A Texture-Polarization Method for Estimating Convective

SEPTEMBER 2001 1577O L S O N E T A L .

q 2001 American Meteorological Society

A Texture-Polarization Method for Estimating Convective–Stratiform PrecipitationArea Coverage from Passive Microwave Radiometer Data

WILLIAM S. OLSON

Joint Center for Earth Systems Technology, University of Maryland, Baltimore County, Baltimore, and NASA Goddard Space FlightCenter, Greenbelt, Maryland

YE HONG

The Aerospace Corporation, Los Angeles, California

CHRISTIAN D. KUMMEROW

Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado

JOSEPH TURK

Naval Research Laboratory, Monterey, California

(Manuscript received 28 September 2000, in final form 19 March 2001)

ABSTRACT

Observational and modeling studies have revealed the relationships between convective–stratiform rain pro-portion and the vertical distributions of vertical motion, latent heating, and moistening in mesoscale convectivesystems. Therefore, remote sensing techniques that can be used to quantify the area coverage of convective orstratiform rainfall could provide useful information regarding the dynamic and thermodynamic processes inthese systems. In the current study, two methods for deducing the area coverage of convective precipitationfrom satellite passive microwave radiometer measurements are combined to yield an improved method. Ifsufficient microwave scattering by ice-phase precipitation is detected, the method relies mainly on the degreeof polarization in oblique-view, 85.5-GHz radiances to estimate the fraction of the radiometer footprint coveredby convection. In situations where ice scattering is minimal, the method draws mostly on texture informationin radiometer imagery at lower microwave frequencies to estimate the convective area fraction.

Based upon observations of 10 organized convective systems over ocean and nine systems over land, in-stantaneous, 0.58-resolution estimates of convective area fraction from the Tropical Rainfall Measuring Mission(TRMM) Microwave Imager (TMI) are compared with nearly coincident estimates from the TRMM precipitationradar (PR). TMI convective area fraction estimates are low-biased relative to PR estimates, with TMI–PRcorrelation coefficients of 0.78 and 0.84 over ocean and land surfaces, respectively. TMI monthly averageconvective area percentages in the Tropics and subtropics from February 1998 are greatest along the intertropicalconvergence zone and in the continental regions of the Southern (summer) Hemisphere. Although convectivearea percentages from the TMI are systematically lower than those derived from the PR, the monthly patternsof convective coverage are similar. Systematic differences in TMI and PR convective area percentages do notshow any clear correlation or anticorrelation with differences in retrieved rain depths, and so discrepanciesbetween TRMM version-5 TMI- and PR-retrieved rain depths are likely due to other sensor or algorithmicdifferences.

1. Introduction

Understanding the complex interaction of convectivecloud systems and their environment has been a majorobjective of meteorological research for many years.The latent heat release and vertical transports of sensible

Corresponding author address: Dr. William Olson, Joint Centerfor Earth Systems Technology and NASA Goddard Space Flight Cen-ter, Code 912, Greenbelt, MD 20771.E-mail: [email protected]

heat, moisture, and momentum by convective systemshave a strong effect on the large-scale circulations inwhich they are embedded, whereas large-scale radiativeand dynamical processes can change the stability char-acteristics of the atmosphere, thereby enhancing or sup-pressing convective activity. The large-scale flow canalso influence the organization of convection and thenature of the vertical transports by convective systems.

In numerical weather prediction models and generalcirculation models, which currently have grid resolu-

1578 VOLUME 40J O U R N A L O F A P P L I E D M E T E O R O L O G Y

FIG. 1. Polarization differences at 85.5 GHz plotted vs average85.5-GHz radiances over (a) ocean and (b) land surfaces. TMI ob-servations are plotted as points (nonraining areas) and open circles(raining areas). Diamonds represent radiative transfer simulations foratmospheres containing oriented, aspherical liquid and ice-phase pre-cipitation. Dashed lines are approximate curves representing purelystratiform and purely convective precipitation conditions.

tions on the order of 100 km, convective processes arehighly parameterized, and the accuracy of simulationsbased upon these models depends upon an adequaterepresentation of convection and mesoscale effects atsubgrid scale. An explicit description of the mesoscaleorganization of convection in model simulations re-quires relatively high grid resolution; simulated con-vective organization and transports can still be sensitiveto the physical parameterizations employed.

