924 JOURNAL OF APPLIED METEOROLOGY -OLUME30Microwave Simulations of a Tropical Rainfall System with a Three-Dimensional Cloud Model ROBERT F. ADLERNASA/Goddurd Space Flight Center, Greenbelt. Maryland HWA-YOUNO M. YEHCaelum Research Corporation. Silver Spring. MarylandGeneral Sciences Corporation. Laurel, Maryland WEI-KUo TAO AND JOANNE SIMPSONNASA /Goddard Space Flight Center, Greenbelt, Maryland(Manuscript received $ June 1990, in final form 8 January 1991)ABSTRACT A three-dimensional cloud model-microwave radiative transfer model combination is used to study therelations among the precipitation and other microphysical characteristics of a tropical oceanic squall line andthe upwelling radiance at pertinent microwave frequencies. Complex bri$htness temperature-rain rate relationsare evident at the full horizontal resolution l.S kin) of the models, with spatial aver~in8 producing smoother,shifted relations in most cases. Nonprecipltating cloud water is shown to be important in understandin~ theresulting distribution of brightnesz temperature. At the mature stage, convective porous of the cloud system~ shown to produce different brightness temperature relations than the stratiform portion, primarily relatedto the distribution of cloud water. The evolution of the convective system from a small convective complexthrough its mature ~tage and the beginning of its dissipation also is shown to result in a variation of bdl~htnesstemperature-rain relations, related to the distribution ofcloud water and the evolution of ice in the precipitatingsystem. The results of the study point to the need to take into account the evolution of nonprecipitating cloudwater and precipitation-sized ice in the retrieval of rain from passive microwave space observations. This effectis evident for both the llfe cycle of individual convective elements and the life cyc!~ of the convective systemas a whole.1. Introduction The retrieval of rainfall information from satellitepassive microwave observations is inherently linked tothe microphysical structure and dynamics of the cloudsystem being observed. Especially with intense convective systems, the four-dimensional relations betweensurface rainfall, suspended hydrometeors, and the resuiting upwelling radiances at various passive microwave frequencies are very complex. The problem isfurther compounded because the hydrometeor contenlsand physical properties of such convective systems aredifficult to measure over a large spatial scale and continuous time period. Most previous simulations of suchrelations have used a simple layered structure (e.g.,Wilheit et al. 1977; Wu and Weinman 1984). Corresponding author address: Dr. Robert F. Adler, Code 973,NASA/Ooddard Space F~ht Center, Greenbelt, MD 20771. The objective of this work is to replace those simplestructures with more realistic, complex ones by usingthe output from a three-dimensional cloud model. Thecloud model gives a complete description of the particlemicrophysics and storm dynamics as a function of timethroughout the cloud volume. Snapshots of the entirecloud at various times of simulation, with all its internalconstituents such as cloud water, rain waler, cloud ice,snow, and graupel serve as the essential starting pointfor this study. The hydrometeor information from thecloud model is then used as input into a microwaveradiative transfer model that calculates the upwellingradiance at the top of the atmosphere. In this way, theresulting brightness temperature (Tb), hydrometeorstructure, and surface rainfall rate relations retain thecomplexity of actual convective cloud systems. Some progress has already been made in the area ofusing cloud models that include ice processes in combination with microwave radiative Lransfer models.JuLY 1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 925Simpson et al. (1988) describe research using a onedimensional, time-dependent cloud model to simulatethe To-rain rate relations at 90 GHz in two differentclimatological regimes as characterized by aircraft observations by Hakkarinen and Adler (1988). The useof a three-dimensional model in this context was firstdescribed by Adler et al. (1988) and in more detail bySimpson et al. (1988), who showed simulations at 10,18, and 90 GHz over a portion of a tropical rain systemand the effect of spatial averaging on the To-rain raterelations. More recently, Mugnai et al. (1990) haveused this approach with a three-dimensional model tosimulate clouds and compare the results with aircraftmicrowave data. In this paper the results of using a three-dimensionalcloud model-radiative model combination will be examined in terms of high-resolution results regardingrelations among the various microphysical quantities,surface rain rate, and upwelling microwave radianceand the area averaging effect on those relations inherentin satellite observations. The effect of the life cycle stageof individual convective elements and of the convectivesystem as a whole on these relations is also analyzed.2. Cloud model and radiative transfer modela. Three-dimensional cloud model The cloud model used in this study is a three-dimensional cloud ensemble model described by Soongand Ogura (1980), Soong and Tao (1980), Tao andSoong (1986), and Tao and Simpson (1989). Themodel is nonhydrostatic and anelastic. Model variablesinclude horizontal and vertical velocities, potentialtemperature, and mixing ratio of water vapor. In addition to the Kessler-type of two-category liquid-water(cloud water and rain) microphysics, a parameterizedthree-category ice-phase (cloud ice, snow, and graupel)scheme is included (Lin et al. 1983; Rutledge andHobbs 1984). The particles comprising the cloud-waterand cloud-ice fields are each assumed to be monodisperse. The precipitating rain, snow, and graupel partitles are distributed in size according to an inverseexponential distribution (Marshall and Palmer 1948).The cloud water and cloud ice are assumed to advectwith the airflow, having no appreciable terminal velocities of their own. Precipating hydrometeors likerain, snow, and graupel, while moving with the horizontal wind, also fall relative to the updraft with theirrespective terminal velocities. The microphysical parameters used in this study are those of Rutledge andHobbs (1984). Microscale turbulent mixing processesare incorporated in the form of eddy diffusion, whichis computed through a turbulent kinetic energy equation (e.g., Klemp and Wilhelmson 1978). A simpleperiodic boundary condition is used in this study. Atime-varying large-scale vertical velocity with its magnitude deduced from observations is imposed in themodel as the main forcing mechanism. A stretchedvertical coordinate is used to give fine resolution in thelower levels where clouds start to form, with coarserresolution in the upper levels of the model. The gridinterval is 230 m at the lowest level and about 1000 mat the highest level. There are 30 vertical grid points,and the depth of the model domain is 16.5 km. Theversion of the model used in this study has 64 x 64grid points in the horizontal, with a grid spacing of1500 m. A simple free-slip upper and lower boundarycondition are used in this study. A leapfrog time integration and a second-order spatial derivative schemeare used.b. Microwave radiative transfer model The basic model used for calculating microwave upwelling brightness temperature is an adaption of theiterative model used by Wilheit et al. (1982). Thetransfer of polarized upward radiation is computedthrough a plane-parallel atmosphere that containsclouds and/or precipitation of liquid and frozen hydrometeors. The hydrometeors absorb, emit, and scatter radiation. This model has been modified to allowa more detailed vertical structure of the atmosphere.The modified radiative transfer model further allowsfor the separate treatment of different classes of iceincluding cloud ice, snow, hail, and graupel. The density and size distribution of the frozen hydrometeorsare consistent with those used in the cloud model. Thedensity of cloud ice is 0.9 g cm-3, while snow and graupel are 0.1 and 0.4 gcm-3, respectively. A realistic account of the effects of radiation in acloudy atmosphere should be concerned with the spatial variability of clouds and the impact of this variability on the radiative processes. Stephens (1988) hasquestioned the appropriateness of modeling the radiative processes in the atmosphere by assuming a planeparallel or a uniform media of simple geometric shape.However, in this study the plane-parallel assumptionis used and appears to give realistic results. In this model simulation, the atmosphere is dividedinto vertical regions with each region characterized bya uniform distribution of each class of hydrometeors.Several classes of particles can coexist in each region.In this study, we use two classes of water (cloud waterand rain water) and three classes of ice (cloud ice, snow,and graupel) from the cloud model. A total of up to19 cloud regions are allowed in the model. Computation of the extinction, scattering, absorption coefficients, and phase function is performed using Mie calculations for various size distribution of each class ofhydrometeors. Bulk radiative parameters are obtainedby integrating over various classes of hydrometeors ineach region. The Mie scattering calculation routinesin the model have been replaced by Mie tables, whichare constructed for different hydrometeor phases anddensities to save computer time (Yeh et al. 1990a).926 JOURNAL OF APPLIED METEOROLOGY VOLUME30The empirical formulas of Ray (1972) are used tocompute the complex refractive indices of liquid water,and the tables of Warren (1984) are used for computingcomplex refractive indices of ice. The Mie scatteringproperties of snow, graupel, and hail are also includedin the Mie table. These hydrometeo~ are commonlyregarded as a mixture of water, ice, and air. The radiative properties of snow and graul:,el are defined interms of dielectric mixture theory (Sadiku 1985 ). Forcloud ice and cloud water, the Rayleigh approximationis assumed in the model calculations. For radiative transfer modeling simulation, Mietheory has been conventionally utili[zed to calculatethe scattering and extinction parameters. It is apparentthat few particles are spherical in nature; falling raindrops are elongated, and snowflakes are well knownfor their intricate forms. The experimental evidencefrom microwave analog measurements, however, indicate that with averaging over random orientation andsize, nonspherical particles scatter in the forward direction