Precipitation Parameterization in a Simulated Mei-Yu Front

Observational and numerical studies have consistently shown the im­ portance of latent heat release associated with frontal precipitation in the development of a Mei-Yu front. However, a systematic evaluation of pre­ cipitation parameterization in the simulation of a Mei-Yu front has been rare in the literature. In order to enhance our understanding on precipita­ tion parameterization of Mei-Yu fronts, this study conducts numerical ex­ periments to evaluate the performance of subgrid-scale cumulus schemes and resolvable-scale microphysics schemes to simulate the Mei-Yu frontal system on 4-5 June 1998 at grid resolutions of 45 km and 15 km, using the Penn State/NCAR mesoscale model MM5. Principal findings are summa­ rized here. • The horizontal extent and intensity of precipitation, the partitioning of precipitation into grid-resolvable and subgrid-scale portions, the verti­ cal thermodynamic profile in the precipitation region and the embedded mesoscale structure are extremely sensitive to the choice of cumulus pa­ rameterization schemes. This is true for both the 45and 15-km grids. • The partitioning of precipitation into subgrid scale and resolvable scale is sensitive to the particular cumulus parameterization that is used in the model, but it is nearly the same on both the 45and 15-km grids for a given cumulus parameterization. •The detailed ice-phase microphysical processes do not have a signifi­ cant impact on the rainfall pattern on either the 45and 15-km grids. How­ ever, the inclusion of cloud ice-snow-graupel microphysical processes in­ creases the total surface precipitation amount by 30 % compared to the amount with only warm rain processes. •Variations in the subgrid-scale cumulus parameterization have a much larger impact on the distribution and amount of Mei-Yu frontal precipita1 Department of Atmospheric Sciences, Chinese Culture University, Taipei, Taiwan, ROG 2 Department of Earth Sciences, National Taiwan Normal University, Taipei, Taiwan, ROG 3 Research and Development Center, Central Weather Bureau, Taipei, Taiwan, ROG *Corresponding author address: Dr. Min-Jen Yang, Department of Atmospheric Sciences, Chinese Culture University, 55 Hua Kang Road, Taipei, Taiwan, 111, ROG Email: mingjen@twister.atmos.pccu.edu.tw

tion than do variations in the resolvable-scale microphysics parameteriza tion at mesoscale grid resolutions of 10-50 km.

