Noda et al.
Progress in Earth and Planetary Science(2023) 10:48
https://doi.org/10.1186/s40645-023-00583-x

Progress in Earth andPlanetary Science

Open Access

REVIEW

Recent global nonhydrostatic
modeling approach without using
a cumulus parameterization to understandthe mechanisms underlying cloud changes due
to global warming
Akira T. Noda1* , Tomoki Ohno1,2, Chihiro Kodama1, Ying‑Wen Chen2,3, Naomi Kuba2, Tatsuya Seiki1,
Yohei Yamada1 and Masaki Satoh1,2

Abstract
Clouds are the primary source of uncertainty in the prediction of climate change. To reduce the uncertainty
of cloud simulations and overcome this difficulty in prediction, many climate modeling centers are now developing
a new type of climate model, the global nonhydrostatic atmospheric model, which reduces the uncertainty aris‑
ing from a cumulus parameterization by computing clouds explicitly using a cloud microphysics scheme. Amongthe global nonhydrostatic atmospheric models used in recent intercomparison studies, NICAM aims to projectclimate change by improving our understanding of cloud changes due to warming and related physical processes.
NICAM is the first global nonhydrostatic model and was developed by our research team. This review summarizes
the outcomes of a recent major five-year research program in Japan for studying climate using NICAM, as well as pro‑viding an overview of current issues regarding the use of global kilometer-scale simulations in high-resolution climate
modeling.
Keywords Clouds, Global nonhydrostatic model, Global warming, High-resolution climate simulation, Model
improvement
1 Introduction
Clouds play an important role in the change in earth’s
surface temperature due to global warming; however,the large uncertainty in the projection of cloud changes*Correspondence:
Akira T. Noda
a_noda@jamstec.go.jp
1
Research Center for Environmental Modeling and Application, Japan
Agency for Marine-Earth Science and Technology, 3173‑25 Kanazawa,
Yokohama, Kanagawa 236‑0001, Japan
2
Present Address: Atmosphere and Ocean Research Institute, The
University of Tokyo, 5‑1‑5 Kashiwanoha, Kashiwa, Chiba 277‑8564, Japan
3
Present Address: AP Communications, 2‑9‑12 Kajicho, Chiyoda, Tokyo
101‑0044, Japan

makes it difficult to better predict climate change. The
Coupled Model Intercomparison Project (CMIP) phase 6
data, the latest dataset of climate change simulations produced by general circulation models (GCMs) from world
climate modeling centers, has updated and improved
our understanding of cloud changes and their underlying mechanisms (Zelinka et al. 2020, 2022). In the CMIP6
dataset, climate sensitivity is the highest ever projected.
Climate scientists have attempted to reduce the wide
uncertainty in climate sensitivity in GCM datasets;
however, the CMIP6 dataset has a larger range of climate sensitivity than past evaluations (Meehl et al. 2020;
Zelinka et al. 2020). In particular, 10 of the GCMs usedin CMIP6 show climate sensitivity exceeding 4.5 K. The© The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/.

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

high climate sensitivity is attributed mainly to a larger
positive feedback due to a reduced cloud albedo in middle and high latitudes (Zelinka et al. 2020), indicating theimportance of clouds to climate. In fact, the CMIP6 dataset shows that cloud feedback is the biggest cause of thelarge uncertainty in climate sensitivity.
To reduce the uncertainty in cloud feedback, Sherwood
et al. (2020) proposed an alternative evaluation methodthat takes into account past observational results, called
the expert assessment. The latest results from the expert
assessment show larger uncertainty in feedback causedby high clouds, because most GCMs fail to simulate theinterannual variation in tropical clouds and associatedupward radiation (Mauritsen and Stevens 2015; Williams
and Pierrehumbert 2017; Zelinka et al. 2022). Zelinka
et al. (2020) show that the large cloud feedback comes
not from a single anomalously large component but froma systematic biased high. These findings suggest a needfor efforts to improve the overall performance of cloud
simulations.
Large uncertainty in the projection of clouds arises
mainly from the fact that most GCMs simulate deep convection using a cumulus parameterization, as they cannot explicitly compute deep convection. It is difficult tomodel cloud processes sufficiently and to adequately
obtain the relevant physical parameters. To improve
cloud projections, several climate modeling centers havelaunched large inter-organizational or international
research projects to develop global nonhydrostatic modeling with kilometer-grid spacing (e.g., Slingo et al. 2022;
Mauritsen et al. 2022). In Japan, the world’s first global
nonhydrostatic model, Nonhydrostatic ICosahedral
Atmospheric Model (NICAM), was developed in theearly 2000s to improve a representation of clouds in a
GCM (Satoh et al. 2014). Since then, NICAM has beenused in several large Japanese climate research projects:
the Innovative Program of Climate Change Projection forthe 21st Century, or KAKUSHIN program in Japanese,from 2007 to 2012; the Program for Risk Information on
Climate Change, or SOUSEI in Japanese, from 2012 to2017; and the Integrated Research Program for Advancing Climate Models, or TOUGOU in Japanese, from 2017
to 2022.
A consistent result of those research projects is theincrease in a coverage of high clouds and decrease in ice
water path in the tropical atmosphere (Iga et al. 2007;
Satoh et al. 2012; Noda et al. 2012). Recent studies also
show that a larger number of optically thin and smallsize clouds contribute to the increase in high clouds in a
warmer atmosphere (Noda et al. 2016; Chen et al. 2016;
Satoh et al. 2018). However, the underlying mechanisms
are not clear. Bretherton et al. (2005) emphasized the roleof aggregation in deep convection due to warming.

Page 2 of 25

For a deeper understanding of cloud changes due towarming, we conducted not only Atmospheric Model
Intercomparison Project (AMIP)-type (Webb et al. 2017)
simulations that consider land–ocean distributions andtopography, but also idealized aqua-planet-type simulations, so-called radiative convective equilibrium (RCE)experiments. Such simpler planet conditions allow us
to systematically examine the responses of physicalparameters to cloud changes in order to study how theroles of physical processes, including cloud microphysics processes and subgrid-scale (SGS) turbulent mixing
processes, in cloud formation would change in a warmer
atmosphere.
In the TOUGOU program, we improved our understanding of cloud changes due to warming using NICAM
and improved how physical processes are modeled in
NICAM, including low-level mixed-phase clouds and
SGS turbulent mixing. The results of this program are
relevant to recent research activities developing highresolution GCMs (Stevens et al. 2019; Slingo et al. 2022),
research into cloud changes due to warming.
The purpose of this review is to present the findingsof the TOUGOU program and to discuss related issues.
The review is organized as follows. Section 2 reviews
research activities based on the results of NICAM thatwas conducted in the TOUGOU program; in particular,
Sect. 2.1 outlines findings regarding changes in clouds
in response to global warming, and Sect. 2.2 describes
notable improvements in physical processes. Section 3
documents the future direction of cloud studies using ahigh-resolution GCM, current related research activities,
and future issues of high-resolution numerical studies.
The conclusion is provided in Sect. 4.

2 Review
2.1 Projection of cloud changes due to warming
2.1.1 Convective aggregation

To evaluate the increase in earth’s temperature, it isimportant to understand how anvil clouds respond to
warming: the fractional coverage of clear-sky regions
increases as tropical deep convection becomes moreaggregated. In such an atmospheric state, the earth canrelease a larger amount of heat from the atmosphere
into space without being shaded by anvil clouds, andvice versa (Fig. 1). To gain knowledge of potential futurechanges in the aggregation of tropical deep convection,
we analyzed 14 km mesh NICAM simulation data forboth present and future climate, assuming a world after
a century (Kodama et al. 2015) to investigate changes in
the fractional coverage of downdraft regions, which isoften used as an index representing the degree of aggregation of deep convection (Coppin and Bony 2015).

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Page 3 of 25

Fig. 1 Schematic of the influence of convective aggregation on outgoing longwave radiation in cases where convection becomes (left) moreaggregated and (right) less aggregated. Wavy upward arrows indicate longwave radiation. Longwave radiations with thick arrows in darker color
and thin arrows in lighter color show those emitted from the earth’s surface and from high clouds, respectively

We first divide the tropics into 10° × 10° subdomains
and compute a mean of vertical velocity at an altitudeof 5 km, < w >, over each subdomain. Then, the modified subsidence fraction, SF’, is defined as the fractional
coverage of negative w′, where w′ = w− < w > in each
10° × 10° subdomain to exclude contributions of largescale circulations. Smaller SF’ values correspond to thestate that convection develops in narrower regions (i.e.,
convection is more aggregated). Figure 2 shows tropical distributions of < w > and SF’ and their changes due
to warming. The distribution of SF’ corresponds wellwith < w > in both the present and future climate. The
two regions with the greatest difference in < w > between
the present and warmer conditions are the Indian Ocean(negative change) and Central Pacific (positive change) in
the tropics, showing a weakened Walker circulation in a
warmer world. The difference in SF’ is mostly negative,
except for some regions such as the Central Pacific.
Furthermore, we focus on the relationshipbetween < w > and SF’ in Fig. 3. The two values are correlated with each other, and they have the same correlation
coefficient of 0.88, even in the different climate states;
this means that the relationship between the intensityof large-scale circulations and convective aggregation isquite similar in the different climate states. In a warmer
climate, the degree of convective aggregation becomes
weaker and corresponds to reduced large-scale circulations. This result is consistent with past studies based on

Fig. 2 <w > averaged in 10° grid boxes in a present (CTL) and b global warming (GW) simulations, along with their difference (i.e., (a) − (b)). d–f are
the same as a, b and c, respectively, but for SF’. From Noda et al. (2019)Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Page 4 of 25

Fig. 3 The relationship between < w > and SF’ a for present (CTL; red dots) and global warming (GW; black dots) simulations, and b their difference(i.e., red minus black). The correlation coefficients of < w > and SF’ are shown above the panels. From Noda et al. (2019)

NICAM simulation data that showed larger numbers ofsmaller-scale clouds in a warmer world (Noda et al. 2014,2016). It also suggests that high clouds that originate
from deep convection cover larger parts of the tropicalatmosphere because they develop to be more scattered(Fig. 1).
2.1.2 Response of ice hydrometeors to surface warming

We also examined how cloud condensates respond tochanges in sea surface temperature (SST) using 14 km
mesh NICAM (Kodama et al. 2015), focusing on thelink between cloud and ice hydrometeors, such as cloud
ice, snow and graupel, which are not ordinarily resolvedin conventional GGMs. The vertical distribution of thetropical mean cloud fraction is plotted against tropicalmean SST (regression) in Fig. 4a, for both the present andwarming climate in AMIP simulations with NICAM and
GCM-oriented Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) Cloud Product. For the present climate, the cloud fraction and SST
have a positive (negative) relationship at altitudes above(below) 14–16 km. This behavior is also found in observations (Zelinka and Hartmann 2011; Chen et al. 2022),
although the relationship is stronger in NICAM simulations than in observations. For the warming climate, therelationship between the vertical profile of the tropical mean cloud fraction and the SST is similar to that in
the present climate, but with an upward shift: the peakof the positive relationship appears at an altitude around18.5 km under warmer conditions. This upwardly shifted
profile corresponds to the increase in height of highclouds in the warming climate. Since the high cloud isformed by ice hydrometeors, such as cloud ice, snow andgraupel, the distribution of ice water content contributedby each ice hydrometeor in relation to SST is also illustrated in Fig. 4b. For the present climate, the vertical profiles of cloud ice and snow are consistent with the cloud
fraction shown in Fig. 4a, although the peak of the positive regression is lower than that for the cloud fraction. In
contrast, the contribution of graupel dominates mainly inthe lower part of the high cloud region and does not havea large influence on the distribution of the cloud fraction.
In the warming climate, the vertical profiles of ice watercontent contributed by cloud ice, snow, and graupel shift
upward. The amplitude of the annual variation in the SST
has a similar scale in the present and warming climates,
while convective activities become stronger in the Central/Eastern Pacific and the cloud fraction doubles in thewarming climate (data not shown). The fact that the variation in the cloud fraction in the warming climate is double that in the present climate may be strongly related tothe difference in convection activities (Chen et al. 2022).
2.1.3 Changes in the responses of cloud microphysics
processes based on radiative convective equilibrium
experiments

One of the advantages of using global nonhydrostatic
models for climate projection science is that they explicitly calculate processes in cloud layers and can relate
cloud feedbacks to changes in the processes associatedwith global warming. Here, we show how the processes
controlling high clouds change with global warming andhow these changes relate to changes in the high-cloud
coverage, focusing on the cloud microphysics. In order
to simplify the problem, high clouds and processes wereanalyzed using RCE simulations. The RCE simulations

