Midlatitude Frontal Clouds: GCM-Scale Modeling Implications

Transcription

1 2729 Midlatitude Frontal Clouds: GCM-Scale Modeling Implications J. J. KATZFEY AND B. F. RYAN CSIRO Atmospheric Research, Aspendale, Victoria, Australia (Manuscript received 8 March 1999, in final form 15 September 1999) ABSTRACT The importance of subgrid-scale processes for the simulation of midlatitude frontal clouds by global models is investigated. The case chosen is a frontal cloud associated with a cool change crossing the southern Australian coastline between 17 and 19 November The Commonwealth Scientific and Industrial Research Organisation limited-area model, Division of Atmospheric Research Limited-Area Model, was run at horizontal resolutions of 30 and 300 km, and the results of the 30-km simulation were then averaged to 300-km resolution. Comparisons and evaluations of the simulations showed that the 300-km simulation failed to develop the frontal clouds. Comparison with the 30-km simulation averaged to 300 km showed the importance of the subgrid-scale vertical motions for this cloud development. In particular, it is found that the covariance of the subgrid-scale terms, although of smaller magnitude when compared with the larger-scale terms, needs to be parameterized to capture correctly the frontal cloud development. It is suggested that parameterization of the subgrid-scale dynamical forcing is important for the correct cloud development in general circulation models. 1. Introduction Accurate climate and weather prediction in grid-scale numerical models requires parameterization of unresolved forcing of cloud processes, which tend to occur on scales too small to be represented explicitly in global climate models (GCMs). In addition, individual effects of small-scale physical processes on the large scale are sometimes difficult to diagnose due to the many and complex interactions between various processes. Physical processes not fully resolved in a climate model simulation of midlatitude systems include frontal structures and circulations embedded in the cloud system, subgrid-scale surface influences on the development of the cloud system, and the effect of cloud layering on the moisture and radiation budgets for the cloud system. The impact of microphysical processes on the moisture and radiation budget, precipitation efficiency of the cloud system, and the feedback of the cloud radiative processes from these midlatitude systems on the climate must also be considered (Stewart et al. 1998). In addition, cloud microphysical processes associated with midlatitude frontal systems, such as subcloud evaporation of precipitation ahead of a cold front, modify the thermodynamic structure of the lower troposphere and have significant implications for the moisture bud- Corresponding author address: J. J. Katzfey, CSIRO Atmospheric Research, Private Mail Bag No. 1, Aspendale, Victoria 3195, Australia. jack.katzfey@dar.csiro.au get and precipitation efficiencies calculated by GCMs and regional climate models nested in GCMs. In their study of the evolution of the oceanic prefrontal subcloud layer of fronts crossing southeastern Australia, Ryan et al. (1989) showed unambiguously that evaporative cooling was an important process in the evolution of the front. More recently, Katzfey and Ryan (1997) modeled the case studied by Ryan et al. using the Commonwealth Scientific and Industrial Research Organisation (CSI- RO) limited-area model, Division of Atmospheric Research Limited-Area Model (DARLAM), run at 30-km resolution. The model simulations showed that the inclusion of the evaporation of precipitation in the model reduced the timing errors in the passage of the front. The model moisture budgets and subcloud structure were similar to that observed by Ryan et al. when subcloud evaporation was included in the simulation, and there were significant differences when it was suppressed. To address these problems of process interactions and subgrid-scale effects, the Global Energy and Water Experiment (GEWEX) Cloud System Study (GCSS) was established with the aim of developing better parameterizations of the important cloud systems in GCMs through an improved understanding of physical processes involved (Browning 1994). The most appropriate tool to develop and to test a physically based parameterization of cloud processes is a cloud system model that spans a broad range of scales in order to capture the unresolved forcing. GCSS Working Group III is using the same case studied by Katzfey and Ryan (1997) 2000 American Meteorological Society