INTRODUCTION
Precipitation is one of the most difficult parameters to forecast in numerical weather pre diction. Despite the substantial reductions in forecast errors for winds, temperatures, sea level pressures and geopotential heights due to improvements in numerical modeling over the past decade, progress in precipitation prediction has been very slow (Olson et al., 1995). Difficul ties in precipitation prediction exist in at least three areas. First, our understanding of precipi tation phenomena is still quite limited. Second, data deficiencies often limit the accuracy of a model's initial conditions, which are crucial in the prediction of precipitating systems. The third difficulty is attributed to the improper representation of both explicit-scale and subgrid scale precipitation processes in a numerical model. The representation of subgrid-scale con vective processes is called cumulus parameterization, and its challenge and complexity have been recognized for many years (Emanuel and Raymond 1993).
A wide variety of cumulus parameterization schemes (CPSs) has been developed and incorporated into numerical models (e.g., Kuo 1974;Arakawa and Schubert 1974;Anthes 1977;Fritsch and Chappell 1980;Betts and Miller 1986;Kain and Fritsch 1993;Grell 1993). Microphysical parameterizations of varying degrees of sophistication have been developed to treat the cloud precipitation processes explicitly on the resolvable scale. Successful applica tions in mesoscale models have been reported in both semi-prognostic tests (Grell et al., 1991) and fully prognostic tests Kuo et al., 1996). However, most of these studies have evaluated one or several CPSs for convective phenomena in specific synoptic environments, mainly midlatitude cases in the continental United States. Kuo et al. (1996) assessed the performance of various subgrid-scale cumulus schemes and resolvable-scale microphysics schemes in the simulation of an explosive oceanic cyclone, using the Penn State/NCAR mesoscale model MM5. Wang and Seaman (1997) presented a comparison of cumulus parameterizations of six precipitation events for both cold and warm seasons over the continental United States, also using the MM5 model. However, a systematic evaluation of the cumulus schemes in the simulation of Mei-Yu frontal systems has been rare in the literature. Because of the lack of a universal conceptual framework for cumulus param eterization (Arakawa 1993), the applicability of any CPS is not obvious when it is applied in an environment different from that where it was originally tested.
The Mei-Yu, which literally means plum rain in Chinese, is a climate regime character ized by the frequent occurrence of mesoscale convective systems during the seasonal transi tion period when summer monsoon advances stepwise northwardly through southeast Asia. In Japan this phenomenon is referred to as the Baiu. The climatological Mei-Yu season in the Taiwan area lasts from mid May to mid June and coincides with a local maximum in the seasonal precipitation distribution.
Mei-Yu fronts are quasi-stationary and often produce long but narrow cloud bands that are clearly visible in satellite imagery. They first appear in southern China during May, move northward over Taiwan and southeastern China from mid May to mid June, then migrate farther north to the Yangtze River region as well as Japan during June and July. The climato logical and synoptic characteristics of Mei-Yu fronts have been extensively studied by meteo rologists in Taiwan, China and Japan (e.g., Chen and Chi 1980;Chen 1983;Matsumoto et al., 197 1;Ninomiya 1984). The frequency of surface frontogenesis during Taiwan's Mei-Yu season indicates that an east-west belt north of Taiwan is the primary location for frontogen esis (Chen and Chi 1980). On average, 4-5 frontal systems affect Taiwan during the Mei-Yu season (Chen 1995). A Mei-Yu front is characterized by a strong moisture gradient and hori zontal wind shear rather than a strong temperature gradient as observed in a typical polar front (Akiyama 1973;Kato 1985). This is true especially near the end of the Mei-Yu season (Chen and Chang 1980).
The Mei-Yu fronts in the vicinity of Taiwan are relatively shallow (cold air depth-1 km) and are usually distorted by the topography of Taiwan and the coastal mountains in southeast ern China (Chen et al., 1989;Chen 1993;Chen and Hui 1992). Vigorous convection and organized mesoscale convective systems, producing heavy rainfall, are often embedded within a Mei-Yu front (Wang et al., 1990;Kuo and Chen 1990). The deep convection and associated latent heat release within mesoscale convective systems play an important role in the mainte nance of the frontogenetical process in a Mei-Yu front (Kuo and Anthes 1982;Hsu and Sun 1994).
A low-level jet (LLJ) with wind speed exceeding 12.5 m s-1 at 850 and 700 hPa is com monly observed in association with a Mei-Yu front and often precedes heavy rainfall events over Taiwan by as much as 12 hours (Chen and. Yu 1988). The LLJ not only transports moisture into the frontal zone but also destabilzes the lower atmosphere, thus providing a favorable environment for the development of heavy precipitation. The LLJ is frequently observed on the warm side of a Mei-Yu front (Chen 1977(Chen , 1983 and is highly ageostropic (Matsumoto et al.,197 1). Hsu and Sun (1994) successfully simulated an LLJ and demon strated that large-scale latent heat release and secondary circulation are the two primary mecha nisms that maintain the LLJ. Hence, an adequate treatment of convection and precipitation processes which are responsible for the release of latent heat is crucial for the success of a numerical simulation of a Mei-Yu front.
In this study, we first examine how well different CPSs perform in a mesoscale model under a given Mei-Yu frontal synoptic condition. Second, we investigate whether increased model resolution improves quantitative precipitation fo recasts and if so, by how much. Third, for cumulus schemes designed originally for large-scale numerical models, we identify the characteristic problems encountered in mesoscale applications. In other words, we determine whether CPSs behave differently at different grid resolutions in the range of 10-50 km.
We perform a sensitivity study of the development of a Mei-Yu front and its associated precipitation characteristics to various precipitation parameterization schemes. A series of numerical simulations of the Mei-Yu frontal system on 4-5 June 1998 are conducted using the Penn State/NCAR nonhydrostatic mesoscale model MM5 at grid resolutions of 45 km and 15 km. The objective of this study is to assess the perlormance of various subgrid-scale cumulus parameterization and explicit-scale microphysics schemes in the simulation of a Mei-Yu fron tal system. We are particularly interested in understanding how different schemes affect the development of a Mei-Yu front, the precipitation distribution and total amount as well as the simulated mesoscale structures.

