A Library of Large-Eddy Simulations Forced by Global Climate Models

Abstract

Advances in high-performance computing have enabled large-eddy simulations (LES) of turbulence, convection, and clouds. However, their potential to improve parameterizations in global climate models (GCMs) is only beginning to be harnessed, with relatively few canonical LES available so far. The purpose of this paper is to begin creating a public LES library that expands the training data available for calibrating and evaluating GCM parameterizations. To do so, we use an experimental setup in which LES are driven by large-scale forcings from GCMs, which in principle can be used at any location, any time of year, and in any climate state. We use this setup to create a library of LES of clouds across the tropics and subtropics, in the present and in a warmer climate, with a focus on the transition from stratocumulus to shallow cumulus over the East Pacific. The LES results are relatively insensitive to the choice of host GCM driving the LES. Driven with large-scale forcing under global warming, the LES simulate a positive but weak shortwave cloud feedback, adding to the accumulating evidence that low clouds amplify global warming.

Introduction

Low clouds play an important role in Earth's energy budget, but they are poorly represented in global climate models (GCMs). Despite some improvements in recent decades, large biases remain in the clouds simulated by the current generation of GCMs. Most GCMs underestimate low cloud cover in the tropics and subtropics (Cesana & Waliser, 2016; Klein et al., 2013; Vignesh et al., 2020). The negative model bias can be as large as 50% in stratocumulus regions near the coast (Brient et al., 2019). In shallow cumulus regions, most GCMs overestimate the optical thickness of low clouds to achieve a reasonable global-mean energy balance despite the low bias in cloud cover. This is referred to as the “too few, too bright” bias (Nam et al., 2012). In addition to and in part as a consequence of their poor simulation in the present climate, how low clouds respond to global warming is a key source of uncertainty in predictions of climate change. While the low-cloud feedback is positive in most GCMs, the magnitude of the feedback has a large intermodel spread and is strongly correlated with the equilibrium climate sensitivity (Bony & Dufresne, 2005; Bony et al., 2006; Schneider, Teixeira, et al., 2017; Zelinka et al., 2020).

It is challenging for GCMs to simulate low clouds because their resolution, which is on the order of 100 km in the horizontal, is too coarse to resolve the boundary layer turbulence and convection controlling the clouds. As a result, GCMs rely on parameterizations to represent these processes, and inadequacies in the parameterizations lead to biases in GCM-simulated clouds. However, large-eddy simulations (LES) can directly resolve cloud dynamics and provide high-fidelity simulations in limited areas, even though they still rely on parameterizations of microphysics. While global LES will not be feasible for decades (Schneider, Teixeira, et al., 2017), data from LES can be used to train and improve GCM parameterizations with data assimilation and machine learning approaches (Schneider, Lan, et al., 2017). So far, LES used for calibrating and evaluating GCM parameterizations have typically been run at a few specific locations, usually associated with field campaigns (e.g., Rauber et al., 2007; Siebesma et al., 2003; Stevens et al., 2005). Idealized large-scale forcing fields are often used in studies comparing LES with GCMs and/or single column models (Zhang et al., 2012, 2013). Regular comparison of LES and single column models that are driven by forcings from GCMs or reanalysis has been done at a few meteorological sites (Neggers et al., 2012). However, the potential of using LES to systematically inform GCM parameterizations has not yet been fully harnessed.

In Shen et al. (2020), we presented a framework for driving LES by large-scale forcings from GCMs. This study uses this framework to expand the data set available for training GCM parameterizations by generating a library of LES across a range of cloud regimes, representing different regions, times of year, and climate states. We focus on low clouds over the East Pacific, using LES driven by large-scale forcings from comprehensive GCMs in both the current and a warmer climate. We use the large-scale forcing from GCMs rather than reanalysis because we found it difficult to close the energy and moisture budgets in reanalysis. As a result, driving the LES with reanalysis requires strong relaxation of temperature and humidity to prevent it from drifting away from observations, as commonly done in previous studies (Atlas et al., 2020; McGibbon & Bretherton, 2017; Zhang et al., 2016).

Section 2 describes the GCM and LES models used in the study and key features of the forcing framework. Section 3 describes simulation characteristics in the LES and compares the LES-simulated with GCM-simulated clouds. Section 4 summarizes the conclusions and discusses potential uses of the data presented in this study.

