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  • View in gallery

    Evolution of the large-scale forcing for the temperature (a), the water vapor mixing ratio (b), and the east–west (c) and north–south (d) wind components averaged over a 3° × 3° data array for the 7-day period during phase III of the GATE. Contour intervals are 2 K day−1 (a), 1 g kg−1 day−1 (b), and 2 m s−1 (c) and (d). Small arrows at the bottom of all panels show timing of the observed nonsquall clusters, squall line, and scattered convection, respectively.

  • View in gallery

    Radar echo composites for nonsquall clusters (1800 UTC 2 September), a squall line (1800 UTC 4 September), and scattered convection (1800 UTC 7 September) from GATE International Meteorological Radar Atlas (Arkell and Hudlow 1977).

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    Surface rainfall rate (with shading showing rates larger than 0.1, 1, and 10 mm h−1) and surface horizontal wind vectors for the nonsquall clusters of 2 and 5 September (a) and (c), squall cluster of 4 September (b), and scattered convection on 7 September (d).

  • View in gallery

    Three-dimensional perspectives of the isosurface of the total condensate mixing ratio of 0.01 g kg−1 from the experiment 3D. (a) Nonsquall clusters at 1800 UTC on 2 September viewed from above the southeast corner. (b) The squall cluster at 1800 UTC on 4 September viewed from the northwest corner. (c) The scattered convection at 1800 UTC 7 September viewed from above the model top.

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    Hovmöller (x–t) diagrams for the surface precipitation rate from the experiment 2D (a) and 2DHR (b). Precipitation intensity larger than 1 and 10 mm h−1 is shown using light and dark shading, respectively.

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    Time evolution of the difference profiles between observations and results of the experiment 3D for (a) the domain-averaged temperature field, (b) the domain-averaged water vapor mixing ratio, and (c) the domain-averaged relative humidity. Contour intervals are 1 K in (a), 0.5 g kg−1 in (b), and 10% in (c).

  • View in gallery

    Profiles of 7-day mean differences between observations and the experiments 3D, 2D, and 2DHR in (a) the domain-averaged temperature field, (b) the domain-averaged water vapor mixing ratio, and (c) the domain-averaged relative humidity.

  • View in gallery

    Evolution of the domain-averaged 6-h mean of the surface rainfall rates estimated using the radar data and different areas that approximately cover the 3° × 3° data array (a and b), and estimated using moisture budget derived from sounding analysis (c). The 7-day mean values are printed inside each panel.

  • View in gallery

    Evolution of the domain-averaged 6-h mean of the surface rainfall rates derived from the numerical experiment 3D (a), 2D (b), and 2DHR (c). The 7-day mean values are printed inside each panel.

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    Evolution of the domain-averaged 6-h mean of the surface sensible heat fluxes obtained in the numerical experiments 3D (a), 2D (b), and 2DHR (c). The 7-day mean values are printed as well. Observational estimates are shown as stars and the mean values are printed in parentheses.

  • View in gallery

    As in Fig. 9 but for the latent heat fluxes.

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    Profiles of 7-day mean updraft (dashed lines), downdraft (dotted lines), and total cloud mass fluxes (solid lines) obtained in the numerical experiment 3D (a), 2D (b), and 2DHR (c).

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    Evolution of the 3-h-averaged profiles of the cloud fraction calculated as explained in text for the numerical experiment 3D (a), 2D (b), and 2DHR (c).

  • View in gallery

    Profiles of 7-day mean cloud fraction for the experiment 3D (thin solid line), 2D (dashed line), and 2DHR (thick solid line).

  • View in gallery

    Profiles of 7-day mean temperature tendencies due to radiative flux divergence calculated off-line using model-generated thermodynamic data for the experiment 2D (thin solid line) and 2DHR (dashed line). The tendency diagnosed by Cox and Griffith (1979) is shown as thick solid line for the reference.

  • View in gallery

    Profiles of day 2 mean temperature tendencies due to radiative flux divergence calculated off-line using model-generated thermodynamic data for the experiment 2D (thin solid line) and 3D (dashed line).

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    Hovmöller (x–t) diagrams for the CAPE (a) and CI (b) as defined in text for the experiment 2D. CAPE (CI) values larger than 1 and 2 kJ kg−1 (larger than 5 and 30 J kg−1) are shown using light and dark shading, respectively.

  • View in gallery

    Evolution of the domain-averaged CAPE (solid lines) calculated as explained in text for the numerical experiments 3D (a), 2D (b), and 2DHR (c). Observed values of CAPE are shown by stars.

  • View in gallery

    Observed 3-h change of the domain-averaged CAPE plotted against 3-h change of CAPE due to the large-scale forcing for the numerical experiment 3D (a) and the experiment 2D (b).

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Cloud-Resolving Modeling of Cloud Systems during Phase III of GATE. Part II: Effects of Resolution and the Third Spatial Dimension

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  • 1 National Center for Atmospheric Research,* Boulder, Colorado
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Abstract

Two- and three-dimensional simulations of cloud systems for the period of 1–7 September 1974 in phase III of the Global Atmospheric Research Programme (GARP) Atlantic Tropical Experiment (GATE) are performed using the approach discussed in Part I of this paper. The aim is to reproduce cloud systems over the GATE B-scale sounding array. Comparison is presented between three experiments driven by the same large-scale conditions: (i) a fully three-dimensional experiment, (ii) a two-dimensional experiment that is an east–west section of the three-dimensional case, and (iii) a high-resolution version of the two-dimensional experiment. Differences between two- and three-dimensional frameworks and those related to spatial resolution are analyzed.

The three-dimensional experiment produced a qualitatively realistic organization of convection: nonsquall clusters, a squall line, and scattered convection and transitions between regimes were simulated. The two-dimensional experiments produced convective organization similar to that discussed in Part I. The thermodynamic fields evolved very similarly in all three experiments, although differences between model fields and observations did occur. When averaged over a few hours, surface sensible and latent heat fluxes and surface precipitation evolved very similarly in all three experiments and evaluated well against observations. Model resolution had some effect on the upper-troposheric cloud cover and consequently on the upper-tropospheric temperature tendency due to radiative flux divergence. When compared with the fully three-dimensional results, the two-dimensional simulations produced a much higher temporal variability of domain-averaged quantities.

The results support the notion that, as long as high-frequency temporal variability is not of primary importance, low-resolution two-dimensional simulations can be used as realizations of tropical cloud systems in the climate problem and for improving and/or testing cloud parameterizations for large-scale models.

Corresponding author address: Dr. Wojciech W. Grabowski, NCAR, P.O. Box 3000, Boulder, CO 80307-3000.

Email: grabow@ncar.ucar.edu.