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Page 5 of 25

Fig. 4 a Vertical distribution of cloud fraction (January 1989–December 2008) regressed onto the SST for a NICAM AMIP-type experiment
under present (aqua) and warming (pink) conditions. b Vertical distribution of ice hydrometeors regressed onto the SST in a NICAM AMIP-type
experiment, where yellow, green, and blue denote ice water content from cloud ice, snow, and graupel, respectively. In b solid and dashed lines
denote present and warming conditions, respectively. Error bars show the standard deviation in the tropical region (30° S–30° N) for each variable.
From Chen et al. 2022, © American Meteorological Society. Used with permission

were conducted with fixed SST, no diurnal cycle ofradiation, and no rotation, using an earth-size sphericalcomputational domain. The qualitative similarity of highcloud cover response to SST changes in RCE and in more
realistic simulations using NICAM have been examined
by Ohno and Satoh (2018) and Ohno et al. (2019, 2020,2021).
First, we examined the dominant cloud microphysicalprocesses for high clouds. Figure 5 shows domain-averaged vertical profiles of the tendencies of cloud ice due tocloud microphysical processes at the equilibrium states at
an SST of 300 K and 304 K. It is evident that the tendencies of cloud ice were dominated by the sedimentation,diffusional growth, sublimation and collection processes
near the cloud top layers (~ 220 K). The sedimentationand collection rates depend on the terminal velocity ofice particles (Pruppacher and Klett 2010). The terminal
velocity of particles generally increases with the decreasein pressure due to the reduction of the aerodynamic

effects (e.g., Heymsfield 2007), which suggests that the
sedimentation and collection are enhanced at lower pressures. The deposition and sublimation rates are proportional to the diffusivity of water vapor in air (Pruppacher
and Klett 2010), which decreases with an increase in airpressure (Montgomery 1947; Hall and Pruppacher 1976).
These facts indicate that the reduction in air pressurein high-cloud layers due to the elevation of high clouds
associated with global warming enhances the dominant
cloud microphysical processes for high clouds. This canlead to the shortening of the lifetime of high clouds andthe reduction of high-cloud cover in warmer climates.
The effects of pressure dependencies of these processeson the high-cloud cover and its response to changes in
SST were examined using sensitivity simulations. We
conducted simulations using a value of 440 hPa as thelower pressure limit for evaluations of the terminal velocity of ice particles (VTp440) and the water vapor diffusivity in air (KVp440). The value of 440 hPa was chosen

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Page 6 of 25

Fig. 5 Domain-averaged vertical profiles of a the net, b positive, and c negative tendencies of ice clouds due to cloud microphysical processes
at equilibrium states in radiative-convective equilibrium simulations with a SST of 300 or 304 K. From Ohno et al. (2021), © The American
Geophysical Union. Used with permission

based on the upper limit of the cloud-top pressure as per
the International Satellite Cloud Climatology Project definition of clouds. Figure 6a and b shows the high-cloud
cover and its response to changes in the SST in the control and sensitivity simulations. The high-cloud covers
also increase in the sensitivity experiments. High-cloud
cover is reduced by suppressing the pressure dependencies of the terminal velocity of ice particles and the water
vapor diffusivity in air (Fig. 6c). The estimated effects ofthe pressure dependencies of the terminal velocity of ice
particles and of the water vapor diffusivity in air on thehigh-cloud response to SST change were both negative(Fig. 6d). These results suggest that the reduction in thetime scales of the dominant processes due to the upward
shift of high clouds in warmer climates reduces highcloud cover (Fig. 7). Note that Fig. 6d also shows complicated responses in different optical thickness clouds, e.g.,
the result of VTp400 shows a remarkable decrease of thinclouds, and small decrease and increase of medium andthick clouds, respectively, while that of KVp400 indicatesa small increase of thin clouds, and remarkable increasesof medium and thick clouds. Further research is needed
to clarify the reason.
2.1.4 Projection of changes of tropical cyclones

It is also important to evaluate how tropical cyclones(TCs) change in a future climate, as they are major meteorological phenomena causing severe damage in a largepart of the world. In order to deepen our understandingof the response of TCs to global warming, we investigatedfuture changes in TC structure and TC seeds (Yamada
et al. 2017, 2021). The projected change in TC frequency
in a future climate differs among different models (Knutson et al. 2020). Some studies have noted the response of
TC seeds (incipient vortices of TCs) to global warming
and the relationship of this response to the frequency ofTC genesis (Vecchi et al. 2019; Hsieh et al. 2020; Lee et al.
2020; Sugi et al. 2020). Following Vecchi et al. (2019),
Yamada et al. (2021) used the outputs of six models in
CMIP6 HighResMIP (Haarsma et al. 2016; Roberts et al.

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Page 7 of 25

Fig. 6 a Domain-averaged high-cloud cover and b its response to a SST change in control simulations (CTRL) and simulations with a lower limitof pressure for the evaluation of the terminal velocity of ice particles (VTp440) and diffusivity of water vapour in air (KVp440). Differences in chigh-cloud cover and d the responses between the control (CTRL) and sensitivity (SENS) simulations. From Ohno et al. (2021)

Fig. 7 Conceptual summary of the effects of a reduction in pressurein high-cloud layers due to the upward shift associated with global
warming on high clouds through the cloud microphysical processes.
From Ohno et al. (2021)

2020a, 2020b) to decompose tropical cyclogenesis into
the contributions of TC seeds and survival rate, which is
the rate of TC seeds developing into TCs. They showedthat tropical cyclogenesis frequency decreased significantly from 1990 to 2049 in the multi-model ensemble,
which is attributed to a decrease in the number of TC

seeds. However, the main contributor varied between
models and their horizontal resolutions. This indicatesthat decomposing tropical cyclogenesis into TC seed andsurvival rate likely addresses the cause of the uncertainty
in the projected frequencies of tropical cyclogenesis inprevious studies.
TCs cause severe disasters, the magnitude of which ismodulated by TC intensity, path and size. How these features will respond to global warming is not fully understood or whether (Knutson et al. 2020). Although GCMs
are a useful tool for assessing future changes in TC activity, a GCM with a lower resolution tends to produce
TCs with a spatial scale larger than that of observed TCs(Camargo et al. 2005). Due to improvements in computing power and modeling, we were able to run a climate
simulation with a finer horizontal grid spacing of 14 km(Kodama et al. 2015). While the 14 km mesh is not likely
to completely reproduce the finer structures of TCs, it
did reproduce broad structures like the primary and secondary circulations as well as the warm core (Yamada
et al. 2017). As horizontal scales of TCs differ from TC
to TC (e.g., Wu et al. 2015), Yamada et al. (2017) evaluated the horizontal scale of TCs as a function of their
lifetime maximum intensities. The result indicated thatthe radial-averaged tangential wind of TCs with a central

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

pressure less than 980 hPa will be enhanced outside theeye wall cloud under warmer climate conditions, even
if their minimum central pressures are in the same category. This enhancement possibly expands the horizontal scale of TCs to a value such as the radius of gale force
wind under warmer climate conditions.
A future change in the spatial distribution of mean TC
size is also important in projections of socio-economic
damage. We regarded the TC size as a radius of 8 m ­s−1
wind (R08), as per Schenkel et al. (2022). R08 was calculated from outputs of NICAM AMIP-type simulations(Kodama et al. 2015; Satoh et al. 2015; Yamada et al.
2017) and was defined as the outermost radius exceeding 8 m ­s−1 in the radial profile of azimuthal-averaged
tangential wind speed at a height of 10 m. The simulation for 1979–2008 was regarded as the control simulation, and the simulation for 2075–2104 was regarded as
the global warming simulation. Figure 8 shows the spatial

Page 8 of 25

distributions of mean R08 and its future change. R08 varied by region and increased with latitude, which is consistent with previous studies (e.g., Merrill 1984; Chavas
and Emanuel 2010; Schenkel et al. 2022). The dependence
on latitude differed between the northern and southernhemispheres (Fig. 8d). Zonal means of R08 increased
between 10° S and 20° S in the southern hemisphere thanin the northern hemisphere due to warming. In terms of
the future change, although the pattern of change wascomplicated on the global ocean area, R08 became larger
over the Arabian Sea, the tropical western North Pacific,
the east coast region of the USA, and the north coast ofAustralia (Fig. 8a–c).
2.1.5 Extratropical cyclones in a warmer climate

Extratropical cyclones play a key role in day-to-day
weather at midlatitudes. Their large-scale dynamical features may be represented satisfactorily by

Fig. 8 Horizontal distribution of the mean 8 m ­s−1 radius (R08) on a 5º × 5º grid box for a the control experiment (CTL) and b the global warming
experiment (GW), and c the difference between them (GW minus CTL). Panel d indicates the zonal mean of R08 in CTL (solid line) and GW (dashedline) for each ocean basin: the North Atlantic (70ºW–20ºW), the eastern North Pacific (180º–120ºW), the western North Pacific (140ºE–180º),
the South Pacific (160ºW–120ºE), and the South Indian Ocean (50ºE–110ºE)

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

coarse-resolution GCMs. However, extratropical cyclones
consist of fine-scale dynamical and microphysical features such as cold and warm fronts and cloud precipitation systems, and a much higher resolution model could
better reproduce the precipitation and intense wind associated with such features. Catto et al. (2019) explainedthat projected future changes in the precipitation area,
fronts, and wind are highly uncertain and suggested theneed for higher-resolution models. Kodama et al. (2019)(hereafter, K19) investigated the response of extratropical
cyclones to global warming using 14 km mesh NICAM.
In this review, we perform a preliminary analysis of HighResMIP NICAM data using a similar approach as K19
and show that cyclone intensity and precipitation in a
future climate depend on the model resolution.
K19 showed that the change in intensity of oceanic
extratropical cyclones (those staying over the ocean for
more than half of their lifetime) due to warming is notevident. This result is also confirmed in this study using
14–56 km mesh NICAM (not shown). Close inspection reveals that the number of moderately intense
extratropical cyclones (e.g., the wind speed between 30

Page 9 of 25

and 50 m ­s−1 at the 850 hPa level) decreases with timein the southern hemisphere (Fig. 9b–d). Note that theextratropical cyclones with stronger wind occur more
frequently as horizontal resolution increases in both
southern hemisphere (Fig. 9a) and the northern hemisphere (not shown), implying the need for 14 km (andmaybe even finer) mesh models to assess the extreme
wind speed, such as higher than 50 m ­s−1, associated withextratropical cyclones.
Figure 10 shows changes in precipitation around thecenter of the oceanic extratropical cyclones due to global
warming. Precipitation increases mainly at the poleward
side of the direction of cyclone movement; this increaseis larger around the intense extratropical cyclones thanaround all the extratropical cyclones. These preliminary
results, consistent with those of K19, do not depend on
the horizontal resolution of the model. Quantitatively,
the simulated precipitation increases with the model resolution, and this trend is more pronounced when averaged over only the intense extratropical cyclones. Such adependence of precipitation change on resolution seems
to correspond to the change in surface air temperature

Fig. 9 Monthly frequency of all the simulated oceanic extratropical cyclones in the northern hemisphere binned by lifetime‐maximum 850 hPa
wind speed (5 m ­s−1 bin size). a Results for 1951–1960 (past) simulated by the 56 km (blue), 28 km (green), and 14 km (red) mesh model. b–d
Changes in 2001–2010 (present-day; green line) and 2041–2050 (future; red line) with reference to the past. The mesh sizes of the model 56 km (b),28 km (c), and 14 km (d), respectively. The gray shadings in (b)–(d) show the results for the past divided by 10

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Page 10 of 25

Fig. 10 Composite of future minus past precipitation amount averaged over all the oceanic extratropical cyclones (top row) and the intense
oceanic extratropical cyclones (bottom row) for (left to right): 56 km, 28 km, and 14 km mesh models. Gray circles indicate the distancefrom the center of the extratropical cyclone in intervals of 500 km(not shown), and further in-depth analysis is needed tounderstand the cause of such a dependency.
2.1.6 Evaluation of effective climate sensitivity

In the present project, we also attempted to evaluate
effective climate sensitivity (ECS) using data from global
nonhydrostatic climate simulations, for the first time inclimate research. According to Shiogama et al. (2014), we
can calculate ECS as,

ECS = −RF/FB,(1)

respectively. Each simulation was conducted for 5 years.
Figure 11 shows change over time in the ECS calculated
from the data for year one to year five. Over that time,
ECS gradually becomes closer to 3.6 ~ 3.7°, values thatare in the uncertainty range of the CMIP5 model results(Andrews et al. 2015). Those conventional GCMs compute deep convection based on a cumulus parameterization, while NICAM does so explicitly based on a cloud
microphysics scheme. It is notable that the results of two
such different types of GCMs show similar ECS values.

where

RF =

R(4 × CO2 ) − R(CTL)
2

(2)

and
FB = ((R(SST + 4K ) − R(CTL))/(T (SST + 4K ) − T (CTL)).