very much like equivalent spheres (e.g., Zerull1976). Wu and Weinman (1984) computed the Tb'semerging at 130- from precipitating clouds and compared Tb's of those assuming spherical and deformedice and water droplets. They showed that the differenceof To's generally is less than 5 K. In order to perform a sufficiently accurate calculation, the atmosphere in the model is divided into upto 200 layers of equal optical thickness. The opticalthickness results from the combination of gaseous andhydrometeor extinction in the atmosphere. The modelhas been described by Yeh et al. (1990b) in more detail.The surface emissivity for over water surface is computed according to Chang and Wilheit (1979). Forsimplicity, the ocean surface is assumed to be smoothwith a wind speed less than 7 m s-~, and the surfacetemperature is set at 291 K. The size distribution of particles is :important in thestudy of any relationship pertaining to cloud microphysics. We have used the Marshall-Palmer (M-P)distribution for rain water and adjusted M-P distribution for snow and graupel (adjusted for intercept)for the entire storm's life cycle. Yeh et al. (1990b),using observed radar data in a microwave radiativemodel simulation of aircraft measurements of mesoscale convective systems, have shown that M-P distribution generally holds well for both rai[n water dropletsand ice particles. In some areas such as a weak convection or downdraft region, however, M-P distribution does not have enough large frozen hydrometeorsto effectively scatter the low-frequency microwave radiation. Other size distributions for the frozen hydrometeors (e.g., Sekhon and Srivastava 1970) are morerepresentative of aggregates and represent extremes inthe ice phase (Heymsfield and Palmer 1986 ). Detailedsensitivity tests with the Gamma distribution (Ulbrich1983) and many other size distributions (Sekhon andSrivastava 1971; Willis 1984) would be of value, butthe limited computational resources available at thepresent time restrict us from doing an elaborate sizedistribution study on the microwaw,- radiative modelover a large area.3. iDescription of case and cross section resultsa. .Rainfall evolution The cloud model simulation usecl in this study isthat of a tropical fast-moving squall line as describedby Tao and Simpson (1989). In the numerical simulation the x coordinate is perpendicular to the squallline and the y axis is parallel to it. The initial statevertical profiles of temperature, mixing ratio, and windare based on those composited for three such GATEsystems by Barnes and Sieckman (1984). A time-varying, large-scale vertical velocity was also applied basedon diagnostic calculations ofOgura et al. (1979). Convective initiation is produced by random temperatureperturbations confined to a square of 8 x 8 grid pointsin the center of the domain. Evolution of the rain pattern during the 4-h modelrun is shown in Fig. 1. The rain parameter plotted hereis actually the vertically integrated hydrometeor content over the lowest 3.8 km converted to rain rate. Thisvertically integrated rain parameter ("rain intensity"is designated in Figs. 2a, b) was chosen as the basic rainparameter of this study (instead of surface instantaneous rain rate) because it produced more easily interpretable results when compared to the radiative calcuhttions, especially at high horizontal spatial resolutions. Figure 2a shows the relation of the verticallyintegrated rain to the model surface rain intensity,showing the scatter due mostly to the 'vertical variationsin the rain column. The area-average relation over a 6X 6 km2 area in Fig..2b indicates that horizontal averaging also reduces the scatter, with the correlationcoel~ticient improving from 0.88 to 0.96. Because therain rate tends to decrease with height, the verticallyintegrated value has a 10% low bias relative to the surface rain rate. When interpreting diagrams in the following sections, especially those dealing with high horizontal spatial resolution, the reader should realize thatthe :scatter in the diagrams would be larger if the surfacerain intensity was plotted instead of the column average. The convection initiates in the center of the domainand gradually develops as a convective cluster with twoareas of heavy rain (Figs. la,b) and an arc-shapedleading edge (Figs. lc-e) propagating toward the leftboundary (down shear direction). The average propagation speed is about 7-8 m s-I, somewhat smallerthan the 11 m s-l of the three composited GATE cases(Barnes and Sieckman 1984), but wiithin the range of7-16 m s-~ of propagation speeds reported in the literature (Tao and Simpson 1989). As the system matures, the original intense convective areas (at times 124 and 134 min) evolve into theJULY1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 9279O7560453O159O756O~ 45- (a) 126 rain........ I ......... I .........I .........I,,~:~,,I ......... I, 15 30 45 60 75 903O15(C) 174 rain........ I ......... I .........I .........I .........I .........I, 15 30 45 60 75 9090 ~<)' : ~::.~:..,;: (e) 234 min::.: : _: .... ::: ....' ...~ 15 30 45 60 75 90 X(km)90756O453O15-- (b) 138 min........ I ......... I .........I .........I .........I .........I, 15 30 45 60 75 90 XCkm)15 30 45 60 75 90 X(km)FIG. 1. Rainfall evolution of the cloud model simulation at fivetime steps: (a) 126, (b) 138, (c) 174, (d) 210, and (e) 234 min.928 JOURiNAL OF APPLIED iMETEOROLOGY VOLUME30 ......so. (a) Ful resolution8o. :~70.60.550.40.30. ..: ,..-.. ~..,,-,... .20. ~' ' '~': ':'."'.' -. . - - ?..~:.... ~.-:,.- .xo. r2:0,77 ..%,..: . .. .o. o. !.o. 2o. Bo. 40. 5Oo 6o. 70. ~to. ~o. loo.100.90.~0o70.60.~50.40.30.20.10.O. (b) 6 km by 6 km area aver~ - r2: 0.92 ~,,'I I I I I I I I I O. tO. 20. ~O. ~O. 50. 60. 70. 80. ~O. lOO. RAIq IqTF. NSITY (MM/t-R) FIG. 2. Correlation between the surface rain intensity and the vertically integrated rain-water content ("rain intensity") from the cloudmodel results at 210 rain simulation time.two main parts of the squall line along the "northwest"and "southwest" flanks of the system (at times 210and 234 min). Between these two intense portions ofthe leading edge, an area of relatively hght rain evolvesthat becomes important in the analysis of the brightnesstemperature results. In the area to the rear of the squallline a stratiform precipitation area with imbeddedconvection develops. The horizontal extent of this region is small in.this three-dimensional run as comparedto that of a two-dimensional run, which has a largerdomain in the x direction. Similar to Nicholls andWeissbluth (1988), Tao and Simpson (1989) have alsocompared the differences between two- and three-dimensional model simulations of a tropical squall linesystem and found that the three-dimensional simulation may result in stronger updrafts, due to the limitation of domain available for the simulation. Thethree-dimensional run also produces, a less extensiveanviil region. But the explosive growth and a convexleading edge associated with the convective region arewell simulated. The three-dimensional run captureswell the general evolution of precipitation in this typeof system, from the developing through the maturestage. The decaying stage is not simulated, althoughupdraft strength is noted to weaken at the later times.b. ("ross section results The vertical structure of the hydrometeors and cloudparameters are the drivers in the radiative transfer calculations that determine the upwelling radiance at thetop of the atmosphere. The first example of the verticalstructure is given in Fig. 3 as cross sections constructedalong the x direction across the leading edge of theconvection and the trailing regions (y = 42 km in Fig.ld) at time 210 min. The four panels contain, respectively, the cross section of vertical velocity (Fig. 3a),the liquid precipitation or rain (Fig. 13b), the nonprecipitating cloud liquid water (Fig. 3c), and the totalice content (a sum of the three classes of ice in thecloud model; Fig. 3d). The horizontal line in Fig. 3denotes the approximate height of the 0-C isotherm. Tihe ice in Fig. 3d extends to an altitude of 13 km,corresponding to the area with vigorous updraft (>30m s'-]) and the large rainfall rate (>80 mm h-~) at x= 22.5 km. Some of the precipitating ice is shown toexist at temperatures above freezing before it melts andconverts to rain water. The maximum ice content is3.6 g m-3 at approximately 400 mb (~7.8 km). Therain water exists almost entirely below the freezinglevel, except in a small area with very strong updrafts.The cloud-water distribution in Fig. 3c shows the mosthorizontal variability, with substantial cloud water existing in the regions of strong updrafts (see Fig. 3a).The collocation of the cloud water and the frozen hydrometeors (e.g., at x = 21 km) is very important inthe radiometric calculations, because the cloud wateris more active in the absorption-emission process whilethe ice acts primarily as a scatterer. At certain locationsassociated with strong, young updrafts, substantialcloud water exists below the freezing level (e.g., at x= 40.5 km). The corresponding radiance calculationsalong the cross section, in terms of brightness temperature T~ are shown in Figs. 4a-d for 10, 19, 37, and85.6 GHz, respectively, along with a plot of rainfallrate. The calculations are presented for a viewing angleat nadir. A~I l0 GHz in Fig. 4a, the nonprecipitating (andnoncloudy) areas have low To due to the low emissivityof the water surface with the T~ about 120 K. This istypical with clear sky over the ocean. Over the precipitation, the T~ values increase sharply with the T~reaching 265 K and the rain intensity (RI) exceeding85 mm h-]. The 10-GHz To follows 'the variations inrain rate fairly well, which is to be expected since theJULY1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 929HEICHT(KM)HEIGHT(KM)O O O O (D (:D (D (DO ~ OO O C; (:D O O O OUD r.. OC~ 09 '~ UO CD P- (D O~ U~ ,-~ (an)aunssaudooe.D ,~ 04 o ~0 to ~ e9 t%l '~ tD- --4 ~ *--~ ~ I I I I I I I I I I I I I I I I I I I I I I I I ~ - ~ ~ ~ ~1 ~.~ ~ >5~ I,~ ':~?';~i ~ ~ ~ 3 ........ ~ ~ -d~ -z8 ~ /% < ~ .~ .~ <: >-g 0 o - ~ , ~ ~:.....::::~:7,::: .:: ....... = ~ ~ ":'o~"<:~ .~ a _m ~ ~ ~ a 0. 0 -0 ~-~:a i-[ I I I I I I I I I I I I I I I I I I I I I I I ~ o o o o o o o oo O 6 o o o o o o o o~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ (a~)aanssaa~930 JOURNAL OF APPLIED METEOROLOGY VOLUME30300.280.260.240.220.200.180.160.140.120.100.80.60.SO0.280.260.240.220.200.180.160.140.12o.1oo.80. 60.3oo.280.260.240.22o.200.~eo.160.~o.~2o.100.80.60.300.280.260.240.220.200.1~0.160.140.120.100. eo. 60. ~0. 