W EI-K UO T AO

ABSTRACT

1. Introduction
The Tropical Rainfall Measuring Mission (TRMM; Simpson et al. 1988, 1996; Kummerow et al. 2000), a joint Japanese–U.S. cooperative earth probe satellite, was successfully launched in 1997 to advance under- standing of the global energy and water cycle. The TRMM precipitation radar (PR) is the first spaceborne precipitation radar and can provide height information based upon the time delay of the precipitation-back- scattered return power (Kozu et al. 2001; Okamoto 2003). This allows vertical profiles of precipitation to be obtained directly over the global Tropics (Iguchi and Meneghini 1994; Iguchi et al. 2000; Iguchi 2007). The high vertical resolution (250 m at nadir) and quasi- vertical beam of the PR allow it t o identify a bright band for a higher percentage of all echoes than can a quasi–horizontally scanning ground radar. Therefore, the classification between convective and stratiform re- gions of mesoscale convective systems (MCS) has be- come more straightforward when utilizing the presence of the bright band (Awaka et al. 1998, 2007). Takayabu (2002) obtained a spectral expression of precipitation profiles to examine convective and strati- form rain characteristics as a function of precipitation- top height (PTH) over the equatorial area observed by the TRMM PR. Based on the results of the spectral precipitation statistics of Takayabu (2002), the spectral latent heating (SLH) algorithm was developed for the TRMM PR in Shige et al. (2004, hereinafter Part I). This method uses PR information (i.e., PTH, precipita- tion rates at t the surface and melting level, and convec- tive/stratiform classification) to select the heating pro- files in lookup tables. Heating-profile lookup tables for the three rain types—convective, shallow stratiform, and anvil rain (deep stratiform with a PTH higher than the melting level)—were derived with numerical simu- lations of tropical cloud systems in the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE; Webster and Lukas 1992), utilizing a cloud-resolving model (CRM). For convective and shallow stratiform regions, the lookup table is based on the PTH. Considering the sen- sitivity of the PR, we used a threshold of 0.3 mm h−¹ to determine the PTH. Properties (i.e., shape and magni- tude) of the convective and shallow stratiform heating profiles show near-monotonic change with PTH, sug- gesting that the distribution of latent heating is a strong function of PTH. On the other hand, the PR cannot observe the PTH accurately enough for the anvil re- gions because of its insensitivity to the small ice-phase hydrometeors (Heymsfield et al. 2000). The anvil heat- ing profile is much more uniform than the convective heating profile in the tropical convective systems, such that the height of maximum anvil heating is not overly sensitive to storm-height observation. Thus, for the an- vil region, the lookup table refers to the precipitation rate at t the melting level P mn instead of PTH. Houze et al. (1980), Gamache and Houze (1983), and Chong and Hauser (1989) showed that the stratiform precipitation falling into the melting layer from the anvil cloud above is a combination of condensate generated in and carried over from the convective region plus condensate that is produced by the anvil region's own upward motion, analyzing the water budgets of a precipitating tropical mesoscale convective system. The contribution by the horizontal transfer of condensate from the convective region to the anvil region is included in the lookup tables (Fig. 7 of Part I). In a subsequent paper (Shige et al. 2007, hereinafter Part II), the universality of the lookup table produced from COARE simulations used in the SLH algorithm was examined for its global application to TRMM PR data and improvements were made to the SLH algo- rithm. In the revised procedure for convective heating retrieval, the upper-level heating amplitude due to ice processes and lower-level heating amplitude due to liq- uid water processes are determined separately. Braun and Houze (1995) showed that the peak heating rate by freezing within the convective region occurs immedi- ately above the freezing level. Based on sensitivity tests, the level separating upper-level heating from lower- level heating is determined to be 1 km above the melt- ing level. The upper-level heating due to ice processes is determined by P f , where P f is the precipitation rate at the level separating upper-level heating from lower- level heating. The lower-level heating due to liquid wa- ter processes is determined by P s , where P s is the pre- cipitation rate at the lowest observable level. In the stratiform region, the heating profile is shifted up or down by matching the melting level in the COARE lookup table with the observed one. The revised SLH algorithm was applied to PR data, and the results were compared with Q 1 profiles that were derived diagnos- tically from the 1998 South China Sea Monsoon Ex- periment (SCSMEX; Lau et al. 2000) Northern En- hanced Sounding Array (NESA) sounding data (Johnson and Ciesielski 2002), where Q 1 is the apparent heat source budget defined in Yanai et al. (1973). Key features of the vertical profiles agree well—in particu- lar, the level of maximum heating. Differences of heat- ing profiles between the western Pacific Ocean (more "top heavy") and the Atlantic Ocean (more "bottom heavy") estimated by the SLH algorithm are also con- sistent with those from the budget study (Thompson et al. 1979; see a review by Cotton and Anthes 1989). Utilizing the information on precipitation profiles, the SLH algorithm retrieves differences in the shape of the convective heating profile between the eastern and western Pacific during the cold phase. The differences in the shape of convective heating profiles across the Pacific are consistent with the results from reanalysis datasets (Back and Bretherton 2006). Large-scale models (i.e., general circulation and cli- mate models) require not only the vertical distribution of Q 1 , but also that of Q 2 , where Q 2 is the apparent moisture sink budget defined in Yanai et al. (1973). Rajendran et al. (2004) developed a new empirical cu- mulus parameterization scheme (ECPS), based on a procedure to improve the vertical distribution of heat- ing and drying over the Tropics. The ECPS utilizes ob- served profiles of Q 1 derived using the TRMM Micro- wave Imager (TMI) convective–stratiform heating al- gorithm (Tao et al. 1993) and the European Centre for Medium-Range Weather Forecasts analysis-based Q 2 . Comparisons between short-range ECPS forecasts and those made with the modified Kuo scheme (Krishna- murti et al. 1983) show a marked improvement in the skill in the ECPS. More improvements may be achieved with the ECPS utilizing both Q 1 and Q 2 profiles derived from TRMM data (J. Rajendran 2005, personal com- munication). However, none of the TRMM heating al- gorithms estimate Q 2 profiles (see a review by Tao et al. 2006). In addition to improving large-scale model simula- tions, physical insights into convection can be gained by having both Q 1 and Q 2 profiles. By combining the Q 1 and Q 2 equations, one can examine the eddy fluxes that have been widely used to measure the intensity of con- vection (e.g., Ninomiya 1968, 1971; Nitta 1972, 1975, 1977; Yanai et al. 1973, 1976; Johnson 1976; Gallus and Johnson 1991). Careful comparison between the verti- cal distributions of Q 1 and Q 2 yields valuable informa- tion on the nature of heating processes (e.g., Nitta and Esbensen 1974; Luo and Yanai 1984; Johnson and Lin 1997). For example, coincident peaks indicate mostly stratiform rainfall, whereas widely separated peaks in- dicate strong eddy fluxes or an important contribution by deep convection. In this study, the SLH algorithm is used to estimate the Q 2 profile. First, differences between Q 1 and Q 2 are examined. Second, Q 2 profiles are reconstructed from CRM-simulated parameters (i.e., convective/stratiform classification, PTH, P s, P mr and P f ) and are compared with the "true" CRM-simulated Q 2 profiles, which are computed directly by the water vapor equation in the model. Third, the SLH algorithm is applied to PR data and the results are compared with Q 2 profiles derived diagnostically from SCSMEX sounding data (Johnson and Ciesielski 2002). It is also applied to PR data for February 1998 and February 1999 to highlight the dif- ferences between El Niño and La Niña events.