Abstract

Two- and three-dimensional simulations of cloud systems for the period of 1–7 September 1974 in phase III of the Global Atmospheric Research Programme (GARP) Atlantic Tropical Experiment (GATE) are performed using the approach discussed in Part I of this paper. The aim is to reproduce cloud systems over the GATE B-scale sounding array. Comparison is presented between three experiments driven by the same large-scale conditions: (i) a fully three-dimensional experiment, (ii) a two-dimensional experiment that is an east–west section of the three-dimensional case, and (iii) a high-resolution version of the two-dimensional experiment. Differences between two- and three-dimensional frameworks and those related to spatial resolution are analyzed.

The three-dimensional experiment produced a qualitatively realistic organization of convection: nonsquall clusters, a squall line, and scattered convection and transitions between regimes were simulated. The two-dimensional experiments produced convective organization similar to that discussed in Part I. The thermodynamic fields evolved very similarly in all three experiments, although differences between model fields and observations did occur. When averaged over a few hours, surface sensible and latent heat fluxes and surface precipitation evolved very similarly in all three experiments and evaluated well against observations. Model resolution had some effect on the upper-troposheric cloud cover and consequently on the upper-tropospheric temperature tendency due to radiative flux divergence. When compared with the fully three-dimensional results, the two-dimensional simulations produced a much higher temporal variability of domain-averaged quantities.

The results support the notion that, as long as high-frequency temporal variability is not of primary importance, low-resolution two-dimensional simulations can be used as realizations of tropical cloud systems in the climate problem and for improving and/or testing cloud parameterizations for large-scale models.

Corresponding author address: Dr. Wojciech W. Grabowski, NCAR, P.O. Box 3000, Boulder, CO 80307-3000.

Email: grabow@ncar.ucar.edu.

1. Introduction

The use of cloud-resolving models (CRMs) in studies of the large-scale role of convective cloud systems raises issues more comprehensive than those arising in cloud-scale process studies. For the most part, this is because more scales of motion are involved, and the physical processes that have to be parameterized (radiation, microphysics, surface fluxes, turbulence) interact with dynamics on a wider range of temporal scales. Two basic issues are the effects of resolution and the third spatial dimension. As far as resolution is concerned, convection organization is a mitigating factor because organization implies that scales larger than individual cloud elements are important (or even paramount). On the other hand, larger cloud systems are produced through organization with the result that domains need to be yet larger to minimize the influence of lateral boundary conditions on the simulations. While organization is most evident in squall lines, it occurs in other cloud systems as well. For example, a wide range of organized regimes was identified in the dynamical study of Moncrieff (1981). A relatively low horizontal resolution (2–3 km grid length) captures the essence of precipitating cloud systems dynamics and their interaction with the large scale, but the effects of resolution on the large-scale effects of cloud systems remain to be fully evaluated.

Since the real atmosphere is obviously three-dimensional, a long-standing question is: How do cloud systems respond under the influence of an extra degree of freedom afforded by third spatial dimension? More specifically, how do the collective effects of loud systems on the thermodynamic budgets, radiative fluxes, and surface fluxes generated using the three-dimensional framework differ from those obtained using the two-dimensional framework? As far as structure of deep convection is concerned, several studies have compared two- and three-dimensional simulations. For instance, Rotunno et al. (1988) concluded that the basic dynamics of long-lived squall lines occurring in strong low-level shear is captured by the two-dimensional framework. On the other hand, a three-dimensional framework is necessary to model the inherently three-dimensional cross-over flow pattern, which is a characteristic property of propagating tropical squall lines (Moncrieff and Miller 1976). A comprehensive review of the three-dimensional characteristics of mesoscale convective systems can be found in Cotton and Anthes (1989). In certain conditions, notably if directional shear of the ambient wind exists, numerical models of organized convection exhibit a variety of three-dimensional features (e.g., Klemp and Wilhelmson 1978; Thorpe and Miller 1978; Tao and Soong 1986; Redelsperger and Lafore 1988; Dudhia and Moncrieff 1989). The effects of rotation also lead to three-dimensional behavior (Skamarock et al. 1994).

Large-scale forcing has been used in some three-dimensional simulations, for example, Lipps and Hemler (1986), Tao and Soong (1986), and Tao et al. (1987). Dudhia and Moncrieff (1987) studied the evolution and transport properties of fully three-dimensional shear-parallel precipitating convection bands in the GARP (Global Atmospheric Research Program) Atlantic Tropical Experiment (GATE). Because of computer limitations the simulation domain was prohibitively small in all these cases (at most a few 10’s of kilometers on a side) to adequately represent large organized cloud systems such as nonsquall cloud clusters and squall lines. Nevertheless, in some simulations the differences between two- and three-dimensional frameworks were rather minor.

Moving to nonprecipitating shallow convection, Moeng et al. (1996) compared results produced by two- and three-dimensional models of convection in the stratocumulus-topped planetary boundary layer. They concluded that some features (e.g., cloud structure) were similar between two- and two-dimensional models even though the momentum fluxes and velocity variances differ considerably. In more basic terms, Werne (1993) has shown that, despite dramatic structural differences between two- and three-dimensional turbulent flows, the two-dimensional framework provides a useful basis for the hard-turbulent scaling of convective heat transfer.

Against this backdrop, we extend the two-dimensional study of Grabowski et al. (1996, hereafter Part I) to three spatial dimensions and use a large horizontal domain (400 km × 400 km) and a 2-km horizontal grid size. In two-dimensional experiments we test the effect of increasing the horizontal resolution by ten-fold. We focus on a period in GATE when a variety of cloud system regimes (nonsquall clusters, a squall line, and scattered convection) developed in association with changes in the large-scale forcing and shear during the passage of an easterly wave. A similar approach was used in a study of the evolution of cloud systems during a 39-day period during Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response (TOGA COARE), which included a major westerly wind burst observed over the tropical western Pacific (Wu et al. 1998). The two-dimensional framework used in the COARE study and in Part I captures many key features of the tropical moist convection (e.g., thermodynamic fields, budgets of temperature and moisture, effects of clouds on radiative processes). A more quantitative comparison between model results and observations than was possible in Part I can be obtained herein, because the model is forced by the B-scale array for which surface fluxes and precipitation estimates exist (see also Xu and Randall 1996).

In Part I (and also in Wu et al. 1998) a moist bias develops, especially during suppressed periods, which follow episodes of strong convection. The enhanced moisture interacts with the radiation and leads to the temperature bias due to the enhanced “greenhouse effect.” It was argued that the moisture bias is a direct consequence of the absence of large-scale forcing for the cloud condensate. Since the model used periodic lateral boundaries, the cloud condensate cannot escape from the computational domain. It can also be argued, however, that (i) spatial resolution applied by the model, (ii) additional degrees of freedom offered by the three-dimensional framework, and (iii) microphysical parameterizations, may also play an important role in the overall model performance. This paper addresses first two aspects; the effects of microphysical parameterizations will be reported in Part III.

