Global climate models (GCMs) produce large errors in cloudiness and cloud radiative forcing when simulating midlatitude, synoptic-scale cloud systems. This is because they do not represent the subgrid-scale processes in these systems that create subgrid variability in cloud optical thickness and cloud top pressure. Improving GCM performance will require a better understanding of these controls on subgrid cloud variability. To begin addressing this issue, this paper uses a mesoscale model, the Regional Atmospheric Modeling System (RAMS), to simulate two case study synoptic storms with much higher resolution than is possible in a GCM. These storms were observed during the Atmospheric Radiation Measurement (ARM) Program's March 2000 Intensive Observing Period (IOP) in the U.S. southern Great Plains (SGP), otherwise knows as ARM case 4. We find that RAMS is able to capture the observed storm morphology, lifecycle, and vertical structure of the atmospheric dynamic and thermodynamic variables. RAMS is also able to capture the observed fine-scale vertical structure and temporal variation of the cloud field. Given this agreement with observations, we then characterize the model-simulated variability in cloudiness and other variables such as vertical velocity. In both storms, there is a high degree of spatial and temporal variability in the vertical motion field across multiple scales. The variability in above-boundary layer cloudiness is closely linked to this dynamical variability. This suggests that a parameterization for subgrid cloud water based on subgrid vertical velocity could be used to improve GCM simulations of midlatitude clouds.
 One of the largest uncertainties in our understanding of climate variability and climate change is the role of cloud feedbacks. Although they have a large radiative impact on the climate system, clouds are not correctly and consistently simulated in global climate models (GCMs) [Cess et al., 1996; Weare and AMIP Modeling Groups, 1996]. For example, several recent studies have demonstrated that GCMs produce large errors when simulating cloudiness generated by synoptic systems [e.g., Katzfey and Ryan, 2000; Klein and Jakob, 1999; Norris and Weaver, 2001; Ryan et al., 2000; Szeto and Guan, 2000; Tselioudis et al., 2000; Tselioudis and Jakob, 2002]. This is a major deficiency: since these clouds typically are both highly reflective and horizontally extensive, they exert a larger impact on the Earth's net radiation budget than any other cloud regime [Harrison et al., 1990]. Incorrect simulation of these clouds in GCMs can cause many problems. For example, surface radiation budget errors in the storm track regions can create errors in SST, sea ice extent, and ocean currents in coupled ocean-atmosphere simulations. Incorrect relative magnitudes of cloud radiative cooling and baroclinic eddy heat transport could lead to unrealistic simulations of middle- and high-latitude climate change [Weaver, 2003].
 One error that is shared by most, if not all, GCMs is simulation of frontal cloudiness that is too uniform, too optically thick, and too high [Norris and Weaver, 2001]. This is generally related to insufficient representation of subgrid-scale processes that create variability in cloud optical thickness and cloud top pressure at smaller scales than those resolved by GCMs. For example, in the warm ascent regions of midlatitude cyclones, GCMs simulate cloudiness that is too horizontally and vertically homogeneous. Observed cloudiness, however, has much more variability in cloud optical thickness and cloud top height, even if the vertical motion averaged over a large area is upward. What the GCMs are missing are the mesoscale (and smaller-scale) motions that strengthen the ascent within part of the column and produce compensating subsidence elsewhere. This subgrid dynamical variability leads to subgrid cloud variability. Additional contributions may come from subgrid variability in other variables, e.g., temperature, humidity, horizontal advection, etc. Besides radiative forcing errors, the fact that these motions and processes are not represented in current large-scale cloud parameterizations can also lead to unrealistic process rates in cloud microphysical schemes [Pincus and Klein, 2000].
 Clearly, therefore it would be desirable to modify existing cloud parameterizations so as to account for this fine-scale cloud variability, thereby leading to improved climate simulations. Fractional and inhomogeneous cloudiness in a GCM grid box resulting from the subgrid distribution of cloud condensate can in principle be diagnosed from the subgrid probability density functions (PDFs) of quasi-conserved variables like total water mixing ratio and liquid water temperature [e.g., Sommeria and Deardorff, 1977; Smith, 1990; Tompkins, 2002]. Building a viable parameterization, however, requires that we develop understanding of the subgrid processes that control these distributions.
 As a step in this direction, our approach in this study is to use a much higher-resolution model than a GCM to investigate the relationships between cloud variability and variability in the driving dynamic and thermodynamic variables at these smaller scales. Our focus is on the cloud systems associated with midlatitude, synoptic-scale cyclones. The purpose of this paper is twofold. First, we wish to establish the validity of our approach, i.e., the ability of our model, the Regional Atmospheric Modeling System (RAMS), to realistically capture observed features of these midlatitude cloud systems. Second, we wish to characterize the subgrid (to a GCM) variability in cloudiness, vertical motion, and other variables as simulated by RAMS.