2. Approach
Figure 1 shows the procedure for refining and vali- dating the Q 2 profile retrieval using the SLH algorithm. Because of the scarcity of reliable validation data and difficulties associated with the collocation of validation data and satellite measurements, a consistency check of the SLH algorithm is performed using CRM-simulated precipitation profiles as a proxy for the PR data. The SLH algorithm estimates Q 2 that is mainly due to pre- cipitation processes, because it is s severely limited by the inherent sensitivity of the PR, which can detect only precipitation-sized particles. Hereinafter, Q 2 estimated by the SLH algorithm is represented as Q 2 p to bring attention to this point. Algorithm-reconstructed Q 2p profiles are derived from CRM-simulated precipitation profiles and are compared with CRM-simulated true Q 2 profiles, which are computed directly from the water vapor equation in the model. The consistency check is a useful and necessary precondition for the application of the algorithm to actual TRMM PR data. CRM- simulated data from TOGA COARE, the Global At- mospheric Research Program Atlantic Tropical Experi- ment (GATE; Houze and Betts 1981), SCSMEX NESA, and the 1999 Kwajelin Atoll Field Experiment (KWAJEX; Yuter et al. 2005) are used as a consistency check. Locations of sounding arrays deployed for TOGA COARE, GATE, SCSMEX NESA, and KWAJEX are shown in Fig. 2 of Part II. Only precipi- tation over ocean is considered in the current investi- gation. Significant differences in precipitation features between ocean and land have been shown by TRMM observations (e.g., Nesbitt et al. 2000; Petersen and Rutledge 2001; Takayabu 2002, 2006; Schumacher and Houze 2003a,b). Continental locations exhibit marked variability in precipitation structure both regionally and seasonally; thus we possibly need to vary the lookup table regionally and seasonally. Simulations of other field experiments [e.g., the Global Energy and Water Cycle Experiment Asian Monsoon Experiment (GAME) in the Indo-China Peninsula (Yasunari 1994) and the Atmospheric Radiation Measurement Program in the southern U.S. Great Plains (Ackerman and Stokes 2003)] are needed to produce lookup tables for precipitation over land but are beyond the scope of this study. For a true test, the SLH algorithm is applied to PR data and the results are compared with Q 2 profiles derived diagnostically from SCSMEX NESA sounding data (Johnson and Ciesielski 2002) in this paper. The CRM used in this study is the two-dimensional version of the Goddard Cumulus Ensemble (GCE) model (Tao and Simpson 1993; Tao et al. 2003). Tropi- cal convective systems in TOGA COARE, GATE, SCSMEX NESA, and KWAJEX are simulated with the so-called cloud ensemble modeling approach, as ex- plained in Part II. Details of model settings were pro- vided in Part II. Note that the TOGA COARE and GATE simulations in this study are not the same as those in Part II. The TOGA COARE and GATE simu- lations in this study were made with the TOGA COARE flux algorithm (Fairall et al. 1996; Wang et al. 1996) and a modification of the conversion of cloud ice to snow in the ice microphysics schemes (Tao et al. 2003) as well as the SCSMEX and KWAJEX simula- tions. The accuracy of the convective–stratiform sepa- ration affects the determination of the vertical distribu- tion of heating and drying. The TRMM PR rain-type classifications, in which brightband identification is very important, cannot be directly applied to GCE out- puts (Awaka et al. 1996). The microphysical schemes utilized in CRMs (e.g., Lin et al. 1983; Rutledge and Hobbs 1984) typically do not contain an explicit de- scription of the partially melted precipitation particles that lead to a bright band of enhanced radar reflectivity. Thus, the GCE convective and stratiform separation method (Lang et al. 2003) is used with some modifica- tions described in Part I to maintain the consistency with the TRMM PR version-6 2A23 convective–strati- form separation algorithm (Awaka et al. 2007). Consid- ering the sensitivity of the PR, we classified model grid points that have a precipitation less than a threshold of 0.3 mm h − ¹ as a nonprecipitating region.
