The potential impact of model horizontal resolution on the simulation of atmospheric cloud radiative effect in CMIP6 models

The simulations of atmospheric cloud-radiative effect (ACRE) from 54 Coupled Model Intercomparison Project phase 6 (CMIP6) models during the historical period of 2000/03–2014/12 are compared and evaluated against the satellite-based Clouds and the Earth’s Radiant Energy System (CERES) products. For ease of comparison, all CMIP6 models are divided into high-, medium-, and low-resolution groups to examine the potential impact of model horizontal resolution change on the simulations of ACRE distribution over the tropical oceans. The results show that ACRE is positive inside the ITCZs but negative in the subtropics and cold tongue areas, owing to the very different radiative forcing between deep and shallow clouds. Simulations of ACRE are sensitive to the model horizontal resolution used and the finer resolution models generally produce a better performance of ACRE simulations against the CERES observations. The reduced ACRE biases in finer resolution models are mainly contributed by the improved longwave ACRE (i.e., LWACRE) simulations, especially over the Pacific and Atlantic cold tongue areas where shallow stratocumulus clouds prevail. Simulations of atmospheric cloud-radiative effect (ACRE) in 54 CMIP6 models are evaluated against the satellite-based observational data. The performance of ACRE simulations is sensitive to the model horizontal resolution used. The finer resolution models generally produce a better performance of ACRE simulations, especially over the cold tongues where shallow stratocumulus clouds prevail. Simulations of atmospheric cloud-radiative effect (ACRE) in 54 CMIP6 models are evaluated against the satellite-based observational data. The performance of ACRE simulations is sensitive to the model horizontal resolution used. The finer resolution models generally produce a better performance of ACRE simulations, especially over the cold tongues where shallow stratocumulus clouds prevail.


Introduction
Clouds play an important role in maintaining the earth's climate system as they energetically interact with atmosphere and ocean through latent heat release associated with precipitation and imposing radiative forcing from both shortwave and longwave components of radiation (Tao et al. 1996;Li et al. 2015Li et al. , 2016Ciesielski et al. 2017). Factors affecting cloud-radiative forcing include cloud optical depth, cloud-top height and area of cloud coverage (Ramanathan et al. 1989). In practice, high clouds tend to warm the atmosphere by intercepting upward thermal radiation from surface while also emitting less outgoing longwave radiation to space due to their much lower cloud-top temperatures. By contrast, low clouds incline to cool the atmosphere through emitting strong

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Terrestrial, Atmospheric and Oceanic Sciences Page 2 of 15 Lin and Yu Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:21 downward longwave radiation flux to the Earth's surface (Slingo and Slingo 1988;Wood 2012). It has been recognized that the interaction between clouds and radiation, i.e., the cloud-radiative effect (CRE), provides substantial impacts on initiating tropical perturbations of various spatial scales. For instance, Ruppert et al. (2020) noted that CRE is important to foster and accelerate the development of tropical cyclones as this effect effectively warms the low-to-middle troposphere to shorten the incubation period of tropical cyclones. Ciesielski et al. (2017) and Zhang et al. (2019) showed that the positive atmospheric cloud-radiative effect (hereafter ACRE) associated with longwave radiative heating from high clouds helps Madden-Julian Oscillation (MJO) conquer the barrier over Maritime Continent and propagate farther eastward. Moreover, Ying and Huang (2016) and Li et al. (2018) argued that the inter-model spread of CRE could be the leading source of tropical sea surface temperature (SST) biases in most Coupled Model Intercomparison Project phase 5 (CMIP5) models.
Thanks to the advanced technology in satellite-based radiative fluxes observations, growing concern has been paid to explore the fidelity of cloud-radiation feedback in the state-of-the-art climate system models. By comparing 43 CMIP5 models with in-situ observations, Wild et al. (2015) showed that most CMIP5 models have overestimated the downward solar and thermal radiation at surface and underestimated the downward thermal radiation over land due to biases in surface albedo and temperature simulations. Later, Wild (2020) compared simulations of radiative fluxes in Coupled Model Intercomparison Project phase 6 (CMIP6) models with those in CMIP5 and Clouds and the Earth's Radiant Energy System (CERES) data. He found that CMIP6 models, in general, produce a better performance of radiative fluxes compared to those in CMIP5 models, although the biases of inter-model spread in CMIP6 models still can't be disregarded.