In the next section we describe the numerical design, followed by an evaluation of the results in section 3. The effects of clouds on radiative fluxes are described in section 4, whereas the differences betwen two- and three-dimensional frameworks in terms of temporal variability are illustrated in section 5. Finally, conclusions are drawn in section 6.

2. Design of the numerical experiments

We refer to Part I for details of the approach and its limitations. The model used in this study, and in Part I, is the anelastic cloud model documented in Clark et al. (1996); see also references in Part I. The Kessler-type bulk warm rain parameterization (Kessler 1969) and the Koenig and Murray (1976) bulk, two-class ice parameterization are used. Type A ice represents slowly falling, low-density ice such as unrimed or lightly rimed particles, and type B, relatively fast-falling, high-density ice such as graupel. Surface fluxes are calculated using a simple bulk scheme as described in Part I. Because of the prohibitive cost of the three-dimensional experiment, the interactive radiative scheme used in Part I was replaced by the diagnosed radiative tendencies (Cox and Griffith 1979) applied homogeneously across the domain. Adding radiative tendencies to the large-scale forcing term for the temperature is consistent with the discussion at the end of section 2 in Part I. Part III will provide a comparison between two-dimensional simulations using both interactive and noninteractive (i.e., diagnosed) temperature tendencies due to radiative fluxes.

The same seven-day period (1–7 September) during GATE phase III examined in Part I is simulated. The objectively analyzed GATE dataset (Sui and Yanai 1986, and references therein) is used to prescribe the evolving large-scale forcing for temperature and water vapor mixing ratio, and evolving large-scale horizontal winds. Contrary to the experiments presented in Part I, however, the area considered herein corresponds to the B-scale sounding array (as in Xu and Randall 1996), namely the hexagon formed by six ships centered at about 8.5°N and 23.5°W and covering an area roughly 3° × 3°. The mean large-scale conditions for that area are derived from the GATE dataset by averaging profiles of moisture, temperature, horizontal wind, and large-scale forcings for the temperature and moisture over the area from 7° to 10°N and from 22° to 25°W. A smaller area is used for two reasons. First, it makes the three-dimensional simulation feasible. Second, radar-derived estimates of the surface precipitation rate and estimates of the surface fluxes exist for the GATE B 3° × 3° area. The SST used is a constant value of 27.2°C—that is, 0.2°C higher than in Part I, which is consistent with the data from the 3° × 3° area (Krishnamurti et al. 1976).

Three numerical experiments are described and analyzed. (i) Experiment 3D is in three dimensions using a 400 km × 400 km horizontal domain with 2-km horizontal grid size. A 42-level vertically stretched grid is used with grid size 100 m near the surface, increasing linearly to 1200 m at the model top. The vertical extent of the domain is 26 km, as in Part I. (ii) Experiment 2D represents a two-dimensional east–west slab of the three-dimensional experiment. All parameters (i.e., vertical grid, microphysical parameterization, surface flux algorithm, etc.) are as in 3D. (iii) Experiment 2DHR has a horizontal grid size an order of magnitude smaller than the other two (i.e., 200 m instead of 2 km). Decreased grid size is also applied in the vertical (100 m up to a height of 2 km, then increasing linearly from 100 m to 500 m near the model top), giving a 102-level model. A 15-s time step is used in experiments 2D and 3D, and 5 s in 2DHR. In other aspects, the experiments are as in Part I (e.g., free-slip, rigid lower and upper boundary conditions; a gravity wave absorber in the uppermost 7 km of the domain; periodic lateral boundary conditions; and the Coriolis acceleration is set to zero).

Data were archived at 20-min intervals, giving 504 time levels for the 7-day simulation. Because of the large number of data (especially experiment 3D), additional compromises were made to facilitate an efficient analysis. For example, the original datasets were sampled only every second grid point in the horizontal direction(s), and all levels above 18 km were omitted. In addition, in the 2DHR experiment the same sampling strategy was also used in the vertical direction. Analyzed results presented herein are mostly based on the reduced datasets. This probably affects the fine details but not the general conclusions because high-resolution information is obviously included.

Figure 1 shows the evolution of the large-scale forcing for the temperature and water vapor mixing ratio, and the east–west and north–south wind components for the period 1–7 September 1974 used to drive the model. As discussed in Part I, the period selected is characterized by a dramatic evolution in the character and organization of the convection. The period begins and ends with relatively weak and random convection, each lasting for about 1 day (1 and 7 September). The maximum large-scale forcing occurs in environments with relatively weak vertical shear on 2 and 5 September and is associated with nonsquall clusters (Arkell and Hudlow 1977). On the other hand, the squall cluster on 4 September is associated with a low-level easterly jet (Fig. 1c), which persists for about two days. The jet is associated with an easterly wave moving into the eastern Atlantic from the African continent and is clearly evident in both east–west and north–south wind components (Figs. 1c,d). As discussed in Part I, dramatic transitions occur in both model-produced and observed cloud systems during this period.

3. Model evaluation

a. Simulated cloud systems

Video animation is the best way to illustrate the evolution and transitions between different cloud system regimes in a three-dimensional framework. Indeed, the animation shows very realistic behavior of the simulated cloud systems in terms of convection development, organization, and decay. The two-dimensional simulations are much easier to document, for example, by using Hovmöller diagrams. We now provide a brief comparison between model results and observations in regard to cloud system organization and movement.

Figure 2 shows composites of radar displays for 1800 UTC on 2, 4, and 7 September 1974 (Arkell and Hudlow 1977) of nonsquall clusters, a squall line, and scattered convection inside the B ship array (e.g., Cheng and Yanai 1989). Figure 2a shows a snapshot of the horizontal precipitation pattern on 2 September associated with several nonsquall clusters organized in a more or less hexagonal pattern. Nonsquall clusters (albeit with different spatial organization, see the discussion below) were also observed at 1200 UTC on 5 September. On 4 September Fig. 2b shows a bow-shaped squall line (centered near 7°N, 23°W) and large echo-free areas. Figure 2c shows scattered radar echoes with evidence of line organization along the northeast–southwest (NE–SW) direction on 7 September. Scattered convection is associated with the weak forcing typical of that day.

Figure 3 shows four examples of the surface precipitation pattern together with the surface horizontal winds from the experiment 3D. The simulated nonsquall cluster of 2 September is shown in Fig. 3a. The similarity of the simulated surface precipitation pattern and the radar composite (Fig. 2a) is very encouraging. The travel speed of the cloud systems in Fig. 3a is estimated by comparing surface precipitation patterns 1–2 h earlier and/or later to the pattern shown in Fig. 3a. The systems move with speeds between 4 and 6 m s−1 in directions ranging from SE to SW. This agrees with observations (LeMone et al. 1984, their Fig. 3; M. A. LeMone 1997, personal communication).