3. Heat and moisture budgets
In diagnostic studies (Yanai et al. 1973; Yanai and Johnson 1993), it is customary to define the apparent heat source Q 1 and the apparent moisture sink Q 2 of a large-scale system by averaging horizontally the ther- modynamic and water vapor equations as
where θ is the potential temperature, q v is the mixing ratio of water vapor, v is the horizontal velocity, w is the vertical velocity, π = (p/P oo) R/C p is the nondimensional pressure, p is the pressure, P 00 is the reference pressure (1000 hPa), C p is the specific heat of dry air at constant pressure, R is the gas constant for dry air, L v is the latent heat of vaporization, z is height, and t is time. The overbars denote horizontal averages. Both Q 1 and Q 2 can be directly related to the con- tributions of cloud effects, which can be explicitly esti- mated by CRMs as
The primes indicate deviations from the horizontal av- erages; ρ is the air density and Q R is the cooling/heating rate associated with radiative processes. The subgrid- scale (smaller than the cloud scale) diffusions are rep- resented by D o and D q , which are usually small relative to other terms above the boundary layer (Soong and Tao 1980). The terms LH and NC are the net latent heating and the net condensation, respectively, due to the phase change of water:
The variables L f and L s are the latent heats of fusion and sublimation, respectively. Variables c, e, f, m, d, and s stand for the rates of condensation of cloud droplets, evaporation of cloud droplets and raindrops, freezing of cloud droplets and raindrops, melting of ice crystals, snow and graupel, deposition of ice crystals, and subli- mation of all ice hydrometeors, respectively. These pro- cesses are not directly detectable with remote sensing (or, for that matter, with in situ measurements). Thus, heating and drying retrieval schemes depend heavily on the use of CRM. The first terms on the right-hand side of Eqs. (3) and (4) are the vertical eddy heat and mois- ture flux convergences from upward and downward cloud-scale motions, respectively. The second terms are the horizontal eddy heat and moisture flux conver- gences, respectively. The precipitation falling at a given time is not related to the drying/moistening (heating/cooling) that is occur- ring at t that instant but rather to the accumulated dry- ing/moistening (heating/cooling) that led up to the pre- cipitation over a finite time period. Therefore, Q 1 and Q 2 should be basically integrated over the time periods encompassing the life cycles of cloud processes produc- ing the precipitation. However, it is extremely difficult to tabulate, for example, the effect of individual meso- scale systems. Instead, we here depend on the statistics. In the CRM simulation, as well as in the real world, cloud systems develop and decay. Although instanta- neous matching between a certain precipitation profile and a drying/moistening (heating/cooling) profile is an ill-posed concept, statistical tabulation could still be done, if the life cycle of cloud systems is realistically reproduced in the CRM. For example, a shallow con- vective precipitation profile may be at a developing stage of a mesoscale system with a certain probability A , and may be just an isolated convection with a prob- ability of 1 − A. The drying/moistening (heating/ cooling) associated with the two cases should be differ- ent. However, if the CRM reproduces the statistics of rain systems sufficiently well, CRM-based tables can statistically represent an average drying/moistening (heating/cooling) profile for a certain precipitation pro- file. We accumulate Q 1 and Q 2 over a period of 5 min for each data sampling, because accumulation over long periods is inadequate for growing convective cells (Shige and Satomura 2000, their Fig. 4a) and fast- moving convective systems. Additional sensitivity tests with periods of 1 and 2 min do not alter the Q 2 profile for the total region but indicate that there are more quantitative differences in convective and stratiform components of Q 2 than in those of Q 1 . In this study, the two-dimensional version of the GCE model was used. Real clouds and cloud systems are three-dimensional. Grabowski et al. (1998), Donner et al. (1999), and Zeng et al. (2007) found larger temporal variability in a two- dimensional simulation than in a three-dimensional simulation. Thus, the sensitivity of Q 2 in convective and stratiform regions to accumulated time might be smaller in the three-dimensional simulation than in the two-dimensional simulation, but such discussion is be- yond the scope of this study. Hereinafter Q 1 and Q 2 accumulated over a period of 5 min for each data sam- pling are represented as instantaneous Q 1 and Q 2 to maintain consistency with Part I and Part II. Figures 2a–f show GCE-simulated average profiles of the heat budget [LH, Q 1 − Q R (hereinafter Q 1 R ) with- out and with horizontal eddy heat flux] and moisture budget [NC, Q 2 without and with horizontal eddy heat flux] for the TOGA COARE 19–26 December 1992 case. The difference between LH and NC around 4.4 km is large (Figs. 2a,d). The maximum of NC around 4.4 km can be explained by a decrease in the saturation water vapor mixing ratio, which is due to the melting of ice particles (Guichard et al. 1997). It is also evident that the NC magnitudes are smaller than the LH mag- nitude above 6 km, because freezing is included in LH [Eq. (5)] but not in NC [Eq. (6)]. The profile of Q 1 R for the total region (Fig. 2b) is close to that of LH for the total region (Fig. 2a), except near the melting level (~4–5 km) and the upper tropo- sphere (~14–16 km). The vertical eddy heat flux con- vergence near the melting level compensates for the distinct LH cooling due to the melting for the total region (Sui et al. 1994; Shie et al. 2003) while that in the upper troposphere offsets the net radiation because the saturation mixing ratio is low at high altitudes; thereby, condensation heating is no longer vital (Mapes 2001; Shie et al. 2003). On the other hand, the profile of Q 2 for the total region (Fig. 2e) does not follow that of NC for the total region (Fig. 2d) and has a more compli- cated shape. Gallus and Johnson (1991) also showed that the profiles of Q 2 associated with a midlatitude squall line are noisier than those of Q 1 using rawin- sonde data. The vertical eddy moisture flux conver- gence is one of the major contributors to Q 2 while the contribution to the Q 1R budget by the vertical eddy heat flux convergence is minor, as noted by observa- tions (Chong and Hauser 1990) and modeling studies [Soong and Tao (1980) and many others]. This differ- ence is explained by the fact that the vertical gradient of the mean water vapor is larger than that of the mean potential temperature. The horizontal eddy heat and moisture flux conver- gences have been neglected by observational and mod- eling studies. However, heat and moisture transport from the