑�
�� ���,�� � ��� � ∆ ����� ����
�� ����

∑������ ∆ �������∑��� ���,�� � ��� � ∆ ����� ����
�� ����∑�� ���� ∆ ����𝑇𝑇��� = 𝑇𝑇
��� + 𝐹𝐹� �𝑇𝑇�,��� − 𝑇𝑇��� � −

�

(6)

����
∑�
�� ���,�� � ��� � ∆ ����� ����
�� ����

∑������ ∆ ���

(5)

(7)

�� is the temperature before the filter is applied. The value 𝐹𝐹� is a coefficient that
where 𝑇𝑇
describes the intensity of the filter. We utilized 𝐹𝐹� = 0.1 in our numerical experiments. The
third term of the left-hand side in each equation is the correction of the internal energy loss.
The energy loss owing to the Shapiro-type filter was distributed equally within each three-layergroup.

- 15 - 15 -Chapter 2

Model discription

For the cases in which the numerical instability could not be suppressed only by a verticalfilter on the temperature fields, we applied a vertical filter also to the horizontal wind field. The
filter for the wind field was the same as that of Shapiro (1971). We have set the intensity
parameter of the filter at 0.1.

- 16 - 16 -

CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.26
CGER-I153-2021, CGER/NIES

Chapter 3
Occurrence condition of the runaway greenhouse state
in a three-dimensional system

This chapter is based on “Ishiwatari M., Takehiro S., Nakajima K., Hayashi Y.-Y. (2002) A
Numerical Study on Appearance of the Runaway Greenhouse State of a Three-Dimensional
Gray Atmosphere. Journal of the Atmospheric Sciences 59(22):3223-3238,” ©American
Meteorological Society. Used with permission.

- 17 - 17 -

Chapter 3

Occurrence condition of the runaway greenhouse state in a three-dimensional system

3.1 Introduction
In this section, we consider occurrence of the runaway greenhouse state of a threedimensional spherical atmosphere in the theoretical framework established by the onedimensional model of NHA92. Results and discussions of in this section are based on Ishiwatari
et al. (1998, 2002) that is the first attempt to perform three-dimensional calculations of theappearance of the runaway greenhouse state. For three-dimensional system with meridionally
non-uniform incoming solar flux and atmospheric circulations, the following two problems are
examined:(I) Whether there exists an upper limit of the solar constant value?
(II) If an upper limit exists, what determines the occurrence condition of the runaway
greenhouse state?
The adopted configuration of the GCM is the most basic one; cloud-free atmosphere, grayradiation, swamp ocean and so on. The adopted framework is, except for the incorporation of
three-dimensional atmospheric motion, basically equivalent to the one-dimensional radiativeconvective equilibrium model of Nakajima et al. (1992) in which the existence of radiation
limits is clarified and the runaway greenhouse state is described in terms of radiation limits.
Using the swamp condition allows the system to reach a statistically equilibrium state in ashorter time than with a slab ocean and is convenient for execution of a large number of runs
with a number of experiments.
We should notify that a critical model bug was found in GCM used by Ishiwatari et al.
(2002). The details are described in Section 3.6. Although quantitative changes in temperaturefield or zonal mean field will emerge by fixing the model bug, we consider that our main resultof this chapter are not changed qualitatively. Therefore, we present the results of Ishiwatari etal. (2002) in the followings.
3.2 Model configuration
As for atmospheric constituent and radiation process, case (1) (case for gray radiation)
described in Section 2.2.3 is adopted. We assume that specific heat and molecular weight ofwater vapor are the same as dry air so that those of the atmosphere are independent of thespecific humidity (mass ratio of water vapor to entire air parcel). According to NHA92, thissimplification does not alter the fundamental thermodynamical structure for the occurrence ofthe runaway greenhouse state. This assumption makes the density of model atmosphere smaller
compared to the reality, and hence the intensity of circulation may be increased. Although thedifference of density does not alter equations of motion in the 𝜎𝜎 coordinate, it causes somechanges in energy equation. We have assumed that the difference of circulation intensity causedby this simplification is small and the dynamical structure of the system, for instance --existence of runaway state--- does not change. Due to the above configurations, the systemutilized is basically the same as that of the one-dimensional radiative-convective equilibrium
model of NHA92, except for the inclusion of atmospheric three-dimensional spherical motion.
The surface albedo can be set to zero. All of the planetary surface is assumed to be “swamp
ocean.”- 18 - 18 -

CGER-I153-2021, CGER/NIESThe values of the model parameters are listed in Table 3.1. Planetary rotation rate Ω ∗normalized by Earth's value, 7.272×10-5 s-1, is set to be 1.0.
Table 3.1 Values of the parameters used in this section.
Parameters of model

Value

Latent heat of water vapor

L=2.4253×106 J kg-1

Partial pressure of dry air at the bottom of atmosphere
Absorption coefficient of water vapor
Absorption coefficient of dry air

𝑝𝑝�� =105 Pa

𝜅𝜅� =0.01 m2 kg-1
𝜅𝜅� =0 m2 kg-1

a=6.37×106 m

Radius of planet

g=9.81 m s-2

acceleration of gravity
global mean surface pressure𝑝𝑝�� =105 Pa

As listed in Table 3.2, eight experiments are performed with different values of solar
constant S. Each experiment is referred to as a letter S followed by the value of solar constantspecified in the experiment. Experiment S1380 is the case corresponding to the present earth.
Since all of the shortwave radiation is assumed to reach the ground surface, the global meanvalue of incoming shortwave radiation at the surface (SSR) is equal to S/4.
The distribution of incoming solar flux is given by the annual and daily average evaluatedwith the present terrestrial orbital parameters. The diurnal and seasonal cycles are notconsidered. The meridional distributions of the solar flux are shown in Fig. 3.1.
The initial condition is the same for all experiments. It is a resting, isothermal (280K)
atmosphere with a constant specific humidity (10-3). For each experiment, the model is
integrated over 1000 days during which the atmosphere reaches a thermally equilibrium state,
if it can. The horizontal resolution utilized in the present study is 32×64 that corresponds tospectral truncation T21. The atmospheric structure expected to be realized in the runaway
greenhouse state requires the increased number of the vertical levels in the upper atmosphere.
The tropopause must be allowed to reach a very high altitude level. Correspondingly, we specify
that the uppermost vertical grid is located at 𝜎𝜎=10-6 and the total number of levels is 32 (Table
3.3). This configuration of the model vertical levels ensures the accuracy of 5 W m-2 in the OLR
calculation throughout the parameter range considered in NHA92. In order to perform
experiment with increased solar constant, upper damping layer described in Section 2.7.2 isused. Time constant of the Newtonian cooling is set to be 10800 s at the uppermost level. The
time constants increase downwards; the value at the seventh level from the top is 75600 s.
Vertical filter is also used as in shown in Table 3.2. We utilize coefficient 𝐹𝐹� = 0.1 fortemperature vertical filter.

- 19 - 19 -

Chapter 3

Occurrence condition of the runaway greenhouse state in a three-dimensional system

Table 3.2 The list of experiments and the values of the solar constant. SSR is the shortwave
radiation flux incoming on the surface. White circles indicate the case where the model
atmosphere reaches a thermally equilibrium state, while cross marks indicate the cases
where it does not. For the details, see the description in Section 3.3. From Ishiwatari etal. (2002), Table 3.
Experiment

Global mean SSR

Variables smoothed byname(W m-2)

vertical filter

S1200

300.0

T

S1380

345.0

T

S1500

375.0

T,u,v

S1550

387.5

T,u,v

S1570

392.5

T,u,v

S1600

400.0

T,u,v

S1700

425.0

T,u,v

S1800

450.0

T,u,v

Notes

∘
∘
∘
∘
∘

×
×
×

Figure 3.1 Meridional distributions of incoming solar radiation flux. Unit is W m-2. Thick solidline, dashed line and dotted line are for S=1380 W m-2, S=1200 W m-2 and S=1800 W
m-2, respectively. Dotted-dashed line indicates the Komabayashi-Ingersoll limit (385.2
Wm-2), and thin solid line indicates the upper-limit value of OLR (355.0 W m-2)
obtained by the NHA92 model. Both of them are calculated with the parameters of thepresent study. From Ishiwatari et al. (2002), Fig. 1.

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CGER-I153-2021, CGER/NIES

Table 3.3 Position of the vertical grid points used in this section: k is the index of vertical level; σ_kand σ_(k+1/2) indicate integer and semi-integer grids, respectively. Horizontal wind,temperature and specific humidity are evaluated at the integer grids, while verticalwind is evaluated at the semi-integer grids. From Ishiwatari et al. (2002), Table 2.

0
1

𝜎𝜎�

0.995

𝜎𝜎���/�

2

0.980

0.970

3

0.950

0.930

4

0.900

0.870

5

0.830

0.790

6

0.745

0.700

7

0.650

0.600

8

0.549

0.500

9

0.454

0.410

10

0.369

0.330

11

0.294

0.260

12

0.229

0.200

13

0.174

0.150

14

0.124

15

7.40 × 10

K

16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32

1
0.990

0.100
5.00 × 10-2

-2

2.54 × 10-2

3.72 × 10-2

1.29 × 10-2

1.89 × 10-2

6.58 × 10-3

9.61 × 10-3

3.34 × 10-3

4.90 × 10-3

1.70 × 10-3

2.49 × 10-3

8.65 × 10-4

1.27 × 10-3

4.40 × 10-4

6.44 × 10-4

2.24 × 10-4

3.28 × 10-4

1.14 × 10-4

1.67 × 10-4

5.78 × 10-5

8.48 × 10-5

2.94 × 10-5

4.30 × 10-5

1.50 × 10-5

2.19 × 10-5

7.60 × 10-6

1.15 × 10-5

3.87 × 10-6

5.66 × 10-6

1.97 × 10-6

2.88 × 10-6

1.00 × 10-6

1.47 × 10-6

4.15 × 10-7

0

- 21 - 21 -

Chapter 3

Occurrence condition of the runaway greenhouse state in a three-dimensional system

3.3 Emergence of thermally runaway states
With GCM described in previous section, Ishiwatari et al. (2002) showed that thermally
runaway states are obtained for increased solar constant. In the followings, we describe theirresults.
Fig. 3.2 shows the time evolution of global mean OLR and global mean surface temperatureof experiments S1200, S1380, S1570 and S1800. As shown in Fig. 3.2a, for the cases with� �1570 W m-2, the global mean OLR becomes equal to the global mean SSR, which is equal
to S/4, in about 500 days, and the atmospheric system reaches a statistically steady state. The
global mean surface temperature also settles down to an equilibrium value (Fig. 3.2b).
In the experiment S1800, on the other hand, the system goes into a thermally runaway state.
The global mean surface temperature keeps increasing (dashed-dotted line in Fig. 3.2b). The
atmosphere emits infrared radiation less than the incoming total solar flux, since the calculated
value of global mean OLR is always less than 450 W m-2 (dashed-dotted line in Fig. 3.2a).
Moreover, the global mean OLR decreases gradually as time goes on, and hence, the excess inthe energy budget, that is, the difference between the given SSR and the global mean OLR,
increases. The atmospheric system does not seem to approach any thermal equilibrium states.
(a)

(b)

Figure 3.2 Time evolutions of (a) global mean OLR (W m-2) and (b) global mean surface
temperature (K). Dashed line, solid line, dotted line and dashed-dotted line indicate
experiments S1200, S1380, S1570 and S1800, respectively. From Ishiwatari et al.
(2002), Fig. 2.

