Fast and Slow Responses of Atmospheric Energy Budgets to Perturbed Cloud and Convection Processes in an Atmospheric Global Climate Model

Cloud and convection strongly modulate atmospheric energy budgets, but the latter's responses often vary across timescales because of complex interactions between fast and slow processes. Here, based on atmospheric model simulations at intermediate state between weather and climate timescales, we investigate how the responses in the global‐mean atmospheric energy budgets evolve over time after simultaneously perturbing various cloud‐scale processes. We find that the responses in radiative and sensible heat fluxes converge much more rapidly compared to condensation heat associated with precipitation, which is attributed to the compensating feedback effects of precipitation on longwave cooling and shortwave heating. Because of energy conservation, uncertainty in long‐term precipitation simulations can be substantially reduced by constraining the fast processes of radiative and sensible heat fluxes. These findings can help economize on computational resources required for model tuning and serve as a crucial link between the convective‐scale and equilibrium‐state outcomes within the model.

• The responses in radiative and sensible heat fluxes converge much more rapidly compared to precipitation • The rapid radiative response is attributed to the compensating feedback effects of precipitation on longwave cooling and shortwave heating • Constraining the fast processes of radiative and sensible heat fluxes can alleviate uncertainty in long-term precipitation simulations

Supporting Information:
Supporting Information may be found in the online version of this article.
processes on model behaviors across a wide range of variables (e.g., temperature, clouds, precipitation, aerosol, wind energy, etc.) and spatial scales (e.g., from large-eddy to convection-permitting and to global scales) (e.g., Carslaw et al., 2013;D. M. H. Sexton et al., 2021;B. Yang et al., 2017).For example, Murphy et al. (2004) found that PPE simulations using a single model projected wide ranges for the changes of many global and regional variables in response to a doubling of atmospheric carbon dioxide levels, which were comparable to those produced by multi-model ensembles.Alternatively, Ben Yang et al. (2013) focused on parametric sensitivities in current climate simulations, with the main purpose to understand the impacts of individual physical processes and how they can interact with grid-scale variables and global circulations.
As we know, long-term GCM simulations can consume abundant computational resources, especially for PPE applications that need many simulation members.Therefore, several recent studies (G.Lin et al., 2016;Ma et al., 2015;Ma et al., 2014;Qian et al., 2018;Wan et al., 2014) have used the short-term PPE strategy instead of the traditional PPE to study the model responses to perturbations in cloud and convection processes.The basic idea is that some variables' biases in long-term climate simulations are close to their errors on weather timescales, which are often shown in the first several days of the simulations and mainly caused by fast processes associated with clouds, convection, and so on (Phillips et al., 2004;Qian et al., 2018;Rodwell & Palmer, 2007;Wan et al., 2014).
Although climate mean-state biases can be highly related to short-term errors in the models, it is not always the case for some important climate variables (D.M. H. Sexton et al., 2019).In fact, many aspects of the climate system related to the atmosphere thermal state and circulation respond much more slowly than clouds do when perturbing cloud-scale processes (G.Lin et al., 2016), which can in turn affect the formations of cloud and convection.Therefore, the responses of different components within the system could vary across timescales until a new equilibrium is finally reached, making it a big challenge to understand the cause-effect relationship among different aspects of the climate system.
In this study, we follow the strategy of short-term PPE using an atmospheric GCM, but extend the length of each member from several days to two months, to provide model responses at intermediate state between weather and climate timescales.Our main purposes are to: (a) investigate the timescale dependence of responses in global-mean atmospheric energy budgets to cloud and convection processes and (b) explore the physical connections between fast responses and slow responses.Our results suggest that some kind of fast processes could serve as reliable indicators for understanding slow responses in the model, which can help economize on computational resources required for model tuning and better understand the linkage between the convective-scale outcomes and the equilibrium-state outcomes within the model.