Methods Experimental Setup

The large-scale forcing is derived from the cfSites output in the Coupled Model Intercomparison Project Phase 5 (CMIP5) archive. cfSites includes high-frequency output at different locations of instrumented sites and field campaigns, as well as a number of climate regimes where the inter-model spread of cloud feedbacks is large (Bony et al., 2011). Dal Gesso and Neggers (2018) have used large-scale forcings derived from the cfSites data to drive single column models and explored the boundary layer cloud response to climate change. The cfSites data has also been used to investigate the diurnal cycle of cloud feedbacks in GCMs (Webb et al., 2015). In this study, we focus on low-cloud regions (mean cloud top height lower than 3 km) over the East Pacific (Figure 1). We use 5-year (2004–2008) averaged large-scale forcings in different months (January, April, July, and October) from the AMIP experiment, which is forced by observed sea surface temperatures (SSTs) and sea ice concentration. The time-averaged forcing does not have a diurnal cycle. We use time-averaged forcing as a first step because it requires shorter LES simulations to reach statistically steady state, and it results in a more manageable LES and forcing library, with smaller files than would be required for storing time-dependent forcing. Also, we found the cloud changes with time-averaged forcing in the warmer climate to be much more robust than those with time-varying forcings because of the large internal variability in the latter case. To test the sensitivity of the results to the host model, we use large-scale forcings primarily from two GCMs: HadGEM2-A and CNRM-CM5. We choose these two models as the tropical low-cloud reflection response to global warming in HadGEM2-A and CNRM-CM5 are at the higher and lower end of the range of CMIP5 models, respectively (Brient & Schneider, 2016). To explore how clouds change in a warmer climate, we run simulations with large-scale forcings from the AMIP4K experiment, where SSTs are increased uniformly by 4 K from the AMIP experiment. In the supplementary information, we additionally show results for a CMIP6 GCM, CNRM-CM6-1, for comparison with the two CMIP5 GCMs. (At the time of this writing, CNRM-CM6-1 is the only CMIP6 model providing the necessary large-scale forcings).

Figure 1. cfSites locations used in this study. The sites cover the transition from stratocumulus to shallow cumulus over the East Pacific. The red crosses highlight site 17 and site 23, two locations on which we focus in this paper. They represent stratocumulus and shallow cumulus cloud regimes, respectively.

The LES are performed using the Python Cloud Large-Eddy Simulation (PyCLES) code (Pressel et al., 2015). PyCLES solves the anelastic equations with specific entropy and total water specific humidity as prognostic thermodynamic variables and uses a third-order, three-stage strong stability preserving Runge-Kutta scheme (Shu & Osher, 1988). The performance of the model on standard test cases has been described in previous papers (Pressel et al., 2015, 2017; Tan et al., 2016). The simulations are forced with prescribed SSTs from the GCM. Surface fluxes are calculated using a bulk scheme with drag coefficients obtained from Monin-Obukhov similarity theory (Byun, 1990). Radiative energy fluxes are calculated with the Rapid Radiative Transfer Model (RRTM; Iacono et al., 2008). The top-of-atmosphere insolation and the insolation-weighted average of solar zenith angle are prescribed from the GCM. Cloud microphysical processes are represented using a one-moment warm-rain microphysics scheme based on Kessler (1995). Subgrid-scale turbulent fluxes are modeled using the Smagorinsky-Lilly closure (Lilly, 1962; Smagorinsky, 1963). We use a doubly periodic domain that is 6,000 m wide in the horizontal and 4,000 m tall in the vertical. The horizontal and vertical resolutions are 75 and 20 m, respectively. The time step is dynamically adjusted to maintain the Courant number close to 0.7; it is on the order of 1 s. The simulations are initialized from the 5-year averaged GCM profiles and are run for 6 simulated days. The results are averaged over the last day, when most simulations have reached a quasi-steady state.

Forcing Framework

The forcing framework is similar to that in Shen et al. (2020). Here we briefly summarize the large-scale forcings in the LES and describe the differences to Shen et al. (2020).

