The atmosphere model in TaiESM is based on CAM version 5.3 (Neale et al., 2010). The dynamic core is Finite-Volume (Lin, 2004) in a hybrid sigma-pressure vertical coordinate. The Rapid Radiative Transfer Model for GCMs (RRTMG; Iacono et al., 2008) with two-stream approximation, correlated k-distribution, and Monte Carlo Independence Column Approximation (McICA; Pincus et al., 2003) is employed to calculate radiative fluxes and heating rates in the atmosphere. The shallow convection and moist turbulence schemes are based on those reported by Park and Bretherton (2009) and Bretherton and Park (2009), respectively. A two-moment cloud microphysics scheme (Morrison and Gettelmen, 2008) is used to predict changes in the mass and number of cloud droplets and to diagnose stratiform precipitation.

The land model in TaiESM is CLM4 (Oleson et al., 2010; Lawrence et al., 2011). The surface albedo is primarily a function of vegetation, soil moisture, solar zenith angle, and snow reflectivity calculated by the Snow, Ice, and Aerosol Radiative Model (SNICAR; Flanner and Zender, 2006), which considers the aerosol deposition of black carbon and dust, effective size of snow grains, and vertical profile of heating. As the albedo of a grid box is determined, it is then adjusted to include the topographic effect on surface solar radiation.

The parameterization for 3D radiation–topography interactions is to evaluate the impact of topography on surface solar radiation, including insolation on various slopes and aspects, shadow cast by nearby mountains, and reflections between surfaces (Lee et al., 2013). It is developed on the basis of numerous “exact” Monte Carlo calculations that simulate the scattering, reflection, and absorption of photons within the 3D atmosphere and surface (Chen et al., 2006; Liou et al., 2007; Lee et al., 2011). The parameterization adjusts surface albedo so that the solar radiation absorbed by the surface in the land model corresponds to the results of the Monte Carlo calculation. Several geographic parameters are used for input, including the slope, aspect, sky view factor, terrain configuration factor, standard deviation of elevation within a grid box, and solar zenith and azimuth angles. Gu et al. (2012) and Liou et al. (2013) demonstrate that this topographic effect can increase the amount of snowpack in the valley and enhance the snowmelt in mountains in the WRF simulations over the western United States. Lee et al. (2015, 2019) also demonstrate that incorporating this parameterization into the Community Climate System Model version 4 (CCSM4) can significantly improve the surface energy budget over the Rocky Mountains and the Tibetan Plateau and thus reduce the systematic cold bias in the CMIP5 models.

The sea ice and dynamic ocean components of TaiESM are from the CICE4 (Hunke and Lipscomb, 2008) and POP2 (Smith et al., 2010) of Los Alamos National Laboratory, respectively. The River Transport Model (RTM; Oleson et al., 2010) is designed to route liquid and ice runoff to the ocean as one of the freshwater input to POP2. The configurations of CICE4, POP2, and RTM in the fully coupled TaiESM simulations are identical to those in CESM1.2.2. Note that there is no land ice model in TaiESM. Therefore, the formation of sea ice from the discharge of the ice sheet to the ocean is not simulated.

To save computational resources, a zero-dimensional slab ocean model without dynamical process is commonly used to simulate the thermodynamic interaction between the atmosphere and ocean. In TaiESM, an efficient 1D mixed-layer model is coupled with the atmosphere component to reveal the impact of the fast evolution in upper-ocean layers. The one-column ocean model Snow–Ice–Thermocline (SIT; Tu and Tsuang, 2005; Tsuang et al. 2009) is designed to simulate the sea surface temperature (SST) and upper-ocean temperature variations with a high vertical resolution, including cool skin, diurnal warm layer, and mixed layer of the upper ocean. SIT calculates changes in temperature, momentum, salinity, and turbulent kinetic energy driven by vertical fluxes parameterized using the classical K approach. Cool skin is derived by considering merely molecular transport for vertical diffusion of heat in the skin layer, where the skin layer thickness is calculated as described by Artale et al. (2002). Beneath the skin layer, eddy diffusivity is determined according to a second-order turbulence closure approach (Gaspar et al., 1990), and the 1 m vertical discretization is deployed down to a 10 m depth for resolving diurnal warm layer. Because of the lack of ocean circulation in the one-column ocean model, the calculated ocean temperatures are weakly nudged to climatology for ocean below 10 m depth to avoid climate drift. SIT and the atmospheric model exchange SST and fluxes at every time step in the tropics (30∘S–30∘ N), whereas climatological SST drives the atmospheric model elsewhere. Note that SIT is not integrated into the dynamic ocean model (POP2); therefore, fully coupled TaiESM simulations do not include SIT.