 In pursuit of these aims, we have taken advantage of the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) Program's March 2000 Intensive Observing Period (IOP) over the ARM site in the U.S. southern Great Plains (SGP). The focus of this IOP is the clouds associated with wintertime, midlatitude, synoptic-scale dynamics. It is referred to as ARM case 4. The extensive observations collected as part of this IOP make it an ideal time period from which to select case studies for our RAMS simulations.
 Our overall approach, blending observational analysis and high-resolution modeling with a focus on a particular cloud regime and a particular case study time period, is consistent with the strategy of the Global Water and Energy Cycle Experiment (GEWEX) Cloud Systems Study (GCSS) [Randall et al., 2003; Jakob, 2003]. The use of a high-resolution model complements observationally based compositing strategies. For example, cluster analysis of satellite and ARM data reveals the characteristic dynamics underlying different cloud regimes [Gordon et al., 2005]. However, it is not possible to investigate the subgrid spatial variability in the variables (such as vertical velocity) associated with these cloud regimes since the available observations only give the large-scale dynamics. A numerical model can simulate clouds and dynamics at much higher resolution and bridge this gap. The disadvantage is that high-resolution simulations are computationally intensive, necessitating a focus on individual case studies, and we must rely on the observational data sets for sufficient temporal sampling.
Section 2 details our method, including a description of RAMS and the simulation setup. Section 3 provides an evaluation of the model performance. Section 4 shows the relationships between the simulated clouds and other model variables. Section 5 presents conclusions.
2.1. Model Description
 RAMS [Cotton et al., 2003] is a limited-area model that solves the full, nonlinear, nonhydrostatic equations of motion for the atmosphere in a terrain-following coordinate system. It has been designed with flexible horizontal and vertical resolutions, featuring two-way grid nesting that embeds high-resolution grids within larger, coarser-resolution model domains. RAMS has been widely and successfully used in the scientific community for a variety of applications from large-eddy simulation to large-scale, regional climate integrations. Of particular relevance to this study is the suite of cloud and precipitation microphysics available in RAMS. This includes prognostic treatments for all microphysical processes in both mixing ratio and number concentration for six species (pristine ice crystals, rain, snow, aggregates, graupel, and hail) and in mixing ratio only for cloud liquid droplets [Walko et al., 1995; Meyers et al., 1997]. The microphysics package interacts with a complementary radiative transfer scheme specifically designed to take advantage of the information on condensate distributions [Harrington, 1997]. Other parameterizations include subgrid-scale transport [Mellor and Yamada, 1982], convection [Kain and Fritsch, 1992], and land surface processes [Walko et al., 2000].
 One note about the microphysics: because of its detailed prognostic scheme with multiple water, ice, and mixed phase species, deciding what fraction of the total condensate the user should consider to be “cloud” is not as straightforward in RAMS as in models (such as many GCMs and models that use GCM-derived cloud parameterizations) that explicitly predefine “cloud” and “precipitation” components of their total hydrometeor material. Of the seven RAMS microphysical species mentioned above, only cloud liquid droplets and pristine ice crystals form by nucleating in situ via direct condensation from water vapor (though all seven categories experience condensation or deposition from vapor). In addition, all except cloud liquid droplets fall out at least part of the time (e.g., ice crystals in cirrus clouds). Each of these six species has a size distribution that evolves with time, and the fall speed of a given particle is governed by its position in this distribution and the physical characteristics of the given species. RAMS itself does not explicitly define for the user what fraction of the total condensate should be designated as “cloud”, as distinct from “precipitation,” nor does it calculate a cloud fraction based on imposed thresholds (e.g., in relative humidity). The user is free to choose which of the simulated species to include in any analysis of cloud properties. Therefore, for the purposes of this study, we examine two different microphysical quantities: the mixing ratio of cloud liquid droplets only and the mixing ratio of total condensate (i.e., the sum of the mixing ratios of all seven microphysical species). Our findings are not particularly sensitive to the specific subset of species we choose to examine. As shorthand throughout the rest of the paper, we will frequently use the terms “cloud” and “cloudiness” interchangeably with these two quantities, most often when discussing total condensate.
 The goals of this study required construction of simulations with the following key characteristics: (1) sufficiently fine spatial and temporal resolution to realistically capture the critical cloud-producing processes, (2) a sufficiently large model domain to generate results from which we can draw conclusions relevant to GCMs, and (3) realistic evolution of the cloud, dynamic, and thermodynamic fields.
 To accomplish this, we use two nested grids, both centered on the ARM SGP site (Figure 1). The outermost grid (grid 1) covers roughly 2200 × 2200 km2, with 12-km horizontal grid spacing. Convection is parameterized on this grid with the Kain-Fritsch scheme. To ensure the correct evolution of the model solution in the context of the synoptic-scale background conditions, grid 1 assimilates the 6-hourly, 2.5° pressure, wind, temperature, and humidity fields from the National Centers for Environmental Prediction (NCEP)/National Center for Atmospheric Research (NCAR) reanalysis project [Kalnay et al., 1996]. During each simulation, the RAMS fields are nudged toward the reanalysis at each model time step in a buffer zone with a width of 16 points at each lateral boundary. The lateral boundary assimilation and nudging in RAMS follows Davies . The purpose of grid 1 is to downscale the synoptic-scale meteorology provided by these boundary conditions in order to provide suitable forcing for the high-resolution domain of interest.
