1. Introduction
In East Asia, monsoon rain is the major source of water, but torrential rainfall is common, every year causing heavy casualties. The Walker circulation and the 30– 60-day oscillation are sensitive to the vertical distribution of latent heat release from tropical clouds (Hartmann et al. 1984; Lau and Peng 1987).
Many large international programs have been conducted in order to increase understanding of the cloud systems producing heavy rainfall. Leary and Houze (1979) classified deep convection into squall lines and cloud clusters, and also reported sudden radar echo intensification following cell mergers. Both dynamic and thermodynamic structures in deep convection have been well documented by Zipser et al. (1981), Barnes and Sieckman (1984), Chong et al. (1987), and Roux (1988). Wind shear plays an important role in both storm organization and movement. Further clarification of the physics of the phenomenon has been attained by using cloud models (Weisman et al. 1988; Rotunno et al. 1988). More recently, LeMone et al. (1998) have reported investigation of the rain patterns over the western Pacific, relating them to low and midlevel wind shear.
To increase understanding of tropical rainfall, the Tropical Rainfall Measuring Mission (TRMM) satellite has been launched and has collected many valuable data. Extensive analysis of TRMM–Lightning Imaging Sensor (LIS) data by Christian et al. (2003) showed a significant difference in lightning activity between tropical continents and oceans. Since the major charge separation mechanism would be riming electrification (Takahashi 1978, 1984), the number concentrations of graupel and ice crystals must differ widely in the two regions. As reported, videosonde data show fewer snow crystals over the western Pacific in contrast to their abundance at Melville Island, near Darwin (Takahashi 1990, 2003; Takahashi et al. 1995; Keenan et al. 2000). Earlier, Churchill and Houze (1984) and Houze and Churchill (1987) reported many irregular ice crystals over the South China Sea and Bay of Bengal, which were different from those in midlatitude clouds. In comparison with videosonde data, those irregular crystals are heavily rimed, columnar crystals, showing an abundance of supercooled drops over an open ocean.
The vertical distribution of the source of apparent heat as reviewed by Johnson (1992) showed peak values at around 5 km in the Tropics, occasionally as low as 3 km.
The present paper presents the results of numerical investigation into how such different microphysical processes affect the development of rain and heat profile. In order to examine these processes, the model requires that various precipitation particles of different sizes and shapes are included.
2. Model
The cloud model is nonhydrostatic, and anelastic with detailed microphysics. The basic formulations for cloud dynamics and microphysics are similar to those given in Takahashi (1976b, 1988).
a. Microphysics
The model formulation of the microphysical processes is as given in Fig. 1. Once a parcel of air attains supersaturation, a certain number of cloud nuclei are activated. Initial cloud droplets, calculated separately at cloud base in a one-dimensional cloud nuclei model instantaneously appear (Takahashi 1976a; Takahashi and Kawano 1998) and grow by condensation (Kovetz and Olund 1969) and collection (Berry 1967). Large raindrops break up (Srivastava 1971) and, as they are lifted above the freezing level, begin to freeze. The probability of freezing given by Vali (1968) has been modified by the laboratory work of Pitter and Pruppacher (1973). The current investigation did not subdivide ice nuclei by deposition, sublimation, contact, or freezing. It will be improved by the ongoing research. Once ice nuclei have been activated (Fletcher 1962), they form ice crystals that are assumed as Gaussian form of modal size, 50-μm radius and a standard deviation of three, and are assumed to increase in radius by depositional growth and in thickness by riming. When their thickness reaches the diameter of an ice disc, they are included as graupel. The growth of ice was calculated by Kovetz– Olund's scheme. Ice particles less than 20 μm in diameter (Nakaya 1954) and splinters ejected during riming (Hallett and Mossop 1974) also act as ice forming particles. They can grow initial ice crystals instantaneously.