The plot for 4 September (i.e., for the squall cluster) is shown in Fig. 3b. Two different clusters are apparent in the figure. The first is located in the NW corner of the domain, identified by the strong surface precipitation on the leading edge and strongly divergent surface winds associated with the mesoscale downdraft. The squall system formed spontaneously under conditions of moderate large-scale forcing and the strongest low-level shear in the easterly wave. It moves in the SW direction with the speed between 12 and 14 m s−1, which agrees with the observations reported in Houze (1977). A second system, aligned in the E–W direction features a double-line structure in the east part of the domain. It moves slowly to the south with speed estimated at 2 m s−1. GATE radar data (Houze 1977, his Fig. 17) indeed show SW–NE lines of convection ahead of the squall cluster, although not as extensive (especially at around 1800 UTC) as the one in Fig. 3b. It should be also noted that during its mature stage (i.e., between 1500 and 1700 UTC) the observed squall cluster was considerably larger than the simulated one (see Figs. 15 and 16 in Houze 1977). This is most likely because the periodic computational domain is too small.

The double cloud cluster that developed on 5 September (and included a decaying squall cluster of 4 September discussed above) was also of much larger horizontal extent than the computational domain (Leary 1979). Nevertheless, the mesoscale structure of clouds and precipitation showed the large degree of organization identified in the GATE ship radars and studied by Leary and Houze (1979). These systems moved slowly (2–5 m s−1) in various directions (Leary and Houze 1979, Fig. 4). The simulated surface precipitation and surface winds at 1200 UTC 5 September are shown in Fig. 3c. The cloud system in the NE part of the domain is the same squall system shown in Fig. 3b in the decaying stage and moving toward the SW at about 10 m s−1. The model failed to predict the transformation of the squall system into a nonsquall system by 1200 UTC as observed, although its travel speed continued to decrease and it eventually evolved into a nonsquall system. The system just ahead of the squall line, aligned in the E–W direction, moves slowly to the south with a speed of about 5 m s−1. The one in the southern part of the domain (aligned in the N–S direction) moves to the west with a speed of about 3 m s−1. Horizontal structure and movement of these two systems resemble some of the observed nonsquall clusters (Leary and Houze 1979). Finally, scattered convection on 7 September (Fig. 3d) shows NE–SW oriented short-line structures aligned parallel to the low-level southwesterly winds, similar to those shown in radar pictures (see Fig. 2c).

Figure 4 shows three-dimensional views of the total condensate field (the sum of cloud water, ice water, and rainwater mixing ratios) corresponding to the three cloud systems discussed above. The various types of clouds that constitute nonsquall clusters, both deep and shallow, as well as narrow cloud bands can be seen in Fig. 3a. The squall line is clearly identified in Fig. 3b by the characteristic highly organized deep convection at its leading edge and extensive anvil clouds (about 100 km long) to the rear. Clouds forming the east–west oriented nonsquall cluster (Fig. 3b) are seen in the background.

The two-dimensional experiments, 2D and 2DHR, do not lend themselves to a detailed comparison with observations that are (visually) three-dimensional. Nevertheless, as documented in Part I and in Xu and Randall (1996), some essential features (e.g., vertical extent or movement of systems) can be evaluated. Space–time (Hovmöller or x–t) diagrams of the surface precipitation for experiments 2D and 2DHR are shown in Fig. 5. The organized spatial and temporal pattern of the surface precipitation is similar. Slowly moving cloud systems dominate the precipitation pattern on 2 and 5 September (travel speeds in the range of 4–7 m s−1), a fast-moving system dominates on 4 September (with the propagation speed around 12 m s−1), and the unorganized pattern associated with scattered convection is more prevalent on 1 and 7 September. This agrees with the results presented in Part I. Note, however, that the two-dimensional squall systems are not as continuous as those simulated either in Part I or in Xu and Randall (1996). Additional two-dimensional simulations (in which larger horizontal domains were used) suggest that this is a result of rather small horizontal extent of computational domains used in experiments 2D and 2DHR.

b. Thermodynamic fields

Figure 6 shows the evolution of the differences between modeled and observed profiles of temperature, water vapor mixing ratio, and relative humidity for experiment 3D. The model-predicted profiles are obtained by averaging the model fields over the entire computation domain and over the 3-h period centered on the time of observations. The observational profiles are averages over the 3° × 3° domain. Figure 6 should be compared with Figs. 5 and 6 in Part I where similar comparison for the larger-domain experiments is displayed. (Plots for the experiments 2D and 2DHR were remarkably similar to these in Fig. 6 of this paper and are not shown.)

The 7-day averaged profiles of the differences between modeled and observed fields for all three experiments are shown in Fig. 7. There are several important features in Figs. 6 and 7. First, the differences between model results and observations appear larger than those in Part I, especially the relative humidity (RH) differences, which peak at over 50% in Fig. 6. However, the absolute differences in the water vapor mixing ratios above 8 km are small compared to the values in the lower troposphere. Note that the maximum differences in relative humidity follow episodes of strong large-scale forcing, namely at days 2 and 5. This is consistent with the explanation proposed in Part I, argued to be due to the lack of large-scale forcing for cloud condensate and because condensate cannot escape from the periodic domain after convection intensity decreases. As discussed in Part I, this appears to be a particularly severe problem in the upper troposphere where cloud condensate contributes significantly to the total water content. Larger differences between model results and observations than those in Part I are consistent with the large-scale forcing maxima (cf. Fig. 1) being much larger over the 3° × 3° area. In other words, stronger large-scale forcing increases convective activity and upper-tropospheric cloud amount. Although other CRMs produce higher middle- and upper-tropospheric relative humidities during periods of weak convection, which directly follow periods of strong convection (e.g., Xu and Randall 1996, their Fig. 14), our bias is particularly strong.

An important difference between Part I and the current results is in the sign of the temperature difference during the second half of the experiment. Part I showed model temperatures warmer than the observations, whereas Fig. 6 shows a cold bias. The warming was attributed to the interaction of the enhanced moisture and cloudiness with longwave radiation through a“greenhouse” effect. Estimated radiative tendencies (Cox and Griffith 1979) are used here as part of the large-scale forcing. As shown later, these are considerably smaller than tendencies diagnosed from a radiation transfer model, therefore the reversed temperature bias is not surprising. Part III will provide a detailed comparison between experiments driven by interactive and diagnosed temperature tendencies due to radiation. The key point is that the enhanced moisture is independent of the sign of the temperature bias.

