Frank and Charles Cohen Department of Meteorology The Pennsylvania State University University Park, PA, U.S.A.

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1 376 THE SIMULATION OF TROPICAL CONVECTIVE SYSTEMS William M. Frank and Charles Cohen Department of Meteorology The Pennsylvania State University University Park, PA, U.S.A. ABSTRACT IN NUMERICAL MODELS Recent numerical modelling studies have shown that forecasts of both tropical and mid-iatitude circulations are highly sensitive to the properties of the parameterized convection. In particular, the vertical profile of diabatic heating specified in the model can affect numerical forecasts significantly on scales ranging from the mesoscale to the global scale. This study utilizes a mesoscale model to explore the properties of tropical mesoscale convective systems. The ultimate goal is to find methods of parameterizing the effects of both convection and of mesoscale circulations in numerical forecast models. The model simulates the life cycle of a typical mesoscale convective line containing deep convective updrafts and downdrafts as well as regions of active mesoscale ascent and descent. The levei of maximum diabatic heating rises with time as an upper levei nimbostratus cloud develops. Overall, the effect of mesoscale circulations is to shift heating towards the upper troposphere. The primary process responsible for the formation of the active mesoscale clouds in the upper troposphere is detrainrnent of cloud air at middle leveis. This has the effect of reducing heating at upper leveis by the convection, so that the total heating profiles of systems with and without active nimbostratus clouds appear to be somewhat similar. However, the timing and location of the rainfall are significantly affected by the formation of the nimbostratus clouds. 1. INTRODUCTION Most of the population and land area of the southern hemisphere lie within the tropics. AlI scales of motion in the tropics are affected significantly by latent heat release, which occurs primarily in mesoscale convective systems. This heating results both from convection and from mesoscale vertical circulations such as upper tropospheric nimbostratus clouds and evaporatively-driven downdrafts. Fig. 1 schematically shows the components of an idealized mesoscale convective system. Many mid-iatitude systems are fundamentally similar. On the mesoscale and synoptic scale the vertical distribution of diabatic heating greatly affects the rates at which weather systems develop. If the heating is concentrated at lower leveis, the systems develop much more rapidly than if the heating occurs aloft. This is true in polar low cyclones (Sardie and Warner, 1983) and in mid-iatitude synoptic scale cyclones

2 377 (Anthes and Keyser, 1979) as we11 as in tropical cyclones. On the global sca1e DeMaria (1985) has shown that both the vertical distribution of the diabatic heating and the timing of the heating (on time scales of a few hours) in the Amazon region are important in simulations of the circulation over South America. Best results were obtained when the levei of maximum heating was specified near mb. Although Houze (1982), Johnson (1984) and others have identified the likely effects of the various components of mesoscale convective systems upon the net heating profile, little is understood about the integrated mean properties of the systems or about how the various components interact and are affected by larger scale circulations. The best approach to these problems seems to be through the use of mesoscale numerical models. Such models are also useful for performing limited area short term forecasts. This study uses the two-dimensional version of the Penn State Mesoscale Model (Anthes and Warner, 1978) to examine the net properties of tropical mesoscale convective systems, and in particular their vertical heating distribution. 2. METHODOLOGY The model is aligned east-west to simulate the ITCZ (Intertropical Convergence Zone) of the E. Atlantic. The grid interval is 20 km with 11 vertical leveis including a bulk boundary layer. The model uses both parameterized convection (described below) and explicitly resolved moist processes simultaneously. The cloud line is initialized by cooling the boundary layer at four consecutive grid points. The cumulus parameterization is that of Frank (1984) and Frank and Cohen (1986). Briefly, it uses steady state updraft and downdraft plume models which include lateral entrainrnent and detrainrnent and the effects of liguid water loading in their formulation. The closure is Eg. 1, a three dimensional version of the continuity eguation applied to the sub-cloud layer: Eg. - ~ M u = M + M d + M (1) 1 states that the updraft mass flux at cloud base is the sum of the grid scale mass flux (M - predicted by the model), the downdraft mass flux (M ) and the environrnental mass flux ~. The downdraft mass flu~ is a function of the updraft mass flux at an earlier time with the lag being inversely proportional to the vertical instability. The environrnental mass flux is assumed to be -0.2 times the mass flux at cloud base. Thus, Eg. 1 is used to specify the updraft mass flux at cloud base, and ali of the other convective parameters are determined by the cloud modelo Aline of clouds develops within the first hour, and rain begins within 2h. Rainfall is maximum between 7-8h. Explicit rain (caused by mesoscale vertical motions) begins at about 4h and is also maximum near 7h. The explicit rain largely reflects the formation of an upper levei nimbostratus cloud a few hours after the initiation of the convection. Details of the evolv1n9 system structure will be shown at the conference. The nimbostratus forms primarily from cloud air detrained in the