Ice crystals at K = 1 coagulate and form snowflakes (Hosler et al. 1957; Sasho 1971) within K = 1 range. Fluctuation of ice crystals was included in Berry's collection scheme. Snowflakes were assumed to be flattened. When less than 10 crystals form a snowflake, the flakes are usually planar (Kajikawa et al. 2002). Ice crystals grow by riming unless they contact supercooled drops falling from above in which case the drops freeze. When the riming density of crystals exceeds 0.7, graupel is transferred to hail (Macklin 1962). When ice particles are completely melted (Mason 1956), they are instantaneously transferred to raindrops. The Kovetz–Olund scheme, which conserves mass and number, was used during particle transition. When drops and snow particles evaporate, they enter into the cloud nuclei and ice nuclei categories, respectively.
b. Equations
Takahashi's (1988) formulation has been rewritten for deep clouds with some simplifications. Eddy diffusion coefficients were calculated by a first-order closure scheme with the equation coefficient chosen as 0.4. This may result in weaker convective activity near the cloud top than occurs in Klemp and Wilhelmson's (1978) second-order closure. However, in as much as the present model is aimed at examining the microphysical effects on the production of rain, this simplification can be justified. There are prognostic equations for velocities, potential temperature, water vapor mixing ratio, supersaturation (Clark 1973), cloud nuclei, ice nuclei and ice particle number concentrations, cloud drops, as well as various precipitation particle numbers. Hail and frozen drops are treated equally in this model. As previously reported (Takahashi and Kawano 1998), maximum supersaturation has been set at 5% in the maritime case and 1% in the continental case.
3. Environmental, boundary, initial conditions, and calculation schemes
a. Environmental conditions
The temperature and humidity profiles are hypothetical but determined in reference to tropical sounding, with a surface temperature of 27°C, which decreases dry adiabatically to 1.4 km, then decreases by 6.5°C km−1 to 8 km, by 3°C km−1 to 10 km, and by 1.5°C km−1 to upper boundary of the model at 12 km (Fig. 2a). Humidity at the ground is 70%, increasing by 10% km−1 to 1.4 km, at which value it remains up to 2.8 km. From 2.8 km to 8.2 km it decreases at 5% km−1, and from there by 10% km−1 to the upper boundary. The CAPE is 2300 m2 s−2. Standard winds in the x direction are −4.5 m s−1 at the lower boundary, increasing linearly to +1.5 m s−1 at 2 km, retaining the same velocity to 3.5 km, where they become northeasterly (Fig. 2b). Two other wind profiles were used: one doubled the velocity of the standard wind and the other the doubled velocity profile with directional velocity added below 2 km.
Since environmental conditions are tropical–maritime, model maritime cases were mainly compared to investigate microphysical effects on the development of rain.
b. Boundary conditions
Open boundary conditions are used for both x and y sides of the model domain (Orlanski 1976), except in the “random impulse” and rainband cases where cyclic conditions apply. The upper and lower boundaries are rigid with free slip conditions. The grid intervals for the x and y axes are 400 m, and for z, 200 m.
Two calculation domains are used: 111 × 111 × 61 for domain S and 227 × 227 × 61 for domain L.
c. Initial conditions
An initial impulse is provided by increasing the potential temperature of a parcel of air by up to 0.3°C as bubbles form, saturating it (Takahashi 1988). For a random impulse, a number from −0.5 to 0.5 is drawn every 5 min. After being divided by total time steps within 5 min, the random impulse is given at each time step for 30 min to the potential temperature at 0.3 km. In order to simulate a rainband, the temperature in an area in the center of the cloud, 10 km wide and below 0.3 km, was increased by 0.5°C, followed by a random impulse at 0.3 km for 30 min in the same area.
d. Calculation scheme
To minimize truncation errors in calculating finite differences, a staggered grid was used. Advection terms are written in flux form and Arakawa's (1966) formulation, which conserves mass and energy, is used in its second-order form. All dynamic and thermodynamic terms are in a leapfrog form with 1-s time steps and time smoothing. Except for the collection process, other microphysical terms are also calculated for 1-s time steps. Drop collection and snowflake formation, which require more computer time, are calculated in 10-s steps.