80. ~o. ~o. ~o. 20. lO. o.Y ' 4:2 km (a) 10 GHz(b) 19 GHz t (c) 37 GHzIIIlllllllllll I~11[1111~[ II~llllllll'~ (d) 86 OHzgO4FIG. 4. The x-z cross section of brightness temperatures at (a) 10, (b) t9,(c) 37, d) 86 GHz, and (e) rain intensity at y = 40.5 km.JULY 1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 931dominating influence on the To is the emission by theliquid water in the cloud, which radiates with an emissivity of approximately 1.0, thereby producing the increases in observed To in contrast to that of the oceansurface. However, the To peak at 10 GHz is broad relative to the sharp peak in the rain rate plot, indicatinga saturation in To even at this low frequency. At 19 GHz (Fig. 4b), a similar transition from clearskies to precipitation is evident with increasing To.However, in the area with the heaviest rain (at x = 24km), which also has the largest total ice content, theTo values at 19 GHz show a relative minimum, indicaring the effect of scattering by ice. Thus the rainmaximum is bracketed by 19-GHz To maxima on either side at positions of moderate rain rate. The warmest To (~260 K) occurs with the young updraft (x= 40.5 km) in the lower levels where there is an abundance of cloud water and a small maximum of rainwater but very little ice (Fig. 3d). Figure 4c shows that at 37 GHz, as we approach thesquall line from the left, there is a sharp increase inTo. The initial maximum is reached further from therain maximum, producing a decided phase shift in theposition of the To maxima from 10 to 19 to 37 GHz.The lowest To values (as low as 140 K) are close to theheaviest rain, with a slight phase shift probably relatedto a positional shift between the ice at higher elevationsand the rain below. The highest To at 37 GHz againoccurs with the cloud water/light rain feature at x= 40.5 km. At 86 GHz, the ice scattering process appears todominate with even the relatively light rain areasshowing a scattering signal. The calculated minimumTo of 80 K indicates that nearly all the upwelling radiation from the surface and the lower part of the cloudare being scattered and that little emission is being generated from the predominant layer of ice particles. Theeffect of emission can still be seen at this frequency atx = 42 km with a slight rise in To indicating the presenceof the suspended liquid water and the near absence ofice. This slight increase in Tb for shallow water clouds,with a rapid decrease in To for deeper clouds with significant ice, has been observed by aircraft at 92 GHz(Hakkarinen and Adler 1988 ). The brightness temperature calculations displayedin the cross section and those discussed in the rest ofthis paper are for a nadir view. However, many keyaircraft and satellite sensors view at an angle of 45 o_50- from nadir. As can be imagined by examining thecross section, this viewing angle may change the relations between the brightness temperature and cloudparameters because of the different cloud volumessampled. Yeh et al. (1990b) have used weighting functions to compare aircraft views of cloud systems at nadirand 45- slant angle. This viewing angle effect, however,will be ameliorated in the satellite observations becauseof the area-averaging of the satellite field of view. In summary, the cross sections ofhydrometeors andcloud parameters and the resulting radiance calculations indicate that the cloud model is reproducing thecomplexity and variety of structures and magnitudesseen in the real atmosphere and that the resulting Tovalues display a wide range of values and relations tothe cloud and rain parameters. Detailed examinationof these relations are presented in the following sections.4. Model-based Tb relations at 10, 19, 37, and 86 GHz for a mature, tropical convective systema. Rain rate map at time 210 rain This section focuses on relations among cloud parameters generated by the cloud model and To valuesat various frequencies calculated from the radiativemodel at a specific time, 210 min, in the cloud modelrun. As can be seen in Fig. I d, the rain pattern at thistime shows the well-developed leading edge of squallline system. The dashed line in Fig. 1 d marks the curvedaxis of highest rain rate in the squall line with maximum rain rates over 150 mm h-~. Lighter rain dominates the area to the rear of the actual squall line,except for a few, isolated convective cores.b. Brightness temperature maps at time 210 min Brightness temperature maps calculated with the radiative transfer model at 10, 19, 37, and 86 GHz usinginput from the cloud model at time 210 min are shownin Figs. 5a-d, respectively. Results are shown at a nadirviewing angle and with an ocean background. Thedashed line in each panel of Fig. 5 is the location ofthe surface rain rate maximum as indicated in Fig. 1 d.At 10 GHz (Fig. 5a), the presence of precipitation produces an increase of To from the background, clear skyTo of I 18 K. Individual rain rate maxima are associatedwith distinct maxima in the To field, including the isolated rain feature in the extreme upper left portion ofthe panels. The arcline of the highest T0's at 10 GHzis collocated with the maximum rain intensity region,as indicated by the dashed line. The scattering effectfrom ice above the intense rainfall area does not showa significant impact at 10 GHz. At 19 GHz (Fig. 5b), there is also an increase in Tofrom the background of 160 K to values of 240 K forlight rain features such as that in the upper left cornerof the panels. However, in the squall line system, theaxis of the highest T0's (dot-dash line) is ahead (to theleft) of the maximum rainfall (dashed line) in an areaof moderate rainfall rate. This shift in relative location(as compared to the 10-GHz map) is related to thepresence of significant ice in the uppefftroposphere asseen in the cross sections in Figs. 3 and 4 and the increased sensitivity to the ice at this higher frequency.As also seen in the cross section, since the largest icecontents are roughly collocated with the strongest updrafts and also with the highest rain rates, the heaviest932 JOURNAL OF APPLIED METEOROLOGY VOLUME3090~60453015 15 30 45 60 75 90 - ....................................... o ';';'"'"'""190 .~ O O c 37 GHz O o7560 o453015756O5015!ci,~llllll III Ifflll Ill III II1111111 ~11~11 III III IIt1111111 IIIIIIi ' (b) 19 GHz'80 ~ o''~ '~ ~i ~ ~15 30 45 6(I 75 90r550-5301515 30 45 60 75 90. 15 30 45 60 X (km)FIG. 5. The calculated brightness temperatures at 210 rain for (a) I0, (b) 19, (c) 37, and (d) 86 GHz.75 9Orain is coincident with To minima at 19 GHz, whereasat 10 GHz they were located with 7~ maxima. Thelowest temperature (180 K) at 19 GHz is found at agrid point (x = 30 km, y = 72 km), which is near thelocation of the maximum RI (>160 mm h-l). Aircraftdata at 18 GHz obtained from overtlights of a deep( 15 km maximum height) convective system describedby Adler et al. (1990) and Yeh et al. (1990b) have aminimum T0 of 190 K, indicating that the model calculated minimum To value is reasonable. Higher T0'scorrespond with less convective regions, where the icecontent is smaller, so that the emission from the liquidwater is more effectively transmitted to the top of theatmosphere. At 37 GHz (Fig. 5c), the pattern of To is similar tothat at 19 GHz, with the maxima in ?~ associated withmoderate rain rates and heavy rain cores associatedwith significant ice and To minima. The distance between the To maximum arcline and the rain rate maximum arcline has increased, compared to the 19-GHzlocation difference. The minimum 7~ of 90 K in Fig.5c is slightly colder than the minimum To ( ~ 110 K)observed in the aforementioned aircraft field measuremerits over deep convection. It should be noted thatJULY 1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 933in the deep convections, the aircraft data viewing at45 - are generally warmer and less fluctuating comparedto the model simulation at nadir angle (Yeh et al.1990b). At 86 GHz, ice scattering dominates and almost theentire squall line system is covered by temperaturedepressions from the clear-sky background To of 250K, with the broad Tb minima associated with rain ratemaxima. Along the edge of the large system, and forthe isolated, weak convective feature in the upper leftcomer, a T0 increase is noted, indicating a near totalabsence of precipitation-sized ice in these areas. Thistype of feature, with a small increase in 86-GHz Tofollowed by a sharp decrease as the convection deepensand ice becomes significant, has been noted in aircraftobservations (Hakkarinen and Adler 1988; Adler andHakkarinen 1990).200.160.t 20.t 00. 80. 80. O.10OHzAVG RAIN INTENSITY (MM/I-IR)c. $catterplots at time 210 min The scatterplots of To at 10, 19, 37, and 86 GHzvenus RI, vertically integrated total liquid water (TLW;including rain water and cloud water), and total icecontent (TIC; including graupel, snow, and cloud ice)at time 210 min are shown in Figs. 6-9, respectively.Results from a total of 4096 (64 x 64) grid points areplotted in each diagram. From these diagrams the general relations between To and key microphysical parameters at the mature stage of the simulated precipitation system emerge, along with clear indications ofthe complexity of those relations when viewed at ahorizontal resolution of 1.5 km. At 10 GHz, the T0's are shown to be well correlatedwith the RI (Fig. 6a), with saturation of the brightnesstemperatures at 270 K occurring at approximately 40mm h-~. The To-rain rate relation is nearly linear inthe 0-15 mm h-~ range at 10 GHz. As expected, theTLW is also strongly related to the To at I0 GHz, whilethe TIC is not (Fig. 6c). The datapoints at low rainrates in Fig. 6a have an interesting distribution, witha concentration of points with a distinct lower edgeand scatter of points at higher To. This skewed distribution of To (at a constant rain rate) is related to thequantity of cloud water at each grid point. Points withonly a small amount of cloud water are located alongthe bottom edge, where the rain water is very closelytied to the rain rate. In locations where cloud water ismore abundant, it adds to the To through the emissionprocess but does not add to the rain rate. In Fig. 6bthe same effect is evident, except the scatter goes to theright side of the line because the cloud water is addingto both the To and the integrated water, but with asmaller impact on the microwave radiance than theprecipitation water. At 19 GHz (Figs. 7a,b), the increase in To from thebackground To ( 160 K) for small rain rates and watercontents is more rapid than that at 10 GHz and alsodisplays the same effect of the cloud water variations ~500. i i i i 1 280. ~ - ' ~=~k. ! ~r..