Explicit and Parameterized Realizations of Convective Cloud Systems in TOGA COARE

Transcription

1 1689 Explicit and Parameterized Realizations of Convective Cloud Systems in TOGA COARE CHANGHAI LIU, MITCHELL W. MONCRIEFF, AND WOJCIECH W. GRABOWSKI National Center for Atmospheric Research,* Boulder, Colorado (Manuscript received 6 March 2000, in final form 13 November 2000) ABSTRACT Convection and cloud processes are examined in a hierarchy of two-dimensional numerical realizations of cloud systems observed during the December 1992 period of the Tropical Ocean Global Atmosphere Coupled Ocean Atmosphere Response Experiment. The hierarchy consists of cloud-resolving simulations at a 2-km resolution, and two sets of 15-km resolution simulations; one attempts to treat convection explicitly and the other parameterizes convection using the Kain Fritsch scheme. The Kain Fritsch parameterization shows reasonable results but shortcomings are found in comparison with the cloud-resolving model. (i) The entraining plumes in the parameterization excessively overshoot the tropopause, which produces a cold bias mostly through adiabatic cooling. The attendant moisture detrainment overproduces cirrus cloud. (ii) Because parameterized downdrafts detrain at the lowest level they generate a surface cold bias. (iii) The scheme fails to represent the trimodal convection (cumulonimbus reaching the tropopause, cumulus congestus around the melting level, and shallow convection regimes) realized by the cloud-resolving simulation and also seen in observations. The lack of shallow convection and cumulus congestus leads to an overprediction of the low-level moisture. (iv) The simulations are sensitive to the magnitude of moisture feedback from the convective parameterization to the grid scale but less sensitive to whether the moisture is in vapor or condensed phase. These deficiencies are mostly a consequence of the single-plume model that represents updrafts and downdrafts in the parameterization scheme, along with the lack of a shallow convection scheme. A more realistic model of entrainment and detrainment that reduces overshoot and represents the cumulus congestus is required. Realistic downdraft detrainment and relative humidity are needed to improve the downdraft parameterization and alleviate the surface temperature bias. 1. Introduction Clouds in large-scale models were until recently assumed to occur simply when the relative humidity in a grid volume exceeded a specified threshold (e.g., 80%). Shortcomings in this diagnostic approach heralded a move to prognostic schemes where cloud condensate and cloud fraction are predicted using time-dependent equations. This has important impacts on cloud radiation interaction. Issues relating to cloud microphysics in this context are reviewed in WCRP (1995). A poorly understood issue concerns the mesoscale organization of convection, a paradigm of which is the mesoscale convective system (also known as a tropical cloud cluster). This kind of system has two primary interactive scales of motion evinced by the convective and stratiform regions (Houze 1989). The organized air- * The National Center for Atmospheric Research is sponsored by the National Science Foundation. Corresponding author address: Dr. Changhai Liu, National Center for Atmospheric Research, P. O. Box 3000, Boulder, CO chliu@ucar.edu flow and the accompanying advection of condensate from the convective region generate stratiform cloud and cirrus in the upper troposphere. This has a marked impact on radiative transfer. It is arguable if the entraining plume used in most convective parameterization and cloud schemes can represent this two-scale process, considering it is not physically compatible with organized airflow and transport (Moncrieff 1981). We chose to examine the Kain and Fritsch (1993) scheme because it represents aspects of mesoscale organization. For instance, it has a reasonably sophisticated downdraft parameterization and convective available potential energy (CAPE) based closure and detrains condensate as well as water vapor to the stratiform region. The existence of the aforementioned two interacting scales deep convection (1 10 km) and mesoscale organization ( km) is at odds with the scale separation principle upon which the theory of convective parameterization ultimately depends. A problem is that the mesoscale component may be explicitly treated while the convective scale is parameterized. In regional models where the horizontal grid length is typically km, both explicit and parameterized convection can occur simultaneously. This aspect has been identified as 2001 American Meteorological Society