In the small drop range at fixed supersaturation, use of the Kovetz–Olund (1969) scheme for condensation and Berry's (1967) scheme during collection agreed well with Takahashi and Lee's (1978) analytical solution. The Kovetz–Olund scheme was replaced with Egan–Mahoney's (1972) moment conserving scheme. At fixed supersaturation, without dynamics, the results were compared with a Kovetz and Olund–Berry combination scheme satisfactory for raindrop simulation (Takahashi 1976a). In a warm cloud the drop classification was halved from 71 to 35 with rainfall intensities agreeing satisfactorily (Takahashi 1976a). In one case, using the present model, all the time steps were halved, resulting in no significant changes. In a two-dimensional model, Δx was halved with the results comparing well with the original Δx value (Takahashi and Kawano 1998).
All calculations were performed on a Hitachi SR8000 at Tokyo University. In domain S, Open Message Passing (MP) shared-memory parallelism with one node [8 Process element (PE); no decomposition] was used while in domain L, Message Passing Interface (MPI) message-passing parallelism with eight nodes (64 PE; 8 × 8 decomposition) was employed. A parallelization technique with two-dimensional horizontal (x–y) domain decomposition was used to handle the large amount of data and to reduce computation time. All processors were controlled and communicated through an MPI library.
Computations were performed in three steps, the first of which investigated the effects of cloud microphysics on the development of rain. The five microphysical model settings used are given in Table 1. In the maritime cases, the number of cloud nuclei potentially able to grow cloud droplets was 300 cm−3 in reference to cloud droplet numbers in Hawaii, and in the continental cases was 1000 cm−3 in reference to the U.S. Great Plains. The number of ice nuclei potentially able to form ice crystals was 1 cm−3 based on the observation of that number in active clouds (Pruppacher and Klett 1997). In “freezing,” the concentration of ice nuclei was set to zero and the drop freezing process enhanced by forcing all supercooled drops larger than 400 μm in radius to freeze below −5°C in reference to videosonde work in Ponape, Micronesia (Takahashi 1990; Takahashi and Kuhara 1993). Ice particles are ejected by ice multiplication process (Hallett and Mossop 1974) at later stages of cloud development. The model setup for maritime ice will represent the maritime continent cases and for the maritime frozen, over the open ocean cases in the western Pacific. The setup for continental ice is for cases over midlatitude continent. Warm cases are calculated to elucidate the role of ice in rain production.
The second step investigated the effect of wind shear on rain patterns. Three wind profiles were employed: standard, doubled standard, and directional winds. The third step in the investigation concerned the organization of rain cells. Small random impulses were given for up to 30 min in all areas or within centered band, and the organization of the rain with different precipitation mechanisms was investigated using the doubled wind velocity.
Rain patterns, rain cell life, precipitation particle growth modes, rain accumulation, cell organization, heating rate profile and rain cell movement within the rainband are the topics focused upon in the investigation.
4. Results
a. Rain patterns
The rainfall amounts varied greatly with different microphysics. The highest rainfall occurred with maritime ice and was almost one order of magnitude higher than in the lowest continental-warm case (Fig. 3). However, for up to around 50 min after the initial impulse, the warm rain process dominated and the rainfall patterns appear quite similar despite the different microphysics.
The outflow associated with rainfall from an initially developed cell (A in Fig. 4) encourages updrafts at both the up- and downwind cloud edges. The rainfall area thus developed elongates along the wind direction. As the rain moves slowly to the west, a new cell develops in the east where the outflow from the primary cell meets the easterlies (B in Fig. 4). In the west, outflows diverge north and south and meet the easterlies. New convective cells develop in the convergence areas and the original rain cell disappears (C in Fig. 4). Outflows from the divergent cells then form new convection between them, thus filling the rain gap (D in Fig. 4).