The large differences between modeled and observed temperature profiles in the upper troposphere, like those in Fig. 5a of Part I, are due to two reasons. First, as mentioned in Part I, the exchange between troposphere and stratosphere might be exaggerated because of poor vertical resolution in the upper part of the computational domain. This results in an incorrect prediction of the height of the tropopause. Since model physics is not sufficient to reproduce variations of the tropopause height in the Tropics (e.g., Reid and Gage 1996), a simple relaxation technique with timescale of the order of a day or so could arguably be used to maintain the observed height of the tropopause. Second, variations of the height of the tropopause due to overshooting convective cloud tops are transformed into a smooth transition between troposphere and stratosphere when domain-averaged teperature profile is calculated. When the smooth model-generated profile is compared with the observed profile, significant differences between the two profiles near the tropopause should not be surprising. This is likely the reason why the 2DHR experiment (i.e., the one in which fine details of the tropopause structure do exist because of the high spatial resolution) shows the largest near-tropopause temperature differences among all the experiments (Fig. 7a).

The 7-day average differences between model and observations are strikingly similar (Fig. 7). This illustrates a key result: the temperature and moisture fields evolve in a very similar fashion in all experiments and are only weakly affected by model resolution and the third spatial dimension. Moreover, the differences from observations in the thermodynamic fields (of the order of 1 K for the temperature and 1 g kg−1 for the moisture) are unlikely to affect other aspects, for example, dynamics of cloud systems and transitions between regimes.

c. Surface precipitation rate

A reason to use a 3° × 3° domain rather than the 9° × 9° of Part I is the availability of data for model evaluation. Radar-derived estimates of the surface precipitation rates and estimates of the surface heat fluxes are available over the GATE B-scale array, which is the hexagon shown in Fig. 2. Figure 8 shows the 6-h average surface precipitation rates for the B array derived from radar data for two areas, which approximately corresponded to the 3° × 3° array (area 9 and area 15, see Hudlow and Patterson 1979), and the surface precipitation rate derived from the thermodynamic budget (Thompson et al. 1979). Although both datasets show similar features (e.g., strongest precipitation corresponding to nonsquall clusters of day 2 and 5, and weaker precipitation for other periods), differences do occur. For example, radar estimates give larger precipitation rates for strong events (day 2 and 5) and smaller rates for periods with weaker convection (e.g., days 1, 3, and 7). This is likely a result of the temporal filtering of the budget data (Sui and Yanai 1986). The 7-day average rates differ by about 15%.

Figure 9 shows the surface precipitation derived from the numerical simulations. All three panels show consistent evolution of the surface precipitation rates, similar to the budget-derived rates. This is a necessary condition because large-scale budgets are used to calculate the model forcing. However, the budgets used in the precipitation estimate differ from those used in the estimation of the large-scale forcing (cf., Thompson et al. 1979; Sui and Yanai 1986). It is satisfying that the 7-day mean precipitation rate is almost the same in all three experiments (about 0.55 mm h−1), and close to the budget-derived value.

The evolution of the instantaneous domain-averaged surface precipitation rates shows the difference between two- and three-dimensional frameworks. The measure of temporal variability we use is the root-mean-square (rms) difference between an instantaneous value of a given quantity (sampled at a rate of 3 per hour), at the time t, and its 3-h mean over the period t − 1.5 h to t + 1.5 h, calculated for the period of days 2–7. (We exclude day 1 because it is affected by model spinup.) The rms differences for the precipitation rates were approximately 0.027, 0.15, and 0.13 mm h−1 for experiments 3D, 2D, and 2DHR, respectively. This shows the rms differences in the two-dimensional experiments are similar, but much larger than in the three-dimensional case. Since the surface precipitation data based on radar observations is available on the hourly basis (Hudlow and Patterson 1979), the rms difference between hourly data and the 3-h averaged data was calculated as well. The rms difference was 0.058 mm h−1 for the period of 2–7 September. This value is between the values from two- and three-dimensional simulations. The lower temporal variability of the surface precipitation in the experiment 3D as compared to observations is likely a consequence of temporal filtering of the budget data.

d. Surface heat fluxes

Figures 10 and 11 show surface sensible and latent heat fluxes from the three experiments, together with the observational estimates (Thompson et al. 1979). The evolution of the surface fluxes generally agree with the observational estimates, and the differences between the three simulations are small. The differences of the 7-day mean values of model and observations are smaller than 10 W m−2, which is close to the observational error. Although the latent heat flux agrees fairly well with the observations, the model sensible heat flux is too large (but differences are small compared to the total heat flux). The overestimation of the surface sensible heat flux is consistent with the results of Wu et al. (1998). Note that the observational estimates do not consider enhancement of surface fluxes due to convection (e.g., Jabouille et al. 1996; Esbensen and McPhaden 1996) and the sensible heat flux seems small compared to other estimates. For instance, Augstein (1979) lists values of 5 and 30 W m−2 for the undisturbed and disturbed ITCZ, respectively. Since most of the 7-day period is convectively disturbed, the 9 W m−2 for the mean observed sensible flux is arguably too small.

The differences between the two- and three-dimensional model frameworks may affect the statistics of the surface flux spatial and temporal variability. Table 1 shows selected statistical measures of the surface heat fluxes over the 6-day period (i.e., excluding day 1). The averages presented were calculated as follows. First, the domain-averaged value of the flux, the standard deviation of the flux spatial distribution, and the average value of the largest 10% flux values inside the domain were calculated for both sensible and latent fluxes and for every time level. Also, estimates of the average surface fluxes were calculated based on the domain-averaged near-surface temperature, moisture, and wind components. The ratio between the domain-averaged surface flux and the flux calculated using domain-averaged values for the temperature, moisture, and wind components was calculated for both fluxes at every time level. This ratio is called the “mesoscale flux enhancement factor.” The above quantities were averaged over the 6-day period and the averages of the largest 10% of the mesoscale flux enhancement factors were calculated. Finally, the rms difference between the instantaneous values of the domain-averaged heat fluxes and the 3-h mean fluxes was calculated. Note that the largest 10% flux value is a measure of the instantaneous spatial variability of the surface fluxes, whereas the largest 10% of the mesoscale flux enhancement factor and the rms differences measure the temporal variability of either the mesoscale flux enhancement factor or the domain-averaged surface fluxes.

Table 1 shows that the 6-day mean standard deviations are 10.7, 8.8, and 9.0 W m−2 for the sensible flux in experiments 3D, 2D, and 2DHR, respectively. The corresponding values for the latent flux are 41.0, 35.7, and 33.3 W m−2. The mesoscale flux variability depends mostly on the variability of surface winds (e.g., Jabouille et al. 1996; Esbensen and McPhaden 1996). Therefore, the largest values of the standard deviation for the experiment 3D might be expected in the fully three-dimensional framework. This is supported by the larger mesoscale flux enhancement factors for the experiment 3D as compared to 2D, although 2DHR shows similar (or larger in the case of the largest 10%) enhancement factors. In general, the standard deviations (about 30% above the mean) and the values of the largest 10% flux (about 60% larger than the mean) demonstrate the large spatial variability of the surface flux.