Model and Parameters
We use the Grid-point Atmospheric Model of the Institute of Atmospheric Physics (IAP) of the Chinese Academy of Sciences (CAS) version 3, that is, GAMIL3, which is the atmospheric component of the Flexible Global-Ocean-Atmosphere-Land System Model Grid-point version 3 (FGOALS-g3) developed at IAP CAS (Li et al., 2020).GAMIL3 is configured with 26 vertical levels and horizontal resolution of about 2° in our PPE simulations.
The number of PPE members increases nonlinearly with the number of parameters because of the interaction effects of parameters on model simulations.To find out the most influential parameters, we first performed a PPE that includes 1024 8-year-long simulations, in which 34 physical parameters within cloud, turbulence, and convection parameterizations in GAMIL3 are perturbed.Based on these results and previous PPE works, we narrow down the number of parameters from 34 to 16 for the short-term PPE in this study, which include 3 parameters related to boundary-layer turbulence and shallow convection, 4 related to deep convection, 7 related to cloud microphysics, and 2 related to cloud macrophysics (Table S1 in Supporting Information S1).

PPE Strategy
Here, a total of 256 parameter sets are generated using the quasi-Monte Carlo (QMC) sampling method.Each parameter set corresponds to a PPE member that consists of 12 two-month simulations initialized at 00 UTC on the first day of each month of a model year.Following Qian et al. (2018), the initial conditions are derived from a multiyear simulation using default parameter values driven by climatological monthly-mean SST.The simulations of the first several days are more related to "fast processes," which respond directly to the perturbed cloud and convection (Ma et al., 2014).With increased integration length, "slow processes" related to thermodynamic or dynamic feedbacks should become more important, making the parametric sensitivities vary with time (Decremer et al., 2014;Xie et al., 2012).

Analysis Method
In Qian et al. (2018), the results on day 3 (i.e., the third day) of each simulation were used for their analyses to avoid both model shock right after model initialization and contaminations of parametric signal by the chaotic nature of atmosphere that are usually nonnegligible after day 5 (Wan et al., 2014).Therefore, before conducting parametric sensitivity analyses, we discard the first two-day simulations and compute the running average for the remain results as below: ,  = 3, 5, . . ., 59 ,  = 4, 6, . . ., 60 where Y is a particular quantity of interest, and t is the index of day.Thus, Y ave (t) is approximate the average of Y during the second half of the selected period.The sample size increases for larger t to reduce the impacts of natural variability.Meanwhile, neglecting the first half of any temporal interval reduces the overlap between the time windows for running averages on different days.Hence, the correlations between different days are mainly attributed to their physical connections rather than just a math problem.We find using a different window for averaging have a very weak impact on our analyses.
The relative contributions of various parameters to the inter-member variances in the PPE are quantified using the generalized linear model (GLM) (Mackinnon & Puterman, 1989), which is applied to build a nonlinear fitting equation between output variables and input parameters.The total variances of the output variables are decomposed into the portions explained by each individual parameter and their interactions.More details about the GLM sensitivity analysis framework can be referred to Hou et al. (2012).