The preliminary version of TaiESM was very cold compared with CESM1.2.2 using the preindustrial greenhouse gas concentrations and aerosol emissions. The most apparent change was the significant increase in cloud cover, particularly low clouds, which was probably induced by GTS cloud macrophysics and SNAP aerosol schemes. Therefore, several parameters associated with cloud formation were adjusted to reduce shortwave cloud forcing. We first explored that aerosol–cloud interactions were very strong in TaiESM with the SNAP scheme. Therefore, the activation rate of aerosols to cloud condensation nuclei was reduced by 10 % in the microphysics scheme to weaken the aerosol indirect effect. The sizes of detrained liquid particles from shallow convection and solid particles from deep convection were increased from 10 µm in CESM1.2.2 to 14 µm and from 15 to 25 µm, respectively. Larger detrained particles have smaller cloud optical depth and shorter suspension time in the air when the detrained water content is the same. Both effects can reduce cloud albedo. Although RHc is removed from the GTS scheme for grid boxes with the presence of condensates, it is still required for the formation of clouds in a cloud-free grid box. The value of RHc was increased from 0.8 in the free atmosphere in CESM1.2.2 to 0.85 in TaiESM to make cloud formation less efficient. After these adjustments, the global mean surface temperature of TaiESM in the preindustrial simulation is comparable to that of CESM1.2.2 while the radiation imbalance at the top of the atmosphere (TOA) is minimized. Note that this model tuning is made only at the spatial resolution of about 1∘. Additional tuning would be required for stable simulations at higher or lower resolutions.

Figure 4 illustrates the time series of several global mean variables in TaiESM piControl. The long-term global mean TOA net flux is 0.086 W m-2, and it decreases by 0.0054 W m-2 in 500 years, but insignificantly. Furthermore, the mean surface net flux is 0.081 W m-2 with an almost identical decreasing trend as TOA net flux. The imbalance at TOA causes heating of the whole model system, and the comparatively smaller imbalance at the surface indicates that a smaller part of excessive energy remains in the atmosphere in piControl. Consequently, the long-term trend of surface air temperature (SAT) is 0.0088 K century-1 in 500 years, which is statistically significant. By contrast, the trend of SST is 0.0047 K century-1, only about half of the SAT trend and insignificant. By breaking down the surface net flux, we found that the energy exchange between the atmosphere and land is less than 10-5 W m-2, whereas the net flux into the ocean is 0.114 W m-2 (figures not shown). The excessive energy enters the deep ocean and leads to a steady increase in global mean ocean temperature of 0.030 K century-1. Therefore, even after a 1000 years' simulation, the system does not reach the thermodynamic equilibrium. In addition, considering that the heat capacity of the entire ocean is approximately 1000 times larger than the atmosphere, the heating rates of the atmosphere caused by the residual net flux (0.005 W m-2) are too small compared with the heating rate of the ocean. It implies that an unknown energy leak may exist in the coupling between the atmosphere and ocean, which requires further investigation in programming to fix this problem.

The annual mean time series of sea ice area in the Northern Hemisphere (NH) and Southern Hemisphere (SH) are exhibited in the bottom panels of Fig. 4. The Arctic sea ice has a small but significant trend of -0.01×106 km2 century-1, corresponding fairly well to the slight warming of the entire model. By contrast, the linear trend of the sea ice area in the Southern Ocean over the 500-year span is almost 0, even though the variation is much larger. The minimal change in the sea ice area indicates that the energy gain of the cryosphere could be negligible compared with other model components. The global mean sea surface salinity (SSS) reduces significantly by -0.0036 g kg-1 century-1. However, it can be found that SSS is almost constant with a slope of about 10-4 g kg-1 century-1 after year 700. On the other hand, there is a small but significant decreasing trend of the global mean ocean salinity of 1.3×10-4 g kg-1 century-1, which is very close to the trend of SSS in the last 300 years.