Fig. 3.3 summarizes the relationship between the externally given global mean SSR andthe global mean OLR obtained at the end of the time integration for all of the experiments.
When S < 1600 W m-2, that is, the global mean SSR is less than 400 W m-2, the global mean
OLR almost exactly equals the global mean SSR, and the atmosphere reaches an equilibrium
state. On the other hand, when S≥1600 W m-2, that is, the global mean SSR is 400 W m-2 orlarger, the atmosphere cannot reach an equilibrium state. All of the results obtained withS≥1600 W m-2 are thermally runaway states characterized by continuous decrease of OLR andcontinuous increase of surface temperature, as is shown for the case of S1800 in Fig. 3.2.

- 22 - 22 -

CGER-I153-2021, CGER/NIES

Figure 3.3 The relationship between global mean SSR and global mean OLR. The values of OLR
at day 1000 are plotted except for S1600 where the value is at day 2000. White circles
represent the cases where the atmosphere reaches an equilibrium state, while crossmarks represent the cases where the atmosphere is in a thermally runaway state. Notethat the values of OLR for thermally runaway states are continuously decreasing.
From Ishiwatari et al. (2002), Fig. 3.

It is now confirmed that there exists an upper limit on the value of solar constant withwhich the three-dimensionally circulating atmosphere reaches a thermal equilibrium state. The
value of the upper limit is about 1600 W m-2, or 400 W m-2 as global mean SSR, in ourconfiguration. In the following sections, we will examine the correspondence of the thermally
runaway states obtained by the three-dimensional calculations with the runaway greenhousestate defined by the one-dimensional model of NHA92. An interpretation of the upper-limit
value of the solar constant will also be given.
3.4 Comparison with a one-dimensional system
Fig. 3.4 shows the meridional distributions of zonal mean OLR and zonal mean surface
temperature for the cases with S൑1570 W m-2 where the atmosphere can reach a thermal
equilibrium state. As the incoming solar flux increases, the meridional distribution of OLR isflattened and the value of OLR approaches about 400 W m-2 at all latitudes. The value of OLR
in the equatorial region ceases to increase at around 390 W m-2 when S=1500 W m-2 and thevalue hardly changes against the further increase of solar constant. In the mid- and high latitudes,
the value of OLR gradually approaches 400 W m-2 with the increase of the solar constant. The
tendency similar to that of OLR distribution appears in the meridional distribution of zonal
mean surface temperature.

- 23 - 23 -Chapter 3(a)Occurrence condition of the runaway greenhouse state in a three-dimensional system(b)Figure 3.4 The meridional distributions of (a) zonal mean OLR (W m-2) and (b) zonal meansurface temperature (K) of the cases in which the system reaches equilibrium states.
Thick solid line, dotted line, dotted-dashed line, dashed line, and thin solid line indicate
experiments S1570, S1550, S1500, S1380, and S1200, respectively. The data aretemporally averaged between days 950 and 1000. From Ishiwatari et al. (2002), Fig. 4.

The asymptotic value of OLR is actually close to the upper limit of radiation which isconstrained by the tropospheric temperature structure as discussed in NHA92. In order to apply
the discussion by NHA92, it is necessary to examine the value of tropospheric relative humidity.
In experiment S1570, the averaged value of relative humidity in the equatorial troposphere isabout 60%. The upper limit of radiation obtained by the one-dimensional radiative-convective
equilibrium model is 385 W m-2 when the value of relative humidity for the radiation scheme
is fixed to be 60%. This value is close to 390 W m-2, the equatorial value of OLR obtained in
our three-dimensional calculations.
Now, we will compare the tropospheric temperature structures of the three-dimensional
results with those of one-dimensional equilibrium solutions to examine whether there exists atendency of the temperature field to approach an asymptotic profile as a function of opticaldepth as discussed by NHA92. Fig. 3.5 shows the temperature structures obtained by the onedimensional radiative-convective equilibrium model in which relative humidity is fixed to be
60%. In Fig. 8a, where the temperature is plotted as a function of pressure, the asymptotic
feature is not obvious; as surface temperature increases, the entire vertical profile is simply
shifted to the positive direction of the temperature axis. However, in Fig. 8b, where thetemperature is plotted as a function of optical depth, the temperature structures closely approachthe curve determined by the saturation water vapor pressure. Especially, for the cases
corresponding to S1600, S1700, S1800, the profiles almost coincide with each other. NHA92
pointed out that the existence of this asymptote is the essential feature for the appearance of
runaway greenhouse state in the one-dimensional equilibrium model.
As for the three-dimensional results, the tropospheric temperature profiles as a function of
optical depth 𝜏𝜏 also seem to have an asymptote (Fig. 3.6b), while the profiles as a function ofpressure scatter just as one-dimensional equilibrium solutions (Fig. 3.6a). The existence of an
asymptote can be observed in the deep troposphere of the thermally runaway states(experiments S1600, S1700, S1800), where 𝜏𝜏 𝜏 1. This is because the specific humidity there
is fairly large as to ensure that temperature gradient almost coincides with that of the saturation
vapor pressure curve.
- 24 - 24 -

CGER-I153-2021, CGER/NIES

(a)

(b)

Figure 3.5 Vertical distributions of temperature obtained by one-dimensional model with relative
humidity of 60% for the radiation scheme. The profiles are plotted by specifying thevalues of temperature at the bottom of atmosphere as those obtained by theexperiments. Ordinates are (a) pressure (Pa) and (b) optical depth. Cross marks
indicate surface temperature. From Ishiwatari et al. (2002), Fig. 5.

(a)

(b)

Figure 3.6 Vertical distributions of zonally averaged temperature at the equator for various
values of solar constant. Ordinates are (a) pressure (Pa) and (b) optical depth. The
profiles obtained in the experiments S1800, S1700, S1600, S1570, S1550, S1500, S1380,
S1200 are plotted. Cross marks indicate surface temperature. From Ishiwatari et al.
(2002), Fig. 6.

Fig. 3.7 shows the relationship between surface temperature and OLR obtained by the onedimensional calculation similar to those given by NHA92 except that the value of relative
humidity for the radiation calculation is varied between 40% and 100%. In Fig. 3.7, the points
representing the equatorial zonal mean values of surface temperature and OLR obtained by thethree-dimensional calculations are also plotted. The surface temperature-OLR relationshipobtained by three-dimensional calculation is well correlated with the curve of the onedimensional model with 60% relative humidity. There exists a slight difference. The causes ofthe difference are that the value of tropospheric relative humidity is larger than 60% inexperiments S1200∼S1500 and that the temperature gap between the surface and the lowest- 25 - 25 -Chapter 3

Occurrence condition of the runaway greenhouse state in a three-dimensional systemlevel of the model, which is allowed in the three-dimensional model but not in one-dimensional
calculations, becomes significant in experiments S1550 and S1570. In thermally runaway states(S1600, S1700, S1800), OLR decreases as the solar constant increases, since the relative
humidity in the upper troposphere increases (not presented here).
As a result of the above discussion, it can be concluded that the asymptotic value of OLR
obtained by three-dimensional calculations corresponds to the upper limit of radiation of the
one-dimensional radiative-convective equilibrium solution in which the value of relative
humidity is taken into account. The existence of the upper limit of OLR in the three-dimensional
system means that the runaway greenhouse state can be defined also in three-dimensional
system as the state realized when the incoming radiation exceeds the upper limit of OLR, thatis, the runaway greenhouse state defined by NHA92.

Figure 3.7 The relationship between surface temperature (K) and OLR (W m-2). Curves
represent surface temperature--OLR relationship obtained by the one-dimensionalradiative-convective equilibrium model with various values of relative humidity forthe radiation scheme. Thin solid line, dotted line, thick solid line and dashed line
indicate 100% of relative humidity (the same as the results of NHA92), 80%, 60% and40%, respectively. Marks represent the relationship between equatorial zonal meanvalues of surface temperature and OLR obtained by GCM. White circles and crossmarks represent the results where the system reaches an equilibrium state and where
the system cannot, respectively. From Ishiwatari et al. (2002), Fig. 7.

- 26 - 26 -

CGER-I153-2021, CGER/NIES

3.5 Circulation structure toward the runaway greenhouse state
In this section, we will observe the change of meridional circulation fields with the increaseof solar constant to examine how the latitudinally uniform distribution of OLR becomes
established and why the subtropical region is not fully dried. According to our results, thesubtropical drying does appear; a careful observation of Fig. 3.4 shows that, in the cases with𝑆𝑆 𝑆 1500 W m-2, the subtropical values of OLR are slightly greater than those at the equator.
However, the subtropical drying does not proceed and the occurrence of a runaway greenhousestate is not prevented.
Figures 3.8, 3.9, and 3.10 show the zonal mean meridional circulation structures of theexperiments S1380, S1570, and S1800, respectively. The plotted data are averaged for 50 days.
In the experiment S1800, the temporal variation is so large that even for the zonal mean fields,
50 days is not enough to smooth out the variation. However, we cannot adapt the longer period
for averaging, since the model atmosphere of the experiment S1800 is in the runaway
greenhouse state and its circulation fields are secularly changing. The plotted period for S1800
is selected as the duration when the Hadley circulation shows relatively clear symmetry aroundthe equator.
With the increase of incoming solar flux, the intensity and height of the Hadley circulation
increases (Figs. 3.8e, 3.9e, 3.10e). Corresponding to this change, the amount of equatorial
precipitation increases, and the peak of heating profile is shifted upward (Figs. 3.8b, 3.9b,
3.10b). It is noteworthy that the downward branch of Hadley cells remains at around ±30° .
The latitudinal width of Hadley cells hardly changes with the change of solar flux, which isconsistent with the theory of Satoh (1994).
Subtropical drying appears for all the experiments in the sense that the values of relative
humidity in the subtropics are less than those of the equatorial region. However, associated with
the intensification of the Hadley circulation, the equatorial relative humidity also decreases, andhence, the difference between the subtropical and equatorial values of relative humidity
decreases (Figs. 3.8d, 3.9d, 3.10d). Relative humidity of the whole Tropics decreases with theincrease of the solar constant, but its value does not become extremely small. Even for theexperiment S1800, the value of relative humidity in the subtropics is not less than 30%.
Consequently, as is evident from the specific humidity fields (Figs. 3.8c, 3.9c, 3.10c), theabsolute amount of water vapor increases steadily in all region including the subtropics. The
increase of humidity in subtropical regions is caused by the increased moisture transport byeddies (figure not shown). The atmosphere becomes optically thick with the increase ofincoming solar radiation as shown in the meridional distributions of optical depth (Fig. 3.11).

- 27 - 27 -

Chapter 3

Occurrence condition of the runaway greenhouse state in a three-dimensional system

(a)

(b)

(c)

(d)

(e)

(f)

Figure 3.8 Meridional structures of the zonal mean circulation fields of the experiment S1380:(a) temperature, (b) condensation heating, (c) specific humidity, (d) relative humidity,(e) mass stream function, and (f) zonal wind. Contour intervals are (a) 5 K, (b)𝟓𝟓 × 𝟏𝟏𝟏𝟏�� K day-1, (c) 𝟐𝟐 × 𝟏𝟏𝟏𝟏�� , (d) 0.05, (e) 5 m s-1, (f) 𝟏𝟏. 𝟎𝟎 × 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 kg s-1,
respectively. Time mean fields between t=950 to 1000 days are plotted. From
Ishiwatari et al. (2002), Fig.8.

- 28 - 28 -

CGER-I153-2021, CGER/NIES

(a)

(b)

(c)

(d)

(e)

(f)

Figure 3.9 Same as in Fig. 3.8 but for the experiment S1570. Contour intervals are the same as inFig. 3.8 except for (c) 𝟏𝟏. 𝟎𝟎 × 𝟏𝟏𝟏𝟏�� . From Ishiwatari et al. (2002), Fig.9.

- 29 - 29 -

Chapter 3

Occurrence condition of the runaway greenhouse state in a three-dimensional system

(a)

(b)

(c)

(d)

(e)

(f)

Figure 3.10 Same as in Fig. 3.8 but for the experiment S1800. Time-mean fields between t=870 to
920 days are plotted. Contour intervals are the same as in Fig. 3.8 except for (b)𝟏𝟏. 𝟎𝟎 × 𝟏𝟏𝟏𝟏�� K day-1 and (c) 0.1. From Ishiwatari et al. (2002), Fig.10.