~.- .-f .- :.' 2~0o ~..I'~ '~ ' 2%O.~ ,~2~. ~ 200. too. 1 ~o. t~. 120.m~ t~.~ so.~ ~. ~o. ~) 20. O. I I I I O. 10. 20. ~. ~. IN~G~TED WATER ~G/SQ.M)300.2~0.200.180.120. 80. 80. O.10. 20. 30. =%0.INTEGRATED ICE (KG/SQ.M) I~G. 6. The scatterplots of horizontal brightness temperatures (To)at 10 GHz versus (a) rain intensity, (b) integrated liquid water, and(c) integrated ice content.934 JOURNAL OF APPLIED METEOROLOGY -OLUME30220.200.160. 80. $0. O. (a) 19GHzO. tO. 20. 30. 40. ~0. 80. 70. 80. 90. 100. EAIN INTENSITY (MM/I-IR)~00.260.200.180.140.t 20. 20. O.INTEGRATED WATER (KG/SQ.M)120.80.60.40- (c) O. tO. 20. 30. 40. INTEGRATED ICE (KG/SQ.M) FIG. 7. Same as Fig. 6, except for To at 19 GHz.SO.seen at that lower frequency. Above 10 mm h-l, asshown in Fig. 7a, the scatter of points increases andthe T0's start to decrease with increasing rain rate. Thisis due to the effect of ice in the cloud as can be seenin Hg. 7c, which shows a strong correlation betweenthe integrated ice content and Tb for the larger ice values. Previous calculations at 18 GHz by Wu andWeinman (1984) show a peak To at 8 mm h-~ and adecrease in T0 at a higher rain rate, but not as sharp adecrease as shown in Fig. 7a. For example, at 48 mmh-~, their calculated To is 228 K compared to 220 Kin this calculation. Their results at 18; and 37 GHz arealso significantly warmer than the previously mentioned aircraft observations. A comparison of Figs. 6cand 7c emphasizes the sharp change in the ice scatteringeffect between 10 and 19 GHz. At 37 GHz (Fig. 8a) the effect of ice is even moredominant in the relations, with the increase in To dueto water emission limited to the 0-7 mm h-~ range(Fig. 8b). At higher rain rates there is significant scatter,but the fitted curve shows a ~harp decrease, clearly tiedto tlhe ice content (see Fig. 8c). The sharp increase inTo tbr low rain rates is followed by the decrease in T0'sdue to the ice producing a highly nonlinear To-rainrate relation. In Fig. 8c, at values of integrated icegreater than 5 kg m-2, the calculated T0's show a packing at a low threshold and a looser scatter toward higherT0's. In a following section, this distribution will berelated to the relative abundance of cloud water. Figures 9a-c show that at 86 GHz 'the scattering dueto ice dominates, although a close examination of theTo versus integrated water (Fig. 9b) indicates a clusterof points with a very rapid increase of To from clearsky conditions at 245 to 280 K with only a small increase in liquid water. The associated features wereevident in Fig. 4d. In Fig. 9a there is large scatter, butthere is obviously a relation betwee:n the 86-GHz Tband[ rain rate. This is an indirect relation with the Tostrongly related to the ice content (Fig. 9c) and therain rate negatively correlated with the ice content. TheT0's can be lower than 60 K when TIC is greater than20 ]kg m-2. The scatter of points at 86 GHz in Fig. 9cis similar to that at 37 GHz with a packing along thelower edge.5. iEffect of spatial averaging on To-rain relations The previous section discussed relations betweenbrightness temperatures at various frequencies and micro]physical parameters, including rain rate, with thesimulated observations at the full horizontal resolutionof the cloud model of 1.5 km. As mentioned, thesehigh spatial resolution calculations are suitable forcomparison with aircraft microwave observations.However, from satellite platforms the size limitationson antennas and other practical aspecXs limit the spatialresolution of the observations to approximately 10-50km. This spatial averaging inherent in the satellite obJULY 1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 935220.200.! 80.160.120. 80. 60. 4O. 20. O.300,28O.140.120. 60. 1I I I I I I I I20. 30. 40. 50. 60. 70. 80. ~0. 100.RAIN INTENSITY (MM/HR)300. i ~ i i i i r i i260. ?e'~..:'~'260. e:? -' ' '-] ':2~0. ~,~ ~: '~2o. ;..i.' ::'. -200. ' ': ~.~'. ,'.: . ' ,~ ~ : . . - . '~.'ic' '-.-'" ..160. ~ ,... *-. ,: ** .. 18o. '.:..'.';-~: ;::..~:'.'. . ' . .'." :J ,.'~:2.~' :..' - -.. . ' .140. . .~..~ ~:r: . ~.:. - . -., .', :,'~ '; -:..: -.' ~2o. .- .- ;.~ ~>,-,,: -...- .100.60. :'i ::7. ~ ..i 60. . %~ - ~ ~ ~0.40' I I * I I I[ O. O. l O. 20. 30. 40. 50. 60. AVG RAIN INTENSITY (MM/HR) 86 ~I I I70. 60. ~0. 100. 10. 20. 30. 40.INTEGRATED WATER (KG/SQ.M)z[.,.,220.200.120. 80. 20. O.INTEGRATED WATER (KG/SQ.M)50.300.260.260.240.220.200.180.180.140.120.100. 80. ~O. 40.20.O. (o) I I I I O. 10. 20. 30. 40. INTEGRATED ICE (KG/SQ.M)lqG. 8. Same as Fig. 6, except for T~ at 37 GHz.300.200.~40.220.200. 80.20.(~)INTEGRATED ICE (KG/SQ.M)lqG. 9. Same as Fig. 6, except for T~ at 86 GHz.936 JOURNAL OF APPLIED METEOROLOGY VOLUME30servations can have a significant impact on the To-rainrate relations because of the nonlinearity of those relations (Short and North 1990). The cloud modelradiative model combination used in this study, withits 96 x 96 km2 horizontal domain, can be used tounderstand the effects of spatial averaging and to simulate current and future satellite obse~rvations. In this study, we average the cloud model simulationresults at 210 min over 6 x 6, 12 x 12, and 24 x 24km2 areas. Four regression curves representing therain rate relations at four different resolutions ( 1.5, 6,12, and 24 km) are shown in Figs. 10a-d, correspondingto the frequencies at 10, 19, 37, and 86 GHz, respectively. The computed points for 12-km resolution arealso shown in each diagram by the black points. InTable 1, the coefficients of polynomials representingthe regression curves at each frequency for various spatial resolutions are depicted. These coefficients are presented to document the derived curve so that the degreeof nonlinearity can be judged. The degree of the polynomial selected to represent the regression is based onthe criterion that the next higher degree of polynomialwould not improve the correlation coefficient by morethan 0.01. The first coefficient is the intercept of theregression curve and the second coefficient is the slope.The absolute value of the second coefficient decreasesin each case with increasing spatial averaging, indicating a shallower or weaker slope for coarser resolutionsat relatively low rain rates. The spatial averaging alsoproduces increasing correlation coefficients (Table 1 )and reduced scatter (compare Figs. 6--9 with Fig. 10),indicating that the complexity of the relations evidentat the high spatial resolution is being smoothed overby the area averaging. This is especially evident at thefrequencies and rain rates where ice in the upper partof the cloud is a connecting link between the To andthe rain rate. At 10 GHz, all the regression curves show a gradualincrease of the To versus RI, indicating the scatteringby ice particles has little effect on the upwelling radiation. The regression curves for area averaging do notextend to high RI ('>40 mm h-t) due to the averagingprocess reducing the maximum rain rate. As the averaging area becomes larger there is decrease in theslope of the To-rain rate relation such that the rainrate associated with a To of 200 K changes from 10 to3002502001501005030025020015010050/ Over water, ~'/?'/ 1.5 km 6 km 12 km(a) 10 GHz ............... 24 km 10 20 30 40 50 300 , 250 ' 20O 150 100 5060 300 250 200 150 100 50(b) 19 GHz ' ' ' 'o'' 10 30 4 50 (c) 37 GHz I I - I - I I '0 10 20 30 40 50 60 - -0 60 5% 60 ~ee x. ~"4 ...... e'~'~. . ........ (d) 86 GHz - I I ' / I '0 10 20 30 40 RAIN INTENSITY (MM/HR)I~G. 10. The regression plots of Tb versus rain intensity over water background at the time step of 210 min for different spatial area averaging ( 1.5, 6, 12, and 24 km). The scattered dots are the data of 12 x 12 km: resolution.JULY1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 937TABLE 1. The coefficients of regression relations between brightness temperatures and rain intensity R at various frequencies for full (1.5 km), 6-, 12-, and 24-kin spatial resolutions over water. The relations are based on the cloud model simulation at 2 l0 rain.Resolution Correlation(km) Constant R R2 R3 R4 R5 coefficient10 GHz1.5 1.190(+2) 8.707 - 1.618(- I) 9.563(-4) 0.9966 1.187(+2) 7.036 -9.036(-2) 0.99612 1.187(+2) 6.394 -8.102(-2) 0.99624 1.187(+2) 5.416 -4.593(-2) 0.999 19 GHz1.5 1.671(+2) t.448(+1) -6.560(-1) 8.103(-3) 0.9736 1.666(+2) 1.005(+1) -3.690 3.718(-3) 0.97612 1.667(+2) 8.480 -3.318(-1) 3.996(-3) 0.97824 1.664(+2) 5.216 -9.226(-2) 0.991 37 GHz1.5 1.799(+2) 3.111(+1) -4.181 2.042(-1) -4.272(-3) 3.228(-5) 0.7276 1.791(+2) 1.845(+1) -1.844 6.558(-2) -9.782(-4) 5.045(-6) 0.86012 1.786(+2) 1.658(+1) -1.176 6.122(-2) -7.412(-4) 0.87624 1.788(+2) 3.627 - 1.157 0.882 86 GHz1.5 2.502(+2) -7.485 1.121(-1) 0.8336 2.506(+2) -5.431 4.537(-2) 0.91412 2.508(+2) -4.336 0.95024 2.494(+2) -3.859 0.97118 mm h-l when going from the high resolution (1.5km) to 24-km resolution. The 24-km spatial resolutionshows an almost linear relationship between RI andTo (Fig. 10a), contrasting with a sharper increase ofTo versus RI for 1.5-, 6-, and 12-km spatial resolutions.At 19 GHz, the hump appearing in the regression curvefor 1.5-km resolution gradually disappears as the spatialresolution degrades, and the double-valued relationgives way to a nearly linear, univalued one. As previously discussed, the correlation between RIand To at 37 GHz for full ( 1.5 km) resolution is ratherlow. The correlation for the 6-km area averaging showsa significant increase (see Table 1 ) and the relativelysharp peak at 5 mm h-1 becomes broader as the areaaveraging goes to 12 km. For the coarsest resolution,the T0's at 37 GHz are rather insensitive to the variationof RI. This is because large area averaging often smearsout the detailed characteristics of the storm structure,and the scattering effect from frozen particles is oftenoffset due to the thermal emission by liquid phase hydrometeors. At 86 GHz, the ice scattering effect is predominantfor RI > 2 mm h-1. All the regression curves clearlyshow an inverse relationship between RI and To's (Fig.9a). The regression curves for 6 km and larger areaaveraging are almost linear. Although the slopes fordifferent resolutions are fairly close to each other, thedegree of correlation improves noticeably for thecoarser resolution. Thus, although at high resolutionthe relation between To and rain rate at 86 GHz has ahigh degree of scatter (see Fig. 9), the area averagingeliminates much of the original scatter, which is dueto ice being the indirect link between rain and To, andalso due to the complex structure of the convectionwhen viewed at high spatial resolutions. The 12-kmaverages are close to the resolution of the observationsfrom the SSM/I satellite instrument, and similar areaaveraged model results have been used to derive a rainalgorithm that was then applied to the satellite datawith reasonable results (Adler et al. 1989).6. The effect of cloud water on Tb relations in the ma ture system This section concentrates on the effect of variationsin cloud water content on To relations at one time (210min) during the evolution of the simulated convectivesystem. As discussed in section 4, at low rain rates Figs.6a and 7a displayed an interesting pattern of points inthe 10- and 19-GHz To-rain rate relations. These patterns are related to the amount of cloud water present,as can be seen in Figs. 1 l a,b, which are blowups ofportions of Figs. 6a and 7a, with the points replacedby characters designating the fraction of total water inthe column that is cloud water. Figure 11 c shows thesame results for 37 GHz, where the cloud-water effect938 JOURNAL OF APPLIED METEOROLOGY VOLUME30Z[ 0% < - < 10%10% < + < 30%30% < ~ < 60%60% < X < 100% xx .?';:c-' X .