Recently, Vannière et al. (2019) conducted a multimodel evaluation of the sensitivity of global energy balance and hydrological cycle to resolution based on 47 atmosphere-only and coupled atmosphere-ocean model experiments, with a horizontal resolution ranging mostly between 25 and 100 km (40 out of 47 experiments). Their study noted a systematic increase in outgoing longwave radiation and decrease in outgoing shortwave radiation due to changes in cloud properties when the model resolution is increased from 100 to 25 km. They also found that the magnitude of the above flux changes can be up to 5 watt m −2 , which is a non-negligible size for climate models when long-term simulations over a few decades or longer are often required.
We also note that while the CMIP program started nearly 20 years ago (in 1995) and has grown into a very large international scientific platform today, climate system models participating the ScenarioMIP (Scenario Model Intercomparison Project) in the newest CMIP6 still contain a wide range of spatial resolutions (e.g., BCC-ESM1 with a 250 km resolution and 26 vertical levels; MIROC6 with a 120 km resolution and 81 vertical levels; CNRM-CM6-1-HR with a 50 km resolution and 91 vertical levels). Because tropical cumulus clouds play an important role in the earth's radiation balance and are one source of climate sensitivity, improving the representation of these clouds in climate models can significantly reduce the uncertainty of climate projections, especially over the cold tongue and subtropical oceans where shallow stratocumulus clouds and their associated radiative effect are poorly represented (Cronin et al. 2006;Sun et al. 2010;Berry et al. 2020).
Previous studies using CMIP-era models mostly focus on the performance of CRE simulations at the atmospheric boundaries (i.e., top-of-atmosphere and earth's surface) rather than within the atmosphere. However, CRE measured at the top-of-atmosphere represents the radiative forcing of clouds imposing on the earth's climate system below the top-of-atmosphere (including atmosphere, land and ocean) and CRE measured at the surface simply denotes the radiative forcing imposing on the earth's surface (including land and ocean). Some recent studies have shown that the net cloud radiative effect might play a critical role in driving the convectively-coupled waves and precipitation extremes in the tropics (Crueger and Stevens 2015;Ciesielski et al. 2017;Zhang et al. 2019;Medeiros et al. 2021).
Because the simulated radiation fluxes are relatively insensitive to changes in model vertical resolution compared to changes in horizontal resolution (see Appendix 1 for more details), the present study thus focus on the potential impact of model horizontal resolution on the simulations of net ACRE in 54 CMIP6 models by comparing model simulation results with the satellite-based observational data. The remainder of this article is structured as follows. Section 2 provides a brief description of the data and methods, including the means for calculating ACRE and the classification of CMIP6 models. Section 3 compares the performance of CMIP6 models of various resolution groups against the satellite-based observational data, along with some discussions of the underlying implications. Major findings are summarized in Sect. 4. are forced by time-varying external and internal conditions from observations over the period of 1850-2014. These historical simulations often serve as an important benchmark for assessing model performance through a quantitative comparison against observations (Eyring et al. 2016). The radiation variables used include shortwave (SW) and longwave (LW) components of upward and downward radiative fluxes at the top-of-atmosphere (TOA) and the earth's surface. Although the CMIP6 historical simulations cover a lengthy 165-year period, only 13 years and 10 months data are used for analysis here to be consistent with the satellite product shown below.
The Clouds and the Earth's Radiant Energy System's Energy Balanced and Filled dataset (CERES-EBAF) is utilized as an observational reference (Wielicki et al. 1996). The CERES instruments provide satellite-based observations of clouds and radiative fluxes at TOA. The radiative fluxes at surface are computed by the EBAF adjustment algorithm. Specifically, the adjustment algorithm forces the computed TOA irradiances to match with the EBAF-TOA irradiances by adjusting surface, clouds, and atmospheric properties. Surface irradiances are subsequently adjusted using radiative kernels Loeb et al. 2018). The CERES-EBAF product provides monthly radiative fluxes (including SW and LW components) at TOA and surface, with a horizontal resolution of 1 • × 1 • from 2000/03 to 2014/12. The cloud-top pressure is taken from the Synoptic TOA and Surface Fluxes and Clouds (CERES-SYN) which is a sub-product of CERES.