(3)
R and T denote the global means of radiation at the topof the atmosphere and of the earth’s surface temperature, respectively. CTL, 4 × ­CO2, and SST + 4 K refer toexperiments on the present climate, quadruple atmospheric ­CO2 concentration, and the increase in SST at 4 K
homogeneously over the globe in the present climate,Fig. 11 Effective climate sensitivity (ECS) evaluated from five-year
experiments of CTL, 4 × CO2, and SST + 4 K using data from the firstyear, first two years, first three years, first four years, and all five years.
From Noda et al. (2019)Noda et al. Progress in Earth and Planetary Science(2023) 10:48

2.2 Model improvement
2.2.1 Low‑level mixed‑phase clouds

This subsection describes the improvement in supercooled liquid water simulations of low-level mixed-phase
clouds over the Southern Ocean. The NICAM singlemoment bulk scheme with six water categories (NSW6)(Roh and Satoh 2014; Roh et al. 2017), which was used
for the CMIP6 project (Kodama et al. 2021), was revised
in reference to the NICAM double-moment bulk schemewith six water categories (NDW6) (Seiki and Nakajima
2014; Seiki et al. 2014, 2015) and satellite observations.
For details of the cloud microphysics schemes, refer tothe original publications or a review of the cloud microphysics schemes used for GCMs (Seiki et al. 2022).
The shortwave cloud radiative forcing biases over theSouthern Ocean in the GCMs had been a longstanding
issue in the past few decades (e.g., Bodas-Salcedo et al.
2012; Williams et al. 2013). In addition, high-resolution
weather forecasting models with more detailed cloud
microphysics schemes had also suffered from the underestimation biases in low-level mixed-phase clouds (e.g.,
Field et al. 2014). Analyses of the three-dimensional liquid-ice partitioning using CALIPSO indicated that the
shortwave biases originate mainly from the underestimation of supercooled liquid water in low-level clouds
over the polar regions (e.g., Forbes and Ahlgrimm 2014;
Tan and Storelvmo 2016). Recently, GCM communities have revealed that an increase in supercooled liquidwater as a result of modifying liquid-ice partitioning efficiently increases the lifetime of low-level clouds over theSouthern Ocean (Forbes and Ahlgrimm 2014; Tan andStorelvmo 2016; Kawai et al. 2019). These studies indicatethat the ice growth speed in low-level clouds over theSouthern Ocean was overestimated in cloud microphysics schemes used for conventional GCMs.
Roh et al. (2020) found that low-level clouds derived
from the NICAM with the NDW6 scheme effectively
represented the characteristics of low-level mixedphase clouds from CALIPSO satellite observations,whereas those from the NICAM with NSW6 remained
biased. Seiki and Roh (2020) confirmed that the biases
clearly appeared within 10 min of the numerical integration, as was shown in past studies. Therefore, Seikiand Roh (2020) demonstrated that the longstanding
biases in ice cloud microphysics schemes can be solved
using a single-column model with no physical processes
other than cloud microphysics and no external forcing. As it takes only one second to integrate six hours
with the single-column model, it was easy to comprehensively test sensitivity experiments. Thanks to thesingle-column model, all the production and reduction
terms in the NSW6 scheme were compared to those in
the NDW6 scheme. The initial condition was prepared

Page 11 of 25

by simplifying the vertical profiles of typical low-level
mixed-phase clouds over the Southern Ocean from the
NICAM global simulations with the NDW6 scheme(see Seiki and Roh (2020) for detail).
The single-column model simulation with the NSW6
scheme successfully reproduced the rapid reduction ofa liquid cloud layer under the supercooled condition,
whereas the simulation with the NDW6 scheme sustained the liquid cloud layer (Fig. 12a-j). The budget
analyses indicated that the Bergeron-Findeisen processexcessively worked in the NSW6 scheme, as was shownin previous studies (e.g., Tan and Storelvmo 2016;
Kawai et al. 2019). In addition, the subsequent occurrence of riming of cloud water by snow and graupel
rapidly consumed supercooled liquid water. To alleviate
the bias in the NSW6, Seiki and Roh (2020) revised four
processes: the initiation of cloud ice was suppressed bychanging the ice nucleation scheme; the initiation ofgraupel through the freezing of rain was suppressed bychanging the auto-conversion and accretion schemes
for cloud water; the initiation of vapor deposition was
delayed with the mixing-ratio threshold of snow andgraupel; and the initiation of riming was delayed withthe cut-off diameter of snow and graupel. Finally, thelifetime of the low-level mixed-phase clouds simulatedusing the revised NSW6 scheme was comparable tothat obtained using the NDW6 scheme (Fig. 12a and k).
The strategy behind this revision was to suppress thegrowth of cloud ice, snow, and graupel in the cloudlayer under supercooled conditions. This approach
can be applied to other atmospheric models that use
single-moment bulk cloud microphysics schemes. In
fact, the Unified Model and the numerical weather
prediction model HARMONIE-AROME applied similar approaches to improve their cloud microphysics
schemes (Furtado and Field 2017; Engdahl et al. 2020).
By contrast, a fundamental issue remains in NSW6, asin most of the single-moment schemes currently available: the diagnosis of number concentration can beaffected by the cloud system. We solve this issue by
using the double-moment approach (which predicts thenumber concentration) only for cloud ice categories.
We also applied this new microphysics scheme to
the global domain. We evaluated the new microphysics scheme using 14 km mesh NICAM temporally integrated for one year. We first compare the difference inthe fractional mixing ratio of water clouds to the sumof water and ice clouds, F (= qc/(qc + qi)), as a function of air temperature in Fig. 13. The data were computed as follows: first, we smoothed the 14 km meshdata down to 2.5° mesh data, and then averaged them
temporally to produce monthly data. Finally, we determined the mixing ratios of cloud water and cloud ice

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Page 12 of 25

Fig. 12 Time series of mixing ratios of cloud water (qc), rain (qr), cloud ice (qi), snow (qs), and graupel (qg) from the single-column simulation
with the NDW6 scheme (a–e), the original (OLD) NSW6 scheme (f–j), and the revised (NEW) NSW6 scheme (k–o). The freezing level (z ~ 220 m)
is indicated by the solid black line. The units are g ­kg–1. From Seiki and Roh (2020), © American Meteorological Society. Used with permission

Fig. 13 Fractional ratio of water clouds to the sum of water and ice
clouds as a function of air temperature using the old (black line)
and new (red line) microphysics schemes. Grey shading with thinouter lines denotes the first and third quartiles at the top and bottom,
respectively, and the thick lines show the second quartiles in a 2.5°
grid box in the same temperature bin. From Noda et al. (2019)

and the temperature at each 2.5° grid value to calculate
F(= qc/(qc + qi)).
The new scheme shows larger fractions of water clouds
at lower temperatures. In the old scheme, for example, the formation of major ice clouds occurs in a range
between − 19 and 0 °C. In the new scheme, however,water clouds develop by − 30 °C. The past observationshows the existence of liquid droplets at an air temperature near − 40 °C, so the result of the new scheme is closer
than that of the old scheme to observations. Figure 13
also shows a larger range of F than in the old scheme at
the same temperature, implying that more room in cloud
feedback associated with mixed-phase clouds is allowed
to occur by improving the processes underlying mixedphase clouds.
Next, we compare shortwave radiation at the top of
the atmosphere and the liquid water path in Figs. 14. The
new scheme improves not only clouds over the SouthernNoda et al. Progress in Earth and Planetary Science(2023) 10:48

Page 13 of 25

Fig. 14 Fields of shortwave radiation at the top of the atmosphere for a observation, and one-year means of results from experiments using b
the old scheme, and c the new scheme. d–f are the same as (a), (b), and (c), but for the liquid water path, respectively. Climatology of the CERES
data and that of the Observation data in (a) and (d) are Multisensor Advanced Climatology Mean Liquid Water Path (MAC-LWP) data are shownin (a) and (d), respectively. From Noda et al. (2021)

Ocean, but also over the tropics, and reduces the bias
in overestimating the reflection of incident solar radiation over the globe, as was found in the old scheme. The
values of the liquid water path increase almost over theentire globe and are closer to the observation, showingthat the improved simulation of optically thick water
clouds leads to a better simulation of shortwave radiation
at the top of the atmosphere. We also confirmed that negative biases in the shortwave radiative field, and relevant
positive biases in the shortwave cloud radiative effect, arealso reduced greatly throughout the year (Fig. 6 in Noda
et al. 2021).
2.2.2 Cirrus clouds

This subsection describes the improvement in cirrus
cloud modeling mainly through the revision of ice terminal velocity and collisional growth in the NDW6 scheme(Seiki and Ohno 2022). Cirrus clouds broadly extend over
the tropics (e.g., Sassen et al. 2008), and their longwave
radiative forcing dominates the earth’s energy budget,
even with their small optical thickness (e.g., Liou 1986).
The dominant cloud microphysical processes in tropicalcirrus clouds are ice nucleation, aggregation, vapor deposition/sublimation, and gravitational sedimentation (e.g.,
Seeley et al. 2019; Ohno et al. 2021). Double-momentbulk cloud microphysics schemes potentially capture
the rapid growth of ice particles by aggregation and thecorresponding increase in ice terminal velocity, which
depends mainly on the maximum dimension.

The present study focused on the uncertainties related
to the simplification of the ice terminal velocity formulation, because modification of this formulation results in astrong change in the global radiation budget (e.g., Mitchell et al. 2008; Hourdin et al. 2017). In general, the ice
terminal velocity υt in bulk cloud microphysics schemes
is approximated by a power law relationship to the maximum dimension D, as follows:υt = aυ Dbυ .

(4)Here, the coefficient aυ and exponent bυ are generally derived by fitting to observations (e.g., Locatelli andHobbs 1974; Heymsfield and Kajikawa 1987). Now, twoissues are involved with this formulation: aυ and bυ aregiven as a global constant; and aυ and bυ are derived by fitting in a narrow size range. Figure 15 shows the dependence of the ice terminal velocity υt on the maximum
dimension D based on the theoretical formulation (Böhm
1989; Mitchell 1996; Seiki and Ohno 2022). It is clear thatthe exponent varies by the size range: bυ approximates 2
at smaller sizes and approaches 0.5 at larger sizes. Therefore, use of a single pair of aυ and bυ results in systematic biases in cloud microphysical processes in global
simulations. The issues in gravitational sedimentation in
the NDW6 scheme were already dealt with by Seiki et al.
(2014) by using additional pairs of aυ and bυ for different
size ranges. However, the issues in collisional growth in
the NDW6 scheme have not yet been solved. Seifert et al.
(2014) showed that use of Eq. (4) causes non-negligible

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Fig. 15 Dependence of the terminal velocity υt (m ­s−1)
on the maximum dimension D (m). In the database compiled
by Mitchell (1996), cloud ice (blue) is assumed to form hexagonal
columns, snow (green) is assumed to comprise assemblages of planar
polycrystals in cirrus clouds, and graupel (red) is assumed to be lump
graupel. From Seiki and Ohno (2022), © American MeteorologicalSociety. Used with permission

errors in the curve of collisional growth. Therefore, Seiki
and Ohno (2022) revised how collisional growth is determined and then examined the impact of this revision on
the simulation of tropical cirrus clouds. Note that heterogeneous and homogeneous ice nucleation were also
revised in the new NDW6 scheme.
The collisional growth terms are evaluated by integrating the collection kernel, which consists of the productof the collisional cross-section and the difference in terminal velocity. However, it is difficult to evaluate the difference in terminal velocity in bulk cloud microphysics
schemes (e.g., Seifert et al. 2014; Karrer et al. 2021). As
a result, in the original NDW6 scheme, the collisionalcross-section and the difference in terminal velocity were
integrated separately. In addition, the power law relationship was used for the ice terminal velocities. In therevised scheme, we numerically integrated the collection
kernel with the Gauss‒Legendre quadrature. Thus, thedifference in terminal velocity can be directly integrated
with the theoretical formulation of ice terminal velocities.

Page 14 of 25

We found that the original scheme overestimatedaggregation between cloud ice to form snow (autoconversion of cloud ice) by approximately 300–400% at
sizes smaller than 20 μm (not shown). This error corresponds to the bias in the terminal velocity due to thepower law relationship (cf. Figure 15). Similarly, accretion of rain on graupel was overestimated in the original scheme (not shown). Therefore, the original scheme
causes severe errors in thin cirrus clouds and intense
rainfall systems.
The lifetime of tropical cirrus clouds was examined in reference to the CloudSat satellite observations (Fig. 16). Here, this study only analyzed cirrus
clouds over the ocean, since cirrus clouds over orographic features are strongly affected by atmosphericdisturbances (Seiki et al. 2019). With the new NDW6
scheme, aggregation of cloud ice and snow significantly decreases, particularly at altitudes above 8 km
(not shown). Correspondingly, the frequency of radar
echoes larger than − 20 dBZ near the tropopause (14–16 km) decreases in the global simulations with the new
NDW6 scheme (Fig. 16b–c). As a result, slowly growing
ice crystals as a result of weak collision and vapor deposition in the new NDW6 scheme maintain thin cirrus
clouds in the upper troposphere. This signal is represented as the distinct mode value of the radar echoesof –30 to –20 dBZ at altitudes above 12 km. In addition, increasing radar echoes toward the cirrus cloudbase (8–12 km) become more distinct when using
the new NDW6 scheme. All the revisions increase
the cirrus cloud fraction over the tropics (Fig. 16d),
and consequently, shortwave cloud radiative forcing
and longwave cloud radiative forcing over the tropics
improve by approximately 4.1 and 7.5 W ­m−2, respectively, compared to the Clouds and Earth’s RadiantEnergy System (CERES) satellite observations. Thesefindings indicate that the lifetime of cirrus clouds isreasonably represented by the revised NDW6 scheme.