~X~t~. *;"18o. : ',,%S ?160. L X~ ~-' x ~ ~.'~' ~ ~ I1~, '~~120.1~. I I I I O. ~. 4. ft. ~. ~0. 1~.(a) GHz300.280.'260.2%0.220.200.t 80.] 80.140.120.100.I I I I 14. 18. 18. 20. AVG RAIN INTENSITY (MM/HR) ......( 'b) ' ' 19 GHz x x ' ~%':~--~?"' ' ' '"+ '~ ++' '%~xxx~x -~.'- . . ' -' . - I I I I I I I I o. 2. 4. ~. 8. 1o. 12. 14. 18. AVG RAIN INTENSITY (MM/HR)300. I ...... (') ' , c 37 OHz280. r x~?,~. ~: ~... . I~~- 5%'~ ~ ~ %*'.~o. ~%~..,.~': +.~ ~''~ . '' ' ~~~2~ ;' ~~" '- : -.2~0. .&'' + ~'.' '* ~*" * ~ * .~* .,x. .. ~ ~,, ~ ' * ' x. ~ ' *~ .. ~ .- ~ '.+e~o. .. -:..~'~'C- % '+'-.,~ ~ ~ - ~, ~.~'200. - ' *~ * '+ ~ - ~. -. ~' ' ~ -"+ ..180. ~ x160.140.120.100. I O. ~.I18. 20. * . s- I I I I ' I I I I ,% $. 8. 1o. 12. 14. 15. 1~. 20.AVG RAIN INTENSITY (MM/HR) FIG. 11. Distribution of cloud water to total liquid-water ratio inthe To-rain intensity scatterplot at (a) 10 GHz, (b) 19 GHz, and (c)37 GHz, based on 210-min simulation time.can now be seen with the rain rate scale expanded. Ascan be seen in the diagrams, over the range of 0-20mm h-' at 10 GHz, 0-10 mm h-~ at 19 GHz, and 04 mm h-~ at 37 GHz, the concentration of points alongthe lower edge of the scatter is associated mainly withlocations where cloud water is essentially absent (valuesof 0%-10% of cloud water to total water ratio). Thedifferent symbols for different cloud-water ratios clearlyshow that the cloud-water effect is dominant in producing the scatter from what would be present withprecipitation water alone. At 10 GHz, the deviationsare up to 30 K with integrated cloud-water ratio > 60%.At the rain/no rain boundary, there is an approximate15 K maximum deviation. Therefore, even at 10 GHzthe variation of cloud water must be Udcen into accountin rain retrievals. At 19 GHz the effbct is even morepronounced, with large (>60%) cloud-water ratio associated with 40 K deviations and nearly that magnitude evident at zero rain rate. At 37 GHz T~'s increaseby 60 K near zero rain rate. Another interesting feature can be seen in Fig. 1 lbat 19 GHz, in the rain rate range of 10-20 mm h-~.Here we see the beginning of the effect of scatteringdue to ice producing reductions in 7;. The scatter inTb values in this rain rate range is, however, related tothe amount of cloud water. The locations of low Tb(<250 K) and rain rate 10-20 mm h-'; have very smallcloud-water content, whereas the higher T~ values havehigher cloud-water amounts. The same effect is evidentat 37 GHz (Fig. 1 lc) at rain rates above 4 mm h-~.The cloud water, which in the model can coexist at thesame altitudes as the ice, can mask the scattering effectof the ice when collocated with it. In the absence ofcloud water the ice produces relatively low T~ values;however, significant cloud water (at the altitude of theice) absorbs and re-emits to produce the higher To. The effect of cloud water at 37 GHz and also at 86GHz can be seen in Figs. 12a,b. Here the plots of Tbversus integrated ice content from Figs. 8c and 9c arerepeated with the characters plotted being a functionof integrated cloud-water content. The points plottedas dots have negligible cloud water and form the lowerboundary of the scatter of points, indicating the lowerTb limit of the effect of the ice scattering. This is especially true at 37 GHz (Fig. 12a). For points at approximately the same ice content, the Tb is correlatedwith the cloud-water content. This relation is due tothe masking effect of the cloud water when it coexistswith the ice, as mentioned earlier. The points showingthe effect of the cloud water are associated with activeupdrafts producing cloud water both above and belowthe freezing level and advecfing it upwards in conjunction with significant ice. For dissipating convectionor stratiform areas of the system where the updraftsare weaker, the condensation rate decreases and cloudwater is rapidly converted to cloud ice, so that little orno cloud water is formed. From Figs. 11 and 12 it is evident that at this oneJULY 1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 939ZE-,300.260.260.220.200.! 80.! 20. 80. 60. O.- <_ ~ (kg~g2+_<3.<_sx ~42o. to. 20.(a) 37 GHz300.280.260.2.0.220.200.180.1 GO.140.120.1 OOo80.$0.40,20, O. O.50. (b) 86 GHz ! [ I t l O. 20. 30. 40, 50. INTEGRATED ICE (KG/SQ.M) FIG. 12. Distribution of integrated cloud water (kg m-e) in theTo-integrated ice scatterplot at (a) 37 GHz and (b) 86 GHz, basedon 210-min simulation time.time in the life cycle of this modeled convective systemthere are important variations in relationships amongthe pertinent variables related to the amount or relativeamount of cloud water. Since the distribution of cloudwater is in turn related to updraft intensity, it is alsorelated to the convective life cycle stage of convectiveelements or areas much smaller than the squall linesystem as a whole. Figure 13 displays maps of the integrated rain water, cloud water, and ice. The moststriking feature is in the cloud-water distribution (Fig.13b), where a distinct absence of cloud water is apparent in the region denoted by "A" in the diagram.As indicated in Fig. 1, the evolution of this squall lineactually involves the development and movement of90756O45301590756O~ 453O15 -2 Ja) Integrated rain water (kg m )15 30 45 60 75 90 =) Integrated cloud water (kg n=),,I ........ I ......... I ......... I ......... I ......... I,,15 30 45 60 75 909O6O453O15(c) Total integrated ice (kg m-2)........ I ........ [ ......... I ......... I ......... ......... ,: ~S 30 45 e0 75 90 x(km) FIG. 13. Horizontal contour map of (a) integrated rain water (2kg m-: interval), (b) integrated cloud water (0.5 kg m-2 interval),and (c) total ice content (2 kg m-2 interval) at 210-min simulationtime.940 JOURNAL OF APPLIED METEOROLOGY VOLUME30two convective centers moving northwestward andsouthwestward (where north is at the top of the diagrams) from near the grid center. Other, weaker convective elements develop to the rear of these two maincenters. Between these two convectiw~ centers a regionof mostly stratiform precipitation dewelops (region A).Although this structure is not consistent with the classical picture ofa stratiform rain area taailing the intenseconvective region of the leading edge of a squall line,it is a plausible and realistic situation. It is from regionA that most of the points plotted as dots (small valuesof cloud water) from Figs. 11 and 12 are found. The vertical structure of area A compared to thesurrounding convection can be seen in~ Fig. 14; a northsouth cross section at x = 28.5 km. The cross sectionsas shown in Figs. 14a-d are vertical wind velocity, rainwater, cloud water, and total ice content, respectively.The accompanying Tb calculations can be seen in Fig.15. Area A in the cross sections shows a number ofcharacteristics of anvil stratiform regions. There is analmost total absence of cloud water (Fig. 14c), as wasevident in Fig. 13b. The vertical velocity field (Fig.14a) in that region has a broad area of weak downdraft,overlain by an area of weak updraft, accompanied bya minimum amount of cloud water (Fig. 14c) associated with the ascent. There is significant ice in areaA, but substantially less than in the adjoining convective cores; the 1.5 g m-3 contour reaches a height ofonly 8 km as compared to those much higher in thecores. The rain-water field (Fig. 14b) in the stratiformregion has a relatively uniform horizontal appearance,as compared to the adjacent convective areas, and agradual decrease of rain-water content below 3 km,indicating low-level evaporation. The brightness temperature fields (Fig. 15 ) show no dramatic differencebetween the convective areas between 25 and 45 kmand the stratiform region. Closer inspection indicatessomewhat lower Tb's at 37 and 86 GHz in the stratiformregion. This difference is due to significant ice in bothregions and the lack of cloud water in the stratiformarea. Thus it is clear that in crucial relations between microphysical quantities (including rain rate) and theirassociated brightness temperatures, the presence ofcloud water plays a secondary (to rain water and ice)but important role, and that this role is related to localupdraft dynamics and the presence of convective orstratiform structures in the rain systen~. This may present potential problems in terms of rainfall retrieval,but it also points to the potential of rain structure retrievals, such as being investigated by Kummerow etal. (1990) and Kummerow (1990) with aircraft andsatellite data.7. Brightness temperature-rain rate relations as func tion of system life cycle stage Brightness temperatures were calculated from thecloud model output at each of the five times for whichFig. 