Horizontal Resolution Sensitivity of the Simple Convection‐Permitting E3SM Atmosphere Model in a Doubly‐Periodic Configuration

We develop a doubly periodic version of the Simple Convection‐Permitting E3SM Atmosphere Model (SCREAM) to provide an efficient configuration for this global convection permitting model (GCPM), akin to a single column model often found in conventional general circulation models. The design details are explained, in addition to the extensive case library associated with the doubly periodic SCREAM (DP‐SCREAM) configuration. We demonstrate that doubly periodic cloud resolving models are useful tools to explore the horizontal resolution sensitivity of GCPMs, in addition to replicating biases seen in the global models. Using DP‐SCREAM, we show that SCREAM exhibits behaviors of a scale aware model as it is able to naturally partition between sub‐grid scale (SGS) and resolved vertical transport across the gray zone of turbulence. We show that SCREAM is reasonably scale insensitive when run at resolutions from 1 to 5 km, but can exhibit sensitivity, particularly for the shallow convective regime, when run at resolutions approaching that of large eddy simulations. We conclude that SGS parameterization improvements are likely needed to reduce this scale sensitivity.

2 of 25 community because of their usefulness and digestible computation cost. While there is a rich history of studies using doubly-periodic CRMs, such models have historically not been able to run in global configurations. However, global and doubly periodic configurations are mutually beneficial, as demonstrated in recent work (Dipankar et al., 2015;Jeevanjee, 2017).
One of the newest additions to the GCPM family is a 3 km model developed by the U.S. Department of Energy (DOE) called the Simple Cloud-Resolving E3SM Atmosphere Model (SCREAM; Caldwell et al., 2021). A 40 day prescribed sea-surface temperature simulation (20 January-28 February 2020) using an immature and untuned version of SCREAM demonstrates the benefits of moving to high horizontal resolution when compared to the conventionally parameterized Energy Exascale Earth System Model (E3SM) run with a comparatively coarse resolution of ∼100 km. Caldwell et al. (2021) reports that many long-standing biases typically associated with conventional GCMs are ameliorated simply by increasing the resolution to the kilometer scale; these include (but are not limited to) Amazon precipitation bias, frequency of light and heavy precipitation, the diurnal cycle of tropical precipitation, vertical structure of tropical convection, and coastal subtropical stratocumulus.
The results of Caldwell et al. (2021) and other recent high resolution modeling studies suggest many long-standing biases can simply be "resolved away." This is exciting and provides prospects for more accurate climate simulations to address pressing questions. However, as it currently stands, GCPMs are still expensive to run and typical simulations are both much shorter in duration and run less routinely than conventional GCMs. The relative increase in computational expense of GCPMs therefore introduces new challenges in terms of model debugging, parameterization implementation, evaluation, and tuning. Historically, many modeling centers have supported SCM configurations for their conventionally parameterized GCMs (Bogenschutz et al., 2020;Gettelman et al., 2019) as a way to provide "rapid feedback" of model performance. These SCMs are often viewed as invaluable, if not essential, tools for model analysis and development (Bogenschutz et al., 2012;Park, 2014). However, a SCM is not appropriate for a GCPM since a process such as deep cumulus convection is expected to be resolved across multiple columns. While one could argue that a SCM could still be valid for boundary layer cloud regimes, or as a tool to develop column-based physics schemes, the application of its use would be limited and situational.
Given the large computational expense of GCPMs, a SCM-like proxy is desired to facilitate fast feedback and encourage science that may be impractical using the global model. To minimize computational cost, options such as a regionally refined model (Tang et al., 2019) or limited area model (Giorgi, 2019) are often supported by modeling centers that provide GCPMs. However, regionally-refined and limited-area configurations are still relatively expensive to run and require expertise to set up for the desired region/regime of interest, so are not really suitable substitutions for SCM capability.
One of the most useful things a doubly-periodic CRM can be used for is to study the horizontal resolution sensitivity and the scale awareness of a GCPM in a computationally efficient manner (Bogenschutz & Krueger, 2013;Larson et al., 2012). Whereas traditional SCMs primarily exercise the GCM's subgrid scale physics, a doubly-periodic CRM will exercise the model's full equation set (i.e., both physics and dynamics). In addition, it is trivial to configure a doubly-periodic CRM with a planar configuration to run with any desired domain size and resolution. This is counter to changing the resolution in a global model, which is often a time consuming process that requires expertise due to the generation of the necessary input files and configuration of the model to run at the new resolution.
Even if a particular GCPM is only configured to run at a particular resolution globally (i.e., 3 km), it is important to gain insights on the horizontal resolution sensitivity of the model to account for future changes in resolution and to ensure results are not dominated by discretization error. Should a particular model possess a large sensitivity in regards to the horizontal resolution, the doubly-periodic CRM can be an efficient vehicle to diagnose the cause while serving as a testbed to exploring modifications and potential parameterization deficiencies to reduce the sensitivity. In addition, a doubly-periodic CRM can be used to gauge if the GCPM is scale aware and diagnose any resolution limits. For instance, can a GCPM model that is configured to run at 3 km still be run at scales approaching that of ∼100 m without any necessary modifications to its equation set or changes in regards to the parameterizations used? As computational power increases and the resolutions of our GCPMs become progressively finer (as they already are in the aforementioned select works of Stevens et al. (2020) and Parishani et al. (2017)), these are critical questions we must ask of our GCPMs.
In this paper we introduce and describe a doubly-periodic version of SCREAM (hereafter denoted as DP-SCREAM). In addition, we use DP-SCREAM for five established and diverse cases to examine the horizontal resolution sensitivity as well as the scale awareness of SCREAM. In this paper we define "scale awareness" as the model's ability to adequately partition between the resolved and sub-grid scale (SGS) transports as the resolution is modified. As an example, it is well established that processes associated with marine stratocumulus are largely SGS for a model with a horizontal resolution of 3 km (Cheng et al., 2010) and thus should be parameterized. As the horizontal resolution increases to that of LES (∼100 m) the expectation is that the parameterized transport gradually shuts off and the resolved dynamics takes over. We define "scale insensitivity" to mean that as the model resolution changes, the representation of clouds and thermodynamics remains relatively robust. It is often considered a prerequisite that a model be scale aware in order to be scale insensitive (Bogenschutz & Krueger, 2013;Cheng et al., 2010;Larson et al., 2012). However, having a model that is scale aware does not guarantee that a model will be scale insensitive, as parameterization deficiencies, when run at relatively coarser resolutions, may degrade the simulation. This paper is outlined as follows; Section 2 will give a brief overview of SCREAM as well as introducing the DP-SCREAM configuration. In Section 3 we discuss the cases run for our experiments as well as the range of horizontal resolutions we run DP-SCREAM for, while Section 4 provides a brief discussion on the computational cost. Section 5 presents the results of these simulations to help us gauge the horizontal resolution sensitivity of SCREAM. Finally, in Section 6 we discuss the implication of our results for not only SCREAM, but for GCPMs at large.

Model Description
In this section we briefly describe SCREAM (Section 2.1) and give an overview of the doubly-periodic version of SCREAM (Section 2.2).