Over the last half-century, several field campaignshave provided data needed for a better understandingof convective systems and their effects. These cam-paigns have focused observations from surface instru-ments, rawinsondes, radar, and aircraft sensors over re-gions spanning areas of about 100 000 km2 and periodsup to several months in order to gather information per-

taining to the microphysics, kinematics, organization,and environmental impact of convective systems. Al-though much has been learned from these campaigns,a more large-scale, long-term perspective can be gainedthrough satellite remote sensing of cloud properties, es-pecially over oceanic regions where long-term moni-toring by other methods is generally unfeasible. Suchobservations could be used to track climatological var-iations in convective organization and transports andprovide a means for validating cloud properties and ef-fects simulated by numerical prediction models.

The capability of satellite passive microwave sensorsto provide quantitative precipitation estimates is nowwell established (see Ebert et al. 1996; Smith et al.1998). Over oceans, passive microwave rain estimatesare possible because there is a fairly direct physicalrelationship between the path-integrated water contentof rain along the sensor line of sight and the upwellingradiances measured by the sensor at frequencies lessthan ;40 GHz. Passive microwave observations can beused to infer other cloud and precipitation propertiessuch as ice-phase precipitation amount or to describethe organization of convective systems. However, theseuses of the data have received much less attention.

Regarding organization, the basic structure of a con-vective system can be described in terms of the pro-portion and distribution of convective and stratiformrainfall within the system (Houze 1989). Previous ob-servational and modeling studies have established therelationships between convective–stratiform rain pro-portion and the vertical distributions of vertical motion,latent heating, and moistening in convective systems(e.g., Houze 1989; Sui et al. 1997; Tao et al. 1993).Therefore, microwave remote sensing techniques thatyield the area coverage of convective or stratiform rain-fall within a sensor footprint may ultimately provideuseful information regarding the dynamic and thermo-dynamic processes in these systems.

In the current study, two methods for estimating thearea coverage of convective precipitation within afootprint of the Tropical Rainfall Measuring Mission(TRMM) Microwave Imager (TMI) are combined tocreate an improved technique that emphasizes thestrengths of both methods. In section 2, the two meth-ods and their merger are described. Applications ofthe combined method to TMI observations of indi-vidual convective systems are presented in section 3,including statistics of intercomparisons with convec-tive area estimates from the TRMM precipitation ra-dar (PR). Monthly estimates of convective area per-centage over the Tropics and subtropics from bothTMI and PR are presented in section 4. A summaryand discussion are included in section 5.

2. Methodsa. Texture-based convective area fraction

It is commonly known (Zipser 1977; Leary andHouze 1979; Houze 1993) that stratiform precipitation


FIG. 2. Imagery of a mesoscale convective system near the Cape Verde Islands in the North Atlantic on 12 Sep 1999. (a), (b) The convectivearea fractions within 85.5-GHz footprints based upon TMI texture and polarization information, respectively. (c) TMI 85.5-GHz imagery.(d) PR-derived convective area fractions at a resolution comparable to the TMI.

regions are associated with relatively weak updrafts anddowndrafts while convective regions are associated withmore vigorous, turbulent updrafts and downdrafts. Ac-cording to mass continuity arguments, a change in ver-tical velocity must be associated with a change in thehorizontal mass field. It is therefore assumed that sub-stantial horizontal gradients of precipitation (and like-wise gradients of microwave radiances) characterizeconvective regions. The texture-based method empiri-cally relates the horizontal variation of microwave ra-diances to the fraction of the TMI footprint area coveredby convective precipitation.

Based on data from the Tropical Ocean and GlobalAtmosphere Coupled Ocean–Atmosphere Response Ex-periment (TOGA COARE), Hong et al. (1999) testedseveral indices, derived from passive microwave radi-

ance measurements, for separating convective and strat-iform rain areas. In that study a convective–stratiformindex (CSI) was developed that combined the local max-imum variation and relative magnitude of radiancesfrom the 19.35-, 37.0-, and 85.5-GHz horizontal polar-ization channels of TMI. Formally,

CSI 5 VM 1 0.5VMe 37h 19h

1 0.25(TB 2 TB ), (1)19h 19h2back

CSI 5 VM 1 (TB 2 TB ), and (2)s 85h 85h2back 85h

CSI 5 (1 2 w )CSI 1 w CSI . (3)s e s s

Here, TByp and TByp-back are the microwave radiance andbackground ‘‘clear-air’’ radiance, respectively, at fre-quency y and polarization p. The variable VMyp is the


local maximum variation of a measured radiance withrespect to its neighbors. At 85.5 GHz, the local maxi-mum variation is defined as,

max (TB 2 TB ), if greater than 085h, j 85hjVM 585h

0, otherwise,

(4)

and at 19.35 and 37.0 GHz, the local maximum var-iation is

max (TB 2 TB ), if greater than 0yp yp,jjVM 5yp

0, otherwise.