2 1690 MONTHLY WEATHER REVIEW VOLUME 129 an issue even in global numerical weather prediction models at km resolution (Moncrieff and Klinker 1997). Nonhydrostatic cloud-resolving models (CRMs), having grid lengths of about 1 km, resolve both convective and mesoscale dynamics and also provide quantities not extensively observable, such as convective updraft/downdraft mass fluxes and condensate. In CRMs the distributions of water vapor, liquid, and ice are calculated at a resolution where the interactions between cloud microphysics and dynamics are treated more realistically than in large-scale models. For these reasons CRMs are the approach of choice of the Global Energy and Water Cycle Experiment (GEWEX) Cloud System Study (GCSS) that seeks to evaluate and improve parameterizations in large-scale models (Browning et al. 1994; Randall et al. 1996). The work reported herein is in this spirit: the Kain and Fritsch (1993) convective parameterization and its effects on convectively generated cloudiness are evaluated using CRMs. Liu et al. (1999) developed a hierarchical modeling approach where the same nonhydrostatic numerical modeling system is used for (i) cloud-resolving simulations, (ii) coarse-resolution simulations (grid length at least 10 km) in which convection is treated explicitly, and (iii) coarse-resolution simulations in which convection is parameterized. Parameterization schemes are evaluated using this approach along with observational analysis. Using this approach Liu et al. (2000) simulated tropical cloud systems observed during 1 7 September in the Global Atmospheric Research Programme (GARP) Atlantic Tropical Experiment (GATE) with an emphasis on transitions among convective regimes in two and three spatial dimensions as the large-scale forcing and wind shear evolved. Herein, the focus is on the physical basis of the Kain Fritsch parameterization per se. In the next section we describe the methodology, followed by the cloud system realizations in section 3 and thermodynamic budgets in section 4. Deficiencies in the parameterization of the physical processes are quantified and ways to overcome them are discussed in section 5. Finally, conclusions are drawn in section Methodology a. Numerical model We use the two-dimensional Eulerian version of the nonhydrostatic anelastic Eulerian/semi-Lagrangian model (EULAG) of Smolarkiewicz and Margolin (1997). The computational domain is 900 km in the horizontal and 30 km in the vertical with a constant vertical grid length of 0.3 km. Periodic lateral boundary conditions are applied and free-slip conditions at the top and bottom of the domain. The uppermost 12 km represents an absorbing layer to damp vertically propagating gravity waves that could otherwise be unrealistically reflected. A bulk cloud microphysical parameterization for liquid condensate (Grabowski and Smolarkiewicz 1996) and a bulk two-category ice parameterization (Grabowski 1999) are used. The surface moisture and sensible heat fluxes are calculated using a simplified version of the Tropical Ocean Global Atmosphere Coupled Ocean Atmosphere Response Experiment (TOGA COARE) surface flux algorithm (Fairall et al. 1996; Wu et al. 1998). The constant sea surface temperature is defined as a spatial average over the COARE Intensive Flux Array (IFA). Subgrid-scale turbulence is represented by the first-order method of Smagorinsky (1963), where the mixing coefficients are proportional to the horizontal resolution and are equal in the horizontal and vertical directions. While reasonable in a cloud-resolving model, in the coarse-resolution experiments the attendant large diffusivity causes excessive upper-level ice clouds (cirrus). In order to eliminate diffusion-induced differences between the two sets of simulations, the mixing coefficients are scaled to a 1-km horizontal resolution, unless otherwise stated. The Kain Fritsch convective parameterization scheme, like most mass-flux-based schemes, uses a single entraining detraining plume model to represent updrafts and downdrafts. It was originally designed to represent midlatitude convection in mesoscale models. Modifications were found necessary for tropical convection (Liu et al. 2000). The updraft radius was reduced from 1500 to 1200 m because tropical convection cores are typically smaller than their midlatitude counterparts (Lucas et al. 1994). The convection scheme is triggered by lifting a 100-mb deep test parcel with the resolvedscale vertical motion to the lifting condensation level (LCL). The resolved-scale vertical velocity threshold [ LCL (m s 1 )] originally used to trigger convection is increased to LCL (m s 1 ). Otherwise, the simulated convection is unrealistically chaotic and scattered. The closure assumes that CAPE is consumed within the time typically taken for convection to advect across a grid cell (typically 30 min to 1 h). The National Center for Atmospheric Research s (NCAR) Community Climate Model cloud-interactive radiative parameterization (Kiehl et al. 1994) is activated at 2-min intervals. In the simulations with parameterized convection the resolved-scale condensate is used in the radiation scheme but the parameterized condensate from the convection scheme is omitted. b. Set of numerical simulations We use the hierarchical approach to examine cloud systems during December 1992 of TOGA COARE. This includes the 6-day period (20 26 December) chosen for the GCSS intercomparison project (Moncrieff et al. 1997; Krueger and Lazarus 1997). The enhanced moisture convergence on 20, 21, 22, and 24