In the continental cases, several rain cells developed along the periphery of the rain areas and grew with time by recruiting the surrounding water vapor (E and F in Fig. 4). They increased up to 30 km in width but weakened quickly after 100 min. Although the maximum rainfall intensity with ice goes to 100 mm h−1 in 90 min, as compared to 50 mm h−1 at 70 min without ice, the periods of heavy rain are short lived. A weak warm rain process is the reason for the weak cell activity. With a steeper lapse rate of 7°C km−1 from 1.4 to 8.0 km; however, continental ice gives a similar rain pattern as does maritime ice with a standard temperature lapse rate.
Large differences are noted in the maritime cases. Because the latent heat release is much higher in drop condensation growth in the maritime cases than in the continental cases, convective activities are more intense. The stronger, low-level outflow produced by the heavier rainfall triggers new, small cell developments in front and to the side of the primary rain area. Additional heat is released during the depositional growth of ice crystals. The enhanced updraft drags surrounding convective cells, uniting them one by one with the main cell. Graupel falling from above captures supercooled drizzle near the freezing level and hail growth is intensified. A large, single area of convection is established and, after 90 min, a rain cell as wide as 40 km has been formed (H in Fig. 4; Fig. 5a).
In the maritime-frozen case where ice crystal concentration are low, heat from drop freezing is insufficient to develop a broad updraft. Turreted cloud cells develop along the periphery of the rain area. These cells grow by absorbing smaller cells but convective downdrafts form a weak rain area in the center, producing a doughnut-shaped rain pattern (I in Fig. 4; Fig. 5b). In this case, the area of major particle growth is also near the freezing level, through hail growth, primarily from frozen drops. In the later time stage when ice particles are supplied through Hallett–Mossop ice multiplication, ice crystals and graupel grew, and rain activity increased.
Only shallow cloud convection developed in the maritime-warm case with no cloud unification. The rain area consisted of a simple assembly of many small cells (G in Fig. 4; Fig. 5c).
When the wind velocity is doubled from that of the standard wind in the maritime-ice case, in 80 min the rain pattern has elongated in the wind direction (J in Fig. 4), but at 120 min the rain cells are more perpendicular to the wind. With directional velocity the rain pattern is a pedal shape (K in Fig. 4) and, because of the weak surface outflow, no new cells develop except in the northwestern corner. With doubled velocity, the amount of rainfall is nearly the same as with the standard wind, but with directional velocity the rainfall is only 60% of that in the standard wind case.
b. Rain cell life, rain conversion, and heating rate
Further analysis was conducted with respect to rain cell life, conversion rate from water vapor to rainwater, and heating rate in maritime cases. With respect to cell life, in the maritime-ice case (Fig. 6a) a large, single rain cell persisted for a long time, producing >50 mm h−1 and increasing in area by absorbing smaller rain cells. In the maritime-frozen case (Fig. 6b), however, rain cells repeatedly merged and disintegrated, particularly in the early period before ice crystals and graupel appeared and, in the maritime-warm case (Fig. 6c), the rain consisted of small, short-lived cells, lasting about 20 min. The broad updraft formed by ice crystal depositional growth helps in keeping a large, single cell. Maritime ice with doubled wind velocity developed a single, large rain cell, although mergers were infrequent compared with the case using the standard wind (Fig. 6d). With directional velocity, the rain cell is small and rarely merges (Fig. 6e).
Raindrop conversion from water vapor increases with time and is calculated at 1.4% (120 min) in the maritime case without ice (MW in Fig. 7). The rate increases to 3.0% as ice crystals develop, illustrating the importance of ice crystals in raindrop formation (MI in Fig. 7). Later in time, in the maritime-frozen case, as the crystals become abundant, the conversion rate increases to 2.6% (MF in Fig. 7). In the continental cases (CI and CW in Fig. 7), however, the conversion rate is limited to 0.5% despite the inclusion of ice crystals. These results show that both ice crystals and large drops play an important role in converting larger amounts of water vapor to rainwater.