 This high-resolution domain (grid 2) covers 750 × 750 km2 with 3-km horizontal grid spacing. On grid 2, convection is simulated explicitly, rather than parameterized. Note that this domain corresponds to the area covered by several typical GCM grid cells. While computationally expensive, this combination of high resolution and relatively large domain size enable us to characterize the sub-GCM grid cell statistics of dynamic, thermodynamic, and cloud variables and their link with the large scale.
 We note that our strategy, i.e., using nested grids combined with assimilation of NCEP reanalysis at the lateral boundaries of the coarse grid, differs in important respects from that employed in Single Column Model (SCM) and Cloud Resolving Model (CRM) investigations of this same ARM case 4 [e.g., see Xie et al., 2005]. Use of a mesoscale model like RAMS complements the SCM and CRM investigations. To begin with, RAMS is a three-dimensional model, while the SCMs are one-dimensional columns and the CRMs are run two-dimensionally. In addition, in the SCMs and CRMs, observationally based large-scale dynamical and thermodynamical forcing from the Constrained Variational Analysis (CVA) [Zhang et al., 2001] is imposed uniformly throughout the model domain, which is a stricter constraint on the model solution than the RAMS lateral boundary conditions. In RAMS, the three-dimensional structure of storm systems from outside the model domain propagate into the interior via the reanalysis boundary conditions; once inside, they evolve according to the RAMS dynamics and physics before propagating out naturally. Furthermore, all properties of the storms simulated on grid 1 (the coarse outer grid), including condensate, are in turn advected into the high-resolution grid 2 domain. This two-stage downscaling procedure provides realistic three-dimensional boundary conditions for our ARM SGP high-resolution simulation domain.
 Both grids 1 and 2 resolve vertical processes with 45 terrain-following, stretched-grid levels. For the land surface we use the standard RAMS 30-arc sec topography data set, land cover types from the Olson Global Ecosystem Database [Olson, 1994a, 1994b], and soil moisture and soil temperature initial conditions from the NCEP/NCAR reanalysis.
 We chose to simulate two storm periods during the March 2000 IOP: 2–3 and 7–8 March. Both of the periods experienced well-developed cyclones but with different amounts of cloudiness and cloud variability over the ARM site. We initialized RAMS with the NCEP/NCAR atmospheric reanalyses on 1200 UT of 1 and 6 March, respectively for the two cases. We then ran each case for 60 hours, of which the first 12–24 can basically be considered spin-up of the atmosphere. (Since we are simulating synoptically forced, wintertime systems, it was not necessary to perform a lengthy spin-up of the land surface variables.)
 An important additional set of questions concerns the impact of changes in model horizontal resolution on the simulated cloud and meteorological fields. This bears directly on the issue of how well GCMs and other coarse-resolution models can represent midlatitude clouds. While not the main focus of this paper, we begin addressing these questions by looking at results from two more simulations of each storm case: one with 12-km grid spacing and one with 48-km grid spacing. For these runs, we used the identical grid 1 domain as for the 3-km runs, but without the nested grid 2. We discuss these results briefly at the end of the paper.
3. RAMS Validation
 To satisfy the first goal of this study, i.e., a demonstration of the effectiveness of high-resolution RAMS simulations as a tool for improving the representation of frontal clouds in GCMs, we have compared the model output with a range of ARM and ARM-related data sets. Here we show some results of these comparisons. It is important to note that we did not set out to exactly duplicate observed dynamics, thermodynamics, precipitation, etc. Instead, we wish to study the processes contributing to cloud variability. Similarity to observed fields in these two cases, particularly for the cloud field, is important for illustrating that what we learn from the model is applicable to the real world, but the agreement need not be identical.
Figure 2 shows GOES 8 false-color composite images for the 2–3 and 7–8 March storms (we obtained these from the ARM External Data Center (available on the Web at http://www.xdc.arm.gov/data/prod/sgp/goes/composite/)). These were created by assigning colors to three channels of a GOES 8 image (red for visible, green for the midinfrared water vapor channel, and blue for the thermal infrared). Only the infrared channels appear in these nighttime images, and the palest (whitest) shades show the coldest brightness temperatures. We show these to give a sense of the overall morphology and orientation of each system. For example, the 2–3 March storm is more limited in meridional extent, with a much shorter cloud band along the north-south length of the front, compared to the 7–8 March storm. However, for the 2–3 March storm, it is the “head” of the comma, rather than the “tail”, that passed over the ARM site. As we will see later, this results in greater persistence of cloudiness and more variable cloud characteristics over the ARM site during 2–3 March compared to 7–8 March.