1 shows the rain rate field. In t]his section we examine the evolution of the To-rain rate relations asthe convective system evolves from a small ensembleof convective elements through a mature stage and toward dissipation. Although the small[ domain does notpermit the evolution of a trailing stratiform region,stratiform areas do develop, and the statistics presentedhere should reflect what would be present in similarsized, and larger scale, systems in nature. Figures 16, 17, 18, and 19 show the To-rain ratescatter plots at each of the five times for each of thefour frequencies. In each of the panels the curve shownis the fitted curve for the To-rain rate relation at time210 min for that particular frequency. In this way thescatter plot for a particular time can be compared tothe statistics for the mature stage (210 min), whichwas discussed in detail in the previous sections. At 10 GHz (Fig. 16 ) the fitted curve from time 210min follows the concentration of points along the loweredge of the scatter of points at that time (Fig. 16d).These points along the lower edge have been determined to be from locations in the stratiform region,which has been shown to be an area with little cloudwater. When that fitted curve from time 210 min iscompared to the scatter of points at 126 (Fig. 16a) and138 min (Fig. 16b), the data points at these early stagesof the convective system tend to f,'dl on the high Toside of the curve in the rain rate range of 5-20mm h-~. At 19 GHz the evolution of the cloud-water effectat rain rates less than 10 mm h-~ (Fig. 17) is evenmore evident. For the early times almost all the pointslie to the left or above of the curve: (from 210 min),as at 10 GHz. As the system matures,, the concentrationof points with small cloud water values extends towardhigher To and higher rain rates. It is clear that the variation in the convective system from an early stage,dominated by convective structures, to a later stage,where a large fraction of the area is covered by stratiform precipitation, affects the distribution of cloudwater and, therefore, the To-rain rate relation for thelow rain rates. These significant differences betweenthe To-rain rate relations for the early, immature timesas compared to the later, mature stage are due to theeffect of the cloud water increasing the total emission,and therefore, the To, without increasing the rain rate.This cloud-water effect is more pronounced at the earlytimes because the convective system is dominated byactive convective cells with strong updrafts, causinghigh rates of condensation and significant cloud water.As the system matures, areas of stratiform rain withlittle cloud water evolve,and the To--rain rate relationsmodify to those of a mature system with a mixture ofconvective and stratiform rain. Retrieval schemes,therefore, must take this into account, most likely byusing a multifrequency approach and solving for thecloud water in addition to the precipitation. For rain rates greater than 30 mm h-~ at 19 GHzJULY I991 ADLER, YEH, PRASAD, TAO AND SIMPSON 941HEIGHT(KM)ooHEIGHT(KM)oo0 0 0 0 0 0 0 0 O0 ~.)0 0 0 0 0 0 0 0 O~r~. 0O O O C:D O O OOCO ~t~ ~O ~D ['- ao~ ~ ~q 0 CO ~0~-4 ~ ~ ~-~0 0 0 0 0 0 ~DO ~D0 0 0 0 0 0 0 UO ~z~~O ~ ~0 ~D ~'- CD (~ O~ U] (8~).~UaSS,~Ud942 JOURNAL OF APPLIED METEOROLOGY VOLUME30300.280.280.240.220.200.180.180.140.120.100. 80.500.280.260.2*0.220.200.180.160,140.120.100. 80. GO.500.280.260.240.220.200.180.160,140.120,100. 80. 60,500,280.260.240.220.200.180.180. 140. 120. I00. 80. 80. 180. 160. 1~0. 120. 100. 80. 60. 40. 20. O.X - 28.5 km (a) 10 GHz(b) 19 GHz(c) 37 GHz(d) 86 GHz30 45A 60 7515. Vertical cross section of brightness temperatures for x = 28.5 km at (a) 10, (b) 19, (c) 37, (d) 86 GHz, and (e) rain intensity.JULY 1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 94380.10 GHz(iO 126 min200.180.120.tO0. 80. 60. 20. O. (b) 138O. l O.20. :BO.40. 50. 60. 70. 80. ~0. t 00.t 60.80.60.40.20.O.260.220,200.140.120.t 00. 60. 40.(-) 174 rain (e) 234 rninO. 10. ~0. 30. ~0. 50. 60. 70. 80. 90. 100.200.180.140.120. 60. 40. (d) 210 n~O. 10. 20. ~0. 40. 50. ~0. 70. 80. ~0. 100. RAIN INTENSITY (MM/HR) FIG. 16. Scatterplots of Tb at 10 GHz versus rain rate for the timeevolution: (a) 126 rain, (b) 138 min, (c) 174 rain, (d) 210 min, and(c) 234 min. The regression line is plotted based on the data at 210rain.RAIN INTENSITY (MM/HR)944 JOURNAL OF APPLIED METEOROLOGY VOLUME30300.260.260.240.2.20.200.160. 40. 20.19 GHz (a) 126 rainO. tO. 20. 30. 40. .~0. ESO. 70. 80. 90. tO0.240.220.200.160.140.120. 60. 40. 20.(b) 138 minO. tO. 20. 30. 40. 50. 60. 70. 80. go. 100.300. i i i I i i220.200. ' "':''' i"-: '180.tGO.140.120.1oo.80.60.4o.20.o. (c) 174 min s I I I [ I I I IO. tO. 20. 30. 40. 50. ~0. 70. BO. 90. 100.300, i i ~ i i i260, . ~-'~,;~ ':c.'L-. -.:.260. -' '~"~:;'" ': '* "'180.160.140.l~O.100.8~.~0.~0.~0.O. (e) 234 min I I [ I I I I I IO. 10. 20. 30. 40. 50. 60. 70. 80. 90. 10(3.300.280.260.200.180. 80. (d) 210 rainO. tO. 20. 30. 40. ~0. 60. 7-1. 80. 90. 100. RAIN INTENSITY (MM/HR)FIG. 17. Same as Fig. 16, except for 19GHz.RAIN INTENSITY (MM/HR)JULY 1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 945there is another dramatic effect of the system life cyclestage on the To-rain rate relation. In the early stages(126 and 138 min), little precipitation-sized ice hasdeveloped and the relations are a function almost solelyof the liquid water, with high brightness temperaturesover 250 K dominating, even at rain rates above 20mm h-~ (see Figs. 17a,b). As the system matures, icecontents increase and the effect of larger particles becomes apparent. From time 126 min to time 136 min,the maximum integrated ice content increases from 10to 20 kg m-2, and at time 174 min it increases to 45kg m-2. The increased ice (at times 174 min and beyond) produces a lowering of the To at moderate andhigh rain rates, thus drastically changing the To-rainrate relation from that at the early times. The lowest19-GHz T0's due to ice scattering (approximately 180K) occur at 174 and 210 min. At time 234 min theconvective system has entered a decaying stage, withweakening updrafts and lower integrated ice contentsand a resulting increase in minimum To at 19 GHz toabout 200 K. The variability of the ice and the varyingeffect of coexisting cloud water on the To, as discussedin section 4, also increases the scatter at the later times,as compared to early in the evolution, when the emission process dominates. Little, if any, effect of the timevariation of ice can be detected at 10 GHz (Fig. 16). The evolution of the ice affects the higher frequencies(37 and 86 GHz) more rapidly due to greater sensitivityto smaller particles and, therefore, to smaller ice concentrations. At 37 GHz (Fig. 18) there is already anoticeable difference between times 126 and 138 min,with the later time showing the greater effect of the icewith lower T0's at rain rates above 10 mm h-~ and alarger scatter of T0's at those rain rates. Again the minimum T0's occur at times 174 and 210 min with aslight warming in the decaying stage (234 min). A verysimilar pattern is evident at 86 GHz (Fig. 19) with amore dramatic shift between the first two times. This section has shown that, within the context ofthe model environment, the relation between the upwelling radiance at the top of the cloud and the rainfallat and near the surface is a definite function of the lifecycle stage of the convective system. This effect is evident at low frequencies ( 10 and 19 GHz) and low rainrates through variations in cloud water related to evolution of the system, from a purely convective one toa structure containing both convective and stratiformstructures. At frequencies at and above 19 GHz theevolution of ice in the cloud system produces a sharpchange in the To-rain rate relations in moving froman almost purely emission regime to one where scattering becomes dominant. This shift also produces alarger scatter in the To-rain rate relations at rain ratesabove 10 mm h-~. However, much of the shift in the relations takesplace in the early stages of the system when the systemis relatively small and has a small volume rain rate andover a relatively short time, so that it is not clear howimportant it is to take this effect into account in devising techniques for satellite rain estimation. To partially address this problem we have examined the Tbrain rate relations as a function of life cycle stage forarea-averaged values for 12 x 12 km2 areas. The resultsshown in Fig. 20 have the scatter points for all fivetimes and the fitted curve based on all the points. At10 GHz, Fig. 20a shows no obvious, large differencebetween the times. However, at 19, 37, and 86 GHz(Figs. 20b-d), where the impact of ice is larger, thereare differences between the three later times at rainrates greater than approximately 8 mm h-~. The areaaveraged calculations at time 174 min lie predominantly below the line, still reflecting the largest ice concentration as was noted in the full resolution results.Moving forward in time, the points tend to fall on eitherside of the curve at time 210 min and above it at time234 min. Thus the effect of the variation of ice in theevolution of the cloud system is evident in the areaaveraged results. Figure 21 is the same as Fig. 20, except that the rainrate scale has been restricted to a range of 0-4 mm h-lin order to look for the cloud water effect at low rainrates in the area-averaged calculations. Although thereis a slight indication that the points for the two earlytimes tend to fall above the line, any difference appearsto be slight. This disappearance, or at least weakeningof this effect when area-averaged, is due to the smallfeatures at the early times, which, when averaged withthe cold ocean background, tend to produce a muchsmaller signal. Therefore, from this simulation, thecloud water, life cycle stage effect at low rain rates doesnot seem to be important when considering area-averaged observations at 12-km resolution.8. Land background statistics So far this paper has presented the simulations ofwhat would be observed over an oceanic convectivesystem. The surface background obviously plays animportant role in determining the field of resulting microwave upwelling radiance. Calculations such as thishave already been presented in this paper with a waterbackground and, with its low background emissivity,will have decidedly different results from those with ahigh-emissivity land background. Although the cloudmodel simulation used here was specifically done forconditions over the oceanic GATE region, and a different cloud system would develop in the cloud modelif the experiment were repeated with a land background, here we have performed a relatively simpleexperiment of repeating the microwave radiative calculations with the same identical cloud system, butwith a land background. Thus we can easily see thedifferences produced by just this one factor. This wouldalso provide a set of calculations more directly comparable to the more abundant overland aircraft microwave observations. The calculations were done at one946 JOURiNAL OF APPLIED METEOROLOGY VOLUME30300.280.260.220.200.120.tO0.80.20. O.37 GHz (a) 126 min~0. 60. 70. 80. 90. 100.300.280.260.220.t80.140.t 20. 80. $0. 40. 20. (b) 138 minO. 10. 20. ~0. 40. ~0. 