The long-term means of several variables in piControl runs performed by CESM1.2.2 and TaiESM are listed in Table 1. The TOA net flux in TaiESM and CESM1.2.2 are both within 0.09 W m-2. The magnitude of imbalance is acceptable, but it could lead to warming of the entire Earth system. The SAT and SST in TaiESM are higher than those in CESM1.2.2 by 0.42 and 0.23 K, respectively. Shortwave (SW) net flux at TOA in TaiESM is larger than CESM1.2.2 by 2.24 W m-2, which might be the primary cause of higher surface temperatures and consequently result in larger longwave (LW) net flux at TOA of 2.23 W m-2. The difference in the clear-sky net SW flux at TOA is only 0.66 W m-2, suggesting that the surface albedo difference is small, whereas the contribution from the difference in cloud reflection is larger. Although the high and low cloud covers in TaiESM are larger than those in CESM1.2.2, the magnitude of SW cloud forcing (SWCF) is smaller in TaiESM. It indicates that clouds in TaiESM are less reflective than that those in CESM1.2.2. By contrast, the differences in clear-sky net LW flux at TOA and LW cloud forcing (LWCF) are 1.67 and 0.59 W m-2, respectively; therefore, the warmer surface and atmosphere have greater contribution to additional outgoing longwave radiation (OLR) in TaiESM. However, the amount of high cloud in TaiESM is substantially larger than that in CESM1.2.2. This implies that the high clouds in TaiESM could be optically thinner. The different relation between cloud forcing and cloud cover in SW and LW in TaiESM is probably due to the GTS scheme, which can produce a larger fraction but less dense clouds compared with the cloud macrophysics scheme in CAM5.

Figure 5 illustrates changes in the global mean near-surface temperature anomaly of TaiESM and two observations – Berkeley Earth Surface Temperature (BEST; Rohde et al., 2013) and Goddard Institute for Space Studies Surface Temperature (GISTEMP; Lenssen et al., 2019) – by using the mean temperature of 1951–1980 as the benchmark. The warming trend of TaiESM is weaker than the observation data during 1850–1935. The evolution of SAT in TaiESM exhibits fluctuation similar to observations, particularly before 1900, but with smaller amplitudes. The magnitudes of cooling induced by major volcanic eruptions, such as Krakatoa (1883), Santa Maria (1902), Agung (1963), and Pinatubo (1991), in TaiESM is close to those in the observational data, implying that the radiative forcing due to stratospheric aerosols is in good agreement with the observations. After 1950, the change in SAT of TaiESM follows the observations and captures the trend of global warming very well. The warming rate of TaiESM during 1950–2005 is 1.12 K century-1, comparable with 1.16 and 1.27 K century-1 of BEST and GISTEMP, respectively.

Figure 6a demonstrates the comparison in the total cloud fraction between TaiESM and the Moderate Resolution Imaging Spectroradiometer (MODIS) Level 3 product during 2001–2012. TaiESM overestimates the total cloud fraction by approximately 3 % globally with a root-mean-square difference (RMSD) of 14.07. Almost all of the Arctic Ocean is overcast in TaiESM, which is approximately 30 % higher than observational data. Cloud fraction is also severely overestimated over the Antarctic continent and the Southern Ocean. TaiESM produces too much cloud over the southern branch of the Intertropical Convergence Zone (ITCZ) in the central and eastern Pacific, implying the prevalence of double ITCZ, which will be discussed in a subsequent section. An excessive amount of clouds is also noted in the Maritime Continent, western equatorial Indian Ocean, and most of the land areas. By contrast, cloud fraction is remarkably underestimated in the Amazon Basin and the subtropical ocean, particularly the stratocumulus near the western coasts of continents. Compared with the synergic CloudSat and Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data during 2006–2010 (Kay and Gettelman, 2009), low clouds in TaiESM are systematically underestimated over the entire tropical and subtropical regions, as shown in Fig. 6c, whereas they are overestimated in high-latitude areas. The total cloud fraction in the tropics is high because of excessive high cloud in the model (Fig. 6b).

Clouds can substantially modulate the radiation field because of its high reflectivity in SW and high absorptivity in LW. Figure 7a illustrates the comparison of SWCF in TaiESM with that in Clouds and the Earth's Radiant Energy System–Energy Balanced and Filled data (CERES–EBAF; Kato et al., 2018) over 2000–2015. In terms of the global mean, SWCF in TaiESM is very close to that of the observational data with a difference of only 0.19 W m-2. Although there is excessive cloud over the polar regions in TaiESM, such as the Southern Ocean near the Antarctic continent and almost all of the Arctic Ocean, SWCF is not as strong as that in the observational data. It could be contributed from the optically thin polar clouds due to the GTS cloud macrophysics scheme and from the positive bias of sea ice albedo in the Arctic Ocean in TaiESM (not shown). In the subtropical and tropical regions, SWCF generally follows the spatial pattern of total cloud fraction – i.e., a larger cloud fraction produces stronger SWCF, such as the storm track in the North Pacific, southern branch of ITCZ, Maritime Continent, western tropical Indian Ocean, and south of the Sahara Desert. However, SWCF is too strong over the Amazon Basin in TaiESM, even though there is an underestimated amount of clouds. By contrast, because of the underestimated total cloud fraction, SWCF in TaiESM is too weak over the stratocumulus areas off the California and Peru coasts as well as over the subtropical Pacific, Atlantic, and Indian oceans in the SH.

