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Latent Heating from TRMM Satellite Measurements 

W.-K. Tao\ E.A. Smith\ 

R. Adler\ Z. Haddad^ A. Hou^ T. Iguchi^ R. Kaka/, T. Krishnamurti^ C. Kummerow^ 

S. Lang^, R. Meneghini\ K. Nakamura^ T. Nakazawa^ K. Okamoto^^ W. 01son^\ S. Satoh^ 

S. Shige^^ J. Simpson^ Y. Takayabu^^ G. Tripoli^^ and S. Yang^^ 

^ Laboratory for Atmospheres, N AS A/Goddard Space Flight Center, Greenbelt, MD 20771, USA 

^ NASA/Jet Propulsion Laboratory-California Inst, of Technology, Pasadena, CA 91109, USA 

^ National Institute of Information & Communications Technology, Tokyo 184-8795, JAPAN 

"^NASA/Headquarters, Washington, DC 20546, USA 

Dept of Meteorology, Florida State Univ., Tallahassee, FL 32306, USA 

^ Dept. Of Atmospheric Science, Colorado State Univ., Fort Collins, CO 80523, USA 

Science Systems and Applications Inc., Greenbelt, MD 20706, USA 
[Mail Code 912, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA] 

^ Hydrospheric Atmospheric Research Center, Nagoya Univ., Nagoya 464-8601, JAPAN 

^ Japan Meteorological Agency-Meteorological Research Institute, Tsukuba 305-0052, JAPAN 

^ Dept. of Aerospace Engineering, Osaka Prefecture Univ,, Sakai, Osaka 599-8531, JAPAN 

^^ UMBC/Joint Center for Earth Systems Technology, Baltimore, MD 21250, USA 
[Mail Code 912, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA] 

^^ Center for Climate System Research, Univ, of Tokyo, Tokyo 153-8904, JAPAN 

^^Dept. of Atmospheric & Oceanic Sciences, Univ. of Wisconsin, Madison, WI 53706, USA 

^"^ School of Computational Sciences, George Mason Univ., Fairfax, VA 22030, USA 
[Mail Code 912.1, NASA/Goddard Space Flight Center, Greenbelt, MD 20771, USA] 

Submitted to 
Bulletin of the American Meteorological Society 

November 2004 



Corresponding Author Contact Information: 

Dr. Wei-Kuo Tao 

Mesoscale Atmospheric Processes Branch, Code 912 

NASA/Goddard Space Fhght Center 

Greenbelt, MD 20771 

(301) 614-6269; tao@agnes.gsfc.nasa.gov 



Popular Summary 
Latent Heating from TRMM Satellite Measurements 

W.-K. Tao, E.A. Smith, 

R. Adler, Z. Haddad, A. Hou, T. Iguchi, R. Kakar, T. Krishnamurti, C. Kummerow, 

S. Lang, R. Meneghini, K. Nakamura, T. Nakazawa, K. Okamoto, W. Olson, S. Satoh, 

S. Shige, J. Simpson, Y. Takayabu, G. Tripoli, and S. Yang 

Submitted to Bulletin of the American Meteorological Society 

Rainfall production is the key ingredient of the Earth's hydrological cycle, the main driver 
of atmospheric and surface water and energy budgets, and the primary diabatic heat source 
within the atmosphere via latent heat release. Fundamentally, latent heat release is a 
consequence of phase changes between the vapor, liquid, and solid forms of water, processes 
which occur spatially and temporally heterogeneously over a precipitating storm's lifecycle. The 
temporally averaged horizontal pattern of latent heating is a major determinant of the Earth's 
general circulation, while the vertical distribution directly modulates large-scale meridional and 
zonal circulations, particularly in the tropics. Moreover, the spatial distribution of latent heating 
exerts significant influence on energetic efficiencies of baroclinic mid-latitude weather systems. 

The Tropical Rainfall Measuring Mission (TRMM) is providing the first comprehensive 
global scale climatology of rainfall over the tropics and sub-tropics. These four-dimensional 
data sets are now being used to estimate the associated space-time latent heating structures. Such 
distributions of rainfall and inferred latent heating will ultimately be used to advance an 
understanding of the global water and energy cycle, and aid in improved predictions of weather 
and climate. This study describes a set of retrieval algorithms being used for estimating latent 
heating from TRMM observations and their consequent applications for the aforementioned 
purposes. The nature of these algorithms and some of the main characteristics of their resultant 
heating products are described. The issue of validation of the heating products is also examined. 
The study concludes with an overview of how latent heating estimates are being used in 
conjunction with global weather and climate models, and remarks intended to stimulate further 
research concerning the topic of satellite-based latent heating retrieval. 



11 



Abstract 

Rainfall production is the fundamental variable within the Earth's hydrological cycle 
because it is both the principal forcing term in surface water budgets and its energetics corollary, 
latent heating, is the principal source of atmospheric diabatic heating. Latent heat release itself is 
a consequence of phase changes between the vapor, liquid, and frozen states of water. The 
properties of the vertical distribution of latent heat release modulate large-scale meridional and 
zonal circulations within the tropics — as well as modifying the energetic efficiencies of mid- 
latitude weather systems. This paper focuses on the retrieval of latent heat release from satellite 
measurements generated by the Tropical Rainfall Measuring Mission (TRMM) satellite 
observatory, which was launched in November 1997 as a joint American-Japanese space 
endeavor. Since then, TRMM measurements have been providing an accurate four-dimensional 
account of rainfall over the global tropics and sub-tropics, information which can be used to 
estimate the space-time structure of latent heating across the Earth's low latitudes. 

The paper examines how the observed TRMM distribution of rainfall has advanced an 
understanding of the global water and energy cycle and its consequent relationship to the 
atmospheric general circulation and climate via latent heat release. A set of algorithm 
methodologies that are being used to estimate latent heating based on rain rate retrievals from the 
TRMM observations are described. The characteristics of these algorithms and the latent heating 
products that can be generated from them are also described, along with validation analyses of 
the heating products themselves. Finally, the investigation provides an overview of how 
TRMM-derived latent heating information is currently being used in conjunction with global 
weather and climate models, concluding with remarks intended to stimulate further research on 
latent heating retrieval from satellites. 



1. Introduction 

The global hydrological cycle with its underlying precipitation controls helps determine the 
behavior of the Earth's weather and climate systems and is central to understanding their 
variability. Some two-thirds of global rainfall occurs over the tropics ^ , where it has a profound 
effect on the general circulation of the atmosphere because rainfall's energetic equivalent, latent 
heating, is the tropical convective heat engine's primary fuel source; Riehl and Malkus (1958). 
At low latitudes, latent heating stemming from extended bands of rainfall modulates large-scale 
zonal and meridional circulations and their consequent mass overtumings (e.g., Hartmann et ah 
1984; Hack and Schubert 1990). Latent heating is also the principal energy source in creation of 
long-lived tropical waves, their growth, vertical structure, and propagation (e.g., Puri 1987 and 
Lau and Chan 1988). Moreover, the distinct vertical distribution properties of convective and 
stratiform latent heating profiles help influence climatic outcomes via their tight control on large- 
scale circulations; Lau and Peng (1987), Nakazawa (1988), Sui and Lau (1988), Emanuel et al. 
(1994), Yanai et al. (2000), Sumi and Nakazawa (2002), and Schumacher et al (2003). 

The purpose of this paper is to describe how reliable latent heating profiles are derived 
from satellite rain rate retrievals, particularly those being made by the Tropical Rainfall 
Measuring Mission (TRMM) satellite. As an example, the Cover Figure provides a color 
depiction of averaged patterns of latent heating determined from TRMM measurements and 
mapped at three vertical levels (2, 5, and 8 km) for a 5-year period (1998-2002), along with the 
associated averaged surface rain rate map. [This diagram is discussed in detail in section 3.2.] 

The TRMM satellite is the centerpiece of a joint rainfall mission between the United 
States' and Japanese space agencies, NASA and J AX A (previously NASD A), providing for the 
first time high quality 4-dimensional measurements of rainfall and the associated space-time 
structures of latent heating over the global tropics and sub-tropics. The TRMM observatory was 
launched in November 1997, in a 350-km orbit inclined 35 degrees to the Earth's equatorial 
plane. The primary rain measuring instruments are JAXA's Ku-band Precipitation Radar (PR) 
and NASA's 9-channel TRMM Microwave Imager (TMI). The papers of Okamoto et al. (1988), 
Simpson et al (1988, 1996), Nakamura et al. (1990), Okamoto and Kozu (1993), Kummerow et 
al. (1998), Kozu et al. (2000), Okamoto (2003), and Smith and Holhs (2003) provide details 
concerning the TRMM observatory, orbit, instruments, data, rain retrieval algorithms, and 
validation. 



1 The tropics are generally defined as the area bounded by the 25°N-25°S latitude zone. 



Latent heating estimation from satellite is rooted in literature associated with the first 
spacebome passive microwave (PMW) rain radiometer, viz., the study by Adler and Rodgers 
(1977) concerning total-column latent heating within tropical cyclones. This study was based on 
measurements from the 19 GHz Electrically Scanning Microwave Radiometer (ESMR), an 
instrument flown on NASA's Nimbus-5 satellite (Wilheit et al 1976). Latent heating is the 
portion of diabatic heating released or absorbed within the atmosphere as a result of phase 
changes of water (i.e., gas to Hquid, liquid to solid, gas to solid, and their reverse processes) — all 
requiring exchanges of heat. The coupled terms describing phase changes are condensation- 
evaporation, freezing-melting, and deposition-sublimation. Latent heating is dominated by phase 
changes between water vapor and small liquid or frozen cloud-sized particles. These processes 
are not directly detectable with remote sensing (or for that matter, with in situ measuring), which 
explains why the retrieval schemes to be described depend so heavily on the use of some type of 
cloud ensemble model (CEM), or in modem nomenclature — cloud resolving model (CRM). 

High resolution CRMs are an outgrowth of limited-area mesoscale models that use detailed 
physical parameterizations, particularly for atmosphere / surface radiative transfer, surface 
radiation-heat-moisture-momentum fluxes, boundary layer heat-moisture-momentum turbulent 
transports, and cloud microphysical processes — along with grid resolutions sufficient to simulate 
the dynamical interactions of individual and ensemble clouds with the large-scale environment. 
High resolution precludes the need for CRM integrations to parameterize the dynamical heat and 
mass flux processes associated with clouds and their lifecycles — as required in all current 
global-scale models. The studies of Soong and Tao (1980, 1984) were some of the first to 
experiment with CRMs, designed to understand interactions between clouds and their larger 
scale environment. Notably, early CRMs could credibly reproduce the statistical properties of 
cloud ensembles as first emphasized by Soong and Tao (1980), Lipps and Hemler (1986), Tao 
and Soong (1986), and Tao et al. (1987). At present, modem mesoscale models used in CRM 
mode (or with CRM nests) are being used to simulate phase changes of water and explicit 
conversion of water species in support of latent heating retrieval from satellite measurements, 
notably the Goddard Cumulus Ensemble (GCE) model developed by Tao and Soong (1986), Tao 
and Simpson (1993), and Tao et al (2003a), the University of Wisconsin Nonhydrostatic 
Modeling System (UW-NMS) developed by Tripoli (1992a-b, 2004), and the Penn State-NCAR 
Mesoscale Model 5 (MM5) described by Dudhia (1993). 