 Comparing with Figure 1 above, we see that the large-scale (12-km) RAMS grid captures these differences in gross structure. Our intent is not to perform a detailed comparison between RAMS and GOES, but this basic level of agreement is a good first-order check on the model performance. Now we move on to a more detailed evaluation of the RAMS simulation results in the high-resolution domain (the 3-km nested grid 2).
3.1. Large-Scale Dynamics and Thermodynamics
 Here we compare the RAMS output with the above mentioned CVA for various dynamic and thermodynamic fields. Since we have not used the CVA to in any way force RAMS, and the RAMS output reflects only the NCEP/NCAR reanalysis lateral boundary conditions and its own internal dynamics and physics, it can be an independent check on what RAMS is doing. As discussed above, our goal here is not to exactly reproduce any particular data set, but instead to investigate the interplay between cloud and dynamical variability within the model. Nevertheless, it is still of general interest to examine the degree of similarity between the RAMS simulations and the CVA.
Figures 3– 5 show comparisons between the CVA and the 3-km RAMS output (averaged over the CVA domain, roughly the size of a GCM grid cell). For zonal and meridional wind (Figure 3) and temperature and water vapor mixing ratio (Figure 4), the agreement is generally reasonably close in terms of both temporal evolution and vertical structure. Differences include a too high meridional jet and a too moist lower troposphere on 2–3 March. Note that the 7–8 March storm is significantly warmer and moister at lower levels than the 2–3 March storm.
 A comparison between surface variables is shown in Figure 5. Again, the agreement is generally relatively good. With some exceptions, RAMS is able to mostly capture the observed evolution of the sea level pressure (SLP) field, the precipitation rate, and the surface incoming shortwave and longwave radiation.
 One of the exceptions is the timing of precipitation in the 7–8 March storm (Figure 5f), highlighting perhaps the most obvious deficiency of the 7–8 March simulation. Specifically, the storm's development seems to be roughly 6 hours behind in RAMS than in reality. A corollary to this time lag is that the simulated storm lies somewhat further to the east at a given point in its lifecycle. This is not particularly apparent in most of the fields we have looked at so far, but it is easily seen in the precipitation comparison. As Figure 5f shows, the observed precipitation peak is nearly absent in RAMS when using the CVA averaging domain. However, if the averaging domain is shifted 1.5° to the east (short-dashed line), the peak emerges, shifted to a later time. The possible reasons for this lag are many, including shortcomings in both the model and the initial/boundary data. Experiments with longer spin-up times and different model resolutions did not produce significantly different results. Another possibility is that the relatively coarse NCEP/NCAR reanalysis driving fields may not provide sufficient detail for precise storm development. This 7–8 March lag has some minor implications for our analysis, which will be discussed in subsequent sections.
3.2. Cloud Vertical Structure
 A key test of model performance is its ability to simulate the vertical structure and temporal evolution of the clouds in these two storms. To evaluate this, we used the active remotely sensed clouds locations (ARSCL) value added product (VAP) [Clothiaux et al., 1999, 2000]. This ARM product blends radar, lidar, and radiometer data to provide a time series of the vertical distributions of cloud. Figure 6 compares the time series of ARSCL cloud layers with RAMS total condensate mixing ratio (i.e., as contributed by all microphysical species) at each time and in each model vertical layer over a single point in space. For the 2–3 March storm, that point is the location of the ARSCL instruments (i.e., the ARM SGP Central Facility). For the 7–8 March storm, because of the timing problem discussed above, we use RAMS output from the same latitude as the Central Facility but shifted slightly to the east. This shift is required to carry out a meaningful comparison between model and observations. The higher-top model clouds associated with the 7–8 March band do not develop until after all the clouds have moved on to the east, so the shift is necessary in order to capture the cloud field at the same point in the storm's lifecycle that the ARSCL observed.
 Beginning with 2–3 March, RAMS captures the major features seen in the observations: the leading high clouds, the thick clouds during the passage of the warm front, the low clouds in the warm sector, the thick clouds during the passage of the cold front, and the low clouds trailing the warm front. The CVA documents two episodes of large-scale mean upward motion (not shown) corresponding to the thick clouds observed by the ARSCL (i.e., from roughly 1200–1800 UT on 2 March and from about 0300–0900 UT on 3 March in Figure 6a), with only broken clouds in between. RAMS simulates this double occurrence of thick clouds. Also, it is worthwhile mentioning that RAMS seems to correctly simulate the shift to a slightly lower cloud base just before 3 March. Because it is RAMS total condensate, including precipitating species such as rain and hail, which is shown in Figures 6b and 6d, the contours often extend all the way to the surface, even though the simulated cloud base does not necessarily do so. In some instances the RAMS cloud tops are higher than reported by the ARSCL, and this is likely a model error, though it is possible that attenuation of the ARSCL instruments in thick clouds might lead to cloud top underestimates.