BRIEF SYNOPSIS OF THE OBSERVED MEI�YU FRONT
During 1-10 June 1998, heavy rainfall occurred over the southwestern plain and moun tains of Taiwan. In that period, the Central Weather Bureau (CWB) issued heavy rainfall warnings for southwestern Taiwan for 10 consecutive days (1-10 June). This 10-day flooding episode induced landslides of various scales and resulted in property and agriculture losses totalling approximately 1 billion NT dollars (approximately 30 million US dollars). The syn optic condition was characterized by the passage of a quasi-stationary Mei-Yu front. During this period, a deep trough of northeast-southwest orientation developed at upper levels (500-200 hPa) over the east coast of China. Although the flooding events lasted from 1 to 10 June 1998, this paper concentrates on the Mei-Yu front and its associated mesoscale precipitation that occurred during the 4-5 June 1998 period.
The surlace analysis at 0000 UTC 5 June 1998 is shown in Fig. 1. Ahead of the front, the wind was mainly southwesterly. Behind the front, the wind varied from northeasterly to north erly. The temperature gradient in the vicinity of the surlace front was weak and characterized by a moderate moisture gradient.
As illustrated by the IR imagery for 0000 UTC 5 June (Fig. 2), a frontal cloud band along the Mei-Yu front extended from Japan to the Luzon Strait (north of the Philippines) to Hainan Island. In particular, there was organized deep convection associated with three mesoscale convective systems (MCSs) in the northern South China Sea, extending westward from the Luzon Strait, Dongsha Island to Hainan Island.

MODEL AND EXPERIMENT DESIGN
The numerical model used in this study is the Penn State/NCAR nonhydrostatic model MM5 (Grell et al., 1994) Version 2.7. The MM5 is a three-dimensional, limited-area, primi tive-equation, nested-grid model with a terrain following <J' (non-dimensional pressure) verti cal coordinate. The physical parameterizations of the model include the Blackadar ( 1979) planetary boundary layer scheme with surface energy flux and friction, the short-wave and long-wave radiation schemes with interaction between clear sky and clouds, the resolvable scale microphysics parameterization and the subgrid-scale cumulus parameterization. The model configuration includes a coarse mesh of 45-km horizontal resolution and a fine mesh of 15-km horizontal resolution (Fig. 3). Domain dimensions for each mesh are 81 X71 for the coarse mesh and 91 x91 for the fine mesh. There are 27 <J' levels in the vertical (surface pressure level to 50 hPa): 1. 00, 0.99, 0.98, 0.97, 0.96, 0.95, 0.94, 0.93, 0.90, 0.89, 0.85, 0.80, 0.75, 0.70, 0.65, 0.60, 0.55, 0.50, 0.45, 0.35, 0.30, 0.25, 0.20, 0. 15,.0

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model is initialized at 0000 UTC 4 June 1998 and the forecast length of each MM5 run is 36 hours (i.e., simulation ends at 1200 UTC 5 June 1998). The initial condition is provided by the analysis field from the Central Weather Bureau Global Forecast System (CWBGFS; Liu et al., 1997), while the boundary condition is provided by the CWBGFS forecast. The sea surface temperature (SST) field is also provided by CWBGFS analysis and is held constant through out the simulations. Table 1 lists the numerical experiments conducted in this study. The sensitivity experi ments of cumulus parameterizations include the schemes of Betts-Miller (1993), and Grell (1993), Kain-Fritach (1993) and Kuo (1974). The sensitivity tests of microphysics parameterizations include the schemes of Warm Rain (Hsie et al., 1984;Kessler 1969), Simple
It should be noted that it would be inappropriate to attribute all the errors in the precipita tion forecast solely to a cumulus or microphysics scheme in this full-prognostic experiment framework (Wang and Seaman 1997). Inaccurracies in other physics parameterization schemes and uncertainities in the initial conditions could also contribute to precipitation forecast errors.
Because of this complexity, it is important that each numerical experiment use the same model setting, identical physics (except the physical scheme being testing) as a common framework and the same initial conditions. This experiment design simplifies the interpretation of the results and facilitates forecast intercomparisons.