Convergence in the Simulated Responses of Precipitation and Energy
Previous studies have indicated the strong parameter impacts on model behaviors (e.g., Qian et al., 2018;B. Yang et al., 2013).Because the relative importance of fast and slow processes is different for different variables, some variables' responses are expected to be less dependent on timescales than others.The atmosphere can acquire or lose energy via radiation, sensible heat, and condensation heat from precipitation process.Thus, we first focus on three objective variables, that is, global-mean precipitation, surface latent heat flux (LH), and the net gain of radiative and sensible heat in the atmosphere (NGRS).Note that the variation of NGRS in the model is mostly attributed to the change in radiative flux.These three variables jointly determine the budgets of energy and moisture in the atmosphere, that is, the net changes in moisture, diabatic heat, and moist static energy (MSE) of the atmosphere equate to LH minus precipitation, precipitation (or condensation heat) plus NGRS, and LH plus NGRS, respectively.
The correlation (R 2 ) across the PPE between simulations on a given day (see Section 2.3) and their counterparts on day 60 for the three selected variables (Figure 1) are used to represent the evolution features of model responses.In the first 10 days of the simulation, R 2 is low (less than 0.3) for the global-mean precipitation (black line).It takes about 30 days to reach 0.9 and gradually approaches 1 during the second half of the simulation, indicating a strong timescale dependence of the precipitation (or condensation heat) response to the perturbated model physics.Similar result is observed for the global-mean LH (red line) except for a relatively higher R 2 in the first several days.Different from precipitation and LH, the response in NGRS is more stable (blue line), with R 2 exceeding 0.9 throughout the entire simulation.This means compared to precipitation and LH, NGRS reaches equilibrium at a much faster rate, which is mainly because of the fast responses of clouds (figure not shown) to the perturbed parameters (Qian et al., 2018;Xie et al., 2012).
With increased timescale, the global-mean precipitation, LH, and NGRS have to balance with one other due to the conservations of moisture and energy.The net changes (in unit of energy) of moisture, diabatic heat, and MSE in the atmosphere all drop from approximate 5 W m −2 at the beginning of the simulation to 0.5 W m −2 on about day 45 (Figure S1 in Supporting Information S1), indicating that the length of two months is nearly sufficient for the atmosphere to reach a quasi-equilibrium state in terms of global-mean analyses.
The lead-lag relationships between any two of the three variables are given in Figure 2 to understand how the balances are established as time evolves.For all the pairs, the contemporaneous R 2 (diagonals in Figure 2) is close to 1 on day 60, conforming the quasi-equilibrium state at the end of the simulation.Some differences are detected among the three pairs.We can see that the distribution pattern of the precipitation-LH relationship (under the control of moisture conservation) (Figure 2a) is almost symmetrical on the two sides of the diagonal.In other words, we do not detect any precipitation response that is leading LH, and vice versa.Therefore, both precipitation and LH experience slow adjustments simultaneously and match each other at the end of the simulation.Differently, the relationship between precipitation and NGRS (under the control of diabatic heat conservation) Figure 2. Lead-lag relationships (i.e., R 2 ) between any two of the three variables, that is, global-mean precipitation, LH, and NGRS, with the diagonals representing the contemporaneous correlation (i.e., lead time equals to zero).(Figure 2b) shows an asymmetrical pattern, and R 2 is much larger when NGRS leads precipitation compared to precipitation leads NGRS.Notably, R 2 between precipitation on day 60 and NGRS on day 3 exceeds 0.9, suggesting that the long-term precipitation simulation is highly determined by the response of NGRS during the first several days of the simulation.Therefore, uncertainty regarding the long-term precipitation simulations could be substantially reduced by constraining NGRS at shorter timescales, which can be achieved by employing tools like parameter optimization (B.Yang et al., 2012) or Bayesian analysis (Qian et al., 2018).Note that noise in a model might be very prevalent when averaging over short periods, so we need to estimate the impact of noise on model metrics based on the day-to-day variances in the model, and utilize it as a scaling factor in normalizing discrepancies between observations and model outputs during the constraining process (Qian et al., 2018).Here, we find the day-to-day variance for the global-mean NGRS contributes less than 5% to the total variance across different PPE members, suggesting that the global-mean NGRS at short timescales can be efficiently constrained.Similar to the precipitation-NGRS pair, the LH-NGRS relationship (under the control of MSE conservation) (Figure 2c) also exhibits an asymmetrical distribution, with high R 2 when NGRS leads LH.