Under the Boussinesq approximation, the thermodynamic (or temperature) budget that can 
be explicitly calculated from CRMs: 



Ql-QR=^Hl/p)[dpWd'/dz] - Vr0'}+ (l/Cp)fL,(c-e)^Lf(f-m) + L/d-s)J (1) 

where the primes indicate deviations from the large-scale environment, i.e., due to cloud 

processes at smaller scales. The variable 6 is potential temperature, p is density, 

R/c 
Jt =(p/ Pfyfy) ^ is non-dimensional pressure (where p and p^^ are dimensional and reference 

pressures, respectively, with p^^ taken as 1000 hPa), and Cp and R are the specific heat of dry air 

at constant pressure and the gas constant of dry air, respectively. The variables (Ly, Lf 1$) are 

the latent heats of condensation, freezing, and sublimation, respectively, while the variables (c, e, 

/, m, d, s) identify the rates of: condensation of cloud droplets, evaporation of cloud droplets and 

rain drops, freezing of water droplets and rain drops, melting of ice crystals, snow flakes, graupel 

and hail, deposition of ice crystals, and sublimation of all ice hydrometeors, respectively. Note 

that the term (1/Cp) [I^(c -e)-\- Lf(f -m)+ L/d -s)J is defined as the latent heating (LH) due to 

microphysical phase changes. 

The term Qj is referred to as the apparent heat source, stemming from the diagnostic 

analysis approach described in a seminal paper by Yanai et al (1973), while g/^ is the radiative 
heating rate associated with radiative transfer processes. Note that the first two terms on the 



right-hand side of (1) are the vertical and horizontal eddy heat flux convergences (Jtfdw'd'/dzJ 



and jtt/'V • F'0'7 for an isosteric column), where the horizontal diffusion term is neglected when 
(1) is spatially averaged over an area suitable for diagnostic analysis. 

Figure 1 illustrates instantaneous latent heating structures associated with both a mid- 
latitude and a tropical mesoscaie convective system (MCS) simulated by the GCE-CRM in a 
two-dimensional framework. The cases were drawn from two field campaigns, the mid-latitude 
continental PRE-STORM and tropical oceanic TOGA-COARE experiments. ^ Evident in the 



2(1) PRE-STORM (Preliminary Regional Experiment for STORM-Central) ~ which took place 
in Kansas and Oklahoma during May-Jun'85 (Cunning 1986), and (2) TOGA-COARE (Tropical 
Ocean-Global Atmosphere — Coupled Ocean- Atmosphere Response Experiment) - which took 
place within Pacific Ocean's warm pool from Nov'92 to Feb'93 (Webster and Lukas 1992; 
Nakazawa 1995). 



figure are: (1) condensation heating in lower to middle troposphere at convective leading edge of 
cloud systems; (2) deposition heating in upper parts of convective and stratiform regions; (3) 
cooling at low levels in stratiform regions stemming from evaporation of rain; (4) cooling from 
melting of precipitation particles, mainly occurring in narrow layer near freezing level; and (5) 
cooling from sublimation adjacent to depositional heating in stratiform region. The alternating 
heating and cooling pattern at upper levels is mainly caused by gravity wave dispersion induced 
by deep convection. This mechanism is more significant for the mid-latitude case because its 
associated convective updrafts are generally stronger. 

Not surprisingly, there are also major differences between the two cases. For example, 
cooling within the stratiform regions is larger and deeper for the mid-latitude case in comparison 
to the tropical case. This is due to the generally drier environment at mid-latitudes. In addition, 
the level separating the heating and cooling layers within the stratiform regions (indicating the 
melting level) is different for the two systems. The primary features of squall line structure 
simulated using the GCE-CRM are generally consistent with observed squall lines; see 
Biggerstaff and Houze (1991) and Jorgensen et al (1997). 

Based on a residue approach, the composite diabatic heating profile of Qj can be derived 

indirectly over a spatial domain by measuring profiles of temperature, pressure, and 3- 
dimensional wind vector from a suitably spaced circumscribing network of radiosondes. This is 
called a "diagnostic heat budget", first described by Yanai et al (1973), extensively studied by 
others (e.g., Nitta 1977, Houze 1982, 1989, 1997; Johnson 1984), and expressed by: 

_ dO ^ - ^dd 
Q\=Jt[—^VVd+w—] (2) 

dt dz 



where Qi represents the sum of LH (i.e., fi-om microphysical phase changes), 71 [dw^OW dz] , 
and g/j, while the right-hand side is the total derivative of 6 (times the non-dimensional 
pressure) measurable from radiosonde data. There is an accompanying Q2 equation for the 
apparent moisture sink (or drying), which is similar to eqn (2) except that 6 is replaced by water 
vapor specific humidity {q) and Qi is replaced by -^2* *-^-? ^^e sum of net 



condensation/deposition and vertical eddy moisture flux convergence {(I^ / Cpjfdw' q^ /dz]). 



Clearly, latent heating estimates from satellite-retrieved rain rate profiles could be assessed 
using Qi budgets determined from CRM simulations, or even from regional- to large-scale 

prediction models and/or global climate reanalysis products (e.g., Nigam et al 2000). However, 
since it will be shown that the current latent heating retrieval schemes are all directly or 
indirectly tied to CRMs, the more independent approach in conducting satellite validation is to 
use the radiosonde-based diagnostic heat budget approach discussed above — this 
notwithstanding inherent uncertainties in such budgets due to instrumental and sampling errors in 
sounding data (e.g., Mapes et al. 2003). Therefore, for purpose of this study, Qj budgets 

diagnosed from sounding observations taken during three TRMM field campaigns (SCSMEX, 
TRMM-LBA, and KWAJEX), as well as other past and current field campaigns (GATE, PRE- 
STORM, TOGA-COARE, and DOE- ARM), are used as the principal validation data sets. ^ 

Figure 2 illustrates the evolution of Qu determined diagnostically from TOGA-COARE 
soundings for the period 19-27 December 1992, and accompanied by explicit calculations from 
the GCE-CRM for the same period. The temporal variations of the two sets of heating profiles 
are in reasonably close agreement. This is because the time-varying large-scale advection of 
temperature and moisture superimposed within the GCE model is the main forcing (Soong and 
Tao 1980), and the simulation is driven by observed advective tendencies from the soundings. 
The structures associated with all five major rainfall events are in close agreement, with the 
exception that the diagnostic results are smoother. This is because the diagnosed Qi quantities 
are calculated using 6-hourly soundings, after which a binomial filter is applied to the resuhant 
time series (Lin and Johnson 1996), whereas the GCE-CRM Qi estimates are based on 2-minute 
statistics of cloud processes, with only a 30-minute running average filter applied. 



^ (1) SCSMEX (South China Sea Monsoon Experiment) — which took place in South China Sea 
environs during May-Jun'98 (Lau et al 2000); (2) TRMM-LBA (TRMM Large Scale 
Biosphere-Atmosphere Experiment in Amazonia) — which took place in Rondonia, Brazil 
during Jan-Feb'99 (Halverson et al 2002, Petersen et al 2002); (3) KWAJEX {TRMM 
Kwajalein Experiment) — which took place in vicinity of Kwajalein Atoll, Republic of 
Marshall Islands during Jul-Sep'99 (Yuter et al 2004); (4) GATE (Global Atmospheric 
Research Programme (GARP) - Atlantic Tropical Experiment) ~ which took place in eastern 
tropical Atlantic Ocean during Jun-Sep'74 (GATE-ISMG 1974, Houze and Betts 1981); and 
(5) DOE- ARM (Department of Energy-Atmospheric Radiation Measurement) Program — 
which supports experiments in Oklahoma at DOE-ARM' s Southern Great Plains-Cloud and 
Radiation Test Bed (SGP-CART) site (Stokes and Schwartz 1994). 



Since CRMs such as GCE and UW-NMS can reproduce vertical heating structures with 
good fidehty for a prescribed forcing, it is possible to use simulations such as those in Fig. 2 to 
establish relationships between vertical hydrometeor profiles retrievable from satellite 
measurements and the associated LH profiles. Therefore, as will be shown, CRM simulations 
are now being used to relate remotely-sensed precipitation structures that are retrieved from 
TRMM sensor data to vertical LH profiles that cannot be directly sensed. In essence, by 
simulating various types of clouds and cloud systems for different geographic locations and 
climate regimes, relationships are created which associate cloud/precipitation hydrometeor 
profiles to LH profiles for different remote sensing applications; see Tao et al (1990, 1993b, 
2000, 2001), Smith et al. (1994a-b), Olson et al. (1999, 2004), Yang and Smith (1999a, 2000), 
Shige et al. (2004), and Yang (2004). 

In section 2, a set of five LH algorithms developed for TRMM applications are described 
Highlights from various applications of the algorithms are presented in section 3 with fiirther 
results for selected validation analyses given in section 4. Section 5 is a discussion of how 
TRMM LH products are currently being used in conjunction with global weather and climate 
models. Finally, section 6 offers conclusions including remarks intended to stimulate fiirther 
research. 
2. Descriptions, Physical Bases, and Synthesis of Latent Heating Algorithms 

In this section, five different LH profile algorithms that have been developed for 
application with the various TRMM rain rate retrieval products are examined. These are referred 
to as the Goddard Convective- Stratiform Heating algorithm (CSH), the Goddard Profiling 
Heating algorithm (GPROF Heating), the Hydrometeor Heafing algorithm (HH), the 
Precipitation Radar Heating algorithm (PRH), and the Spectral Latent Heating algorithm (SLH). 
The CSH, GPROF, and SLH algorithms require the complete complement of cloud model data 
generated by a CRM. Table 1 provides a summary of the algorithms including their principal 
authorship, the main algorithm inputs, identification of data sets to which they have been 
applied, and the notional space-time resolutions associated with the algorithms. To aid in 
understanding these algorithms and in the interpretation of their results given in sections 3-5, a 
compilation of their general strengths and weakness are given in Table 2. 

The application of the various algorithms to TRMM precipitation data sets is not 
completely general. For example, as currently implemented the PRH and SLH algorithms 



confine themselves only to PR-generated rain rate retrievals. The PR rain retrieval scheme is 
referred to as TRMM standard algorithm 2a25, a level-2 rain rate profile algorithm in which 
level-2 signifies that it produces results on an instantaneous time-basis and at the full ground 
resolution associated with a given radar beam. [Note that a level-3 algorithm produces monthly- 
averaged rain rates over a 5-degree grid mesh.] The PR rain profile algorithm is coupled to 
another level-2 algorithm that denotes whether a given rain rate profile represents convective or 
stratiform rainfall conditions (TRMM standard algorithm 2a23). [The papers of Iguchi et al. 
(2000) and Meneghini et al (2000) describe the methodology of the level-2 PR algorithms.] 

Alternatively, the GPROF Heating algorithm is strictly configured for applications directly 
to TMI radiance data, as part of the TMI level-2 precipitation algorithm, referred to as the 
TRMM standard algorithm 2al2. The TMI level-2 algorithm produces density profiles of 
precipitating liquid and ice hydrometeors, suspended liquid and ice hydrometeors, latent heating, 
and surface rain rates - as well as an estimate of the convective fraction of rain. Because the 
TMI radiometer swath width is three times that of the PR radar (i.e., wide swath versus narrow 
swath), the spatial duty cycle of the GPROF Heating algorithm is three times that of the PRH and 
SLH algorithms. On the other hand, because the effective ground resolution of the TMI 
retrievals is lower than that of the PR, the GPROF Heating algorithm retrievals lack the 
sharpness and detail of PR-based retrievals. [The papers of Kummerow et al (1996, 2001) and 
Olson et al (1999, 2004) describe the methodology of the level-2 TMI precipitation algorithm.] 