SCREAM
The model version used in this study is very similar to SCREAMv0 as documented in Caldwell et al. (2021), so only a brief description is given here. The development of SCREAM is designed to fulfill the US DOE mission of focusing on compute-intensive frontiers in climate science. The SCREAM code base, including DP-SCREAM, is currently being converted C++ to exploit performance on exascale machines. In this work we use the Fortran version of SCREAM.
SCREAM consists of nonhydrostatic fluid dynamics, a SGS turbulence and cloud fraction scheme, a microphysics scheme, a radiation scheme, an energy fixer, and a prescribed-aerosol functionality. Specifically, the dynamical core uses the new nonhydrostatic version of the High Order Method Modeling Environment (HOMME-NH; Taylor et al., 2020). The turbulence scheme is the Simplified Higher Order Closure (SHOC), which is a unified cloud macrophysics, turbulence, and shallow convective parameterization centered around a double-Gaussian assumed probability density function (PDF; Bogenschutz & Krueger, 2013). The microphysics scheme is based on the Predicted Particle Properties (P3) scheme of Morrison and Milbrandt (2015). The gas optical properties and radiative fluxes are computed using the RTE + RRTMGP radiative transfer package (Pincus et al., 2019). While Caldwell et al. (2019) used a prescribed-aerosol version of E3SM's modal aerosol model, the simulations used here employ an even simpler aerosol implementation that prescribes both cloud-condensation nuclei number and aerosol radiative properties from an E3SMv2 simulation. This new aerosol scheme is known as Simple Prescribed Aerosol.

Doubly Periodic SCREAM
The development of DP-SCREAM was broken into three pieces. First, the nonhydrostatic version of HOMME was extended to run on a planar domain. Second, infrastructure changes were needed to enable our code base to run on a domain of identically-forced columns and with the same location information. Third, the large library of cases and scripts developed for the E3SM SCM was extended to also work with DP-SCREAM.

Planar HOMME
The HOMME-NH dynamical core (Taylor et al., 2020) used in SCREAM solves the multicomponent compressible Euler equations in a rotating reference frame using Eulerian horizontal coordinates and a Lagrangian vertical coordinate, making the shallow atmosphere and traditional approximations. The lower boundary is a fixed 10.1029/2022MS003466 4 of 25 material boundary, and the upper boundary is a (moving) constant pressure top material boundary. HOMME-NH uses mimetic finite differences in the vertical with a Lorenz staggering and collocated compatible spectral elements (SEM) in the horizontal, and a vertical remapping for all variables to handle vanishing Lagrangian layer thickness. The SEM method as used in HOMME-NH relies on a meshing of the physical domain into a grid of conforming quadrilateral elements, which can be described by combining information about their topology and their geometry. Grid topology is the connectivity of individual elements to each other. Grid geometry is the shape and size of each element. It is possible to have two grids with the same topology and different grid geometry. A simple example is uniform doubly periodic grids with the same number of grid cells in x and y but different horizontal element sizes Δx and Δy.
The SEM method works on arbitrary unstructured quadrilateral grids, and HOMME-NH was mostly coded this way. However, there were several aspects of the implementation that were specialized to spherical grids. Specifically, the horizontal SEM operators and the grid topology/geometry generation routines both assumed a spherical grid. Therefore, in this work we extended the internal treatment of SEM to handle planar doubly periodic meshes. This involved the following changes to HOMME-NH: 1. Removed the dependence of the SEM derivative operators (divergence, gradient, curl, etc.) on spherical geometry (specifically the radius of the sphere) and replaced with general versions valid for any geometry through the use of a runtime constant equal to 1 in the doubly periodic configuration and spherical radius in the spherical configuration. These new operators remain bitwise identical in the spherical configuration to the old operators, and therefore the planar version of HOMME can be used to investigate the horizontal and vertical numerics. 2. Added a new grid topology generation routine for doubly periodic planar quadrilateral topology. This topology is isomorphic to the torus, and therefore differs fundamentally from spherical topology. 3. Added a new grid geometry generation routine for doubly periodic planar geometry with uniform Δx and Δy element sizes, corresponding to the topology above.
By separating topology generation from geometry generation, it will be easy to add the ability to create novel grids such as non-uniform planar meshes or arbitrary ellipsoidal meshes in the future. Additionally, we implemented several commonly used planar test cases to validate the new model: the hydrostatic gravity wave, nonhydrostatic gravity wave (NHGW), and rising bubble tests from Melvin et al. (2019). We did not add the ability to handle lateral boundaries: this would have been a major piece of software engineering since the assumption that each edge has elements on both sides is deeply integrated into the HOMME-NH code. In recent work the final features of spherical HOMME were implemented for the planar version of HOMME-NH: C++ support through Kokkos, semi-Lagrangian advection of tracers and the ability to use separate grids for physics and dynamics (physgrid). Therefore, the planar version of HOMME-NH now provides the same features of spherical HOMME-NH.

Infrastructure Design
Similar to the E3SM SCM, DP-SCREAM uses forcing files derived by IOPs to provide the necessary initial conditions, large-scale forcing, and surface fluxes (if available). DP-SCREAM makes extensive use of the existing E3SM SCM infrastructure, but with many modifications to suit the needs for this new configuration. Among these modifications is the need to make all SCM related routines work on multi-node parallelism. The E3SM SCM was coded with the intention that it would only be run on a single-processor, however it is essential that DP-SCREAM be run with multiple processors to ensure efficient run time. In addition, the interfaces of the atmosphere and land parallel input and output routine also needed to be heavily modified to ensure that DP-SCREAM uses the same location and heterogeneous surface type throughout its domain for the particular case being run.
In DP-SCREAM, the domain size and horizontal resolution are determined by the user on the fly and the planar domain is set up to have the appropriate number of columns in the x and y direction to satisfy this. However, we still need to use E3SM domain files at initialization to determine on what point of the globe our domain will be set up at. By default, DP-SCREAM uses the files associated with ne30 resolution (corresponding to approximately 1° horizontal resolution) to determine the surface type of our domain, but not to initialize the atmospheric state. When the user submits a particular DP-SCREAM case the model uses the latitude and longitude specified in the IOP file to be the point location for that particular run. This point is determined to ensure consistent radiation computation across all columns, in addition to ensuring the correct surface type is used for that case.
The surface type is determined by searching the E3SM domain files. The grid cell in the ne30 file that is closest to the IOP latitude and longitude determines whether the model is operating over a land, ocean, or sea ice tile (or some combination/fraction of these). If operating over a land point, for example, then the land model is initialized identically for each column in the planar domain that matches the closest point to the IOP latitude and longitude. If operating over an ocean point then the data ocean model is initialized similarly. Should the location include a combination of land/ocean/sea ice tiles then each of the those surface schemes will contribute their fractional share (which does not currently occur in any of the cases in the supported DP-SCREAM library). We note that at the time of this writing it is only possible to run DP-SCREAM with a data ocean model, as opposed to a fully interactive ocean. The land model can be run interactively or with surface fluxes specified (given they are provided in the IOP forcing file). In DP-SCREAM there is no Coriolis force. In addition, at the time of this writing we note that DP-SCREAM does not support varying topography or surface roughness across the domain.
The atmosphere is initialized identically at all columns using the horizontal winds, temperature, and water vapor (u, v, T, and q, respectively) specified at the desired start time in the IOP forcing file. To spin up the turbulence, random perturbations are added to the initial profile of temperature in all cells below 900 hPa. The location and magnitude of these perturbations can be adjusted by the user in the namelist settings.
A new routine has been added to provide the option of nudging DP-SCREAM to the IOP observations for u, v, T, and q. While the E3SM SCM has an existing routine to nudge to IOP observations, it is not suitable for use in DP-SCREAM where there are many active columns with large horizontal spatial variability. Considering only T (though treatment of q, u, and v are analogous), the horizontal domain average ( ) is computed at each level.
The temperature nudging tendency is then computed at each model level as where τ is the relaxation time scale (set by default to 3 hr for DP-SCREAM, but easily modified by the user via namelist settings) and dt is the model timestep. The temperature at each grid point is then updated by applying this tendency. We note that nudging is not typically turned on by default when using DP-SCREAM and its usage is case dependent (see Section 2.2.3), with the ability to be switched on/off by the user via namelist option.
To account for the effects of subsidence or ascent from large-scale vertical velocity (ω), which is often specified in the IOP forcing files, a simple routine was added to compute this effect on T, q, u, and v. Using T as an example (analogous for q, u, and v) the tendency due to large-scale subsidence is computed as: (2)