2 2730 JOURNAL OF CLIMATE VOLUME 13 TABLE 1. All simulations used 18 sigma layers and 120-s time step. Control runs allowed partial cloud cover per grid box. Run Resolution Grid Characteristic RUN30 RUN30NP RUN30NE RUN30NH RUN300S RUN300 RUN300NP 30 km 30 km 30 km 30 km 300 km 300 km 300 km Control No partial clouds No subcloud evaporation No resolved-scale latent heating Small domain Control No partial clouds FIG. 1. CFRP network showing the positions of the upper-air stations Adelaide, Mount Gambier (MG), and King Island (KI) together with the ships HMAS Kimbla (K) and MV Sprightly (S). The domain shown was used for the 30-km simulations. Four averaged regions (300 km 300 km) centered on the observing sites are marked as solid boxes. The boxes on the 300-km grid used to compare the 30- and 300-km simulations are indicated by the dashed boxes and are labeled m2 and m4. to develop a midlatitude methodology for testing physically based parameterizations of cloud processes in cloud-resolving and mesoscale models. This case is examined further here in an attempt to understand how model resolution affects the simulation of cloud processes. Our aim is to use the validated simulation of the case study of Katzfey and Ryan (1997) to examine the effect of averaging the characteristics of a cold front onto the GCM scale. This is done by diagnosing the relative contributions of the means, standard deviations, and various covariances in the thermodynamic and moisture equations in the 30-km horizontal resolution simulation averaged onto the 300 km 300 km grid. These terms are then compared with the same terms calculated from a simulation carried out at 300-km resolution. A summary of the various simulations completed for this case is presented in section 2, along with a discussion of the implication these results have on the development of the frontal cloud. Section 3 presents the results of averaging the 30-km simulation onto a 300-km grid for two grid boxes. The relative importance of the covariance terms in the advection equation is also discussed. The paper concludes with a summary of the results. 2. The case study and discussion of the simulations The case chosen for study is a cool change that approached and crossed the southern Australian coastline between 17 and 19 November The cool change passed through the Cold Fronts Research Program (CFRP) upper-air observing network shown in Fig. 1 (see Ryan et al. 1989). The CFRP network included upper-air stations at HMAS Kimbla (K), MV Sprightly (S), King Island (KI), and Mount Gambier (MG). Because the intention of this paper is to investigate the requirements for a typical climate model to capture frontal cloud development, areal averages for the four 300 km by 300 km boxes shown in Fig. 1 were computed, each approximately centered on an upper-air station. However, in order to more accurately compare with the 300-km simulation discussed later, only averages for the two dashed boxes labeled m2 and m3, which match the grid boxes of the 300-km grid, will be discussed. Note that box m4 is over land and this led to some differences in the development of the structure of the frontal system compared with the other boxes. Box m2 was chosen because the time passage of the frontal system through this box was close to that for box m4. Katzfey and Ryan (1997) give a detailed description of the CSIRO limited-area model, DARLAM, used to simulate this event along with an analysis and validation of the 30-km resolution simulation (called RUN30). The European Centre for Medium-Range Weather Forecasts (ECMWF) analysis, interpolated to the model grid, was used to initialize and provide boundary conditions. All simulations used the same time step (120 s) and number of vertical levels (18 unequally spaced sigma levels). Because the ECMWF analysis used to initialize all runs had a horizontal resolution of 2.5 latitude and longitude, similar to the 300-km model grid, the impact of different initial states was minimized. The additional simulations completed are given in Table 1. RUN30NP is a simulation at 30-km resolution that did not use the partial cloud-cover algorithm from Rotstayn (1997) to test the importance of subgrid-scale clouds at 30-km resolution. RUN30NE is the same as RUN30NP except that evaporative cooling has been suppressed to investigate the importance of this process to the simulation. RUN30NH is the same as RUN30NP except that the latent heat from grid-scale rain or ice has been set to zero, allowing an investigation of the forcing in the cloud layer resulting from the release of latent heat. However, convective heating from the cumulus parameterization scheme is retained. RUN300S

3 2731 FIG. 2. Mean sea level pressure (every 1 hpa), and surface wind vectors at 0600 UTC 18 Nov 1984 for (a) RUN30, (b) RUN300, and (c) 300-km average of RUN30. is a simulation with a domain just slightly larger than RUN30, but with a horizontal resolution of 300 km. Since this simulation had only a small number of grid points (12 11), the boundary data strongly controlled the simulation (the weights of the boundary forcing decreased exponentially away from the boundary) and the results from this simulation are not discussed further. Another 300-km simulation, RUN300, had an extended domain in order to minimize the boundary effects that were evident in RUN300S. RUN300NP is the same as RUN300 except that the partial cloud parameterization was not used. In order to document the general performance of the 30- and 300-km simulations, the mean sea level pressure (MSLP) distributions for RUN30, RUN300, and RUN30 averaged to 300-km resolution at 0600 UTC on 18 November 1984 are shown in Fig. 2. Katzfey and Ryan (1997) have shown that the 30-km model simulation compares well with the observations reported by Ryan et al. (1989). As expected with the change in horizontal resolution, RUN30 has a much more detailed structure than RUN300. The major differences between RUN30 and RUN300 at this time are the generally smoother features in RUN300, with no indication of the mesoscale high near the southern box or low centers farther west and over Adelaide. Both simulations have the trough in roughly the same position. A fairer comparison for RUN300 is with the 300-km average of RUN30 shown in Fig. 2c. But even with the averaging, there are features not present in RUN300, such as the low southwest of Adelaide. More significant differences are evident in the precipitation and cloud fields generated by RUN30 and RUN300. Figure 3 shows the 48-h total, resolved and convective rainfall totals; the RUN30 totals over land are comparable to the observations (not shown). As noted by Katzfey and Ryan (1997) much of the resolvedscale precipitation evaporates before reaching the ground, especially for box m2, resulting in relatively less resolved-scale precipitation for this box. The convective precipitation is largest along the coast where there is a combination of adequate moisture and surface heating. The resolved and convective rainfall totals in RUN300 are much less, and are located farther south, than for RUN30, especially for the resolved-scale precipitation. As will be shown, the resolved-scale amounts in RUN300 are much smaller than RUN30 because there is virtually no cloud to generate any precipitation. In order to investigate the cause of this difference in precipitation, the distribution of the vertically integrated cloud plus precipitation and 500-hPa vertical motion fields for RUN30 and RUN300 at 0900 UTC 18 November are shown in Fig. 4. Note the lack of both vertical motion and cloud plus precipitation in RUN300 compared to RUN30. Even when RUN30 is averaged to 300 km, RUN300 has much less cloud and precipitation particles and vertical motion. In particular, the 300-km average of RUN30 shows the magnitude of ascent near Adelaide of greater than 0.8 Pa s 1, while in RUN300 the ascent is only around 0.2 Pa s 1. Evidently the vertical motion in RUN300 is lacking even when compared with the 300-km average of RUN30. Two possible hypotheses for the lack of cloud and precipitation at 300-km resolution are (i) the lack of moisture in the conveyor belt, and (ii) weak vertical motions. All simulations had similar amounts of water

4 2732 JOURNAL OF CLIMATE VOLUME 13 FIG. 3. A 48-h precipitation (mm) event ending 0000 UTC 19 Nov 1984 for (a) and (b) total precipitation, (c) and (d) resolved-scale precipitation, and (e) and (f) convective-scale precipitation for RUN30 (left) and RUN300 (right). Contours used: 0, 0.5, 1, 2, 4, 8, 16, and 32 mm.