Subsidence

Large-scale subsidence gives rise to a source in the specific entropy (s) and specific humidity (q_t) equations, [Image Omitted. See PDF] [Image Omitted. See PDF]here, w = dz/dt is the vertical velocity, $$\left(\tilde{\cdot }\right)$$ denotes a GCM value, and ⟨⋅⟩ denotes the time mean. To estimate the time-averaged vertical velocity from the pressure velocity in GCMs, we follow the approximation in Atlas et al. (2020), [Image Omitted. See PDF]where $${\tilde{\omega }}_{s}$$ is the pressure velocity at the surface and ρ is the density. The function f(p) is sigmoidal in pressure p and is equal to 1 at the surface, decaying to 0 at the tropopause: [Image Omitted. See PDF]here, p_s is the surface pressure and p_t is set to 250 hPa. This approximation ensures that the vertical velocity is 0 at the surface.

Advection

Horizontal advection and vertical eddy advection are prescribed directly from the GCM as [Image Omitted. See PDF] [Image Omitted. See PDF]where c_p is the isobaric specific heat capacity of air; T is temperature; and s_d and s_v are specific entropies of dry air and water vapor, respectively. The terms S_hadv and J_hadv represent horizontal advection of specific humidity and temperature, and S_veddy and J_veddy represent vertical eddy advection of specific humidity and temperature. All four advection terms are derived from the GCM. The cfSites output includes total advective tendencies of specific humidity (S_adv) and temperature (J_adv). We obtain the horizontal advective tendencies from the total advective tendencies as the residuals [Image Omitted. See PDF]and [Image Omitted. See PDF]the vertical eddy advective tendencies are derived as [Image Omitted. See PDF]and [Image Omitted. See PDF]

Relaxation

As the geostrophic winds or large-scale pressure gradients are not available in the cfSites data set, unlike in Shen et al. (2020), the large-scale momentum forcing is not applied. Instead, the horizontal winds are relaxed to the GCM profiles on a timescale of 6 hr. Free-tropospheric temperatures T and humidities q_t are relaxed to GCM profiles to prevent drifting from realistic conditions. The relaxation timescale varies with height as [Image Omitted. See PDF]relaxation forcing is commonly used when driving LES or single column models with GCMs or reanalysis, and the timescale is usually a few hours (e.g., Neggers et al., 2012; Randall & Cripe, 1999; Zhang et al., 2012). In this study, we set τ_r = 24 hr, z_r = 3,500 m, and z_i = 3,000 m, for simplicity and clarity, irrespective of low-cloud regime. (In principle, at least the relevant height scales for the relaxation should depend on the large-scale flow).

Characteristics of Large-Scale Forcings at the cfSites Locations

Figures 2a and 2b show the large-scale vertical velocity at different sites in the two GCMs in July. The cfSites locations on which we focus in this study are characterized by large-scale subsidence. The maximum subsidence is about 1 cm s⁻¹ off the coast of California (site 17) and decreases when moving away from the coast. The vertical profiles of large-scale subsidence between the two GCMs are similar over most regions, but show some differences near the coast of Peru (sites 2 and 3), where CNRM-CM5 has much stronger subsidence at site 2 and weak ascent in the boundary layer at site 3.

Figure 2. Vertical profiles of (a,b) large-scale vertical velocity, (c,d) horizontal advection of temperature, and (e,f) horizontal advection of specific humidity in (a,c,e) HadGEM2-A and (b,d,f) CNRM-CM5 at different sites in July.

Figures 2c–2f show the horizontal advection of temperature and specific humidity at different sites in the two GCMs in July. There is advective cooling and drying in the lower troposphere in both the northeast and southeast Pacific, which is consistent with northeasterly and southeasterly winds, respectively. In HadGEM2-A, the boundary layer height increases from the coast to the open ocean, and there is advective heating and moistening right above the boundary layer. The horizontal advective tendencies in CNRM-CM5 are qualitatively similar to those in HadGEM2-A; however, they show larger variability among different sites, and again substantial differences near the coast of Peru.

Figures 3a–3f show the SSTs and surface fluxes at different sites in July. The SSTs increase from the coast to lower latitudes by about 10 K. The GCM-simulated latent heat fluxes have a minimum of about 50 W m⁻² near the coast of Peru (sites 2–3) and a maximum of over 200 W m⁻² in the tropical ocean (sites 11–15). The sensible heat fluxes are smaller than 20 W m⁻² for most sites. The LES simulate similar spatial variations in the latent heat fluxes, albeit on average with about 12% weaker magnitudes than those in the HadGEM2-A GCM. The relative differences in the sensible heat flux between the LES and GCMs are larger (up to about 64%); however, overall the surface fluxes are dominated by the latent heat fluxes. The discrepancies in surface fluxes are partially due to different surface wind speeds between the LES and GCMs, as shown in Figures 3g and 3h. For CNRM-CM5, however, the smaller surface wind speeds in the LES are not consistent with the stronger sensible heat fluxes, suggesting some differences in the LES- and GCM-simulated boundary layer properties. The LES and GCMs are further compared in Section 3.2.