The values of the mesoscale flux enhancement factor fall within the range presented in Jabouille et al. (1996) and Esbensen and McPhaden (1996) but the differences between two and three dimensions are surprisingly small. As far as temporal variability is concerned, the differences between two- and three-dimensional frameworks are not as large as for the surface precipitation: the surface flux rms differences differ by a factor of about 3 between 3D and 2D/2DHR experiments. The 2DHR experiment has the largest temporal variability of surface fluxes.

e. Cloud mass fluxes

The cloud mass flux is a key quantity in most convection parameterization schemes; therefore, a measure of the effects of three-dimensionality is especially pertinent. The updraft and downdraft mass fluxes are averaged over the whole domain for grid points with a total condensate larger than and equal to 0.1 g kg−1. The total cloud mass flux is the sum of updraft and downdraft mass fluxes. Figure 12 shows profiles of the 7-day-averaged cloud mass fluxes for experiments 3D, 2D, and 2DHR. The downdraft mass fluxes are about half of the updraft mass fluxes in all three experiments. The averaged profiles are fairly similar for all three experiments, consistent with the similarity between the evolution of mean thermodynamic profiles. However, an enhancement of both updraft and downdraft mean mass fluxes occurs at low levels in two-dimensions.

Concerning the evolution of cloud mass fluxes, the largest values correspond to the nonsquall clusters (days 2 and 5) and the squall line at day 4 (not shown). However, significant differences in the magnitude of the maxima (minima) of the updraft (downdraft) cloud mass fluxes occur between the two- and three-dimensional experiments during these periods. In general, the two-dimensional experiments have larger (smaller) maxima (minima) of updraft (downdraft) cloud mass fluxes. Because the cloud mass flux is significantly affected by the sampling technique applied to compress the datasets, a more detailed analysis will be presented in a future paper. As an example, the rms differences between the instantaneous values of the mass fluxes and the 3-h mean fluxes were calculated at 4 km. The differences for the updraft were 0.87, 5.9, and 3.3 hPa h−1, and for the downdraft 0.40, 3.1, and 2.1 hPa h−1, for experiments 3D, 2D, and 2DHR, respectively.

4. Effects of clouds on radiative fluxes

Since the numerical simulations use prescribed radiative tendencies, an important question is the effect of two- and three-dimensional cloud systems on the radiative fluxes. It will be demonstrated that clouds in all three simulations affect radiative fluxes in a similar way.

Figure 13 shows the time-height evolution of the 3-h-averaged cloud fraction for the three experiments. Figure 14 shows the 7-day mean profiles. A gridbox is defined as cloudy if the sum of the cloud water and type-A ice mixing ratio exceeds 0.01 g kg−1. Such a height-independent threshold (cf. Tao et al. 1987) is consistent with the notion that a given concentration of condensate particles has the same effect on radiative fluxes regardless of the height at which it is located, provided the optical properties of condensate particles are the same. (To be consistent, however, the threshold should be specified in terms of the concentration not the mixing ratio.) The height-independent threshold leads to similar evolution of the cloud fraction in all three experiments (e.g., the peak cloudiness occurs in the upper troposphere at the end of days 2, 4, and 5). However, some differences between low- and high-resolution experiments are evident for periods with weak convection (e.g., second halves of days 3 and 7), especially in the upper troposphere. The 7-day mean upper-tropospheric profiles (Fig. 14) differ considerably between low- and high-resolution experiments. These differences are likely due to effects model resolution has on the horizontal advection of the upper-tropospheric clouds. These clouds are likely to spread faster in the upper troposphere in low-resolution experiments because of larger numerical diffusion. However, effects related to cloud dynamics cannot be ruled out as the 2DHR experiment shows some features not observed in low-resolution experiments. For instance, updraft–downdraft circulations at the bottom of anvil clouds are common in the 2DHR experiment. These are reminiscent of the circulations associated with mammatus clouds beneath thunderstorm anvils (e.g., Stith 1995).

The model-predicted cloud fractions can be compared to the whole-sky camera observations (Holle et al. 1979) as in Xu and Randall (1996, their Fig. 16). The most evident difference between model results and observations is a distribution of cloudiness with height. For the period selected (1–7 September), the observations give approximately constant cloud amounts at different heights, whereas model data (Fig. 14) clearly indicate strong increase of cloud amount with height. Note that a similar trend is apparent in model results in Fig. 16 of Xu and Randall (1996) as well. The enhanced upper-tropospheric cloudiness in model simulations is consistent with the enhanced upper-tropospheric moisture (Figs. 6, 7c) and points to the effects of periodic boundary conditions combined with the lack of the large-scale forcing for the cloud condensate.

The effects of the modeled thermodynamic fields on radiative fluxes is documented in the next two figures. In this analysis, the University of Utah radiation code (Fu and Liou 1992, 1993; Fu et al. 1995) was applied to every column of the 7-day dataset (archived every 20 min) for the two-dimensional experiments. Similar analysis is performed for day 2 only (i.e., strongest convection) for the three-dimensional experiment. Figure 15 shows 7-day mean temperature tendencies associated with the divergence of both shortwave and longwave radiative fluxes for experiments 2D and 2DHR. The 7-day mean of the temperature tendency from Cox and Griffith (1979) is also shown for reference. When averaged over the entire troposphere, the Cox and Griffith (1979) profile provides considerably stronger radiative cooling compared to the profiles diagnosed by the radiation model. The profiles for the experiments 2D and 3D for day 2 are shown in Fig. 16. In general, the radiative cooling profiles from the radiation model are very similar for the low-resolution experiments 2D and 3D. Because of the differences in the upper-tropospheric cloud cover, the resolution appears to have some effects on the upper-tropospheric radiative cooling. The differences near the surface are due to better vertical resolution, which helps resolve the near-ground minimum of the longwave cooling in 2DHR. Evolution of radiative tendencies for the entire 7-day period (not shown) is similar for both low- and high-resolution two-dimensional experiments with a very strong diurnal cycle in the upper troposphere.

5. Temporal variability

So far, the analysis presented in this paper emphasized similarities between all three experiments as far as collective effects of convection on the large-scale environments is concerned. In several places, however, the differences in terms of the evolution of model-predicted mean quantities were mentioned. The higher temporal variability in the two-dimensional experiments is quantified in this section.