The global mean of LWCF in TaiESM is significantly weaker (by 4.31 W m-2) than that in CERES–EBAF. As illustrated in Fig. 7b, TaiESM underestimates LWCF worldwide, and the magnitude of the LWCF bias generally follows the bias of high cloud. Positive LWCF bias only exists in some regions over the tropical ocean with too many high clouds in TaiESM. However, although more high clouds exist along the northern branch of the ITCZ, LWCF is weaker in the model. The remarkable negative LWCF bias seems incompatible with the overestimated high clouds because more high clouds should be able to intercept more LW radiation from the surface. This inconsistency is probably due to the lower altitude of the high clouds or the less dense clouds in TaiESM.

Figure 8a illustrates the comparison of SST between TaiESM and the Hadley Centre Sea Ice and Sea Surface Temperature dataset (HadISST; Rayner et al., 2003). The regions with a long-term mean sea ice concentration larger than 15 % are not used for calculations of the mean and RMSD. The global mean bias of SST in TaiESM is 0.01 K with an RMSD of 1.05 K. The overestimated SST over the Southern Ocean and subtropical South Pacific is probably induced by additional downward SW radiation because of the inaccurate microphysical properties of polar clouds (Kay et al., 2016) and the negative bias of cloud fraction as shown in Fig. 6a. The warm bias in the major upwelling regions off the western coasts of the Americas and Africa is a common deficiency in many climate models (Griffies et al., 2009), caused by insufficient spatial resolution of the atmosphere and ocean. Warm bias can also be found in the North Atlantic including the coast of North America, the Labrador Sea, and south of Greenland. Negative biases exist in most of the North Pacific and subtropical North Atlantic, probably because of overestimated wind stress in these regions.

Although the SST bias in TaiESM is very small, the global mean SAT in TaiESM is substantially colder than the observational data (by 0.49 K with an RMSD of 1.68 K). This result indicates that the temperature over land and sea ice in TaiESM is severely underestimated (Fig. 8b). Cold bias exists over most of the polar regions, the Tibetan Plateau, and tropical land areas (e.g., Amazonia, central Africa, and southeast Asia). It must be due to the excessive cloud that reflects excessive sunlight. SAT bias over the ocean generally follows SST bias, except that the SAT bias in the subtropical South Pacific is very small despite the warm SST bias.

Figure 9 illustrates the mean precipitation over 1979–2005 in TaiESM and Global Precipitation Climatology Project (GPCP; Huffman et al., 2009) 1-Degree Daily (1-DD) data. TaiESM overestimates the global precipitation by 0.38 mm d-1 with an RMSD of 1.11 mm d-1. The most pronounced bias in TaiESM is the double ITCZ – a common issue in most contemporary GCMs (Lin, 2007; Hirota and Takayabu, 2013) and in CESM1 (C.-c. Wang et al., 2015). The precipitation rates of both the northern and southern ITCZ branches are extremely strong. The overly intense convection strengthens the subsidence and consequently produces too little rainfall along the Equator. Precipitation is also overestimated in the Maritime Continent, while it is severely underestimated in Borneo. In TaiESM, the land–sea contrast in precipitation is not as apparent as in the observation over the warm pool region. The South Pacific convergence zone (SPCZ) is also too strong and too parallel to the ITCZ. The dipole bias in the tropical Indian Ocean, excessive rainfall in the western part and scant rainfall in the eastern part, still exists as in NCAR models (Gent et al., 2011). There is also a double ITCZ bias in the Atlantic Ocean in that the southern branch is too strong and the northern branch is too weak. In South America, precipitation over the Amazon Basin is considerably underestimated, whereas excessive orographic precipitation can be found along the Andes (Cook et al., 2012).