a. Precipitation verification
There may be little doubt that to simulate convection phenomena a CPS is needed for a numerical model with a grid resolution of 45 km. However, it is not as clear-cut whether a CPS is needed at a grid resolution of 15 km or whether any of the commonly used CPSs are applicable at that scale (Kuo et al., 1996;Wang and Seaman 1997). None of these CPSs have been designed specifically for a 15-km grid. In fact, only the Grell scheme and Kain-Fritsch scheme were developed and tested for resolutions as small as 20-25 km, while the Kuo scheme and Betts-Miller scheme were originally applied at much coarser resolutions. Therefore, the implementation of these CPSs at a 15-km grid requires further evaluation. With the increase in computational power, the real-data operation of mesoscale modeling now advances to the 10-15 km grid scale; hence, it is important to objectively assess the performance of a variety of cumulus schemes on the 10-15 km grid scale to facilitate future model design.
All CPSs have disposable parameters that may be "tuned" to enhance their performance for a given type of convective system, for example a Mei-Yu frontal convection. Thus, the performance of these CPSs for the convection and precipitation associated with a Mei-Yu front needs to be examined.
In this set of cumulus experiments, the Simple Ice scheme (Dudhia 1989) is used for microphysics parameterization on both the 45-km and 15-km grids. Figure 4 shows the 6-h accumulated total (parameterized and resolved) rainfall (1800 UTC 4 June to 0000 UTC 5 June 1998) on the 45-km grid as predicted by each cumulus experiment. Comparing Fig. 2 and Fig. 4, it is recognized that the Mei-Yu frontal rainfalls are produced in all cumulus ex periments, although their locations are farther north compared with satellite observations. Note that these precipitation forecast errors do not solely result from the chosen cumulus scheme. Some errors may be due to a poor representation of the initial moisture field, especially over the data-sparse South China Sea area. Other errors may be related to the coupling of cumulus schemes with other physical parameterization schemes and the improper representation of sharp gradients associated with water substance in numerical techniques.
The rainfall prediction in the Grell (GR) experiment ( Fig. 4b) is in good agreement with satellite observations in terms of the Mei-Yu frontal precipitation pattern and organization. The Betts-Miller (BM) experiment ( Fig. 4a) has reasonable performance with regard to Mei Yu frontal precipitation and is similar to that of the GR experiment, except that it over-predicts the rainfall area over the northern South China Sea. The Kain-Fritsch 4c) shows similar frontal precipitation forecast results to those of the GR and BM experi ments, but the rainfall area is too widespread and the rainfall intensity is too weak, especially over the subtropical open ocean. The rainfall forecast in the Anthes-Kuo (AK) experiment ( Fig. 4d) is not as good as that in other experiments since it fails to represent the organized MCSs over the northern South China Sea, and it underestimates the frontal precipitation. Figure 5 illustrates the 6-h rainfall forecasts of these four cumulus experiments on the 15km grid for the same time period. It is clear from Fig. 5 that more detailed mesoscale struc tures on precipitation and pressure fields can be found with the increase in grid resolution. Therefore, the simulated rainfall pattern and intensity have more pronounced variations among each cumulus experiment on the 15-km grid.

b. Parameterized versus resolved precipitation
As is typical in the evaluation of an operational modeling system, the comparisons pre sented thus far have focused on total precipitation (Figs. 4 and 5) without regard to whether the rainfall is produced through resolvable-scale processes or through parameterized processes. In a numerical model that uses both subgrid-scale and grid-scale precipitation schemes, a "" reasonable partition between parameterized and resolved rainfall is very important to produce realistic simulations of precipitation events and to prevent the occurrence of excessive static instability (Kuo et al., 1996). This is because the subgrid-scale cumulus scheme represents a more rapid upward transport of heat and moisture, and hence it can stabilize a vertical grid column faster than the grid-scale microphysics scheme.  Figure 6 shows the horizontal distribution of 6-h (1800 UTC 4 June to 0000 UTC 5 June) accumulated parameterized (left column) and resolved (right column) rainfall predicted by various cumulus schemes on the 45-km grid. The BM experiment produces widespread pa rameterized precipitation along the Mei-Yu front and over the Luzon Strait and northern South China Sea (Fig. 6a); the resolvable-scale precipitation (Fig. 6b), in this case, shows very few rainfall cores along the frontal boundary. The GR experiment produces considerably smaller amounts of parameterized precipitation along the Mei-Yu front than does the BM experiment (Fig. 6c), with rainfall amounts generally less than 8 mm/6 h. Very little parameterized pre-a ) , ., � etts-� ill er \ p� am � . !� rized)