The CSH and HH algorithms are not restricted to applications with any particular TRMM 
rainfall algorithm - with the constraint that the CSH algorithm requires explicit information 
concerning whether a given rain profile is convective or stratiform in nature. Both of these 
algorithms can be applied to rain profiles from the level-2 PR or TMI algorithms, or to rain 
profiles from the level 2 Combined PR-TMI retrieval algorithm referred to as TRMM standard 
algorithm 2b31 (also a narrow swath algorithm because it requires PR data). [The papers of 
Haddad et al (1997) and Smith et al (1997) describe the methodology of the level-2 Combined 
PR-TMI algorithm.] Moreover, the HH algorithm can be used with rain profile products derived 
from any other type of satellite or radar platform. The CSH algorithm requires information on 
surface rain rate, the fractions of convective and stratiform precipitation, and a geographic 
locater/storm type flag (poinfing to pre-calculated LH profiles contained in look-up tables), 



whereas the HH algorithm requires vertical profiles of precipitation mass fluxes (either or both 
liquid and frozen phases), which are directly proportional to rain rates. 
2.7 CSH algorithm 

Diagnostic budget studies (e.g., Houze 1982 and Johnson 1984) and cloud modeling studies 
(see review by Tao 2003) have shown that the characteristic LH vertical profile in the anvil 
region of tropical MCSs is considerably different than the characteristic LH vertical profile in the 
convective region. Generally, for both observed and simulated convective systems, evaporative 
cooling in the lower troposphere below a bow-shape positive heating profile for the remaining 
upper cloud layers (peaking in the upper troposphere), is the dominant feature within a stratiform 
precipitation region (the archetypal, S-shape curve stratiform LH profile), while a combination of 
vertically continuous condensation and deposition heating (peaking in the middle troposphere) is 
the dominant feature for the convective rain stage (forming the archetypal, deep, all-positive, 
bow-shape curve convective LH profile). Based on these findings, the convective-stratiform 
heating (CSH) algorithm was developed - described by Tao et al (1993b), with additional 
references conceming its applications summarized in Table 1 . 

The CSH algorithm is designed for computational efficiency and robustness in that it uses 
pre-calculated information on the physical relationships between rainfall and latent heating, 
cannot generate pathological estimates, and is applicable to input from any level-2 (or level-3) 
TRMM rain profile algorithm. It relies on the principle that under steady-state conditions, 
surface precipitation is equivalent to the vertically integrated net condensation/deposition in the 
atmosphere. The foundations of the algorithm are pre-calculated look-up tables associated with 
convective and stratiform Qj profiles, generated primarily from GCE-CRM simulations that 

have been normalized by surface rain rate. In addition to the model calculations, observations 
drawn from the diagnostic studies of Yanai et al (1973), Houze and Rappaport (1984), Johnson 
(1984), Houze (1989), Chong and Hauser (1990), and Gallus and Johnson (1991) are used to 
enhance the variance properties of the initial Qj profiles in the look-up tables. Normahzed 

convective and strafiform Qj profiles, appropriate for an observed region and cloud type, are 

selected from the look-up tables, scaled by the TRMM-retrieved convective and stratiform rain 
fractions, then combined to yield the total Qj profile. Emphasis has been given to ensuring that 

the vertical structures of the retrieved Qj profiles are physically consistent with those found from 



diagnostic budget studies. Therefore, it can be anticipated that some level of disagreement will 
arise between the CSH algorithm and various other algorithms not so constrained. 

The implementation of CSH described here employs surface convective / stratiform rain 
rates derived from the PR algorithm, applied on time scales ranging from 3 hours to 1 month and 
space scales ranging from 50 to 500 km. A distinguishing feature of the CSH algorithm is that it 
has been used extensively for regions and time periods associated with a number of field 
programs for which diagnostic-based Qj profiles are available for comparison and contrast with 

reconstructed and retrieved profiles. To date, field program data that have been examined in 
conjunction with the CSH algorithm include: (1) GATE, (2) EMEX 4, (3) PRE-STORM, (4) 
TOGA-COARE, (5) SCSMEX, (6) TRMM-LBA, (7) KWAJEX, and (8) DOE-ARM. 

2.2 GPROF Heating algorithm 

The GPROF Heating algorithm is designed specifically for applications with TMI PMW 
radiance observations. A large database of explicitly related hydrometeor and Qj-Qr profiles 

generated by GCE-CRM and MM5-CRM simulations is pre-calculated, along with PMW 
radiances calculated using a radiative transfer model (the combined result is called a cloud- 
radiation data base). Thus, given a set of TMI-measured radiances, the look-up table is scanned 
to identify those profiles exhibiting radiative characteristics consistent with the observations. 
The radiatively consistent profiles are then composited using a Bayesian approach to retrieve a 
best estimate of the hydrometeor and heating profiles. 

Originally developed for applications to SSM/I data, the Bayesian method has been 
adapted for applications to TMI radiance data, and it is effectively integrated with the 
GPROF TMI precipitation retrieval algorithm (see Olson et al 1999, 2004). Versions of 
GPROF have been used by Rodgers et al. (1998, 2000) to diagnose latent heating 
distributions in Hurricane Opal and Supertyphoon Paka, to study the relationships between 
heating and storm intensification. Recently Yang et al (2004) demonstrated that vertical 
profiles of GPROF latent heating were fairly consistent with independent estimates derived 
from Kwajalein dual-Doppler radar data and SCSMEX rawinsonde analyses 

2.3 HH algorithm 



4 EMEX (Equatorial Monsoon Experiment) — which took place in ocean tropics north of 
Australia during Jan-Feb'87 (Webster and Houze 1991). 



Without reference to pre-calculated LH profiles in look-up tables, it is possible to treat each 
layer of the atmosphere independently, estimating the net flux of water mass in or out of the 
layers and assuming under steady-state conditions, that the fluxes are compensated by some local 
decrease (increase) of hydrometeors by microphysical processes. A decrease is thus associated 
with evaporation, melting, or sublimation cooling, whereas an increase is associated with 
condensation, freezing, or deposition heating — and thus the basis for a hydrometeor mass flux 
heating algorithm. The first application of a LH algorithm applied to actual satellite-retrieved 
hydrometeor profiles was a HH scheme — performed by Smith et al (1992) on Pacific 
Supertyphoon Thelma, using Special Sensor Microwave Imager (SSM/I) measurements from a 
Defense Military Satellite Program (DMSP) satellite. Based on a different HH algorithm 
formulated by Tao et al (1990), Tao et al (1993b) used the Thelma hydrometeor retrievals to 
produce an alternate set of LH profiles - found to be generally similar to those from the Smith et 
al (1992) study. The hydrometeor profiles themselves were retrieved from the level-2 rain rate 
profile algorithm of Smith et al (1994a-b, 1998). [This scheme derives cloud microphysical 
profiles for cloud-radiation databases from the Tripoli (1992a) UW-NMS model run in nested- 
CRJVl mode, and can be tailored for use with any type of PMW radiometer and/or radar data.] 

In the Smith et al (1992) HH scheme, LH profiles are calculated from vertical derivatives 
of precipitation mass flux profiles, i.e., separate liquid and frozen hydrometeor mass fluxes with 
appropriate accounting for the various latent heats of phase change above and below the melting 
level. Moreover, the algorithm can include the effect of the mass flux of non-precipitating cloud 
droplets undergoing vertical advection ~ assuming a cloud-scale vertical velocity parameter is 
specified. Noting that all condensation / deposition heating is initiated during formation of non- 
precipitating hydrometeors, Tao et al (1993b) described an alternate means to account for latent 
heating due to suspended but vertically advected hydrometeors, i.e., by using coefficients 
associated with condensation (deposition) of small liquid water droplets (ice particles). 

Further development of the HH algorithm, its verification, and global applicafions are 
found in the studies of Yang and Smith (1999a-b, 2000). These studies accounted for cloud- 
scale vertical velocity using a multiple-linear regression equation based on hydrometeor profile 
densifies as the independent variables of regression. For applications with retrievals from 
TRMM level-2 algorithms, the current scheme uses truncated Legendre polynomial 
representations of precipitation mass fluxes from surface to precipitation top height (PTH) before 



in 



taking vertical derivatives, thus preventing retrieval noise from producing unrealistically large 
positive / negative heating rates. For applications with the PR or Combined algorithms, no 
accounting is made for latent heating by deposition-sublimation and freezing-melting processes 
above and below the melting level since the sensitivity of the TRMM PR is only 17 dBZ ~ 
insufficient for detection of every class of frozen precipitation, particularly smaller and/or less 
dense graupel particles. For applications with the TMI algorithm, terminal (fall) velocities of 
precipitating hydrometeors (both rain and graupel) are calculated assuming that the mass spectra 
of both types of hydrometeor are distributed according to a Marshall-Palmer size distribution 
function. 
2 J PRH algorithm 

The PRH algorithm, as described by Satoh and Noda (2001), uses PR-based retrievals 
(precipitation profile and convective/stratiform rain fractions) to estimate the vertical LH 
structure. First, an initial-guess vertical velocity profile is estimated based upon the vertical 
precipitation structure and convective/stratiform classification. The vertical velocities are used 
to evaluate a hydrometeor conservation equation under steady state conditions. In stratiform 
regions, the LH profile is derived directly from the hydrometeor conservation equation (similar 
to HH algorithm implementation). In convective regions, if a net increase of hydrometeors due 
to microphysics is inferred from the conservation equation, then the associated LH profile is 
calculated based upon the vertical motion profile, assuming saturated adiabatic ascent. An 
iterative method is used to adjust the original vertical motion profile to ensure that vertically 
integrated net heating and surface rain rates are consistent. 
2.5 SLH algorithm 

Spectral representation of precipitation profiles obtained from the PR algorithm by use of a 
small set of distinct profile properties, as reported by Takayabu (2002), provide the basis for the 
spectral latent heating algorithm (SLH) — introduced by Shige et al. (2004). This algorithm is 
currently intended for only PR-retrieved rain rate profiles. Akin to the CSH algorithm, a set of 
three look-up tables is produced using the GCE model associated with three types of rainfall: (1) 
convective, (2) shallow-stratiform, and (3) deep anvil stratus. Specifically, however, the look- 
up tables are indexed according to the vertical information of rain profiles: PTH for convective 
and shallow stratiform rain, and melting-level rain intensity for anvil (or deep stratiform) rain. 



11 



The naming ^spectral' comes from this spectrally indexed table, and it is designed so in order to 
reduce the dependency of tables on the GCE-CRM simulations of specific field campaigns. 