3 1691 FIG. 1. Evolution of the advective tendencies of (a) temperature (K day 1 ) and (b) water vapor mixing ratio (g kg 1 ), (c) east west wind (m s 1 ) and (d) north south wind (m s 1 ) averaged over IFA during Dec December corresponds to episodes of organized deep convection. The zonal wind is characterized by a lowertropospheric westerly burst and an upper-tropospheric easterly. The meridional wind component is relatively weak. Figure 1 shows the evolution of the IFA-averaged advectively generated large-scale tendencies for temperature and water vapor mixing ratio and the horizontal wind components (Wu et al. 1998). The advective cooling and moistening are treated as a forcing in the temperature and moisture prediction equations and the domain-averaged horizontal wind is relaxed to the spatially averaged IFA soundings (Grabowski et al. 1996). We performed a set of six two-dimensional experiments (three-dimensional experiments were beyond our computational means). These are summarized in Table 1. The cloud-resolving control simulation (called CRM) is used to evaluate the coarse-resolution explicit realizations (the EXP series) and the parameterized convection (the PAR series). Note that the microphysics parameterization prognostically calculates the grid-scale precipitation and cloud. EXP1 investigates the overprediction of upper-level cloud arising from the convective parameterization in PAR1. EXP2 differs from EXP1 in that the nonscaled (default in EULAG) subgrid diffusion is used to examine the dependence of quantities such as cloud amount on mixing. In PAR1 the Kain Fritsch parameterization is applied. In PAR2 the condensate feedback in the Kain Fritsch scheme is eliminated. In PAR3 the detrained condensate is converted into an equivalent water vapor detrainment but the corresponding evaporative cooling is included and total moisture and energy are conserved. 3. Cloud system realizations Tropical convection is often organized into multiscale cloud systems defined as populations or ensembles of

4 1692 MONTHLY WEATHER REVIEW VOLUME 129 TABLE 1. Numerical experiments. Experiment Grid length Subgrid-scale mixing Moisture physics Condensate feedback CRM EXP1 EXP2 PAR1 PAR2 PAR3 2km 15 km 15 km 15 km 15 km 15 km Scaled to a 1-km grid mesh Scaled to a 1-km grid mesh Proportional to the square root of grid mesh Scaled to a 1-km grid mesh Scaled to a 1-km grid mesh Scaled to a 1-km grid mesh Bulk microphysics Bulk microphysics Bulk microphysics Bulk microphysics and Kain Fritsch scheme Bulk microphysics and Kain Fritsch scheme Bulk microphysics and Kain Fritsch scheme N/a N/a N/a Yes None Equivalent water vapor feedback moist convection that interact strongly with radiation, boundary layer, and surface fluxes. The regime of organization depends on the large-scale forcing (advection of temperature and moisture) that generates CAPE and on the dynamical effects of environmental shear (Moncrieff 1981). a. Resolved convection (CRM) The deep convection on 20, 21, 22, and 24 December occurs in strong large-scale advective forcing. The December period displays persistent westward-moving mesoscale systems (cf. Figs. 1a,b and Fig. 2a) organized by the vertical shear (see Fig. 1c). During the last two days of the simulation, coexisting cloud systems move eastward steered by the westerly winds. Figure 3 shows the differences among the observed and simulated temperature, water vapor mixing ratio, and relative humidity. The simulated quantities are horizontal and time averages over 6-h periods centered on the times of observation. A tropospheric cold bias of 1 2 K persists throughout the 8-day integration (Fig. 3a). This bias occurs in all models that participated in the GCSS intercomparison project (Moncrieff et al. 1997; Krueger and Lazarus 1997). It has been attributed to inaccuracies in the objectively analyzed temperature and moisture forcing (Emanuel and Zivkovic-Rothman 1999; Krueger and Lazarus 1997) stemming from systematic errors in radiosonde humidity measurements (Zipser and Johnson 1998) and/or from the absence of condensate forcing (Wu et al. 1998). The time mean profile in Fig. 4a shows a cold bias of about 1.8 K throughout most of the troposphere. The temporal variability of the water vapor fields show a difference of less than about 1 g kg 1 (Fig. 3b). The moist bias persists during the weak forcing (suppressed convection). The time-averaged profile in Fig. 4b displays a moist bias with a maximum value of about 0.2 g kg 1 between 3 and 7 km, a dry bias above 7 km, and both positive and negative bias below 3 km. Relative humidity is overpredicted throughout the troposphere (Fig. 3c), which is consistent with the cold and moist bias. Figure FIG. 2. Time space plot of the surface precipitation rate for (a) the 2-km CRM simulation and (b) the 15-km simulation with parameterized convection (PAR1). The light and dark shading correspond to the intensity greater than 1 and 10 mm h 1, respectively.