(5)

In (4) and (5), the subscript j refers to any of the eightneighboring TMI footprints surrounding the footprintbeing analyzed. The local maximum variation is usedhere because the relatively low resolution of the satellitemicrowave observations may smear emission or scat-tering gradients in any particular direction.

Since convection is generally associated with heavy

precipitation, the relative magnitude of the radiance withrespect to a background radiance is added to the CSI[third term on the right-hand side of (1) and second termon the right-hand side of (2)]. The background radianceis defined as the average of clear-air radiances from theeight neighboring TMI footprints surrounding the foot-print being analyzed. Over ocean, a footprint is clas-sified as clear air if the mean cloud water content belowthe freezing level, retrieved using the algorithm of Kar-stens et al. (1994), is less than 0.06 g m23. Over land,clear-air footprints are identified based upon the screen-ing algorithm described in Adler et al. (1994) and Huff-man et al. (1995). Since the background radiance is anaverage of neighboring clear-air radiances, it has a sta-bilizing effect on the relative magnitude. Therefore, theaddition of the relative magnitude to CSIe and CSIs helpsto temper these indices in situations where the VM arecorrupted by a single bad radiance measurement amongthe neighboring footprints.

The final index, CSI, is a weighted sum of the emis-sion and scattering indices [see (3)]. The weighting fac-tor ws increases with the relative amount of scatteringin the microwave footprint:

0, TB . TB85h 85h2backw 5 (TB 2 TB )/80 K, TB 2 80 K , TB , TB (6)s 85h2back 85h 85h2back 85h 85h2back1, TB , TB 2 80 K. 85h 85h2back

Therefore, the horizontal variation of the 85.5-GHz ice-scattering depression mainly determines CSI when sig-nificant ice is present, whereas the horizontal variationof emission at 19.35 and 37.0 GHz mainly determineCSI when little ice is present.

Hong et al. (1999) demonstrated that as sensor res-olution degrades, the likelihood of observing a mixtureof convective and stratiform rainfall within the sensorfootprint increases. Over 6 km 3 6 km areas, which areabout the size of the TMI’s highest-resolution footprints,the contribution to the total rain flux by mixed regions(here defined as regions where convective rain covers30% to 70% of the total area) was about 30%, based

upon an analysis of TOGA COARE shipboard radardata. The contribution from mixed regions increased toabout 50% for 12 km 3 12 km areas, which are com-parable to the footprints of the highest-resolution Spe-cial Sensor Microwave Imager (SSMI) channels. There-fore, instead of classifying TMI footprints as convectiveor stratiform, these authors related CSI to the fractionof the footprint area covered by convective rainfall(hereinafter, the convective area fraction) by matchingthe cumulative distribution of convective area fractionsderived from the TOGA COARE shipboard radar datato the cumulative distribution of synthesized TMI CSImeasurements. The resulting empirical relationship iswell-approximated by

0, CSI , 30 K22f 5 1.333 3 10 (CSI 2 30 K), 30 K # CSI # 105 K (7)CSI

1, CSI . 105 K.

Readers are referred to Hong et al. (1999) for a moredetailed description of the texture-based convective–stratiform separation method.

b. Polarization-based convective area fraction

An alternative formula for convective area fraction is


suggested by the analyses of SSMI observations bySpencer et al. (1989) and Heymsfield and Fulton(1994a,b). These authors found significant differences,on the order of 5 K or greater, between the verticallyand horizontally polarized 85.5 GHz radiances in strat-iform precipitation regions over land, whereas regionsof strong convection were nearly unpolarized at 85.5GHz. Although the physical basis of these polarizationdifferences has not been verified, the aforementionedauthors hypothesized that aspherical, precipitation-sizedice particles such as snow or aggregates would tend tobecome oriented as they fall through the relatively weakupdrafts or downdrafts of stratiform regions, resultingin preferential scattering in the horizontal polarization.The more vigorous, turbulent updrafts of convective re-gions would cause ice hydrometeors to lose any pre-ferred orientation, leading to similar scattering signa-tures in both polarizations.