For the first two categories, convective and shallow stratiform, the look-up tables are 
indexed according to the PTH. For the third category, anvil stratiform rain, the indexing 
parameter for the associated look-up table is rain rate at the melting level. It is because that PR 
can measure the perspiration at the melting level as can a ground-based radar (e.g., Leary and 
Houze 1979), although it cannot observe the PTH accurately enough at the upper-levels of the 
anvils where small ice-phase hydorometors dominate. Needed inputs for the algorithm are 
convective/shallow-stratiform/anvil stratus rain index, surface rain rate (Ps), and either PTH or 
rain rate at the melting level (Pm). The advantage of this scheme is that fiindamental heating 
differences between shallow and deep stratiform rain stages emerge in the diagnosed LH profiles 
~ stemming from using distinct information concerning the precipitation descriptor (PTH or 
Pm). Another advantage is that LH profiles arising during the anvil decay stage with no surface 
rain can be diagnosed, because the normalizing parameter for the tabulated LH profiles (i.e., a 
denominator) is Pm - Ps — which does not go to zero if Ps goes to zero. 
2.6 Algorithm synthesis 

The CSH, GPROF Heating, and SLH algorithms could be used to estimate Q] and Qr 
along with LH as described in eqn (1), because they use the complete complement of cloud 
model data generated by CRMs, which includes explicit calculations of the total apparent heat 
source (Qj) and its components involving heating due to phase changes of water species (LH), 



vertical eddy heat flux convergence JtfdwV/dzJ ^ and radiative heat exchange (Qr)^ The 
estimation of Qr using these methods introduces new challenges, however, since infrared data (in 
addition to radar or PMW radiometer data) would be required to infer radiative fluxes from non- 
precipitating clouds or clear regions. The HH and PRH algorithms estimate only the LH term 
because they are not explicitly connected to CRM-generated databases, but instead on vertical 
precipitation mass fluxes either diagnosed from retrieved hydrometeor density profiles (such as 
those from the TMI algorithm) or calculated directly from retrieved precipitation rates (such as 
those from the PR or Combined algorithms). Unlike the table look-up approaches, the HH and 
PRH algorithms calculate LH characteristics directly from vertical gradient structures within 
precipitation mass flux profiles ~ regardless of their source. 



17 



A preliminary comparison between earlier versions of three of the algorithms (CSH, 
GPROF Heating, and HH) was performed for February-1998 TRMM data by Tao et al (2001). 
The results of the study indicated that the horizontal distributions of latent heat release retrieved 
by the three schemes were similar and closely related to surface rainfall. They all were able to 
identify areas of major convective activity, including well-defined sectors of the Intertropical 
Convergence Zone (ITCZ) within the central and east Pacific, and along the Southern Pacific 
Convergence Zone (SPCZ). The major differences between the algorithms pertained to the 
altitude (level) of maximum heating. The CSH estimates exhibited one level of maximum 
heating with the level varying between different geographic locations ~ features in general 
agreement with diagnostic budget studies. A broader heating maximum, often with two 
embedded peaks, was generally obtained with the GPROF and HH algorithms, and the 
sensitivity of the estimated heating profiles to variations in convective activity were less 
pronounced. 

Since all five of the algorithms are still undergoing development and improvement, and 
since comprehensive intercomparisons of the current versions of the algorithms with independent 
diagnostic estimates are still to be performed, it is only possible to assign general strengths and 
weaknesses - and then in mostly relative teniis. In this vein, the effects of the different sets of 
simplifying assumptions on the various algorithms' LH properties needs careful study. For 
example, the HH and PRH algorithms are similarly constrained by hydrometeor conservation 
under a steady-state assumption but under different formulations for LH generation. The other 
three algorithms are all directly CRM-based, but differ insofar as the cloud type classification 
schemes, the look-up table indexing strategies, and the detailed properties of the pre-calculated 
look-up table heating profile entries. 

Therefore, the relative accuracy of the methods depends on how representative the 
tabulated CRM-based profile information and/or dynamical-microphysical simplifying 
assumptions are for a given situation. Modeling studies based upon CRMs suggest that the 
instantaneous relationships between hydrometeor profiles and heating profiles at a scale of -10 
km are somewhat ambiguous, and so extraction of specific heating information from a full 
resolution retrieved hydrometeor profile is problematic. Thus, the use of tabulated heating 
profiles representing averaged vertical structures for a set of sensor observations, is justified. It 
is also justified to take space-time averages of instantaneous/footprint-scale estimates over a 



1^ 



specified domain to obtain meaningful estimates, since averaging reduces random error effects. 
For example, Shige et al (2004) found that spatial averaging of instantaneous/footprint-scale 
SLH heating estimates over an area of ~50 x 50 km was required to reduce random errors in 
SLH- reconstructed profiles to acceptable levels. 

On the other hand, all algorithms that utilize look-up tables are subject to systematic errors 
arising from both model deficiencies, and the improper assignment of the tabulated structures to 
a given set of sensor observations, cloud system type, and climate regime. In some cases, the 
sensor observations may not provide sufficient information for the algorithm to return 
unambiguous estimates of heating. For example, artifacts in GPROF Heating estimates arise 
from the relatively low spatial resolution and thus restricted information content of the TMFs 
PMW observations (Olson et al 2004). Since TMI observations contain less information 
regarding both vertical and horizontal hydrometeor structures than PR observations, the GPROF 
Heating algorithm must rely to a greater extent on its CRM database to physically constrain 
heating profile estimates, resulting at times in systematic errors. [Note, the main practical 
advantage of the GPROF algorithm and the CSH and HH algorithms when applied to TMI 
observations, is that the TMI instrument produces three times the duty cycle of the PR 
instrument.] 

Perhaps the most important source of systematic error arising from current look-up table- 
based algorithms is that the set of tabulated heating structures do not completely represent the 
full spectrum of real-atmosphere structures. Since the tabulated structures for the CSH, GPROF 
Heating, and SLH algorithms are derived from CRM simulations, and since the associated CRM 
simulations have been performed for only a limited range of environmental conditions and 
storm-precipitation cases, it is fair to say that no look-up table has yet been created which is fully 
populated and robust. However, this limitation is expected to be mitigated as greater emphasis is 
brought to bear on the problem and improved computer technology is used. Ultimately, this will 
lead to a greater number of CRM simulations, at higher spatial resolutions and increased domain 
sizes, and with greater consideration given to synthesizing the resultant information content. 
3. Diabatic Heating Structures Estimated from Individual Algorithms 

Application of the TRMM latent heating algorithms is being conducted over a range of 
space and time scales, from order 10 to 500 km spatially, and from instantaneous to monthly 
temporally. Whereas there is no preferred scale for calculating latent heating, but a variety of 



Id 



applications for the use of latent heating products, research is ongoing to determine the optimal 
minimal scales at which the latent heating retrievals can be considered rehable. 
3.1 Instantaneous latent heating structure 

Several of the TRMM latent heating algorithms have been designed to determine 
instantaneous rain rates and heating profiles at satellite footprint resolution, even though the 
eventual space-time resolutions may be intended to be evaluated at larger scales ~ typically from 
0.25 to 5 degrees spatially and from a few hours to monthly temporally. The rationale for 
operating the algorithms at the highest possible resolutions is that the systematic error in the 
average of high-resolution estimates of heating is generally less than the systematic error of a 
single heating estimate made at the scale of the average. Therefore, even though instantaneous, 
footprint-scale estimates may contain undesirable errors and/or noise, spatial averaging and/or 
filtering can reduce the random effects to acceptable levels, while ensuring that the smoothed 
products contain a minimum of systematic error. [Note that frequent temporal sampling is 
needed whenever a problem involves diurnal variability, which for rainfall processes can be high 
amplitude over both oceans and continents; see Yang and Smith (2004).] 

The major objections to estimating instantaneous latent heating rates at high spatial 
resolution (say the -4 km PR nadir beam resolution) is that such estimates either require an 
assumption of steady-state microphysical conditions (as in HH or SLH), or they will contain 
significant random errors that must be suppressed by averaging (as in GPROF). The debate on 
this issue also involves the fact that although microphysical phase changes take place virtually 
instantaneously and thus embrace the notion that latent heating is an immediate process, the 
source of latent heating occurs at the microphysical cloud drop/ice crystal nucleation scale. It 
may be argued that the precipitation distributions that are observed by a spacebome radars or 
radiometers are the end product of vertical air motions [strongly linked to latent heating; see 
Mapes and Houze (1995)] occurring just prior to the observations. Therefore, since the actual 
latent heating process is not directly detectable by radars or radiometers, it is a certainty that a 
given algorithm will produce errors in instantaneous estimates since the detection methodology 
is at least one step removed from the physics of the problem — regardless of how such errors are 
mitigated by spatial averaging and/or filtering. 

Figure 3 illustrates instantaneous and high resolution (-4 km) rain rates and LH structures 
is an intense Atlantic tropical cyclone (Hurricane Bonnie) retrieved by the HH algorithm, based 



1^ 



on the vertical derivative of rain mass flux from the Combined TMI-PR rain retrieval algorithm. 
To suppress spurious noise before taking vertical derivatives, the rain rate profiles used for the 
calculations are vertically filtered by truncating higher order terms from Legendre polynomial 
representations of the rain profiles. The structure of the hurricane eye and the convective rain 
spiral bands are well captured. Rain water appears at high altitudes in the presence of deep 
convection, such as around 200 km along the track seen in the middle panel of Fig. 3. 
Widespread weaker rain rates are located between the convective cells. In the weak rain areas, 
rain rates are mostly concentrated in the middle to lower troposphere where stratiform conditions 
are prevalent. Deep latent heating is always associated with the strongest convective cells (lower 
panel of Fig. 3). Peaks of maximum latent heating vary with different conditions. For example, 
one peak is located at 3-5 km at 180 km along the track, while another is at 3-4 km at 200 km 
along the track. The altitudes of the LH maxima are generally at or below 5 km. Evaporative 
cooling occurs in the lower troposphere in these stratiform regions. 

Overall, the general structure of latent heating based on the HH algorithm is heuristically 
correct for a hurricane, although it is important to recognize that the level of maximum heating is 
lower than found from other studies of tropical cyclones. As noted in section 2.3, this is because 
the current version of the Combined PR/TMI algorithm (as well as the PR algorithm) does not 
produce precipitation by any but the largest frozen hydrometeors. By including the effect of all 
precipitating snow and graupel (that is the non-sensed mass), the level of maximum heating 
would be elevated. However, because the HH algorithm cannot account for what is not 
bestowed by the PR insofar as hydrometeor profile completeness, its application with the current 
versions of the Combined and PR algorithms camiot produce realism in upper-level heating rates. 
[Note that the next version of the Combined algorithm will include a CRM-based frozen 
precipitation mode to enable a synthetic (model) account of deposition-sublimation and freezing- 
melting processes above and below the melting level, ensuring that the HH algorithm will 
eventually produce complete LH profiles with PR-based precipitation information.] 

Presented in Figure 4 are estimates of instantaneous surface rain rate, convective rain rate, 
and vertical cross-sections (spatially averaged to 28 km) of total rainwater content and Qi-Qr 
from an application of the GPROF Heating algorithm. These quantities are derived from TMI 
observations of a squall line in the tropical North Atlantic Ocean. Heaviest rains are seen along 
the convective leading edge of the system, while generally lower rain intensities are observed in 



1^ 



the trailing stratiform areas to the north and west of the leading edge. The transect A-B (Fig. 4- 
panel c) is nearly perpendicular to the leading edge, traversing both the convective and stratiform 
regions. The leading edge convection is characterized by relatively high rain water contents, 
exceeding 1 g m'^ near the surface. Horizontally collocated with the maximum rain water 
contents are the maximum estimated heating rates, exceeding 9*^0 h'* between 5 and 8 km 
altitude. Stratiform rains (horizontal coordinates less than 120 km) are associated with maximum 
water contents at midlevels; the decrease of water contents in the lower troposphere is due to 
evaporation of rain, and cooling rates - -l^C h"^ are estimated in this region. The overall heating 
structures are similar to those in Fig. 1, except that the fine features simulated by the GCE-CRM 
are not observed due to the coarser resolution of the GPROF Heating algorithm's TMI radiance 
input. 