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. cipitation is produced outside the frontal boundary. However, organized precipitation cells with a scale of six to eight grid points (270-360 km) are evident in the resolvable-scale precipi tation for the GR experiment (Fig. 6d). One such cell near the Mei-Yu front has a maximum 6-hourly precipitation of 115 mm. The KF experiment also produces widespread parameter ized precipitation along the Mei-Yu front (Fig. 6e). Light precipitation is found ahead and behind the frontal boundary and also over the northern precipitation of stronger intensity and covering a smaller area is predicted along the frontal boundary (Fig. 6f). The AK experiment (Figs. 6g and 6h), in sharp contrast to the GR experi ment, exhibits very little resolvable-scale rain but a large amount of parameterized rain. The parameterized precipitation produced by the AK experiment covers a larger area than does that by the other cumulus experiments (BM, GR, and KP).
From the results presented above (Fig. 6), it is evident that for the simulated Mei-Yu frontal system there is a significant variation in the partitioning, intensity, and distribution of parameterized and resolved rainfall among the precipitation predictions using different cu mulus schemes. Similar results are found in Kuo et al. (1996) in the simulation of an explosive oceanic cyclone. It should be noted that although this set of experiments uses the same pre cipitation parameterization on the resolvable scale (Simple Ice microphysics scheme), the re-solved precipitation pattern and amount differ widely. This suggests that the parameterized heat and moisture transports on the subgrid scale have significant influences on the tempera ture and moisture distributions on the explicit scale in each cumulus simulation. This, there fore, results in a different intensity and distribution of explicit-scale precipitation despite the use of the same microphysics scheme.
The evolution of the domain-average 6-hourly precipitation and its parameterized and resolvable-scale components on the 45-km grid is shown in Figs. 7a-c. The total precipitation amount (Fig. 7a) increases steadily during the first 24 hours of simulation in all experiments. The Kain-Fritsch, Betts-Miller, and the Anthes-Kuo experiments are all quite effective in pro ducing parameterized precipitation during the first 12 hours of the simulation (Fig. 7b). Th rough out the forecast period (36 hours), large variations in the partitioning between parameterized and resolvable-scale precipitation are seen (Figs. 7b and 7c). The Betts-Miller experiment produces the largest amount of parameterized rainfall at nearly all hours. The Anthes-Kuo experiment produces slightly less but comparable amounts of parameterized precipitation. The Kain-Fritsch experiment produces even less parameterized rainfall (Fig. 7b). Relatively small amounts of parameterized rainfall are generated by the Grell experiment.
Resolvable-scale rainfall (Fig. 7c) also displays considerable variations among these ex periments. The AK experiment yields the smallest amount of resolvable-scale rainfall, whereas the GR experiment yields the largest. Resolvable-scale precipitation of all four cumulus ex periments increases substantially. This behavior indicates that as time increases, more and more grid points become saturated and more precipitation takes place on the grid-resolvable scale. The ratio of parameterized to total (parameterized and resolved) rainfall is illustrated in Fig. 7d. The 50% intercept marks the time that precipitation changes from predominantly subgrid scale to predominantly resolvable scale. For the GR experiment, the crossover occurs between hour 6 and hour 12, and it occurs at hour 24 in the KF experiment. In the AK and BM experiments, as noted previously, parameterized precipitation predominates throughout the 36-h simulation period.
The reason that the Grell scheme produces so little parameterized precipitation is that the parameterized rainfall produced by the Grell scheme is strongly affected by the precipitation efficiency parameterization and an automatic shut-off switch which is turned on when the precipitation efficiency is too low (Kuo et al., 1996). Due to this design in the precipitation efficiency parameterization, it is found that this switch causes the scheme to shut off quickly, consequently forcing the resolvable-scale scheme to take over frequently, which then results in little parameterized precipitation. The lack of resolvable-scale precipitation in the Anthes Kuo scheme is likely caused by the strong dependence on parameterized precipitation to mois ture convergence (Kuo et al., 1996). In the Anthes-Kuo scheme, the amount of parameterized rainfall is proportional to the column-integrated moisture convergence with a coefficient (l b), in which the parameter bis a function of the environmental relative humidity (see Appen dix A for more details). When a precipitation system begins to evolve, the environment is close to saturation, and b becomes very small. Then all the moisture supply through column integrated moisture convergence has to be condensed as parameterized precipitation, leaving little or no moisture for the resolvable-scale precipitation.
The evolution of the domain-average 6-hourly precipitation and its parameterized and  .. resolvable-scale components on the 15-km grid is presented in Fig. 8. The most striking feature in Figs. 7 and 8 is that the partitioning of model-predicted precipitation is vastly differ ent from one scheme to another. At both 45-km (Fig. 7d) and 15-km (Fig. 8d)  throughout the entire integration period. On the other hand, the GR experiment quickly switches from parameterized to resolved-scale dominance of precipitation around hourJ2. The KF and BM experiments produce a rainfall partition somewhat between that of the GR and AK experi ments. Overall, the ratio of parameterized to total precipitation remains roughly the same as grid size decreases, with the exception of the BM experiment. The change in the partitioning of the rainfall with respect to grid resolution for the Betts-Miller scheme may be explained in part by the choice of the relaxation time scale r (Wang and Seaman 1997). In principle, r should be reduced in the Betts-Miller scheme as the grid size is decreased so that appropriate subsaturation is maintained (Betts and Miller 1993). However, in this study the same value of r = 50 min is used at both 45-km and 15-km resolutions.
Although the rainfall partitionings in the KF, GR, BM and AK experiments are very different from each other in the simulation of the Mei-Yu front, Figs. 7d and 8d show that the ratios of parameterized to total precipitation remain approximately the same as the grid size decreases from 45 km to 15 km in each experiment. This suggests that the characteristics of these CPSs, although very dif f erent from each other, are relatively insensitive to mesoscale grid resolutions ranging between JO km and 50 km. Similar findings are reported in Kuo et al. (1996) for an oceanic cyclogenesis case and in Wang and Seaman (1997) for six precipitation events over the United States.
c. Sounding verification Figure 9 shows the observed sounding of 0000 UTC 5 June 1998 on Dongsha Island where all cumulus experiments produce some precipitation. Figure 10 is the corresponding model soundings for various cumulus parameterization experiments on the 15-km grid. Com paring Figs. 9 and 10, it is clear that the soundings produced by both the BM and GR experi ments simulate the vertical profiles of temperature and moisture quite well� the KF experiment is the second best, but, in contrast, the sounding profile in the AK experiment is too moist and too unstable. To be specific, the sounding profile in the BM experiment (Fig. lOa) is condi tionally unstable at the low levels. Its structure follows the reference sounding used in the Betts-Miller scheme that assumes an equilibrium in which weak convective instability is bal anced by water loading. The GR experiment (Fig. 1 Ob) also displays a conditionally unstable atmosphere below 800 hPa. The KF experiment (Fig. lOc) produces a near moist-neutral sounding above 700 hPa, with very little convective available potential energy (CAPE) for an air parcel lifted above 900 hPa. The sounding in the AK experiment is extremely unstable (Fig. IOd); an air parcel lifted from 1000 hPa remains positively buoyant all the way to the top of the troposphere. Such a sounding cannot exist in a precipitating environment, but it is possible in the AK experiment because the parameterized precipitation in the Anthes-Kuo scheme is not dictated by the amount of CAPE but rather by the grid-scale moisture conver gence (Kuo et al., 1996). Therefore, there is no guarantee that the Anthes-Kuo scheme elimi nates the CAPE. Also, the specified parabolic heating profile in the Anthes-Kuo scheme does not necessarily lead to a moist neutral sounding even if there is a significant amount of precipi tation.