Turk and Vivekanandan (1995), Petty and Turk(1996), and Schols et al. (1997) more recently per-formed microwave radiative transfer calculations forclouds of oriented, aspherical ice hydrometeors andfound polarization differences exceeding 5 K at 85 GHz,supporting the earlier hypothesis. Roberti and Kum-merow (1999) obtained similar polarization differencesbased upon Monte Carlo radiative simulations. Theirresults suggest that in addition to ice particle orientation,the relative amounts of asymmetric snow and morespherical graupel in convective and stratiform precipi-tation regions could contribute to the observed polari-zation differences. A greater abundance of oriented,asymmetric snow particles in stratiform regions yieldedpolarization differences greater than 10 K at 85 GHz,while a greater abundance of spherical graupel in con-vective regions produced polarization differences lessthan 5 K.

In Olson et al. (1999) the approximately inverse rela-tionship between 85.5-GHz polarization difference andconvective fraction was utilized to constrain retrievals ofprecipitation and latent heating from SSMI observations.In the current study, a somewhat different analysis of 85.5-GHz polarization data is performed to infer the convectivearea fraction within the TMI footprint.

In Fig. 1, TMI-observed 85.5-GHz polarization differ-ences are plotted versus average 85.5-GHz radiances.These observations are derived from TMI overpasses of10 organized convective systems over ocean (Fig. 1a) andnine systems over land (Fig. 1b), sampled from the firstthree years of the TRMM mission. Organized convectivesystems, such as squall lines and tropical cyclones, areselected here because they generally produce microwavescattering by ice-phase precipitation at 85.5 GHz and areoften characterized by significant proportions of convec-tive and stratiform precipitation. It follows that these sys-tems best illustrate the relationships between microwavepolarization difference and scattering; relationships thatform the foundation of the polarization-based method forestimating convective area fraction. TMI data from all

footprints in the swath segments containing the convectivesystems are plotted in Fig. 1; that is, precipitation-freefootprints have not been filtered.

Overlaid on the TMI observations of Fig. 1 are ra-diative-transfer-model-simulated 85.5-GHz polarizationdifferences and average radiances for atmospheres con-taining layers of rain, cloud, and ice-phase precipitation.The model atmosphere is characterized by tropical pro-files of temperature and water vapor, and a layer ofnonprecipitating cloud liquid water with a water contentof 0.5 g m23 between 1- and 6-km altitude is assumed.Embedded in this atmosphere is a homogeneous rainlayer between the surface and 4 km. The equivalent rainrate of the rain layer is varied in steps from 0 to 50 mmh21. For each rain rate, the thickness of a capping grau-pel layer is varied between 0 and 8 km, and the equiv-alent water content of graupel within the layer is as-sumed to be equal to the rain water content. Raindropsare assumed to be oblate spheroidal, the oblateness in-creasing with equivalent spherical volume diameter.Graupel particles are conical in shape, with a constantdensity of 0.6 g cm23. Both rain and graupel are orientedsuch that the long axes of the particles are parallel tothe earth’s surface. Calculations of the upwelling radi-ances at 53.48 incidence (close to the 52.88 incidenceangle of the TMI) are performed using a polarized mul-tistream radiative transfer method (Evans and Stephens1991). Because the earth’s surface is entirely obscuredby absorbing cloud water in the rain-free model at-mosphere at 85.5 GHz, only overocean radiative cal-culations are considered in the intercomparisons of Fig.1. Details of the radiative modeling can be found inTurk and Vivekenandan (1995), and Petty and Turk(1996).

Note first, in Fig. 1a the relatively large observedpolarization differences, many greater than 20 K, thatcharacterize cloud-free regions over the ocean. Thesepolarization differences are due to the highly polarizedemission from the ocean surface that is only partiallyabsorbed by water vapor in a clear atmosphere. Cloudsin the atmosphere strongly absorb the polarized surfaceemission, and thermal emission from the absorbingcloud droplets raises the observed upwelling radiancesat 85.5 GHz. The transition from cloud-free to cloudyatmospheres creates the nearly vertical branch of plottedpoints corresponding to average 85.5-GHz radiancesgreater than 230 K in Fig. 1a.

A cloud liquid water vertical path exceeding about 1kg m22 renders the cloudy atmosphere almost com-pletely absorbing, and nearly unpolarized blackbodyemission close to the cloud-top temperature at the freez-ing level (273 K) is observed. This limit is confirmedby the radiative transfer model calculations, which in-dicate a maximum average radiance of 272.5 K with a0.1-K polarization difference for an atmosphere con-taining only nonprecipitating cloud with a liquid waterpath of 2.5 kg m22.