DP-SCREAM Case Library
The DP-SCREAM case library is shared with the E3SM SCM case library (Bogenschutz et al., 2020), which includes more than 25 cases ranging from continental and maritime deep convection to marine stratocumulus, mixed phase arctic clouds, and various flavors of shallow cumulus convection (see Tables 1 and 2 from Bogenschutz et al. (2020)). The IOP case library contains both well-established benchmark cases useful for gauging how SCREAM stacks up against other models as well as more modern cases for which novel observational constraints are available. For DP-SCREAM we have also added a radiative convective equilibrium RCE case based on Wing et al. (2018).
Our library is continuously growing and users can keep up-to-date on current case offerings and specifics by visiting https://github.com/E3SM-Project/scmlib/wiki. At this location users can clone the Github repository to obtain scripts to run each case. Each script is set up to run with SCREAM's default 3.25 km horizontal grid spacing in the x and y direction and with the domain size that is most appropriate for that case (e.g., a larger domain for deep convection and smaller domain for boundary layer clouds). However, domain size and resolution can easily be modified by the user via the namelist. To run DP-SCREAM a user simply needs to modify the header of the script (obtained from Github repository) for the desired case and the model will run on out-of-the-box on any E3SM supported machine.

Experiment Design
In this study we run five cases spanning a range of cloud and convection regimes. In addition, we run these cases for horizontal grid spacings ranging from 100 m to 5 km. The exact choice of resolutions we select to run, including the domain size, is dependent on the actual case. For instance, cases which include deep cumulus convection will need to be run with a much larger domain than cases consisting primarily of boundary layer clouds. The specific domain size and resolution that is run for each case is mentioned in the case description and summarized in Table 1.
We include two cases of deep cumulus convection (one maritime and the other continental), one shallow cumulus case, one marine stratocumulus case, and one mixed-phase arctic cloud case. The continental deep cumulus case is the Atmospheric Radiation Measurement 1997 (ARM97) IOP that occurred at the ARM southern great plain (SGP) site in June and July 1997 (Xie et al., 2002;Xu et al., 2002). The maritime deep convection case is the Global Atmospheric Research Program's Atlantic Tropical Experiment (GATE, Houze & Betts, 1981), phase III. The Rain in Cumulus over Ocean (RICO) field study (Rauber et al., 2007) is used to simulate precipitating maritime shallow convection. The first research flight (RF01) of the second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS; Stevens et al., 2003) field study is used to evaluate SCREAM's ability to simulate subtropical marine stratocumulus. Finally, we simulate a 12 hr subset of a cold air outbreak single-layer mixed phase cloud case from the Mixed-Phase Arctic Cloud Experiment (MPACE) IOP, known as MPACE-B.
The simulation specifics of the cases performed can be found in Table 1.
In short, the deep convection cases are run in a horizontal domain size of 200 km in the x and y directions and with Δx = Δy = 500 m, 800 m, 1.5 km, 3 km, and 5 km. The boundary layer cloud cases are run with a horizontal domain size of 50 km in the x and y directions and with the same horizontal resolution suite as the deep convection cases, but with the addition of Δx = Δy = 100 m.
We note that the primary motivating factor for this work is to gain an understanding on the horizontal resolution sensitivity. Therefore, to eliminate any potential ambiguity in the results relating to time step, we choose to run each case with the same time step settings for all resolutions. All cases are run with SCREAM's standard 128 vertical levels as documented in Caldwell et al. (2021). We note that all cases at all resolutions are run with the exact same code base, tuning parameters, and parameterization suite. Table 2 provides a summary of the computational resources required to run DP-SCREAM for a variety of configurations when run on NERSC's Cori-Knights Landing (Knights Landing) Nodes. For comparison, computational resources are also provided for the E3SM SCM (Bogenschutz et al., 2020) and global SCREAMv0 (Caldwell et al., 2021). Focusing on the default 3 km SCREAM resolution, we find that running boundary layer cloud cases (domain size of 50 km × 50 km) requires a trivial amount of computational resources. While this is certainly more expensive than the nearly negligible cost of running a traditional SCM, it still represents a "drop Note. Note that all cases use the standard 128 vertical level configuration. The GATE and ARM97 cases are run with Δx = Δy = 500 m, 800 m, 1.5 km, 3 km, 5 km, 10 km, and 16 km while the DYCOMS-RF01, MPACE-B, and RICO cases are run with Δx = Δy = 100 m, 500 m, 800 m, 1.5 km, 3 km, 5 km. Note. Core hours on Cori-Knl are computed as wall time in hours × number of nodes × QOS factor × charge factor. Cori-knl charge factor is 0.2 and regular queue charge factor is 1. in the bucket" when compared to running SCREAM globally. While the cost of running with a larger domain for Δx = 3 km (200 km × 200 km domain), which is typically required for deep convective cases, is an order of magnitude higher than the smaller domain the cost is still relatively meager.

Computational Cost
As expected, the cost of running DP-SCREAM becomes more expensive as resolution increases. For example, the cost of running Δx = Δy = 100 m for a domain of 200 km × 200 km is more expensive than running SCREAMv0 globally. This is precisely why we did not perform such simulations in this paper; but recognize that running DP-SCREAM at LES-like resolutions for deep convection should be explored in future work.

Results
We will present results starting with our deep convection cases, ARM97 and GATE. Following this we will analyze our warm phase boundary layer cloud cases RICO and DYCOMS-RF01. Finally, results will be presented for MPACE-B, which represents mixed phase stratocumulus.
While the focus of this paper is to examine the horizontal resolution sensitivity of SCREAM, we will also compare the quality of the overall simulations to observations or LESs, where available.