Figure 3. (a,b) Surface temperature, (c,d) sensible heat flux, (e,f) latent heat flux, and (g,h) surface wind speed at different sites in July. Blue and orange dots represent the LES and the GCM, respectively. The host GCMs are (a,c,e,g) HadGEM2-A and (b,d,f,h) CNRM-CM5.

Results LES-Simulated Low Clouds

Figure 4 shows the cloud cover, cloud liquid water path (LWP), cloud base and cloud top at different sites in the LES driven by HadGEM2-A. The LES sample a wide range of cloud regimes. Near the coasts of Peru (sites 2–4) and California (sites 17–18), the simulations produce stratocumulus with cloud cover near 100%. The cloud cover decreases rapidly when moving away from the coast and is about 20%–30% in shallow cumulus regions over the open ocean. The transition from stratocumulus to shallow cumulus is also seen in the decrease in LWP and the increase in cloud top height from the coast to the open ocean.

Figure 4. (a) Cloud cover, (b) cloud liquid water path (LWP), (c) cloud base height, and (d) cloud top height at different sites in the LES driven by HadGEM2-A in different seasons. Missing points indicate the cloud top height is higher than 3,000 m.

The cloud properties at different locations have distinct seasonal variations. In the stratocumulus regions off the coasts, cloud cover and LWP are higher in July and October in both hemispheres. In the shallow cumulus regions over the Southeast Pacific, cloud cover and LWP peak in July and show low values in January and April. The cloud base is highest in July and lowest in January, while the cloud top is generally higher in January than in July, suggesting some seasonal variation in the thickness of clouds. In the shallow cumulus regions over the Northeast Pacific, cloud cover and LWP show high values in April and low values in July. The cloud base is highest in April and lowest in July, and the seasonal variation in the cloud top generally follows that in the cloud base height.

The cloud properties in the LES driven by CNRM-CM5 are shown in Figure 5. Unlike the LES driven by HadGEM2-A, this LES does not simulate a stratus cloud layer near the coast of Peru (site 3), consistent with the differences in large-scale properties to HadGEM2-A, and the propensity for mean ascent in the region in CNRM-CM5 (Figure 2). In the shallow cumulus regions, the cloud fraction and LWP in some seasons are higher than that in the LES driven by HadGEM2-A, which largely results from differences at the cloud top. The LES driven by CNRM-CM6-1 simulate similar cloud properties (Figure S1 in Supporting Information S1).

Figure 5. Same as Figure 4 but for LES driven by CNRM-CM5.

Figures 6 and 7 show the vertical profiles of large-scale forcings and cloud properties of two sites over the Northeast Pacific in HadGEM2-A in July, representing the cloud regimes of stratocumulus (site 17) and shallow cumulus (site 23). The large-scale subsidence is stronger at site 17 than at site 23. There is horizontal advective cooling and drying in the boundary layer at both sites, and their tendencies are stronger at site 17. The advective tendencies are consistent with the lower-level winds, which are northerly near the coast (site 17) and northeasterly away from the coast (site 23).

Figure 6. Vertical profiles of (a) large-scale vertical velocity, (b) horizontal advection of temperature, (c) horizontal advection of specific humidity, (d) zonal wind, (e) meridional wind, (f) total water specific humidity, (g) liquid potential temperature, (h) vertical velocity variance, (i) cloud fraction, and (j) cloud liquid water specific humidity in the LES driven by HadGEM2-A at site 17 in July. The dashed lines represent the GCM profiles.

Figure 7. Same as Figure 6, but for site 23 in July.

Figure 8 shows the timeseries of cloud cover and LWP at sites 17 and 23. The LES reach quasi-steady states in 1–2 days at both sites, although the relatively small domain size leads to high-frequency oscillations especially for shallow cumulus. The LES simulate stratocumulus under strong subsidence and advective cooling and drying at site 17, with a cloud top at around 1,000 m and a cloud fraction close to 100% (Figure 6i). The stratocumulus layer is slightly decoupled from the subcloud mixed layer, as seen in the vertical profiles of total water specific humidity, liquid potential temperature, and vertical velocity variance below the inversion (Figures 6f–6h). This decoupling may be due to the strong advective cooling at the bottom of the cloud layer (Figure 6b). At site 23, the LES simulates a shallow cumulus layer with a cloud base at around 500 m and a cloud top at around 1,600 m. The cloud fraction and the corresponding vertical velocity variance have two peaks (Figures 7i and 7h): just above the lifted condensation level and just below the inversion. The anvil resulting from the detrainment of cumulus updrafts is ubiquitous in the LES simulations of shallow cumulus sites.