Figure 5a shows instantaneous LH profiles retrieved by both the PRH and SLH algorithms, 
spatially averaged to 50 km resolution, associated with: (1) a Pacific tropical cyclone (Typhoon 
Jelawat) in its developing stage (upper diagram), and (2) a mesoscale convective system over the 
tropical ocean northwest of Australia (lower diagram). The PR-estimated rain rates that are used 
as input for these two LH algorithms are also shown. Overall, for the tropical cyclone case, there 
are many similarities between the PRH and SLH profiles. For example, both indicate strong 
heating on both sides of the eye. In addition, for both algorithms, strong heating is found in a 
very narrow shaft in the lower troposphere to the right of the eye. Away from the eye/eyewall 
region, the heating patterns are similar to those observed and simulated by CRMs in the 
stratiform region of mesoscale convective systems (Houze 1982, 1997; Tao et al 1993b, 2000; 
Lang et al 2003). On the other hand, there are major differences between the two sets of heating 
profiles. First of all, PRH heating is confined to the same altitude range with the rainfall profiles, 
while SLH algorithm retrieve the rainfall well over the rain. This difference is reflected to the 
larger amplitude at the higher altitudes in horizontal mean profiles in Figure 5 a. Secondly, the 
SLH level of maximum heating is lower than for PRH (examine the upper and lower right-hand 
panels of the upper diagram). The cooling region retrieved by the PRH algorithm in the lower 
troposphere is stronger than that of the SLH algorithm. PRH also produces low-level cooling in 
its convective region — which is likely spurious. The SLH heating structure has smoother 
features than PRH because SLH uses a table look-up scheme based on averaged CRM-generated 
profiles. The general structures of the SLH-generated Qi-Qr and LH profiles are similar except 



17 



that the Q]-Qr profile exhibits a heating maximum of greater intensity and at a higher aUitude 
(upper-right-hand panel of upper diagram). 

The SLH and PRH latent heating analyses associated with an offshore Australian 
mesoscale convective system are illustrated in the lower diagram of Fig. 5a. Again, the PR- 
estimated rain rates that are used as algorithm input are shown in the diagram. Strong heating 

(>10'*C h"^) is always associated with large rain rates (> 50 mm h"0 in the convective region of 
the squall system. There is weak heating aloft and cooling below in the trailing stratiform 
region. Both averaged Qi^Qr and LH profiles peak at middle levels (about 6 km according to 
the upper-right-hand panel of the lower diagram). For this case, the SLH-retrieved level of 
maximum heating is higher than that of the tropical cyclone case. This is because the convective 
system is in its mature stage while the tropical cyclone system is in its developing stage. As is 
evident in the upper-right-hand panel, both the averaged Qj^Qr and LH profiles peak at middle 
levels (-6 km). This is in good agreement with the heating maximum found in the mid- 
troposphere for the Australian Monsoon Experiment (AMEX) convective systems reported by 
Frank and McBride (1989). The estimated LH profile has a distinct cooling extreme near 4 km 
due to melting processes. On the other hand, the estimated Q]-Qr profile does not indicate any 
cooling near 4 km because the eddy heat flux convergence compensates for the cooling due to 
melting. As with the tropical cyclone case, PRH yields stronger cooling in the lower troposphere 
while SLH heating exhibits smoother features. 

Figure 5b goes on to show the instantaneous/50 km resolution LH structure of a mid- 
latitude squall line retrieved using only the PRH algorithm. The PR-observed radar reflectivities 
and estimated rain rates used as algorithm inputs are also shown. The radar reflectivity pattern is 
similar to that of an observed PRE-STORM squall line (Rutledge et al 1988). Strong heating 
(>10*'C h'^) is always associated with large rain rates (> 50 mm h'*) at the leading edge of the 
squall system. There is weak heating aloft and cooling below in the trailing stratiform region. 
These features are similar to those simulated by CRMs (e.g., Fig. lb firom Lang et al 2003), to 
observafions (e.g., Johnson and Hamilton 1988), and to GPROF retrievals (Fig. 4 cross-section). 
The LH profile shown in the right-hand panel is also similar to both CRM and observational 
results. 

As Figures 3, 4, and 5a-b illustrate, regardless of the differences in spatial resolution, the 
instantaneous LH profiles retrieved by the four different heating algorithms qualitatively agree 



1» 



with one another for insofar as tropical cyclones (HH, PRH, and SLH), oceanic squall lines 
(GPROF Heating and PRH), and a tropical oceanic MCS (PRH and SLH). Quantitatively, 
however, there are differences. Some are caused by the different resolutions and filtering 
techniques employed by the different algorithms, and some by the different algorithm inputs. 
Foremost are the differing physical assumptions of the algorithms themselves. As a typical 
example drawn from the above analysis, PRH consistently produces LH profiles with stronger 
cooling in the lower troposphere. Therefore, a comprehensive algorithm intercomparison using 
common data sets has been planned for the near future to understand and perhaps mitigate as 
many of these differences as possible (further discussed in section 5). 
3,2 Temporal and spatial averages 

The upper three panels of the Cover Figure illustrate 5-year mean apparent heating at three 
different altitudes (2, 5, and 8 km) over the global tropics from the CSH algorithm using the PR- 
based level-3 rainfall product. The Q] profiles are calculated by averaging two normalized 
convective and stratiform kemel heating profiles (scaled according to PR-retrieved surface rain 
rates and weighted by the convective / stratiform fractions) at a grid scale of 2.5 degrees, for 
either oceanic or continental conditions. The normalized convective / stratiform kemel profiles 
are created by averaging all 16 (4) oceanic (continental) base profiles in the CSH algorithm's 
complete library of 20 heating profile pairs distributed regionally and according to storm type. 

As expected from the design of the CSH algorithm, the horizontal distribufion of the 
estimated Q] structure is similar to the pattern of surface rainfall (lower panel of the Cover Fig.), 
especially at middle and upper levels. For example, a well defined ITCZ in the east and central 
Pacific Ocean and Atlantic Ocean, a well-defined SPCZ in the central-southem Pacific Ocean, 
and broad areas of precipitation events spread over the continental regions are all evident. Also, 
strong latent heat release in the middle and upper troposphere (5^C day"^ and greater) is always 
associated with heavier surface precipitation. Heating in the upper troposphere over the Pacific 
and Indian Oceans covers a much broader area than the heating over Africa, South America, and 
the Atlantic Ocean. Notably, the clearly evident differential heating distribution between land 
and ocean in the upper troposphere is capable of generating strong horizontal gradients in the 
thermodynamic fields that can then interact with the global circulation. 

An interesting feature seen in the Cover Fig. is the relatively weak heating-cooling 
behavior (-1 to 1^*0 day"*) at 2-km over the Pacific and Indian Oceans. This may be due to the 



IQ 



moisture content over the Pacific being generally high and concomitant cooling by evaporation 
of rain drops in the lower troposphere being weak over moister areas. Another explanation is 
that convective heating and stratiform cooling in the lower troposphere compensate one another. 

Figure 6 shows the 5-year vertical average Qj profiles for spring, summer, autumn, and 
winter over the entire global tropics — plus the continents and oceans separately. Globally, the 
summer and autumn seasons show stronger heating associated with heavier rainfall. Over land, 
the summer season exhibits the strongest heating. Heating pattems during the spring and autumn 
seasons are similar. Significant cooling in the lower troposphere occurs over the continents but 
not over the oceans. The level of maximum heating and its magnitude over the oceans separately 
are very similar to the global average because 70% of the Tropics is covered by ocean. 

Figure 7 illustrates the Qi structures associated with two climate events, an El Nino 
episode from December 1997 through February 1998 and a La Nina episode from December 
1998 through February 1999. The diagrams in the two left-hand panels show retrieved heating 
anomalies for the two events (relative to a 3-year mean commencing Dec '97), with the greatest 
anomalies occurring over the equatorial Pacific, west Pacific, and Indian Oceans. The Qi 
pattems over the maritime continent, North America, and Africa are similar. Monthly time 
series of Qi profiles over the tropics and their deviations from the 3-year mean are shown in the 
right-hand panel of Fig. 7. The level of maximum heating is approximately 7.5 km. The 
variations of the level of maximum heating and its magnitude are small. This is because global 
tropical rainfall accumulations for El Nino and La Nina are virtually identical as observed by the 
PR. However, there are cold and warm anomalies during the El Nino and La Nina periods. 
These features are due to the fact that the PR observes a higher percentage of stratiform 
precipitation during the El Nino episode, which leads to stronger retrieved low-level cooling as 
compared to La Nina. 
4. Validation of Algorithms 

Validation of LH profiles retrieved from satellite is not straightforward because there is no 
instrument (i.e., no '"latent-heatometer'') or direct means to measure this quantity, and as a result, 
there is no primary calibration standard by which the validation process can be adjudicated. This 
is mainly because diagnostic heat budget analysis is not an exact science (Mapes et al. 2003). 
Thus, just as satellite rainfall retrieval must rely on indirect strategies to achieve validation 
(Smith and HoUis 2003), latent heating retrieval must also rely on indirect approaches. 



70 



4A Comparing CRM heating with algorithm-reconstructed & diagnostically-estimated heating 

Consistency checking involving CRM-generated heating profiles and both algorithm- 
reconstructed and diagnostically-estimated heating profiles is a useful step in evaluating the 
performance of a given latent heating algorithm. In this process, the CRM simulation of a time- 
dependent precipitation process (multiple-day time series) is used to obtain the required input 
parameters for a given latent heating algorithm. The algorithm is then used to "reconstruct" the 
heating profiles that the CRM simulation originally produced, and finally both these sets of 
conformal estimates (model and algorithm) are compared against coincident estimates of 
diagnostically-based heating derived from rawinsonde observations. Such observations from 
various field experiments, as well as simulations of individual precipitation systems, have been 
used for such consistency checks (Tao et al 1993b, 2000; Olson et al 1999, 2004; Shige et al 
2004). 

In the following two examples, diagnostic results from the TOGA-COARE Intensive Flux 
Array (IFA) for 19-27 December 1992 (refer to Fig. 2) are used for consistency checking with 
both the CSH and SLH algorithms. In the first example. Figure 8 illustrates the evolution of Qi 
heating reconstructed by the CSH algorithm from GCE-CRM simulation data, averaged over the 
TOGA-COARE IFA. The algorithm-reconstructed profiles are in close agreement to those 
determined diagnostically from soundings, as well as to those from the original GCE-CRM 
simulation. This is evident by comparing the Fig. 8 with the Fig. 2 results and noting that the 30- 
minute filtering first applied to the GCE-CRM time series is also applied to the reconstructed 
time series. [Heating profiles selected in the CSH algorithm's look-up table are GCE-CRM time- 
averaged (6-hour) heating profiles from 19-27 December 1992.] As noted, the heating profiles 
based on the GCE-CRM should be in close agreement with those from the diagnostic 
calculations, because the GCE model is driven by large-scale advective forcing in temperature 
and water vapor, and therefore the model's simulated rainfall is just the response to that forcing. 
However, using simulation output from the GCE-CRM as a means to parameterize the CSH 
heating algorithm does not necessarily guarantee accurate Qi retrievals. For example, errors in 
surface rain rates as determined from the accompanying rain algorithm can lead to errors in 
retrieving heating magnitudes along the vertical profile, while errors in convective/stratiform 
rainfall fractions via classification can lead to errors in retrieving the levels of maximum heating. 