- 30 - 30 -

CGER-I153-2021, CGER/NIESAs for the temperature fields, the meridional difference of temperature decreases as thesolar flux increases (Figs. 3.8a, 3.9a). In the runaway greenhouse state (Fig.3.10a), themeridional difference of temperature almost disappears, which corresponds to thedisappearance of meridional contrast of OLR profile. In the equilibrium states (S1570),
however, detailed examination of Fig. 3.9a shows that subtropical temperature is significantly
lower than that of the equator, although the meridional contrast of OLR is fairly small (Fig.
3.4a). This is because the changes of latitudinal profiles of temperature and humidity with theincrease of solar flux have opposite effects on the change of subtropical OLR; cold subtropics
cause OLR to be smaller, while dry subtropics cause OLR to be larger.
The results of this compensation can be observed in Fig. 3.12, which shows the meridional
structure of temperature with optical depth as the vertical coordinate. For the experiment S1570,
whose solar constant is just below the value for entering the runaway greenhouse state, thewater vapor amount in the subtropical regions is relatively smaller than that of the equatorial
region, and hence the 𝜏𝜏 = 1 surface in the subtropical regions is located at the lower altitude(Fig. 3.11b). On the other hand, the temperature profile has its maximum at the equator anddecreases toward both poles (Fig. 3.9a). Consequently, the temperature profile on the surfaceof 𝜏𝜏 = 1 is more uniform than that on the surface of constants (Fig. 3.12b). The latitudinal
profile of OLR tends to be flat even in the experiments where the solar constant is below
runaway value, although there still exists a significant amount of latitudinal temperature
difference. In those ways, the values of OLR at all latitudes gradually approach the equatorial
limit as the value of the solar constant is increased toward this limit.
There should be an increase of poleward heat transport to have a latitudinally uniform OLR
distribution, since the latitudinal gradient of incoming heat supply increases as the solar
constant increases. This actually is achieved by the increase of latent heat flux. Figure 3.13
shows the latitudinal distributions of heat fluxes. With the increase of the solar constant, latent
heat flux dominates radiation flux in the surface heat budget. This tendency is most notable in
the runaway greenhouse state (Fig. 3.13c), in which the surface radiation flux almost vanishes
and most of the incoming heat is supplied to the atmosphere in the form of latent heat flux.
Correspondingly, in the profile of precipitation, in addition to the increase at equatorial peak(Figs. 3.13b,c), there appear new precipitation peaks around latitude ±60° .The large amountof latent heat release caused by precipitation in those higher latitudes contributes to therealization of the meridional homogenization of temperature.

- 31 - 31 -

Chapter 3

Occurrence condition of the runaway greenhouse state in a three-dimensional system

(a)

(b)

(c)

Figure 3.11 Meridional structure of zonal mean optical depth in the experiments (a) S1380, (b)S1570, and (c) S1800. Here, 𝝈𝝈 is used as the vertical coordinate. The contour
intervals are (a) 0.05, (b) 0.2, and (c) 5.0, respectively. The shaded areas in (c)represent the area with optical depth less than 1. From Ishiwatari et al. (2002), Fig.11.

- 32 - 32 -

CGER-I153-2021, CGER/NIES

(a)

(b)

(c)

Figure 3.12 Meridional structure of temperature with the optical depth as the vertical coordinate
in the experiments (a) S1380, (b) S1570, and (c) S1800. The areas without data
correspond to the regions below the ground surface. The contour intervals are (a)2.5K, (b) 2.5K, and (c) 5.0K, respectively. From Ishiwatari et al. (2002), Fig.12.
- 33 - 33 -Chapter 3

Occurrence condition of the runaway greenhouse state in a three-dimensional system

(a)

(b)

(c)

Figure 3.13 The meridional distributions of vertical energy fluxes in experiments (a) S1380, (b)S1570, and (c) S1800. Thick solid line, dashed line, dotted line, dashed–dotted line,
and thin solid line indicate condensation heating (RAIN), evaporation flux (EVAP),
OLR, net longwave radiation at the surface (SLR), and sensible heat flux (SENS),
respectively. Unit is W m-2. The condensation heating of (c) has its maximum valueof 920 W m-2 at the equator. From Ishiwatari et al. (2002), Fig.13.

- 34 - 34 -

CGER-I153-2021, CGER/NIES

3.6 Remarks
As mentioned in Section 3.1, we found a critical bug in the implementation of moist
convective adjustment (MCA) scheme in the general circulation model used by Ishiwatari et al.
(2002). That is, the sign of the switching-on condition of MCA scheme was opposite: MCA
was activated at the saturated grid point where the vertical stratification was more stable thanthe moist adiabat. Moreover, in the course of performing re-experiments for bug-fix, it was
found that integration periods were insufficient for reaching statistically equilibrium states inthe experiment of Ishiwatari et al. (2002). We performed some re-experiments with a bug-fixedmodel and found that the results are not changed qualitatively although quantitative changes intemperature field or zonal mean field emerged. Therefore, we consider that our main results ofthis chapter are not changed qualitatively.
3.7 Summary
We have performed a series of numerical experiments using a GCM with a gray atmosphereto investigate a possible three-dimensional counterpart of the runaway greenhouse state definedby NHA92 with a one-dimensional radiative-convective equilibrium model. The experimental
results show that, even when the effects of spherical geometry and atmospheric motion are
included, there exists an upper limit of OLR which the atmosphere with water vapor as an
infrared absorber can emit. The experiments also show that when the value of the solar constantexceeds the upper limit of OLR, the atmosphere sets into a thermally runaway state. The upperlimit value is constrained by the vertical structure of the atmosphere in the equatorial region.
As the solar constant increases, the thermal structure becomes uniform in the latitudinal
direction, and the values of OLR at all latitudes approach the equatorial limit. The equatorial
vertical structure of temperature and radiation can be well described by the one-dimensionalradiative-convective equilibrium model of NHA92 by considering the actual value of relative
humidity realized in the three-dimensional system. This fact indicates that the thermally
runaway state obtained by the three-dimensional calculation is the realization of the runaway
greenhouse state defined by NHA92. It is concluded that we can predict the emergence of the
runaway greenhouse state by comparing the value of global mean SSR with the upper limit of
OLR calculated by the use of the one-dimensional radiative-convective equilibrium model withthe relative humidity considered. The condition for the occurrence of runaway greenhouse statein the three-dimensional system is that the global mean value of incoming flux, neither the
maximum nor the minimum of the latitudinal distribution of incoming flux, exceeds the upper
limit of OLR.

- 35 - 35 -

Chapter 3

Occurrence condition of the runaway greenhouse state in a three-dimensional system- 36 - 36 -

CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27
CGER-I153-2021, CGER/NIES

Chapter 4
Circulation structure of planets with a peculiar distribution ofincoming solar radiation flux:
climate of synchronously rotating planets

This chapter is based on “Noda S., Ishiwatari M., Nakajima K., Takahashi Y.O., Takehiro S.,
Onishi M., Hashimoto G.L., Kuramoto K., Hayashi Y.-Y. (2017) The circulation pattern andday-night heat transport in the atmosphere of a synchronously rotating aquaplanet:
Dependence on planetary rotation rate. Icurus 282., 1-18,” ©The author(s), Published by
Elsevier Inc. This is an open access article under the CC BY license.
( http://creativecommons.org/licenses/by/4.0/ )- 37 - 37 -

Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets

4.1 Introduction
In this chapter, we present the result of Noda et al. (2017) who investigate the climate ofsynchronously rotating planets which have fixed day-side and night-side. Noda et al. (2017)
focused on the dependence of circulation structure on planetary rotation rate Ω *. The
atmospheric circulation structure, which should be related to day-night energy transport, hasbeen shown to depend on the planetary rotation rate (Showman et al., 2013). Using a GCM witha slab ocean, Merlis and Schneider (2010) obtains a day-night thermally direct circulationin the case with Ω*=1/365, whereas high-latitude westerlies emerge in the case with Ω*=1.
The latter circulation pattern is similar to that obtained earlier by Joshi (2003) with Ω*=1.
Merlis and Schneider (2010) names the two circulation regimes the “slowly rotating regime”
and the “rapidly rotating regime”, respectively. However, there is little information on thetransition between these two regimes. Edson et al.(2011) explores the Ω* dependence of theatmospheric circulation structures of both dry and moist planets, and shows that, in addition to
the two regimes similar to those identified by Merlis and Schneider (2010), a regime with astrong westerly zonal wind in low latitudes appears with intermediate values of Ω*. It is also
shown that, for the dry planet condition, an abrupt change of zonal wind velocity occurs andmultiple equilibria with hysteretic behavior exist between Ω*=0.109 and Ω*=0.25. However,corresponding multiple equilibria for the aquaplanet have not been described clearly.
As for day-night energy transport, Merlis and Schneider (2010) shows that the amounts ofmoist static energy transport are almost the same for the two cases with Ω*=1/365 and Ω*=1,
but there is no information about energy transport for intermediate values of Ω*. Edson etal.(2011) describes Ω* dependences of minimum, maximum, and globally averaged meansurface temperature, but does not present that of energy transport. The dependence of day-night
energy transport on Ω*, together with possible constraints on it, remain to be explored.
In Noda et al. (2017), a series of GCM runs with Ω* incremented by small steps is
performed under a simple setup considering a moist planet that rotates synchronously. They
confirmed that, for the same value of incoming solar flux as that of the present Earth's,
statistically equilibrium states are obtained and the runaway greenhouse state does not occur
for various values of Ω* including those that are not closely examined in the previous studies.
Noda et al. (2017) also examined how Ω* affects the atmospheric circulation structure andday-night energy transport, and consider what determines the amount of day-night energy
transport. In the followings, details of the results obtained by Noda et al. (2017) are presented.
4.2 Model configuration
As for atmospheric constituent and radiation process, the same configuration as Section 3.2(case (1), case for gray radiation, described in Section 2.4) is used. The values of molecularweight and specific heat of dry air are set to 28.964×10-3 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
18.0×10-3 kg mol-1 and 1810.0 J K-1 kg-1, respectively.
- 38 - 38 -

CGER-I153-2021, CGER/NIESSame as Section 3.2, all of the planetary surface is assumed to be “swamp ocean.” Thesurface albedo is set to zero. Same configurations as Section 3.2 are used except for planetaryrotation rate. We use 16 values of planetary rotation rate, Ω*: Ω* =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 Ω followed by the value of Ω*. For example, Ω0.05 is the case with orbital
period of 20 Earth days. Note that changing Ω* with fixed solar constant means changing theluminosity of the central star. Although no planet with Ω* = 0 exists in reality, we examine
the circulation structure of this idealized non-rotating planet as the limiting case of small Ω*.
The synchronously rotating planet is configured with the obliquity set to zero, and the
distribution of incoming solar flux fixed to the planetary surface (Fig. 4.1) according to𝑆𝑆����� � 𝑆𝑆� 𝑚𝑚𝑚𝑚𝑚𝑚�0, cos ∅ cos�𝜆𝜆 𝜆 𝜆𝜆� ��(4.1)

where 𝜙𝜙 is latitude and 𝜆𝜆 is longitude, with subsolar longitude 𝜆𝜆� =90∘ and solar constant𝑆𝑆� =1380 W m-2, which is about 88% of the threshold value (𝑆𝑆� =1570 W m-2 ) to enter the
runaway greenhouse state obtained by the non-synchronously rotating aquaplanet experiment
by Ishiwatari et al. (2002).

Figure 4.1 Horizontal distribution of the incoming solar flux [W m-2] given by Eq. (4.1). Contour
interval is 300 W m-2. From Noda et al. (2017), Fig. 1.