5 2733 FIG. 5. West east vertical cross section of potential temperature (K, dashed contours every 5 K), vertical motion (contours as in Fig. 4, Pa s 1 ), and cloud plus precipitation (shaded, g kg 1 ) at 0900 UTC 18 Nov 1984 for (a) RUN30, (b) RUN300, and (c) 300-km average of RUN30. Cross-section contours and locations as indicated in Fig. 4. FIG. 4. The 500-hPa vertical motion (Contours: 0, 0.2, 0.4, 0.8, 1.6, and 3.2 Pa s 1 ) and vertically integrated cloud plus precipitation [shaded contour interval indicated (bottom) g kg 1 ] at 0900 UTC 18 Nov 1984 for (a) RUN30, (b) RUN300, and (c) 300-km average of RUN30. vapor (not shown), indicating the lack of moisture was not an issue. Therefore, the question is why RUN300 did not develop sufficient vertical motions, keeping in mind that these plots are after 33 h of simulations and nonlinear development has likely occurred during this time. To investigate the difference in vertical structure between RUN30 and RUN300, Fig. 5 shows the potential temperature, cloud, and precipitation, and vertical velocity for the east west cross sections indicated in Fig.

6 2734 JOURNAL OF CLIMATE VOLUME 13 FIG. 6. The 500-hPa vertical motion (Pa s 1 ) and vertically integrated cloud plus precipitation (shaded, g kg 1 ) at 0900 UTC 18 Nov 1984 for (a) RUN30NP, (b) RUN30NH, and (c) RUN30NE. Contours as in Fig It is very clear that the vertical motion in RUN30 is much larger and has much more detail than in RUN300. In RUN30, the cloud is located primarily in the regions of updrafts. The region of low-level descent located in the middle of the cross section is related to the evaporative cooling of the precipitation falling from above causing the air to sink. Note the cool dome of air evident in the potential temperature field, which has a weak meso high pressure area associated with it (see Fig. 2). As was pointed out in Katzfey and Ryan (1997), this pressure jump was evident in the observations. The vertical motions are very weak and the potential temperature gradients are very smooth in RUN300 compared with RUN30, and even compared with the 300-km average of RUN30. Only a little cloud plus precipitation is evident in RUN300 along this cross section, located in the region of greatest ascent, but no resolved-scale precipitation was evident, as shown in Fig. 3. It is significant to note that the subsidence, and some hint of the cooling associated with the evaporation, is evident in the 300-km average of RUN30, indicating it projects onto this large scale, especially for the subsidence. There are several possibilities to explain why the vertical motions in RUN300 did not develop as much including weak large-scale gradients (causing weak convergence/divergence and therefore weak large-scale ascent), lack of subgrid-scale effects (such as diabatic heating or vertical ascent), or lack of feedback between the vertical motion and the latent heat released during cloud formation. The results shown for the cross sections in Fig. 5 support the first two possibilities, as the gradients are generally weaker in RUN300 versus RUN30, and there is definitely subgrid-scale vertical ascent in RUN30 not evident in RUN300. The lack of the large-scale ascent in RUN300 is even evident when compared with the 30-km simulations averaged to 300 km. Subgrid-scale latent heating effects can be partly investigated by comparing RUN30 (with partial cloudiness) with RUN30NP. The 500-hPa vertical motion and vertically integrated cloud plus precipitation for RUN30NP (Fig. 6a) are very similar to RUN30, indicating that most of the 30-km grid containing stratiform cloud was explicitly resolved at that resolution. The fields for RUN30NP are only slightly weaker, suggesting minor subgrid-scale effects at 30 km. Evidently, the contribution to the total cloud cover and latent heat from grid points with partial cloud was very small at 30-km resolution. On the other hand, RUN300NP (the 300-km simulation with no partial cloudiness within each grid box, not shown) generated even less cloud and precipitation than RUN300. Although the RUN300 simulation captured the moisture associated with the conveyor belt, the weak vertical motion generated very little condensate, and hence little diabatic heating. The cloud and precipitation in RUN30 is primarily located in the mesoscale updraft regions (Figs. 4a and 5a), indicating that the cloud is being generated by mesoscale motions within the synoptic system. Because RUN300 has no mesoscale structure, it does not develop the cloud band or the system as in RUN30. The suppression of latent heat release of resolvedscale processes in RUN30NH leads to a reduction in vertical motion (see Fig. 6b), except for one region near Adelaide [where there was some convective rain (Fig. 3b)] and near the lateral boundaries (where the simulation was forced to be more similar to the other runs).