60. 70. 80. 90. 100. l-i .... 2~0o o ~. ~:;~:-~' '7. : "5' ~ . ** * * ~.., '.. 2 ' ~ ~. -. 220. ~'~~~ 2~.~ teO. - :' - '~' ' -' 160.m~ 140.~ 12o. -. ~ ~ - ..~ ~.' =,* ?.~ t~. '- 'Z '~ CO.ffi60.40.20.(c) 174 min300.280.200.180.t 40. 80. $0. 40. 20. (e) 234 rainO. 10. 20. ~0. 40. ~0. I O. 70. 80. 90. 100.300.280.260.240.220.200.180.160.140.120. .100. t I $0- 40, 20, O. (d) 210 min I I I I [ I I I IO. 10. 20. 30. 40. 50. C~O. 7'0. 80. ~0. 100. RAIN INTENSITY (MM/HR)FIG. 18. Same as Fig. 16, except fi)r 37 GHz.RAIN INTENSITY (MM/HR)JULY 1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 947300. ~ i )280. ~ . .i. . .260..::::'~- . .240. ';i" '~220.200.t 80.t 60.[4.0.120.I00.60.60.40.20.O.86 GHz (a) 126 rain I I I I I [ I I IO. tO. 20. 30. 40. 50. 60. 70. 80. 50. tO0.300.280.260.240.220.200. 300. i i i 260. I.,~...:./. 260. "' '~ 240.i'~::.'~. 220. 200. 16o.~. 160. l*O.~e3 120. ~oo. 60. 60.I~1 40.20. .. , - -.. - % .~' .- . .o . . . . o~: o: ' ?; ::--<:: :~.. : (c) 174 min I I I I I ~ I I Io. 10. 20. 30. 40. 50. 60. 70. 80. 90. l(30.80.60.40.20. (e) 234 min O. 10. 20. 30. ~0. 50. 60. 70. 80. 90. 100.160.140.120.60.60. 40. 20. O. (b) 138 minO. 10. 20. 30. 40. 50. 60. 70. 80. 90. tO0. ::: i-:;' -'.' -"~.%% ~-: . ' o.'~. ~, '. -:. ..5. :' '-..'.- ..;,' :. --. -.1 -.. .":E~,: %::- .~'"' - ' - :":~ ~' 7~:-.' '-~ - - ~. .~ -.'~, .~. ~ .o .: o~ - o : . S i'. - . ~ --: . -fi--- -- ~ :..: ~: - .. .% . . . -. : .: . .. . - .-300. [ I - I i280. ~i~"~ "':'~'260, *;~' '' ' "' * ~ ';:' '- ' : ~-2*0. ~ i.:220.200.~60.160.140.120.100.80.60.40.20. (d) 210O. 10. 20. 30. 40. 50. 60. 70. 80. 90. 100.RAIN INTENSITY (MM/HR)FIG. 19. Same as Fig. 16, except for 86 GHz.RAIN INTENSITY (MM/HR)948 JOURNAL OF APPLIED METEOROLOGY VOLUME30LM2502OO150100 026O2402202O0180160140 0 .[.+e J - !-+.,~x eA ~ + - ~26 mi~ ~ -- - 138 min. ~ x 174 min. ~ - 210 min. + 234 min.,(a) 10GHz (12kin x 12kin) 10 20 30 40 + + ++*o(c) 37 GHz 10 20 30260 I'240200180 0~00200100+ 4 - X+ XXX(b) 19 GHz ~ I ~ I , I , 10 20 30+ (d) 86 GHz 0 , I ~ I i I40 0 1 0 20 304O4O RAIN INTENSITY (MM/HR)FIG. 20. Scatterplots of T, venus rain rate for the area averaging ( 12 X 12 km2) at five time steps. The regression line is based on the composite data of the five time steps.time (210 min) with an assumed constant surfaceemissivity of 0.90 and a surface temperature of 291 K.Results of the calculated brightness temperature versusrain intensity are shown in Fig. 22. At 10 GHz (Fig. 22a), the T0's increase from 265K for no-rain areas to 275 K when rain intensity isgreater than 20 mm h-~. Since the land surface emissivity is assumed to be 0.90, the blackbody assumptionof rain and cloud water increases the; T0's because ofthe increase in emissivity, even though the physicaltemperature of the radiating body has decreased fromthat of the surface to the rain- and cloud-water layer.If higher surface emissivity (e.g., 0.95 ) and higher surface temperature had been assumed in the calculations,no increase in To would be evident. The ice scatteringeffect is not obvious at this frequency, although closeexamination does reveal a very slight decrease in Towith increasing rain rate above 20 m.m h-~. The difference between the simulations over land and wateroccurs where the rain intensity is less than 40 mm h-~(see Fig. 6a). While the value of 10 GHz observationsfor rain estimation over ocean are cle.ar, no significantsignal due to rain over land exists. At 19 GHz (Fig. 22b), the T0's decrease with increasing rain intensity. The major differences betweenthose over land and over water are in the lighter rainareas (<15 mm h-l; see Fig. 7a). Figure 23 displaysresults of aircraft observations matched with rain ratesdeduced from ground-based radar data for an intenseconvective case over land studied by Adler et al. (1990).Comparison with aircraft observations at 18 GHz(Fig. 23a) indicates a generally good agreement, withobserved minimum T0's of 195 K and the same general slope and saturation being reached at about 50mm h-~. At 37 GHz (Fig. 22c), the T0's decline with increasing rain intensity more rapidly than those at 19 GHz.This obviously is due to the stronger effect of ice scattering on T0's at 37 GHz than at 19 GHz. The agreement with the aircraft observations is good consideringthe differences in the two cloud systems. The minimumobserved To of approximately 100 K agrees well withthe calculations, although the calculated T0's show asharper rate of decrease. The T0's of the current calculation fall between the aircraft observations and theT0's calculated by a simple model (Wu and Weinman1984), which is based on a tropical sounding profile.As shown in Adler et al. (1990), the Wu and Weinman]ULY I991 ADLER, YEH, PRASAD, TAO AND SIMPSON 949150 130~- ~ a, 138 min.~/: 120 ~/~' x 174 min._,~ - 210 min.210200 f190 eex A .~ i~' 180 ~' ~x+ (a) 10GHz (12km x 12km) + 234min.~ 110 , i , i , I , 160 , I , i , I , 0 I 2 3 4 0 1 2 3 4~..=, ~o~ ., ..... .~ ~o~ . ..;.,. ~~~o~ . . ..~~o .. ~,o~ .~.. ~o~ 200 ; 240 :. 190 ~~,:' ~ 230 z c) 3~GHz, ~ , ~ , ~ , ~ ~ , ~ , ~ 170 210 0 I 2 3 4 0 1 2 3 4RAIN INTENSITY (MM/HR)FIG. 21. Same as Fig. 20, except for the blowup between 0-4 mm h-1.results are warmer than the aircraft observations by asmuch as 45 K when rain intensity is about 30 mm h-~.The current results, however, are warmer than the aircraft data by less than 25 K. At 86 GHz (Fig. 22d), the To-rain rate relationshiphas little difference over land and water except in thelight rain area (<2 mm h-~; see Fig. 9a). The T0's atthis frequency saturate quickly at the upper part of theprecipitation, and therefore the surface properties havelittle impact on the upwelling To's. The model calculations again compare well with the aircraft observations (Fig. 23c). The effect of area averaging on the T0's over land isshown in Fig. 24 and Table 2. The area averaging overland generally has less effect on the To-rain rate relationthan over water background. The To's over land havea more nearly linear decrease with increasing rain rateat high resolution, in strong contrast to the highly nonlinear relations for the over water situation. The primary effect of the area averaging on the land background relations is, therefore, to reduce the scatter, although there is some shift in the slope of the relations,especially at 86 GHz. It is evident from Fig. 24 that37- and 86-GHz satellite observations should have astrong signal related to rain over land, although theconnection between the rain and the To is dependenton the suspended precipitation ice and is therefore sensitive to cloud structure. This indirect link between therain at the bottom of the column and the upwellingradiance is probably the reason there is still significantscatter in these area-averaged relations. The implicationfor rain estimation over land is that the 37- and 86GHz observations have a strong but noisy rain signal.9. Conclusions The cloud model-microwave radiative transfermodel combination has been shown in this paper tobe an important mechanism in the study of the relations among the various microphysical characteristicsof a tropical, oceanic squall line system, including thesurface rain rate and the upwelling radiance at variouspertinent microwave frequencies. The relations wereshown to be complex, especially when viewed at thefull horizontal spatial resolution of the cloud model(1.5 km). Brightness temperature-rain rate relations950 JOURNAL OF APPLIED METEOROLOGY VOLUME30Z300.280.280.240.220.200.180.160.120.tOO. 80. 80. O. Over land (a) 10 GHz I I I ~ I I I I IO. tO. 20. 30. 40. SO. 80. 70. 80. go. 100. 300.- 280. 260. 240. 220. 200. 180. 160. 140. 120. 100. 80. 60. 40. 20. O. I I I I I IO. tO. 20. 30. 40.(b) 19 GHz I I I70. BO. ~0. lO0.300.280.260.240.220.200.180.160.120. 80. 60. 20. O.300.280.260.'240.220.200.180.180.140.120.100. 80. GO. 40. 20. O. (c) 37 GHz (d) 86 GHz I ~ I I ~ I I I I I I I I I I I I IO. 10. 20. 30. 40. 50. ~50. 70. 80. 90. 100. O. tO. 20. 30. 40. ~0. ~::~). 70. 1~0. cJO. I00. RAIN INTENSITY (MM/HR)FIG. 22. Scatterplots of T~ versus rain rate over land at the time 210 min for (a) 10 GHz, (b) 19 GHz, (c) 37 GHz, and (d) 86 GHz.for the various frequencies give the general results asexpected from previous investigators using simple,schematic models, but also point to the variability ~ntroduced by the structure of the raining clouds, especially with regard to the variability of ice in the cloud.Results at 19, 37, and 86 GHz were shown to be significantly affected by ice in the modeled convectivesystem, although the 10-GHz results showed very littleeffect. Spatially averaged T~-rain rate results, made inorder to simulate relations appropriate to satellite observations, show reduced scatter as compared to thehigh-resolution results, but also show changes in slopebecause of the nonlinear characteristics of the highresolution relations. Nonprecipitating cloud water has a significant impact on the To-rain relations. The results at a timeduring the mature phase of the conve(~ve system showthe cloud water variability affecting the brightnesstemperatures in two ways. First, at low rain rates thepresence of significant cloud water produces higher To'sthan are noted in areas with little c, loud water. Thebrightness temperature deviations increase as a directfunction of frequency from 10 to 37 GHz, with magnitudes from 10-60 K. The second effect occurs at 19,37, and 86 GHz at higher rain rates associated withsignificant ice. The ice produces scattering, which inturns lowers the brightness temperature. However, theexistence of supercooled cloud water coexisting withthe ice reduces the effect of the ice by absorbing andreemitting the radiation, thus increasing the upwellingradiance at the top of the cloud. The effect increaseswith increasing frequency with deviations of 80 K atJULY 1991 ADLER, YEH, PRASAD, TAO AND SIMPSON 9513o0.| , ~ , , , , , ~ ~ 300.~)37(~Hz(b280.4E.~. (a) 1 8 GHz 280.260. ~ + Angle' 4 5 260. 0 + , 0z~o. . ~o. ~ + Ano~:4~ - + 220.ZZ0. 180. ++ o + _ + +'"' ,.. ~. 60. 4o. I I I I I I I I I I 4o.0. 10. 20. 30. 40. 50. 60. ?0. 80. 90. 100. 0. 10. 20. 30. 40. 50. 60. 10. 80. 90. t00.RAIN INTENSITY (MM/HR)RAIN INTENSITY (MM/HR)300.280.260.240.220.200.180.160.140.120.80.60.40.I II I I I(c) 90 GHzNadir viewO ++ + + + +++ \ _+ +-++ +~. '+; -+ * '~"~--~:-+.__ + ++*+:T:-$ ,o+-~- -I- + T +' I .I I I I I I I I (d) 181 GHz o Nadir view 280.~,. 260. 240.~1, 220. 200. 180. 180. 1410,~ 120.~ 100.I--I~ 80. 60. 40.++ ++$ + + o + + + + + o oI I I I I I I I I t t I t I I I I 1o. 10. 20. 3o. 40. 50. 60. 70. 80. ~0. I00. o. 10. 2o. 3o. ,m. r,o. so. 