Figure 10 presents the annual mean of sea ice concentration in the Arctic Ocean and Southern Ocean in TaiESM, and the black lines indicate the 15 % mean concentration from the National Snow and Ice Data Center (NSIDC) Climate Data Record (CDR) of passive microwave sea ice concentration version 3 (Peng et al., 2013), during 1979–2005. In the NH, TaiESM severely overestimates sea ice concentration over the North Pacific, particularly in the Sea of Okhotsk. TaiESM also overestimates sea ice in the Barents Sea and near the east coast of Greenland but slightly underestimates sea ice in the Labrador Sea. In the SH, sea ice in TaiESM is generally in agreement with the observation. Excessive sea ice is noted in the area south of New Zealand, but in the Indian Ocean region, sea ice is scant. This deviation follows the SST bias presented previously.

Figure 11 illustrates the temporal evolution of the annual sea ice concentration in TaiESM compared with that in the CDR. The change in NH sea ice in TaiESM generally captures the trend in the observation before 2002. However, there is an increase in TaiESM in the last 4 years, in contrast to an accelerated reduction in observational data. This sea ice increase could be a fluctuation in a climate simulation, and it requires longer integration for additional investigation. In the SH, a decreasing trend of the sea ice concentration can be found in TaiESM, whereas it remains almost unchanged in observational data. Because there is no land ice model in TaiESM, the discharge of the ice sheet from the Antarctic continent to the Southern Ocean, the major source of SH sea ice, cannot be simulated accurately. Consequently, the sea ice concentration in the SH could be controlled primarily by temperature in TaiESM, leading to an unrealistic temporal evolution.

To evaluate the ENSO behavior during 1976–2005 in TaiESM, the HadISST sea surface temperature and MRE2 reanalysis data in the same period are used. The observed and simulated spectra of the Nino 3.4 index presented in Fig. 12 reveal the adequate ability of TaiESM in reproducing the periodicity of El Niño. The observed Nino 3.4 index exhibits three statistically significant peaks between 2 and 6 years. TaiESM is able to simulate three spectral peaks with slightly shorter periods, while the amplitudes of all three peaks are larger than observations.

The anomalies of surface temperature, sea level pressure, and near-surface wind in December–February when the ENSO is at the mature stage are shown in Fig. 13, which is the composite of five and six El Niño events in observation and TaiESM simulation, respectively. The simulated SST anomaly (SSTA) is evidently larger in both amplitude and spatial coverage than the observed one and with the maximum shifted westward to the central equatorial Pacific compared with the observation, which is the common bias in many climate models. The horseshoe-like negative SSTA in the northwest, southwest, and west of the positive SSTA is stronger and covers much larger areas than the observed one. This over-simulated SSTA structure leads to some marked biases in the simulated atmospheric circulation and temperature, such as the cold bias in the western North Pacific and Maritime Continent, warm bias in the western Indian Ocean and Bering Sea, and too strong a convergence in the eastern equatorial Pacific.

The overall performance of the TaiESM historical simulation during 1979–2005 is evaluated by comparing it with other CMIP5 models following the metrics introduced by Gleckler et al. (2008). Figure 14 shows the normalized space–time root-mean-square error (RMSE) of selected variables from TaiESM, several CMIP5 models, and a multi-model ensemble (MME) against reanalysis and observation datasets. The reference data of air temperatures (TA), zonal and meridional wind velocities (UA and VA), and geopotential height (ZG) at various pressure levels, as well as the surface air temperature (TAS), are from the Collaborative Reanalysis Technical Environment (CREATE) Multi-Reanalysis Ensemble version 2 (MRE2; Potter et al., 2018). The observational precipitation (PR) data are from GPCP. Upward longwave radiation in the total sky (RLUT) and clear sky (RLUTCS) and upward shortwave radiation in the total sky (RSUT) and clear sky (RSUTCS) are from CERES-EBAF. It is expected that the errors of CMIP5 MME are generally the smallest. TaiESM has the smallest bias in PR among all CMIP5 models, and its performance in RSUT and RLUT is also very good. The relatively poor performance in TAS is primarily due to the cold bias over land and sea ice areas. The RMSEs of all variables in TaiESM are smaller than the median CMIP5 error, indicating that the performance of TaiESM is above average among all CMIP5 models. The performance of TaiESM is comparable to that of CESM1-CAM5, and they have similar strengths and weaknesses. Note that three variables with an RMSE larger than the median in CESM1-CAM5 are all improved in TaiESM.