 For 7–8 March, RAMS simulates the single, narrow band of high, thick clouds associated with the frontal passage. As with the 2–3 March case, the cloud top and cloud base heights are generally comparable between model and observations. One problem is that RAMS clearly misses the thin cirrus (above 9000-m altitude) that is apparent in the ARSCL prior to the appearance of the thick cloud band. Possible sources of this error include insufficient vertical resolution in the model upper troposphere or insufficient water vapor at these altitudes.
 This generally good overall agreement between modeled and observed clouds is encouraging. Since RAMS is able to realistically simulate many key details of cloud vertical structure and time/space variability, we have greater confidence that our analysis will yield useful insights into the factors that control cloud variability in midlatitude storms.
4. RAMS Results
4.1. Horizontal Organization and High-Resolution Structure
 Our eventual goal is to comprehensively characterize the key drivers of cloud variability at scales too fine to be resolved in a GCM, and this paper represents our first step toward this goal. We begin with an overview of the horizontal organization of various fields as simulated on the 3-km RAMS grid. Figures 7 and 8 present snapshots from the 2–3 and 7–8 March runs. These maps, at a single model time (during the middle of each storm) and single vertical level (in the midtroposphere) give a sense of the internal structure present within each storm over the whole RAMS grid 2. The four shaded contour maps in Figures 7 and 8 show vertical velocity, cloud liquid water mixing ratio, total condensate mixing ratio, and saturation water vapor mixing ratio (directly corresponding to temperature). We also plot the horizontal wind vectors on each map. The basic picture is not sensitive to the choice of a specific midtropospheric vertical level: the ∼4-km altitude shown here is usefully representative because it is low enough to contain substantial concentrations of cloud liquid droplets in addition to ice and mixed phase particles.
 The box drawn on each map encloses a 288 × 288 km2 subdomain (i.e., roughly the size of a single GCM grid cell) for which we will later compute various averages and other statistics. This subdomain is centered on the ARM Central Facility for the 2–3 March storm but is shifted to the east for the 7–8 March storm in order to capture the full range of clouds present in this storm, including high-top clouds, as discussed above.
 Key points from Figures 7 and 8 follow. First, a great deal of horizontal structure exists in the various fields at multiple spatial scales, particularly for vertical velocity, cloud liquid, and total condensate. There is a clear correspondence between the spatial variability in the vertical motion and the cloud/condensate fields. Small-scale updrafts in excess of 1 m s−1 are embedded within the larger-scale organization of gentler vertical motions, and these local peaks are associated with the highest values of cloud liquid and total condensate. To better illustrate the correspondence between the vertical motion and cloud fields, Figure 9 shows a “filmstrip” comparison for time sequences spanning 2–3 and 7–8 March. The close coevolution of vertical velocity and cloud liquid water is striking. While visual comparisons can be misleading, the sub-GCM grid-scale dynamical variability in RAMS seems to be directly driving variability in cloud water across a range of spatial scales.
 Clearly, a given amount of vertical motion will not necessarily lead to the same amount of cloudiness at all locations. For example, generally high relative humidity (not shown) in the “shield” portion of 2–3 March storm means that positive (upward) vertical velocity events there are almost always associated with cloud; this is not the case in the drier postfrontal region to the south and west. The predominantly upward motion in this part of the storm is of course itself a major cause of the more humid environment. Horizontal variations in temperature, and hence saturation mixing ratio, can in principle also modulate the link between vertical motion and cloud amount. As shown in Figures 7 and 8, the saturation mixing ratio field seems to have less fine structure than either vertical velocity or clouds, and not much systematic correspondence with either. Previous research has shown that the distribution of total water mixing ratio is more important than the distribution of saturation mixing ratio for determining mesoscale variations in boundary layer clouds [Tompkins, 2003]. On the basis of this, horizontal uniformity of saturation mixing ratio is an assumption that is frequently employed in the so-called “statistical” cloud parameterizations mentioned in the Introduction, since, given this assumption, the amount of condensate can be calculated by integrating the PDF of total water mixing ratio upward from the single value of saturation mixing ratio. The results shown here suggest this might be a reasonable assumption for frontal clouds as well, so long as the grid size is not too large. Temperature variations of course still play a major role in other aspects of the cloud field, such as variations in the partitioning of the total condensate into liquid, ice, and mixed phased species.