7 2735 However, the reduction in vertical motions is not as great as noted for RUN300 (Fig. 4b), indicating it is not just the lack of latent heat that causes the lack of cloud development in RUN300, although it might have had some contribution. The impact of below-cloud diabatic heating on the simulation was examined by comparing RUN30 and RUN30NE (where all subcloud evaporation of precipitation was suppressed). Katzfey and Ryan (1997) showed the suppression of subcloud evaporative cooling affected the movement of the front. Furthermore, in the vicinity of the front, evaporation in the subcloud layer significantly decreased the precipitation reaching the ground. RUN30NE (Fig. 6c) indicates that while there were changes (especially below cloud base), the lack of evaporation of precipitation had only a minor effect on either the heating or the vertical motions within the cloud layer. These experiments support the assertion that the lack of cloud in RUN300 is, in part, due to the inability of the coarse grid to generate the midtropospheric vertical motion. Of course this is partly related to the weaker positive feedback loop (weaker vertical ascent less cloud formation less latent heating less vertical ascent). This weaker positive feedback implies that subsequent development would also be weaker, with a lack of spinup of the system over time. It is therefore concluded that the main reason for the lack of frontal clouds in RUN300 is a lack of mesoscale vertical motions, which are unresolved at 300-km resolution. The impact of resolution is investigated further in the next section. 3. GCM-scale box averages The aim of this section is to examine systematically the time evolution of a typical GCM-sized grid (300 km) of the base variables and the subgrid-scale terms (as determined from the 30-km simulation) that can contribute to the development of the system and therefore need to be parameterized. a. Averaging model equations In order to investigate the impact of resolution on the simulation of the frontal cloud, the basic equations will be averaged from the 30- to the 300-km grid. The temperature and moisture equations can be formulated as follows: T T T RT T L u (C E) (1) t x y cp Ps cp and q q q q u (C E), (2) t x y where T is temperature, q is water vapor mixing ratio, u and are the horizontal wind components, is the normalized terrain following vertical motion, is the pressure vertical motion, P s is the surface pressure, c p is the specific heat of air, L is the latent heat of vaporization, C is the rate of condensation (primarily of cloud ice), and E is the rate of evaporation (primarily of rainwater when the relative humidity is less than 100% in the absence of cloud water). For details of the cloud microphysical parameterization, see Katzfey and Ryan (1997). The condensation rate term (C) is calculated by evaluating all the advective terms in the temperature and moisture equations to give an intermediate temperature T* and mixing ratio q*. The temperature and moisture equations are adjusted isobarically so that the environment cannot be supersaturated with respect to water when cloud water is present or ice when cloud ice is present. Thus, [q* q s(t*)] C. (3) Ldq s(t*) 1 cdt [ ] When a simulation is averaged to a coarser horizontal resolution, the temperature and moisture equations can be rewritten using the standard Reynolds averaging procedure: T T T RT T T T u u t x y cp Ps x y RT T L (C E ) and (4) cp Ps cp q q q q q q q u u t x y x y (C E ), (5) where T and q are the mean for the region of the domain and T and q are the subgrid-scale deviations from the mean. If a coarse-resolution simulation and a high-resolution simulation averaged onto the coarse grid are compared, the difference between the changes in temperature and mixing ratio for the two simulations will depend on the size of the covariance terms. These subgrid-scale effects of the advection covariance terms will also affect the nonlinear condensation/evaporation adjustment procedure. b. Model averaging at the GCM scale RUN30 has been analyzed in accordance with the specifications set down for the GCSS Working Group III workshop that was held at Goddard Institute for Space Studies (GISS) in New York from 1 to 3 November The horizontal and vertical grid lengths (dx, dy, and dz) and the time step (dt) for the model simulation are 30 km, 30 km, 0.5 km, and 120 s, p

8 2736 JOURNAL OF CLIMATE VOLUME 13 FIG. 7. Time pressure plots of mean potential temperature (every 5 K) for boxes m2 and m4, respectively. (a) and (d) RUN30 and (b) and (e) RUN300. Horizontal std dev of potential temperature (every 0.5 K) for boxes m2 (c) and m4 (f) from RUN30. respectively. The horizontal and vertical GCM-sized grid lengths (DX, DY, and DZ) used in RUN300 and for the averaging of RUN30 are 300, 300, and 0.5 km, respectively. The results presented here were sampled once an hour (DT). No averaging was done in the vertical, with both simulations and the averaged data using the 18 sigma levels. The regional mean of a prognostic variable a is defined as adxdydzdt a, (6) DXDYDZDT where the summation is taken over all the grid points within the subdomain DX, DY, DZ of the GCM-scale grid box and over the time interval DT. The variance var a is defined as 2 (a a ) dxdydzdt var a (7) DXDYDZDT and the standard deviation is std dev (var a ) 1/2. c. Analysis of averaging the basic variables on the GCM scale In order to further investigate the impact of the Reynolds averaging over the 300-km grid, the hourly data from RUN30 have been averaged onto a 300-km grid (RUN ). Any variable A 30 from the 30-km simulation can be averaged to the 300-km grid by averaging 300 the surrounding 100 points in RUN30, labeled A 30. RUN gives the mean value, and the difference between RUN30 and RUN gives A. RUN300 gives a value of A 300 that reflects the development of A during 300 the 300-km simulation. The values for A 30, A 30, and A 300 will be shown for the oceanic box m2. 1) POTENTIAL TEMPERATURE The mean potential temperatures averaged over the 300-km boxes m2 and m4 for RUN30 are shown in Figs. 7a and 7d and RUN300 are shown in Figs. 7b and 7e. Above the 310-K potential temperature contour, the