To calculate the radiative effect introduced by clouds, i.e., namely the "cloud radiative effect" (CRE), across various CMIP6 models, radiative fluxes under clear-sky condition are required. It is noted that CERES-EBAF and CMIP6 recalculate the radiative transfer model by removing the effect of clouds, but still maintaining the basic thermodynamic structure of atmosphere (Cess and Potter 1987;Potter et al. 1992;Wild et al. 2019), to derive the clear-sky radiative fluxes at TOA and surface. All data The CMIP6 models are classified into three groups according to the size of grid cell averaged over the tropics (30° S-30° N). Notations H, M and L denote the highresolution ( < 14, 000 km 2 grid −1 ; 19 models), the medium-resolution ( 14, 000−40, 000 km 2 grid −1 ; 18 models), and the low-resolution ( > 40, 000 km 2 grid −1 ; 17 models) groups, respectively. The unit of resolution shown is 10 3 km 2 grid −1 for brevity are re-gridded to a horizontal resolution of 2.5 • × 2.5 • prior to analysis.

Atmospheric cloud radiative effect
The net radiation heating (or cooling) into the atmospheric column ( R net ) can be obtained by subtracting the net SW and LW radiative fluxes at the earth's surface from those at TOA, which can be explicitly expressed as (Bui et al. 2016;Chen et al. 2016;Bui and Yu 2021) where the subscripts "top" and "sfc" denote the top of atmosphere and surface, respectively; the superscripts ↓ and ↑ denote the downward and upward fluxes, respectively. All radiation variables in Eq.
(1) are in units of watt m −2 . We may further divide R net into SW and LW components as where Following Bui and Yu (2021), the ACRE is calculated as the difference between all-sky and clear-sky conditions (former-latter), which can be expressed as where R net all−sky and R net clear−sky represent the net radiation heating (or cooling) into the atmospheric column under all-sky and clear-sky conditions, respectively. Physically, ACRE measures the total radiative forcing (including SW and LW components) within the atmosphere due to the existence of clouds.
Likewise, the SW and LW components of ACRE can be expressed as Since climate models prescribe the downward SW radiative flux at TOA ( SW (1)

Classification and evaluation methods
For ease of comparison, we classify 54 CMIP6 models into three groups, including high-resolution, mediumresolution and low-resolution groups, according to the size of grid cell. Specifically, we divide the global tropical area (30° S-30° N) by the total number of grid points to obtain the size of grid cell (in unit of km 2 grid −1 ) for each model. In the present study, high-resolution ( < 14, 000 km 2 grid −1 ) group consists of 19 models, medium-resolution ( 14, 000−40, 000 km 2 grid −1 ) group 18 models, and low-resolution ( > 40, 000 km 2 grid −1 ) group 17 models (see Table 1 for a summary). The output resolution (longitude/latitude grids) does not exactly represent the model horizontal resolution in conducting numerical simulation since atmospheric models in CMIP6 use different discretization methods (e.g., finite difference, spectral method or finite volume) in solving the dynamic parts of model equations (Kalnay 2004). However, with very few exceptions, we find that the output resolution coincides very well with the model horizontal resolution, i.e., higher horizontal resolution models generally produce finer longitude/latitude grids (see Table AII.5 of IPCC AR6 WGI (2021) for comparison). In practice, the high-, medium-, and low-resolution groups of CMIP6 models defined above correspond roughly to model horizontal resolutions of ≤ 100 km, 101-169 km, and ≥ 170 km, respectively. The reason for using the above ranges is to ensure a similar sample size between different groups. The popular Taylor diagram, which combines statistical information of correlation coefficient (hereafter CC) and normalized standard deviation (hereafter SD) along with the centered root-mean-square difference into a single plot (Taylor 2001), is utilized to evaluate the performance of various CMIP6 models in reproducing the observed ACRE distribution over the tropical oceans against the satellite-based CERES products.