The heating rate has been calculated as in Yanai et al. (1973) and radiation has not been considered since radiative heating is typically lower than cloud latent heat. The average values for up to 90 min show two peaks at different heights (Fig. 8). The lower peak at around 2.6 km (+5°C) occurs through drop condensation growth and the higher at around 4.5 km (−6°C) by ice crystal depositional growth. Maritime ice, as the most active cloud system keeps high heating up to 8 km. In the later period in maritime ice, a small heating rate sink occurred at a low level due to wide-range subsidence and drop evaporation. Although the heat profile is almost the same in the directional velocity case as with the standard wind, doubled velocity gives a slightly higher release at the higher level. With directional velocity, the lack of small cell development results in less heat released at the lower level. Heating in the upper level in continental ice is lower than with maritime ice because of weaker cloud activity.
c. Storm structure and precipitation particle growth modes
Although other cases show similar profiles, the case with directional velocity was selected at 120 min as a typical thunderstorm cell because of its simple convective pattern (Fig. 9a). The prominent model characteristics are a stepwise, tilted updraft, low pressure near the freezing level, high pressure close to the surface at the maximum rainfall intensity, a negative temperature deviation at the surface near the frontal edge and just below the melting level, and positive temperature deviation in the downdraft. The apparent formation of a weak cold dome in the model may be the result of calculating the temperature deviation from the initial temperature instead of using an average of the modified temperature. Moist air is lifted up along a sloped updraft. The low-level airflow to the west of the cloud triggered new cells close to the frontal edge of main cell that merged in succession into the main rain cell. Three rain peaks appeared: one from a developing area, the second from the main area, and the third from the thick anvil.
The mixing ratio profiles illustrate the growth of ice crystals and graupel by depleting cloud drops in a wide area in the upper level of the main cell, the formation of hail near the freezing level, and the decrease in drizzle (40 < r < 400 μm) at the same level. It rains heavily below the highest updraft column (Fig. 9b).
Figure 9c gives the number density profiles at different distances from storm frontal edge in the model cloud. At the front at the location marked A in Fig. 9a, hail grows near the freezing level where frozen drops capture supercooled drops. Depression of larger drops above the freezing level illustrates active drop freezing. In the area of peak rainfall (location marked B), production of hail occurs both in the upper cloud and near the freezing level. Graupel falling from above capture supercooled drizzle, forming hail just above the freezing level. The sudden decrease in the number of drizzle-sized drops illustrates efficient capture by graupel and hail. In the thick, upper cloud layers, small hail prevails ahead of the transition zone (location marked C) and then, at higher levels, hail formation diminishes, replaced by the growth of graupel behind the transition zone (location marked D).
In the maritime-frozen case, however, hail, originating in frozen drops, grows in the turreted convective columns and graupel are carried upward.
d. Rainwater accumulation
In the case with maritime ice, rainfall intensities increase abruptly as the cell merges (Fig. 10a). Drizzle mixing ratio increased in intensity during cell merging [80 min in Fig. 10b(d)]. The mixing ratio profile is characterized by a high hail growth rate near the freezing level [Fig. 10b(e)]. Just below this level the raindrop mixing ratio increases further (Fig. 10c). As in the particle growth modes previously discussed, graupel falling from above forms hail by capturing supercooled drizzle transported from a merged cell. Greater mixing ratios of drizzle during cell merging (80 min) suggests the importance of previous drop growth in a merging cell.
The second rain accumulation process may be seen in a large rain cell. In maritime-ice at 120 min, a large rain cell contains several areas of convection. There is an extremely high rainfall intensity where the areas coincide (Fig. 11a). Analysis of the number density profiles show rapid, large raindrop growth at low altitudes (B), attributable to mixing of large drops from neighboring cells (A and C of Fig. 11b).