9 2737 potential temperature structure is not modified significantly by the passage of the cool change in either RUN30 or RUN300. The major differences between the two runs are below 310 K. For box m2, the prefrontal air over the ocean is slightly warmer than for RUN300 (compare the location of 295-K contours around 0000 UTC 18 November). For box m4, the difference is greater, possibly indicating stronger surface heating in RUN30 (remember this box was mostly land). These results suggest that RUN300 does not capture the intensity of the prefrontal warm air. However, in general, the differences are relatively minor. The standard deviation (std dev) of potential temperature from RUN30 is shown for box m2 (Fig. 7c) and box m4 (Fig. 7f). Note that there is no spatial variability for the boxes in RUN300 since each is just one grid point. For the ocean point (m2) the potential temperature std dev is a maximum in the lower and upper troposphere, and since the ocean temperatures were smooth and did not vary in time, the std dev in the lowest model level is relatively small. The large lowtroposphere std dev is caused by potential temperature changes associated with the advection of warm air from Australia, the evaporation of precipitation in the subcloud layer, and the low-level baroclinicity of the cool change. The larger std dev in the upper troposphere are related to changes in the tropopause. The magnitude of the std dev is an indication that prefrontal and postfrontal potential temperature fluctuations in the boundary layer are not small on scales below 300 km. In the region of the front this std dev is between 1 and 3 K. The large std dev near the surface in grid box m4 results from the solar heating of the land points within this box during the day (note that the peak std dev is during the daytime hours between 0000 and 1200 UTC on 17 November and between 0000 and 1200 UTC on 18 November). These results indicate strong temperature fluctuations across the GCM-sized gridbox during the passage of the frontal system, which will have implications for the advection. Obviously, RUN300 has zero std dev for a 300- km box (since it is one grid point) and so is unable to capture explicitly this subgrid-scale variability. 2) U AND V COMPONENTS OF THE HORIZONTAL WIND The U component of the wind field for RUN30 averaged over boxes m2 and m4 is shown in Figs. 8a and 8d; while Figs. 8b and 8e show the U component of the wind field for RUN300 in the same boxes. The easterly component extends from the surface to 900 hpa for all the simulations. However, much greater temporal variation is evident in RUN30 around the front, implying greater horizontal gradients. The passage of the front just after 1800 (m2) and 1200 (m4) UTC 18 November is indicated by the change of the low-tropospheric easterlies to westerlies. As indicated in the MSLP in Fig. 2, the locations of the trough and the cold front were generally similar in RUN30 and RUN300. The std dev of the U component of RUN30 over the 300-km boxes (Figs. 8c and 8f) shows a minimum just ahead of the front in the low troposphere for box m2, suggesting that the mesohigh in this region is about 300 km wide. The larger std dev in the mid- to upper troposphere is an indication of the influence of the moist processes on the wind field. As for the U component, the V component of the wind in RUN30 has more structure than in RUN300 (see Fig. 9). RUN30 forms a northerly maximum of V between 600 and 800 hpa, as well as an upper-level maximum for box m2 around 300 hpa, both of which are associated with the baroclinic zone (Figs. 9a and 9d). For RUN300 (Figs. 9b and 9e), the overall pattern is similar, but the meridional wind is weaker for box m4. Similar to the U component, the std dev of the V component in RUN30 (Figs. 9c and 9f) is largest near the front, particularly between 200 and 400 hpa for box m4, and between 700 hpa and the surface for both boxes. 3) VERTICAL MOTION The 300-km box average of RUN30 vertical motion shows low troposphere ascent ahead of the front and strong ascent along the front (Figs. 10a and 10d). The descent within areas of evaporating precipitation below cloud base are clearly indicated, especially for box m2, between 0600 and 1200 UTC on 18 November. The large ascending motion above the surface front is more intense and extends to higher levels in the land box, most likely related to the additional heating associated with the convection for this box. The vertical motions in RUN300 (Figs. 10b and 10e), although showing ascent along the frontal zone, are much broader and weaker than for the box averages of RUN30. The ascent is greater for the ocean box (m4), which is located farther south and farther along the conveyor belt, in contrast to the greater ascent for the northern land box in RUN30. Neither box in RUN300 has any subcloud descent near the front, indicating little or no subcloud evaporation of precipitation. Considerable std dev of the vertical motion within the RUN30 boxes around the front, greater than the box mean, suggests that a significant percentage of the vertical motion is sub-300-km grid scale (Figs. 10c and 10f). The peak in std dev around 1200 UTC 17 November for box m4 is related to the increase of northerly winds ahead of the front and to the frictional decoupling of the boundary layer winds at night causing subgridscale vertical motion as the air accelerates southward over the land. Over the ocean, the cool ocean temperatures cause a stable boundary layer throughout the day. These results reinforce the idea that the ascent of the conveyor belt in RUN300 is slow to develop and is weaker and farther south than for RUN30. In addition,

10 2738 JOURNAL OF CLIMATE VOLUME 13 FIG. 8. Time pressure plots of mean U wind component (every 5 m s 1, positive eastward) for boxes m2 and m4, respectively. (a) and (d) RUN30 and (b) and (e) RUN300. Horizontal std dev of U wind component (every 1 m s 1 ) for boxes m2 (c) and m4 (f) from RUN30. most of the vertical motion is subgrid scale and could not be adequately resolved. 4) HEAT BUDGET The heat budget here is defined to be the net heating/ cooling associated with all precipitation processes, such as condensation and evaporation. In RUN30 there is large-scale in-cloud heating and subcloud cooling of K day 1 (Fig. 11). The box-average model results are consistent with the values from a similar box used by Katzfey and Ryan (1997) to compare the model values with those diagnosed by Ryan et al. (1989). Indeed, similar large-scale heating structures are present in all the box averages (m1 to m4). The diabatic cooling at low levels is associated with the evaporation of precipitation. The convective heating in the boxes (not shown) is significantly smaller than the resolved heating for both boxes. As suggested before, there is some convective heating over the land as seen in box m4 ( 9 K day 1 ), but negligible convective activity over the ocean in box m2 (not shown). The large-scale heating and cooling in both grid boxes of RUN300 are negligibly small and are not shown. There is some convective heating ( 30 K day 1 ) taking place in box m2 toward the end of the simulation, an indication that at this resolution the model is close to resolving the subgrid-scale ascent for this portion of the conveyor belt. There is no significant release of latent heat in box m4. The heat budget analyses support the hypothesis that the observed latent heat release in the conveyor belt is not triggered at 300-km resolution. d. Interpretation of the means and standard deviations The mean variables in the 300-km boxes show that RUN300 fails to capture much of the development of the frontal band that is resolved in RUN30, even when averaged to 300 km. One possible reason why the 300- km simulations may not capture this development is that