Figure 8. Time series of (a) cloud cover and (b) liquid water path in the LES driven by HadGEM2-A. Blue and orange lines represent sites 17 and 23 in July, respectively.

Comparison to GCM and Sensitivity to Large-Scale Forcing

We compare the LES-simulated boundary layer properties with those in the host GCM, HadGEM2-A (Figures 6d–6j, 7d–7j). At site 17 in July, the GCM produces a less well-mixed boundary layer and weaker inversion than the LES. The GCM and LES-simulated winds differ by about 1 m s⁻¹ in the boundary layer. The cloud base in the GCM is very close to the surface and lower than that in the LES by about 400 m, while the cloud top heights are similar between the GCM and the LES. The maximum cloud fraction and cloud liquid water in the GCM are much smaller than in the LES, and LWP in the GCM is about 40% smaller. At site 23, the GCM produces a higher and deeper shallow cumulus layer. The difference in wind velocities is similar to that at site 17. The cloud base in the GCM is slightly lower than in the LES, while the cloud top in the GCM is about 500 m higher. The cloud fraction and cloud liquid water in the GCM are much larger. The GCM only produces one peak in cloud fraction in the middle of the shallow cumulus layer, as opposed to the two peaks at the bottom and the top of the cloud layer in the LES.

The mismatch between LES and GCM boundary layer heights sometimes leads to unrealistic large-scale forcings in the LES. For example, when the inversion height in the LES lies below that in the GCMs, the dry advection in the GCM's boundary layer is applied to the free troposphere above the inversion in the LES. This results in a local minimum in the specific humidity (e.g., Figure 7f), which may lead to excessive entrainment drying, affecting the cloud. Another potential issue is that the advective warming right above the GCM boundary layer may strengthen the buoyancy jump at the inversion in the LES and may thus affect entrainment at the cloud top. Note that this issue may be amplified for time-varying forcings. To prevent some of these issues, previous studies using GCMs and/or reanalysis to drive LES have often nudged the specific humidity to some reference humidity when it drops below a threshold (Blossey et al., 2013; Tan et al., 2016). In addition, idealized horizontal advective tendencies are often specified to balance the vertical advective tendencies and the radiative cooling (Blossey et al., 2013; Zhang et al., 2012). To keep the forcing framework simple and easily applied to different GCMs and cloud regimes, we do not specify these additional constraints on the large-scale forcings, at the expense of occasional mismatches between LES and GCM vertical structures.

Figure 9a compares LWP at all sites simulated by HadGEM2-A and LES. The spread of LWP at different sites is much smaller in the LES than in the GCM, and there is no correlation between the LES and the GCM. In the shallow cumulus regions, LWP is systematically larger in the GCM, mostly resulting from a deeper cloud layer. The difference can be as large as 60 g m⁻² at several sites (e.g., over the North Pacific). In the stratocumulus regions, the LWP differences between the GCM and the LES are smaller, although the maximum cloud fraction in the stratocumulus layer in the GCM is always much smaller than in the LES. This is because the cloud layer is usually much thicker in the GCM (e.g., Figures 6i and 6j).

Figure 9. Scatter plot of LWP in the LES and GCM at different sites in different seasons. Blue and orange dots represent stratocumulus (Sc, defined as cloud fraction larger than 0.9) and shallow cumulus (Cu) in the LES, respectively. The host GCMs are (a) HadGEM2-A and (b) CNRM-CM5.