A third accumulation process may be seen in the case with directional velocity (Fig. 12a). At 80 min a tornadolike mesocirculation may be seen at about midlevel (3.1 km) in the northern rain branch. As the downdraft propagates downward, the updraft extends upward from the midlevel, low pressure region (Figs. 12a,b). The temperature decreases in the mesocirculation region. There is a cloud-free area in the center of the column extending to the surface. Air surrounding the column rotates as it ascends. High liquid water contents extend as high as 8 km. An abundant cloud drop supply from the column wall enhances both graupel and hail growth. Graupel grow rapidly as they fall and there is a greater growth of hail with a maximum near the freezing level (Fig. 12c).
e. Rain organization in an ensemble model
With maritime ice, the low-level cloud cells initially (40–60 min) lined up along the low-level winds, merged with some growing cells and tended to line up along the mid- to upper-level winds (120 min). Among rain cells lining along the mid- to upper-level winds, several rain cells gather near the center and at 120 min (L in Fig. 4), and at 130 min, the cloud cluster suddenly breaks up and forms a circular rain ring 60 km in diameter, which persists (M and N in Figs. 4, and first six panels in Fig. 13). The same ring shape is noticed in cloud cells at 5.1 km. A central cross section shows lowering of the water vapor mixing ratio within the ring.
In the maritime-warm and maritime-frozen cases, the low-level cells also initially tend to line up along the lower-level winds. With time, the cloud cells at 5.1 km, as well as the rain cells lie along the mid- to upper-level winds. However, the clouds at 1.1 km lie at both the low-level and mid- to upper winds. Although the rain cell size increased to 10–20 km in MF, a slightly smaller than MI, MW stays small at a few kilometers, even after 150 min. No clear main organization was detected in both cases.
With maritime cases, the accumulated rainfall tends to increase somewhat linearly (Fig. 13 next to last panel) as long as the warm-rain process dominates rain production. When the ice phase begins to contribute to precipitation, rainfall increases with time at a steeper rate. The accumulated rainfall amount is highest with maritime ice and lowest in maritime warm, the difference being about threefold.
At 90 min, the heating rate profile peaks at about 3 km in maritime-warm and maritime-frozen conditions but, because of the depositional growth of ice, peak height goes to about 5 km with maritime ice (Fig. 13 last panel). Because of development of many small clouds that eject drops outside from the cloud top, enhancing drop evaporation, negative values prevail in all cases at low levels even at earlier time. Just above 3 km the melting process results in a sharp negative drop in the heating rate profile with maritime ice. As the ice phase is activated in MF, the peak heating rate height moves to 5 km.
f. Cells in the rainband models
The rain cells lined up along the leading, western edge of the cloud earlier in the case with maritime ice. As the cloud developed, the outflow from the rain-induced downdraft produced new cells forward of the cloud band. As the new cells forward were absorbed into the main cloud, the rainband increased in width. As the ice phase became active, a tilted updraft was formed, enhancing trailing and eastern cloud cells (110 min). The outflow from them strengthened the forward cell formation, increasing the rainband there (120 min) as it diminished at the rear (130 min, Fig. 14 first five panels).
In the maritime-frozen case, however, the heavy rain continued at the cloud's trailing edge. With maritime-warm conditions, isolated cells develop sporadically in front of the narrow rainband, moving west by absorbing new small cells.
The accumulated rainfall was highest with maritime ice and lowest in maritime warm (Fig. 14 next to last panel). Although the heating rate profiles were similar to those in isolated cells, there was no heat sink in the lower levels of the cloud, even at later times in the model runs (Fig. 14 last panel).
5. Discussion
With changing microphysics, model simulations exhibit great diversity in rain patterns (Fig. 4). An important feature is the formation of a large, single rain cell that only develops in the maritime-ice case. Heat generated by ice crystal depositional growth aids in the development of a large updraft. With wind shear, the updraft is sloped. The downdraft produced by precipitation drag forces induces an airflow, which helps trigger the formation of new cells in front and beside the main cell. The new cells merge with the main cell and are incorporated into its updraft field. Through these steps a sloped updraft forms and the single, large rain cell persists (Fig. 5a). In continental ice, however, the updraft profile was rather vertical due to weaker activities of merging cells.