 Visual examination of Figures 7–9 suggests multiple scales of organization of the vertical motion field, from very fine-scale, intense, “convective-like” updrafts and downdrafts, up to larger, more “mesoscale” features. This is better quantified in Figures 10 and 11. Figure 10 shows vertical velocity power spectra for both storms, computed for the 288 × 288 km2 subdomain indicated on Figures 7 and 8. The peak power occurs roughly around the 10–15 wave number range (i.e., ∼20–30 km), suggesting that the features organized at these scales dominate the dynamical variability. On the other hand, very strong, smaller-scale vertical motions embedded within this larger-scale variability are easily visible in vertical velocity frequency histograms (Figure 11). Some number of points within the 288 × 288 km2 subdomain experience positive (upward) vertical velocities in excess of 2, 5, or even 10 m s−1. However, the total fraction of RAMS grid cells experiencing this at any one time is extremely small. Advection of hydrometeors from these intense updraft cores, while undoubtedly occurring, does not seem to be playing a major role in determining the broad characteristics of the condensate distribution across the domain, at least at midtropospheric levels. A specific example from Figure 7 illustrates this: At the junction of the OK, KS, and MO borders, there is a zone of strong upward motion which is also associated with large mixing ratios of cloud liquid and total condensate. This location also coincides with some of the strongest horizontal winds in the domain, blowing from SW to NE. In spite of this, the adjacent, immediately downwind subsidence region just across the border into MO is largely free of clouds. The relative importance of detrainment and subsequent advection of hydrometeors from strong convection does increase at higher altitudes.
4.2. GCM-Equivalent Spatial Statistics
 To generalize the results shown in the previous section, we now examine various horizontal spatial statistics of the model output in the 288 × 288 km2 subdomain indicated on the maps in Figures 7 and 8. All statistics in this subdomain are separately calculated for each model vertical level and each time, and we display them here as time-height plots for the duration of each of the two RAMS simulations. Before calculating these statistics, we first averaged the 3-km RAMS grid cell output to 12-km boxes in order to smooth out some of the noise in the various fields.
Figure 12 shows the horizontal mean and standard deviation of vertical velocity in this subdomain. Together, these quantities summarize the spatial and temporal variability in the simulated vertical motion field. The differences between the two storms are readily apparent, for example, the shorter duration of the 7–8 March storm over the ARM site and the generally weaker vertical motion. In both cases the standard deviation is several times the mean, reflecting the strong horizontal variability seen in Figures 7–11. The rising motion in both storms extends throughout much of the depth of the troposphere, with peak rising motion at midlevels.
 We wish to compare this dynamical variability with the spatial and temporal variability of the cloud field. When discussing cloud variability, it is possible to examine a number of different quantities that provide different but complementary information. For example, do clouds occur at all or not? When they occur, how thick and how high are they on average? In this context, we will look at condensate amount, cloud occurrence versus nonoccurrence, and cloud top height.
 Starting with mean mixing ratio of cloud liquid droplets only and total condensate (Figure 13), we see a good correspondence between the updraft peaks (shown in Figures 12a and 12c) and the middle and high clouds. For the 2–3 March storm, RAMS simulates thicker clouds in two, or perhaps three, bands associated with local maxima in upward motion between roughly 1200 UT on 2 March and 0600 UT on 3 March. These clouds penetrate up to about 8 km as liquid and above 10 km as ice and mixed phase species. The 7–8 March clouds have a similar vertical structure and a similar association with vertical motion, but only for a single cloud band. As we would expect, this relationship between upward motion and cloud does not necessarily hold in the boundary layer.
Figure 14 shows two different measures of variability associated with the total condensate distributions shown in Figures 13b and 13d. First is the cloud frequency of occurrence at each time and vertical level, i.e., how much of the horizontal domain the clouds “fill up”, which we define as the number of RAMS grid cells in the 288 × 288 km2 subdomain with at least some condensate. (In this case we use a threshold of 0.0001 g kg−1 as our cutoff for indicating the presence of “cloud;” the results are not particularly sensitive to the specific value chosen.) This quantity could be considered to be the analogue of cloud fraction in a single GCM grid box. The second is the horizontal standard deviation of total condensate for all “cloudy” points (i.e., again for points with values above the same threshold). As expected, each measure gives somewhat different information. For example, large standard deviations occur both with large cloud occurrence, where mean condensate it also large, but also with lower cloud occurrence and lower mean condensate values (i.e., “broken” clouds).
Figure 15 summarizes some of the interrelationships between vertical motion and cloud contained in Figures 12–14. First, we see in Figures 15a and 15b that the standard deviation of vertical velocity is generally proportional to the mean. This proportionality is not constant, however, as there are times when the standard deviation is larger relative to the mean than at others. For example, compare the mean and standard deviation around 1200 UT on 2 March and just after 0000 UT on 3 March. Total column condensed water (Figures 15c and 15d) closely follows the vertical velocity, as mean condensate varies with mean vertical velocity and the standard deviation of condensate varies with the standard deviation of vertical velocity. For example, the standard deviation of column condensate stays large just after 0000 UT on 3 March even though the mean has dropped significantly.
 Similarly, for cloud top height (Figures 15e and 15f) and cloud occurrence (Figures 15g and 15h) the high-top clouds that fill up the domain the most generally occur when mean upward motion is largest. Spatial variability in cloud top height responds strongly to spatial variability in vertical motion. For example, for the 2–3 March storm, much larger cloud top height variability occurs after 1800 UT on 2 March, during a more broken cloud period (with smaller mean total condensate, cloud top height, and cloud occurrence) when the standard deviation of vertical velocity relative to the mean is largest.