For each Ω*, we perform 10 runs. As will be discussed in the following sections, we haverecognized that initial condition dependence appears for certain values of Ω*; different typesof circulation patterns result from slightly different initial conditions. The initial condition foreach run is an isothermal (280K) resting atmosphere with a small temperature perturbation in
the form of random noise with amplitude of 0.1 K added to all grid-points; we prepare ten- 39 - 39 -

Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets

different perturbation fields for the ten runs. Each run is integrated for 2000 Earth days, and thedata from the last 1000 days are used for analysis. The horizontal resolution utilized in thepresent study is 32×64 that corresponds to spectral truncation T21. The number of verticallevels is set to 16. The model top level is set to 𝜎𝜎=0.02. We performed test runs for several
values of Ω* employing 32 vertical levels with the top level of 𝜎𝜎=9.2×10-5. The results show
no qualitative change in either the atmospheric circulation characteristics or the energy budget
compared with those with 16 vertical levels; the change in 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 Ω* = 1, and confirmedthat the large scale circulation and the surface temperature patterns are mostly unchanged.
These sensitivity tests show that the vertical and horizontal resolutions are adequate for thepresent purpose.

4.3 Dependence of the atmospheric circulation characteristics on the planetary rotationrate
In all runs the atmosphere reaches a statistically equilibrium state; the runaway greenhousestate does not emerge. Fig. 4.2 shows temporal changes of the global mean values of surface
temperature and OLR obtained in four typical runs with different values of Ω*. In every case,the atmosphere settles down after about 300 days to a statistically equilibrium state in which
both global mean surface temperature and OLR fluctuate around their equilibrium values. The
temporal mean values of global mean surface temperature and the magnitudes of temperaturefluctuation differ among runs.
(a) Ts(b) OLR

Figure 4.2 Time series of global mean quantities. (a) Surface temperature [K] and (b) OLR[Wm-2]. Green, light-blue, black, and red lines indicate Ω0.0, Ω0.15, Ω0.75, andΩ1.0, respectively. From Noda et al. (2017), Fig. 2.

The structure of the atmospheric circulation varies with Ω*. Fig. 4.3 summarizes thevariety of global distributions of time mean surface temperature for various values of Ω*. For- 40 - 40 -

CGER-I153-2021, CGER/NIES

each value of Ω*, the result of a single run arbitrarily chosen from the ten runs is plotted. In
Fig. 4.3, 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 Ω0.05-Ω0.8(Fig. 4.3b-m), while it is absent in the other cases. Second, the equatorial region is generally
warmer in Ω0.0-Ω0.8 (Fig. 4.3a-m), while the mid-latitude regions are warmer in the othercases. 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 Ω0.6-Ω0.8 (Fig. 4.3i-m),
while it is absent or weak in the other cases. This last feature reflects the presence of northsouth asymmetric variability with long time scales, as will be described in Section 4.4.3.
(a) Ω0.0(b) Ω0.05(c) Ω0.1(d) Ω0.15(e) Ω0.2(f) Ω0.25(g) Ω0.33(h) Ω0.5(i) Ω0.6(j) Ω0.67(k) Ω0.7(l) Ω0.75(m) Ω0.8(n) Ω0.85(o) Ω0.9(p) Ω1.0

Figure 4.3 Horizontal distributions of 1000-day mean surface temperature for all of thecomputed values of Ω*. Contour interval is 5 K. From Noda et al. (2017), Fig. 3.

- 41 - 41 -

Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets

For a more quantitative description of the general dependence of the atmosphericcirculation structure on Ω*, bearing in mind the three features of the surface temperature fields
identified above, we examine the Ω*-dependences of four quantities. These are the surface
temperatures at the subsolar and antisolar points, the upper tropospheric zonal mean zonal windat the equator, and a measure of north-south asymmetry in the surface temperature with shorttime scale transients filtered out defined by∆�� �𝑇𝑇� � ≡

�

��

�/�

��

���������������������������������� �𝑇𝑇� �𝜆𝜆, 𝜙𝜙� − 𝑇𝑇� �𝜆𝜆, −𝜙𝜙�� 𝑑𝑑𝑑𝑑 cos 𝜙𝜙 𝑑𝑑𝑑𝑑
��

(4.2)

where 𝑇𝑇�� is the 50 day running average of surface temperature, and the overbar means the
temporal average over 1000 days. Fig. 19 shows the Ω* dependences of these four quantities.
Note that the ten runs for each value of Ω* are plotted separately. Now we can identify two
separate branches of atmospheric states: one extending from Ω*=0.0 to Ω*=0.8 (hereafter,
the small-Ω branch), and the other from Ω*=0.7 to Ω*=1.0 (hereafter, the large-Ω branch).
Between Ω*=0.7 and Ω*=0.8, these two branches coexist, giving multiple equilibria. The
preference between the two branches in the range of the multiple equilibria seems to depend on
the value of Ω*; the ratio of runs on the large-Ω branch increases from 10% for Ω* = 0.7 to
80% for Ω* = 0.8. The branch taken by a particular run depends on small differences in theinitial conditions. It is determined in the first ∼500 days of the model integration, and there isno switching to the other branch after that. Note that those shown in Fig. 4.3k-m belong to thesmall-Ω branch by chance; there are also runs belonging to the large-Ω branch for this rangeof Ω*, with surface temperature structure similar to those shown in Fig. 4.3n-p.
In Fig. 4.4 we observe that the atmospheric circulation characteristics change continuously
but markedly on the small-Ω branch. When Ω*=0, both zonal mean zonal wind and northsouth asymmetry are negligible. As Ω* increases, the westerly wind intensifies rapidly, andthe night side surface temperature rises rapidly, both of which are tied to the appearance of theequatorial warm belt identified in Fig. 18b-m. The temperature at the subsolar point falls at first,
then rises. The north-south asymmetry remains small. Around Ω *=0.5, the north-south
asymmetry increases, and continues to increases with increase of Ω*. The asymmetry has been
identified in Fig. 4.3i-m, but is not evident in cases Ω0.2-Ω0.5 (Fig. 4.3e-h), where, as will
be shown later, the temporal scale of the variability is short compared with the averaging periodof 1000-days. Until the end of the small-Ω branch at Ω*=0.8, the values of temperature at
the subsolar and antisolar points remain high, and the zonal mean wind at the equator maintains
its strength. On the large-Ω branch, the upper tropospheric zonal mean wind is easterly. The
temperature is lower than that of the small-Ω branch at both the subsolar and antisolar points,
and north-south asymmetry is weak. Changes in the four circulation characteristics are rather
small over the entire range (0.7 ≲ Ω* ≲ 1) of the large-Ω branch.
- 42 - 42 -

CGER-I153-2021, CGER/NIES(b) T s(λ=270°, φ=0)(a) Ts (λ=90°,φ=0)(d) ΔNS [Ts](c) ū (φ=0°, σ=0.17)

Figure 4.4 Ω * 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
𝜎𝜎=0.17, and (d) degree of north-south asymmetry of surface temperature defined by
Eq. (4.2) in the text [K]. The values are temporal averages between day 1000 and day
2000. All 10 runs for each Ω * case are plotted. Red and blue lines are ensemble
averages for the small-ΩΩ and the large-ΩΩ branches, respectively. From Noda et al.
(2017), Fig. 4.

4.4 Typical atmospheric circulation structures
In order to understand the atmospheric circulation and its dependence on Ω* on thesynchronously rotating planet, we examine here the spatial structures and temporal variation of
the solutions in detail. Although the circulation structure changes more or less continuously asΩ* changes on the small-Ω branch as implied in Figs. 4.3 and 4.4, we can classify thecirculation structures into three types according to the zonal wind structure and the temporalvariability. They are, in order of the planetary rotation rate where they appear, Type-I,
characterized by day-night convection, Type-II, characterized by a broad equatorial westerly
jet and a north-south symmetric stationary wave-like pattern that turns out to be a stationary- 43 - 43 -

Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets

Rossby wave, and Type-III, characterized by long time scale north-south asymmetric variability.
In the large-Ω branch we can classify the circulation structure as Type-IV, characterized by apair of mid-latitude deep westerly jets. For each of the four types, we choose one case andexamine it in detail below.
4.4.1 Type-I: Day-night convection (Case Ω0.0)
The Type-I circulation appears in cases with very small values of Ω*, and is characterized
by day-night convection; it is similar to those obtained with small Ω* in earlier studies (Merlisand Schneider, 2010; Edson et al., 2011). We examine Case Ω0.0 as a representative case ofType-I.
The time mean structure of the atmospheric circulation in case Ω0.0 is shown in Fig. 4.5.
Upper tropospheric horizontal flow diverges toward the night side (Fig. 4.5b) from theconcentrated upward motion at the subsolar point, where intense precipitation develops (Fig.
4.5e). The outflow is strong not only in the upper troposphere (σ ∼0.23) but also at the middle
levels around σ ∼0.55 (Fig. 4.5c). In the middle troposphere, the entire planet except at thesubsolar point is covered with a widespread, weak, and almost homogeneous downward flow
(Fig. 4.5c). In the lower troposphere (σ ∼0.9), the air flow diverges from the antisolar point andreturns to the day side, connected to the flow converging toward the subsolar point.
The surface temperature distribution (Fig. 4.5h) closely follows the incoming solar flux
distribution (Fig. 4.1). The night side surface temperature is almost homogeneous; its variation
is as small as 10 K, being by far the smallest among all the experiments. The surface pressure
distribution (Fig. 4.5a) 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 (Figs. 4.5aand 4.5c). Temperature on the night side is generally highest in the middle levels (σ ∼0.6) andlower nearer the surface (Fig. 4.5c). In contrast, temperature in the heat low around the subsolar
point (20∘ ≤ 𝜆𝜆 𝜆 160∘ ), increases with decreasing altitude.
The hydrological cycle is governed by the direct day-night circulation. Surface evaporation
has its maximum at the subsolar point, and is very small over the whole night side (Fig. 4.5f).
Rainfall occurs almost exclusively around the subsolar point (Fig. 4.5e). The middle level
outflow from the subsolar point (Fig. 4.5c) advects moist air into the night side, producing
relatively moist tongues (0.45≤ σ ≤0.65, λ < 210∘ and λ > 320∘ ) (Fig. 4.5d). However, themagnitude of the vertically integrated water vapor flux (Fig. 4.5g) is fairly small compared tothose for the other circulation types.

- 44 - 44 -

CGER-I153-2021, CGER/NIES(a) Ps & (u,v) at 𝜎𝜎=0.99(b) Φ & (u,v) at 𝜎𝜎=0.17(c) T & (u, 𝜎𝜎� ) at eq.

(d) q at eq.

(e) Rain(f) Evap(g) � 𝑞𝑞 𝑑𝑑𝑑𝑑 & � 𝑞𝑞𝑞𝑞 𝑑𝑑𝑑𝑑(h) TsFigure 4.5 Day 1000 to day 2000 temporal mean fields for case Ω0.0. (a) Surface pressure (color
shading) [Pa] and horizontal wind vectors [m s-1] at the lowest level. Contour intervalof surface pressure is 5×102 Pa, and the unit vectors of zonal and meridional wind are- 45 - 45 -

Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets

20 m s-1. (b) Horizontal wind vector [m s-1] and geopotential [J kg-1] at 𝝈𝝈=0.17. Unit
vector indicates 25 m s-1. Contour interval of geopotential is 500 J kg-1. (c) Verticalwind -�� [s-1] and zonal wind [m s-1] (vector), and temperature [K] (color) in theequatorial vertical section. Unit vectors of vertical wind and zonal wind are
1.67×10 - 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 2×10-3. (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 [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. From Noda et al. (2017), Fig. 5.