convective region to the stratiform region may be important because of the embedded mesoscale cir- culation (i.e., ascending front-to-rear flow and descend- ing rear inflow) within a squall line (Gallus and John- son 1991). As discussed in Part II, there are differences between profiles of Q 1 R without and with horizontal eddy heat flux in the convective and stratiform re- gions—in particular, around the melting level (Figs. 2b,c). Much larger differences between profiles of Q 2 without and with horizontal eddy moisture flux in the convective and stratiform regions are found in Figs. 2e,f. The horizontal eddy moisture flux convergence compensates low-level drying and midtropospheric moistening in the convective regions while compensat- ing low-level moistening and midtropospheric drying in the stratiform regions. The Q 2 profiles with horizontal eddy heat flux in the convective and stratiform regions (Fig. 2f) are similar to the results from Johnson (1984), who partitioned the total Q 2 profile of Yanai et al. (1973) into convective and stratiform components. Two different mechanisms for the double-peak struc- ture in Q 2 often seen in tropical budget studies (Reed and Recker 1971; Yanai et al. 1973; Johnson 1976) have been proposed: 1) the combined but vertically sepa- rated drying effects of convective and stratiform re- gions (Johnson 1984) and 2) midtropospheric moisten- ing by vertical eddy moisture convergence in the con- vective region (Lafore et al. 1988; Caniaux et al. 1994). Lafore et al. (1988) and Caniaux et al. (1994) argued for the latter one based on their numerical simulations of a West African squall line during Convection Profonde Tropicale (COPT)-81. Although the profile of Q 2 in the total region for the TOGA COARE case does not ex- hibit a prominent double-peak structure, the Q 2 profile without horizontal eddy heat flux in the convective re- gion characterized by midtropospheric moistening (Figs. 2e) is in good agreement with that in the convec- tive region simulated by Caniaux et al. (1994, their Fig. 22b). Lafore et al. (1988) and Caniaux et al. (1994) neglected horizontal eddy moisture flux convergence, as do most previous studies, and thereby may have overestimated the role of the vertical eddy moisture convergence. Lafore et al. (2002) recently simulated a West African system during the Hydrological Atmo- spheric Pilot Experiment (HAPEX)-Sahel and pointed out the importance of the horizontal eddy flux conver- gence of heat, moisture, and momentum. The SLH algorithm estimates Q 1 R and Q 2 that is mainly due to precipitation processes ( Q 1 R p and Q 2 p ), because it is severely limited by the inherent sensitivity of the PR that can detect only precipitation-sized par- ticles. It is noticed in Fig. 2 that the Q 2 in the nonprec- ipitating region is of the same order as that in the strati- form region while the Q 1 R profile in the nonprecipitat- ing region is negligible. This is consistent with the results from Nitta and Esbensen (1974), which show that moistening rates are about a factor of 3 larger than heating/cooling rates during the undisturbed Barbados Oceanographic and Meteorological Experiment (BOMEX) period in the trade wind belts, attributable to larger contribution of eddy fluxes in Q 2 than in Q 1 R - Thus, we cannot expect that differences between Q 2 p and Q 2 are as small as those between Q 1 Rp and Q 1 R .
4. Algorithm
a.  Construction of lookup tables
The Q2o profile lookup tables have been constructed for the three rain types: convective, shallow stratiform, and deep stratiform, with and without surface rain (Fig. 3). For the construction of lookup tables, the GCE- simulated precipitation profiles and corresponding Q 2 p profiles from the four subperiods of 9-day duration (10– 18 December 1992, 27 December 1992–4 January 1993, 9–17 February 1993, and 18–26 February 1993) are used. Figure 3a shows the lookup table for convective rain. The GCE-simulated precipitation profiles with a 0.3 mm h− 1 precipitation-top threshold and corresponding Q 20 profiles are accumulated and averaged for each PTH with model grid intervals. Properties (i.e., shape and magnitude) of convective Q 2p profiles show less monotonic changes with PTH than do those of Q 1 R p (Part II, their Fig. 5a) because the contribution of eddy fluxes is larger in Q 2p than in Q 1 Rp . The convective Q 2p profiles with a PTH lower than 8 km are characterized by moistening around PTH levels resulting from an ex- cess of evaporation over condensation and drying be- low, such as in trade wind cumulus (Nitta and Esbensen 1974). This feature is consistent with convective heating profiles characterized by cooling aloft (Part II, their Fig. 5a). As for the stratiform precipitation, the GCE-simu- lated precipitation profiles with a 0.3 mm h − 1 precipi- tation-top threshold and corresponding Q 2p profiles are also averaged for each PTH (Fig. 3b). However, as mentioned earlier, we cannot expect the PR to retrieve the small ice-phase precipitation and observe the PTH accurately enough in the upper-level regions of the an- vils where small ice-phase hydrometeors dominate. Therefore, only the stratiform Q 2p profiles with a PTH lower than 4.4 km (shown in Fig. 3b), characterized by moistening below PTH levels and drying aloft, are used as the shallow stratiform Q 2p profile lookup table for the SLH algorithm. Figure 3c shows a lookup table for anvil (deep strati- form with a PTH higher than the melting level) rain. PR can measure the precipitation rate at the melting level, as can surface-based radar (e.g., Leary and Houze 1979), although it cannot observe the PTH accurately enough in the upper-level regions of the anvils. Thus, for the anvil region, the lookup table refers to the pre- cipitation rate at the melting level P m instead of PTH (Part I). The anvil profiles with a PTH higher than the melting level are characterized by upper-level drying and lower-level moistening, which is also found in ob- servations (e.g., Johnson and Young 1983). The upper- level drying in these anvil regions is largely due to con- densation and deposition, whereas the lower-level moistening is largely due to evaporation of raindrops. The height of the level separating upper-level drying and lower-level moistening decreases with ¯ P m , where tildes denote the variables in the lookup table. The cooling around the melting level increases with ¯ ∑ m (see Fig. 7a of Part II). Thus the saturation water vapor mixing ratio decreases, resulting in an increase of NC around the melting level, which accounts for the low- ering of the level separating upper-level drying and lower-level moistening. Note that the lookup table for anvil rain does not fully capture the variability in the upper-level drying of the stratiform rain region. Al- though drying above 12 km is found for the anvil pro- files with a PTH higher than 12 km in Fig. 3b, a set maximum height for Q 2 ρ profiles can be seen around 12 km in Fig. 3c.