In the directionally sheared wind case chosen as a typical thunderstorm (Fig. 9), which shows similar patterns as in rainband model, both dynamic and thermodynamic structures show many similarities to reported observations of squall lines (Chong et al. 1987; Roux 1988). The agreement with a West African squall line lies in the stepwise, downshear, sloped updraft, the negative temperature and pressure deviations at about 700 mb, and the high radar echo intensity below the freezing level.
Storm splitting, reported by Klemp and Wilhelmson (1978) has not been found for the model given here in which the microphysical parameterization calculates the terminal velocity of rainwater from the rainwater content. Overestimation of terminal velocity might lead to easier splitting of a storm system. Multicell structures reported by Fovell and Ogura (1989) also have not been found in the present model. The two-dimensionality of their model may account for the differences.
Figure 5 shows that in the maritime-warm case, only an assembly of cells results, while in the maritime-frozen case, tall, turreted cells form along the periphery of the main cell, resulting in a doughnut-shaped rain pattern. With higher sheared wind velocity, the rain cell grows early along the wind direction but later changes more toward the perpendicular. A pedal-like rain pattern is formed with directional shear (Fig. 9). Distribution of downward momentum transport in wide directions is the reason for the weak outflow. One interesting observation is the simulation of a tornadolike mesocirculation in the northern branch (Fig. 12). The midlevel mesocirculation with a central, cloud-free column is similar to that reported by LeMon and Doswell (1979).
The most notable results are those referring to precipitation particle growth modes in storm clouds (Fig. 9). Forward in the cloud, large drops, grown by the warm rain process, freeze just above the freezing level and grow by capturing surrounding supercooled drops. The major precipitation process occurs in the area of the sloped updraft. As ice crystals grow, the updraft increases and the cloud grows taller. Graupel, formed in the upper levels, now fall and capture supercooled drops transported from a forward area and hail production is accelerated near the freezing level. Hail formation also occurs near the cloud top where the updraft is strongest. In the lower level at the rear of the storm, the hail growth process is retarded, while hail formed higher in the cloud begins to fall. Farther to the rear, in the upper cloud layers, hail production ceases, and the radar echoes weaken. The interval may correspond to the “transition zone” reported in squall lines (Biggerstaff and Houze 1991). Even farther to the rear of the storm, there is renewed graupel growth and the radar echo intensity increases. Videosonde observation of a “Hector” squall line seems to support the model results (Takahashi and Keenan 2004).
A unique rain accumulation process was noticed at cell merging (Fig. 10). The growth of drizzle drops in the merging cells that are being incorporated into the main cell accelerates hail growth near the freezing level and plays a critical role in the accumulation of rainwater near the freezing level (Fig. 15). In a merging cell, convection forms large drops at the upper part of cloud. As the cell merges, the earlier formed drops grow larger in the organized updraft of the main cell and assist graupel growth. Leary and Houze (1979) have reported sudden radar echo intensification during cell merging, and videosonde data reported by Takahashi et al. (2001) show accelerated growth of graupel and frozen drops near the freezing level during cell merging in Baiu clouds. The rainwater mixing ratio increases again just below the melting level. The intrusion of hail-originated raindrops into warm rain-originated raindrops below, accelerates the collection process.
The model results demonstrate two other rain accumulation patterns. When raindrops, grown in different cells, mix in a common downdraft column in a large rain cell, their growth is accelerated by collection because of the increase in large-sized drops (Fig. 11). This may partly explain the sometimes reported, high radar echo intensity near the surface.
The model's third rain accumulation process occurred in a rotating cell in the case with directional shear. Because of the strong updraft in this case, a great many cloud droplets formed along the periphery of the rotating column, subsequently forming graupel and hail over a range of height in the column (Fig. 12). Sudden increase of lightning flashes in association with tornados (Williams et al. 1999) may be related to this high hail growth event.