Results and discussions
To obtain an overview of the connection between model horizontal resolution and radiation simulations, Fig. 1 demonstrates the scatter plots of absolute (uncentered) root-mean-square difference (hereafter RMSD) for the six radiation variables as a function of model horizontal resolution against the CERES-EBAF data. The six radiative fluxes (all under all-sky condition) for evaluation include the upward SW and LW radiative fluxes at TOA (i.e., SW   (Fig. 1c) range between 10 and 17 watt m −2 in the high-resolution group, notably increase to between 11 and 23 watt m −2 in the medium-resolution group, and further increase to between 14 and 28 wattm −2 in the low-resolution group. Except for different ranges of RMSD, SW ↑ top (Fig. 1a), LW ↑ top (Fig. 1b), LW ↓ sfc (Fig. 1d) and LW ↑ sfc (Fig. 1f ) also demonstrate a similar resolution-dependent picture, implying the sensitivity of cloud-radiation simulation to model horizontal resolution. The exceptional low sensitivity of SW ↑ sfc (Fig. 1e) to model horizontal resolution is not surprising as its spatial distribution is controlled by the surface conditions (e.g., land-sea distribution, topography, soil moisture and vegetation), which are relatively steady in space and time compared to clouds.
The overall performance of various CMIP6 models in representing the observed radiative fluxes can be better evaluated using the Taylor diagram (see Fig. 2). For the upward SW radiative flux at TOA ( SW ↑ top ) (Fig. 2a), the low-resolution group merely produces a qualified performance skill (CC = 0.57 and SD = 0.9). The performance skill significantly improves from low-to medium-resolution (CC = 0.72 and SD = 0.9) groups and continues to improve from medium-to high-resolution (CC = 0.75 and SD = 0.91) groups, indicating the sensitivity of model horizontal resolution in simulating the cloud-albedo (cooling) effect. Moreover, most CMIP6 models tend to produce SD values of SW ↑ top smaller than one, implying an underestimate of its spatial variability compared to observations. Similar resolution-dependent results in spatial variability are found in SW ↓ sfc (Fig. 2c) and SW ↑ sfc (Fig. 2e). The sensitivity of radiation simulation to model resolution also exists for the LW components. As shown in Fig. 2b, the simulated upward LW radiative flux at TOA ( LW ↑ top ) improves from low-(CC = 0.82 and SD = 0.93) to medium-resolution (CC = 0.86 and SD = 0.95) groups, and continues to improve to from medium-to high-resolution (CC = 0.89 and SD = 0.97) groups. Similar resolution-dependent results are noted in LW ↓ sfc (Fig. 2d) and LW ↑ sfc (Fig. 2f ) except for slight differences in CC and SD values. Table 2 summarizes the statistical information of model performance for three different resolution groups. In conclusion, the impact of model horizontal resolution on the simulations of SW and LW radiation fluxes at TOA and surface is evident. The finer horizontal resolution models generally produce a better simulation of the cloud-radiation coupling at TOA and surface.
Using Eqs. (1) and (4), Fig. 3 shows the Taylor diagram of various CMIP6 models in reproducing the observed ACRE. As shown, most CMIP6 models properly reproduce the observed ACRE distribution, with CC values ranging from 0.70 to 0.95 and SD values from 0.7 to 1.3 against the CERES-EBAF data. The high-resolution group, on average, produces the best performance (CC = 0.91 and SD = 0.89), followed by the mediumresolution group (CC = 0.89 and SD = 0.91) and, lastly, the low-resolution group (CC = 0.85 and SD = 0.89), which are generally consistent with the results shown in Fig. 2.
To understand where the improvement shown in Fig. 3  exactly comes from, Fig. 4 compares the ACRE distribution derived from CERES-EBAF with those from three different resolution groups of CMIP6 models. As shown in Fig. 4a, positive ACRE occurs over the broader ITCZs, with a peak warming intensity over 40 watt m −2 ; while  Table 1. The orange, green and purple circles denote the ensemble means of high-, medium-and low-resolution groups, respectively. The statistical information of the six radiative fluxes for three different groups of CMIP6 models is presented at the top-right corners Page 7 of 15 Lin and Yu Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:21 negative ACRE appears over the subtropical oceans, with a peak cooling intensity stronger than − 20 watt m −2 over the cold tongue areas, which are very consistent with previous studies using the same CERES-EBAF satellite product (e.g., see Fig. 4d of Allan (2011)). We note that differences of ACRE between various resolution groups are generally smaller within the ITCZs (where ACRE > 0) compared to those in the cold tongue areas (where ACRE < 0) (see Fig. 4a-d for comparison). In short, biases of ACRE are reduced mainly over the Pacific and Atlantic cold tongues as the model horizontal resolution increases.