7A 



In the second example, Figure 9 shows analogous information for both the CSH and SLH 
algorithms, except in terms of latent heating, and in direct comparison to the equivalent quantity 
from a GCE-CRM simulation. Whereas Q} and Qr can be similar order terms over regional 
domains for extended space and time periods (e.g.. Smith 1986, and Smith and Shi 1995), for 
mesoscale convection and precipitation processes, the difference between column-integrated Qj 
and LH is small. This is because LH, which generally ranges from 10-50''C day*^ dominates 



over Qr (which is typically a cooling process of some 0.5-2.0''C day"^) and over JtfdwWdzJ 
(which can be negligible during certain types of active convective events such as those found by 
Soong and Tao 1980 and Johnson et al. 2002). [These scale relationships are illustrated in 
Figure 10 based on the GATE cloud modeling analysis of Tao and Soong (1986).] 

It is evident in Fig. 9 that the temporal variations of both the CSH- and SLH-reconstructed 
profiles are generally similar to variations in the GCE-CRM-simulated profiles. In particular, 
both the CSH- and SLH-reconstructed profiles capture the evolution of a quasi-2-day oscillation 
which occurred during the period 1800 UTC 23 - 1800 UTC 25 December 1992, an oscillation 
that had been noted earlier by Takayabu et al (1996). As pointed out by Shige et al. (2004), there 
are noteworthy improvements in the SLH-reconstructed profiles for the shallow-convective stage 
from 1800 UTC 23 to 0600 UTC 24 December 1992 and the anvil decay stage from 0600 UTC 
to 1800 UTC 25 December 1992. Shallow convection can be retrieved by the SLH algorithm, 
because it uses observed information on precipitation depth (i.e. PTH). Heating profiles in the 
decaying stage with no surface rain (e.g., 1200 UTC 25 December) can also be retrieved by the 
SLH algorithm. This comes from utilizing the precipitation rate at the melting level for anvil 
rain. Also, both the CSH- and SLH-reconstructed results are smoother than the GCE-CRM 
calculations because the associated lookup tables contain averaged profiles for each height index. 
4.2 Explicit comparison of satellite retrievals with diagnostic calculations 

Several TRMM field campaigns, specifically SCSMEX, TRMM-LBA, and KWAJEX, 
were conducted between May 1998 and September 1999, focusing on validation of TRMM 
rainfall products (i.e., vertical hydrometeor and rain rate profiles, and vertical distribution of 
latent heating). Since LH profiles cannot be directly measured, CRMs are needed in designing 
LH algorithms to provide the link between rain rate structures and LH structures. Consequently, 
one of the key objectives behind the TRMM field campaigns was to obtain observations of the 
thermodynamical, dynamical, and microphysical structure and evolution of MCSs, as well as 



ri 



individual convective clouds and the large-scale environments in v^hich they were embedded. 
CRMs require such observations for initial conditions, as well as for validation of model- 
diagnosed latent heating. 

Figure 1 1 draws attention to why a variety of field campaigns are so important in the 
development and validation of LH algorithms. The four pairs of diagrams in the figure illustrate 
fundamental differences in the characteristic organization of precipitating convective systems as 
observed and simulated in the three aforementioned TRMM field campaigns, as well as in a 
DOE- ARM field campaign conducted in June 1997. The instantaneous model realizations of 
precipitation conditions for the four different cases emphasize the underlying variants within the 
general organizational structure of convective storms. 

Regarding the two westem Pacific cases in Fig. 11, the SCSMEX simulation exhibits an 
intense tropical squall line structure without significant stratiform cover, whereas the KWAJEX 
simulation exhibits a more random distribution of convective cells with extensive stratiform 
debris. For both of these tropical ocean cases, which describe the respective dominant modes of 
rainfall behavior associated with the two study regions, most of the surface precipitation 
originates as graupel. For the North American mid-west continental DOE-ARM case, the storm 
also develops as a squall line. However, it is considerably weaker than the SCSMEX case, but at 
the same time exhibits more instability and precipitation downstream of the propagating 
convective line. For the two TRMM-LBA cases, consisting of both easterly and westerly regime 
MCSs, the westward propagating storm is long-lived, well-organized, juxtaposed with a massive 
gravity outflow boundary, and exhibits microphysical properties of a maritime MCS. 
Conversely, the westerly regime case appears as a shorter-lived, fractured, smaller, more linear 
precipitation structure, displaying weaker convection without any well-defined outflow 
boundary, and exhibits the microphysical properties of a continental storm with high cloud bases 
(i.e., a deeper boundary layer). [The studies of Halverson et al. (2002) and Petersen et al. (2002) 
have investigated, in detail, the contrasting meteorological properties of central Amazon's 
easterly and westerly storm regimes.] 

In considering the detailed LH properties associated with various observation periods of the 
TRMM field campaigns. Figures 12a-b illustrate the variability of rainfall (Fig. 12a) and 
apparent heating (Fig. 12b) within the KWAJEX study area during the course of three separate 
time sequences from the campaign's intensive observational period (lOP). In Fig. 12a, rainfall 



JA 



observations are obtained from both the Kwajalein dual-polarization Doppler radar (KPOL), and 
the standard TRMM PR-only algorithm. In Fig. 12b, the 5-day, 3-day, and 15-day sequences are 
periods during which the meteorological sounding data were of sufficient quality to make 
calculations of the Q] budget, while at the same time specifying initial conditions for 
integrations of the GCE-CRM, i.e., calculations to be compared to the sounding budgets. 

The salient features seen in the various diagrams of Figs. 12a-b are: (1) the KPOL and PR 
radars' rain rate estimates are fairly consistent, considering their different viewing perspectives 
and measuring frequencies, (2) the differences between the 2D and 3D GCE-CRM simulated rain 
rates are largely negligible, denoting that latent heating rates reported in earlier 2-dimensional 
CRM literature, before 3 -dimensional modeling became computationally practical, are likely 
representative, (3) the GCE-CRM hourly rain rates are in close correspondence with the KPOL 
radar's hourly rain rates, denoting that the modeled, vertically-integrated apparent heating rates 
are also likely to be sound, (4) the diagnostically-derived and GCE-CRM Q] calculations are in 
excellent quantitative agreement, as perhaps could be anticipated given the prior result, 
particularly for the three ITCZ excitation periods (monsoon flow regimes) occurring on August 
1 1, August 19, and September 2 ~ but also for moderate and weak convective systems, (5) the 
agreement between diagnosed and modeled apparent heating rates vary from poor to good during 
periods of negative Qj heating, i.e., when radiative cooling processes dominate for suppressed 
convection conditions (subsiding troposphere) or for cloud-top radiative cooling in the presence 
of weak convection when upper cloud latent heating rates are small, reinforcing the view of 
many that accurately simulating radiative transfer in partly cloudy tropical atmospheres remains 
elusive, and finally (6) at the scale of the KPOL radar observing domain, latent heating is a 
stochastic process, with individual layer LH rates modulating from approximately -7 to 70°C 
day" . These KWAJEX results draw attention to how important accurate rain retrieval is to 
satellite-based latent heating estimation, plus they provide motivation for employing high spatial 
resolution in the retrieval process to account for the intrinsic spatial heterogeneity of the heating 
field. 

Switching the focus to the SCSMEX field campaign and actual explicit validation of 
TRMM algorithm heating retrievals based on diagnostic calculations, Figure 13 shows a 
comparison between CSH and GPROF Heating algorithm-retrieved heating, sounding-based 
(diagnostic) heating, and GCE-CRM-based heating during SCSMEX's most convectively active 



7A 



period (May 15 - June 20 1998). The study area for this comparison takes place over 
SCSMEX's Northern Enhanced Sounding Area (NESA), a -6 x 10 deg latitude-longitude box in 
the northern oceanic region of the South China Sea. As emphasized in the discussion of Fig. 1 1, 
because of the significant variability of convective systems, selecting appropriate heating profiles 
from the CSH algorithm's look-up table for specific convective events is non-trivial. For this 
comparison, two different approaches for selecting tabulated profiles have been used. In the first 
approach, normalized heating profiles representing general tropical oceanic (gto) conditions are 
obtained by averaging profiles from a look-up table based on a set of diagnostic studies and a 
growing (but still limited) set of GCE-CRM simulations - see Figs. 3 and 4 in Tao et al (2000). 
In the second approach, normalized heating profiles representing South China Sea (scs) 
conditions and indexed according to geographic location and month-of-year, are used. Regarding 
GPROF, a climatological radiative heating profile is added to the GPROF estimates of Qj-Qr to 
obtain an approximate Qj, which can be more directly compared to the rawinsonde diagnostic 
estimates; Olson et al (2004). The CRM database used in the GPROF algorithm is the standard 
2al2 operational database. 

For the CSH-gto approach, the algorithm-retrieved Qi heating magnitudes are somewhat 
greater than the sounding-derived magnitudes. Nevertheless, there is agreement insofar as 
various key features of the vertical profiles, particularly concerning the level of maximum 
heating and the slight boundary layer cooling feature. For the CSH-scs approach, the retrieved 
profile magnitudes are in better agreement with the sounding-derived estimates, particularly in 
the upper troposphere where the retrieved and diagnostic magnitudes are in close correspondence 
~ but also in both the middle and much of the lower troposphere. On the other hand, the second 
approach exhibits greater departures insofar as boundary layer cooling, and also indicates a level 
of maximum heating some 0.5-1 km lower than the diagnostic calculation. This latter difference 
is consistent with the GCE-CRM-simulated level of maximum heating - also being some 0.5-1 
km lower than the diagnostic calculation. Of interest is that the difference between the GCE- 
CRM profile and the diagnostic profile is effectively opposite to that of the difference between 
the CSH-scs profile and the diagnostic profile, i.e., the GCE-CRM result is in closest 
correspondence in the middle and lower troposphere with larger differences in the upper 
troposphere. Neither of the two CSH approaches replicate the relative heating maximum at 



?.^ 



-15.5 km seen in the diagnostic profile. [See Tao et al (2003b) for further discussion 
concerning this SCSMEX intercomparison.] 

The mean GPROF Heating profile for the same SCSMEX period is similar in structure to 
the diagnostic profile (i.e., broad agreement between the level of maximum heating and 
boundary layer cooling). The salient differences are that in the boundary layer and just below the 
freezing level, GPROF cooling is greater than found in either the CSH-gto or diagnostic results. 
Although not yet fully understood, these cooling features are attributed to biases in the 
algorithm's CRM database, coupled with the limited information content of the radiometer data. 
The aim of a future investigation by the authors will be to identify and correct biases in the 
current physical parameterizations of CRM's, as they pertain to the simulation of microphysical 
and latent heating distributions. A more in-depth analysis of the GPROF heating comparisons to 
SCSMEX NESA data can be found in Olson et al (2004). 
5. Global Modeling Applications 

Whereas assimilation of TRMM rainfall data has proven to be an effective technique for 
improving predictive skill in global weather prediction models (e.g., see Bauer et al 2002; Hou 
et al 2000a-b, 2001, 2004; Krishnamurti etal 2000a-b, 2001; and Marecal et al 2002), use of 
explicit latent heating information for initialization and/or assimilation in global models is a 
research topic just beginning to re-emerge. The recent studies are motivated by early pioneering 
research in latent heating assimilation by Wang and Warner (1988), Puri and Miller (1990), 
Raymond et al. (1995), and others. Two global models, one from Florida State University (FSU) 
and the other from the NASA/Goddard Space Flight Center (GSFC), are currently using TRMM- 
based LH data sets to improve cumulus parameterization schemes and identify physical 
shortcoming with such schemes. 