Deep Cumulus Convection
In this section we present results for two deep convection cases; one continental (ARM97) and one maritime (GATE). For the ARM97 case we focus on an 8-day active period featuring several strong deep convective events, starting on 23 June 1997; while for GATE we simulate the entire 20 day case. Figure 1 displays the evolution of the domain averaged precipitable water for the duration of both cases. Overall, the observed temporal evolution of precipitable water is generally well captured by all model configurations for both cases, with a few exceptions. All resolution configurations are generally too moist for the majority of the ARM97 case, while an apparent wet bias develops for all DP-SCREAM simulations near the final 5 days of GATE. With regards to the horizontal resolution sensitivity, the GATE case tends to show a much wider spread among model simulations when compared to the ARM97 case, where a monotonic increase of precipitable water occurs from 3 km to 500 m resolutions. It is interesting to note that the 3 and 5 km simulations tend to agree best with observations throughout the course of the 20 day GATE simulation (Figure 1b). On the other hand, for ARM97 we see that the various DP-SCREAM configurations are fairly robust as the differences due to resolution are negligible compared to the differences relative to observations.
The horizontal and temporally averaged cloud profiles for both cases are displayed in Figure 2. We first focus on the results for ARM97. While all simulations show the same general characteristics in terms of the cloud fraction (Figure 2a), the low-level cloud amount and liquid water mixing ratio decrease systematically with increasing resolution, while the resolution of cloud amount and liquid/ice mixing ratios at higher levels do not vary monotonically with resolution. The low-level cloud sensitivity is further demonstrated when looking at the liquid cloud mixing ratio profiles (Figure 2b). Whereas the simulations with Δx > 1 km are robust within the boundary layer, the 800 and 500 m simulations produce significantly less cloud liquid, with a monotonic decrease as resolution increases. In addition, we see some sensitivity of cloud liquid between the model simulations at the mid-levels (3-6 km in altitude), corresponding to cumulus congestus. Figure 2c displays the averaged cloud ice profiles. It is important to note that the P3 microphysics scheme includes all ice phase hydrometeors in the cloud ice mixing ratio (therefore, caution must be exercised when comparing our results for this quantity with previously published work using different models for similar cases). In general, we see a reasonable agreement between the various resolution configurations in terms of the magnitude, however the altitude of maximum cloud ice in the 500 m simulation is a bit lower when compared to the simulations at the kilometer scale.
Overall, the resolution sensitivity for GATE cloud related profiles is similar to that of the ARM97 case. The upper tropospheric clouds are reasonably robust as resolution changes, while boundary layer clouds exhibit the largest sensitivity. However, unlike ARM97, which showed little difference in the solution of low clouds for our 1.5, 3, and 5 km cases (Figure 2), in GATE we see a near monotonic decrease in the cloud amount mixing ratio and depth of the shallow clouds as the resolution increases for all of our experiments. The sensitivity of SCREAM in regards to the representation of boundary layer cumulus will be explored in greater detail in Section 5.2. On the other hand, the apparent robustness of SCREAM to simulate upper-level clouds is encouraging and appears to be less sensitive to horizontal resolution when compared to similar work by other modeling centers, such as (Jeevanjee & Zhou, 2022), though we recognize that a direct comparison to that work cannot be made.
The horizontal and temporally averaged differences in temperature and moisture, computed relative to observations at the ARM SGP site and during GATE, are shown in Figure 3. In terms of temperature biases, both cases show reasonable insensitivity with respect to resolution, though the ARM97 case exhibits a bit more sensitivity within the boundary layer (below an altitude of 3 km). However, a much larger spread can be seen when examining the moisture biases, and this is especially true for the GATE case. For the continental cumulus case, the largest spread in moisture biases reside within the mid-levels often where cumulus congestus is found. This is consistent with the relatively large spread between cloud liquid water at these levels for ARM97. In fact, all simulations for ARM97 and GATE suffer from large positive moisture biases in the mid-levels, which reflects an underrepresentation of cumulus congestus that was found to be a chronic bias in SCREAM (Caldwell et al., 2021).
In terms of GATE (Figure 3d), while all simulations exhibit a fairly strong dry bias near the top of the boundary layer, the 500 m run is considerably more moist and agrees best with observations. The dry bias associated with the coarser resolution runs near 2.5 km in altitude indicates an overestimate of both the magnitude and vertical extent of the cloud liquid water associated with boundary layer clouds. In general, Figure 3d suggests that the 500 m run has more skill in representing both the magnitude and vertical extent of low clouds associated with tropical convection when compared to the lower resolution counterparts. Though it is interesting to note that the moist bias associated with cumulus congestus appears to get worse with increasing resolution and is the primary driver of the sensitivity seen in total precipitable water ( Figure 1b). Figure 4 quantifies the total accumulated precipitation in addition to the averaged values for the cloud water path, ice water path, shortwave cloud radiative effect (SWCRE), and longwave cloud radiative effect (LWCRE) for the duration of the ARM97 and GATE simulations (with a 3-hr spin-up time removed). For the accumulated precipitation, both cases are very robust with regards to horizontal resolution and generally agree well with observations; though all simulations have a wet bias for the GATE case. While not shown, there is no apparent resolution sensi tivity seen in terms of the timing of precipitation for both cases.
Not surprisingly, there is considerably more sensitivity with resolution when examining the averaged liquid water paths, particularly for the GATE case. This is in agreement with the analysis presented in Figure 2, which showed a decrease of liquid water as the resolution increases. This is in contrast to the ice water path, which shows much more stability across the range of resolutions for both cases, but especially for ARM97. This further suggests that low level clouds are the primary drivers for systematic resolution differences within SCREAM.
Averages of the SWCRE and LWCRE are displayed on the bottom row of Figure 4. SWCRE and LWCRE are two important metrics in climate models that are often tuned to maintain radiation balance as resolution changes. Thus, the hope is that the scale sensitivity of SWCRE and LWCRE is minimal so that time-consuming retuning of the model is not necessary should the resolution of the global model change. Despite fairly large differences in the liquid water path, especially for GATE, the SWCRE values are surprisingly robust for most model simulations. Meanwhile, the LWCRE shows modest sensitivity to resolution for the ARM97 case while it is generally robust for GATE. This suggests that high clouds in the tropics may not need significant retuning as SCREAM's resolution is increased.
To gain an understanding of SCREAM's scale awareness for deep convection, we examine the total moisture flux and how the partitioning is represented across scales. First we focus on the ARM97 results. Figure 5a depicts the total moisture flux ( , which represents the sum of the resolved and SGS contributions. For ARM97 we see robust agreement between the various resolution configurations, with some minor differences within the mid and lower layers of the troposphere. This is the type of behavior we would expect to see for a model that is scale insensitive. Examining how this total flux is partitioned between resolved and SGS contributions as the resolution changes, however, provides insights on the scale awareness. Figures 5b and 5c display the resolved and SGS contributions of ′ ′ for ARM97, respectively. Unlike the total ′ ′ , we would expect there to be differences in the partitioning of the SGS and resolved fluxes as resolution changes. Indeed, we see that for the simulations with Δx > 1 km SHOC is responsible for parameterizing a majority of the vertical transport of moisture within the boundary layer. However, the 800 and 500 m resolutions show an inherent scale separation in which the boundary layer turbulence and shallow convection is partially resolved and partially subgrid-scale. This scale separation is consistent with the analysis of Cheng et al. (2010). This is encouraging behavior as it demonstrates the hallmarks of a scale aware model in its ability to naturally partition between SGS and resolved processes as the resolution increases. Section 5.2 will exploit the scale awareness of SCREAM on a larger range of resolutions for boundary layer cloud cases. Regarding the GATE case, while we do see very good agreement between all of our simulations for the total flux, the 500 m simulation does exhibit a smaller magnitude in the lower-to-mid troposphere when compared to the coarse resolution simulations. This is generally in agreement with our findings of the 500 m simulation producing less cloud amount at these levels.
The SGS and resolved profiles of ′ ′ for GATE are displayed in Figures 5e and 5f, respectively. In terms of the SGS component, we see similar behavior to that of the continental deep convective case, where results for the simulations with Δx > 1 km are very similar and with an apparent scale separation when the resolution is reduced to 500 m. This indicates that SCREAM's SGS parameterization is doing less work as the resolution increases, but the scale separation is not as pronounced as in ARM97. We also note that the magnitude of the SGS flux produced by SCREAM for Δx = 3 km is about 50% less than that of the LES filtered result of an idealized GATE case (Moeng et al., 2010). The resolved transport has similar strength across resolutions, whereas the expectation is for the magnitude to increase at higher resolutions. This suggests that resolved dynamics may be overly active for the lower resolution configurations, due to underactive SGS representation, and could be a principle driver for the resolution sensitivity seen in low clouds (Bogenschutz & Krueger, 2013).
We note that for ARM97 and GATE (and for the boundary layer cloud cases to be presented) we also examined the partitioning between resolved and SGS turbulent kinetic energy and liquid water potential temperature flux  . These quantities behaved very similar to the total moisture flux, thus we focus solely on that term for the sake of brevity.