The opposite signs of ACRE between ITCZs and cold tongue areas shown in Fig. 4 can be linked to the very different radiative forcing between deep and shallow clouds. In practice, the higher cloud-top height associated with deep clouds warms the atmosphere by decreasing the upward emission of LW radiation; while the lower cloud-top height associated with shallow clouds cools the atmosphere through emitting strong downward longwave radiation flux to the Earth's surface (Slingo and Slingo 1988). To elaborate, Fig. 5 shows the spatial distribution of cloud-top pressure derived from the CERES-SYN data averaged over the same period of 2000/03-2014/12. As expected, the spatial distribution of cloud-top pressure is very similar to that of ACRE, with positive ACRE occurring over areas of higher cloud top, with the zero contours of ACRE in CERES-EBAF coinciding well with the contours of 700 hPa cloud-top pressure.
The above arguments can be justified by dividing the tropical domain into positive and negative ACRE areas prior to conducting the statistical analyses. As shown in Fig. 6, while most CMIP6 models produce a better performance over the positive ACRE areas compared to that over the negative ACRE areas, the improvement from low-to medium-resolution groups, or from mediumto high-resolution groups, is small over the positive ACRE areas. In contrast, the improvement is larger over the negative ACRE areas, with significantly higher CC and lower SD values as the model horizontal resolution becomes finer. The reason for such a contrast can be attributed to the distinct spatial sizes between deep and shallow clouds. For instance, based on satellite and aircraft observations, Wood and Field (2011) found that larger cloud sizes (> 300 km) associated with deep convection often occur over the Indo-Pacific warm pool; while smaller cloud sizes (< 100 km) appear over the eastern Pacific cold tongue where shallow convection prevails. Since shallow clouds in nature have a smaller spatial scale, the areas dominated by shallow clouds (ACRE < 0) is thus more sensitive to the model resolution change. This finding is consistent with Bui et al. (2019) who conducted a series of CMA5 (Community Atmospheric Model, version 5) simulations with four different horizontal resolutions (4°, 2°, 1° and 0.5°) and showed that a higher horizontal resolution run inclines to produce more shallow convection compared to the coarser ones.
According to Eqs. (5a) and (5b), we divide ACRE into shortwave (SWACRE) and longwave (LWACRE)  . 3 The Taylor diagram summarizing the performance skills of ACRE simulations in 54 CMIP6 models against the CERES-EBAF observations. The purple, green and orange circles denote the ensemble means of low-, medium-, and high-resolution groups, respectively. The statistical information of ACRE for three different groups of CMIP6 models is presented at the top-right corners Page 8 of 15 Lin and Yu Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:21 components to see which component of radiation dominates the spatial pattern of ACRE. Figure 7 compares the spatial distribution of SWACRE and LWACRE between different resolution groups with the CERES-EBAF data. From CERES-EBAF (Fig. 7a), we note that SWACRE is mostly positive in the tropics, except over the northern Indian Ocean and South China Sea, with values between -5 and 10 watt m −2 . Simulations of SWACRE are all positive (mostly < 5 watt m −2 ) over the tropics, with relatively little dependence on the model horizontal resolution (see  The spatial pattern of ACRE derived from a CERES-EBAF, b high-resolution, c medium-resolution, and d low-resolution groups of CMIP6 models. The color (or contour) interval is 5 watt m −2 Page 9 of 15 Lin and Yu Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:21

Concluding remarks
In the present study, simulations of ACRE from 54 CMIP6 models are compared and evaluated against the satellite-based CERES products to examine the potential impact of model horizontal resolution on ACRE simulations. For ease of comparison, we divide all CMIP6 models into three groups according to their grid size averaged over the tropics (in km 2 grid −1 ). Among the 54 CMIP6 models, the high-resolution group ( < 14, 000 km 2 grid −1 ) consists of 19 members, the medium-resolution group ( 14, 000−40, 000 km 2 grid −1 ) 18 members, and the lowresolution group ( > 40, 000 km 2 grid −1 ) 17 members. Major findings of this study are below: (1) Climatologically, ACRE is positive in the ITCZs but negative in the subtropics and cold tongues, owing to the very different cloud-radiation feedback associated with deep and shallow clouds. (2) The biases of ACRE simulations are mainly contributed by the LW component of cloud-radiative effect (i.e., LWACRE), indicating the dominance of LW cloud-radiation coupling in determining the ACRE distribution over the tropical oceans. (3) From an ensemble mean point of view, the impact of model horizontal resolution on ACRE simulations is evident. The finer horizontal resolution models generally produce a better simulation of the cloud-radiation coupling, especially over the Pacific and Atlantic cold tongues where shallow clouds prevail.