4.4.2 Type-II: Stationary Rossby wave on broad equatorial westerly jet (Case Ω0.15)
The Type-II atmospheric circulation structure appears for 0.05 ≲ Ω ∗≲ 0.2 and ischaracterized by a warm region on the night side (Fig. 4.3b-d) below an intense broad equatorial
westerly wind as shown in Fig. 4.4c, 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 Ω* by Edson et al. (2011). We examine Case Ω0.15 as a representative case of TypeII.
The time mean structure of the atmospheric circulation in case Ω0.15 is shown in Fig. 4.6.
The most notable feature is the emergence of a broad and deep westerly wind that covers almost
the whole depth of the troposphere (Fig. 4.6c) of the low-latitudinal region (Fig. 4.6b). In thebottom layer near the surface, a trace signature of day-night circulation can still be noted (Fig.
4.6a). The location of maximum rainfall and the associated deep updraft are shifted eastward
from the subsolar point by about 20∘ (Fig. 4.6c and Fig. 4.6e), possibly due to moistureadvection by the deep westerly wind. The surface temperature peak is also shifted eastward
from the subsolar point by 25∘ (Fig. 4.6h). A similar eastward shift emerges also in the othercases on the small Ω branch, explaining the drop in subsolar point surface temperature atΩ*∼ 0 (Fig.4.4a). The peak of evaporation remains at the subsolar point (Fig. 4.6f). In fact,

the latent heat flux around the equator on the day side changes little over the range of Ω*
examined in this study. The insensitivity to Ω* results from the employment of the swamp
surface condition and cloud free condition; the incoming shortwave radiation reaching the
ground surface has fixed geographical distribution, and must be approximately balanced by
the energy loss by latent heat of evaporation. The surface pressure minima are located at (𝜆𝜆, 𝜙𝜙)~ (120∘ , ±15∘ ); these are not only to the east of the subsolar point, but also off the equator(Fig. 4.6a). The higher-latitude regions are characterized by intense wavenumber one stationary
waves manifested as the ridge around 𝜆𝜆 𝜆 150∘ and the cyclones around (𝜆𝜆, 𝜙𝜙)∼ (330∘ ,±60∘ ) (Fig. 4.6b). The pressure signatures are generally geostrophic, and have an equivalentbarotropic vertical structure suggested by the low surface pressure signatures below the upper
level low pressure area (Fig. 4.6a).
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 𝜆𝜆=180∘ (Figs. 4.6c and- 46 - 46 -

CGER-I153-2021, CGER/NIES

4.6d). A considerable portion (about one fourth) of the water vapor transported to the night sideat 𝜆𝜆 =180∘ returns to the day side at 𝜆𝜆=360∘ (figure not shown). At 𝜆𝜆=180∘ , 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 the eastward wind associated with the intensewavenumber one stationary waves and near surface westward wind near the equator. Rainfall
is no longer focused at the subsolar point, as it is associated with the moisture transport, andsome amount of rainfall occurs even in the night hemisphere (Fig. 4.6e) despite the negligibly
small amount of surface evaporation. Also due to the enhanced water vapor transport, thecolumn integrated moisture content around the antisolar point reaches about three times that inCase Ω0.0 (Fig. 4.6g). Actually, column integrated moisture content increases considerably
also on the day side; the peak value near the subsolar point in Case Ω0.15 is about 1.5 times
the value of that in Case Ω0.0, and its associated greenhouse effect results in the rise of surface
temperature following the drop near Ω*∼0 (Fig. 4.4a).
It is notable that the horizontal distribution of surface temperature closely follows that ofcolumn moisture content on the night side (Figs. 4.6g and 4.6h); in an extensive region of highcolumn 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 athigher latitudes. The energy budget at the ground surface explains this close relationship;
because incoming solar flux is absent and both latent (∼2 W m-2) and sensible (∼-4 W m-2) heat
fluxes are negligibly small on the night side, the upward thermal radiation flux (∼230 W m-2)
at the surface almost balances the downward longwave radiation from the atmosphere that is
exclusively emitted by water vapor, the only radiatively active component in this model.

- 47 - 47 -Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets(a) Ps & (u,v) at 𝜎𝜎=0.99(b) Φ & (u,v) at 𝜎𝜎=0.17(c) T & (u, 𝜎𝜎� ) at eq.

(d) q at eq.

(e) Rain(f) Evap(g) � 𝑞𝑞 𝑑𝑑𝑑𝑑 & � 𝑞𝑞𝑞𝑞 𝑑𝑑𝑑𝑑(h) TsFigure 4.6 Same as Fig. 4.5 but for case Ω0.15, except that the unit vector in (b) is 50 m s-1 andthe unit vector of vertical wind in (c) is 2.5 × 10-6 s-1. From Noda et al. (2017), Fig 6.

- 48 - 48 -

CGER-I153-2021, CGER/NIES

When all Type-II cases are compared, the broad equatorial jet is stronger for the cases withlarger value of Ω* as indicated in Fig. 4.7, where the values of mass weighted global mean
zonal wind velocity in Type-II are shown. Moreover, for Ω*≳0.2, the wind speed is close to
the absolute values of the intrinsic phase speed of the normal mode Rossby wave of LonguetHiggins (1968). The thin line in Fig. 4.7 shows the intrinsic phase speed of the meridionallygravest normal mode Rossby wave with wave number one, which we calculate with the spectral
method of Kasahara (1976). Considering the vertical structure of the waves appearing in TypeII, we assume an equivalent depth of 10000 m, which is the value for the barotropic mode in an
isothermal atmosphere of 245 K. The rough coincidence of the speed of the broad eastward
equatorial jet and that of the intrinsically westward propagating normal mode Rossby wave foreach Ω* suggests that the wavenumber one planetary scale stationary wave in Type-II isresonantly excited on the broad westerly jet. Other evidence for the resonant excitation is theΩ*-dependence of the amplitude and phase of the stationary wavenumber one waves. The
cyclonic regions associated with the waves are expressed as the north-south symmetric cold
regions in the night side mid to high latitudes (Fig. 4.3). For Ω* from 0.05 to 0.2, the amplitudeof the cyclonic regions is generally large. The longitudinal phase difference between the
precipitation maximum and the cyclonic centers is about 270∘ for Ω*=0.05. This is thelargest 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 Ω* increases, the phase difference
decreases, dropping below 180∘ for Ω*=0.25 and 0.33.
For Ω*≳0.25, the westerly wind does not reach the normal mode Rossby wave speed.
Our preliminary analysis reveals that, in these cases, mid-latitude transient disturbances, which
may originate from baroclinic instability given the development of meridional temperature
gradient (not shown), transport westerly momentum poleward and decelerate the broad westerly
jet. Detailed analysis on the nature of the transient disturbances and their possible role as the“governor” of the equatorial jet remains to be performed.

- 49 - 49 -Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets

Figure 4.7 Mass weighted global mean zonal wind velocity for cases with Ω* from 0.0 to 0.33
(circles). Absolute value of westward phase velocity of the zonal wavenumber one
gravest Rossby normal mode is indicated by the thin line for comparison. From Noda
et al. (2017), Fig. 7.

4.4.3 Type-III: Long time scale north-south asymmetric variability (Case Ω0.75)
The Type-III atmospheric circulation structure appears on the small- Ω branch for0.5≲Ω*≲0.8. The temporally averaged characteristics of Type-III are similar to those of TypeII in terms of the strong eastward equatorial jet, but, as shown in Fig. 4.4d, differ in the presenceof significant north-south asymmetric long time scale variability.
Before considering the Type-III circulation structure in detail, we summarize the Ω*
dependences of the amplitude and the typical oscillation period of the north-south asymmetricvariability. Fig. 4.8 compares the time series of zonal mean surface pressure in four cases withdifferent values of Ω*. In Case Ω0.2, where Type-II structure develops, a quasi periodic
oscillation with amplitude of ∼20 hPa and a temporal scale of ∼10 days is notable. In Case
Ω0.5, in addition to an oscillation with ∼20 day period, a slower, north-south asymmetricvariability is evident; its period and amplitude are ∼40-100 days and ∼45 hPa, respectively.
In cases with larger Ω*, the slow, north-south asymmetric variability is more intense and its
characteristic period is longer; in Case Ω0.67, the amplitude is ∼80 hPa, and the period is∼1000 days. In Case Ω0.75, the amplitude is as large as ∼160 hPa, and, looks almost
permanent in Fig. 4.8d. However, by conducting several extended experiments, we haveconfirmed that the asymmetry does change its sign over a long time; the pressure deviation
reverses at around t=25000 days for the run shown in Fig. 4.8d. Furthermore, the sign of theasymmetry is determined by chance; in the ten runs conducted for Ω0.75, Type-III structureappears in four runs (not shown), and, during the period shown in Fig. 4.8d, two of them havea positive pressure anomaly in the northern high latitudes, and the remaining two are negative.
We conclude that, despite the development of the distinct long time scale north-south
asymmetric variation, the structure of the atmospheric circulation is, in a statistical sense, north- 50 - 50 -

CGER-I153-2021, CGER/NIES

south symmetric, consistent with the symmetry of the applied solar flux.
Considering the characteristics of the north-south variation, we examine Case Ω0.75 asrepresentative of Type-III, where the north-south asymmetry appears as a quasi stationary
structure that persists throughout the 1000 days of the temporal average. As shown in Fig. 4.8d,
northern (southern) high latitudes are occupied by high (low) pressure throughout the averaging
period. The north-south asymmetric features discussed below are naturally reversed in the time
period when the surface pressure in the northern (southern) hemisphere is low (high). We also
note that the north-south asymmetric atmospheric circulation features develop also in GCM
experiments with higher horizontal resolution (T42 and T85), although they appear in slightly
different ranges of Ω* (see Section 4.6), so we believe their emergence itself is insensitive tomodel resolution.
(a) Ω0.2(b) Ω0.5(c) Ω0.67(d) Ω0.75

Figure 4.8 Latitude--time distribution of zonal mean surface pressure [Pa] for (a) Ω0.2, (b) Ω0.5,(c) Ω0.67, and (d) Ω0.75. From Noda et al. (2017), Fig. 8.

- 51 - 51 -

Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets

The time mean structure of the atmospheric circulation in case Ω0.75 is shown in Fig. 4.9.
The deep westerly flow along the equator (Fig. 4.9bc), and the associated eastward advectionof water vapor (Fig. 4.9dg) resulting in a warm belt along the equator in the night hemisphere(Fig. 4.9h), are features similar to those in Type-II (Fig. 4.6). However, except for the
distribution of evaporation, which is strongly constrained by insolation as was discussed forType-II, most of the off-equatorial features exhibit north-south asymmetry in contrast to thenorth-south symmetry in Type-II. Northern (southern) high latitudes are covered with surface
high (low) pressure (Fig. 4.9a). The low pressure area in the day hemisphere also exhibits northsouth asymmetry; the low pressure center in the southern hemisphere is much more intense thanits counterpart in the northern hemisphere. Being in geostrophic balance with the pressure
gradient around the polar pressure anomalies, north-easterly (north-westerly) wind prevails at
the surface in northern (southern) mid latitude (arrows in Fig. 4.9a). This brings dry (moist) air
into the mid latitudes of the day (night) hemisphere (Fig. 4.9g) crossing the day-night boundaryat 𝜆𝜆=180∘ , inducing the north-westward (south-eastward) development of the mid-latitude
precipitation zone (Fig. 4.9e) and the north-south asymmetry of surface temperature in both the
day and night hemispheres (Fig. 4.9h) through the anomaly in downward thermal radiation.
Two additional features characterize the north-south asymmetry. First, the westerly region
extends farther poleward in the southern hemisphere than in the northern hemisphere (Fig.
4.10a), where intense baroclinic disturbances develop (not shown here), presumablytransporting westerly momentum downward. Second, there is a baroclinic zonal wavenumber
one feature (Fig. 4.9ab) which has markedly north-south asymmetric meridional phase tilt
(Fig. 4.10b); the phase lines tilt from northwest to southeast in a wide latitudinal zone fromthe northern high latitudes (𝜙𝜙 𝜙 +70∘ ) to southern mid latitudes (𝜙𝜙 𝜙 -40∘ ), crossing theequator. The phase tilt of the zonal wavenumber one feature, which implies southward transport
of westerly momentum from northern to southern hemispheres, presumably contributes todriving the mid-latitude westerly jet in the southern hemisphere noted above (Fig. 4.10a).
According to our preliminary analysis (not shown here) of the vorticity sources following
the formulation of Sardeshmukh and Hoskins (1988), the meridionally tilted wavenumber one
feature seems to be forced jointly by tropical and extratropical precipitation (Fig. 4.9e); theheating near the subsolar point, which is distributed mainly in the northern tropics around(𝜆𝜆, 𝜙𝜙)=( 120∘ , +12∘ ), can be regarded as an excitation source of a Rossby wave that contributes
the northern half of the wavenumber one structure. Meanwhile the latent heating associatedwith the precipitation band in southern mid latitudes distributed around (𝜆𝜆, 𝜙𝜙)=( 180∘ , -30∘ ),can be regarded as an excitation source of a Rossby wave that contributes the southern half.
Upward cascade of baroclinic eddies developing in the westerly jet could also contribute to thesouthern half. The distribution of mid-latitude precipitation seems to be, in turn, induced by thenorth-south asymmetry of moisture flux associated with surface pressure as described in theprevious paragraph. Combining these features, the north-south asymmetry may possibly bemaintained through a positive feedback loop, so that the asymmetry tends to have long life time.
Quantitative examination of the dynamics of this possible feedback loop remains for futurestudies.