We examine the evolution of the convective available potential energy (CAPE) and convective inhibition (CI) calculated as follows. First, for every column and for every time level (rather than for mean thermodynamic profiles of every time level), a parcel was assumed to rise pseudoadiabatically from the ocean surface and thermodynamic properties of the parcel were then calculated. Second, parcel buoyancy was calculated according to
i1520-0469-55-21-3264-e1
where subscript p refers to the parcel temperature and moisture at a given level; variables without the subscript represent model-predicted fields within a given column;and ϵ = Rυ/Rd − 1. Using (1), CAPE and CI were estimated according to
i1520-0469-55-21-3264-e2a

Finally, domain-averaged values of CAPE and CI were calculated to give representative values at a given time level. In addition, similar analysis was performed for the observational dataset—that is, for nine columns of the 3° × 3° sounding data array. (The surface data are not included in the gridded dataset and they were calculated by vertical extrapolation of the two lowest level data, i.e., at 991 and 946 hPa.) Although more sophisticated calculation of CAPE and CI is possible, this would affect only the actual values of CAPE and CI, and not their evolution, which is examined herein.

Figure 17 is a Hovmöller (xt) diagram of the CAPE and CI for the experiment 2D. The relation between precipitation pattern (Fig. 6a) and patterns of CAPE and CI is apparent. For example, during the squall line period (day 4), the lowest CAPE and highest CI correspond to the stratiform precipitation trailing behind (i.e., to the right of) the squall line. The association of the patterns of precipitation with patterns of CAPE and CI is also evident during other periods. In general, regions of suppressed CAPE and enhanced CI are related to precipitation-induced cloud-scale and mesoscale downdrafts which bring air with low equivalent potential temperature down from higher levels. This is also evident in the spatial variability of precipitation, CAPE, and CI in the experiment 3D (not shown).

Evolution of the domain-averaged CAPE for the three experiments and for the observations is shown in Fig. 18. The composite analysis presented in Thompson et al. (1979, Figs. 2 and 19) shows the lowest (highest) CAPE values during the passage of the easterly wave trough (ridge), which approximately correspond to the nonsquall clusters on 2 and 5 September (squall cluster on 4 September). Unfortunately, this is not very well represented in the analysis of the sounding data shown in Fig. 18, which might be due to the lack of the surface data in the gridded GATE dataset. On the other hand, this pattern is fairly well represented in the model results, arguably with the exception of the three-dimensional experiment (perhaps related to the coexistence of the squall and nonsquall clusters on 4 September in the experiment 3D, see Fig. 3b). The oscillations of CAPE in first half of day in experiments 2D and 3D (and in first few hours in 2DHR) represent the spinup of the model as the weak large-scale forcing leads to gradual accumulation of CAPE, which is later released in a burst of convection apparent in Figs. 4a and 17. Most importantly, however, the smooth evolution of the CAPE in the three-dimensional experiment contrasts with the much larger temporal variability in the two-dimensional case. This is in agreement with the behavior of the domain-averaged surface fluxes, surface precipitation rates, and cloud mass fluxes as mentioned in previous sections.

The differences in the temporal evolution of CAPE between two- and three-dimensional model results persist even if several-hour time averaging is applied. For example, the quasi-equilibrium hypothesis (Arakawa and Schubert 1974) is typically investigated by comparing observed changes of CAPE with the changes due to the effect of the large-scale forcing. The effect of the large-scale forcing on CAPE was calculated by modifying the temperature and moisture profiles at every model column according to the large-scale forcing terms over a 15-min period and calculating the new values of CAPE. The original and new values of CAPE were then used to estimate the rate of changes of CAPE due to the effect of the large-scale forcing. Finally, these rates were averaged over the 3-h period and plotted against the 3-h change of CAPE observed inside the domain. Figure 19 shows the result for the experiments 3D and 2D. Experiment 2DHR shows a similar pattern as 2D (not shown). Significant differences do exist between two- and three-dimensional simulations even after averaging over a 3-h period.

6. Conclusions

We showed that the mean thermodynamic fields, surface precipitation, surface heat fluxes, and the mesoscale flux enhancement factor, as well as the effects of clouds on the radiative fluxes, are similar between the three-dimensional experiment (3D) and the two-dimensional experiments (2D, 2DHR). Analysis of the low- and high-resolution two-dimensional experiments reveals that model resolution has some effect on upper-tropospheric cloudiness during suppressed periods, which directly follow episodes of strong convection, and on the upper-tropospheric temperature tendency due to the radiative flux divergence. The 7-day mean cloud mass flux is similar in all three experiments although the low-level updraft and downdraft cloud fluxes were larger in two dimensions, especially during episodes of strong large-scale forcing. For quantities like mesoscale enhancement of the surface fluxes or radiative tendencies (that are affected indirectly by convection), the similarity is more surprising. These results are consistent with earlier comparisons between two- and three-dimensional simulations (e.g., Lipps and Hemler 1986; Tao and Soong 1986; Tao et al. 1987). It should be borne in mind, however, that the model response is constrained by the prescribed large-scale forcing, which is identical in all three experiments.

The similarities in mean properties are particularly encouraging regarding the use of the CRM-generated cloud-scale quantities (that are fully consistent with the observed large-scale fields but are impossible to directly obtain from observations alone) in the development of physically based parameterizations for global models. The fact that two-dimensional realizations are evidently adequate in this regard is important—not only are two-dimensional systems easier to numerically simulate but they are also analytically more tractable than three-dimensional systems. For example, the convective regimes and the attendant transports derived by Moncrieff (1981) as two-dimensional paradigms of organized convection are a way to introduce the concept of mesoscale organization into parameterization schemes. This concept has previously been tested as a feasibility study (e.g., Miller and Moncrieff 1983). It is an aspect that is presently being further explored in the context of convective momentum transport because this is arguably the distinguishing feature of organization as it affects the large-scale circulations.

The evolution of quantities featured the largest difference between the two- and three-dimensional frameworks. However, when comparing two- and three-dimensional simulations, the physics and the statistics of the problem are difficult to separate. Physical differences between two- and three-dimensional moist convection are associated, for example, with the structure of convective updrafts and downdrafts (e.g., Bretherton 1987, section 4f). Also, a response of the stratified atmosphere to the localized heating (e.g., Bretherton and Smolarkiewicz 1989) will differ in details betwen two- and three-dimensional frameworks. Many types of convection are inherently three-dimensional and although a conditionally unstable atmosphere will obviously convect in two dimensions, it would be surprising if it had the same life cycle as in three dimensions.

The statistical aspects rely on the number of convective elements present in the computational domain at any given time. For example, snapshots of the surface precipitation field (i.e., Figs. 3 and 5) show that usually just a few areas with heavy precipitation occur in the domain in experiments 2D and 2DHR, whereas many coexist in the experiment 3D. It follows that domain-averaged precipitation at a given time is estimated using many gridpoints with nonvanishing surface precipitation in the experiment 3D, whereas only a few are used in the experiments 2D and 2DHR. Thus, a higher temporal variability of domain-averaged precipitation (or any other measure of convective activity) is to be expected in the two-dimensional case.