5 1693 FIG. 3. Time height plot of the difference between the domain-averaged profile in CRM and observations for (a) temperature, (b) water vapor mixing ratio, and (c) relative humidity. 4c indicates that the horizontal and time mean difference is generally less than 15% in the lower troposphere with maxima in the upper troposphere. Figure 5 displays the evolution of the modeled surface sensible heat flux, latent heat flux, and precipitation averaged over the domain and during a 3-h period. The 6- hourly in situ measurements (Lin and Johnson 1996) and the 3-hourly satellite-derived data (Curry et al. 1999) are presented for comparison. There is satisfactory correspondence between the simulated and observed temporal variability in the latent heat flux. The mean value is close to the satellite estimate but about 10% larger than the buoybased observations. In contrast, the modeled sensible heat flux is markedly larger, which is consistent with the cold bias near the surface (Fig. 3a). The simulated precipitation shows an excellent agreement with the budget estimate in terms of both the temporal distribution and the 8-day mean, which is not surprising considering the large-scale moisture advection (forcing) is specified. The satellite-derived precipitation is larger and more variable than either the CRM or the observational budget results. Direct quantitative comparisons are difficult for several reasons. First, the forcing is a horizontal average over the IFA whereas, in reality, synoptic variability may affect it. Second, errors arise from instrument measurements and retrieval assumptions. Third, representativeness is an issue. Lin and Johnson s data are averages from four buoys and are not necessarily representative of the IFA at large. In contrast, the satellite estimate represents the average over a region larger than the IFA (4 S 0.5 N and E). The COARE surface fluxes estimated from the buoy measurements are accurate to about 10 W m 2 (Webster and Lukas 1992). The difference in the simulated latent fluxes lies within this margin, although the sensible heat fluxes differences are somewhat larger. Figure 6 shows the time series of the domain-averaged outgoing longwave radiation (OLR) at the top of the atmosphere in the simulation and the corresponding satellite measurements (Rossow and Zhang 1995). The maximum discrepancy in OLR during the first day is a spinup artifact due to the absence of clouds in the initial state. The 8-day CRM average is 16 W m 2 larger than the observed, but the mean over the last 7 days is closer to observations.

6 1694 MONTHLY WEATHER REVIEW VOLUME 129 FIG. 4. Profiles of the domain- and time-averaged bias (model minus observation) for (a) temperature, (b) water vapor mixing ratio, and (c) relative humidity in CRM (thick solid) and simulations with parameterized convection (PAR1: dashed, PAR2: dotted, and PAR3: thin solid). Figure 7 shows the horizontally and time-averaged distributions of cloud fraction and total condensate (cloud water q c rainwater q r ice q i ) mixing ratios. A grid box is assumed to be 100% cloudy when the condensate exceeds 0.01 g kg 1 but otherwise is designated to be clear. Figure 7a indicates that the condensate is concentrated in midtroposphere with the maximum of about 0.43 g kg 1 just above the melting level, less than 0.1 g kg 1 below 4 km and negligible above 16 km. The individual components (not shown) reveal that the cloud water and rainwater make comparable contributions to the total liquid water content at lower levels. The cloud fraction in Fig. 7b exhibits a maximum of about 0.52 at about 11 km. There is a secondary maximum of 0.46 near the melting level, correlated with the peak condensate amount. b. Parameterized convection (PAR1) The space time diagram of surface precipitation in Fig. 2b shows that the major convective systems move similarly as in CRM, but otherwise significant differences occur. The parameterization produces shorterlived and intermittent convection, a problem also seen in the GATE simulations (Liu et al. 2000). This may stem from how convection is triggered in the parameterization scheme. The triggering of convection in cloud-resolving models is more realistic because explicit interactions of the downdraft outflows with the boundary layer winds are allowed (Moncrieff and Liu 1999). Time height sections of the temperature, water vapor mixing ratio, and relative humidity differences from observations are similar to those from CRM (not shown).

7 1695 FIG. 5. Evolution of (a) the domain-averaged surface latent heat flux, (b) sensible heat flux, and (c) precipitation in CRM (solid) and the simulation with parameterized convection PAR1 (dashed). Circles and stars represent satellite observations (Curry et al. 1999) and buoy observations in (a) and (b) and the budget estimate in (c) (Lin and Johnson 1996), respectively. Numbers in the brackets are mean values. FIG. 6. Evolution of the domain-averaged OLR in CRM (solid line) and the simulation with parameterized convection PAR1 (dashed line). Stars represent observations (Rossow and Zhang 1995), and numbers in the brackets are mean values. There are systematic cold and moist biases. PAR1 produces a larger cold bias near the surface and near the tropopause, as well as a larger moist bias in the lower troposphere. The respective time-averaged bias profiles in temperature (Fig. 4a) exhibit similar vertical distributions, but with significant differences at the surface and above 13 km. PAR1 generates a moist bias below 7 km and a dry bias above (Fig. 4b). The relative humidity bias in Fig. 4c is slightly greater but the distribution is otherwise similar. The surface fluxes and precipitation evolution (Fig. 5) are similar to their CRM counterparts and to those observed. The 8-day mean latent heat flux is 159 W m 2, which is slightly larger than in CRM (156 W m 2 ) and the satellite estimate (150 W m 2 ). The mean sensible heat flux reaches 42 W m 2, larger than for CRM (34 W m 2 ), and significantly larger than either the satellite-derived value (11 W m 2 ) or the buoy measurements (16 W m 2 ). The temporal variability and mean value of the precipitation in CRM and PAR1 agree with the satellite-derived estimate during weak forcing. For the satellite estimate, significant peaks occur during the strong forcing on 20, 22, and 24 December, the temporal mean being about 20% larger than the simulated values. In contrast to the explicit realizations (CRM, EXP1 and EXP2), precipitation in PAR1 con-