One of the important results of these studies is related to the patterns of rain and the organization of rain cells in the cloud ensemble model. The most important is the formation of a rain ring, 60 km wide, in maritime ice (Fig. 13). Cell-to-cell interaction may be more advantageous in producing organized downdrafts with maritime ice forming large cloud systems. By forming a downdraft area at the center, a ring rain system persists.
LeMone et al. (1998) reported that the rain pattern tends to line up perpendicular to the low-level winds; however, rain cells rather line up along mid- to upper winds. The reason for the difference is not clear but may lie in the termination of the model run earlier in the storm's lifetime. Robe and Emanuel (2001) have reported linear rainbands as observed at a later period in a cloud ensemble model without explicit microphysics, however. It is interesting to note that among rain cells aligning with the mid- to upper winds, a circular ring suddenly appears. Mori (1995) has reported occasional ring-shaped rain patterns in ship-based radar returns in the Coupled Ocean–Atmosphere Response Experiment (COARE) area.
A significant result of the study was the difference in the development of the rainbands with different precipitation mechanisms. With maritime ice, the rainband moved by enhancing new cells forward within the cloud band. The rain cells in the maritime frozen case keep growing at the rear of the main cloud. In the maritime-warm case, narrow, forward rain cells advance by successively absorbing new cells.
Two peaks in the heating rate source were calculated as in Yanai et al. (1973): one at around 3 km by drop condensation, and the other at around 5 km by ice depositional growth. Heat is extended to higher levels by vertical advection. The apparent increase in the heat release peak height shown by Johnson (1992) for the Australian Monsoon Experiment (AMEX) may indicate the transfer of the precipitation process from warm rain to cool rain as the cloud develops. A heating rate sink calculated in the later time was of greater extent in the ensemble model. Although Johnson (1992) suggested the anvil as contributing to the cooling, it appears at a much earlier time in the ensemble model through drop evaporation in the many small convective clouds.
6. Conclusions
A three-dimensional cloud model with explicit microphysics model has been used to investigate the effects of microphysics and wind on the patterns of rain and their organization. The studies showed that, even in tropical areas, ice crystals play an important role in rain patterns and accumulation, heating rate profiles, and the organization of rain cells.
In maritime cases, heavier rainfall induces outflow and triggers new cells forward and to the sides of the main cell. In absorbing the new cells, the main cell enlarges. The structure of rain cells differs greatly with different microphysics: maritime ice produces a large, single rain cell; maritime frozen produces doughnut-shaped rain; and maritime warm rain forms an assembly of small rain cells.
During the passage of a storm, rain begins with frozen drops and shifts to a hail growth process near the freezing level. Hail grown at the upper levels then dominate and are finally replaced by graupel.
Very high rain accumulation occurred near the freezing level during cell merging. Graupel falls from a higher level in the main cell, capturing supercooled drizzle from a merging cell. The prior growth of drizzle in the merging cell is of obvious importance to the process. Two other processes that lead to high precipitation particle growth have been suggested. One is the enhancement of raindrop growth as drops grown in different cells mix in a common downdraft. The other is a rotating cloud column in which water drops at the higher periphery of the column favor the growth of graupel and hail.
Latent heat peaks were calculated at two different levels: 3 km by drop condensation and 5 km by ice depositional growth. As ice crystals grow, the heating rate source extends to higher levels by advection. In the ensemble model, a heating rate sink appears early in the lower levels from the development of many small clouds. With maritime ice, the appearance of a ring of rain suggests intensive cell-to-cell interaction. Rainband moves as new rain cells are formed forward.
Since ice crystal concentrations differ greatly between the open ocean and the maritime continent, different rain patterns and cell organizations may be expected to occur in different regions of East Asia.
Acknowledgments
The authors would like to express their sincere appreciation to Prof. A. Sumi who gave constant encouragement throughout this study. The authors express their gratitude for the valuable comments and suggestions from the anonymous referees. We were supported by funding from the Center for Climate System Research, The University of Tokyo, the Ministry of Education, Culture, Sports, Science and Technology, Government of Japan, and the Japan Aerospace Exploration Agency.
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