 We can further quantify the dependence of condensate amount on the intensity of upward or downward motion. Figure 16 plots midtropospheric cloud liquid water and total condensate averaged into vertical velocity bins. Each of the 50 bins used for the averaging contains the same number of points, 1/50 of the total sample. As shown in Figure 16, the dependence of cloud liquid or total condensate on vertical velocity is roughly linear for upward motion, though there is progressive flattening of slope at the highest values, particularly for total condensate mixing ratio. For downward motion, the slope is either flat or even shows an increase with increasing subsidence. Advection of hydrometeors from intense updrafts into immediately adjacent downdrafts, along with “saturation” of cloud amount (large or small) for extreme values of upward and downward motion, likely are responsible for these changes in slope. The differences in dynamical intensity and total cloudiness between the two storms are also apparent in Figure 16. We note that this bin analysis yields a qualitatively similar relationship between vertical motion and cloud to that found by Norris and Weaver  and Weaver and Ramanathan  for vertical motion and top-of-atmosphere cloud radiative forcing.
 Also plotted in Figure 16 are bin averages for the 3-km RAMS output averaged up to 12, 24, and 48 km, respectively. Note that the slopes of the curves and the major features remain constant over this averaging. This is consistent with the idea, suggested by Figures 7–11, that it is the more “mesoscale” (e.g., 20- to 30-km features) dynamical variability that is most responsible for the main cloud variability in this domain, as opposed to the smallest-scale, most intense vertical motions.
 Finally, Figure 17 shows the spatial correlation between horizontal variability in vertical velocity and horizontal variability in cloud liquid droplets or total condensate within the 288 × 288 km2 domain. As with the standard deviations shown earlier, we calculated the correlation coefficients only for “cloudy” points with values greater than the 0.0001 g kg−1 threshold. Consistent with preceding results, the correlations are generally high and positive in the middle and upper troposphere, largely exceeding 0.6, and even 0.8, in the core ascent regions of both storms. Low-level clouds have correlations that are much weaker. Correlations are generally weaker or negative for the thin clouds occurring above 10 km and the clouds occurring before and after the main period of strong updrafts. These clouds likely result from detrainment and probably are either blown off from their region of formation or represent clouds left behind after the strong updrafts have ceased.
 Correlations between horizontal variability in cloud amount and quantities like water vapor mixing ratio or relative humidity (not shown) are similarly strong, reflecting the importance of the upward and downward motions in these storms for vertical water vapor transport. Finally, consistent with our discussion in section 4.1, correlations between cloud amount and temperature or saturation vapor pressure (also not shown) are much weaker than between cloud and vertical velocity.
4.3. Impact of Changing Horizontal Resolution
 Before concluding, we briefly examine the changes in the RAMS simulations of these storms when using coarser horizontal resolution. Investigating this sensitivity is relevant to the issue of understanding the causes of errors in GCM simulations of midlatitude clouds, though a comprehensive investigation of the role of horizontal resolution is beyond the scope of this study.
Figure 18 shows mean total condensate for the 3-km, 12-km, and 48-km RAMS runs in the 288 × 288 km2 subdomain. Focusing on the core time period of each storm, we see that the concentration of hydrometeors in the middle and upper troposphere decreases as the resolution coarsens. This is particularly striking for the 7–8 March storm: the 48-km run fails to produce any cloud shield at all. For the 2–3 March storm, the distinction between individual bands of thick clouds disappears with decreasing resolution. Recalling the comparison with the ARSCL shown in Figure 6, it seems clear that the performance of the model relative to the observed cloud vertical structure degrades significantly at these lower resolutions.
Figure 19 suggests one reason for these resolution-caused differences. It shows that mean upward motion weakens with decreasing resolution, and the strongest upward motion does not penetrate as high in the atmosphere. As with the distinct cloud bands in Figure 18, the separate episodes of upward motion visible in the 2–3 March 3-km simulation disappear. There is a direct correspondence between the lack of middle and upper tropospheric vertical motion and the lack of middle and upper tropospheric cloud, consistent with the results in the previous section showing the close link between vertical motion variability and cloud variability.
 The fact that the 12- and 48-km simulations do not simulate the same large-scale mean vertical motion field as the 3-km simulation is notable. This suggests that coarse-resolution models like GCMs, lacking the more intense, deeper-penetrating but smaller-scale ascent regions, may not be able to simulate the correct synoptic-scale storm intensities. One way to look at this is that the problem with frontal clouds in GCMs may not simply be a cloud parameterization problem, but also a dynamics problem. With incorrect large-scale mean vertical motion, and associated errors in quantities such as water vapor convergence, even a perfect parameterization would give incorrect results.