Fig. 16 Diagram of the contoured frequency of the 94 GHz radar echo by altitude from a CloudSat satellite observations, b global simulations
using the original version of the NDW6 scheme, and c those using the revised version of the NDW6 scheme. The vertical profiles of the cirrus cloud
fraction are also indicated (d). From Seiki and Ohno (2022), © American Meteorological Society. Used with permission

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

2.2.3 Consideration of SGS ice condensation in a turbulent
closure scheme

Turbulent processes play important roles in the life cycleof various types of clouds (e.g., Squires 1958; Klaassen
and Clark 1985; Grabowski 1993, 2007; Grabowski and
Clark 1993; Gasparini et al. 2019); as such, the representation of moist processes in turbulent schemes is crucial
for their performance. In general, turbulent schemes
assume that the time scale of SGS cloud condensation
is sufficiently shorter than that of turbulent mixing, andthey employ saturation adjustment-type approaches(e.g., Olson et al. 2019). However, the time scale of ice
condensation is several orders of magnitude longer thanthat of liquid water, and the phase relaxation time forice clouds under typical conditions is several orders ofmagnitude longer than the time-step length commonlyused in the past relevant numerical studies (Heymsfieldand Miloshevich 1995; Khvorostyanov and Curry 2014;
Gryspeerdt et al. 2018). These studies speculate that theuse of a saturation adjustment-type approach for representing SGS ice clouds in turbulent schemes overestimates the effects of the phase change on the turbulent

Page 15 of 25

mixing. This background knowledge motivated us toreconsider the representation of ice phase clouds in a turbulent closure scheme and to evaluate the effects of thisscheme on the high-cloud cover in response to global
warming.
The effects of the saturation adjustment-type approachfor simulating SGS ice clouds in turbulent schemes onhigh clouds and their response to a warmer climate were
investigated by a sensitivity study based on RCE simulations (Ohno et al. 2020). Figure 17 shows the domainaveraged high-cloud cover at the equilibrium state in
the RCE simulations with and without an SGS condensation scheme for ice water condensate and with SSTs of
300 and 304 K. The suppression of SGS ice condensation
reduced the high-cloud cover and altered the sign of thecloud cover response to the SST change, results that are
similar to the effects of reducing the turbulent diffusivity
K by reducing the turbulent mixing length (Ohno et al.
2019).
Next, the effects of SGS ice clouds on K were investigated. Figure 18a and b shows binned vertical profiles ofK calculated with and without the SGS ice condensation

Fig. 17 Domain-averaged cloud cover for a total, b thin, c medium, and d thick high clouds for the simulations with and without an SGS
condensation scheme for ice water condensate (labeled as ICE and NOICE, respectively) using SSTs of 300 (black) and 304 (red) K. e Cloud coverresponse to increasing SST for the total (purple), thin (green), medium (blue), and thick (orange) high clouds. High clouds were defined basedon the International Satellite Cloud Climatology Project definition of cloud types (Rossow and Schiffer 1999). From Ohno et al. (2020), © The
Meteorological Society of Japan. Used with permission

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Page 16 of 25

Fig. 18 Binned vertical profiles of the turbulent diffusivity K (color and white lines) and the ice condensate (black lines) calculated a with and b
without the SGS ice condensation scheme in the turbulent closure scheme, sorted by the ice water path. K and ice water path were calculatedusing a snapshot dataset from the ICE simulation with an SST of 300 K. c and d are the same as (a) and (b), respectively, for the simulation
with an SST of 304 K. From Ohno et al. (2020)

scheme sorted by the ice water path, respectively. K and
ice water path were calculated using a snapshot dataset from the ICE simulation with an SST of 300 K. The
values of K were large at the convective core region andin the vicinity of the cloud top in both cases due to thefrequently occurring static instability (not shown). The
static instability was enhanced by the SGS ice condensation scheme. Consequently, the magnitude of K in
the upper troposphere was generally larger with the
SGS ice condensation scheme than without it. Similar
results can be seen with an SST of 304 K, as shown in
Fig. 18c and d. The impacts of suppressing the SGS ice
condensation scheme for the turbulence scheme on K
were consistent with those of reducing the turbulent
mixing length in the study of Ohno et al. (2019). These
results indicate that the application of the SGS ice condensation scheme for the turbulence scheme changedhigh cloud covers and their response to a change in SST
by altering the static stability in the cloud layers.

Since the phase relaxation time of ice clouds is much
longer than that of liquid clouds, the effect of the phasechange in ice clouds on the dynamical fields through thebuoyancy should be smaller than those of liquid phase
clouds. This suggests that the application of a saturation adjustment-type approach for representing SGS ice
clouds in the turbulent scheme overestimates the turbulent diffusivity and causes model biases in the high-cloudfields.
2.2.4 Impacts of ice hydrometeors on a radiative field

Optical characteristics differ depending on the types of
ice hydrometeors. However, most GCMs simplify thetreatment of those ice species, which often causes errors
in modeled radiative fields. It is also an interesting application of a high-resolution GCM to evaluate the extent
to which the simplified cloud modeling leads to model
biases, knowledge of which can hint at the source oferrors in recent GCM simulations. Here, we show how

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

the ice hydrometeors, such as cloud ice, snow and graupel, that are simulated in NICAM, may affect the simulated field of longwave radiation. We use 3-month-longsimulations during boreal summer from 1 June to 31
August 2004 with 14-km mesh NICAM using a doublemoment bulk cloud microphysics scheme (Seki and
Nakajima 2014). To estimate the radiative effect attributed to each ice hydrometeor, the radiation transfer
model MSTRNX (Sekiguchi and Nakajima 2008), whichis the same radiative code as implemented in NICAM,
is run offline. We designed four experiments, as follows:‘ctrl’ represents the longwave radiative effects attributed
to all ice hydrometeors (i.e., cloud ice, snow, and graupel); ‘no_s’ represents all ice hydrometeors except snow;‘no_gs’ represents all ice hydrometeors except snow andgraupel; and in ‘allice’, snow is replaced by cloud ice toestimate the maximum longwave cloud radiative forcing.
The effect on the outgoing longwave radiation (OLR)
for each experiment is plotted in Fig. 19a–c, and theeffect on the cloud optical depth (COD) is plotted inFig. 19d–f. COD is underestimated and OLR is overestimated in ‘no_s’ (Fig. 19a and d) and ‘no_sg’ (Fig. 19b
and e). This effect is prominent in the tropics and in thestorm track regions at mid-latitudes, where cloud ice
and snow are abundant. The positive bias in OLR due tothe removal of snow leads to an average bias of 1 W ­m–2

Page 17 of 25

and reaches a maximum bias of 2 W ­m−2 in the Indian
Ocean region (Fig. 19a). The effect on the OLR field
attributed to graupel is negligible, as seen by the effecton the OLR fields in ‘no_s’ and ‘no_sg’, although the effecton the COD field attributed to graupel is non-negligible(Fig. 19d and e). By contrast, OLR is underestimated over
the tropics and mid-latitudes when snow is replaced bycloud ice (Fig. 19c), due to the overestimation of COD(Fig. 19f ). The underestimation of OLR reaches − 0.4 W­m−2 over the Indian Ocean (–0.2 W m­ −2 on average overthe intertropical convergence zone). The horizontal distribution of these effects of snow on OLR is similar tothat estimated from CloudSat observations (Waliser et al.
2011) and GCMs (Li et al. 2016). However, the magnitude of the effect is about half that reported in previous
studies. This difference is due mainly to the vertical distribution of ice hydrometeors (Chen et al. 2018).
2.2.5 Improvement of bulk microphysical scheme by bin
schemeWe also improved the two-moment bulk microphysics
scheme based on a bin microphysics scheme to improve
the simulation of water clouds in NICAM. Kuba et al.
(2020) compared the two-moment bulk scheme (NDW6,
based on Seifert and Beheng (2006) and modified slightly
by Seiki and Nakajima (2014)) and the two-moment bin

Fig. 19 Difference in the OLR field between control (‘ctrl’) and a ‘no_s’, b ‘no_sg’, and c ‘allice’, and difference in the COD field between ‘ctrl’ and d‘no_s’, e ‘no_sg’, and f ‘allice’. From Chen et al. 2018, © The Meteorological Society of Japan. Used with permission

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Page 18 of 25

scheme (developed by Kuba and Fujiyoshi (2006) andmodified by Kuba and Murakami (2010)). Their aim
was to constrain the parameters in cloud bulk schemes
by using observational data from satellite remote sensing. They used a dynamic-kinematic model to avoid theinteractions between cloud microphysics processes anddynamics. Kuba et al. (2020) also used the Joint Simulator for Satellite Sensors (hereafter referred to as the
Joint-Simulator; Hashino et al. 2013; Satoh et al. 2016)
to calculate the horizontally averaged radar reflectivity Zm and the optical depth from the cloud top τd. They
studied the conversion processes from cloud droplets toraindrops in shallow cumulus clouds. In their study, they
conducted sensitivity experiments on vertical velocity,
the concentration of cloud condensate nuclei, and size
distribution parameters and studied the relationships
between τd and Zm.
In Kuba et al. (2020), the size distributions of cloud
droplets and raindrops for the bulk scheme are represented by generalized gamma distributions, as follows:fa (x) = αa xυa exp −a xµa ,(5)where a = c for cloud droplets, a = r for raindrops, and x
is the mass of a cloud droplet or a raindrop.
Figure 20 shows the relationship between the domainaveraged accumulated surface rainfall at 120 min andthe cloud droplet number concentration near the cloudbase at about 15 min using the bulk and bin schemes for
thin, medium-thickness, and thick clouds. For the bulk
scheme, the values of (vc, vr) in the generalized gamma
distributions were varied in Fig. 20 (a: (1, − 1/3), b:(− 1/3, − 1/3), c: (1, 1), d: (− 1/3, 1). The values of (1, − 1/3)
for (vc, vr) are based on Seifert and Beheng (2006) andSeiki and Nakajima (2014). The rainfall amount at
120 min was similar between the bulk and bin schemes
for the thick clouds (green circles in Fig. 20a − d) andthe smaller numbers of cloud droplets. Conversely, therainfall amount was smaller in the bulk scheme thanin the bin scheme for clouds with a large number ofcloud droplets, particularly for the thin clouds (shownas black circles whose cloud droplet number concentrations are 160 ­cm−3 and larger). In the case of (vc, vr)
values of (− 1/3, 1), the difference between the bulk andbin schemes is small (Fig. 20d). Decreasing the shapeparameter vc from 1 to − 1/3 leads to an increase in theauto-conversion rate, and an increase in νr from − 1/3
to 1 decreases the width of the raindrop size distribution (which means a decrease in the falling velocity ofraindrops). In the bulk scheme, a decrease in the falling
velocity of raindrops increases the falling time (whichmeans an increase in rain production).
Kuba et al. (2020) also compared bin and bulk schemeswith (vc, vr) of (1, − 1/3) and (− 1/3, 1) using the relationships between horizontally averaged radar reflectivity Zm
and optical depth from the cloud top τd. Figure 21 showsthat the optical thicknesses of droplets with a radiuslarger than 8 μm were similar to those of all dropletsin the case of the bin scheme (see Fig. 21a and d). Thismeans that almost all droplets simulated using the bin
scheme had a radius larger than 8 μm near the cloud top.
However, with the bulk scheme, the optical thicknessesof droplets with a radius larger than 8 μm were smaller

Fig. 20 Relationship between the domain-averaged accumulated surface rainfall at 120 min and the cloud droplet number concentrationnear the cloud base at about 15 min, for thin (black), medium-thickness (red) and thick (green) clouds. Closed and open circles show the resultsof the bin scheme and the bulk scheme, respectively, with (νc, νr) values of a (1, − 1/3), b (− 1/3, − 1/3), c (1, 1), and d (− 1/3, 1). From Kuba et al. (2020)

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Fig. 21 Relationships between horizontally averaged radarreflectivity (Zm) and optical depth from the cloud top (τd) for the caseof thin clouds with polluted cloud condensate nuclei. Results
are shown for a the bin scheme, b the bulk scheme with (νc,νr) = (1, − 1/3), c the bulk scheme with (νc, νr) = (− 1/3, 1). d–f are
the same as a–c, respectively, but excluding droplets with a radiusless than 8 μm from the calculation performed by the Joint Simulator.
The flow of time is drawn in black, red, green and blue. From Kuba
et al. (2020)

than those of all droplets (see Fig. 21b and e, c and f ).
The results of the bulk scheme using (vc, vr) of (–1/3, 1)
and excluding raindrops with a radius less than 8 μm
(Fig. 21f ) are most similar to those of the bin scheme(Fig. 21a and d). Above, we suggested a set of improved
parameters in a bulk microphysics scheme to evaluate thegrowth of cloud droplets to rain according to the degreeof atmospheric pollution. In future, the bulk scheme willneed to be improved for other meteorological conditions
using the method described in Kuba et al. (2020).
2.2.6 CMIP6 HighResMIP simulations