3 378 middle leveis and advected to the rear of the storm. However, the vertical velocity is upward in the stratiform cloud, and the cloud is therefore very active producing condensation heating and rainfall. Fig. 2 shows the vertical profile of the diabatic heating at a grid point in the convective line. The parameterized convection results in heating throughout the middle leveis with cooling at the top and bottom. Evaporation of detrained'cloud and rain water (explicit cooling) is concentrated in the upper leveis producing a net heating profile with a distinct heating maximum in the lower leveis. This is similar to the profiles observed in GATE during the early stages of convective system life cycles, before the development of nimbostratus clouds (Frank, 1978). Fig. 3 shows the vertical heating components by explicit processes in the stratiform rain region behind the convection. In the current simulation the vertically integrated heating is small, but there is a significant tendency to warm the upper leveis and cool the lower troposphere. When the system is considered as a whole, the effect of the mesoscale circulations is to raise the net levei of the heating with time (Fig. 4). This is in qualitative agreement with the conceptual model of Houze (1982) and the diagno,stic study of Johnson (1984). The simulated convective line shows a distinct life cycle that is very similar to those observed in numerous studies of tropical convective systems. The model is therefore assumed to be suitable for tests of the effects of various processes on the properties of the simulated systems, and results of a few such tests are summarized. Radiative processes increase the system rainfall and the strength of the stratiform cloud. Changing the drop size distribution to reduce the number of small drops increases rainfall noticably but has only a small effect on the system heating profile. Finally, eliminating lateral detrainment from the updrafts results in a more rapidly developing cloud line with heating concentrated in the upper troposphere. However, this latter simulation does not produce a nimbostratus anvil since it provides no moist unstable air to the middle levels. Interestingly, the vertical distribution of diabatic heating in the run without lateral detrainrnent from updrafts (and virtually no stratiform rain) is rather similar to the net profile produced by the more realistic detraining cloud simulation with significant stratiform rain. The major difference between the two simulations is in the timing and location of the rainfall. 4. CONCLUSIONS The cumulus parameterization described above has proved to be useful for simulating mesoscale convective systems in mesoscale models. Based on the simulations described in this paper, it is concluded that the nimbostratus clouds associated with tropical convective systems form largely as a result of mid-ievel detrainrnent of moist unstable air from convective updrafts. The effect of these clouds is to shift the level of maximum heating upward and secondarily to increase the overall system rainfall and lifetime. Radiative processes appear to play a significant role in the dynamics of the systems as hypothesized

4 379 by Gray and Jacobson (1977) and Webster and Stephens (1980). It is hoped that this and future research will lead to improved methods of parameterizing the effects of mesoscale and convective circulaions in large scale weather forecasting models. 5. REFERENCES Anthes, R.A. and D. Keyser, 1979: Tests of a fine-mesh model over Europe and the United States. Mon. Wea. Rev., 107, Anthes, R.A. and T.T. Warner, 1978: Development of hydrodynamic models suitable for air pollution and other meteorological studies. Mon. Wea. Rev., 106, DeMaria, M., 1985: Linear response of a stratified tropical atmosphere to convective forcing., J. Atmos. Sei., 42, Frank, W.M. and C. Cohen, 1985: Properties of tropical cloud ensembles estimated using a cloud model and an observed updraft population. J. Atmos. Sei., ~, Frank, W.M., 1984: A cumulus parameterization scheme incorporating sub-grid-scale convective forcing. Proc. 15th Tech. Conf. on Hurricanes and Tropical Meteorology, Miami, Amer. Meteor. Soe., Frank, W.M., 1978: The life cycles of GATE convective systems. J. Atmos. Sei., ~, Gray, W.M. and R.W. Jacobson,Jr., 1977: Diurnal variation of deep cumulus convection. Mon. Wea. Rev., 105, Houze, R.A.,Jr., 1982: Cloud clusters and large-scale vertical motions in the tropics. J. Meteor. Soe. Japan, 60, Johnson, R.H., 1984: Partitioning heat and moisture budgets into cumulus and mesoscale components: Implications for cumulus parameterization. Mon. Wea. Rev., 112, Sardie, J. and T.T. Warner, 1983: On the mechanism for the development of polar lows. J. Atroos. Sei., 40, Webster, P.J. and G.L. Stephens, 1980: Tropical upper-tropospheric extended clouds: Inferences from Winter MONEX. J. Atmos. Sei., 11,

5 o E Q. 600 ~ (:-1 cu I- ~ mu "'200Km ce~ (env.) - I- ~I Jd sfc cd i Figure 1. Schernatic of a typical rnesoscale convective systern showing the convective updrafts (cu), convective downdrafts (cd), convective environrnent (ce), rnesoscale updraft (rnu), rnesoscale downdraft (rnd) and environrnent. 100 P (mb) 200 T 8h 300,,,, '" \ : I lo, " ", 700 BOO \\ 900,.,, \ : \\ I,, ) - PARAM. --- EXPU CIT - TOTAL o BO 100 Heating (Cid) Figure 2. Total diabatic heating at a grid point in the convective line at t = 8h (heavy line), contribution of the parameterized convection (narrow line) and explicit heating (dashed). Units are degrees per day.

6 T 8h 300,,,,, ' , P (mb) 700 / ",,-,,, _.,,, - EVAP. --~ CONDENS. ".' ICE lodo o 20 Heat i ng (C!d) Figure 3. Diabatic heating in the stratiform cloud region due to explicit condensation (solid line), evaporation (dashed) and melting of frozen precipitation (dotted). IDO 200 EXPERIMENT 1 300, (mb) 700 :- --- T 4h -T 8h... T 12h IDoo O D Heating (C!d) Figure 4. Diabatic heating averaged over a 200 km area containing the entire mesoscale convective system at t = 4h (dashed), 8h (solid) and 12h (dotted).

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