b. Procedure of Q 2p retrieval
The procedure for Q 2 ρ retrieval is the same as that for heating retrieval (Part II) except for using the Q 2p tables (Fig. 3). The SLH algorithm utilizes the observed information on precipitation type (convective or strati- form), PTH, P s, P m , and P f . The convective region is then separated into a shallower convective region and a deeper convective region. On the other hand, the strati- form region is separated into a shallow stratiform re- gion and an anvil region based on the PTH in compari- son with the melting level. The algorithm then derives Q 2 ρ profiles based on the following procedure for each of the four regions (Fig. 4). For shallower convective regions (Fig. 4a), as well as shallow stratiform regions (Fig. 4b), a Q 2p profile cor- responding to the PTH is selected in the convective Q 2 ρ profile (Fig. 3a) and PTH-based shallow stratiform Q 2p profile (Fig. 3b) lookup tables, respectively. The ampli- tude is determined by
For deeper convective regions (Fig. 4c), the upper- level drying due to ice processes is determined by
Likewise, the lower-level drying due to liquid water processes is determined by
Because the differences in convective heating profile shape resulting from the relative importance of liquid and ice water processes that vary from case to case become prominent for higher PTH (see Fig. 6 of Part II), the separate determination of the upper-level and lower-level heating amplitudes has been only applied to convective rain with PTHs that are 3 km higher than the separating level in Part II. The above procedure of Q 2n retrieval is also applied to convective rain with the same PTH as the heating retrieval to maintain consis- tency with the heating retrieval. For anvil regions with a PTH higher than the melting level (Fig. 4d), on the other hand, the Q 2p profile cor- responding to P m is selected in the anvil Q 2p profile lookup table (Fig. 3c). The upper-level drying ampli- tude is then determined by
The evaporative moistening rate below the melting level in the anvil regions is proportional to the reduc- tion of the precipitation profile toward the surface from the melting level. The downward decrease of the inten- sity of anvil rain below the melting layer has been sta- tistically indicated in the PR observation (see Fig. 2 of Takayabu 2002) as well as in case studies of traditional radar observations (e.g., Leary and Houze 1979). Thus, the algorithm computes the lower-level moistening am- plitude Q 10w as a function of the difference of rainfall rate between the surface and the melting level P m − P s :
The above procedure allows us to estimate the Q 2p pro- files in the anvil regions both with and without surface precipitation. For a given P m , the algorithm computes stronger lower-level moistening for anvil regions with- out surface rain than for anvil regions with surface rain. The Q 2p profile is shifted up or down by matching the melting level of the COARE lookup table with the ob- served one, as in the heating retrieval.
5. Consistency check
a.  Time-averaged profiles
Four 8-day periods from TOGA COARE (19–26 De- cember 1992), GATE (1–8 September 1974), SCSMEX NESA (2–9 June 1998), and KWAJEX (6–13 Septem- ber 1999) are used for a consistency check of the SLH algorithm, as shown in Fig. 5. For each period, Q 2 ρ profiles were reconstructed using the simulated param- eters (i.e., convective/stratiform classification, PTH, P x , P m , and P t ) as input. The algorithm-reconstructed Q 2p profiles from the GCE-simulated precipitation profiles are compared with GCE-simulated true Q 2 profiles for the convective, stratiform, nonprecipitating, and total regions. For the COARE case, the SLH algorithm with the COARE lookup table produces good agreement be- tween the SLH-reconstructed Q 2p and GCE-simulated Q 2 profiles for convective and stratiform regions (Fig. 5a). The reconstructed total Q 2p profile is in good agreement with the model except for the lowest levels where moistening due to nonprecipitating processes is dominant. For the GATE case, the COARE lookup table re- sults in less agreement between the SLH-reconstructed and GCE-simulated profiles for convective and strati- form regions (Fig. 5b). The SLH-reconstructed drying at z = 1–3 km is weaker than the GCE-simulated dry- ing for the convective region, whereas the SLH-recon- structed moistening at z = 1–3 km is weaker than the GCE-simulated moistening for the stratiform region. Despite compensating errors at z = 1–3 km from each component (convective and stratiform), the SLH-re- constructed drying at z = 2–6 km is stronger than the GCE-simulated drying for the total region. This dis- crepancy is mostly explained by moistening in nonprec- ipitating regions that SLH cannot reconstruct. The COARE lookup table produces good agreement between reconstructed Q 2 p and simulated Q 2 profiles for the SCSMEX convective and stratiform regions (Fig. 5c). In addition to good agreement for the con- vective and stratiform regions, the contribution of the nonprecipitating region to the SCSMEX total Q 2 profile is small, leading to good agreement for the reconstructed Q 2 ρ and simulated Q 2 profiles for the SCSMEX total region. For the KWAJEX case, the SLH-reconstructed dry- ing below z = 4 km is weaker than the GCE-simulated drying for the convective Q 2 profiles, whereas the SLH- reconstructed moistening below z = 4 km is weaker than the GCE-simulated moistening for the stratiform Q 2 profiles, similar to the GATE case. Because of com- pensating errors below z = 4 km from each component (convective and stratiform), the reconstructed total Q 2p profile is in good agreement with the model except for the lowest levels where moistening due to nonprecipi- tating processes is dominant. The differences between the SLH-reconstructed Q 2 p and GCE-simulated Q 2 shown here are larger than those between the SLH-reconstructed Q 1 Re and GCE- simulated Q 18 (Part II, their Fig. 9). This is because the Q 2 profiles are noisier than those of Q 1 R because of larger contributions from eddy fluxes. The SLH algo- rithm cannot estimate the effect (moistening) of the nonprecipitating area, which also leads to a discrepancy with the GCE results. Nevertheless, the SLH-recon- structed total Q 2ρ profiles are in good agreement with the GCE-simulated ones, especially for the case in which the contribution of the nonprecipitating region to the Q 2 budget is small.