8 1696 MONTHLY WEATHER REVIEW VOLUME 129 parameterized condensate is not taken into account), so the total is smaller than in CRM except near the tropopause. The largest discrepancy occurs in midtroposphere. Nevertheless, the vertical distributions in the two experiments show similar trends. In contrast, the cloud fraction (Fig. 7b) is larger in the coarse-grid simulation at upper levels and comparable to CRM below the melting level. This suggests that the parameterized convection penetrates to higher altitudes than the resolved convection. Similar behavior occurred in the NCAR Mesoscale Model Version 5 that also used the Kain Fritsch parameterization (Su et al. 1999). This aspect is examined in section 5. FIG. 7. Profiles of (a) the domain- and time-averaged condensate and (b) cloud fraction in CRM (thick solid), PAR1 (dashed), EXP1 (dotted), and EXP2 (thin solid). tains both grid-scale (explicit) and cumulus parameterization contributions. The parameterization accounts for about half of the total rainfall and more during weak forcing. Apart from during spinup, the OLR time series (Fig. 6) resembles observations and is smaller than in CRM. The 8-day average is 178 W m 2 or 16 W m 2 less than in the explicit experiment but identical to observations. The difference is likely correlated with the more extensive cirrus in the coarse-resolution simulation. Figure 7a depicts the grid-scale condensate (i.e., the 4. Thermodynamic budgets The apparent heat source Q 1 and the apparent moisture sink Q 2 (Yanai et al. 1973) are used to diagnose the effects of convection on the large-scale thermodynamics. These quantities can be explicitly estimated from the model datasets: L Ls L Q1 (c e ) (d s ) ( f m ) cp cp cp ( w ) D Q r, (1) z t cu L Ls 1 Q2 (c e d s ) ( w q ) c c z p L L q Dq, (2) cp cp t cu where the overbar variables represent the horizontal average; the prime variables the deviation from the average; ( p/1000) p R/c the Exner function; D and Dq the subgrid flux of and q, respectively; c, e, f, m, d, and s the mean condensation, evaporation, freezing, melting, deposition and sublimation rates, respectively; and c p, c, R c p c, L, L f, and L s the specific heat of dry air at constant pressure, specific heat at constant volume, the gas constant, and the latent heats of condensation, fusion, and sublimation, respectively. The first three terms on the right-hand side of Eq. (1), the grid-scale microphysical processes, are calculated directly from the simulations. The next four terms represent eddy grid-scale (resolved) transport, subgrid mixing, the effect of the parameterized convection in the coarse-grid experiment, and radiative heating, respectively. The corresponding terms for moisture are found in Eq. (2). a. Convective heating Figure 8 shows the horizontally and time-averaged profiles for CRM and PAR1. The model-produced Q 1 distributions agree well with observations, which is to p

9 1697 FIG. 8. Heat budget. (a) Q 1, (b) phase changes, (c) eddy transports, (d) subgrid-scale diffusion, and (e) radiative heating. The solid and dashed lines correspond to CRM and PAR1, respectively. The dotted line in (a) represents observations and in (b) the parameterized heating.