The large-scale forcing used to drive the LES is dependent on the host GCM. Figure 10 shows the vertical profiles of large-scale forcings and cloud properties in the LES driven by the two GCMs, HadGEM2-A and CNRM-CM5, at sites 17 and 23 in July. At site 17, CNRM-CM5 has a stronger subsidence, a stronger advective cooling, and a weaker advective drying in the boundary layer compared to HadGEM2-A. Consistent with the stronger subsidence, the cloud top is lower in the LES driven by CNRM-CM5, but the cloud thickness and the maximum cloud fraction and cloud liquid water in the LES driven by forcing from the two GCMs are similar. While there are some differences in the GCM-simulated cloud profiles, the cloud layers in both GCMs are thicker than that in the LES, and the maximum cloud fraction and cloud liquid water are smaller. At site 23, compared to HadGEM2-A, CNRM-CM5 has a weaker subsidence and a stronger boundary layer cooling and drying. The LES driven by forcings from the two GCMs yields similar vertical profiles of shallow cumulus in general, except that the cloud fraction at the cloud top is larger in the LES driven by CNRM-CM5. However, the differences between the GCMs are much larger. Compared to HadGEM2-A, the GCM-simulated shallow cumulus layer in CNRM-CM5 has a lower cloud top and much smaller cloud fraction and cloud liquid water.

Figure 10. Vertical profiles of large-scale vertical velocity, horizontal advection of temperature, horizontal advection of specific humidity, cloud fraction, and cloud liquid water specific humidity for (a) site 17 and (b) site 23 in July. Blue and orange lines represent LES driven by the large-scale forcing from HadGEM2-A and CNRM-CM5, respectively. Dashed lines represent the host GCMs.

Figure 11 compares the differences in the GCM- and LES-simulated LWP at all sites in different seasons. The magnitudes of the differences between the LES are smaller than 15 g m⁻² for most cases. The difference between the GCMs are much larger. In general, LWP in CNRM-CM5 is smaller than in HadGEM2-A, and the magnitudes of the differences are as large as 40–50 g m⁻² at several sites. The magnitudes of the differences averaged over all cases in the LES and the GCMs are 2.0 and 23.9 g m⁻², respectively. As a result of the smaller LWP, CNRM-CM5 is slightly closer to LES compared to HadGEM2-A, although there is still not much correlation between the GCM- and LES-simulated LWP (Figure 9b). The LWPs in the two CNRM GCMs are more similar, but the differences in LWP between LES driven by CNRM-CM5 and CNRM-CM6-1 are still smaller than those between the GCM-simulated LWPs (Figure S2 in Supporting Information S1).

Figure 11. LWP differences (CNRM-CM5 minus HadGEM2-A) at different sites between (a) LES driven by large-scale forcing from the GCMs and (b) the GCMs themselves. Gray colors indicate the cloud top in at least one of the LES simulations is higher than 3,000 m. In the GCMs, LWP is calculated as the vertical integral of cloud liquid water from the surface to 3,000 m.

The differences between the LES and the GCM should be interpreted with caution. One caveat is that the LES is forced by long-time mean forcing, while in the GCM the large-scale forcing varies with time. Using time-varying forcing in the LES is computationally expensive as it requires much longer simulations to achieve steady states. For a more systematic comparison with the LES data presented in this paper, one should use a single column model with the same parameterizations as in the GCM and with the same time-mean forcing used to drive the LES. Nevertheless, the fact that the LES forced by large-scale forcings from the two GCMs agree with each other while the GCMs simulate very different clouds still suggest possible biases in the GCM parameterizations.

Low Cloud Response to Climate Change

One advantage of the forcing framework is that it can be applied to generate LES of changed climates. While previous studies have used LES to simulate cloud responses to idealized climate perturbations (e.g., Blossey et al., 2013; Blossey et al., 2016; Bretherton et al., 2013; Radtke et al., 2021; Tan et al., 2017), driving LES with a GCM allows more realistic representation of changes in large-scale forcings. In this study, we run a set of simulations with large-scale forcings from the AMIP4K experiment, where SST is uniformly increased by 4 K.