MICROPHYSICS EXPERIMENT
Based on high-resolution cloud-model simulations for an intense midlatitude squall line, Yang and Houze (1995) indicate that hydrometeor types and ice-phase microphysical pro cesses can significantly affect rainfall distribution, amount, and internal mesoscale structure 409 within a precipitation system. Therefore, another important factor to determine simulated precipitation is the resolvable-scale microphysics parameterization scheme. In this set of sen sitivity experiments the Kain-Fritsch scheme is used for cumulus parameterization on both the 45-km and 15-km grids. Figure 11 shows the 6-h accumulated total (parameterized and re solved) rainfall (1800 UTC 4 June to 0000 UTC 5 June 1998) on the 45-km grid predicted by each microphysics run. Figure 12 is the corresponding precipitation forecast on the 15-km grid. It is clear from Figs. 11 and 12 that the predicted rainfall distribution by each micro physical experiment is very similar on both the 45-km and 15-km grids. Figures 13 and 14 show the domain-average precipitation and its partition for this set of experiments on the 45-km grid and 15-km grid, respectively. The Warm Rain (WR) experi- ment (Hsie et al., 1984), with the inclusion of warm rain (condensation and evaporation) pro cesses only, produces the least precipitation. The Mixed Phase (MP) experiment (Reisner et al., 1998) produces slightly more rainfall than the WR experiment. This result indicates that the ice physics in the Mixed Phase scheme contributes positively to rainfall because the lower saturation vapor pressure over ice than over water allows �or the condensation of water vapor �) G�, gdarq,Gra�pel ,?,L) Mt�ed �R.ase "" at subfreezing temperature when cloud ice is included. The Simple Ice (SI) experiment (Dudhia 1989) produces precipitation amounts slightly greater than the MP experiment, but the differ ence is very small since the physical processes between the two schemes (Simple Ice and Mixed Phase) are similar despite the inclusion of supercooled liquid water in the Mixed Phase scheme. This suggests that the inclusion of supercooled liquid water effects in the resolvable scale microphysics scheme does not contribute significantly to surface precipitation for a 45km/15-km grid. Finally, the comparison between the Simple Ice and Goddard Graupel (GG) experiments shows that the inclusion of graupel-type ice microphysics (Tao and Simpson 1993) produces 10-15% more surface precipitation throughout the period of the simulations (36 hours). In other words, the inclusion of cloud ice-snow-graupel microphysical processes increases the surface precipitation amount by 30% compared to the amount with only warm rain processes.
The results from the comparison are similar to the findings of Mccumber et al. (1991 ), which indicate that the inclusion of ice-phase microphysical processes increases the model predicted rainfall amount and improves the simulation results. Based on sensitivity experi- ments from cloud-resolving model simulations, Mccumber et al. (1991) show that the optimal mix of bulk ice hydrometeors for tropical cloud cluster simulation is cloud ice-snow-graupel. This microphysics experiments on Mei-Yu frontal precipitation also show that the optimal mix of bulk ice hydrometeors is cloud ice-snow-graupel, similar to the findings of Mccumber et al. (1991). It is clear from Figs. 13b and 14b that parameterized precipitation is nearly the same in all experiments in this set. Evidently, subgrid-scale precipitation is little affected by the use of any particular resolvable-scale scheme. This is different from the results of the cumulus ex periments (see Figs. 7b and Sb), in which it is noted that the same resolvable-scale microphys ics scheme produces widely different precipitation amounts and distributions depending on the cumulus parameterization used. Apparently, v a riations in the subgrid-scale cumulus pa rameterization have a much larger impact on the distribution and amount of Mei-Yu frontal precipitation than do variations in the resolvable-scale microphysics parameterization at mesos cale grid resolutions of 10-50 km.