At this stage it appears that the direct use of satellite (and or other ground-based) diabatic 
heating profile information for atmospheric modeling requires a physical initialization design. 
For example, T.N. Krishnamurti and his colleagues at FSU, using the Krishnamurti et a/. (1991) 
global-spectral model as the host, have developed a new experimental cumulus parameterization 
scheme - aptly called ECPS. This scheme uses past model analysis data sets to relate Qj-Qr 
heating to TRMM-retrieved latent heating. In closing this problem, they have found it necessary 
to use a limited number of vertical modes (expressed by a few empirical orthogonal functions) to 
relate model-generated heating to its satellite-observed counterpart. During a training phase, Q] 



7(i 



and Q2 profiles drawn from TRMM data sets coincident with profiles from ECMWF analyses 
were acquired. After rotated principal component (RPC) analyses were performed on the heating 
(Ql) and drying (Q2) profiles over tropical convective regions, the first three RPC modes were 
found to explain most of the meaningful observational variance. Expressing Q] and Q2 profiles 
as a linear combination of the first three dominant RPCs produced close agreement in associating 
the large-scale variables. Tests now being conducted with the ECPS parameterization scheme in 
conjunction with the Q] - Q2 estimation scheme are producing realistic vertical distributions of 
heating and drying for a cumulus environment. 

As shown in Figure 14, preliminary tests with ECPS result in improved precipitation and 
circulation predictions at 48 and 72 hours. This suggests that explicit assimilation of sateUite- 
retrieved LH profiles is a promising new avenue of NWP research. Obviously, further studies 
are needed to quantify how much prediction improvement can be obtained in moving from 
surface rainfall-based data assimilation (and/or PMW radiance-based assimilation) to LH-based 
data assimilation. However, in purely theoretical terms, it is the vertical distribution of diabatic 
heating that lies at the heart of the key underlying physical process that has never been resolvable 
using standard observations (from either soundings or weather satellite data) for model 
initialization and/or assimilation. 

Research is also taking place at GSFC to develop variational techniques to assimilate 
TMI-derived convective and stratiform LH rates within the general framework of parameter 
estimation, using disposable parameters in the relevant moist physics scheme as the control 
variables. The focus is to explore the feasibility of improving global climate analyses and 
weather forecasts through the assimilation of satellite-retrieved LH profiles that are radiatively 
compatible with multichannel PMW radiometer radiances. Such optimization of physical 
parameterizations in the context of data assimilation can provide valuable information for 
diagnosing model deficiencies and guiding the improvement of the parameterization schemes. 

There is a final application worth mentioning, also involving NWP modeling, in which 
satellite -retrieved LH profiles represent an important commodity. As the number of NWP 
models subjected to initialization by retrieved LH profiles increases, substanfive improvements 
in forecasting capabilities via "superensemble" techniques are expected to take place. The 
superensemble approach has been invoked as a powerful tool for improving the robustness of 
weather and climate forecasts, as has been emphasized in studies from the FSU modeling group 



7.7 



(viz., Krishnamurti et al 2000a-b; Vijaya Kumar et al 2003; Williford et al 2003; Yun et al 
2003). The goal of superensemble forecasting is to reduce overall uncertainties — as well as to 
better estimate errors associated with the various models, their physical parameterizations, and 
the ingested data sets. Thus, to the degree that satellite LH profiles can constrain initialization of 
forecasts and/or guide initializations through pre-forecast assimilation periods, superensemble 
forecasting may be able to exploit satellite-retrieved LH products in further reducing 
uncertainties for ensemble problems that are particularly sensitive to diabatic heating processes. 



l« 



6. Recommended Future Research 

Three of the TRMM LH algorithms (i.e., CSH, GPROF Heating, SLH) require CRM- 
simulated cloud data sets involving pre-calculated heating profiles. As noted earlier, given the 
concern with systematic errors arising from too few available CRM simulations creating scarcity 
effects in the data bases, the number of heating profiles associated with different types of clouds 
and convective systems occurring at a variety of geographic locations and throughout the 
seasonal cycle, will eventually have to be increased. Observations from additional field 
experiments will also have to be used to provide new types of initial conditions for the CRMs, as 
well as to help validate the CRM-simulated LH calculations themselves. Heating profiles 
obtained from numerical model simulations and large-scale model reanalyses should also be 
compared with those fi-om the CRMs and the associated retrieval algorithms. 

Such comparisons will help identify the sahent physical processes leading to similarities 
and differences produced by the CRMs and the retrieval algorithms. In addition, data from field 
campaigns that provide extensive and high quality in situ microphysical observations, including 
TRMM-LBA and KWAJEX, will be useful in validating and improving CRM-generated 
microphysics. Marzano et al. (1996), Panegrossi et al. (1998), Smith et al. (2002), and Fiorino 
and Smith (2004) have already addressed various issues concerning how improved 
microphysical representations in radiative transfer models can improve microwave-based 
precipitation retrieval. This is important because representative microphysics is essential in 
reproducing, within a modeling framework, the key four-dimensional features of latent heating. 

It is also important that diagnostically-based heating profiles obtained during the TRMM 
field campaigns, as well as fi"om other field campaigns such as those conducted by the DOE- 
ARM program, be compared to corresponding heating profiles from the different TRMM 
algorithms to ensure thorough validation. In this type of validation study, Doppler radar 
observations, particularly dual-Doppler observations that can accurately resolve the horizontal 
mesoscale wind field, would be extremely valuable (e.g., see DOE-ARM related paper by 
Clothiaux et al. 2000), although the greater abundance of single-Doppler observations, which can 
be also be used to infer horizontal wind divergence and vertical motion (related to diabatic 
heating), should also be exploited (e.g. Mapes and Lin, 2004). Doppler radar comparisons could 
help quantify errors within the current LH algorithms and help guide the way to the development 
of a next generation of algorithms. 



IQ 



Notably, as a follow-up to this study, a comprehensive intercomparison between the 
different LH algorithms for various common TRMM data sets is now planned for 2005. This 
study will consider the major heat and moisture budget terms, i.e., LH, g/, Qr, and 



JT[dw'd7dzJ . Also, global analyses will be used to identify and compare the large-scale 
circulation patterns for important retrieval periods and for key periods of earlier field campaigns 
including the GATE and TOGA-COARE tropical ocean field campaigns. These will be useful 
because in extending what is learned from local field campaign observations to other parts of the 
tropics where campaigns have yet to be conducted, use of latent heating "similarity" assumptions 
are inviting. However, whereas it might be reasonable to expect that LH structures associated 
with distinct tropical oceanic phenomena such as westerly wind bursts or super cloud clusters 
(that usually arise under comparable large-scale circulation fields with similar SST conditions) 
might not be all that different (e.g., Lau et al 1989), these assumptions deserve careful attention. 
Since all the algorithms can all produce instantaneous LH profiles at the scale of the satellite 
footprint, and given that spatial averaging is effective in reducing noise in instantaneous heating 
profiles, identification of an optimal spatial scale and selection of appropriate filters for use with 
instantaneous LH algorithms is another important issue that needs resolution and consensus in 
the future study. 

Once such research is completed and likely during the 2005 time frame, the first standard 
LH products for TRMM will be publicly released. This represents a welcome step because 
widespread dissemination of high resolution, globally-distributed, and continuous LH 
information to the research community, a data product that a decade ago was considered beyond 
reach, will enable compelling new investigations into the thermo-hydro-dynamical complexities 
of storm life cycles, diabatic heating controls and feedbacks related to meso-synoptic 
circulations, and the influence of diabatic heating on the atmospheric general circulation and the 
Earth's climate system in general. 



10 



7. Acknowledgements 

The authors extend their appreciation to Professors Robert Houze of the University of 
Washington, Richard Johnson of Colorado State University, Michio Yanai of the University of 
California at Los Angeles, and Edward Zipser of the University of Utah whose willingness over 
the years to discuss their ideas concerning atmospheric latent heating has had profound influence 
on various ideas central to this paper. This research has been supported by an assortment of 
TRMM Science Team grants under the auspices of both the National Aeronautics and Space 
Administration (NASA) and the Japan Aerospace Exploration Agency (JAXA). The authors 
wish to thank to Drs. Kwo-Sen Kuo and Chung-Lin Shie of the NASA/Goddard Space Flight 
Center for preparing the Cover Figure and Figure 12, respectively, and to Mr. Ken'ichi Ito of the 
Remote Technology Center of Japan for preparing Figure 5. 



^1 



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Afi 



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41 



List of Tables 

Table 1: Summary of CSH, GPROF Heating, HH, PRH, and SLH latent heating retrieval 
algorithms, in which key references, essential algorithm input parameters, past case studies, 
and relevant space-time resolutions of heating calculations are provided. [Wherever + 
symbols precede citations in "References" column, corresponding + symbols in other 
columns denote associated information vis-a-vis those citations. In "Alg" column, 
"RECON" indicates Reconstruction and "COMB" indicates Combined, while in 
"Resolution" column, inst indicates instantaneous, hr indicates 1 hour, dy indicates 1 day, 
and mo indicates 1 month.] 

Table 2: General strengths and weaknesses of CSH, GPROF Heating, HH, PRH, and SLH 
latent heating retrieval algorithms. 



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List of Figures 

Cover Figure: Five-year mean Qi heating rates at 8, 5, and 2 km AGL (upper 3 panels) along 
with surface rain rates (lower panel) over global tropics determined by Goddard Space Flight 
Center (GSFC) Convective- Stratiform Heating (CSH) algorithm applied to 1998-2002 
Precipitation Radar (PR) measurements acquired from Tropical Rainfall Measuring Mission 
(TRMM) satellite. [See related article by Tao et al] 

Figure 1: Height-length cross-sections of GCE-CRM generated LH (""C day'^) consisting of sum 
of heating by condensation, freezing, and deposition, and cooling by evaporation, melting, 
and sublimation - associated with mid-latitude continental (PRE-STORM) squall line (upper 
panel) and tropical ocean (TOGA-COARE) MCS (lower panel). [Discussions of simulations 
are in Tao et al (1993a, 1995, 1996), Wang et al (1996), Lang et al (2003).] 

Figure 2: Evolution of apparent heat source profile {Qi) averaged over TOGA-COARE IFA for 
8-day period (19-27 December 1992) - derived diagnostically every 6 hours by Lin and 
Johnson (1996) (upper panel) and simulated every 2 minutes by GCE-CRM (lower panel). 
[Contour interval is S'^C day"\] 

Figure 3: Upper panel shows plan view of near-surface rain rates for Hurricane Bonnie (22 
August 1998) retrieved from TRMM PR/TMI Combined algorithm; middle panel shows 
vertical nadir cross-section of along-track rain rate profiles; and lower panel shows vertical 
nadir cross-section of along-track LH profiles from HH algorithm. 

Figure 4: ULH and URH panels show TMI-retrieved surface and convective rain rates from 
GPROF rain algorithm- for squall line in North Atlanfic Ocean on 7 April 1998. Lower 
panel shows height-length cross-section (-28-km horizontal resolution) of total precipitation 
water content (color shading in g m'^) and Q]-Qr diabafic heating (contours in °C h"^) from 
GPROF Heating algorithm. 