Figure 12 shows the change in large-scale forcings and cloud properties in the control and warmer climates at site 17 and site 23 in July in LES driven by HadGEM2-A. At site 17, the large-scale subsidence in the free troposphere is about 20%, or 5% K⁻¹, weaker in the warmer climate. The horizontal advective cooling weakens in the subcloud layer and near the top of the cloud, but strengthens in the lower part of the cloud layer; the change in the advective drying is small. Consistent with weakened subsidence, the cloud top rises slightly in the warmer climate. The cloud base rises more than the cloud top, resulting in a slight thinning of the stratocumulus layer and a decrease in LWP by 13%. The thinning of the cloud layer is likely related to the deepened specific humidity jump at the inversion under warming, which results in more efficient entrainment drying at the cloud top (e.g., Bretherton & Blossey, 2014; Bretherton et al., 2013). At site 23 (Figure 12b), the weakening of the large-scale subsidence is not uniform with height. Above the cloud top, the subsidence weakens by about 8%, or 2% K⁻¹. The change in the advective tendency of temperature in the boundary layer is small, while the magnitude of the horizontal advective drying increases in the subcloud layer and near the cloud top. Overall the shallow cumulus layer does not change much under warming. There is a slight decrease in cloud fraction near the cloud base. The cloud top rises slightly, and there is an increase in the anvil cloud fraction and cloud liquid water. However, given the large sensitivity of the anvil cloud fraction to large-scale forcings (Figure 10), the change may not be robust across LES driven by different GCMs.

Figure 12. Vertical profiles of large-scale vertical velocity, horizontal advection of temperature, horizontal advection of specific humidity, cloud fraction, and cloud liquid water specific humidity for (a) site 17 and (b) site 23 in July. Blue and orange lines represent LES driven by the large-scale forcing from the AMIP and AMIP4K experiments in HadGEM2-A, respectively.

Figure 13 shows the changes in cloud properties at all sites in different seasons. Near the coasts, the changes in cloud cover and LWP in response to warming are sometimes large, which is usually associated with a change in cloud regimes. However, in shallow cumulus regions, cloud cover and LWP generally do not change or decrease slightly under warming, leading to a small positive shortwave cloud feedback (a small decrease in the magnitude of the shortwave cloud radiative effect). In general, the LES forced by CNRM-CM5 also simulate slightly weaker shortwave cloud radiative effects under warming (Figure 14). The magnitude of the cloud response is stronger at several sites in the shallow cumulus regions, which is mostly due to the change in the anvil cloud fraction and cloud liquid water. The changes in cloud properties under warming in the LES driven by CNRM-CM6-1 are less uniform (Figure S3 in Supporting Information S1). The changes in cloud properties are stronger near the coast. In the shallow cumulus regions, the shortwave cloud feedback is in general positive over the Northeast Pacific but negative over the Southeast Pacific.

Figure 13. Percentage changes in (a) cloud cover, (b) LWP, and (c) shortwave cloud radiative effect resulting from a 4K increase in SST in the LES driven by HadGEM2-A. Gray colors indicate the cloud top in the LES in the current or warmer climate is higher than 3,000 m.

Figure 14. Same as Figure 13 but for LES driven by CNRM-CM5.

Figure 15 compares the LES- and GCM-simulated shortwave cloud feedback averaged over all seasons for the two GCMs. The shortwave cloud feedback is mostly positive in both the LES and the GCM, except at a few sites in CNRM-CM5. While near the coast the feedback magnitude can be as large as 6 W m⁻² K⁻¹ in the LES driven by HadGEM2-A, over the shallow cumulus regions the magnitude is generally smaller than 1 W m⁻² K⁻¹. This is consistent with estimates of shallow cumulus feedback in previous LES studies (Bretherton, 2015; Nuijens & Siebesma, 2019) and with observationally constrained low cloud feedbacks in recent studies (Cesana & Del Genio, 2021; Myers et al., 2021). However, the shallow cumulus feedback in HadGEM2-A is around 2–4 W m⁻² K⁻¹, much stronger than that in the LES. In CNRM-CM5, the shortwave cloud feedback is weaker and closer to that in the LES (Figure 15b). The comparison for CNRM-CM6-1 is shown in Figure S4 in Supporting Information S1. On average, the CNRM-CM6-1 simulated shortwave cloud feedback is also closer to that in the LES, although the differences are large at some sites over the Northeast Pacific.

Figure 15. LES (blue) and GCM (orange) simulated shortwave cloud feedback under a 4 K increase in SST. The host GCMs are (a) HadGEM2-A and (b) CNRM-CM5. The results are averaged over all seasons.

We emphasize again that the difference in the cloud feedback between the LES and GCM should be interpreted with caution. Besides the difference in time-mean and time-varying large-scale forcings as mentioned in Section 3.2, the shortwave cloud feedback in the GCM includes contributions from mid-level and high-level clouds, which are not present in the LES. The difference may also be smaller for other GCMs, as the low-cloud feedback in HadGEM2-A is stronger than in most other GCMs. The climate change simulations provide not only an opportunity to investigate mechanisms governing cloud feedbacks in LES under more realistic changes in large-scale forcings. They are also a valuable data set for evaluating and calibrating GCM parameterizations, as previous studies have shown it is difficult to guarantee that data-driven parameterizations trained on the current climate remain accurate in a warmer climate (O’Gorman & Dwyer, 2018).