b. Error estimation
In the SLH algorithm, lookup tables are constructed based on the assumption that Q 2p profiles correspond statistically to precipitation profiles or precipitation pa- rameters (i.e., convective/stratiform classification, PTH, P s , P m , and P t ). However, the instantaneous grid- cell relationship between precipitation profiles and Q 2p is somewhat ambiguous. Part II performed a prelimi- nary evaluation of the horizontally averaged estimates and found that horizontal averaging over an ~30-km width was required to reduce random errors in the SLH-reconstructed heating profiles to acceptable lev- els. Following the method of Part II, a preliminary evalu- ation of the horizontally averaged estimates of Q 2n for the COARE, GATE, SCSMEX, and KWAJEX peri- ods used in the consistency check is performed. The Q 2p profiles were reconstructed grid by grid for each 8-day period using the simulated parameters as input. The differences between the reconstructed Q ρ 2 profiles and the simulated Q 2 were then examined statistically to find the errors in the instantaneous gridcell estimates using the table method. Larger root-mean-square (rms) errors were found for Q 2ρ (Fig. 6) than for Q 1 Rρ (Part II, their Fig. 10). Although the rms errors of Q 1 Rp at the PR footprint scale (4 km) are smaller than 16 K 2 h − 2 , those of Q 2 ρ are much larger than 16 K 2 h − 2 . A major reason is the larger contribution of eddy fluxes in the Q2p budget than in the Q1Rp budget. Averaging over ~60 km in width reduces the rms to about 1 K 2 h − 2 . From these results, averaging over ~60 km in width is recommended in order to use the SLH algorithm esti- mates of Q 2 quantitatively.
6. PR applications
In this section, the Q 2 p retrieval is applied to precipi- tation profiles from version 6 of the TRMM PR 2A25 dataset (Iguchi 2007), which is instantaneous and at footprint-scale (i.e., a level-2 product). Shige et al. (2006) recently investigated the consistency between TMI-observed brightness temperatures (TBs) and those simulated from PR2A25 version-5 (V5) and ver- sion-6 (V6) rain profiles over the central Pacific using a radiative transfer model. They showed that simu- lated TBs from PR V6 exhibits better agreement with observed ones than those from PR V5, implying the algorithm improvements. For stratiform regions, the Q20 profile is shifted by matching the melting level of the COARE lookup table with the observed climato- logical melting level. Brightband height estimates from version 6 of TRMM PR 3A25, 5°-spatial-resolution gridded monthly composite of instantaneous and foot- print-scale data (PR 2A25), are also used as the melting levels.
a.  Comparison of Q 2 profiles over the SCSMEX
NESA region
In Part II, the accuracy of the SLH-retrieved heating was evaluated by comparison with a rawinsonde-based analysis of diabatic heating for the SCSMEX NESA derived by Johnson and Ciesielski (2002). Key features of the vertical profiles agree well—in particular, the level of maximum heating. Here, the accuracy of the SLH-retrieved Q 2 p is evaluated by comparing with a rawinsonde-based analysis of Q 2 for the SCSMEX NESA derived by Johnson and Ciesielski (2002). Figure 7 shows a comparison between SLH-retrieved Q 2p from version 6 of the TRMM PR datasets and sounding-based Q 2 during the campaign's most convec- tively active period (15 May–20 June 1998). This period also coincides with the time during which the budget analysis was considered to be most reliable because of the completeness of the sounding network. Mapes et al. (2003) suggested that averages of about 30 days reduce sampling errors in the rainfall-rate estimate (propor- tional to integrated Q 1 or Q 2 ) to 10% for the SCSMEX NESA. There is very good agreement in several key features of the vertical profiles—in particular, below the melting level (5 km). It is evident from Fig. 7 that the Q 2 o drying magnitudes are smaller than the sound- ing-derived magnitudes in the upper troposphere above 9 km. The Q 2 p estimates from PR data are subject to sampling errors caused by the PR’s narrow swath width (~215 km), leading to a discrepancy with the sounding estimates (see Grecu and Olson 2006, their Fig. 9). The SLH algorithm is severely limited by the inherent sen- sitivity of the PR, which can detect only precipitation- sized particles. During the growing phase of a congestus cloud, the cloud top and radar-echo top may correlate well (Kingsmill and Wakimoto 1991). However, during the decaying phase of a cumulonimbus cloud, the two tops may differ considerably, leading to an underesti- mation of drying in the upper troposphere. The lookup table for the anvil based on P m (Fig. 3c) does not fully capture the variability in the upper-level drying of the stratiform rain region, which also accounts for the un- derestimation of drying in the upper troposphere.