- 52 - 52 -

CGER-I153-2021, CGER/NIES(a) Ps & (u,v) at 𝜎𝜎=0.99(b) Φ & (u,v) at 𝜎𝜎=0.17(c) T & (u, 𝜎𝜎� ) at eq.

(d) q at eq.

(e) Rain(f) Evap(g) � 𝑞𝑞 𝑑𝑑𝑑𝑑 & � 𝑞𝑞𝑞𝑞 𝑑𝑑𝑑𝑑(h) TsFigure 4.9 Same as Fig. 4.6 but for case Ω0.75, except that the unit vector of vertical wind in (c)is 1.3××10-6 s-1. From Noda et al. (2017), Fig. 9.

- 53 - 53 -

Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets(a) Zonal mean zonal wind(b) Eddy Stream Function at 𝜎𝜎=0.17

Figure 4.10 Structure of the atmosphere averaged from day 1000 to day 2000 for case Ω0.75:(a) zonal mean zonal wind, and (b) eddy stream function at 𝜎𝜎=0.17. From Noda etal. (2017), Fig. 10.

4.4.4 Type-IV : Mid-latitude westerly jets (Case Ω1.0)
The Type-IV atmospheric circulation structure is found over the entire large-Ω branch forΩ*≳0.7, and is characterized by somewhat Earth-like mid- to high- latitudes westerly jets. Thisis similar to the structures obtained by Merlis and Schneider (2010) and Edson et al.(2011) with
Ω* = 1. We examine Case Ω1.0 as a representative case of Type-IV.
The time mean structure of the atmospheric circulation in case Ω1.0 is shown in Fig. 4.11.
The mid latitudes are occupied by westerly winds through the whole depth of the troposphere(Fig. 4.11a and Fig. 4.11b). The low latitudes are occupied by easterly wind, but only in theupper troposphere. The lower tropospheric circulation along the equator (Fig. 4.11c) is morestrongly controlled by the day-night contrast; zonal wind near the surface converges to form
the upward motion at the subsolar point, and diverges around the antisolar point compensatedby the broad downward motion. In the off-equatorial latitudes, latitudinal tilting of zonal
wavenumber one wave features are notable, but these have generally baroclinic verticalstructure, in contrast to the barotropic Rossby wave in Type-II. Polar regions are covered withdeep low pressure areas. The precipitation and water vapor distributions are more complicatedthan those on the small-Ω branch. Precipitation (Fig. 4.11e) is most intense in a zonally aligned
V-shaped region extending from the equatorial point (𝜆𝜆,𝜙𝜙)∼(110∘ , 0∘ ) to (𝜆𝜆, 𝜙𝜙)∼(30∘ , ±25∘ ),loosely overlapping the low pressure area in the western part of the day hemisphere (contours
in Fig. 4.11a). The wings of the V-shaped precipitation region intrude into the night side fromthe regions around 𝜙𝜙=±25∘ at 𝜆𝜆=360∘ . There is also a pair of zonally elongated precipitation
zone in the higher latitudes, which start at (𝜆𝜆, 𝜙𝜙)∼(45∘ , ±45∘ ) and extend to (𝜆𝜆, 𝜙𝜙)∼(330∘ ,±80∘ ) on the night side. The distribution of column integrated water vapor content roughly
follows that of precipitation (Fig. 4.11g), but the areas of greatest moisture content are located
far from the equator, poleward of the high-latitude parts of the equatorial V-shaped strong
precipitation area at (𝜆𝜆, 𝜙𝜙)∼(30∘ , ±30∘ ).
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CGER-I153-2021, CGER/NIES

The distribution of night side surface temperature (Fig. 4.11h) closely follows that of theatmospheric water vapor content (Fig. 4.11g) as in the cases on the small-Ω branch. However,reflecting the complex structure of humidity, temperature varies longitudinally; it is warmer tothe east along 𝜙𝜙 𝜙 ±30∘ , whereas it is warmer to the west along 𝜙𝜙 𝜙 ±50∘ . Also the
distribution of surface temperature on the day side is affected by the distribution of water vapor
content; the highest surface temperature appears at (𝜆𝜆, 𝜙𝜙)∼(80∘ , ±40∘ , the locations that arequite far from the subsolar point and below the belts of large water content (deep blue colors of
Fig. 4.11g). The values of surface temperature at the subsolar and antisolar points are lower
than the respective values in Types -II or -III (Figs. 4.4a and 4.4b) resulting from the reductionof atmospheric water content compared to those cases.

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Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets(a) Ps & (u,v) at 𝜎𝜎=0.99(b) Φ & (u,v) at 𝜎𝜎 =0.17(c) T & (u,𝜎𝜎� ) at eq.

(d) q at eq.

(e) Rain(f) Evap(g) � 𝑞𝑞 𝑑𝑑𝑑𝑑 & � 𝑞𝑞𝑞𝑞 𝑑𝑑𝑑𝑑(h) TsFigure 4.11 Same as Fig. 4.9 but for case Ω1.0 except that unit vector of the vertical wind in (c)×10-6 s-1. From Noda et al. (2017), Fig. 11.
is 2.5×- 56 - 56 -

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4.5 Day-night energy transport
4.5.1 Dependence on Ω*
In this section, we examine how day-night energy transport changes with Ω*, responding
to the considerable variation of the atmospheric circulation structure described in the previous
section. We analyze OLR on the night side, 𝐹𝐹𝑂𝑂𝑂𝑂𝑂𝑂 , day-night dry static energy transport, 𝐹𝐹𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ,and day-night latent energy transport, 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙 , which, in equilibrium states, satisfy the energybalance of the night side:𝑇𝑇���� + 𝑇𝑇��� − 2 𝜋𝜋 𝑅𝑅�� 𝐹𝐹��� = 0(4.3)

2 𝜋𝜋 𝑅𝑅�� (𝐹𝐹��� + 𝐹𝐹���� − 𝐹𝐹��� + 𝐿𝐿𝐿𝐿) + 𝑇𝑇���� = 0(4.4)

𝑇𝑇���� and 𝑇𝑇��� are calculated assuming the approximate balances of heat and moisture budgets
in the night side atmosphere, which are

2 𝜋𝜋 𝑅𝑅�� � 𝐹𝐹���� − 𝐿𝐿� + 𝑇𝑇��� /𝐿𝐿 = 0(4.5)

where 𝐹𝐹𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 is surface evaporation flux, 𝐹𝐹𝑆𝑆𝑆𝑆𝑆𝑆 is net upward longwave radiation flux at thesurface, 𝐹𝐹𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 is surface sensible heat flux, P is precipitation, and L is latent heat of water
vapor. All of the terms are 1000-day mean values spatially averaged over the night side.
Fig. 4.12 shows Ω* dependences of, 𝐹𝐹𝑂𝑂𝑂𝑂𝑂𝑂 𝑇𝑇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 /(2 𝜋𝜋 𝑅𝑅�� ), and 𝑇𝑇𝑙𝑙𝑙𝑙𝑙𝑙 /(2 𝜋𝜋 𝑅𝑅�� ). All 10 runs
are plotted for each value of Ω*. The most remarkable feature is that total energy transport isalmost unchanged regardless of the branch of the solution and the value of Ω*, while thepartition into 𝐹𝐹𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 and 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙 changes. For Ω*∼0, where the Type-I structure appears, 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙
is negligible, as atmospheric water vapor content is very small (Fig. 4.5g). As Ω* increases
and the Type-II structure appears, 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙 rapidly increases, but 𝐹𝐹𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 decreases
correspondingly, keeping the sum of the two (𝐹𝐹𝑂𝑂𝑂𝑂𝑂𝑂 ) almost unchanged. The increase of 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙
results from the development of the deep broad westerly wind (Figs. 4.6b and 4.6c) together
with the increase of moisture in the day hemisphere (Fig. 4.6d). Further increase of 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙 anddecrease of 𝐹𝐹𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 continue for larger Ω * as the Type-III with north-south asymmetricvariability appears. 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙 exceeds 𝐹𝐹𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 at Ω*=0.33 and 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙 reaches about twice 𝐹𝐹𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 at
the large-Ω end of the small-Ω branch (Ω*=0.8). Still, the sum of the two (𝐹𝐹𝑂𝑂𝑂𝑂𝑂𝑂 ) is kept
almost constant. At the transition from the small-Ω branch to the large-Ω branch around Ω*∼0.75, 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙 suddenly reduces by about half. Nevertheless, an equally abrupt increase of
𝐹𝐹𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 means that total heat transport changes only a little. The decline of 𝐹𝐹𝑙𝑙𝑙𝑙𝑙𝑙 at the transition
results from the associated disappearance of the broad westerly wind at low latitudes. The typeIV structure has a pair of deep mid-latitude westerly jets blowing through the day and nightsides (Fig. 4.11b), but they cannot transport as much water vapor as the broad equatorial
westerly wind in the Type-II or Type-III cases, because the water vapor mixing ratio in the midlatitudes is smaller than in the lower latitudes. The variation of total day-night energy transport
is less than 2% over the wide range of Ω*, while the atmospheric circulation structure varies- 57 - 57 -

Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets

considerably. Day-night total energy transport scarcely depends on the atmospheric circulation
structure.
We have already seen in Fig. 4.4b that surface temperature at the antisolar point changes
greatly with the change of Ω*. This seems perplexing, since day-night total energy transport
is almost constant. However, if we examine the hemispherically averaged temperature, thechange is only modest. Fig. 4.12b shows Ω* 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 of almost 50 K (Fig. 4.4b). This results from the compensation between the temperature
variations in the lower and higher latitudes; in Type-II and Type-III, surface temperature in the
low latitudes including the antisolar point is high, while regions of low surface temperatureappear in the higher latitudes associated with the large amplitude Rossby waves (Fig. 4.3b-m).
The remaining modest changes of averaged temperatures can be explained mainly by thechange of mean column water vapor content.
(a) Day-to-Night Heat Fluxes(b) Mean Surface Temperature

Figure 4.12 (a) Ω* dependences of outgoing longwave radiation on the night side, 𝐹𝐹��� (∘), daynight dry static energy transport per unit area, 𝑇𝑇���� /(2 𝜋𝜋 𝑅𝑅�� ) (black triangle),and day-night latent energy transport per unit area, 𝑇𝑇��� /(2 𝜋𝜋 𝑅𝑅�� ) (××). Units are-2[W m ]. All 10 runs for each Ω * case are plotted. Blue and red lines represent
ensemble averages for the small-ΩΩ and the large-ΩΩ branches, respectively. (b)Same as (a) but for global mean (∘), day side mean (××), and night side mean (Box)of surface temperature [K]. From Noda et al. (2017), Fig. 12.