Impacts of Individual Cloud/Convection Processes and Related Mechanisms
In this section, we aim to investigate how the process-level perturbations can affect the model responses presented above.We use GLM to quantify the individual and interaction effects of parameters on the simulations, which show very different evolution features with time for different variables (Figure 3).
Given the slow convergence in the simulated precipitation response (Figure 1), it is expected that the parametric sensitivity for precipitation is highly dependent on timescale (Figure 3a).Apparently, at the beginning of the simulation, the deep-convection parameter zm_ke related to the evaporation of precipitation plays the most important role in the precipitation simulation, which contributes to more than 50% of the total variance.The macrophysics parameter cf_rhminl1, which is the threshold of relative humidity for low-cloud formation, is the second most important parameter.With the increase of timescale, the contribution from zm_ke decreases and nearly disappears after day 20.In contrast, the impacts of the microphysics parameter mg_dcs related to the conversion from cloud to rain becomes increasingly important, explaining about 50% of the total variance.Meanwhile, the parameter zm_rhcrit related to the relative humidity threshold for triggering deep convection starts to play a considerable role in the precipitation simulation.
The parametric sensitivity of LH also shows a strong dependence on timescale (Figure 3b).Unlike precipitation, cf_rhminl1 and the boundary-layer parameter uw_ccrit are the two most important parameters for the LH simulation in the first several days, which explains the relatively low R 2 between precipitation and LH at that time (Figure 2a).As timescale increases, the importance of cf_rhminl1 decreases, but still contributes to about 20% of the total variance in the LH simulation.Similar to the precipitation results, mg_dcs becomes the most important parameter for LH in the second half of the simulation.
Compared to precipitation and LH, the sensitivity of NGRS to parameters shows a weak variation with timescale (Figure 3c) because of its rapid convergence.Throughout the entire simulation, mg_dcs and rh_rhminl1 are the two most important parameters for the NGRS simulation.Because both precipitation and LH need to adjust toward matching NGRS (Figure 2), the parametric sensitivity of NGRS in the first days of the simulation largely determines the sensitivities of precipitation and LH on longer timescales, which has important implications for model tuning applications.
Above analyses have revealed the adjustment of long-term precipitation response to short-term NGRS, whereas no such adjustment is observed in the opposite direction.However, the underlying causes remain unclear given the belief that feedback effects from precipitation on radiation were nonnegligible, as previously suggested (B.Yang et al., 2012).To understand the radiation-precipitation relationship in our simulations, we show in Figure 4 the responses of precipitation, LH, and some other process-level variables to several key parameters as a function of the timescale.
We first investigate the impacts of the parameter mg_dcs (black lines in Figure 4), which is the most important for NGRS throughout the entire simulation and for precipitation and LH in the second half of the simulation.In the model, NGRS and its sensitivity are mainly contributed by shortwave heating (SWH) and longwave cooling (LWC) in the atmosphere.It is found that larger mg_dcs causes weakened LWC (Figure 4j) but has a weak effect on SWA (Figure 4i).The response in LWC can be explained by the rapid increase in ice water path (IWP; Figure 4h), which acts to heat the atmosphere, especially the mid-to-high troposphere (L'Ecuyer & McGarragh, 2010).Meanwhile, the precipitation response to mg_dcs is small at the beginning of the simulation.Given the reduced LWC but nearly-unchanged condensation heat from precipitation, the atmosphere must warm up.As we can see, the atmosphere temperature gradually increases from day 3 to day 60, with the warming rate higher at 500 hPa than at 850 hPa (Figures 4e and 4f) as explained earlier, which enhances the atmospheric stability.As a result, convection is continuously suppressed until a new equilibrium is reestablished between convective heating and LWC (Figures 4a and 4b).Also, because the increasing temperature tends to release more long-wave radiation, we do see a weakening trend in the LWC response during the first half of the simulation.However, this feedback effect is overall weak compared to the convection response, making precipitation gradually adjust to balance NGRS.Meanwhile, the atmosphere becomes more humid (Figure 4d) due to the suppressed precipitation.The more water vapor in the atmosphere but less precipitation suggests a weakened circulation, which is likely responsible for the reduced near-surface wind speed and surface LH flux (Figures 4l and 4k).In general, the responses of precipitation, radiative fluxes, and LH, as well as their temporal variations are mainly occurring in the tropics featured with high temperature and moisture availability (Figures S2 and S3 in Supporting Information S1).
The parameter zm_ke (red lines in Figure 4) controls the evaporation rate of convective precipitation.Therefore, larger zm_ke causes less convective and total precipitation but more stratiform precipitation at the beginning of the simulation (Figures 4a-4c).As time evolves, more moisture remains in the atmosphere (Figure 4d), which in turn decreases the efficiency of precipitation evaporation.Therefore, we can see a tendency for the response of convective precipitation to decrease in the first half of the simulation.At the same time, the increased water vapor in the lower troposphere leads to both stronger LWC and SWH (Figures 4j and 4i).However, because of their offsetting effects, the sensitivity of NGRS to zm_ke is small.As a result, the imbalance between NGRS and condensation heat from precipitation causes a cooler atmosphere (Figures 4e and 4f), preventing the atmosphere from holding more water vapor.Then, the response of total precipitation gradually decreases, following the response of NGRS.Note that although with a relatively weak impact on the global-mean precipitation at the end of the simulation, the parameter zm_ke can still strongly affect regional precipitation (Figure S3b in Supporting Information S1).We can also see an increasing trend in the near-surface wind speed (Figure 4l), which might be attributed to the increased fraction of stratiform precipitation.Compared to convective precipitation, stratiform precipitation is featured with stronger spatial heterogeneity, which acts to intensify the circulation (B.Yang et al., 2013).However, because of the canceling effects between the moister low troposphere and stronger wind, LH is only slightly increased (Figure 4k).
The last parameter investigated here is cf_rhminl1 (blue lines in Figure 4), which is important for the LH simulations.Compared to the above two parameters, the responses of almost all the selected variables to cf_rhminl1 show very weak dependence on timescale.The direct response by using larger cf_rhminl1 (i.e., higher threshold of relative humidity for low-cloud formation) is a considerable reduction in liquid water path (LWP; Figure 4g), which further leads to weaker LWC (L'Ecuyer & McGarragh, 2010) (Figure 4j) in the atmosphere.Given the importance of low-cloud radiative cooling in maintaining shallow circulation, the reduced LWC might lead to weakened near-surface wind (Figure 4l) and thus less LH flux (Figure 4k).The low-level moisture is nearly unchanged (Figure 4d), suggesting that the moistening effect due to less-active cloud formation is rapidly compensated by the reduced LH flux at the surface.