Figure 5a: Five panels of upper diagram show latent heating analysis for tropical Pacific 
Typhoon Jelawat in developing stage (2 August 2000) in which arrows indicate location of 
eye, while five panels of lower diagram show identical analysis for MCS over tropical ocean 
north-west of Australia (16 February 1998). For each of two diagrams, ULH, MLH, and 
LLH panels show height-scan cross-section of PR-retrieved rain rate profile (mm h'^), along 
with SLH-generated and PRH-generated LH profiles ("^C h'*), respectively. Two pairs of 
URH and LRH panels show area-mean vertical profiles of both SLH-generated Q]-Qr (red) 
and LH (black), plus PRH-generated LH (black), all in ^C h ^ 

Figure 5b: Four panels of diagram show latent heating analysis for mid-latitude Oklahoma 
squall line (10 May 1999). ULH, MLH, and LLH panels show height-scan cross-sections of 
TRMM-PR-observed radar reflectivity profile (ZE in dBZ), PR-retrieved rain rate profile 
(mm h"'), and PRH-generated LH profile CC h'\ respectively. LRH panel shows area-mean 
vertical profile of PRH-generated LH in °C h ^ 



4^ 



Figure 6: Five-year (1998-2002) mean Qj profiles estimated from CSH algorithm for spring, 
summer, autumn, and winter over entire tropics (left panel), continental tropics (middle 
panel), and oceanic tropics (right panel) - all based on TRMM-PR retrievals. 

Figure 7: TRMM-PR-based Qj heating anomalies at 8 km AGL for El Niiio episode during DJF 
1997-98 (ULH panel) and La Nina episode during DJF 1998-99 (LLH panel) - generated by 
CSH algorithm. Average 3-year (1997-99), 3-month El Niiio episode, and 3-month La Niria 
episode heating and heating-anomaly profile pairs over entire tropics are shown in right-hand 
panel in black, red, and blue, respectively. 

Figure 8: Evolution ofQ] profile reconstructed from GCE-CRM simulation by CSH algorithm 
averaged over TOGA-COARE IFA for 8-day period (19-27 December 1992) ~ compare to 
results in Fig. 2. Reconstruction uses CRM parameters retrievable from PR data as input 
(i.e., surface rain rate and convective/stratiform fractions). [Contour interval is 5*^C dayV] 

Figure 9: Evolution of LH profile (5-min time-step) from: GCE-CRM simulation (upper panel), 
SLH algorithm reconstruction (middle panel), and CSH algorithm reconstruction (lower 
panel), averaged over TOGA-COARE IFA for 8-day period (19-27 December 1992). 
Contour interval is S^'C day"*. GCE-CRM simulated convective/shallow-stratiform/anvil 
stratus fractions, surface rain rates, PTHs, and mehing level rain rates are used as inputs to 
SLH scheme with profiles averaged over 512x512 km grid mesh. [From Shige et al. 2004.] 

Figure 10: Cloud model simulation of GATE vertical profiles of heating rate by condensation 

(c), evaporation (e), vertical eddy heat flux convergence (Jtfdw'B'/dzJ )^ and cloud 
partition of apparent heating (Qi[cldJ) - along with diagnostic calculations of Qi - Qr (using 
radiosonde data), all in units of "^C hr'V [From Tao and Soong (1986).] 

Figure 11: Three left-most pairs of diagrams illustrate isometric projections of volume 
hydrometeor distributions (upper panels) and plan- view surface rain rates (lower panels) for 
instantaneous realizations from GCE-CRM simulations of SCSMEX, KWAJEX, and DOE- 
ARM MCS storm cases. Upper panel iso-surface color scheme assigns white for cloud 
droplets and ice crystals, blue for snow, red for graupel and hail, and green for rain. Right- 
most pair of diagrams illustrate near-surface, forward-modeled radar reflectivities for 
TRMM-LBA easterly regime (upper panel) and westerly regime (lower panel) MCS cases, 
also based on GCE-CRM simulations. 

Figure 12a: KWAJEX rainfall time series consisting of measured and modeled rain rates. Both 
KPOL-Radar measurements and TRMM-PR retrievals are given for entire lOP, while GCE- 
CRM simulated estimates are provided from Aug 29 through Sep 12 (both 2D and 3D CRM 
designs are used to provide simulated rainfall). [Top diagram from Yuter et al. (2004).] 

Figure 12b: KWAJEX heat budget time series consisting of diagnostically-calculated and GCE- 
CRM-simulated Q] profiles for three different time sequences during lOP (upper, middle, 
lower panel pairs illustrate 5-, 3-, 15-day time series, respectively). Green and red contours 
indicate positive and negative Q] regions, respectively. 



4^ 



Figure 13: Qi profiles from diagnostic calculations (Johnson and Ciesielski 2002), GCE-CRM 
simulation, PR-based CSH algorithm, and TMI-based GPROF algorithm averaged over -^6 x 
10 deg lat-lon box designated as SCSMEX-NESA for 37-day period (15 May - 20 June 
1998). Two sets of look-up-table profiles are used with GCE-CRM and CSH algorithm 
representing conditions for: (1) South China Sea (scs), and (2) general tropical ocean (gto). 
Color insert is isometric rendition of GCE model simulation for 24 May 1998, where white, 
blue, red, and green iso-surfaces denote cloud droplets - ice crystals, snow, graupel - hail, and 
rain, respectively. [Most surface rainfall is produced by meUing graupel.] 

Figure 14: GPCP precipitation for 8 February 1998 representing blend of satellite retrievals and 
rain gauge observations (upper panel), Florida State University global spectral model (FSU- 
GSM) day-2 forecast from ECPS experiment (middle panel), and FSU-GSM day-2 forecast 
from control experiment (lower panel). [From Rajendran et al 2004.] 



47 



Retrieved Latent Heating ( 5-yr / Jan'98 - Dec' 02 ) 
TRMM ^ TRMM ^ 



30 60 90 120 ISO 180 -150 -120 -90 -60 -^Q 




30 60 90 120 150 180 -150 -120 -90 -«0 -^tt 




-1 



"C day 

(upper LH scale) 



150 180 -150 -m 
1 2 



m 



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mm day'' 

(lower RR scale) 



12 



Cover Figure: Five-year mean Q] heating rates at 8, 5, and 2 km AGL (upper 3 panels) along 
with surface rain rates (lower panel) over global tropics determined by Goddard Space Flight 
Center (GSFC) Convective- Stratiform Heating (CSH) algorithm applied to 1998-2002 
Precipitation Radar (PR) measurements acquired from Tropical Rainfall Measuring Mission 
(TRMM) satellite. [See related article by Tao et al.] 



dR 



PRE-Storm 




^ 300 

S 500 

£ 600 

700 

800 

900 



300 



TOGA-COARE 




100 150 200 

x-grid (km) 

Figure 1: Height-length cross-sections of GCE-CRM generated LH (°C day"^) consisting of sum 
of heating by condensation, freezing, and deposition, and coohng by evaporation, melting, 
and sublimation — associated with mid-latitude continental (PRE-STORM) squall line (upper 
panel) and tropical ocean (TOGA-COARE) MCS (lower panel). [Discussions of simulations 
are in Tao et al (1993a, 1995, 1996), Wang et al (1996), Lang et al (2003).] 



40 



Diagnostic Qi 



(0 
Q. 

0) 



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12/20 12/21 12/22 12/23 12/24 12/25 12/20 12/27 



Model Q] 




1000 
12/10 



12/21 12/22 12/23 12/24 12/26 12/26 12/27 

Day of Month 



Figure 2: Evolution of apparent heat source profile (Ql) averaged over TOGA-COARE IFA for 
8-day period (19-27 December 1992) - derived diagnostically every 6 hours by Lin and 
Johnson (1996) (upper panel) and simulated every 2 minutes by GCE-CRM (lower panel). 
[Contour interval is S^'C day"*.] 



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Typhoon Jelawat (2 August 2000 (orbit 15,432) 

PR2A25 roA-n rate (angle='27) 



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S300 SS20 3340 3360 

scan, nuinber 

PRH (vr.^) latent heating (angle=27) 



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(K hr-) 
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Tropical Ocean NW of Australia (16 February 1998 (orbit 2,681) 



PR2A25 Tavn. rate (angle=Na<ivr) 




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Figure 5a: Five panels of upper diagram show latent heating analysis for tropical Pacific 
Typhoon Jelawat in developing stage (2 August 2000) in which arrows indicate location of 
eye, while five panels of lower diagram show identical analysis for MCS over tropical ocean 
north-west of Australia (16 February 1998). For each of two diagrams, ULH, MLH, and 
LLH panels show height-scan cross-section of PR-retrieved rain rate profile (mm h"^), along 
with SLH-generated and PRH-generated LH profiles C*C h"^), respectively. Two pairs of 
URH and LRH panels show area-mean vertical profiles of both SLH-generated Qi-Qr (red) 
and LH (black), plus PRH-generated LH (black), all in X \i\ 



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100 



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1000 L I I I I I I I I I I I I I I I— 

12/10 lS/20 12/21 12/22 12/23 12/24 12/26 12/26 12/27 

Day of Month 



Figure 8: Evolution of Q] profile reconstructed from GCE-CRM simulation by CSH algorithm 
averaged over TOGA-CO ARE IFA for 8-day period (19-27 December 1992) - compare to 
results in Fig. 2. Reconstruction uses CRM parameters retrievable from PR data as input 
(i.e., surface rain rate and convective/stratiform fractions). [Contour interval is 5°C day'.] 



'>R 



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SLH Algorithm-Reconstructed LH 



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12/19 12/20 12/21 12/22 12/23 12/24 12/25 12/26 12/27 



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0- 










12/19 12/20 12/21 12/22 12/23 12/24 12/25 12/26 12/27 

Day of Month 

lu — ^5 — ir 



Heating Rate ("C day-^) 

Figure 9: Evolution of LH profile (5-min time-step) from: GCE-CRM simulation (upper panel), 
SLH algorithm reconstruction (middle panel), and CSH algorithm reconstruction (lower 
panel), averaged over TOGA-COARE IFA for 8-day period (19-27 December 1992). 
Contour interval is 5°C day"'. GCE-CRM simulated convective/shallow-stratiform/anvil 
stratus fractions, surface rain rates, PTHs, and melting level rain rates are used as inputs to 
SLH scheme with profiles averaged over 512 x 512 km grid mesh. [From Shige et al. 2004.] 



SQ 



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Figure 10: Cloud model simulation of GATE vertical profiles of heating rate by condensation 

(C), evaporation (e), vertical eddy heat flux convergence (Jt[dw'67dzJ )^ and cloud 
partition of apparent heating (Qi[cld]) - along with diagnostic calculations of Qi - Qr (using 
radiosonde data), all in units of °C hr■^ [From Tao and Soong (1986).] 



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Diagnostic 



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12 



Figure 13: Q] profiles from diagnostic calculations (Johnson and Ciesielski 2002), GCE-CRM 
simulation, PR-based CSH algorithm, and TMI-based GPROF algorithm averaged over ~6 x 
10 deg lat-lon box designated as SCSMEX-NESA for 37-day period (15 May - 20 June 
1998). Two sets of look-up-table profiles are used with GCE-CRM and CSH algorithm 
representing conditions for: (1) South China Sea (scs), and (2) general tropical ocean (gto). 
Color insert is isometric rendition of GCE model simulation for 24 May 1 998, where white, 
blue, red, and green iso-siufaces denote cloud droplets - ice crystals, snow, graupel - hail, and 
rain, respectively. [Most surface rainfall is produced by melting graupel.] 



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