Warm Phase Boundary Layer Clouds
Though SCREAM's default resolution of 3.25 km allows circulations associated with deep convection to be permitted, motions associated with boundary layer clouds and shallow convection are still largely unresolved at this resolution (Cheng et al., 2010) and remain a challenge for GCPMs to properly represent. The results from ARM97 and GATE strongly suggest that SCREAM has a resolution sensitivity for shallow convection. In this section we focus on two liquid boundary layer cloud cases. The first represents a maritime subtropical stratocumulus case based on the first RF01 of the second DYCOMS (Stevens et al., 2005) with the second case focused on RICO (van Zanten et al., 2011), which represents a maritime precipitating shallow convective regime.
Unlike our previously examined GATE and ARM97 cases, we can afford to run 100 m resolution simulations for both RICO and DYCOMS-RF01, which puts us in the range of what is typically considered to be a LES.
Where available, we compare DP-SCREAM simulations against the LES mean and spread from van Zanten In that study, they show that the LES ensemble average could plausibly reproduce the characteristics of the observed clouds, and thus we treat LES as a numerical benchmark for this case. For DYCOMS-RF01 we compare to the LES mean and spread from Stevens et al. (2005), in addition to select observations. The time evolution of the vertically integrated low cloud and cloud liquid water path for both cases is presented in Figure 6. First we focus on the results for the stratocumulus case. For both cloud amount and liquid water path, it is clear that SCREAM's resolution sensitivity is small compared to the inter-model spread of LES. All SCREAM simulations are able to maintain a near solid cloud deck, which was observed, throughout the 4 hr simulation (Figure 6a). There are slightly larger differences for the liquid water path (Figure 6b) as the 800 and 500 m simulations produce more cloud liquid than the remainder of the simulations, yet overall SCREAM simulations still have much less spread than the LES ensemble.
In contrast, for the RICO case the LES mean and spread is characterized by a short spin-up period at the start of the simulation, which quickly transitions to a quasi-steady state of ∼20% cloud cover and 20 g/m 2 of vertically integrated cloud water (Figures 6c and 6d, respectively). In terms of the DP-SCREAM simulations, while it is apparent that all resolutions can adequately produce vertically integrated cloud water and cover that are characteristic of a shallow convective regime, there are some key differences between the simulations. The first is that the coarser resolution simulations, chiefly 3 and 5 km, tend to produce larger values of vertically integrated cloud fraction and liquid water when compared to the higher resolution simulations. Second, the coarser resolution simulations also seem to suffer from a longer spin-up time with more of a quasi-oscillatory behavior when compared to the steady state solutions provided by the high resolution DP-SCREAM simulations and LES. Though the high resolution 500 and 100 m DP-SCREAM simulations tend to achieve a steady state solution, we note that these simulations underestimate the vertically integrated low cloud and liquid water. Thus, it is readily apparent that there is much more sensitivity for RICO than DYCOMS-RF01 and is consistent with our findings for shallow convective clouds associated with ARM97 and GATE.
More differences between the cases and simulations emerge when we examine the vertical structure of clouds in Figure 7. For DYCOMS-RF01, we generally see good agreement among the SCREAM simulations and LES for both cloud fraction and cloud mixing ratio (Figures 7a and 7b, respectively), though with some subtle characteristic differences. For instance, the simulations with Δx > 1 km tend to produce more solid cloud cover when compared to the simulations with Δx < 1 km. In terms of the cloud liquid water, all SCREAM simulations produce more cloud when compared to the LES mean (Stevens et al., 2005) and generally fall within the uncertainty of observations. This is particularly impressive since the vertical resolution in SCREAM is considerably more coarse compared to that used in LES (i.e., Δz ≈ 40 m for SCREAM, within the boundary layer, and 5 m for LES). The satisfactory simulation of marine Sc by DP-SCREAM is in agreement with the global SCREAM analysis presented in Caldwell et al. (2021). These results are also similar to the recent work of Shi et al. (2018) who did simulations of DYCOMS-RF01 with Δx ranging from 100 m to 1 km with a dynamic reconstruction model. Significantly larger spread is seen when examining the RICO case (Figures 7c and 7d). While all DP-SCREAM simulations produce cloud fraction and cloud liquid water magnitudes that are characteristic to that of shallow cumulus, there is sensitivity in regards to the vertical structure of the clouds. It is clear that the 3 and 5 km simulations tend to produce clouds that are too shallow in vertical depth, with cloud tops that are nearly 1 km lower when compared to the LES ensemble. These results are also consistent with the global simulation analysis presented in Caldwell et al. (2021). In fact, it is not until the resolution is increased to 100 m in DP-SCREAM when the vertical structure of the clouds is satisfactory. Furthermore, van Zanten et al. (2011) reports that most LES members have a double peak in cloud fraction and liquid water, one near cloud base and the other near cloud top, which is not evident in any of the DP-SCREAM simulations. It should be noted that while DP-SCREAM exhibits a horizontal resolution sensitivity for RICO and shallow convection in general, it is far less than the sensitivity exhibited by CRMs that contain simple turbulence closures (Cheng et al., 2010;Radtke et al., 2021), though more sensitive than CRMs with more complex turbulence treatments . Thus, it is interestingly consistent that SCREAM seems to fall in the middle of these works for shallow convection as it contains a turbulence scheme of moderate complexity.