Summary and Discussions
We investigated the fast and slow responses of atmospheric energy budgets to cloud and convection processes in an AGCM based on short-term PPE simulations, with each PPE member consisting of 12 two-month simulations to provide model responses at intermediate state between weather and climate timescales.Our results indicated that, in terms of global mean, the responses of radiative and sensible heat fluxes to the perturbed parameters converge much more rapidly compared to precipitation and the LH flux.Along with the model integration, the global-mean precipitation, LH, and NGRS (i.e., the sum of the radiative and sensible heat fluxes) have to balance one other due to energy conservation principles, making both precipitation and LH experience slow adjustments to match NGRS at the end of the simulation.Hence, a substantial reduction in uncertainty regarding long-term precipitation simulations can be achieved by constraining the radiative and sensible heat fluxes at shorter timescales.This finding highlights the potential of fast processes as reliable proxies for understanding slow responses, which can help modelers economize on computational resources required for model tuning in model development process.
We further found that the initial increase in NGRS can be predominantly attributed to perturbations in the mg_ dcs parameter.A larger mg_dcs value tends to stabilize the atmosphere by modifying the vertical contrast in atmospheric heating, resulting in the suppression of convection.This adjustment process requires approximately 30 days to reach equilibrium.In contrast, the initial response in convection, primarily driven by variations in the zm_ke parameter, has nearly offsetting effects on LWC and SWH, leading to an imbalance in diabatic heating rate within the atmosphere.Consequently, the accumulated water vapor (due to reduced convection) eventually precipitates.The above feedback processes explain the underlying cause for the adjustment of long-term precipitation response to short-term radiative and sensible heat fluxes, whereas no such adjustment is observed in the opposite direction.This discovery serves as a crucial link between the convective-scale outcomes and the equilibrium-state outcomes within the model, which are the main concerns of the model physics parameterization community and the model application community, respectively.
In the future, we intend to explore the timescale dependences of model responses at regional scales, which can be different from global-mean results and more related to circulation changes.It is also important to acknowledge that within the current framework of the atmosphere model, we are unable to quantify the model's responses to parameter perturbations associated with the ocean processes.The primary challenge to comprehensively understand the ocean processes is the computational cost associated with running a substantial number of lengthy ensemble simulations with a coupled model.Although beyond the scope of this paper, it is crucial to recognize the necessity for future research to incorporate a coupled model and account for the influence of ocean processes.Specifically, we should place more emphasis on studying the energy and momentum fluxes at the air-sea interface.A reasonable starting point would be to focus on persistent model biases observed in coupled simulations, such as the double-ITCZ and cold tongue problems over the eastern Pacific (Oueslati & Bellon, 2015) and the dipole pattern of precipitation biases over the tropical Indian Ocean (Long et al., 2020).

Figure 1 .
Figure 1.Evolution of correlation (R 2 ) across the PPE between simulations on different days and their counterparts on day 60 (after running average) for global-mean precipitation, latent heat flux (LH), and the net gain of radiative and sensible heat in the atmosphere (NGRS).

Figure 3 .
Figure 3. Fractions of the variance of global-mean (a) precipitation, (b) LH, and (c) NGRS explained by individual parameters and parameter interactions (i.e., "Int") as a function of simulation length.

Figure 4 .
Figure 4. Responses of different global-mean variables to several key parameters as a function of simulation length.The 256 simulation members are divided into eight discreet bins in terms of each parameter value, and the response to a given parameter is defined as the differences between the eighth and first bin based on that parameter.