11 2739 FIG. 9. Time pressure plots of mean V wind component (every 5 m s 1, positive northward) for boxes m2 and m4, respectively. (a) and (d) RUN30 and (b) and (e) RUN300. Horizontal std dev of V wind component (every 1 m s 1 ) for boxes m2 (c) and m4 (f) from RUN30. if the northern and western boundaries are too close to the developing front during the first 24 h of the simulation, the boundary conditions may inhibit development. This was certainly the case with RUN300S. However, the boundary forcing for both RUN300 and RUN300 are well removed from the region of the front. Another possible reason for the poor development of the front is that the physical processes associated with the front are poorly modeled in the 300-km simulation. This occurs in the cloud layer when there is insufficient latent heat released and in the subcloud layer when there is insufficient evaporative cooling. It is suggested that in these circumstances, the 300-km resolution simulation is unable to generate the required vertical motions needed to maintain and develop the frontal circulation. Consequently, there is a weakening of the horizontal wind field and a reduction in the meridional transport of heat. The weakening of the horizontal wind field reduces the convergence and divergence in the vicinity of the front, leading to further weakening of the mean vertical motion field, and hence the vertical transport of heat and moisture. As was shown in Figs. 4 and 5, the variability in the cloud water fields mirrors the variations in the vertical motion, indicating the importance of the subgrid-scale vertical motion on the generation of clouds. The subgrid-scale variability of vertical motion in RUN30 for 300-km areas (as indicated by the nonzero std dev, Fig. 10) is a direct result of the model developing sub-300- km scale mesoscale structures. However, the changes in the flow field generating the divergence fields that caused the vertical motion are rather subtle and are dependent upon the cloud field itself, that is, the subcloud descent due to evaporative cooling. The previous results show that the 300-km simulation did not adequately capture the frontal cloud band. Computing the 300-km averages and std dev of the 30-km simulation showed that the subgrid-scale variability can be as important as the 300-km grid box mean. This raises several important issues that need to be addressed in

12 2740 JOURNAL OF CLIMATE VOLUME 13 FIG. 10. Time pressure plots of mean vertical motion (, every 1 Pa s 1 ) for boxes m2 and m4, respectively. (a) and (d) RUN30 and (b) and (e) RUN300. Horizontal std dev of vertical motion (every 2 Pa s 1 ) for (c) boxes m2 and (f) m4 from RUN30. evaluating GCM and nested simulations. In order to develop a parameterization to encompass these features, one needs to evaluate the covariance terms in (4) and (5). These covariance terms are evaluated in the next section. e. Covariance terms The covariance terms in (4) and (5) for the 300-km areas are examined using RUN30 in order to gain insight into where these terms are important and possibly suggest how they might be parameterized. Although both the horizontal and vertical advection terms of the temperature and moisture equations have been examined, only results for the horizontal advection of temperature are presented here. The 800-hPa horizontal advection of potential temperature for RUN30 at 0900 UTC 18 November is shown in Fig. 12a. A complicated pattern of warm and cold advection is evident along the baroclinic zone, although there is a large area of warm air advection (WAA) of greater than 40 K day 1 located west of Tasmania and cold air advection (CAA) of less than 30 K day 1 located west of Adelaide. If the horizontal potential temperature advection is averaged over 300- km boxes, the larger-scale pattern of WAA and CAA becomes more apparent, with WAA ahead of the system and CAA behind, but with reduced peak values ( 15 to 20 K day 1 and 20 to 25 K day 1 ). Using the 300-km averaged variables to compute the advection gives a very similar pattern (not shown). The difference between the averaged advection and the advection using the averaged quantities (Fig. 12c) is about an order of magnitude smaller than advection itself and is largest along the baroclinic zone. These results suggest that if the temperature, moisture, and winds in the 300-km simulation had developed in a manner similar to the 300- km averaged variables, the advection would be similar to the 300-km average from RUN30. As was done for the base variables, a measure of the subgrid-scale variability of the advection is computed using the standard deviation of the advection in RUN30