Before the TOUGOU program, NICAM simulation data
had been analyzed mostly by developers and users of the
NICAM code. Recent advances in computer technology
now allow us to perform much longer-term NICAM simulations. In this context, Haarsma et al. (2016) proposed
the HighResMIP to endorse model intercomparison projects in CMIP6, which we consider to be a good opportunity not only to contribute to the CMIP community but
also to try NICAM simulations at scales of more thanhalf a century.
Practical climate simulations using NICAM originatedfrom NICAM AMIP-type simulations (Kodama et al.
2015), in which NICAM.12 with a mesh size of 14 km

Page 19 of 25

was used. Here, NICAM adopts a release number (e.g.,“12”) based on the last 2 digits of the year when major
updates from the previous release version are completed. NICAM.12 successfully simulated a wide varietyof phenomena, particularly the distribution and seasonal
march of tropical cyclogenesis, and the simulation data
were intensively used for an analysis of tropical cyclones(Satoh et al. 2015; Yamada et al. 2017; Matsuoka et al.
2018; Sugi et al. 2020), among others. However, major
issues remained in the simulation of basic-state climatology such as surface air temperature, cloud, and precipitation, which motivated us to develop NICAM.16
and its CMIP6 version, NICAM.16-S (“-S” represents theuse of a single-moment cloud microphysics scheme), as
reported in Kodama et al. (2021). In summary, the updateof the single-moment bulk cloud microphysics scheme(Roh and Satoh 2014; Roh et al. 2017) affected the vertical distributions of snow and cloud ice, leading to better
simulations of the amount of high thin cloud. In addition, the improved treatment of natural and anthropogenic aerosols; updates to the land surface model, surface
albedo, and sea ice thickness; and the introduction of an
orographic gravity wave drag scheme together contributed to an improvement in the simulation of climatology.
NICAM.16-S was used to simulate timeframes of a century with 56 and 28 km mesh and a decade with 14 km
mesh to produce a dataset for CMIP6 HighResMIP. The
simulated year per day (SYPD) of NICAM.16-S on the
Earth Simulator 3 (NEC SX-ACE system) was 0.22–0.63
for 14–56 km mesh using 10–160 nodes and 40–640 MPI
processes (Table 7 in Kodama et al. 2021), and it often
took comparable time to wait for the job to start on the
Earth Simulator 3. The time needed to perform postprocessing—such as remapping and adding metadata tomeet the CMIP6 standard format—was comparable tothat required for the simulation itself. The total data sizeof the final product was 115 TB for the 11-year 14 km
mesh dataset and 261 TB for the 101-year 28 km meshdataset. The HighResMIP dataset is now widely used inclimate research (e.g., Roberts et al. 2020b; Yamada et al.
2021; Liang-Liang et al. 2022; Priestley and Catto 2022).

3 Future directions
Future changes in weather and climate extreme events ina changing climate with global warming are a great concern, and they are intensively assessed in Chapter 11 of
the Sixth Assessment Report of the Intergovernmental
Panel on Climate Change (IPCC 2021; Seneviratne et al.
2021). Among extreme events, the torrential rain andviolent wind associated with mesoscale convective systems or TCs are represented more accurately by high-resolution models. Global storm-resolving models, or global
kilometer-scale models, with a horizontal mesh size ofNoda et al. Progress in Earth and Planetary Science(2023) 10:48

O(km), are becoming popular. Their use for modeling
future changes in extreme events is prospective (Satohet al. 2019; Slingo et al. 2022). Studies of future changes
in TCs require global high-resolution simulations thatsimultaneously reproduce large-scale circulations andthe inner structure of TCs that consider the interactionof the atmosphere–ocean coupled system (Knutson et al.
2020). We studied future changes in TCs in Sect. 2.1.4,
in which the atmospheric 14-km mesh model was used.
Ideally, the simulations for the TC projection should bewith a global atmospheric-ocean coupled kilometer-scalemodel. In particular, to assess near-future changes in
TCs in a world with a 1.5 °C or 2.0 °C warming level, alarge number of decadal ensemble simulations with suchkilometer-scale-type models are eagerly awaited. A highresolution version of Database for Policy Decision-Making for Future Climate Change or d4PDF (Ishii and Mori
2020) is also in high demand for more accurately assessing projected changes in TCs. Such experiments using
global kilometer-scale models will allow us to project not
only TCs (Sect. 2.1.4) but also related processes of mesoscale convective systems, such as convective aggregation (Sect. 2.1.1) and upper clouds (Sect. 2.1.2).
Several scientific and technical challenges must be
overcome to establish NICAM as a kilometer-scale climate model. How such a model should be configured forclouds in kilometer-scale climate simulations remains
under debate. Although the kilometer-scale model
resolves deep convection, albeit partially, it is obviousthat its spatial resolution is completely insufficient for
representing shallow convection and boundary-layer
clouds. By and large, there are two possible approaches toachieve this: the explicit cloud microphysics (i.e., cloudresolving) approach, and the cloud parameterization (i.e.,
GCM) approach. In the former approach, vertical resolution and turbulent mixing may be key to dealing with theissue of lower-level clouds. For example, refining the vertical resolution only for a specific physics scheme (Yamaguchi et al. 2017) may be a promising approach. Flux
adjustment, albeit classical, may also be an option for
representing some scientific targets such as TCs. In thelatter approach, additional empirical schemes such as ashallow convection scheme may be introduced. Anotherpopular scheme is eddy diffusivity/mass flux or EDMF
parameterization (e.g., Suselj et al. 2022), in which eddy
diffusivity and mass flux formulations are used to represent downdraft and updraft regions, respectively. In bothcases, it is necessary to consider the applicability of theschemes to a kilometer-scale grid box and also to consider the relative role of and consistency between parameterization schemes and microphysics schemes.
In terms of modeling technology, accelerating the computation is necessary to run the model at the climate

Page 20 of 25

scale. As previously stated in this review, the SYPD of
the 14 km mesh NICAM on the Earth Simulator 3 isaround 0.22. The model speeds up by a factor of around
1.8 if most of the double-precision floating-point arithmetic is replaced with single-precision (Nakano et al.
2018). Owing to the excellent weak-scaling performanceof NICAM (Yashiro et al. 2016), the wall-clock time permodel time-step is almost constant when the horizontal
grid spacings are halved and the number of computation
nodes is quadrupled. Note that the time-step interval
should be halved to halve the horizontal grid spacings.
According to a benchmark, our model runs a few times
faster on the Fugaku supercomputer than on the Earth
Simulator 3. Therefore, we expect an SYPD of around
0.3 for the 3.5 km mesh NICAM on the supercomputer
Fugaku, which is comparable with that for the 5 km meshcoupled ICON model (Hohenegger et al. 2022). Other
possible approaches for speeding up computation include
reducing the required byte-per-flops with even lower
floating-point arithmetic (e.g., Paxton et al. 2022), performing calculations faster with the aid of accelerators,
and replacing physics schemes with AI-based surrogate
models (Arakawa et al. 2022). In addition, implementing an analysis platform on the supercomputer or cloudbased system is urgently needed to reduce the timeneeded for data transfer. Future technological trends
in climate simulation are discussed in detail in WMO(2021).

4 Conclusions
We have reviewed the results of global nonhydrostatic
simulations using NICAM to examine future changes
in clouds, which were conducted in the core Japanese
research program for climate change, the TOUGOU program, in the five fiscal years since 2017. This review also
describes current research activities around the world
and future issues in high-resolution climate modeling.
For the projection of clouds, previous NICAM studies
have predicted a larger number of high clouds, which ischaracterized by a larger number of smaller high clouds
in a warmer atmosphere and then an increase in thehigh-cloud amount. However, it was not clear why highclouds change in such a way. The lack of knowledge about
the underlying mechanisms has been a large motivation
behind our climate research.
Noda et al. (2019) reveals that a key factor was a
reduced degree of disorganized tropical convection due
to warming. In a warmer atmosphere, the smaller degreeof cloud organization leads to a more scattered development of high clouds, which then change to cover a larger
area of the tropical atmosphere. In fact, our results showthat the large-scale circulation strongly correlates withthe degree of cloud organization, suggesting that tropicalNoda et al. Progress in Earth and Planetary Science(2023) 10:48

convection obtains more vapor from a boundary layer.
In addition, large-scale ascendant flows act to generate
convection. Further efforts are needed to gather observational data in order to evaluate the modeled result. We
also evaluated changes in the vertical structure of ice species in high clouds due to warming and their relationshipto changes in surface temperature.
Using RCEs also enabled us to systematically examine processes regarding clouds by using a sensitivity
analysis of the cloud processes, and we found a change
in behavior of cloud microphysics processes to cloud ice
in a warmer atmosphere. Conventionally, most previous studies focus on a change in cloud-top temperature
due to climate change (e.g., Hartman and Larson 2002;
Zelinka and Hartmann 2010); by contrast, less attention
has been paid to the role of a change of cloud-top pressure. It is well recognized that the mean altitude of highclouds increases in a warmer atmosphere (e.g., Zelinka
et al. 2013), which also means that cloud-top pressure
decreases (Zelinka and Hartmann 2010). Our study firstpointed out that reduced cloud-top pressure plays animportant role in reducing the lifetime of anvil clouds byenhancing the deposition growth of cloud ice from vapor,thereby leading to an increase in sedimentation.
We also investigated changes in well-organized cloud
disturbances, such as TCs and extratropical cyclones, due
to warming. The modeled projection of a reduced number of TCs is attributed to a reduced number of TC seed;by contrast, the survival rate of TCs (defined as a ratioof the number of TCs to TC seeds) is almost identical.
We also showed that TC size increases with latitude, on
average, and its regional characteristics. We also identified a larger number of moderately intense extratropical
cyclones in warming climate.
We also evaluated an effective climate sensitivity, whichis the first attempt based on data from global nonhydrostatic climate simulations. In practical terms, the detailed
value of climate sensitivity can depend on cloud schemes
and their parameters (e.g., Kodama et al. 2012). Therefore, in the next step, we need to improve our knowledgeof the extent to which microphysics parameters affectcloud feedback processes and eventually climate sensitivity, as well as how those parameters can be constrained
based on observation data in future. Those efforts willlead to a better estimation of the climate sensitivity of ourplanet.
To improve the performance of future global nonhydrostatic simulations, we have also proposed methods toimprove the physical processes in such global high-resolution models, including low-level mixed-phase clouds,
cirrus, warm rain, and SGS turbulent mixing processes,
along with evaluating the importance of taking precipitating categories of ice species into account.

Page 21 of 25

Efforts to develop a new type of climate model thatis capable of resolving storms, like NICAM, have beenenthusiastically pursued in world climate modelingcenters. A global nonhydrostatic model is a useful
tool for climate research; however, it has many aspects
that could be improved, as we have reviewed here. For
example, further efforts are needed to improve thephysical schemes regarding clouds and the spatial resolution to better simulate the behavior of clouds. For
advanced climate research, it is important that these
efforts continue and that research groups around theworld collaborate and cooperate in sharing knowledge.
Abbreviations
AMIP	Atmospheric Model Intercomparison Project
CALIPSO	Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations
CERES	Clouds and Earth’s Radiant Energy System
CMIP	Coupled Model Intercomparison Project
COD	Cloud optical depth
ECS	Effective climate sensitivity
GCM	General circulation model
NDW6	NICAM double-moment bulk scheme with six water categories
NICAM	Nonhydrostatic icosahedral atmospheric model
NSW6	NICAM single-moment bulk scheme with six water categories
OLR	Outgoing longwave radiation
R08	Radius of 8 m ­s−1 wind
RCE	Radiative convective equilibrium
SGS	Sub-grid scale
SST	Sea surface temperature
SYPD	Simulation year per dayTC	Tropical cyclone
Acknowledgements
We acknowledge two anonymous reviewers for helpful comments that
improved the original manuscript. This study was supported by the Inte‑grated Research Program for Advancing Climate Models (TOUGOU) Grants
JPMXD0717935457 and the Advanced Studies of Climate Change projec‑tion (SENTAN) JPMXD0722680395 from the Japanese Ministry of Education,
Culture, Sports, Science and Technology. CK acknowledges the Environment
Research and Technology Development Fund (JP-MEERF20172R01) of theEnvironmental Restoration and Conservation Agency of Japan (ERCA), JSPS
KAKENHI Grant Number JP17H04856, and JSPS KAKENHI Grant Number
JP20H05728. The simulations and analysis for parts of NICAM simulations wereconducted using the Earth Simulator and the supercomputers K and Fugaku.
Author contributions
ATN led the NICAM research in the TOUGOU project, coordinated the review,and contributed to Sects. 1, 2.1.1, 2.1.6, 2.2.1, and 4. TO contributed to
Sects. 2.1.3 and 2.2.3. CK contributed to Sects. 2.1.5, 2.2.6, and 3. YWC contrib‑
uted to Sects. 2.1.2 and 2.2.4. NK contributed to Sect. 2.2.5. TS contributed to
Sects. 2.2.1 and 2.2.2. YY contributed to Sect. 2.1.4. MS contributed to Sect. 3.
All authors read and approved the final manuscript.
Funding
This study was supported by the Integrated Research Program for Advanc‑ing Climate Models (TOUGOU) Grants JPMXD0717935457 and the Advanced
Studies of Climate Change projection (SENTAN) JPMXD0722680395 from theJapanese Ministry of Education, Culture, Sports, Science and Technology. CK
was also supported by the Environment Research and Technology Develop‑
ment Fund (JP-MEERF20172R01) of the Environmental Restoration and Con‑
servation Agency of Japan (ERCA), JSPS KAKENHI Grant Number JP17H04856,
and JSPS KAKENHI Grant Number JP20H05728.