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CGER-I153-2021, CGER/NIES

4.5.2 Moist atmosphere radiation limit constraint
As described in the previous subsection, the total amount of day-night energy transport isfound to be insensitive to the change of Ω* and to the associated change of atmosphericcirculation structure. The invariance of day-night total energy transport is equivalent to theinvariance of day side OLR, because the day-night total energy transport is equal to thedifference between the day side OLR and the incoming solar flux; the latter is constant in thepresent study. It has been recognized that, in the framework of a 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 in relation to the constraint on the day side OLR from the radiation
limit of a moist atmosphere.
Fig. 4.13 shows the relationship between surface temperature and OLR on the day side
obtained by the present GCM calculations superposed on the relations obtained by the onedimensional radiative convective equilibrium model described in Chapter 3 with several
specified values of tropospheric relative humidity. The relationship between surface
temperature and OLR is sampled at the grid points within the 120∘ × 120∘ rectangularregion centered on the subsolar point from the run for each Ω* described in the previous
section.
In all the GCM runs, the maximum values of OLR are between 400 and 430 W m-2, andlie under the values of the radiation limits in the one-dimensional calculation, given that thevalues of relative humidity averaged over the troposphere on the day side of the GCM runs
are within the range 60-80%. 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 isconstrained by the radiation limit of a moist atmosphere on a water covered planet. Now
recalling that the system is in a statistically equilibrium state, the amount of day-night totalenergy transport should be equal to the difference between the incoming solar flux and theradiation limit of a moist atmosphere. The results of our GCM calculations indicate that thechange in atmospheric circulation structure associated with the change of Ω* does not modify
drastically the mean value of atmospheric humidity, and hence does not affect the value of theradiation limit. This explains the general insensitivity of day-night energy transport to Ω*
obtained in the present GCM calculations.

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Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets

Figure 4.13 Relationships between surface temperature and OLR obtained by the GCM and by
the one-dimensional (vertical) radiative-convective equilibrium model. The GCM
results are shown as colored dots: purple, light blue, green, and pink dots indicate
runs Ω0.0, 0.15, 0.75, and 1.0, respectively. Data are from the grid points in the 𝟏𝟏𝟏𝟏𝟏𝟏∘
× 𝟏𝟏𝟏𝟏𝟏𝟏∘ rectangular region centered on the subsolar point. Crosses in black circles
indicate the values at the subsolar point. Black lines are the one-dimensional model
results with tropospheric relative humidity of (in order from the top) 50, 60, 70, 80,
90, and 100 %, respectively. From Noda et al. (2017), Fig. 13.

4.6 Dependence on resolution
Because of the large number of experiments required to examine the Ω* dependence of
circulation structures, including the possibility of multiple equilibrium solutions, thehorizontal resolution of the GCM used in this study is limited to T21. In this section, we checkthe resolution dependence of the results, by briefly describing the results obtained in models
with higher resolution, T42 and T85, focusing on some of the features that may be resolution
sensitive. For T42, we have performed 10 runs for each of several selected values of Ω*. For
T85, only one run was performed for each values of Ω*. In a qualitative sense the main results,
namely the existence of the four types of solutions, are not sensitive to the model's resolution,
as shown below. Figs.4.15a and 4.15b show the upper tropospheric zonal mean zonal wind at
the equator for various values of Ω* in the T42 and T85 models, respectively; for T42, all runs
for each Ω* are plotted. These figures share the main features seen with T21 resolution(Fig.4.4c): there are two branches of solutions, and the equatorial zonal wind velocity for each
Ω* is insensitive to the resolution. And, at least in the T42 model, the two branches coexist
over a range of Ω* giving multiple equilibria, although the values of Ω* with multiple- 60 - 60 -

CGER-I153-2021, CGER/NIES

equilibria are about 0.1 smaller than in the T21 model. In the case of the T85 model, as we canonly perform one run for each Ω*, the existence of multiple equilibria cannot be confirmed.
However, the overall behavior is not inconsistent with that in T42; the value of Ω* for theupper end of the small Ω branch is the same.
Fig. 4.14 shows the values of mass weighted zonal mean wind speed for different values ofΩ* obtained in the runs with T21, T42 and T85 resolutions, compared with the intrinsic phasespeed of the Rossby wave normal mode. In a qualitative sense, we can confirm the main featuresdescribed in Section 4.4.2; i.e., the mass weighted zonal mean wind speed closely follows orslightly exceeds the Rossby wave phase speed for 0.0 ≲ Ω* ≲ 0.2, and levels off for larger
Ω*. The only slight exception is Ω0.15 in T85, where the zonal mean wind is decelerated bytransient disturbance whose nature is unclear.

Figure 4.14 Same as Fig. 4.7, but showing values for horizontal resolutions of T42 (squares) andT85 (triangles) in addition to those for T21 (circles). From Noda et al. (2017), Fig. A.2.

Figs. 4.15c and 4.15d show the measure of the north-south asymmetry of surface
temperature defined by Eq. 4.2 for various values of Ω * in the T42 and T85 models,
respectively; for T42, all runs for each Ω* are plotted. Compared to the corresponding figure
for T21 resolution (Fig. 4.15d), the degree of north-south asymmetry seems to be weaker inhigher resolution models. Still, we can identify features largely free from resolution
dependence: the monotonic increase of the degree of north-south asymmetry on the small-Ωbranch, and the smaller degree of north-south asymmetry on the large-Ω branch. The temporalscales of the north-south asymmetric variability are of the same order of magnitude for allmodel resolutions (not shown). The spatial structure of the north-south asymmetric variability
in Type III, i.e., toward the large-Ω* end of the small-Ω branch, is also common to all model
resolutions. Fig. 4.16 shows the horizontal structures of surface pressure in the T42 and T85- 61 - 61 -

Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planetsmodels for Ω* = 0.6 averaged for 500 days during which high (low) pressure occupies thenorth (south) pole. A comparison with Fig. 4.9a showing the structure of the variability forΩ* = 0.75 in the T21 model confirms that all resolutions share the same major features, suchas the longitudes of the low pressure area in the southern day hemisphere and the high pressurearea in the southern night hemisphere.
(a) �� (𝜙𝜙=0, 𝜎𝜎=0.17) in T42(b) � (𝜙𝜙=0, 𝜎𝜎=0.17) in T85(c) Δ�� [𝑇𝑇� ] in T42(d) Δ�� [𝑇𝑇� ] in T85

Figure 4.15 (a), (b) Same as Fig. 4.4c but for the T42 model (a) and T85 model (b), and (c), (d)same as Fig. 4.4d but for the T42 model (c) and T85 model (d). From Noda et al.
(2017), Fig. A.1.

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CGER-I153-2021, CGER/NIES(a) Ps Ω0.6 T42(b) Ps Ω0.6 T85

Figure 4.16 Mean surface pressure distributions for Ω0.6 in the T42 model (a) and T85 model(b) for 500 days during which high (low) pressure occupies the north (south) pole.
From Noda et al. (2017), Fig. A.3.

4.7 Summary
Numerical experiments are performed using a cloud-free, swamp aquaplanet GCM with agray absorption coefficient for longwave radiation and with the Earth's solar constant. The valueof planetary rotation rate normalized by the Earth's value, Ω*, is varied from 0 to 1. For allΩ* cases, statistically equilibrium states are obtained; the runaway greenhouse state does not
emerge. The circulation structures obtained are classified into four types: Type-I characterized
by day-night convection, Type-II characterized by a broad equatorial westerly jet and astationary Rossby wave, Type-III characterized by a long time scale north-south asymmetricvariability, and Type-IV characterized by a pair of mid-latitudinal westerly jets. Types-I, II, andIII evolve continuously from one to another as Ω* increases, constituting one branch of thesolution referred to as the small-Ω branch, whereas Type-IV belongs to a different branchreferred to as the large-Ω branch (Fig.4.4). For 0.7 ≲ Ω* ≲ 0.8, multiple equilibrium states
emerge; both Type-III and Type-IV are allowed. The dependence of the amount of day-night
energy transport on Ω* is analyzed. It is confirmed that the amount is large enough to preventthe day side atmosphere from entering a runaway greenhouse state. Moreover, the amount isfound to be almost insensitive to Ω * despite the drastic change in the structure of theatmospheric circulation, although the partition into latent and sensible energy transports varies.
Day side OLR in the experiments is analyzed and compared with the values obtained with a
one-dimensional radiative convective model. The results strongly suggest that day side OLR isconstrained by the radiation limit of a moist atmosphere; the details of the circulation structure
do not greatly change atmospheric humidity, so the value of the radiation limit is unchanged.
This explains the invariance of day-night energy transport, as it is equal to the difference- 63 - 63 -

Chapter 4 Circulation structure of planets with a peculiar distribution of incoming solar radiation flux:
climate of synchronously rotating planets

between incoming solar flux and day side OLR. The former is a constant prescribed amount inthis study, and the latter is constrained by 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 a more complete investigation on
their sensitivity to Ω* than previous studies. The ``slowly rotating regime'' and the ``rapidly
rotating regime'' identified by Merlis and Schneider (2010) presumably correspond to the smallΩ branch and the large- Ω branch in the present study, respectively. However, thecorrespondence is not certain because they present the horizontal distributions of atmosphericvariables for only two values of Ω*. Circulation structures similar to those of Type-I and TypeIV are obtained for those two values of Ω*, but it remains unclear whether they obtained
atmospheric structures similar to Type-II and Type-III. The dependence of the circulation
structure on Ω* obtained by Edson et al.(2011) 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 Ω*. These features are similar to
those obtained in the present study.

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CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27
CGER-I153-2021, CGER/NIES

Chapter 5
Preliminary results obtained for cloudy atmospherewith non-gray radiation- 65 - 65 -

Chapter 5

Preliminary result obtained for cloudy atmosphere with non-gray radiation

5.1 Introduction
In Chapter 3, the occurrence condition of the runaway greenhouse state and the dependenceof the climate on the solar constant were investigated using a gray radiation scheme. In thischapter, the preliminary results obtained by a GCM with a non-gray radiation scheme arepresented shortly. The following two problems were examined:
(I)
(II)

Does an OLR upper limit exist also in non-gray radiation?
If an OLR upper limit exists, what determines the limit value?