10 1698 MONTHLY WEATHER REVIEW VOLUME 129 be expected because they are mainly determined by the large-scale forcing (Fig. 8a). The slightly larger apparent heating in the observations is indicative of the systematic cold bias of the simulations. The diabatic heating associated with phase changes dominates the Q 1 budget (Fig. 8b) with maximum heating in midtroposphere about the same (14 K day 1 ) in both. The diabatic heating profile for PAR1 contains explicit and parameterized contributions, comparably partitioned. The smaller heating rate in the km layer in PAR1 as compared to CRM is explained as follows. The Kain Fritsch parameterization represents adiabatic cooling resulting from overshooting cloud tops. If the ascent in the singleplume model is too strong in the upper troposphere (i.e., entrainment is too small), the plumes will penetrate too deeply. The attendant adiabatic cooling and the sublimation of the detrained condensate will therefore be too large. The corresponding excessive moisture (water vapor plus condensate) detrainment is responsible for the cirrus overprediction near the tropopause (explained in more detail later). The resolved-scale eddy transport is small and its sign is highly variable (Fig. 8c) in both CRM and PAR1. It is not surprising that the values are larger in CRM because of the much higher resolution (2- vs 15-km grid length). Subgrid-scale diffusion (Fig. 8d) is significant only below 6 km and largest near the surface because of sensible heat transport from the warm ocean. The vertical distributions of subgrid-scale diffusion are similar in CRM and PAR1. The radiative heating profiles (Fig. 8e) are also similar and largest around 12 km near the cirrus top (Fig. 7b). Heating occurs above 14 km and in a shallow layer around 4.5 km beneath a secondary maximum in cloudiness. (The larger cooling below 13 km in CRM is due to the shallower convection and correspondingly less extensive cirrus; see Fig. 7.) b. Convective drying For easy comparison with the heating, the moisture budget is expressed in temperature units of K day 1 using the identity L q c p T. (It follows that in the following discussion convective drying corresponds to warming, and moistening to cooling, respectively.) The simulated Q 2 budget (Fig. 9) corresponds well to observations for the same reasons as Q 1. The convective drying almost balances the moistening by large-scale forcing (Fig. 9a). The low-level convective drying in PAR1 is slightly less than in either CRM or observations, consistent with the water vapor bias (Fig. 4b). At middle and upper levels, the difference among the simulations and observations is minimal. The difference in the drying due to phase changes is relatively greater than that in heating (Fig. 9b) because the moisture transport by convective eddies dominates the sensible heat transport. Compared with Q 1, the grid-scale moisture transport (cf. Figs. 8c and 9c) is more efficient than the heat transport. It dries the atmosphere below and moistens it above 2 km. The largest drying and moistening occurs at the lowest level and around 4.5 km, respectively. The low-level drying and upper-level moistening are larger in CRM due to the larger explicit transport. Subgrid diffusion is small and irregularly distributed in both simulations (Figs. 8d and 9d), but it significantly enhances the low-level moistening in the lowest kilometer through water vapor transport from the ocean surface. 5. Parameterization issues For the most part, the Kain Fritsch parameterization is satisfactory, but specific deficiencies are identified. Of note are the upper-level and surface cold bias arising from the parameterized cooling, the low-level moist bias, and the cirrus overprediction. We attribute these issues to deficiencies in the single-plume representation of the convective mass flux. Cloud-resolving models provide accurate estimates of convective mass flux, which is a key quantity in parameterization. a. Updrafts and downdrafts Figure 10 compares the profiles of the horizontally and temporally averaged updraft and downdraft mass fluxes derived from the parameterization in PAR1 with the values calculated explicitly from CRM. The updraft mass fluxes in convective cores are distinguished from weak ascent in the stratiform region (Lucas et al. 1994), and from gravity waves, by requiring the absolute value of the vertical velocity to exceed 1ms 1 and the total condensate to exceed 0.01 g kg 1. The specified velocity threshold significantly affects the updraft (and downdraft) mass fluxes but not its shape (Figs. 10a,b). In order to examine the sensitivity to the condensate criterion, the mass fluxes were computed using a threshold as large as 0.1 g kg 1 (not shown). The results were very similar to those in Fig. 10, proving the condensate threshold is not critical. Because mesoscale circulations are crudely represented on a 15-km grid, a threshold cloud mass flux should properly delineate between convective and convectively generated mesoscale circulations (e.g., the stratiform ascent and mesoscale downdraft). Only the deep convection part of mesoscale systems should be parameterized at a 15-km resolution. This is different from climate models whose resolution (grid length of hundreds of kilometers) requires that both convective and mesoscale components be parameterized. Figure 10a shows that compared to CRM, the parameterized updraft mass flux in PAR1 has a more uniform profile and is much smaller below the 8-km level and larger above. The CRM updraft mass flux is largest in the 2 5-km layer. We attribute this maximum to convection with tops around the melting level (approximately 5 km). While the more energetic cumulonimbus

11 1699 FIG. 9. Moisture budget. (a) Q 2, (b) phase changes, (c) eddy transports, and (d) subgrid-scale diffusion. The solid and dashed lines correspond to CRM and PAR1, respectively. The dotted line in (a) represents observations and in (b) the parameterized portion. penetrate the tropopause, their contribution to the cloud mass flux is comparatively small. This is consistent with the analyses of TOGA COARE shipboard radar measurements (Johnson et al. 1999) that identified three cloud categories: cumulonimbus, cumulus congestus, and shallow convection. The latter is not parameterized in PAR1, and only the deep cumulonimbus category is represented by the single entraining plume model in the Kain Fritsch scheme. The resulting absence of the cumulus congestus implies smaller upward water vapor transport from the lower troposphere and likely contributes to the low-level water vapor bias. On the other hand, the large parameterized upper-level mass flux implies deeper and stronger convection that will penetrate the tropopause and cool the environment through adiabatic cooling and sublimation of the detrained condensate. Thus, we attribute overshoot-generated cooling to the cold bias, and the accompanying excessive moisture detrainment is responsible for the cirrus overprediction. The convective downdrafts in CRM extend throughout the troposphere, and the shape of the mass flux profile mirrors the updraft flux but is smaller in magnitude. On the other hand, in PAR1 the parameterized downdraft mass flux is concentrated below 6 km and is smaller except in the lowest 1 km. The unrealistic downdraft detrainment near the ground is responsible for the excessive surface cold bias in PAR1. Figure 10c shows that the space- and time-averaged downdraft relative humidity in CRM is a function of altitude, ranging from more than 90% near the melting level to less than 80% near the surface. In the Kain Fritsch parameterization, however, the relative humidity in downdrafts is not allowed to fall below 90%. Consequently, the parameterized downdrafts will be moister than the explicit downdrafts in CRM.