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Availability of data and material
Readers should refer to the original manuscript mentioned in each figure cap‑tion. Data for figures without reference to an original manuscript in the cap‑tion may be available upon request by contacting the corresponding author.

Declarations
Competing interests
The authors declare that they have no competing interest.
Received: 5 March 2023 Accepted: 7 August 2023

References
Andrews T, Gregory JM, Webb MJ (2015) The dependence of radiative forcing
and feedback on evolving patterns of surface temperature change inclimate models. J Clim 28:1630–1648
Arakawa T, Yashiro H, Nakajima K (2022) Development of a coupler h3-OpenUTIL/MP. In: HPCAsia2022: International conference on high perfor‑
mance computing in Asia-Pacific Region, January 2022. Association for
Computing Machinery, New York, p 72. https://​doi.​org/​10.​1145/​34928​
05.​34928​09
Bodas-Salcedo A, Williams KD, Field PR, Lock AP (2012) The surface down‑
welling solar radiation surplus over the Southern Ocean in the met
office model: the role of midlatitude cyclone clouds. J Clim 25:7467–
7486. https://​doi.​org/​10.​1175/​JCLI-D-​11-​00702.1
Böhm HP (1989) A general equation for the terminal fall speed of solid hydro‑
meteors. J Atmos Sci 46(15):2419–2427. https://​doi.​org/​10.​1175/​1520-​
0469(1989)​046%​3c2419:​AGEFTT%​3e2.0.​CO;2
Bretherton CS, Blossey P, Khairoutdinov M (2005) An energy-balance analysis
of deep convective self-aggregation above uniform SST. J Atmos Sci
62:4273–4292
Camargo SJ, Barnston AG, Zebiak SE (2005) A statistical assessment of tropical
cyclone activity in atmospheric general circulation models. Tellus A
57:589–604. https://​doi.​org/​10.​1111/j.​1600-​0870.​2005.​00117.x
Catto JL, Ackerley D, Booth JF, Champion AJ, Colle BA, Pfahl S, Pinto JG, Quint‑
ing JF, Seiler C (2019) The future of midlatitude cyclones. Curr Clim
Change Rep 5:407–420. https://​doi.​org/​10.​1007/​s40641-​019-​00149-4
Chavas DR, Emanuel KA (2010) A QuikSCAT climatology of tropical cyclone
size. Geophys Res Lett 37:L18816. https://​doi.​org/​10.​1029/​2010G​L0445​
58
Chen Y-W, Seiki T, Kodama C, Satoh M, Noda AT, Yamada Y (2016) Highcloud responses to global warming simulated by two different cloud
microphysics schemes implemented in the nonhydrostatic icosahedral
atmospheric model (NICAM). J Clim 29:5949–5964
Chen Y-W, Seiki T, Kodama C, Satoh M, Noda AT (2018) Impact of precipitating
ice hydrometeors on longwave radiative effect estimated by a global
cloud-system resolving model. J Adv Model Earth Syst 10(2):284–296.
https://​doi.​org/​10.​1002/​2017M​S0011​80
Chen Y-W, Satoh M, Kodama C, Noda AT, Yamada T (2022) Projection of highclouds and its link to ice hydrometeors: An approach by using longterm global cloud-system resolving simulations. J Clim 35:3495–3514.
https://​doi.​org/​10.​1175/​JCLI-D-​21-​0150.1
Coppin D, Bony S (2015) Physical mechanisms controlling the initiation of
convective self-aggregation in a general circulation model. J Adv Model
Earth Syst 7:2060–2078. https://​doi.​org/​10.​1002/​2015M​S0005​71
Engdahl BJK, Thompson G, Bengtsson L (2020) Improving the representationof supercooled liquid water in the HARMONIE-AROME weather forecast
model. Tellus A 72(1):1697603. https://​doi.​org/​10.​1080/​16000​870.​2019.​
16976​03
Field PR, Cotton RJ, McBeath K, Lock AP, Webster S, Allan RP (2014) Improving a
convection permitting model simulation of a cold air outbreak. Q J Roy
Meteor Soc 140:124–138. https://​doi.​org/​10.​1002/​qj.​2116
Forbes RM, Ahlgrimm M (2014) On the representation of high-latitude bound‑ary layer mixed-phase cloud in the ECMWF global model. Mon Wea Rev
142:3425–3445. https://​doi.​org/​10.​1175/​MWR-D-​13-​00325.1

Page 22 of 25

Furtado K, Field P (2017) The role of ice-microphysics parametrizations indetermining the prevalence of supercooled liquid water in high-resolu‑
tion simulations of a Southern Ocean midlatitude cyclone. J Atmos Sci
74:2001–2021. https://​doi.​org/​10.​1175/​JAS-D-​16-​0165.1
Gasparini B, Blossey PN, Hartmann DL, Lin G, Fan J (2019) What drives the life
cycle of tropical anvil clouds? J Adv Model Earth Syst 11:2586–2605.
https://​doi.​org/​10.​1029/​2019M​S0017​36
Grabowski WW (1993) Cumulus entrainment, fine-scale mixing, and buoyancy
reversal. Quart J Roy Meteor Soc 119:935–956. https://​doi.​org/​10.​1002/​
qj.​49711​951305
Grabowski WW (2007) Representation of turbulent mixing and buoyancy
reversal in bulk cloud models. J Atmos Sci 64(10):3666–3680. https://​doi.​org/​10.​1175/​JAS40​47.1
Grabowski WW, Clark TL (1993) Cloud-environment interface instability: part
II: extension to three spatial dimensions. J Atmos Sci 50(4):555–573.
https://​doi.​org/​10.​1175/​1520-​0469(1993)​050h0​555:​CEIIP​Ii2.0.​CO;2
Gryspeerdt E, Sourdeval O, Quaas J, Delanoë J, Krämer M, Kühne P (2018)
Ice crystal number concentration estimates from lidar–radar satellite
remote sensing—part 2: controls on the ice crystal number concen‑
tration. Atmos Chem Phys 18:14351–14370. https://​doi.​org/​10.​5194/​
acp-​18-​14351-​2018
Haarsma RJ, Roberts MJ, Vidale PL, Senior CA, Bellucci A, Bao Q, Chang P, Corti
S, Fuckar NS, Guemas V, von Hardenberg J, Hazeleger W, Kodama C,
Koenigk T, Leung LR, Lu J, Luo JJ, Mao J, Mizielinski MS, Mizuta R, NobreP, Satoh M, Scoccimarro E, Semmler T, Small J, von Storch JS (2016)
High resolution model intercomparison project (HighResMIP v1.0)
for CMIP6. Geosci Model Dev 9:4185–4208. https://​doi.​org/​10.​5194/​
gmd-9-​4185-​2016
Hall WD, Pruppacher HR (1976) The survival of ice particles falling from cirrus
clouds in subsaturated air. J Atmos Sci 33:1995–2006. https://​doi.​org/​
10.​1175/​1520-​0469(1976)​033h1​995:​TSOIP​Fi2.0.​CO;2
Hartmann DL, Larson K (2002) An important constraint on tropical cloudclimate feedback. Geophys Res Lett 29:1951. https://​doi.​org/​10.​1029/​
2002G​L0158​35
Hashino T, Satoh M, Hagihara Y, Kubota T, Matsui T, Nasuno T, Okamoto H(2013) Evaluating cloud microphysics from NICAM against CloudSat
and CALIPSO. J Geophys Res Atmos 118:7273–7292. https://​doi.​org/​10.​
1002/​jgrd.​50564
Heymsfield AJ (2007) On measurements of small ice particles in clouds. Geo‑phys Res Lett 34:L23812. https://​doi.​org/​10.​1029/​2007G​L0309​51
Heymsfield AJ, Kajikawa M (1987) An improved approach to calculating
terminal velocities of plate-like crystals and graupel. J Atmos Sci
44:1088–1099. https://​doi.​org/​10.​1175/​1520-​0469(1987)​044%​3c1088:​
AIATCT%​3e2.0.​CO;2
Heymsfield AJ, Miloshevich LM (1995) Relative humidity and temperature
influences on cirrus formation and evolution: observations from wave
clouds and FIRE II. J Atmos Sci 52:4302–4326. https://​doi.​org/​10.​1175/​
1520-​0469(1995)​052h4​302:​RHATI​Oi2.0.​CO;2
Hohenegger C, Hohenegger C, Korn P, Linardakis L, Redler R, Schnur R,
Adamidis P, Bao J, Bastin S, Behravesh M, Bergemann M, Biercamp J,
Bockelmann H, Brokopf R, Brüggemann N, Casaroli L, Chegini F, Datseris
G, Esch M, George G, Giorgetta M, Gutjahr O, Haak H, Hanke M, Ilyina
T, Jahns T, Jungclaus J, Kern M, Klocke D, Kluft L, Kölling T et al (2022)
ICON-Sapphire: simulating the components of the earth system andtheir interactions at kilometer and subkilometer scales. Geosci Model
Dev. https://​doi.​org/​10.​5194/​gmd-​2022-​171
Hourdin F, Mauritsen T, Gettelman A, Golaz J-C, Balaji V, Duan Q, Folini D, Ji D,
Klocke D, Qian Y, Rauser F, Rio C, Tomassini L, Watanabe M, Williamson D(2017) The art and science of climate model tuning. Bull Am Meteorol
Soc 98(3):589–602. https://​doi.​org/​10.​1175/​BAMS-D-​15-​00135.1
Hsieh T, Vecchi GA, Yang W, Held IM, Garner ST (2020) Large-scale control on
the frequency of tropical cyclones and seeds: a consistent relationshipacross a hierarchy of global atmospheric models. Clim Dyn 55:3177–
3196. https://​doi.​org/​10.​1007/​s00382-​020-​05446-5
Iga S, Tomita H, Tsushima Y, Satoh M (2007) Climatology of a nonhydro‑
static global model with explicit cloud processes. Geophys Res Lett
34:L22814. https://​doi.​org/​10.​1029/​2007G​L0310​48
IPCC (2021) Climate Change 2021: The physical science basis. Working GroupI contribution to the sixth assessment report of the intergovernmental
panel on climate change. Cambridge University Press, Cambridge