The representation of the liquid water potential temperature ( ) and total water mixing ratio ( ) vertical structures are presented in Figure 8. With regards to the marine stratocumulus case (top row of Figure 8), while all SCREAM simulations are able to reasonably produce the well mixed vertical structure when compared to the LES mean and spread, there are some differences. For example, all SCREAM simulations tend to be a bit warmer than LES within the boundary layer and the simulations with Δx > 1 km do not appear to be as well mixed in regards to within the surface level. In addition, there are differences near the boundary layer top in terms of the thermodynamic structure for nearly all simulations and we believe this to be due to SCREAM's relatively coarse vertical grid for this case. Future work should address SCREAM's sensitivity with regards to vertical resolution for stratiform clouds.
Results for the RICO case (Figures 8c and 8d), on the other hand, show clear differences among the DP-SCREAM simulations and when compared to the LES ensemble. All SCREAM simulations are able to capture the well mixed sub-cloud layer and are in general agreement with LES, the exception being the 100 m run which is too dry. The larger differences occur within the cloud layer, which is not surprising given the differences in the vertical extent of clouds in Figure 7. It is obvious that the 100 m simulation is the only DP-SCREAM experiment that is able to adequately capture the sharp increase in static stability, as compared to the initial profile ( Figure 4 in van Zanten et al. (2011)), while the remainder of the simulations struggle to break through the conditionally unstable layer. This likely occurs because the SGS parameterization fails to provide adequate countergradient gradient fluxes. The dynamics cannot compensate for this due to the coarse resolution of the 500 m to 5 km simulations, which cannot resolve the large eddies associated with shallow cumulus. This is counter to the DYCOMS-RF01 case where SCREAM performs satisfactorily, as mixing is predominately local for that regime.
While the simulation of cloud characteristics for DYCOMS-RF01 is relatively scale insensitive, the resolution range between 100 m and 5 km represents a large theoretical gap for this regime (Cheng et al., 2010); thus we need to determine if SCREAM can gracefully handle the transition between parameterized and resolved turbulence. Figures 9a-9c displays the total, resolved, and SGS moisture flux for all SCREAM resolutions and LES (for the total flux) for the DYCOMS case. While the agreement for the total ′ ′ is reasonable and mostly falls within the LES ensemble window, we do note that the simulations with Δx < 1 km tend to have a stronger flux throughout the depth of the boundary layer when compared to the coarse resolution simulations.
What we expect to be different in the SCREAM simulations is how the SGS and resolved fluxes are partitioned as the resolution changes. Figures 9b and 9c demonstrate that for the simulations with Δx > 1 km nearly all of the turbulent transport is provided by the SGS SHOC parameterization, with little resolved. This is to be expected for this case given the scale analysis of Cheng et al. (2010). As we move to the 800 and 500 m resolutions we see that we are clearly within the gray zone of turbulence, with vertical transport partially resolved and partially SGS. Furthermore, at our LES-like horizontal resolution of 100 m we note that nearly all turbulence is resolved, with the exception of near the surface. The fact that SCREAM is able to adequately partition between parameterized and resolved turbulence across scales without any adjustments to the code, tunable parameters, or changes to the parameterization suite is very encouraging, with the benefits further discussed in the summary (Section 6). Though we do note that the LES filtering of Cheng et al. (2010) shows a scale separation for grid sizes Δx < 1 km for the stratocumulus regime, consistent with SCREAM simulations, it appears that SCREAM likely partitions from resolved to SGS transports a bit too abruptly.
Analogous results for the RICO case are presented in Figures 9d-9f. With regards to the total flux, only the 100 m simulation has reasonable agreement with the LES ensemble, though it should be noted that the 500 m to 5 km simulations are reasonably robust even if the quality is poor. In addition, we find that even though DP-SCREAM struggles to capture some of the quantitative aspects of the trade cumulus regime with grid sizes of 500 m to 5 km, we do find that SCREAM is reasonably scale aware for this regime, depicted by the partitioning of SGS and resolved turbulent transports. However, the magnitudes of the resolved fluxes for the 5 and 3 km simulations are higher than the LES filtered results of Cheng et al. (2010) suggest them to be. This indicates that the resolved dynamics is attempting to compensate for the lack of mixing provided by the SGS parameterization. These results strongly suggest that the quality of coarse resolution simulations and scale sensitivity across the gray zone could be improved by addressing issues of SGS representation pertaining to the shallow cumulus regime.