Finally, we would like to use a schematic diagram, with a simple radiation budget analysis respectively over the warm pool (5° S-5° N, 155° E-165° E) and cold tongue (25° S-15° S, 85° W-95° W), to highlight the very different cloud-radiation feedback associated with deep and shallow clouds (Fig. 8). Over the warm pool, Page 10 of 15 Lin and Yu Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:21 high SST facilitates the development of deep convective clusters (e.g., cumulonimbus and congestus clouds), which are often accompanied by anvil clouds near the tropopause. Since the atmosphere is nearly transparent to SW radiation but opaque to LW radiation, the LW component of radiation will dominate the radiative forcing introduced by clouds. As a result, the much lower cloud-top temperature of deep clouds tends to warm the atmosphere (ACRE > 0) by keeping more thermal radiation within the earth's climate system (e.g., SWACRE = 0.7, LWACRE = 39.2 and ACRE = 39.9 watt m −2 ). On the contrary, over the cold tongue, deep convection is suppressed by the compensating subsidence and the inversion layer in the lower troposphere, favoring the formation of shallow clouds (e.g., stratocumulus clouds and trade wind cumuli). As shown in Fig. 8 for the longwave component of CRE at the Erath's surface and TOA, shallow clouds emit much stronger downward longwave radiation at surface compared with that at TOA, thereby leading to the negative value of ACRE over the cold tongue (e.g., SWACRE = 7.2, LWACRE = − 27.8 and ACRE = − 20.6 watt m −2 ). While we've provided the potential impact of model horizontal resolution on ACRE simulations from an ensemble mean point of view, however, the different biases of ACRE simulations in the state-of-art CMIP6 models may not be solely caused by the model resolution change but may be also influenced by other physical processes, such as different treatments of cumulus  Fig. 4, but dividing ACRE into SWACRE (left panels) and LWACRE (right panels), with a and e from CERES-EBAF, b and f from high-resolution, c and g from medium-resolution, and d and h from low-resolution groups of CMIP6 models. The color (or contour) interval is 5 watt m −2 Fig. 8 A schematic depiction of two major cloud types and the estimated CRE from CERES-EBAF averaged over the Pacific warm pool (5° S-5° N, 155° E-165° E; left) and cold tongue (25° S-15° S, 85° W-95° W; right), respectively. The CRE budgets are divided into SW (orange numbers) and LW (green numbers) components at both TOA and surface. The SWACRE (orange numbers with frame) and LWACRE (green numbers with frame) budgets, taken as the differences between TOA and surface (former-later), are also displayed. Positive and negative CRE represent heating and cooling effects, respectively. The unit of radiation budget is watt m −2 Lin and Yu Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:21 parameterization (Wu et al. 2009;Li et al. 2020;Li et al. 2021) and boundary layer air-sea heat exchange scheme (He et al. 2018;Takahashi and Hayasaka 2020), or different designs of model dynamic cores (Jun et al. 2018). Further studies are needed to elucidate the complex cloud-radiation coupling in the CMIP6 models based on more observational and modeling evidences.

Appendix 1: Sensitivity to model vertical resolution
We note that horizontal and vertical resolutions are important in the simulation of cloud-radiation interaction and it is beneficial to improve the performance of climate models through a more balanced selection of horizontal and vertical resolutions, which is better than improving only one side (Roeckner et al. 2006). However, a recent study by Ingram and Bushell (2021) argued that most state-of-the-art climate models already have a fineenough vertical resolution (> 30 vertical levels) such that there is only a weak correlation between increases in vertical resolution and changes in climate sensitivity.