CONCLUSIONS AND DISCUSSION
With the increase in computational power, the separation of parameterized processes and grid-resolved processes in a numerical model becomes more obscure. Therefore, a systematic For the same cumulus parameterization scheme, the ratio of parameterized to total rainfall changes very little as the grid resolution increases from 45 km to 15 km. This is surprising because it might be expected that tiie resolvable-scale (or large scale) forcing and destabiliza tion would change considerably with any reduction in grid size. The similarity in the gross precipitation characteristics at different grid sizes for the same cumulus scheme indicates that the fundamental closure assumption used in each cumulus scheme has a more profound influ ence on the behavior of the scheme than does the dependence of the grid-scale (or large scale) forcing on the grid size.
The examination of model soundings on Dongsha Island where all cumulus schemes pro duce some precipitation reveals significant differences in vertical stability. The simulated sounding produced by the Anthes-Kuo experiment is highly unstable to moist ascent, possess ing substantial amounts of CAPE. Such unstable sounding is unrealistic and cannot be ob The second set of microphysics experiments on the 45-km/15-km nested grid reveals that the precipitation pattern of the Mei-Yu front is little affected by the microphysics schemes employed. The addition of ice-phase microphysics results in a modest increase in the amount of precipitation. A refinement in ice-phase microphysics from the inclusion of supercooled liquid water produces a similar amount of surface precipitation, compared to that without mix phased processes. To the next level of complexity, the inclusion of graupel microphysical processes increases surface precipitation 10-15% further, or the inclusion of cloud ice-snow graupel microphysics increases surface rainfall by 30% compared to that with only warm rain processes. Therefore, it is found that some level of ice-phase microphysics processes is re quired to produce a quantitative precipitation forecast with a reasonable degree of accuracy in a 45-km/15-km mesoscale model. However, fu rther improvement can be made with the con sideration of more detailed ice-phase processes. Nevertheless, one would expect that as the grid resolution increases fu rther (grid size of 5 km or less), the detailed ice-phase microphysi cal processes would have a stronger impact on the precipitation distribution and amount.
The comparison of these two sets of sensitivity experiments clearly shows that subgrid scale cumulus parameterization has a much more profound influence on the precipitation dis tribution than does the resolvable-scale microphysics parameterization on the 45-km/15-km grids. This finding can be explained by the fact that cumulus parameterization, through its redistribution of heat and moisture, can significantly affect the resolvable-scale temperature, moisture and vertical motion fields. Thu s, it affects the intensity of latent heating and its horizontal and vertical distribution of precipitation. On the other hand, the functioning of a cumulus parameterization is only weakly sensitive to changes in the cloud microphysics on the resolvable scale. The two main factors determining the effectiveness of a cumulus param-eterization are the large-scale destabilization and the closure assumptions used in the scheme. Cloud microphysics on the resolvable scale has little effect on these two factors.
Considerable effort has been devoted to the study of convection and its representation in · numerical models over the past 30 years (Emanuel and Raymond 1993). However, no general theory of cumulus parameterization is available (Arakawa 1993). No single scheme has been proven to work effectively and perfectly across a range of grid sizes and across a wide range of weather systems from mesoscale convective systems to typhoons, tropical cloud clusters and Mei-Yu fronts. This problem becomes even more complicated in a numerical model at grid resolutions of 10-50 km when a mesoscale precipitating system is partly resolved and partly parameterized (Molinari and Dudek 1992). Finally, much work remains to be done to under stand how cumulus and microphysics parameterizations interact with other components of a model, especially in the mesoscale grid resolutions of 10-50 km. Improv�ments in the model' s initial conditions through three-dimensional or four-dimensional data assimilation techniques are also crucial so as to reduce errors in precipitation forecasts.