To clearly distinguish the effects of physics and statistics, one should perform an ensemble of two-dimensional experiments and apply averaging over these experiments to calculate the mean properties (cf. Xu and Randall 1996, section 2). This approach is applied in Part III to show that the low temporal variability of the three-dimensional simulation can indeed be approached by averaging data from several two-dimensional realizations.

Although realistic cloud systems and transitions between different cloud system regimes were simulated (especially in three dimensions), comparisons between model thermodynamic fields and estimates derived from field measurements are far from perfect. In particular, the model-produced upper-tropospheric moisture and cloud fields were too high when compared to the observations. This paper addressed only issues arising from spatial resolution and the third spatial dimension. In general, these have a rather minor effect on the thermodynamic budgets but the microphysical parameterizations could play a significant role. This aspect will be explored in the next part of this series.

We rest our case by saying that, as long as high-frequency temporal variability is not of primary importance, bulk properties and collective effects of the tropical convection are sufficiently similar in two and three dimensions to be useful in parameterization development. This does not rely on strict deterministic agreement, but rather involves time-averaged statistical aspects.

Acknowledgments

Numerical experiments were performed on NCAR’s CRAY YMP supercomputers. Internal review of the manuscript by Jack Herring is gratefully acknowledged, as is the careful editing of the manuscript by James Pasquotto. We thank Prof. Richard Reed for the data used in Figs. 8, 10, and 11. Comments by three anonymous reviewers led to the final version of this paper. This work is supported by NCAR’s Clouds in Climate Program (CCP). The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the NSF.

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Fig. 1.
Fig. 1.

Evolution of the large-scale forcing for the temperature (a), the water vapor mixing ratio (b), and the east–west (c) and north–south (d) wind components averaged over a 3° × 3° data array for the 7-day period during phase III of the GATE. Contour intervals are 2 K day−1 (a), 1 g kg−1 day−1 (b), and 2 m s−1 (c) and (d). Small arrows at the bottom of all panels show timing of the observed nonsquall clusters, squall line, and scattered convection, respectively.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 2.
Fig. 2.

Radar echo composites for nonsquall clusters (1800 UTC 2 September), a squall line (1800 UTC 4 September), and scattered convection (1800 UTC 7 September) from GATE International Meteorological Radar Atlas (Arkell and Hudlow 1977).

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 3.
Fig. 3.

Surface rainfall rate (with shading showing rates larger than 0.1, 1, and 10 mm h−1) and surface horizontal wind vectors for the nonsquall clusters of 2 and 5 September (a) and (c), squall cluster of 4 September (b), and scattered convection on 7 September (d).

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 4.
Fig. 4.

Three-dimensional perspectives of the isosurface of the total condensate mixing ratio of 0.01 g kg−1 from the experiment 3D. (a) Nonsquall clusters at 1800 UTC on 2 September viewed from above the southeast corner. (b) The squall cluster at 1800 UTC on 4 September viewed from the northwest corner. (c) The scattered convection at 1800 UTC 7 September viewed from above the model top.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 5.
Fig. 5.

Hovmöller (x–t) diagrams for the surface precipitation rate from the experiment 2D (a) and 2DHR (b). Precipitation intensity larger than 1 and 10 mm h−1 is shown using light and dark shading, respectively.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 6.
Fig. 6.

Time evolution of the difference profiles between observations and results of the experiment 3D for (a) the domain-averaged temperature field, (b) the domain-averaged water vapor mixing ratio, and (c) the domain-averaged relative humidity. Contour intervals are 1 K in (a), 0.5 g kg−1 in (b), and 10% in (c).

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 7.
Fig. 7.

Profiles of 7-day mean differences between observations and the experiments 3D, 2D, and 2DHR in (a) the domain-averaged temperature field, (b) the domain-averaged water vapor mixing ratio, and (c) the domain-averaged relative humidity.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 8.
Fig. 8.

Evolution of the domain-averaged 6-h mean of the surface rainfall rates estimated using the radar data and different areas that approximately cover the 3° × 3° data array (a and b), and estimated using moisture budget derived from sounding analysis (c). The 7-day mean values are printed inside each panel.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 9.
Fig. 9.

Evolution of the domain-averaged 6-h mean of the surface rainfall rates derived from the numerical experiment 3D (a), 2D (b), and 2DHR (c). The 7-day mean values are printed inside each panel.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 10.
Fig. 10.

Evolution of the domain-averaged 6-h mean of the surface sensible heat fluxes obtained in the numerical experiments 3D (a), 2D (b), and 2DHR (c). The 7-day mean values are printed as well. Observational estimates are shown as stars and the mean values are printed in parentheses.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 11.
Fig. 11.

As in Fig. 9 but for the latent heat fluxes.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 12.
Fig. 12.

Profiles of 7-day mean updraft (dashed lines), downdraft (dotted lines), and total cloud mass fluxes (solid lines) obtained in the numerical experiment 3D (a), 2D (b), and 2DHR (c).

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 13.
Fig. 13.

Evolution of the 3-h-averaged profiles of the cloud fraction calculated as explained in text for the numerical experiment 3D (a), 2D (b), and 2DHR (c).

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 14.
Fig. 14.

Profiles of 7-day mean cloud fraction for the experiment 3D (thin solid line), 2D (dashed line), and 2DHR (thick solid line).

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 15.
Fig. 15.

Profiles of 7-day mean temperature tendencies due to radiative flux divergence calculated off-line using model-generated thermodynamic data for the experiment 2D (thin solid line) and 2DHR (dashed line). The tendency diagnosed by Cox and Griffith (1979) is shown as thick solid line for the reference.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 16.
Fig. 16.

Profiles of day 2 mean temperature tendencies due to radiative flux divergence calculated off-line using model-generated thermodynamic data for the experiment 2D (thin solid line) and 3D (dashed line).

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 17.
Fig. 17.

Hovmöller (x–t) diagrams for the CAPE (a) and CI (b) as defined in text for the experiment 2D. CAPE (CI) values larger than 1 and 2 kJ kg−1 (larger than 5 and 30 J kg−1) are shown using light and dark shading, respectively.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 18.
Fig. 18.

Evolution of the domain-averaged CAPE (solid lines) calculated as explained in text for the numerical experiments 3D (a), 2D (b), and 2DHR (c). Observed values of CAPE are shown by stars.

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Fig. 19.
Fig. 19.

Observed 3-h change of the domain-averaged CAPE plotted against 3-h change of CAPE due to the large-scale forcing for the numerical experiment 3D (a) and the experiment 2D (b).

Citation: Journal of the Atmospheric Sciences 55, 21; 10.1175/1520-0469(1998)055<3264:CRMOCS>2.0.CO;2

Table 1.

Statistical measures of the surface sensible and latent heat fluxes for the three experiments discussed in the paper. See text for details.

Table 1.

* The National Center for Atmospheric Research is sponsored by the National Science Foundation.

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