Some experiments on the runaway greenhouse state in non-gray atmosphere have been
performed using GCMs. Yang et al. (2013) discuss the occurrence condition of the runaway
greenhouse state of synchronously rotating planets. Yang et al. (2013) showed that, with anatmosphere-ocean coupled model, the threshold value of solar constant for the occurrence ofthe runaway greenhouse state on synchronously rotating planets was larger than that for planetswith an incoming solar flux distribution similar to that of the Earth's which have a diurnalchange. As the reason for the difference in the threshold value, they proposed that the increaseof albedo was caused by the generation of dense cloud around the subsolar point. Leconte et al.
(2013) performed a GCM experiment with an increased solar constant for Earth's incoming
solar flux distribution in order to consider the climate in the distant future when the value ofsolar constant will increase due to the time evolution of the Sun. They showed that equilibrium
states were obtained with 375 W m-2 of the global mean incoming solar flux, which is a larger
value than the OLR limit obtained by one-dimensional models. As the reason for the difference,
they proposed that the intensification of drying in the subtropical region caused the increase in
infrared radiation, which balanced the increased incoming solar flux. The results of these twostudies seem to suggest that the occurrence condition of the runaway greenhouse state isdetermined in a complicated way according to model configuration.
However, we consider that the occurrence condition of the runaway greenhouse state isdetermined in a simpler way. From the results of Chapters 3 and 4, we suggest that theoccurrence of the runaway greenhouse state is determined by whether the global mean incoming
solar flux exceeds the OLR limit in all cases, although the threshold value of the solar constantfor the occurrence of the runaway greenhouse state will change according to cloud distribution
and/or incoming solar flux distribution. In this section, we examine the effect of cloud on theoccurrence condition of the runaway greenhouse state using a GCM including a non-grayradiation scheme and a simple cloud model.
5.2 Model configuration
As for atmospheric constituents and radiation processes, case (2) (case for Earth's radiation)
described in Section 2.4 was adopted. The amount of cloud water was calculated by solving thetime-dependent equation of cloud water with a given cloud extinction time, as described in
Section 2.5. The value of the cloud extinction time was set to 1500 sec for the cloudy case and0 sec for the cloudless case. The value of the solar constant S was varied in the range between
1366Wm-2 and 2200W m-2 The value of planetary rotation rate Ω was varied in the range
between 0.0 and 1.0. Two kinds of the distribution of incoming solar flux were considered:- 66 - 66 -

CGER-I153-2021, CGER/NIES(1) Earth radiation case: distributions evaluated with the present terrestrial orbital parameters.
The diurnal and seasonal cycles were considered.
(2) Synchronously rotating planet radiation case: distribution shown in (Fig. 4.1).
The entire surface was assumed to be a swamp ocean. The value of surface albedo was set
to be 0.15. The resolution of GCM was T42L26.
5.3 Results
A numerical experiment with changing solar constant was performed for two kinds of
distributions of incoming solar flux: cases (1) and (2) described in the previous section. Fig. 5.1
shows the results of all runs. The cross mark represents the result in which the value of the
global mean OLR was smaller than the global mean absorbed solar flux and the global meansurface temperature kept increasing. These cases are considered to correspond to the runaway
greenhouse state. The threshold values of the occurrence of the runaway greenhouse state wereabout 1600W m-2 for the cloudless cases regardless of solar flux distributions. On the other
hand, for the cloudy cases, the threshold values changed according to the solar flux distribution.
The threshold values for the Earth radiation distribution cases were similar both for the
cloudless case and the cloudy case. These values were almost the same as the value obtainedby Leconte et al. (2013), 1500W m-2. The threshold values for the synchronously rotating planet
distribution cases exceeded 2000 W m-2.
As described above, the threshold value for the occurrence of the runaway greenhouse statechanged according to model configuration, and the global mean incoming solar flux ranged
from 450W m-2 to 550W m-2. Contrary to the incoming solar flux, the difference in the thresholdvalue of OLR was much smaller (Fig. 5.1b). The threshold values of OLR were about 300
W m -2 for all cases. It is considered that an upper limit of OLR exists also for cloudy
atmospheres with non-gray radiation, and that the runaway greenhouse state emerges when the
global mean incoming solar flux exceeds the OLR threshold value, i.e., 300 W m-2. The valuesof relative humidity became small for cases in which the amount of absorbed solar flux
increased. It is considered that the threshold values obtained in this experiment correspond to
the OLR maximum value determined according to the values of relative humidity, since the
OLR maximum value which an atmosphere can emit has a negative dependence on relative
humidity. The difference in threshold values was larger than the difference in the maximum
absorbed incoming solar flux and is considered to be caused by the difference in albedo. For
the cloudy cases with S=1366 W m-2, the global mean albedo was 0.36 and 0.42 for the Earthradiation case and the synchronously rotating planet radiation case, respectively. The amountof cloud water at subsolar point for the synchronously rotating planet radiation case was larger
than that for the Earth radiation case. The difference in the amount of cloud water caused thedifference in albedo. The result that cloud water amount and albedo increase for thesynchronously rotating planet radiation case is consistent with the results obtained by Yang etal. (2013).

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Chapter 5

Preliminary result obtained for cloudy atmosphere with non-gray radiation

(a)

(b)

Figure 5.1 (a) Relationship between Ω* and global mean OLR, (b) Relationship between Ω*and solar constant divided by 4.0. The squares and circles represent the cases in which
equilibrium states were obtained. The crosses represent the case in which the runaway
greenhouse state emerged. The red marks represent the cloudy case withsynchronously rotating planet distribution of solar flux. The blue marks represent thecloudy case with Earth-like distribution of solar flux. The yellow marks represent thecloud-free case with synchronously rotating planet distribution of solar flux. The
green marks represent the cloudy case with Earth-like distribution of solar flux.

5.4 Summary
It is shown that, for the non-gray radiation cases, there exist OLR maximum values
regardless of the existence of cloud or the distribution of incoming solar flux. The runaway
greenhouse state emerges when the global mean incoming solar flux exceeds the OLR
maximum value. This condition is the same as the occurrence condition of the runaway
greenhouse state for gray atmosphere discussed in Chapter 3. These results suggest that theoccurrence of the runaway greenhouse state is determined by a common condition regardlessof model configuration.
It should be noted that there remains an important problem of the occurrence condition of
the runaway greenhouse state for the non-gray radiation cases. The problem is to determine theradiation limit by using a vertical one-dimensional model with a non-gray radiation scheme
used in this section, as discussed in Chapter 3, and to examine the correspondence of thethreshold value obtained by the GCM experiment to the radiation limit.

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CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27
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Chapter 6
Conclusion and discussion- 69 - 69 -

Chapter 6 Conclusion and discussion

6.1 Summary
In this monograph, the results of numerical experiments using GCMs for various values ofsolar constant and two types of horizontal distribution of incoming solar radiation flux are
described. With a simple model configuration such as gray radiation and swamp ocean, thefollowing results were obtained.
(a) The condition for the occurrence of runaway greenhouse state in the three-dimensional
system is that the global mean value of incoming flux – i.e., not the maximum or theminimum of the latitudinal distribution of incoming flux – exceeds the upper limit of OLR.
The results of a preliminary experiment using a non-gray radiation scheme also suggest thatthe occurrence of the runaway greenhouse state is determined by a common condition
regardless of model configuration, that is, excess of the global mean incoming solar flux
over the OLR maximum value.
(b) Climate states of synchronously rotating planets were obtained for Earth's value of the solar
constant. Statistically equilibrium states were obtained regardless of the value of planetaryrotation rate, but the circulation structure changed drastically according to the values ofplanetary rotation rate. The amount of day-night energy transport was large enough toprevent the dayside atmosphere from entering a runaway greenhouse state and was almost
insensitive toΩ*. The invariance of the day-night energy transport was caused by the factthat the dayside OLR was constrained by the radiation limit.
The common conclusion for the above results is that the radiation limit is important for
determining the climate of planets under various conditions: the radiation limit determines thevalue of the runaway threshold of solar constant even in three-dimensional systems and theamount of the day-night energy transport in synchronously rotating planets.
6.2 Ongoing problem and future plans
In numerical experiments described in this monograph, values of the solar constant larger
than Earth’s value were used. A drastic change in climate occurs also when the value of thesolar constant is decreased from that of the present Earth, in which case a globally ice-covered
state will occur. The globally ice-covered state has been discussed for examining the possibilityof a snowball Earth state in the Neoproterozoic Era (e.g., Hoffman et al., 1998: Baum andCrowley, 2001).
One-dimensional energy balance models (EBMs) show that a slight decrease in the solar
constant results in an ice-covered Earth (Budyko, 1969; Sellers, 1969). Budyko (1969) andSellers (1969) discuss multiple equilibrium solutions: ice-free state, globally ice-covered state,
and partially ice-covered state, using climate regime diagrams that show the existence rangesof climate states in the solar constant – ice-line latitude plane. In their model, Earth’s radiation
is parameterized in a very simple way and the runaway greenhouse state is not considered. The
dependence of climate on the value of solar constant had not been examined with a model that
includes both the runaway greenhouse state and globally ice-covered state until around the year
2000. Ishiwatari et al. (2007) is the first attempt to draw a climate regime diagram including
the runaway greenhouse state. Ishiwatari et al. (2007) present a climate regime diagram- 70 - 70 -

CGER-I153-2021, CGER/NIES

including both the runaway greenhouse state and globally ice-covered state, and they show thepossibility of the coexistence of the ice-covered state, the partially ice-covered state, and the
runaway greenhouse state for a given, common solar constant value. However, a model bug
described in Chapter 3 was found in 2019, and the paper has been retracted. Therefore, we could
not include the results of Ishiwatari et al. (2007) in this monograph. We have submitted thecorrected paper (Ishiwatari et al., submitted to J. Geophys. Res.) based on a re-experiment with
an appropriately corrected GCM.
In addition to the results described in this monograph, a new climate regime diagram thatwill be presented in the corrected paper (Ishiwatari et al., submitted to J. Geophys. Res.) will
be a basic concept for considering the variety of climates and the habitability of exoplanets.
However, the critical values of the occurrence of drastic climate changes may vary according
to model configuration, such as the value of albedo, the details of the radiation scheme, theradiation effect of clouds, and so on. Especially, the dynamics of the ocean is undoubtedly an
important element to be examined when considering the variety of climates. We are now
preparing a paper on a solar constant dependence experiment for a horizontal distribution ofsolar flux adopted in Chapter 3 using an atmosphere-ocean coupled model (Kawai et al., in
preparation). For the habitability of synchronously rotating exoplanets, the effect of ocean
dynamics has been considered. Hu and Yang (2014) performed a series of climate simulations
using a coupled atmosphere-ocean model with parameters following Gliese 581g. They foundthat the ocean contributed greatly to the day-night hemisphere energy transport and that thepartition of the heat transport into atmospheric and oceanic transport varied considerably
depending on the atmospheric CO2 concentration and the incoming shortwave flux from thecentral star. The inclusion of a dynamically active ocean may possibly affect the insensitivityof day-night energy transport to the planetary rotation rate. This issue remains as a focus of
future studies.

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Chapter 6 Conclusion and discussion- 72 - 72 -

CGER’S SUPERCOMPUTER MONOGRAPH REPORT Vol.27
CGER-I153-2021, CGER/NIES

Acknowledgements
The numerical integrations were performed using the supercomputer (NEC SX series) of
the Center for Global Environmental Research, National Institute for Environmental Studies,and the computational resources of RIKEN Center for Computational Science. The softwareand local computation/information environments were constructed by using the resources of
GFD-DENNOU CLUB (URL; http://www.gfd-dennou.org). The source codes of theatmospheric general circulation model and the energy balance model are available at
http://doi.org/10.5281/zenodo.3514110.
This study was supported by MEXT KAKENHI Grant Number JP23103003 of the Ministryof Education, Culture, Sports, Science and Technology, Japan JSPS KAKENHI Grant Numbers
JP15740286, JP20540223, JP25400219, JP19H01947, the Astrobiology Center Program of the
National Institute of Natural Sciences (NINS) (Grant Number AB311025), global COE
program G11 ''Foundation of International Center for Planetary Science'' of the Japan Society
for the Promotion of Science.

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Contact person
Masaki Ishiwatari
Graduate School of Science, Hokkaido University
Kita 8, Nishi 5, Kita-ku, Sapporo, Hokkaido, 060-0808 Japan
Phone: +81-11-706-3564, E-mail: momoko@gfd-dennou.org
https://www.gfd-dennou.org/index.html.en- 75 - 75 -

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Numerical studies on the variety of climates of exoplanets
using idealistic configurations

Masaki Ishiwatari, Kensuke Nakajima, Shin-ichi Takehiro,
Yuta Kawai, Yoshiyuki O. Takahashi, George L. Hashimoto,
Youhei Sasaki and Yoshi-Yuki Hayashi

Center for Global Environmental Research

CGER-I153-2021

National Institute for Environmental Studies, Japan