b.  El Niño–La Niña
Figures 8a,b show the monthly mean surface rainfall (mm day¯¹) for February 1998 and February 1999, re- spectively. Drying/moistening structures over the six oceanic regions (western Pacific, central Pacific, eastern Pacific, South Pacific, Indian Ocean, and Atlantic Ocean) shown in Fig. 8 will be examined and compared. Heating structures over the same regions were exam- ined in Part II. Figures 9 and 10 show the monthly mean convective, stratiform, and total Q 2 p profiles derived from the SLH algorithm for six locations over the tropical oceans for February 1998 and February 1999, respectively. Total Q 1Rp profiles derived from the SLH algorithm are also shown. Note that the total Q 1 Rp profiles are not the same as in Part II but are estimated using the Q 1 R R profile lookup tables derived from the TOGA COARE simulations made with the TOGA COARE flux algo- rithm (Fairall et al. 1996; Wang et al. 1996) and a modi- fication of conversion of cloud ice to snow in the ice microphysics schemes (Tao et al. 2003). However, the differences are very small. A maximum at low levels (~0.5 km) is found in the SLH-estimated total Q 2p profile over the western Pa- cific for February 1998 (Fig. 9a). This low-level maxi- mum in the SLH-estimated total Q 2p profile comes from the SLH-estimated convective Q 2p profile with a low-level maximum, reflecting the abundance of shal- low convection. Diagnostic budget studies over western Pacific regions (Reed and Recker 1971; Nitta 1972; Yanai et al. 1973; Lin and Johnson 1996) indicate a double-peak structure with a minimum near 4 km. Whereas the SLH-estimated mean Q 2 ρ profile for Feb- ruary 1999 shows a minimum near 4.5 km, the SLH- estimated mean Q 20 profile with the low-level maxi- mum for February 1998 does not resemble those deter- mined from the diagnostic budget studies. Note that diagnostic budget studies over the western Pacific do not contain periods corresponding to the warm phases of ENSO, except for 2 months in the period from March to July of 1958 in Nitta (1972). The SLH-esti- mated mean Q 2 ρ profile for February 1998 resembles the mean Q 2 profile with a lower-level maximum over the GATE region (Nitta 1978; Thompson et al. 1979), which is due to a different cloud population with more shallow convection and lower sea surface temperatures (SSTs) in the GATE region. Deep convection over the western Pacific is suppressed during the warm phase of ENSO (February 1998) relative to the cold phase (Feb- ruary 1999) because of lower SSTs. Thus, the difference in the SLH-estimated mean Q 2 ρ profile between Feb- ruary 1998 and February 1999 may be reasonable. There are dramatic differences in total Q 2 ρ profiles over the central and eastern Pacific between the 1998 El Niño event and the 1999 La Niña event. First, these differences can be attributed to those in stratiform rain fraction (Schumacher and Houze 2003a). Second, the shape of convective Q 2 p profiles also affects total Q 2 p profiles. The convective Q 2 ρ profiles are shallower dur- ing La Niña than El Niño. Part II pointed out that the SLH-estimated heating profile over the South Pacific for February 1998 is very similar to the vertical distribution of heating during the undisturbed BOMEX period in the trade wind belts (Nitta and Esbensen 1974) and to that during episodic trade wind regimes over the western Pacific (Johnson and Lin 1997). On the other hand, the SLH-estimated Q20 profile with low-level drying over the South Pacific for February 1998 is not similar to the vertical distribu- tion of Q 2 with low-level moistening during the undis- turbed BOMEX and to that during episodic trade wind regimes over the western Pacific. A possible reason for the differences is that the contribution from the non- precipitating region to the Q 2 budget, which SLH can- not retrieve, is large. Another reason is that there is larger geographical variability in Q 2 profiles than in Q 1 profiles. For example, Lin and Johnson (1996) indi- cated that, although the heating profiles over different regions of the western Pacific warm pool are similar to one another, the drying/moistening profiles are signifi- cantly different. The SLH-estimated Q 2p profiles over the Atlantic Ocean for February 1998 and February 1999 resemble the mean Q 2 profile with a lower-level maximum that was determined from a diagnostic budget study during GATE (Nitta 1978; Thompson et al. 1979) and simu- lated by the GCE model (see Fig. 5b). It is somewhat awkward to compare February Q 2 profiles in the At- lantic Ocean with published Q 2 profiles from GATE, which occurred in boreal summer. Also, the selected area for the Atlantic Ocean includes the trade wind area (Augstein et al. 1973) where the Q 1 and Q 2 pro- files should be different from those from GATE. For a more direct comparison with the GATE profiles, the SLH-estimated Q 1 R ρ and Q 2 ρ profiles over the area from 5° to 15°N latitude and from 20° to 30°W longi- tude, which roughly corresponds to the GATE region, are shown in Fig. 11. There is a good agreement in the key features of the Q 2p profiles—in particular, for the levels of maximum drying. Thus, it is shown that the SLH algorithm can estimate differences in Q 2p between the western Pacific and the Atlantic Ocean as well as those in Q 1 , which are also consistent with the results from the budget study (Thompson et al. 1979; see a review by Cotton and Anthes 1989). Over the Indian Ocean, even indirect validation us- ing the results of diagnostic studies for different years is difficult because of the lack of observations. 1 The SLH- estimated Q 20 profile shape over the Indian Ocean for February 1998 resembles that over the western Pacific for February 1999, whereas that over the Indian Ocean for February 1999 resembles that over the Atlantic Ocean. The differences in the SLH-estimated Q 2n over the Indian Ocean between February 1998 and February 1999 are consistent with those in the SLH-estimated Q 1R over the Indian Ocean between February 1998 and February 1999.
c.  Variability of Q ρ profile
The average profiles shown in Figs. 9 and 10 may not be very representative because there are large spatial and temporal variabilities in rainfall over a larger re- gion such as those selected in Fig. 8. Following the ap- proach used in Part II, we used contoured frequency by altitude diagrams (CFADs; Yuter and Houze 1995) to provide the actual variability of drying/moistening pro- file shapes. Many of the negative values in the low-to-middle tro- posphere in Figs. 12a–e and Figs. 13a,b,d are associated with evaporation in the stratiform region, suggesting large variability in stratiform rain fraction over the re- gions. The distinct peak in the frequency of drying at levels below 2 km is also evident for all six geographic areas for both February 1998 and February 1999 in the CFADs (Figs. 12 and 13), corresponding to a drying peak at the lowest levels seen in the mean convective Q 2p profiles (Figs. 9 and 10). It is inferred from the convective Q 2p -profile lookup table (Fig. 3a) that shal- low convection with PTHs lower than 4 km accounts for this distinct peak. The CFADs of mean Q 1 and Q 2 over the intensive flux array during TOGA COARE based on a 6-hourly analysis have been shown by Johnson and Ciesielski (2000, their Fig. 3). Direct comparison of the CFADs shown in Figs. 12 and 13 with those in Johnson and Ciesielski (2000) cannot be done, because the CFADs shown in Figs. 12 and 13 are derived from monthly mean Q 2p profiles at 0.5° resolution. Still, there is a striking difference. In the CFAD of Q 2 in Johnson and Ciesielski (2000), there is some contribution to negative values of Q 2 in the lowest 2 km from shallow cumulus clouds and sub-cloud-layer eddies during nonprecipitat- ing periods of the TOGA COARE intensive observing period (Johnson and Lin 1997). On the other hand, there is almost no contribution to negative values of Q 20 in the lowest 2 km from shallow cumulus clouds and sub-cloud-layer eddies, although there is some con- tribution to negative values of Q 2p in the lowest 2 km from stratiform rain. Again, the SLH algorithm cannot retrieve moistening for a nonprecipitating region be- cause of the sensitivity of the PR.