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Ishii M, Mori N (2020) d4PDF: Large-ensemble and high-resolution climate
simulations for global warming risk assessment. Prog Earth Planet Sci
7:58. https://​doi.​org/​10.​1186/​s40645-​020-​00367-7
Karrer M, Seifert A, Ori D, Kneifel S (2021) Improving the representation of
aggregation in a two-moment microphysical scheme with statistics
of multi-frequency Doppler radar observations. Atmos Chem Phys
21(22):17133–17166. https://​doi.​org/​10.​5194/​acp-​21-​17133-​2021
Kawai H, Yukimoto S, Koshiro T, Oshima N, Tanaka T, Yoshimura H, Nagasawa R(2019) Significant improvement of cloud representation in the global
climate model MRI-ESM2. Geosci Model Dev 12:2875–2897. https://​doi.​
org/​10.​5194/​gmd-​12-​2875-​2019
Khvorostyanov VI, Curry JA (2014) Thermodynamics, kinetics, and microphys‑
ics of clouds. Cambridge University Press, New York. https://​doi.​org/​10.​
1017/​CBO97​81139​060004
Klaassen GP, Clark TL (1985) Dynamics of the cloud-environment interface
and entrainment in small cumuli: two-dimensional simulations in theabsence of ambient shear. J Atmos Sci 42:2621–2642. https://​doi.​org/​
10.​1175/​1520-​0469(1985)​042h2​621:​DOTCE​Ii2.0.​CO;2
Knutson T, Camargo S, Chan J, Emanuel K, Ho C-H, Kossin J, Mohapatra M,
Satoh M, Sugi M, Walsh K, Wu L (2020) Tropical cyclones and climatechange assessment: Part II. Projected response to anthropogenic
warming. Bull Am Meteor Soc 101:E303–E322. https://​doi.​org/​10.​1175/​
BAMS-D-​18-​0194.1
Kodama C, Noda AT, Satoh M (2012) An assessment of the cloud signals simu‑
lated by NICAM using ISCCP, CALIPSO, and CloudSat satellite simulators.
J Geophys Res 117:D12210. https://​doi.​org/​10.​1029/​2011J​D0173​17
Kodama C, Yamada Y, Noda AT, Kikuchi K, Kajikawa Y, Nasuno T, Tomita T,
Yamaura T, Hiroshi HG, Hara M, Kawatani Y, Satoh M, Sugi M (2015) A
20-year climatological of a NICAM AMIP-type simulation. J Met Soc
Japan 93(4):393–424
Kodama C, Stevens B, Mauritsen T, Seiki T, Satoh M (2019) A new perspective
for future precipitation change from intense extratropical cyclones.
Geophys Res Lett 46:12435–12444
Kodama C, Kodama C, Ohno T, Seiki T, Yashiro H, Noda AT, Nakano M, Yamada
Y, Roh W, Satoh M, Nitta T, Goto D, Miura H, Nasuno T, Miyakawa T, Chen
Y-W, Sugi M (2021) The Nonhydrostatic ICosahedral Atmospheric Model
for CMIP6 HighResMIP simulations (NICAM16-S): experimental design,model description, and impacts of model updates. Geosc Model Dev
14(2):795–820. https://​doi.​org/​10.​5194/​gmd-​14-​795-​2021
Kuba N, Fujiyoshi Y (2006) Development of a cloud microphysical model andparameterizations to describe the effect of CCN on warm cloud. Atmos
Chem Phys 6:2793–2810. https://​doi.​org/​10.​5194/​acp-6-​2793-​2006
Kuba N, Murakami M (2010) Effect of hygroscopic seeding on warm rain
clouds—numerical study using a hybrid cloud microphysicalmodel. Atmos Chem Phys 10:3335–3351. https://​doi.​org/​10.​5194/​
acp-​10-​3335-​2010
Kuba N, Seiki T, Suzuki K, Roh W, Satoh M (2020) Evaluation of rain microphys‑
ics using a radar simulator and numerical models: comparison of
two-moment bulk and spectral bin cloud microphysics schemes. J Adv
Model Earth Syst. https://​doi.​org/​10.​1029/​2019M​S0018​91
Lee C-Y, Camargo SJ, Sobel AH, Tippett MK (2020) Statistical-dynamical downs‑
caling projections of tropical cyclone activity in a warming climate: twodiverging genesis scenarios. J Clim 33:4815–4834. https://​doi.​org/​10.​
1175/​JCLI-D-​19-​0452.1
Li J-LF, Lee W-L, Waliser D, Wang Y-H, Yu JY, Jiang X, L’Ecuyer T, Chen Y-T, Kubar
T, Fetzer E, Mahakur M (2016) Considering the radiative effect of snow
on tropical Pacific Ocean radiative heating profiles in contemporary
GCMs using A-Train observations. J Geophys Res Atmos 121:1621–1636.
https://​doi.​org/​10.​1002/​2015J​D0235​87
Liang-Liang L, Jian L, Ru-Cong Y (2022) Evaluation of CMIP6 HighResMIP
models in simulating precipitation over Central Asia. Adv Clim Change
Res 13:1–13. https://​doi.​org/​10.​1016/j.​accre.​2021.​09.​009
Liou K-N (1986) Influence of cirrus clouds on weather and climate processes: aglobal perspective. Mon Wea Rev 114(6):1167–1199. https://​doi.​org/​10.​
1175/​1520-​0493(1986)​114%​3c1167:​IOCCOW%​3e2.0.​CO;2
Locatelli JD, Hobbs PV (1974) Fall speeds and masses of solid precipitation
particles. J Geophys Res 79(15):2185–2197. https://​doi.​org/​10.​1029/​
JC079​i015p​02185
Matsuoka D, Nakano M, Sugiyama D, Uchida S (2018) Deep learning approachfor detecting tropical cyclones and their precursors in the simulation by

Page 23 of 25

a cloud-resolving global nonhydrostatic atmospheric model. Prog Earth
Planet Sci 5:80
Mauritsen T, Stevens B (2015) Missing iris effect as a possible cause of mutedhydrological change and high climate sensitivity in models. Nat Geosci
8:346–351
Mauritsen T, Redler R, Esch M, Stevens B, Hohenegger C, Klocke D, Brokopf R,
Haak H, Linardakis L, Röber N, Schnur R (2022) Early development andtuning of a global coupled cloud resolving model, and its fast response
to increasing CO2. Tellus A 74(1):346–363. https://​doi.​org/​10.​16993/​
tellu​sa.​54
Meehl GA, Senior CA, Eyring V, Flato G, Lamarque J-F, Stouffer RJ, Taylor
KE, Schlund M (2020) Context for interpreting equilibrium climate
sensitivity and transient climate response from the CMIP6 Earth systemmodels. Sci Adv 6:eaba1981
Merrill RT (1984) A comparison of large and small tropical cyclones. Mon Wea
Rev 112:1408–1418. https://​doi.​org/​10.​1175/​1520-​0493(1984)​112,1408:​
ACOLAS.​2.0.​CO;2
Mitchell DL (1996) Use of mass- and area-dimensional power laws fordetermining precipitation particle terminal velocities. J Atmos Sci
53(12):1710–1723. https://​doi.​org/​10.​1175/​1520-​0469(1996)​053%​
3c1710:​UOMAAD%​3e2.0.​CO;2
Mitchell DL, Rasch P, Ivanova D, McFarquhar G, Nousiainen T (2008) Impactof small ice crystal assumptions on ice sedimentation rates in cirrus
clouds and GCM simulations. Geophys Res Lett 35:L09806. https://​doi.​
org/​10.​1029/​2008G​L0335​52
Montgomery RB (1947) Viscosity and thermal conductivity of air and diffusivityof water vapor in air. J Meteor 4:193–196. https://​doi.​org/​10.​1175/​1520-​
0469(1947)​004h0​193:​VATCO​Ai2.0.​CO;2
Nakano M, Yashiro H, Kodama C, Tomita H (2018) Single precision in the
dynamical core of a nonhydrostatic global atmospheric model: evalua‑tion using a baroclinic wave test case. Mon Wea Rev 146:409–416
Noda AT, Oouchi K, Satoh M, Tomita H (2012) Quantitative assessment of diur‑nal variation of tropical convection simulated by a global nonhydro‑
static model without cumulus parameterization. J Clim 25:5119–5134
Noda AT, Satoh M, Yamada Y, Kodama C, Seiki T (2014) Responses of tropi‑
cal and subtropical high-cloud statistics to global warming. J Clim
27:7753–7768
Noda AT, Seiki T, Satoh M, Yamada Y (2016) High cloud size dependency inthe applicability of the fixed anvil temperature hypothesis using global
nonhydrostatic simulations. Geophys Res Lett 43(5):2307–2314. https://​doi.​org/​10.​1002/​2016G​L0677​42
Noda AT, Kodama C, Yamada Y, Satoh M, Ogura T, Ohno T (2019) Responses ofclouds and large-scale circulation to global warming evaluated frommultidecadal simulations using a global nonhydrostatic model. J Adv
Model Earth Syst. https://​doi.​org/​10.​1029/​2019M​S0016​58
Noda AT, Seiki T, Roh W, Satoh M, Ohno T (2021) Improved representation of
low-level mixed-phase clouds in a global cloud-system-resolving simu‑
lation. J Geophys Res Atmos. https://​doi.​org/​10.​1029/​2021J​D0352​23
Ohno T, Satoh M (2018) Roles of cloud microphysics on cloud responses to sea
surface temperatures in radiative-convective equilibrium experiments
using a high-resolution global nonhydrostatic model. J Adv Model
Earth Syst 10:1970–1989. https://​doi.​org/​10.​1029/​2018M​S0013​86
Ohno T, Satoh M, Noda AT (2019) Fine vertical resolution radiative-convective
equilibrium experiments: Roles of turbulent mixing on the highcloud response to sea surface temperatures. J Adv Model Earth Syst
11:1637–1654
Ohno T, Noda AT, Satoh M (2020) Impacts of sub-grid ice cloud physics ina turbulence scheme on high clouds and their response to global
warming. J Met Soc Japan 98:1069–1081. https://​doi.​org/​10.​2151/​jmsj.​
2020-​054
Ohno T, Noda AT, Seiki T, Satoh M (2021) Importance of pressure changes inhigh cloud area feedback due to global warming. Geophys Res Lett.
https://​doi.​org/​10.​1029/​2021G​L0936​46
Olson JB, Kenyon JS, Angevine WA, Brown JM, Pagowski M, Sušelj K (2019)
A description of the MYNN-EDMF scheme and the coupling to othercomponents in WRF–ARW. NOAA Techn Memorandum OAR GSD.
https://​doi.​org/​10.​25923/​n9wm-​be49
Paxton EA, Chantry M, Klöwer M, Saffin L, Palmer T (2022) Climate modeling in
low precision: effects of both deterministic and stochastic rounding. J
Clim 35:1215–1229

Noda et al. Progress in Earth and Planetary Science(2023) 10:48

Priestley MDK, Catto JL (2022) Improved representation of extratropical
cyclone structure in HighResMIP models. Geophys Res Lett. https://​doi.​
org/​10.​1029/​2021G​L0967​08
Pruppacher H, Klett J (2010) Microphysics of clouds and precipitation. Springer,
Dordrecht. https://​doi.​org/​10.​1007/​978-0-​306-​48100-0
Roberts MJ, Camp J, Seddon J, Vidale PL, Hodges K, Vanniere B, Mecking J,
Haarsma R, Bellucci A, Scoccimarro E, Caron LP, Chauvin F, Terray L,
Valcke S, Moine MP, Putrasahan D, Roberts C, Senan R, Zarzycki C, Ullrich
P (2020a) Impact of model resolution on tropical cyclone simulation
using the HighResMIP-PRIMAVERA multi-model ensemble. J Clim
33:2557–2583. https://​doi.​org/​10.​1175/​JCLI-D-​19-​0639.1
Roberts MJ, Camp J, Seddon J, Vidale PL, Hodges K, Vanniere B, Mecking J,
Haarsma R, Bellucci A, Scoccimarro E, Caron LP, Chauvin F, Terray L,
Valcke S, Moine MP, Putrasahan D, Roberts CD, Senan R, Zarzycki C,
Ullrich P, Yamada Y, Mizuta R, Kodama C, Fu D, Zhang Q, Danabasoglu
G, Rosenbloom N, Wang H, Wu L (2020b) Projected future changes intropical cyclones using the CMIP6 HighResMIP multi-model ensemble.
Geophys Res Lett. https://​doi.​org/​10.​1029/​2020G​L0886​62
Roh W, Satoh M (2014) Evaluation of precipitating hydrometeor parameteriza‑
tions in a single-moment bulk microphysics scheme for deep convec‑
tive systems over the tropical central Pacific. J Atmos Sci 71:2654–2673.
https://​doi.​org/​10.​1175/​JAS-D-​13-​0252.1
Roh W, Satoh M, Nasuno T (2017) Improvement of a cloud microphys‑
ics scheme for a global nonhydrostatic model using TRMM and asatellite simulator. J Atmos Sci 74:167–184. https://​doi.​org/​10.​1175/​
JAS-D-​16-​0027.1
Roh W, Satoh M, Hashino T, Okamoto H, Seiki T (2020) Evaluations of the ther‑modynamic phases of clouds in a cloud-system resolving model using
CALIPSO and a satellite simulator over the Southern Ocean. J Atmos Sci
77(11):3781–3801. https://​doi.​org/​10.​1175/​JAS-D-​19-​0273.1
Rossow WB, Schiffer RA (1999) Advances in understanding clouds from ISCCP.
Bull Am Meteor Soc 80:2261–2287. https://​doi.​org/​10.​1175/​1520-​
0477(1999)​080%​3c2261:​AIUCFI%​3e2.0.​CO;2
Sassen K, Wang Z, Liu D (2008) Global distribution of cirrus clouds from Cloud‑
Sat/Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations(CALIPSO) measurements. J Geophys Res 113(D8):D00A12. https://​doi.​
org/​10.​1029/​2008J​D0099​72
Satoh M, Iga S, Tomita H, Tsushima Y, Noda AT (2012) Response of upper clouds
in global warming experiments obtained using global nonhydrostatic
model with explicit cloud processes. J Clim 25:2178–2191
Satoh M, Tomita H, Yashiro H, Miura H, Kodama C, Seiki T, Noda AT, Yamada Y,
Goto D, Sawada M, Miyoshi T, Niwa Y, Hara M, Ohno T, Iga S, Arakawa
T, Inoue T, Kubokawa H (2014) The non-hydrostatic icosahedral atmos‑
pheric model: description and development. Prog Earth Planet Sci 1:18.
https://​doi.​org/​10.​1186/​s40645-​014-​0018-1
Satoh M, Yamada Y, Sugi M, Kodama C, Noda AT (2015) Constraint on futurechange in global frequency of tropical cyclones due to global warming.
J Met Soc Jpn 93:489–500. https://​doi.​org/​10.​2151/​jmsj.​2015-​025
Satoh M, Noda AT, Seiki T, Chen Y-W, Kodama C, Yamada Y, Kuba N, Sato Y(2018) Toward reduction of the uncertainties in climate sensitivity due
to cloud processes using a global non-hydrostatic atmospheric model.
Prog Earth Planet Sci 5:67. https://​doi.​org/​10.​1186/​s40645-​018-​0226-1
Satoh M, Stevens B, Judt F, Khairoutdinov M, Lin S, Putman WM, Düben
P (2019) Global cloud-resolving models. Curr Clim Change Rep
5:172–184. https://​doi.​org/​10.​1007/​s40641-​019-​00131-0
Satoh M, Roh W, Hashino T (2016) Evaluations of clouds and precipitations in
NICAM using the joint simulator for satellite sensors. CGER’s Super‑computer Monograph Report. Vol. 22. Center for Global Environmental
Research, Tsukuba. https://​www.​cger.​nies.​go.​jp/​publi​catio​ns/​report/​
i127/​en/
Schenkel BA, Chavas D, Lin N, Knutson T, Vecchi G, Brammer A (2022) North
Atlantic tropical cyclone outer size and structure remain unchanged by
the late twenty-first century. J Clim 36(2):359–382. https://​doi.​org/​10.​
1175/​JCLI-D-​22-​0066.1
Seeley JT, Jeevanjee N, Langhans W, Romps DM (2019) Formation of tropicalanvil clouds by slow evaporation. Geophys Res Lett 46(1):492–501.
https://​doi.​org/​10.​1029/​2018G​L0807​47
Seifert A, Beheng KD (2006) A two-moment cloud microphysics parameteriza‑tion for mixed-phase clouds. Part 1: model description. Meteor Atmos
Phys 92:45–66. https://​doi.​org/​10.​1007/​s00703-​005-​0112-4