12 1700 MONTHLY WEATHER REVIEW VOLUME 129 FIG. 10. Profiles of (a) the updraft mass fluxes, (b) downdraft mass fluxes, and (c) relative humidity in downdrafts in CRM when the total condensate exceeds 0.01 g kg 1 and the absolute value of the vertical velocity exceeds 1 m s 1 (solid line), 2 m s 1 (dashed line), and 0.5 m s 1 (dotted line). The thick solid line represents the parameterized mass flux in PAR1. The updraft and downdraft fluxes both depend upon the subjectively specified vertical velocity threshold but, as Figs. 10a and 10b show, the above arguments are valid throughout a range of thresholds. The key points are (i) the convection in CRM consists of multiple cloud types (with correspondingly different entrainment rates), and (ii) the parameterized convection is deeper and has larger mass fluxes and detrainment in the upper troposphere. Like the convective mass fluxes, the relative humidity of the downdrafts in CRM also depends on the strength of the downdraft cores. As indicated in Fig. 10c, the larger the vertical velocity threshold, the less saturated the downdrafts. b. Overprediction of cloud amount Cloud amount and condensate distribution affect radiative transfer in important ways. In the explicit (CRM and EXP series) simulations these quantities are calculated prognostically by the microphysical parameterizations. In CRM the microphysical processes are explicitly coupled to cloud-scale and mesoscale dynamics, whereas in PAR1 they are empirically partitioned into grid-scale and parameterized components. This aspect is likely resolution dependent. PAR1 overpredicts the cirrus cloud fraction. Were the subgrid-scale convective cloud taken into account the

13 1701 overprediction would be even worse. The overprediction could be resolution dependent because of the subgrid diffusion. A larger grid spacing causes stronger mixing and greater cloudiness as demonstrated in the two explicit experiments, EXP1 and EXP2, that are identical except for the subgrid diffusion formulation. The diffusion in EXP1 is scaled to a 1-km grid length, whereas in EXP2 it is proportional to the square root of the horizontal resolution (the default in EULAG). Figure 7 shows the horizontally and time-averaged condensate and cloud fraction profiles. The cloud fraction is significantly larger at upper levels in EXP2 but the condensate amount is comparable. Noting that the EXP1 and CRM cloud fractions are comparable, we conclude the overprediction of upper-level cloudiness in PAR1 is not due to diffusion; rather, it is a deficiency of the cumulus parameterization. Because the entraining plumes in the Kain Fritsch scheme penetrate more deeply than the explicit convection in CRM (Fig. 10) and the plume detrains only at the uppermost level, the detrainment of water vapor and condensate is the cause of excessive upper-tropospheric cloudiness. c. Condensate feedback Most cumulus parameterization schemes feed water vapor back to the large-scale environment. Kain Fritsch also accounts for condensate generated by parameterized convection. The importance of direct condensate (hydrometeor) feedback from subgrid convection was advocated by Molinari and Dudek (1992) based on the simulated interaction between convective regions and stratiform regions of convective systems. Zhang et al. (1994) argued that the magnitude of the moisture detrainment rate is more important than type (i.e., cloud water, rainwater, cloud ice, snow, or water vapor). We conducted two sensitivity experiments to investigate condensate feedback. In PAR2, the condensate detrainment is suppressed so the amount of total moisture feedback is decreased accordingly. In PAR3, the condensate detrainment is converted into an equivalent water vapor detrainment and the resultant evaporative cooling is included. The mean temperature and water vapor bias profiles are shown in Fig. 4. When the condensate feedback is neglected (PAR2), the modeled temperature throughout the troposphere is cooler than in the full feedback experiment (PAR1). The difference is striking in the 6 14-km layer. The temperature difference is mostly associated with the radiative cooling difference (Fig. 11) which, in turn, is reflected in the cloudiness (Fig. 12). A comparison of Figs. 12a and 12b shows that condensate feedback mostly increases the extent of upperlevel cloud fraction (cirrus). This suggests that the overprediction of cirrus in the full feedback simulation is due to excessive condensate detrainment in the cumulus parameterization. The impact on water vapor is also noticeable when condensate detrainment is deactivated. FIG. 11. Profiles of the domain- and time-averaged radiative heating in PAR1 (solid), PAR2 (dashed), and PAR3 (dotted). The condensate feedback moistens the grid column and thus explains why the simulation without condensate detrainment is drier. When condensate feedback is converted into equivalent water vapor feedback, the modeled temperature is warmer at middle and upper levels but slightly cooler at lower levels compared to the full feedback experiment (Fig. 4a). Cloud radiative interaction can only partially account for the temperature difference (Fig. 11) because the condensate and cloud amount are similar (Fig. 12). In summary, the simulations are sensitive to the total amount of detrained condensate and water vapor but comparatively insensitive to the phase of water fed back to the grid scale. 6. Conclusions We evaluated the Kain Fritsch parameterization by employing a hierarchy of two-dimensional simulations of cloud systems observed during December 1992 of TOGA COARE. The hierarchical approach employs a cloud-resolving model, explicit 15-km resolution simulations, and ones that apply the Kain Fritsch cumulus parameterization. Overall, the Kain Fritsch scheme represents the macrophysical properties of the cloud systems reasonably well, but we identified specific shortcomings. First, there is a systematic tropospheric cold bias common to all cloud-resolving and single-column models used in the GCSS model intercomparison (Moncrieff et al. 1997; Krueger and Lazarus 1997). This is thought to stem from errors in the large-scale advective forcing, the lack of condensate forcing or a combination of these factors.