13 2741 FIG. 11. Time pressure plots of grid-scale condensational heating (every 5 K day 1 ) from RUN30P for boxes (a) m2 and (b) m4. for 300-km boxes (Fig. 12d). As anticipated from inspection of Fig. 12a, this quantity is greatest along the front, with magnitudes comparable to the advection itself, indicating that the subgrid-scale variability is not negligible compared to the mean advection. The pattern of subgrid-scale advection [not shown, computed as the difference of the 30-km advection (Fig. 12a) and the 300-km averaged advection (Fig. 12b)] is very similar to the 30-km advection. The 300-km box average of this quantity is zero. The horizontal advection for RUN300 (Fig. 12e), shows a generally similar pattern of WAA and CAA as for the 300-km average (Fig. 12b), but the WAA does not extend as far north, the CAA is located slightly farther west, and the magnitudes are reduced. As was previously stated, it is the nonlinear feedbacks of the generally small subgrid-scale features that eventually cause changes in the 300-km mean base variables. In order to assess the development of this feedback, the time evolution of the horizontal advection of potential temperature is now investigated for the 300-km ocean box (m2). The box-averaged advection in RUN30 (Fig. 13a) clearly shows the low troposphere WAA ahead of the front, and the CAA after frontal passage (around 1800 UTC 18 November). The WAA is also evident in the mid- to upper troposphere preceding the front. Both WAA and CAA are evident in the upper troposphere/ lower stratosphere in association with fluctuations in the tropopause. Finally, a hint of CAA is evident near 900 hpa around 0900 UTC 18 November in association with the mesohigh and the dome of cold air caused by the evaporation of precipitation. Using the 300-km averaged variables to compute the advection gives a nearly identical pattern of advection as the averaged advection in RUN30 (Fig. 13b), similar to what was noted in the horizontal plots shown in Fig. 12. The time evolution of the difference of these two quantities for box m2 (Fig. 13c) is very small, with the largest values (around 1 K day 1 ) just ahead of the front, especially in the low troposphere around the mesohigh. The time evolution of the subgrid-scale variability of the advection, as indicated by the std dev of the advection over the 300-km box (Fig. 13d), shows a general increase from near zero initially to over 4 K day 1 ahead of the front (around the same times and levels as the largest subgridscale advection noted in Fig. 13c). The low initial values of variability result from the coarse initial conditions. Now that we know the time evolution of the subgridscale effects on the 300-km scale from RUN30, we can compare this with the time evolution of the horizontal advection of potential temperature in RUN300 (Fig. 13e) and compute the difference (Fig. 13f) of the RUN300 advection from the 300-km average of RUN30 (Fig. 13a). For the first 6 h, the advections are similar, but the differences tend to grow in time. Investigating how this time evolution of the differences relates to the evolution of the std dev of the advection (Fig. 13d) suggests that it is the growth in the subgrid-scale variability that leads to the growth in differences in the 300-km average advection for RUN300 and RUN30. Remember that the advection using the 300-km average temperatures and winds (Fig. 13b) gives similar values to the 300-km average advection, suggesting that if the grid values in RUN300 developed similarly to the 300- km averaged values, the advection in RUN300 would be similar to the advection using the 300-km averaged variables (or the average advection from RUN30). Because at the start of the run, all simulations started from

14 2742 JOURNAL OF CLIMATE VOLUME 13 FIG. 12. Horizontal advection of potential temperature at 800 hpa at 0900 UTC 18 Feb 1984: (a) advection from RUN30, (b) 300-km area-averaged advection from RUN30, (c) difference 300- km area-averaged advection and advection using the 300-km area-averaged variable from RUN30, (d) std dev of advection for 300-km areas from RUN30, (e) advection from RUN300. (Contours: every 10 K day 1 for (a) and (c) and every 5 K day 1 for (b), (d) and (e) with negative values shaded except for (d). the same initial state, the differences between RUN30 averaged to 300-km and RUN300 are the result of nonlinear feedbacks of the subgrid-scale processes that then affect the evolution of the 300-km averaged quantities. Averaging the RUN30 results to 300 km gives the pattern one can expect from a model run at a 300-km resolution. Without parameterizing the covariance terms, all calculations involve only the grid box mean state variables, missing all subgrid-scale contributions. At any given time, the difference between the mean advection and advection using the mean variables is not large. However, the subgrid scale evidently affects the time evolution of the mean variables, and therefore the covariance of these mean variables. The results of av-

15 2743 FIG. 13. Time pressure plots of averaged horizontal advection of potential temperature for box m2: (a) advection from RUN30 and potential temperature, (b) advection using 300-km area-averaged variables from RUN30, (c) difference of 300-km area-averaged advection and advection using the 300-km area-averaged variable from RUN30, (d) std dev of advection from RUN30, (e) advection from RUN300 and potential temperature, (f) difference of RUN30 advection and RUN300 advection. (Contours: every 5 K day 1 except every 1Kday 1 for (c). Additional 2.5 K day 1 for (d). Negative values shaded except for (d).