'M. ao. so. tee.RAIN INTENSITY (MM/HR)RAIN INTENSITY (MM/HR) FIG. 23. Scatterplots (+) of aircraft observed Tb versus radar-estimated rain rate from flight lines I and 2 combined. Theadditional points (O) are calculations from Wu and Weinman ( 1984): (a) 18 GHz (vertical polarization), (b) 37 GHZ (verticalpolarization), (c) 92 GHz, and (d) 181 GHz.86 GHz. Both of these effects related to cloud waterare in turn related to the variable structure within thecloud system. Areas with active, strong updrafts havesignificant cloud water, whereas anvil stratiform areashave very little. Thus the results indicate that the vertical structure of the cloud, especially the distributionof cloud water, is significant in determining the upwelling radiance. The life cycle stage in the evolution of the convectivesystem was also shown to be important in the relationof rain to the upwelling radiance. Examination of fivetimes during the evolution of the modeled systemshowed that as it developed from a small, convectivecomplex to a mature system, the brightness temperature-rain rate relations changed. Initially the system isdominated by young convective structures with significant cloud water and relatively little ice. Thus theTb's tend to be higher than in the mature stage, becauseat low rain rates the cloud water is adding to emission,and at high rain rates the lack of ice is also producing952 JOURNAL OF APPLIED METEOROLOGY VOLUM-303O0 ~._~ _- ~.~ ..... --. _ 250 2oo Over land ~0 km 100 6 km~ (a) 10 GHz 12 krn ............... 24 kmfiLM . , - , - , , - , - 50 0 10 20 30 40 50i~. 300 ........C~ 250 ""~20015010050 (b) 19 GHz0 10 2O 3O 4O 5060300 ,250;200;150 ~100 ' (C) 37 GHz 50 , , , - ~ - , 0 1 0 20 30 40 503O0250 ' ' rr 'XO, ':....200 '150 ~ ~,~100 ' (d) 86 GHz50 , - , [ , ,0 1 0 20 30 40 506O60 RAIN INTENSITY (MM/HR)FIG. 24. The regression plots of To versu~s rain intensity over land background at 210 rain for different spatial area averaging ( 1.5, 6, 12, and 24 kin). The scattered dots are the data of 12 X 12 km2 resolution.TABLE 2. Same as Table 1, except for over land.Resolution Correlation(km) Constant R R2 R3 coefficient 10 GHz1.5 2.632(+2) 9.506(-1) -1.592(-2) 0.9546 2.632(+2) 8.569(-1) -1.495(-2) 0.98012 2.632(+2) 7.732(-1) -1.441(-2) 0.97324 2.632(+2) 5.931(-1) -7.481(-3) 0.994 19 GHz1.5 2.698(+2) -8.208(-1) -4.311(-3) 0.7666 2.698(+2) -5.677(-1) -1.140(-2) 0.89112 2.697(+2) -4.114(-1) -2.065(-2) 0.93824 2.695(+2) -7.707(-1) 0.962 37 GHz1.5 2.693(+2) -4.992 6.254(-2) 0.8616 2.695(+2) -3.675 2.195(-2) 0.93012 2.697(+2) -3.166 0.96124 2.687(+2) -2.851 0.977 86 GHz1.5 2.780(+2) -1.456(+1) 4.906(-1) 5.314(-3) 0.8926 2.785(+2) -9.641 2.105(-5) 1.820(-3) 0.94312 2.785(+2) -6.906 5.259(-2) 0.97124 2.770(+2) -5.335 0.975higher Tb's. As the system develops, more ice is generated and anvil stratiform regions develop, and therelations take on the appearance of the mature system.At the last time examined, the updrafts in the modeledsystem were somewhat weaker, produced less ice, andtherefore caused slightly higher Tb's at 19 GHz andabove. These results indicate that the life cycle stageof a system should be considered when trying to retrieverain information from passive microwave observations.However, area averaging at the various stages appearedto reduce, but not eliminate this effect. Calculations with a land background substituted forthe ocean underneath the same simulated clouds produced brightness temperatures comparable with aircraftmicrowave observations of a deep convective systemwith a land background. Thus the model combinationused in this paper produces reasonable brightness temperature-rain rate relations and allows the explorationof the complexity of the relations beyond what is available currently from observations. More detailed comparison between model results and observations areneeded as well as sensitivity tests of the models themselves.JULY I991 ADLER, YEH, PRASAD, TAd AND SIMPSON 953 The results of this paper confirm the strong rain signal of the various microwave frequencies, but point tothe limitations of using a single frequency or a limitedrange of frequencies in deriving accurate rain estimations from satellite microwave observations. Cloudwater effects in the emission portion of the spectrum,ice-scattering effects at frequencies as low as 19 GHz,life cycle effects on both the thunderstorm scale andthe scale of the entire mesoscale convective system,and the effect of area-averaging nonlinear relations overthe satellite field of view complicate the rain estimationproblem. However, the observations also contain information about all these effects and provide an opportunity to retrieve new types of information. A multifrequency approach using a wide range of frequencies,such as described by Kummerow et al. (1990), shouldmove us forward toward increasing the accuracy of ourretrieved rain rates and at the same time retrieve information concerning the vertical structure of the hydrometeors, the amount of cloud water, and the lifecycle stage of the precipitating system.REFERENCESAdler, R. F., N. Prasad, W.-K. Tad, H.-Y. M. Yeh, R. A. Mack and J. Simpson, 1988: Microwave observations and modeling of deep convection. Tropical Rainfall Measurements, Theon and Fu gono, Eds., Deepak, 185-191.--, A. J. Negri, N. Pmsad, and W.-K. Tad, 1989: Cloud model based simulations of satellite microwave data and their appli cation to an SSM/I algorithm. Fourth Conf on Satellite Me teorology and Oceanography, San Diego, Amer. Meteor. Soc., J12-J15.--, R. A. Mack, N. Prasad, H.-Y. M. Yeh and I. M. Hakkarinen, 1990: Aimrafi microwave observations and simulations of deep convection from 18-183 GHz. Part I: Observations. J. Atmos. Oceanic Technol., 7, 377-391.Barnes, G. M., and K. Sieckman, 1984: The environment of fast and slow-moving tropical mesoscale convective cloud lines. Mon. Wea. Rev., 112, 1782-1794.Chang, A. T.-C., and T. T. Wilheit, 1979: Remote sensing of at mospheric water vapor, liquid water, and wind speed at the ocean surface by passive microwave techniques from the Nimbus 5 satellite. Radio $ci., 14, 793-802.Hakkarinen, I. M., and R. F. Adler, 1988: Observations of convective precipitation at 92 and 183 GHz: Aircraft results. Meteor. Atmos. Phys., 38, 164-182.Heymsfield, A. J., and A. G. Palmer, 1986: Relationships for deriving thunderstorm anvil mass for CCOPE storm water budget esti mates. J. Climate Appl. Meteor., 25, 691-702.Klemp, J. B., and R. B. Wilhelmson, 1978: The simulation of three dimensional convective storm dynamics. J. Atmos. Sci., 35, 1070-1096.Kummerow, C. D., 1990: Rain and rain system structure from SSM/ I measurements. Preprint, American Meteorology Society Fifth Conf Satellite Meteorology and Oceanography, London, 241 246.--, I. M. Hakkarinen and J. A. Weinman, 1990: Determination of precipitation profiles from airborne passive microwave ra diometric measurements. J. Atmos. Oceanic Technol., 8, 148 158.Lin, Y.-L., R. D. Farley and H. D. Orville, 1983: Bulk parameter ization of the snow field in a cloud model. J. Climate Appl. Meteor., 22, 1065-1092.Marshall, 1. S., and W. M. Palmer, 1948: The distribution of raindrops with size. J. Meteor, 5, 165-166.Mugnai, A., H. J. Cooper, E. A. Smith and G. J. Tripoli, 1990: Sim ulation of microwave brightness temperatures of an evolving hailstorm at SSM/I frequencies. Bull. Amer. Meteor. Soc., 71, 2-13.Nicholls, M. E., and M. J. Weissbluth, 1988: A comparison of two dimensional and quasi-three-dimensional simulations of a tropical squall line. Mon. Wea. Rev., 116, 2437-2452.Ogura, Y., Y.-L. Chen, J. Russell and S.-T. Soong, 1979: On the formation of organized convective systems observed over eastern Atlantic. Mort. Wea. Rev. 107, 426-441.Ray, P. S., 1972: Broadband complex refractive indices of ice and water. Appl. Opt., 11, 1836-1844.Rutledge, S. A., and P. V. Hobbs, 1984: The mesoscale and microscalestructure and organization of clouds and precipitation in midlatitude cyclones. Part XII: A diagnostic modeling study of precipitation development in narrower cold-frontal rainbands. J.Atmos. Sci., 41, 2949-2972.Sadiku, M. N. O., 1985: Radiative index of snow at microwave fre quencies. Appl. Opt., 24, 572-575.Sekhon, R. S., and R. C. Srivastava, 1970: Snow size spectra and radar reflectivity. J. Atmos. Sci., 27, 299-307. , and ,1971: Doppler observations of drop size distributions in a thunderstorm. J. Atmos. Sci., 28, 983-994.Simpson, J., R. F. Adler and G. R. North, 1988: On some aspects of a proposed tropical rainfall measuring mission (TRMM). Bull. Amer. Meteor. Soc., 69, 278-296.Soong, S.-T, and Y. Ogura, 1980: Response of trade-wind cumuli to large-scale processes. J. Atmos. Sci., 37, 2035-2050.--., and W.-K. Tad, 1980: Response of deep tropical clouds to mesoscale processes. J. Atmos. Sci., 37, 2016-2034.Stephens, G. L., 1986: Radiative transfer through arbitrarily shaped optical media. Part I: A general method of solution. J. Atmos. Sci., 45, 1818-1836.Tad, W.-K., and S.-T. Soong, 1986: The study of the response of deep tropical clouds to mesoscale processes: Three-dimensional numerical experiments. J. Atmos. Sci., 43, 2653-2676. , and J. Simpson, 1989: Modeling study of a tropical squall-type convective line. J. Atmos. Sci., 46, 177-202.Ulbrich, C. W., 1983: Natural variations in the analytical form of the raindrop size distribution. J. Climate Appl. Meteor., 22, 1764-1775.Warren, S. G., 1984: Optical constants of ice from the ultraviolet to the microwave. Appl. Opt., 23, 1206-1225.Wilheit, T. T., A. T. C. Chang, J. L. King, E. B. Rodgers, R. A. Nieman, B. M. Krupp, A. A. Milman, J. S. Stratigos and H. Siddalingaiah, 1982: Microwave radiometric observations near 19.35, 92, and 183 GHz of precipitation in tropical storm Cora. J. Appl. Meteor., 21, 1137-1145.Willis, P. T., 1984: Functional fits to some observed drop size dis tributions and parameterizations of rain. J. Atmos. Sci., 41, 1648-1661.Wu, R., and J. A. Weinman, 1984: Microwave radiances from pre cipitating clouds containing aspherical ice, combined phase, and liquid hydrometeors. J. Geophys. Res., 89, 7170-7178.Yeh, H.-Y. M., N. Prasad and R. F. Adler, 1990a: Tabulation of Mie properties for an effective microwave radiative model. Meteor. Atmos. Phys., 42, 105-112. --, R. A. Mack and R. F. Adler, 1990b: Aimraft microwave observations and simulations of deep convection from 18-183 GHz. Part II: Model results. J. Atmos. Oceanic Technol., 7, 392-410.Zerull, R. H., 1976: Scattering measurements of dielectric and ab sorbing nonspherical particles. Beitr. Phys. Atmos., 49, 166 188.