Figure 8.
Temporally and horizontally averaged profiles of liquid water potential temperature (left column) and total water mixing ratio for the DYCOMS-RF01 (top row) and Rain in Cumulus over Ocean (RICO) (bottom row) cases, averaged over the last hour for DYCOMS-RF01 and four hours for RICO. Large eddy simulation results follow that as explained in Figure 6.

Mixed Phase Stratocumulus
Many climate and weather models tend to have difficulty simulating the observed frequency and persistence of Arctic mixed-phase clouds (e.g., Morrison and Pinto (2006)), thus we simulate MPACE-B to determine the horizontal resolution sensitivity of SCREAM for this challenging cold-air outbreak case. Klein et al. (2009) presented results from the MPACE-B intercomparison study with many participating CRMs. They found not only a large spread among the CRMs, but that a large majority of these models underpredicted the liquid water path by a factor-of-three, though models with sophisticated microphysics agreed better with the observed values of liquid and ice water path. Figure 10 presents the average values of cloud liquid and cloud ice water paths, over hours 4 through 12, for SCREAM simulations and the observed values reported in Klein et al. (2009), as well as the median value from the CRMs used in that study. In terms of liquid water path, we see that SCREAM simulations do not suffer from the large underestimate that plagued the CRM intercomparison. Instead, all SCREAM simulations are well within the uncertainty of observations and are reasonably insensitive to resolution, with the 5 km and 100 m simulations being relative outliers. In terms of the ice water path, SCREAM simulations have little resolution for the DYCOMS-RF01 (top row) and Rain in Cumulus over Ocean (RICO) (bottom row) cases, averaged over the last hour for DYCOMS-RF01 and four hours for RICO. Large eddy simulation results follow that as explained in Figure 6. sensitivity and slightly overestimate ice mass. It is important to note, however, that P3 microphysics includes suspended ice and snow as one species, which is likely contributing to the higher values produced by SCREAM.
The time evolution of the ice and cloud water paths are displayed in Figure 11. In terms of the ice water path, all DP-SCREAM simulations have the same general characteristics, displayed by ice water that tends to increase over time. There is much more spread in terms of the liquid water path, where it is clear that the 5 km and 100 m cases show the most sensitivity. The 100 m case simulates less cloud liquid water, compared to the rest of the simulations, which appears to slowly deplete over time. While this spread is greater than that of the marine stratocumulus case, it is still less than that reported by the CRM intercomparison of Klein et al. (2009) and all SCREAM simulations are in reasonable agreement with observations. However, it is a bit disappointing that no apparent convergence with resolution is found.
The vertical structure of the observed and simulated cloud fraction is presented in Figure 12. The observed cloud fraction (Figure 12a) is provided by two aircraft flights and ground based radar/lidar averaged over hours 4 through 12 of the case. The simulated cloud fraction profiles (Figure 12b) show the SCREAM results as well as the mean and spread of the CRM intercomparison study. While the simulated SCREAM cloud profiles are fairly robust, it is clear that SCREAM tends to simulate cloud base and top at a higher altitude than the CRM envelope. While it is not surprising that the characteristics of the simulated cloud profiles are different between SCREAM and the CRM intercomparison, given the vastly different simulated liquid water paths, it is not clear if SCREAM cloud profiles agree better with observations versus that of Klein et al. (2009). Though the cloud deck in SCREAM is too high in altitude compared to the aircraft observations, most simulations agree well with the radar/lidar profiles. The exception is the 100 m case, which produces a cloud deck too high in altitude when compared to all observational sources. Figure 13 displays the vertical structure of the temporally averaged cloud liquid and cloud ice mixing ratios for the SCREAM simulations. The general structure of the cloud profiles are realistic and relatively robust among all SCREAM simulations, though we note a subtle shift of the cloud deck upward in altitude as the resolution increases. This is most apparent when comparing the cloud liquid profiles of the 5 km simulation with the 100 m simulation. The 100 m simulation produces much less liquid water compared to most other simulations and with a much higher cloud deck; both of which appear to be at odds with observations. While this may seem counterintuitive, as we expect the simulation quality to improve as resolution increases, it is still difficult to capture the very-fine-scale processes that drive entrainment using 100 m resolution (Mellado, 2017). Nevertheless, the ability of SCREAM to simulate cloud liquid amounts at all resolutions that are in decent agreement with observations is encouraging. While profiles of cloud ice all show the same general characteristics, there are differences related to the progressively increasing altitudes of the simulated cloud. In addition, the Δx < 1 km simulations tend to produce more ice than the Δx > 1 km simulations.
The tendencies of microphysics processes contributing to the budgets of the cloud liquid and ice mixing ratios are displayed in Figure 14. The formulations of the cloud liquid and ice budgets are found in equations B1 and B6 in Morrison and Milbrandt (2015), respectively. In nature, cloud liquid is generated mainly by condensation near cloud base, which is balanced primarily by losses to riming and evaporation in the middle of the cloud layer. Cloud ice is formed by nucleation and droplet freezing near cloud top, grows in mass by vapor deposition and riming through the cloud layer, and loses mass through sublimation as it falls below cloud base.
In terms of the SCREAM cloud liquid budget, the condensation tendency (provided by SHOC; Figure 14b) is the dominate term. For this source term we see that while the 5 km and 100 m simulations are outliers in  Klein et al. (2009), with associated uncertainty bars. We note that SCREAM ice water path values includes both non-precipitating ice and snow since P3 microphysics does not distinguish between the two. The Median Intercomparison cloud resolving model values reflect those reported by Klein et al. (2009). terms of magnitude, the remainder of the simulations are fairly robust showing a drying tendency within the mid cloud layer. For most other terms, the 500 m to 3 km simulations are all reasonably robust, with exception of the sink to rain number from collision (Figure 14g), which is the smallest term in the budget. The total tendency for ice ( Figure 14i) shows less sensitivity to resolution than for liquid, but with the 5 km simulation being a relative outlier. For cloud ice mixing ratio, the source from rime mass dominates the budget (Figure 14l) with the vapor deposition providing the largest sensitivity between model resolutions ( Figure 14k).  The thermodynamic profiles for each resolution are displayed in Figure 15. In general, the 100 m simulation is the clear outlier for both temperature and moisture when compared to the rest of the simulations. The 100 m simulation is characterized by a reduction of q t in the upper half the boundary layer, which Klein et al. (2009) note in nearly all their CRM simulations and comment that this is unrealistic behavior, due to the underestimate of q l . In this case, the 3 and 5 km simulations tend to produce the most well mixed boundary layer structures and the q t profiles appear to be the most realistic given that we would expect a smaller jump between q t in the cloud layer versus that in the sub-cloud layer (Klein et al., 2009). In terms of θ l , the coarser resolution simulations, which tend to contain more cloud liquid water and less ice precipitation, act to keep the boundary layer more well mixed. This is counter to the 100 m simulation which has less cloud top cooling and more ice precipitation acting to produce larger vertical gradients.
The temporally averaged total, SGS, and resolved moisture fluxes ( ′ ′ ) are displayed in Figure 16. While there is somewhat reasonable agreement in the total flux for most simulations (Figure 16a), the 5 km simulation appears to be the outlier within the sub-cloud and cloud layer. When breaking down into components of SGS ( Figure 16b) and resolved (Figure 16c) transports, we see the desired shift of energy from the SGS to resolved scales as the resolution increases. However, without energy spectra filter results from LES it is difficult to ascertain whether the magnitudes for each grid size is representative of what we expect or not and should be explored in future work.
The fact that a significant portion of transport is being carried out by resolved scales at the 5 and 3 km simulations may be a bit unrealistic for a boundary layer cloud case such as MPACE-B and could potentially point to deficiencies in SCREAM's SGS turbulence scheme to handle this regime. In the future, gauging the appropriate SGS and resolved turbulence partitioning for each grid size should be diagnosed for DP-SCREAM in a manner similar to Moeng et al. (2010). Nonetheless, it is interesting that the simulations with greater SGS contributions (1.5 and 3 km) tend to produce the most realistic cloud and thermodynamic structures. The 100 m simulation, on the other hand, which relies very little on SGS transport, tends to have the most unrealistic simulation which could point to deficiencies that need to be addressed with the microphysics scheme. There is potential that deficiencies exist in both the microphysics and turbulence schemes and compensating errors between the two are leading to more acceptable solutions for the 0.8-3 km range.
Nonetheless, while SCREAM struggles in some aspects to simulate the MPACE-B case across scales, the satisfactory solution of clouds at many resolutions (including the default SCREAM resolution of 3.25 km) and less spread when compared to the CRM study of Klein et al. (2009) is encouraging. Future work should take a deeper look at the microphysical budgets and properties in SCREAM and the potential role they could be playing in the horizontal resolution sensitivity. In addition, it should be reminded that SCREAM's vertical grid is relatively coarse for stratiform clouds, thus exploring the role of vertical resolution sensitivity for mixed case stratocumulus should also be pursued.