14 1702 MONTHLY WEATHER REVIEW VOLUME 129 FIG. 12. Profiles of (a) the domain- and time-averaged condensate and (b) cloud fraction in PAR1 (solid), PAR2 (dashed), and PAR3 (dotted). Second, a low-level moist bias is evident. Third, a cold bias occurs near the tropopause with an accompanying overprediction of cirrus, and also at the surface. Fourth, cumulus with tops in the middle troposphere are not adequately represented. We attributed most of the specific shortcomings to parameterized mass flux having a more uniform distribution than in CRM. This difference stems from the updraft entrainment/detrainment by the single entraining plume model used in the Kain Fritsch scheme (and in most mass-flux-based convective parameterizations). It generates excessive detrainment of water vapor and condensate in the upper troposphere and therefore the cloud fraction is too large. Overshooting cloud tops are responsible for the adiabatic cooling on the grid scale. The concentrated downdraft detrainment at the lowest level contributes to the large cold bias near the ground. The influence of the detrainment of condensate from the convection to the environment was quantified. Deactivating the subgrid to grid-scale condensate feedback decreases the total moisture feedback and significantly reduces cloud fraction. In turn, this enhances the midlevel radiative cooling and upper-level heating. When the condensate feedback is converted into the equivalent water vapor feedback but total moisture feedback and energy are conserved, the simulated condensate, cloud fraction, and water vapor fields resemble their counterparts in the full feedback case. Results are therefore relatively insensitive to the phase of moisture fed back to the grid scale. The two-dimensional simulations of TOGA COARE systems reported here shows that the Kain Fritsch scheme reasonably represents cloud system properties in different shear and large-scale forcings [cf. Liu et al. (2000) for cloud systems in GATE]. The convective systems during December 1992 of TOGA COARE were organized by the effects of vertical shear. The Kain Fritsch scheme partially represents aspects of organized convection such as downdrafts and the condensate detrainment that maintains the stratiform region of convective systems. A more realistic representation of midlevel detrainment is required to alleviate the overshooting cloud-top problem and to represent convection with tops around the melting level. It is not known whether a modified entraining/detraining plume model will be adequate, or whether a new process model that accurately represents organized airflow is necessary to correct the shortcomings of the Kain Fritsch parameterization in conditions of organized convection. Acknowledgments. We acknowledge Jimy Dudhia and Xiaoqing Wu for their comments on the manuscript. The National Center for Atmospheric Research is sponsored by the National Science Foundation. This research is supported by the NASA TRMM Grant NAG REFERENCES Curry, J. A., C. A. Clayson, W. B. Rossow, R. Reeder, Y.-C. Zhang, P. J. Webster, G. Liu, and R. S. Sheu, 1999: High-resolution satellite-derived dataset of the surface fluxes of heat, freshwater, and momentum for the TOGA COARE IOP. Bull. Amer. Meteor. Soc., 80, Browning, K. A., and Coauthors, 1994: GEWEX Cloud Systems Study (GCSS) Science Plan. IGPO Publication Series No. 11, World Climate Research Programme, Geneva, Switzerland, 62 pp. and 3 appendices. Emanuel, K. A., and M. Zivkovic-Rothman, 1999: Development and evaluation of a convection scheme for use in climate models. J. Atmos. Sci., 56, Fairall, C. W., E. F. Bradley, D. P. Rogers, J. B. Edson, and G. S. Young, 1996: Bulk parameterization of air-sea fluxes for Tropical

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