7. Summary and future work
In this study, the SLH algorithm was used to estimate Q 2 profiles from PR data together with Q 1 R profiles. There are two differences between Q 1 R and Q 2 . First, the eddy moisture flux convergence is one of the major contributors to the Q 2 while the contribution to the Q 1 R budget by the eddy heat flux convergence is minor. Second, Q 2 in the nonprecipitating region is of the same order as that in the stratiform region whereas the Q 1 R profile in the nonprecipitating region is negligible, which is consistent with the results from Nitta and Es- bensen (1974) that show that moistening rates are about a factor of 3 larger than heating/cooling rates during undisturbed periods in the trades. This is attrib- utable to a larger contribution of eddy fluxes in Q 2 than in Q 1 R . These two factors lead to larger errors in Q 2 than in Q1R- The Q 2 p profiles were reconstructed from CRM- simulated parameters (i.e., convective/stratiform classi- fication, PTH, P s , P m , and P t ) with the COARE table and then were compared with CRM-simulated true Q 2 profiles, which were computed directly from the water vapor equation in the model. COARE, GATE, SCSMEX, and KWAJEX periods were used for the consistency check. The consistency check indicates that discrepancies between the SLH-reconstructed Q 2p and GCE-simulated Q 2 profiles, especially at low levels, are larger than those between the SLH-reconstructed Q 1 RP and GCE-simulated Q 1 R profiles. Larger discrepancies in Q 2p at low levels are due to moistening in the non- precipitating region that SLH cannot reconstruct. The SLH algorithm was applied to PR data, and the results were compared with Q 2 profiles derived diag- nostically from SCSMEX sounding data. Although dis- crepancies between the SLH-retrieved and sounding- based profiles for Q 2 are larger than those for Q 1 R , key features of the vertical profiles agree well. The Q 2 p drying magnitudes are smaller than the sounding-de- rived magnitudes in the upper troposphere, which are attributable to three reasons. First, the Q 2p estimates from PR data are subject to sampling errors that result from the PR's narrow swath width (~215 km). Second, the SLH algorithm is severely limited by the inherent sensitivity of the PR, which can detect only precipita- tion-sized particles. Third, the lookup table for the anvil based on P m does not fully capture the variability in the upper-level drying of the stratiform rain region. The SLH algorithm was also applied to PR data for February 1998 (El Niño) and February 1999 (La Niña). The differences in the SLH-estimated Q 2 p between February 1998 and February 1999 are consistent with those in the SLH-estimated Q 1 R between February 1998 and February 1999. It is shown that the SLH al- gorithm can estimate differences of Q 2 ρ between the western Pacific Ocean and the Atlantic Ocean as well as those of Q 1 ρ that are consistent with budget results (Thompson et al. 1979; see a review by Cotton and Anthes 1989). Although the SLH-estimated heating profile over the South Pacific for February 1998 is very similar to the vertical distribution of heating during the undisturbed BOMEX period in the trade wind belts (Nitta and Es- bensen 1974) and that during episodic trade wind re- gimes over the western Pacific (Johnson and Lin 1997), the SLH-estimated Q 2 p profile with low-level drying over the South Pacific for February 1998 is not similar to the vertical distribution of Q 2 with low-level moist- ening during the undisturbed BOMEX and that during episodic trade wind regimes over the western Pacific. A possible reason is that SLH cannot retrieve moistening for a nonprecipitating region because of the sensitivity of the PR. Measurements from other sensors will have to be integrated to obtain a more accurate estimation of Q 2 profiles. For example, TRMM Visible and Infrared Scanner data provide information on the population of shallow, nonprecipitating cumulus clouds that have im- portant moistening effects, thereby, perhaps, helping in the retrieval of Q 2 profiles. In this study, the two-dimensional version of the GCE model was used. Real clouds and cloud systems are three-dimensional. The availability of exponentially increasing computer capabilities has resulted in three- dimensional CRM simulations for multiday periods with large horizontal domains becoming increasing prevalent. Larger temporal variability in the two-di- mensional simulation than in the three-dimensional simulation was found by Grabowski et al. (1998), Don- ner et al. (1999), and Zeng et al. (2007). Tao et al. (2000) pointed out that the GCE three-dimensional model-simulated Q 2 budget is in better agreement with observations in the lower troposphere than is its two- dimensional counterpart. We are now performing the three-dimensional CRM simulations to compare lookup tables from the two- and three-dimensional CRM simulations. Acknowledgments. This study is supported by the Ja- pan Aerospace Exploration Agency/Earth Observation Research Center (JAXA/EORC) TRMM project. The first author is also supported by funding from JST Cor- poration–Core Research for Evolution Science and Technology (CREST). He thanks Prof. Richard Johnson of the Colorado State University for his com- ments. Yukari N. Takayabu expresses her heartfelt gratitude to the late Prof. Tsuyoshi Nitta for motivating her to develop the latent heating algorithm utilizing TRMM PR data. Author W.-K. Tao is mainly sup- ported by the NASA Headquarters (HQ) Atmospheric Dynamics and Thermodynamics Program and the NASA TRMM. He thanks Dr. R. Kakar at NASA HQ for his support of GCE development over the past de- cade. The authors thank two anonymous reviewers for their constructive comments, which improved the clar- ity of the presentation in this paper. The TRMM prod- ucts in this paper were provided by JAXA. The Grid Analysis and Display System (GrADS) package was utilized for the figures.