Summary and Discussion
In this paper we develop a doubly periodic version of SCREAM that we call DP-SCREAM. Since SCREAM is a GCPM, it is therefore far more computationally expensive when compared to conventional GCMs, which often support very efficient configurations known as SCMs to aid in model analysis at the process level and debugging Figure 14. Temporally and horizontally averaged profiles of the cloud liquid (top two rows) and ice (bottom row) tendency budgets. All profiles averaged over hours 4 to 12. Specifically, (a) total cloud liquid tendency, (b) cloud droplet condensation, (c) cloud droplet autoconversion to rain, (d) cloud droplet accretion by rain, (e) collection of cloud water by ice, (f) immersion freezing droplets, (g) source for rain number from collision of rain/ice above freezing and shedding, (h) cloud droplet evaporation, (i) total ice tendency, (j) deposition/condition freezing nucleation, (k) vapor deposition, (l) source from rime mass, (m) sublimation of ice, and (n) melting of ice. ±symbols denote a source/sink term to the total tendency. of model development. Thus, DP-SCREAM fills the need and serves as SCREAM's proxy for a SCM-like utility, which offers rapid feedback of model performance at the process level.
One of the major benefits of DP-SCREAM is that it allows the user to choose the model domain and grid size on the fly. This is unlike changing the resolution of a global model, which often requires time consuming generation and testing of the necessary input files. In DP-SCREAM, this is trivial and allows for one to easily explore the resolution sensitivity of the model. While SCREAM is currently run globally with a grid spacing of 3.25 km in the horizontal, higher resolutions are expected as computational capabilities advance. Even in the near term, scientists  will likely run SCREAM with regional mesh refinement that pushes toward the sub-kilometer scale within their regions of interest. DP-SCREAM can give indications on how SCREAM will perform at these resolutions and what tuning (or code) requirements may be necessary as the resolution is pushed into uncharted territories.
Work presented in this paper is related to recent efforts by other modeling centers (Dipankar et al., 2015;Jeevanjee, 2017). However, we focus on a more diverse set of cloud regimes and subject SCREAM to a wider range of resolutions than presented in the aforementioned works. In this paper we run DP-SCREAM for five cases, spanning a range of cloud regimes, and for grid sizes ranging from 100 m to 5 km. It is common for GCPMs to be run with horizontal grid sizes anywhere from 1 to 5 km. However, we choose to run many of our simulations at scales that LESs are typically run to see how SCREAM handles moving across the "gray zone" of turbulence. In this work we seek to gain an understanding on the horizontal resolution sensitivity of SCREAM. This can be done by examining the scale awareness and scale insensitivity aspects of SCREAM.
Results presented in this paper provide evidence that SCREAM can reasonably partition between resolved and SGS transports as we move across scales. As an example, using the results from the marine stratocumulus case of DYCOMS-RF01, at 3 and 5 km resolution the vertical transport of moisture is almost completely parameterized by SHOC. As the resolution is increased toward 100 m, SHOC mostly shuts off while allowing resolved dynamics to take over. This general behavior is true for all cases examined in this paper. However, our results also suggest that this partitioning between SGS and resolved transport as we move across scales may be a bit too abrupt in some cases, as seen in our subtropical stratocumulus case, or not pronounced enough in others, such as in the maritime tropical convection case. Improving this in future development work could help to reduce the horizontal resolution sensitivity in SCREAM.
Nonetheless, this scale aware behavior in SCREAM is important because it means that we can increase the resolution of SCREAM (either globally or in RRM mode) without the need of manually shutting off or swapping out parameterizations, avoiding any tricky ambiguities typically associated with gray zone modeling. It also means that it may be possible to use DP-SCREAM as a LES process model, though much validation would be needed to make this a reality. We believe that any GCPM using a PDF-based parameterization such as SHOC, Cloud Layers Unified by Bi-normals (Golaz et al., 2002), or Intermediately Prognostics HOC (Cheng & Xu, 2008) would likely possess scale aware characteristics. However, many GCPMs use simple turbulence closures that were intended to be used at LES scales (Khairoutdinov & Randall, 2003) and are generally not scale aware at CRM resolutions (Bogenschutz & Krueger, 2013). We encourage other modeling centers to investigate the scale awareness of their GPCMs using a doubly periodic configuration.
While all cases presented in this paper experience at least some degree of scale sensitivity, stratiform clouds are the least sensitive to horizontal resolution. This is especially encouraging for the DYCOMS-RF01 case as the LES intercomparison study (Stevens et al., 2005) found a large sensitivity between the participating members, whereas SCREAM is generally robust when moving across scales. The largest sensitivity in SCREAM is associated with the shallow convective regime. This is demonstrated in the results of RICO, ARM97, and GATE cases though it appears to be particularly exacerbated for tropical and subtropical oceanic cases. For simulations with Δx > 1 km SCREAM tends to produce shallow clouds that contain too much cloud water and are too shallow in depth. In other words, they appear to have characteristics of broken stratocumulus clouds. This is in agreement with the preliminary global assessment presented in Caldwell et al. (2021), so on one hand it is encouraging that DP-SCREAM can replicate biases seen in the global model. As the resolution decreases to Δx < 1 km, DP-SCREAM tends to simulate shallow convective clouds that are in better agreement with LES and observational reference, with clouds that are deeper in vertical extent. This suggests that SHOC, which serves as SCREAM's parameterization for shallow cumulus, should be improved or tuned to reduce the scale sensitivity seen in shallow convective regimes.
In general, the simulation of deep cumulus convection is relatively robust as represented by results of precipitation, top of atmosphere radiative fluxes, and especially upper-level clouds. However, some sensitivity can be seen when SCREAM is run with Δx < 1 km and these differences are primarily found within the lower-to-mid troposphere. This sensitivity appears to be introduced when SCREAM goes from a grid spacing of 1.5 to 0.8 km, representing an apparent scale separation. Indeed, this is often the gap where deep convection goes from being merely "permitted" to "resolved." The results related to our findings on scale sensitivity means that SCREAM will likely need some degree of retuning if the resolution is changed globally, but it would likely be modest if that resolution is kept between 1 and 5 km and more substantial if resolution is reduced below 1 km.
The DP-SCREAM exemplars examined in Section 5 provide evidence that the model produces credible simulations of a range of cloud regimes. Although detailed comparisons with observations and benchmark simulations for each case are beyond the scope of the present work, comparisons of the essential characteristics of the simulations show reasonable agreement to previous descriptions of these cases and compare well to previous CRM studies. However, the treatment of shallow convection in SCREAM warrants the most attention for improvement and we believe this to be the case for most GCPMs. In addition, we note the general behavior that SCREAM simulations do appear to get better as resolution increases. While this result is not surprising, the exception to this rule appears to be mixed phase Arctic clouds. For the MPACE-B case the majority of simulations agree quite well with observations, yet the 100 m case produces cloud i.e., generally considered to be too high in altitude with smaller than observed cloud liquid water values. This apparent and unusual sensitivity could suggest a need to examine potential deficiencies of the microphysics treatment within SCREAM. In addition, while the 100 m RICO simulation produces much better cloud characteristics and thermodynamic structure than the lower resolution simulations, when compared to LES, it suffers from a dry bias in the representation of cloud liquid water.
Using a doubly periodic configuration of SCREAM we were able to address many questions pertaining to SCREAM. By running a particular model at a range of resolutions it not only provides information for how that model may perform globally at different resolutions, but also provides key information for its default resolution. Thus, we highly encourage other modeling centers to develop and support doubly periodic configurations for their GCPM. Bogenschutz (2023b) provides the software used to produce simulations presented in this paper, while the data used in the analysis of the paper is provided in Bogenschutz (2023a).