Page 24 of 25

Seifert A, Blahak U, Buhr R (2014) On the analytic approximation of bulk
collision rates of non-spherical hydrometeors. Geosci Model Dev
7(2):463–478. https://​doi.​org/​10.​5194/​gmd-7-​463-​2014
Seiki T, Nakajima T (2014) Aerosol effects of the condensation process on aconvective cloud simulation. J Atmos Sci 71:833–853. https://​doi.​org/​
10.​1175/​JAS-D-​12-​0195.1
Seiki T, Ohno T (2022) Improvements of the double-moment bulk cloud
microphysics scheme in the Nonhydrostatic ICosahedral Atmospheric
Model (NICAM). J Atmos Sci 80:111–127. https://​doi.​org/​10.​1175/​
JAS-D-​22-​0049.1
Seiki T, Roh W (2020) Improvements in supercooled liquid water simulationsof low-level mixed-phase clouds over the Southern Ocean using asingle-column model. J Atmos Sci 77:3803–3819. https://​doi.​org/​10.​
1175/​JAS-D-​19-​0266.1
Seiki T, Satoh M, Tomita H, Nakajima T (2014) Simultaneous evaluation of ice
cloud microphysics and nonsphericity of the cloud optical properties
using hydrometeor video sonde and radiometer sonde in situ observa‑
tions. J Geophys Res Atmos 119:6681–6701. https://​doi.​org/​10.​1002/​
2013J​D0210​86
Seiki T, Kodama C, Noda AT, Satoh M (2015) Improvements in global cloudsystem resolving simulation by using a double-moment bulk cloud
microphysics scheme. J Clim 28:2405–2419. https://​doi.​org/​10.​1175/​
JCLI-D-​14-​00241.1
Seiki T, Kodama C, Satoh M, Hagihara Y, Okamoto H (2019) Characteristics ofice clouds over mountain regions detected by CALIPSO and CloudSat
satellite observations. J Geophys Res Atmos 124(20):10858–10877.
https://​doi.​org/​10.​1029/​2019J​D0305​19
Seiki T, Roh W, Satoh M (2022) Cloud microphysics in global cloud resolving
models. Atmos Ocean 60(3–4):477–505. https://​doi.​org/​10.​1080/​07055​
900.​2022.​20753​10
Sekiguchi M, Nakajima T (2008) A k-distribution-based radiation code and its
computational optimization for an atmospheric general circulation
model. J Quant Spectrosc Ra 109:2997–2793
Seneviratne, S, Zhang X, Adnan M, Badi W, Dereczynski C, Luca AD, Ghosh S,
Iskandar I, Kossin J, Lewis S, Otto F, Pinto I, Satoh M, Vicente-Serrano
SM, Wehner M, Zhou B (2021) Weather and climate extreme events ina changing climate. In: IPCC (eds) Climate Change 2021: The PhysicalScience Basis. Working Group I contribution to the Sixth Assessment
Report of the Intergovernmental Panel on Climate Change, Cambridge
University Press, Cambridge, p 1513
Sherwood SC, Webb MJ, Annan JD, Armour KC, Forster PM, Hargreaves JC,
Hegerl G, Klein SA, Marvel KD, Rohling EJ, Watanabe M, Andrews T,
Braconnot P, Bretherton CS, Foster GL, Hausfather Z, von der Heydt
AS, Knutti R, Mauritsen T, Norris JR, Proistosescu C, Rugenstein M,
Schmidt GA, Tokarska KB, Zelinka MD (2020) An assessment of earth’s
climate sensitivity using multiple lines of evidence. Rev Geophys
58:e2019RG000678. https://​doi.​org/​10.​1029/​2019R​G0006​78
Shiogama H, Watanabe M, Ogura T, Yokohata T, Kimoto M (2014) Multi-param‑
eter multi-physics ensemble (MPMPE): a new approach exploring theuncertainties of climate sensitivity. Atmos Sci Lett 15:97–102
Slingo J, Bates P, Bauer P, Belcher S, Palmer T, Stephens G, Stevens B, Stocker
T, Teutsch G (2022) Ambitious partnership needed for reliable climate
prediction. Nat Clim Change 12:499–503. https://​doi.​org/​10.​1038/​
s41558-​022-​01384-8
Squires P (1958) Penetrative downdraughts in cumuli. Tellus 10(3):381–389.
https://​doi.​org/​10.​3402/​tellu​sa.​v10i3.​9243
Stevens B, Satoh M, Auger L, Biercamp J, Bretherton CS, Chen X, Düben P, Judt
F, Khairoutdinov M, Klocke D, Kodama C, Kornblueh L, Lin S-J, Neumann
P, Putman WM, Röber N, Shibuya R, Vanniere B, Vidale PL, Wedi N, Zhou
L (2019) DYAMOND: the dynamics of the atmospheric general circula‑tion modeled on non-hydrostatic domains. Prog Earth Planet Sci 6:61.
https://​doi.​org/​10.​1186/​s40645-​019-​0304-z
Sugi M, Yamada Y, Yoshida K, Mizuta R, Nakano M, Kodama C, Satoh M (2020)
Future changes in the global frequency of tropical cyclone seeds. SOLA
16:70–74
Suselj K, Smalley M, Lebsock MD, Kurowski MJ, Witte MK, Teixeira J (2022)
Coupling warm rain with an eddy diffusivity/mass flux parameteriza‑
tion: 1. Model description and validation. J Adv Model Earth Syst
14:e2021MS002736. https://​doi.​org/​10.​1029/​2021m​s0027​36
Tan I, Storelvmo T (2016) Sensitivity study on the influence of cloud micro‑
physical parameters on mixed-phase cloud thermodynamic phaseNoda et al. Progress in Earth and Planetary Science(2023) 10:48

partitioning in CAM5. J Atmos Sci 73:709–728. https://​doi.​org/​10.​1175/​
JAS-D-​15-​0152.1
Vecchi GA, Delworth TL, Murakami H, Underwood SD, Wittenberg AT, Zeng F,
Zhang W, Baldwin JW, Bhatia KT, Cooke W, He J, Kapnick SB, Knutson
TR, Villarini G, van der Wiel K, Anderson W, Balaji V, Chen J-H, Dixon KW,
Gudgel R, Harris LM, Jia L, Johnson NC, Lin S-J, Liu M, Ng CHJ, Rosati A,
Smith JA, Yang X (2019) Tropical cyclone sensitivities to ­CO2 doubling:roles of atmospheric resolution, synoptic variability and backgroundclimate changes. Clim Dyn 53(9):5999–6033. https://​doi.​org/​10.​1007/​
s00382-​019-​04913-y
Waliser DE, Li J-LF, L’Ecuyer TS, Chen W-T (2011) The impact of precipitating ice
and snow on the radiation balance in global climate models. Geophys
Res Lett 38:L06802. https://​doi.​org/​10.​1029/​2010G​L0464​78
Webb MJ, Andrews T, Bodas-Salcedo A, Bony S, Bretherton CS, Chadwick R,
Chepfer H, Douville H, Good P, Kay JE, Klein SA, Marchand R, Medeiros B,
Siebesma AP, Skinner CB, Stevens B, Tselioudis G, Tsushima Y, Watanabe
M (2017) The Cloud Feedback Model Intercomparison Project (CFMIP)
contribution to CMIP6. Geosci Model Dev 10:359–384. https://​doi.​org/​
10.​5194/​gmd-​10-​359-​2017
Williams IN, Pierrehumbert RT (2017) Observational evidence against strongly
stabilizing tropical cloud feedbacks. Geophys Res Lett 44:1503–1510.
https://​doi.​org/​10.​1002/​2016G​L0722​02
Williams KD, Bodas-Salcedo A, Déqué M, Fermepin S, Medeiros B, Watanabe M,
Jakob C, Klein SA, Senior CA, Williamson DL (2013) The transpose-AMIP
II experiment and its application to the understanding of Southern
Ocean cloud biases in climate models. J Clim 26:3258–3274. https://​doi.​
org/​10.​1175/​JCLI-D-​12-​00429.1
WMO (2021) Future of weather and climate forecasting. World MeteorologicalOrganization, Geneva
Wu L, Tian W, Liu Q, Cao J (2015) Implications of the observed relationshipbetween tropical cyclone size and intensity over the western northPacific. J Clim 28:9501–9506. https://​doi.​org/​10.​1175/​JCLI-D-​15-​0628.1
Yamada Y, Satoh M, Sugi M, Kodama C, Noda AT, Nakano M, Nasuno T (2017)
Response of tropical cyclone activity and structure to global warming
in a high-resolution global nonhydrostatic model. J Clim 30:9703–9724.
https://​doi.​org/​10.​1175/​JCLI-D-​17-​0068.1
Yamada Y, Kodama C, Satoh M, Sugi M, Roberts MJ, Mizuta R, Noda AT, Nasuno
T, Nakano M, Vidale PL (2021) Evaluation of the contribution of tropical
cyclone seeds to changes in tropical cyclone frequency due to global
warming in high-resolution multi-model ensemble simulations. Prog
Earth Planet Sci 8:11. https://​doi.​org/​10.​1186/​s40645-​020-​00397-1
Yamaguchi T, Feingold G, Larson VE (2017) Framework for improvement byvertical enhancement: A simple approach to improve representationof low and high-level clouds in large-scale models. J Adv Model Earth
Syst 9:627–646
Yashiro H, Terai M, Yoshida R, Iga S-I, Minami K, Tomita H (2016) Performance
analysis and optimization of Nonhydrostatic ICosahedral Atmospheric
Model (NICAM) on the K Computer and TSUBAME2.5. In: Proceedings ofthe platform for advanced scientific computing conference, Lausanne,
Switzerland, 8–10 June, 2016
Zelinka MD, Hartmann DL (2010) Why is longwave cloud feedback positive? J
Geophys Res 115:D16117. https://​doi.​org/​10.​1029/​2010J​D0138​17
Zelinka MD, Hartmann DL (2011) The observed sensitivity of high clouds tomean surface temperature and anomalies in the tropics. J Geophys Res
116:D23103. https://​doi.​org/​10.​1029/​2011J​D0164​59
Zelinka MD, Klein SA, Taylor KE, Andrews T, Webb MJ, Gregory JM, Forster PM(2013) Contributions of different cloud types to feedbacks and rapid
adjustments in CMIP5. J Clim 26:5007–5027. https://​doi.​org/​10.​1175/​
JCLI-D-​12-​00555.1
Zelinka MD, Myers TA, McCoy DT, Po-Chedley S, Caldwell PM, Ceppi P, Klein SA,
Taylor KE (2020) Causes of higher climate sensitivity in CMIP6 models.
Geophys Res Lett 47:e2019GL085782. https://​doi.​org/​10.​1029/​2019G​
L0857​82
Zelinka MD, Klein SA, Qin Y, Myers TA (2022) Evaluating climate models’
cloud feedbacks against expert judgment. J Geophys Res Atmos
127:e2021JD035198. https://​doi.​org/​10.​1029/​2021J​D0351​98

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims in pub‑lished maps and institutional affiliations.

Page 25 of 25