Conclusions and Discussion

In this study, we have generated a library of LES spanning a range of low-cloud regimes at multiple locations over the East Pacific, by driving LES with large-scale forcings from CMIP5 GCMs. The LES can simulate the transition from stratocumulus off the coasts to shallow cumulus away from the coasts. The LES results are not very sensitive to the host GCM used to derive the forcings; the differences between clouds simulated by LES driven by different host GCMs are much smaller than the differences between the GCM-simulated clouds. The mismatch between the LES and GCMs may suggest biases in GCM turbulence, convection, and cloud parameterizations. We also used the GCM-driven LES to simulate clouds under climate change with a 4 K increase in SST. In the LES, there is generally a small decrease in cloud cover and LWP in the warmer climate, which results in a weak positive shortwave cloud feedback.

The LES setup has limitations. The domain size is very small, and, as a result, the LES-simulated clouds lack mesoscale and larger-scale variability. Some previous studies have shown how domain size affects convective organization and precipitation onset (Blossey et al., 2021; Vogel et al., 2016, 2020; Yamaguchi et al., 2017); however, the domain size had only modest impact on the mean thermodynamic profiles in LES in a few studies (Blossey et al., 2021; Vogel et al., 2020). Because all simulations in this study have no or little precipitation (<1 mm day⁻¹) and we only focus on the domain-mean profiles, we do not expect the results to be strongly affected by the domain size. For example, Figure S5 in Supporting Information S1 shows the result for one LES case in this study on two different domain sizes (6 and 12 km). Increasing the domain size by a factor of 4 yields almost identical mean cloud fraction and cloud liquid water profiles. We use time-mean forcings because it requires shorter simulations, and as a result the LES may not correctly reproduce clouds in response to the more realistic time-varying forcings. The increase of computational capacity in recent years has enabled LES with realistic forcing over large domains, which can capture more realistic mesoscale variability in turbulence and clouds (e.g., Heinze et al., 2017; Stevens et al., 2019). In this study, we choose to use a relatively simple LES setup (a small domain and time-mean forcings) in order to simulate more cases.

Convective parameterizations in GCMs have been evaluated against the few existing LES cases in previous studies (e.g., Cohen et al., 2020; Larson et al., 2012). The objective of the LES library is to expand the data set available for calibrating GCM parameterizations. To this end, the LES results should be compared with single-column models driven by the same time-mean large-scale forcings, and ideally with the same parameterizations for other physical processes such as radiation and microphysics, to bracket off any mismatches between LES and single-column models that would be caused by differences in setup or parameterizations. The convective parameterization schemes can be calibrated by minimizing mismatches between relevant statistics simulated by LES and single-column models, for example, with Bayesian methods (Cleary et al., 2021). The LES of changed climates provide a valuable data set for out-of-sample tests for evaluating parameterizations that were calibrated with present-climate LES. The experimental design allows an iterative workflow, where GCM parameterizations can learn from LES results, and LES can be run with new large-scale forcings from the GCM with improved parameterizations. While this study focused on low clouds over the East Pacific, driving LES with large-scale forcings from GCMs can be done anywhere on the globe. Optimal experimental design approaches can be used to select the locations to generate LES that are most informative about parameterizations (Schneider, Lan, et al., 2017).

The LES of changed climates can also be used to investigate mechanisms of cloud feedbacks under realistic changes in large-scale forcings. This will be explored in more detail in future work.

Acknowledgments

We thank Yassine Tissaoui and Simone Marras for helpful discussion. We gratefully acknowledge the generous support of Eric and Wendy Schmidt (by recommendation of Schmidt Futures), the Audi Environmental Foundation, Heising-Simons Foundation, and the National Science Foundation (grant AGS-1835860). The simulations were performed on Caltech's High Performance Cluster, which is partially supported by a grant from the Gordon and Betty Moore Foundation. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

Data Availability Statement

CMIP5 data can be accessed at https://esgf-node.llnl.gov/projects/cmip5/. The LES codes are available online at https://zenodo.org/record/6326276. The LES library is available online at https://data.caltech.edu/records/20052 (Shen, 2022).