Figure 20, similar to the bin plots shown in Figure 16, summarizes these differences between the 3-km runs on the one hand and the 12- and 48-km runs on the other. One key point is that, for a given amount of upward motion, the 12-km and 48-km simulations of the 2–3 March storm produce more condensation. We only show the 2–3 March storm in Figure 20 because the 48-km simulation of the 7–8 March storm produced essentially no cloud above the lower troposphere. Therefore, assuming the 3-km simulations represent “truth,” the coarser-resolution simulations are deficient both because they produce insufficient vertical motion, even when averaged over large scales, and, for a given amount of this vertical motion, they produce too much cloud.
 A more comprehensive investigation of these resolution-induced differences is a topic for future work. For example, the picture is complicated by the role of the convection scheme, which operates in the 12-km and 48-km runs (and would operate in a GCM), but not on the fine grid of the in the 3-km runs. The 3-km simulations are better at producing stronger, deeper vertical motions than the coarser runs, and these feed directly into the model's microphysics scheme, producing more condensate. The vertical motions resolved on the 12- or 48-km grid similarly produce clouds directly, but in addition the convection scheme communicates with the model microphysics indirectly via its adjustments to the resolved-scale thermodynamics. Clearly, for this choice of model and convection scheme, this is not as efficient a combination for creating middle and upper level cloudiness as explicit simulation at higher resolution.
5. Summary and Conclusions
 In this study we have used a mesoscale model, RAMS, run at much higher resolution (3-km horizontal grid spacing) than is possible in a GCM, to investigate the relationship between fine-scale variability in clouds and their driving dynamic and thermodynamic variables. Two case study synoptic storms observed during ARM case 4 were examined.
 We first established the effectiveness of our approach by showing that RAMS was able to realistically capture the observed features of these midlatitude cloud systems. Specifically, there was generally reasonably good agreement between RAMS and the observations for storm morphology, lifecycle, and the vertical structure of the atmospheric dynamic and thermodynamic variables. In addition, RAMS was able to capture the observed fine-scale vertical structure and temporal variation of the cloud field. For the 2–3 March storm, this included correctly simulating the leading high clouds, the double occurrence of thick clouds associated with two distinct episodes of large-scale mean upward motion during the passage of the warm front, the low clouds in the warm sector, the thick clouds during the passage of the cold front, and the low clouds trailing the warm front.
 We next characterized the subgrid (to a GCM) variability in cloudiness and vertical motion as simulated by RAMS. We found a high degree of spatial and temporal variability in the vertical motion fields of both storms, associated with mesoscale organization (e.g., rainbands) embedded within the synoptic-scale system, as well as with convection embedded within the mesoscale organization. The spatial and temporal variability in above-boundary layer cloudiness (i.e., hydrometeor concentration) was closely linked to this dynamical variability. The close relationship between vertical motion and cloudiness was apparent in spatial map comparisons and in more general statistics computed over GCM grid cell equivalent size regions. The horizontal spatial statistics of key variables are consistent with strong control of sub-GCM grid-scale condensate variability by vertical velocity. The differences between the 3-km runs and runs carried out with 12-km and 48-km grid spacing are also consistent with this conclusion, though important questions remain to be investigated.
 These findings suggest that a parameterization for subgrid cloud water variability based on subgrid vertical velocity variability would improve GCM simulations of midlatitude clouds. Such a parameterization might, for example, attempt to prognose subgrid variance in total water mixing ratio from the subgrid variance in vertical velocity as diagnosed from the grid-resolved dynamics. This leads naturally to an additional set of questions to be answered in future work. Specifically, can the characteristics of the fine-scale vertical velocity organization be determined from the large-scale fields? What is the interrelationship between the synoptic-scale, mesoscale, and convective-scale processes in these midlatitude cloud systems, and how does this affect the spatial and temporal variability of the clouds?
 In addressing these future questions, we intend to build on and extend work shown here. For example, certain refinements to the RAMS simulations might be desirable. These include using higher vertical resolution in the middle and upper troposphere to improve the representation of layer clouds there, using higher horizontal resolution to more fully capture convection, and carrying out simulations with higher-resolution initial and boundary conditions. In addition, there are many more ARM and ARM-related data sets with which we can evaluate the model. These include radar, lidar, and radiometric measurements, VAPs from satellite, ground-based, and aircraft instruments, and radar and rain gauge networks.
 Finally, in spite of the computational expense, we will eventually need to simulate a much larger number of cases to collect a more comprehensive database of model output. From this we will be able to develop improved statistics of the relationships between cloud, dynamic, and thermodynamic variables and between the different scales of motion present in midlatitude systems. These statistics will be used to help build, test, and refine future parameterizations of subgrid variability in cloud properties.
 This work was supported by DOE ARM grant 63332-1018730-0007407. The authors thank two anonymous reviewers for their helpful comments. The first author thanks Robert Walko for answering numerous RAMS questions.