value M tfJ
(3 x 10-5 kg m·2 s·l) in the column. Then the moisture convergence is partitioned into the moistening of the column and parameterized precipitation, such that the precipitation PR is defined as: where b = 2(1 -<RH>) and <RH> is the mean relative humidity of the grid column. This scheme does not include a cloud model nor parameterized convective downdrafts.

b. Grell scheme
The Grell scheme (1993) is a one-cloud version of the Arakawa-Schubert scheme (1974) with parameterized downdrafts, and it was first applied in the Penn State/NCAR mesoscale model. The closure used by the Grell scheme is the quasi-equilibrium assumption, as pro posed by Arakawa and Schubert (1974). The subgrid precipitation PR is calculated as : where !1 is the integrated condensate in the updraft, m b is the cloud-based mass flux of the updraft, and (1 -p) is the precipitation efficiency, which is assumed to be a function of the mean wind shear in the lower troposphere. The effects of the convective-scale downdrafts (Cheng and Arakawa 1990) are parameterized in this scheme.

c. Kain-Fritsch scheme
The Kain-Fritsch scheme (Kain and Fritsch 1993) is similar to the Fritsch-Chappell scheme (1980), but with improvements made in the detrainment effect an d cloud model . It was also first applied in the Penn State/NCAR mesoscale model. The closure assumption in the Kain Fritsch parameterization is the same as that used in the Fritsch-Chappell scheme. The convec tion is determined by the convective available potential energy (CAPE) on a grid point. Once convection is triggered, the CAPE is assumed to be removed in a grid column within an advec tive time period (roughly 30 min)_ The Kain-Fritsch scheme utilizes an improved cloud model , which is mass-conservative , allows cloud-environment interaction, includes parameterized moist downdrafts and which has a detailed representation of cloud physics, including entrain ment and detrainment across the cloud edge. The parameterized precipitation PR is computed as : PR =E S, where Eis the precipitation efficiency, and Sis the sum of the vertical fluxes of vapor and liquid at about 150 hPa above the lifting condensation level (LCL).

d. Betts-Miller scheme
This version of Betts-Miller scheme (Betts and Miller 1993) is similar to that currently used in the operational eta model (Janj ic 1994) at the National Center for Environmental Pre diction (NCEP). Unlike the other three CPSs, the Betts-Miller scheme is a lagged convective adjustment scheme. It adjusts the model's thermal and moisture structure toward specified reference profiles that represent the quasi-equilibrium state established by deep convection (Betts 1986). The parameterized precipitation PR resulting from this adjustment is defined as: where q is the model's specific humidity, q R is the reference profile specific humidity (a fu nc tion of height) , r is the time scale for which the adjustment occurs, and Pr and p8 are pressures at cloud top and bottom, respectively. The parameters used to specify the temperature and moisture profiles and the adjustment time scale are the same as those used by the NCEP eta model, which may or may not be applicable to Mei-Yu frontal precipitation.

A Brief Review of Microphysics Parameterization Schemes
Here each microphysics parameterization scheme tested in this study is briefly described. Details of the parameterization formulations appear in the referenced papers.

a. Wa rm Rain scheme
This Warm Rain scheme is described in Hsie et al. (1984), and it basically considers the warm-rain processes as first discussed in Kessler (1969). In this scheme, prognostic equations are included for water vapor, cloud water and rain water. Evaporation in unsaturated layers is included.

b. Simple Ice scheme
This Simple Ice scheme was developed by Dudhia (1989) and it considers warm cloud processes below and cold cloud processes above the freezing level. Instantaneous freezing and melting take place at the 0°C level. No supercooled liquid water is allowed above the melting level. In other words, only a simplified treatment of ice microphysical processes is considered.

c. Mixed Phase scheme
The Mixed Phase scheme was developed by Reisner et al. (1998) and this scheme uses five prognostic equations for water vapor, cloud water, rain water, cloud ice and snow. Be cause the scheme allows for the coexistence of liquid water and ice above the freezing level, the effect of supercooled liquid water is taken into consideration.

d. Goddard Graupel scheme
The Goddard Graupel scheme was developed by Tao and Simpson (1993) and it includes six classes of water substance, especially graupel. The addition of graupel permits an even more complete treatment of the precipitation processes.