16 2744 JOURNAL OF CLIMATE VOLUME 13 eraging the 30-km simulation onto a 300-km grid for the CFRP case suggests that there is a need for the 300- km scale grids (GCMs) to parameterize the effect of the covariance terms in the heat and moisture transport equations. The enhancement of these transport terms will then force changes in the diabatic terms in the heat transport equation, which can lead to further development. These results suggest that the parameterization of the subgrid-scale covariance terms and vertical motions may be necessary in order to generate the clouds correctly and thereby getting the correct diabatic heating. f. Parameterization requirements for climate simulations The current study has established the need to parameterize the mesoscale motions associated with the Australian cool change. The exact form of the parameterization needed to account for the covariance terms in the heat and moisture equations is not yet clear, although the analysis of this case study suggests a methodology. This methodology is indeed that advocated by the GEWEX CSS, whereby the development of parameterizations for the unresolved forcing of cloud processes in GCMs is undertaken by analyzing a broad range of scales rather than any individual process. The tool for such studies is cloud-resolving and/or mesoscale models. As part of the activities of the GCSS Working Group III, this case currently forms the basis of an integrated study using four limited-area models at 20-km resolution, three cloud-resolving models at 5-km resolution and two single column models. The model results are being compared with each other, and with both the CFRP field observations and the International Satellite Cloud Climatology Project satellite data, in order to improve simulations of frontal clouds (Ryan et al. 2000). 4. Summary In this study, the impact of resolution on the development of frontal clouds is investigated for an Australian cold front developing on November Simulations were completed at 30- and 300-km horizontal resolution and for 18 vertical levels, nested within the ECMWF analyses. The main emphasis of this study was to document the differences between a mesoscale model run and a model run at typical GCM resolution. Although the 300-km simulation had the frontal trough in approximately the correct location, it significantly underpredicted the precipitation and clouds in comparison with the 30-km simulation. The possible causes for this deficiency were first investigated by completing several 30-km simulations testing the impact of different physical processes: partial cloudiness for grid boxes, latent heating, and subcloud evaporation of precipitation. Partial cloudiness had only a minimal impact on the 30-km simulation, suggesting that the main development of the frontal cloud was adequately resolved at 30 km. Elimination of latent heat showed weaker development of vertical motion and clouds, but not nearly as weak as in the 300-km simulation. The subcloud evaporation, although affecting the subcloud layer, did not have a significant impact on the development of the midtropospheric vertical motions and clouds. A detailed look at these simulations suggested that the main reason for the lack of development in the 300-km simulation was the lack of subgrid-scale vertical motion. To elucidate further the reasons for the lack of development, the 30-km simulation was then averaged to 300-km by 300-km areas in order to compare it with the 300-km simulation. One unique aspect of this comparison was the computation of the standard deviation of the 30-km simulation over the 300-km grid in order to determine the degree of subgrid-scale variability, which was unresolved by the 300-km simulation. The variables investigated had different regions of enhanced subgrid-scale variability, both in time and in the vertical. For temperature, the variability was maximized near the surface and the tropopause; for the wind components, there was no preferred area of variability. The subgridscale variability of the vertical velocity, maximized in the midtroposphere, was of comparable magnitude to the mean, indicating the subgrid-scale variability was not negligible. The importance of the covariance terms in the advection of temperature and moisture was determined by using the 30-km simulation and its 300-km average to determine the relative contributions of the advection by the mean and covariance terms. It was found that the mean advection was similar to the advection using the mean variables. This suggests that it was the nonlinear interactions of the relatively small subgrid-scale processes, especially subgrid-scale vertical motion, that then caused changes in the mean variables. Although the covariance terms are smaller than the mean terms in the thermodynamic equation, the effect of these terms can have significant impact for simulations longer than 6 12 h. The forcing from these covariance terms may be as important, or even more important, than the diabatic effects associated with cloud microphysical processes. This study suggests that the subgrid-scale vertical velocity is the primary mechanism for cloud formation and that coarse simulations without these terms will not generate realistic cloud and latent heating distributions. This lack of realistic cloudiness will also have a large impact on the microphysical and radiational characteristics of the simulations. The case chosen for this study was a typical cold front in Australia. It is expected that similar results would be found for other situations around the world. Although the 30-km simulation verified reasonably well, there were some deficiencies in this simulation of the cloud field, such as lack of prefrontal midlevel clouds (Ryan et al. 2000). Higher-resolution simulations (5 km)

17 2745 have been completed as part of the GCSS Working Group III analysis of this case that show additional and more realistic cloud structures and additional subgridscale variability. This implies that any parameterization developed to account for the subgrid-scale features may well be applied at various resolutions, though this would depend on the form of the parameterization and would need to be thoroughly tested. Because the subgrid-scale terms are of smaller magnitude relative to the mean terms, an appropriate subgrid-scale parameterization may be created, assuming appropriate dependencies on the larger-scale values can be found. This study suggests some relationship between the baroclinicity and the subgrid-scale terms. The development of such a parameterization is the subject of current research. Acknowledgments. This paper is partly a response to the goals set by the GCSS Working Group III. The paper has benefited greatly from the discussions with colleagues during WCRP-sponsored GCSS Working Group III workshops held during 1995 in New York and during 1997 in Echuca, Victoria, Australia. The paper is a contribution to the CSIRO Climate Change Research Program and has been funded in part by the Australian Department of the Environment, Sport, and Territories. The first author would like to thank the developers and maintainers of the FERRET graphics and analysis program at NOAA/PMEL. REFERENCES Browning, K. A., and Coauthors, 1994: GEWEX Cloud System Study (GCSS) Science Plan. IGPO Publication Series, Vol. 11, World Climate Research Programme, 62 pp. Katzfey, J. J., and B. F. Ryan, 1997: Modification of the thermodynamic structure of the lower troposphere by the evaporation of precipitation: A GEWEX Cloud System Study. Mon. Wea. Rev., 125, Rotstayn, L. D., 1997: A physically based scheme for the treatment of stratiform clouds and precipitation in large-scale models. I: Description and evaluation of the microphysical processes. Quart. J. Roy. Meteor. Soc., 123, Ryan, B. F., K. J. Wilson, and E. J. Zipser, 1989: Modification of the thermodynamic structure of the lower troposphere by the evaporation of precipitation ahead of a cold front. Mon. Wea. Rev., 117, , and Coauthors, 2000: Simulations of a cold front by cloudresolving, limited-area, and large-scale models, and a model evaluation using in situ and satellite observations. Mon. Wea. Rev., in press. Stewart, R. E., K. K. Szeto, R. F. Reinking, S. A. Clough, and S. P. Ballard, 1998: Midlatitude cyclonic cloud systems and their features affecting large scales and climate. Rev. Geophys., 36,