To test the sensitivity of simulated radiation biases to model vertical resolution, we show the root-mean-square deviation for the six simulated radiative fluxes against the CERES data as a function of model vertical resolution (Fig. 9). Unlike the apparent dependence on model horizontal resolutions shown in Fig. 1, the radiation biases are quite insensitive to the vertical resolution change as some lower vertical resolution models even outperform the higher ones. For instance, CESM2 with 100 km horizontal resolution and 32 vertical levels (labeled "7") produces a better performance than CESM2-WACCM with the same horizontal resolution but using 70 vertical levels (label "9"). A similar situation also occurs for a pair of ACCESS models (labeled "1" and "2"). The above results motivate us to focus on the impacts of horizontal resolution on ACRE simulations in CMIP6 models.

Appendix 2: Impacts on tropical circulation and precipitation
This appendix section investigates how tropical circulation and precipitation features differ in different resolution groups and their association with the ACRE biases. To highlight the contrast, we only compare the difference between high-and low-resolution groups because the medium-resolution group exhibits a pattern more or less in between the high-and low-resolution ones.
To explore the connection between simulated ACRE and precipitation of various intensities, we first sort the daily rainfall output into 100 percentile bins according to the rainfall rate. A rainfall event (or day) is defined when the rainfall rate is greater or equal to 0.1 mm day −1 . Accordingly, the first few tenths of percentile bins represent light rain events associated with shallow convection while the last few tenths of percentile bins denote heavy-rain events associated with deep convection (Bui et al. 2019;Bui and Yu 2021). Figure 10 shows the spatial distributions of ACRE averaged respectively over total rainfall events ( > 0.1 mm day −1 ), light rain events ( < 5 mm day −1 ) and heavy rain events ( > 10 mm day −1 ) for both high-and low-resolution groups. As shown, light rain events well explain the ACRE cooling features (including spatial pattern and intensity) over the cold tongue and subtropical oceans, and the high-resolution group generates a cooling intensity closer to the total ACRE compared to the low-resolution one (see Fig. 10a-d for comparison). In contrast, heavy-rain events dictate the ACRE Fig. 9 Same as Fig. 1, but showing the dependence of RMSE on model vertical resolution. Models classified as high-, medium-and low-vertical resolution groups are highlighted in orange ( ≥ 80 levels; 19 models), green (41-79 levels; 19 models) and purple ( ≤ 40 levels; 16 models), respectively. All radiative fluxes are under all-sky condition and are averaged over the global tropical ocean from 30° S to 30° N Page 12 of 15 Lin and Yu Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:21 Fig. 10 The spatial distribution of ACRE averaged over all rainfall events ( > 0.1 mm day −1 ) for a high-resolution b low-resolution groups of CMIP6 models. Likewise, c and d show ACRE distribution averaged only over light rain events ( < 5 mm day −1 ) while e, f show ACRE distribution averaged only over heavy rain events ( > 10 mm day −1 ), respectively, for the high and low-resolution groups. The color interval is 7 watt m −2 Lin and Yu Terrestrial, Atmospheric and Oceanic Sciences (2022) 33:21 warming features over the warm pool regions, accounting for approximately 50% of the total ACRE warming (see Fig. 10a, b, e and f for comparison). We also note that the ACRE warming pattern derived from heavy rain events shows little dependence on model resolution change. The above results readily confirm that the simulated ACRE is more sensitive to model resolution change in areas dominated by shallow convection (e.g., cold tongue and subtropical oceans).
To see how tropical circulation responds to ACRE biases in different horizontal resolution groups, Fig. 11 shows the spatial patterns of ACRE and 850-hPa wind anomalies, calculated as the differences between model simulations and observations, composited over the high-and low-resolution groups. As shown, the lowresolution group produces a greater magnitude of ACRE biases across most of the tropical domain compared to the high-resolution one. Particularly, the low-resolution group generates greater warm ACRE anomalies (or, alternatively, underestimates the magnitude of ACRE cooling shown in Fig. 4a) over the southeastern Pacific and Atlantic (i.e., cold tongue) and the subtropical northeastern Pacific. In response to these warm ACRE anomalies, the low-resolution group produces a stronger response of wind anomalies in opposite direction to the mean trade winds, leading to weaker easterly trade winds over the above areas compared to the high-resolution group.