In precipitating clouds, weak microwave scattering


FIG. 3. Same as Fig. 2, but for a convective system over the tropical North Atlantic on 1 Oct 1998.

by raindrops and stronger scattering by precipitation-sized ice particles reduce the upwelling cloud-top ra-diance by diverting the upwelling emission from lowerlevels. Note the congregation of observations along anapproximate 458 diagonal line in Fig. 1a, indicating in-creasing 85.5-GHz polarization difference with decreas-ing average 85.5-GHz radiance. These observationsgenerally correspond to stratiform areas in mesoscaleconvective systems. An empirical linear fit to these‘‘purely stratiform’’ observations is shown in the figure.Also in Fig. 1a, the radiative transfer model simulationsincorporating oriented ice hydrometeors exhibit a sim-ilar trend, with polarization differences generally in-creasing with decreasing average radiances. As scatter-ing by ice-phase precipitation becomes very strong, andsimulated average radiances fall below 160 K, the sim-ulated polarization differences level off and then de-

crease. The TMI observations suggest that these mod-eled combinations of very-low-average radiance andlarge polarization difference do not occur naturally, like-ly because the large concentrations of ice-phase precip-itation required can only be supported by strong, con-vective updrafts.

In contrast, radiative transfer simulations based uponatmospheres containing randomly oriented ice particlesyield relatively small polarization differences. Haferman(2000; 2000, personal communication) calculated po-larization differences less than 2 K at 85.5 GHz in ra-diances upwelling from optically thick clouds of pre-cipitating ice. This limiting case is represented by thezero-polarization ‘‘purely convective’’ line in Fig. 1a.If it is assumed that TMI footprints at 85.5 GHz areessentially filled with precipitation but contain differentproportions of convective and stratiform precipitation,


then a combination of the partially polarized purelystratiform model radiances and nearly unpolarized pure-ly convective model radiances within each TMI foot-print could explain the scatter of observed 85.5-GHzaverage radiances and polarization differences that fallbetween these limits. The clustering of observationsnear the purely stratiform model curve is due to thegreater frequency of occurrence of stratiform precipi-tation that also tends to fill the TMI 85.5 GHz footprints.Smaller-scale convective elements occur less frequentlyand may be mixed with stratiform precipitation withinthe sensor’s field of view.

It is evident from Fig. 1b that over land, the polari-zation of 85.5-GHz radiances in rain-free areas is verylow, but the relationship between average radiances andpolarization differences at 85.5 GHz in precipitation re-gions is similar to that observed over ocean.

If it is assumed that TMI 85.5-GHz polarization dif-ferences are essentially zero in purely convective re-gions, and that they follow a quasi-linear relationshipwith average 85.5-GHz radiances in stratiform regions,then an estimate of the convective area fraction withinthe sensor footprint is given by

0, POL . POLstrat POLf 5 1 2 , POL $ POL $ 0 (8)POL stratPOLstrat1, POL , 0,

where

POL 5 TB 2 TB , and (9)85v 85h

TB 1 TB85v 85hPOL 5 a 1 b. (10)strat 1 22

In the empirical linear relationship relating the polari-zation difference to the average 85.5-GHz radiance instratiform regions, the constants a (20.192) and b (52.4K) have been adjusted to obtain a best fit with the clusterof TMI observations. Here, the broad assumption is thatthe footprint is completely filled with precipitation, suchthat the polarized (nearly unpolarized) emission fromthe ocean (land) surface does not contribute significantlyto the total observed radiance. Given the oblique view-ing angle of the TMI (52.88 angle of incidence) and therelatively small footprint of the 85.5 GHz channels (5km 3 7 km), this is not too unreasonable an assumption.However, small convective cells that only partially fillthe TMI footprint over ocean (land) could lead to anunderestimate (overestimate) of the convective areafraction.

One final note: plotted in Fig. 1 are several obser-vations of negative polarization differences at 85.5 GHzover ocean and land surfaces. A physical basis for theseobservations is yet to be determined. In theory, negativepolarization differences could be due to scattering by

vertically oriented asymmetric ice particles, but mea-surement errors cannot be ruled out.

c. Merger of techniques

Figures 2 and 3 illustrate the strengths and weak-nesses of the texture-based ( f CSI) and polarization-based( f POL) methods for estimating the convective area frac-tion within a TMI footprint. A tropical convective sys-tem near the Cape Verde Islands was observed by theTMI on 12 September 1999, and the corresponding tex-ture- and polarization-based convective fractions aredisplayed in Figs. 2a and 2b, respectively.

For comparison, TMI-observed 85.5-GHz radiancesare shown in Fig. 2c, and convective area fraction es-timates from applications of the Awaka et al. (1998)method to TRMM PR data are presented in Fig. 2d.The Awaka et al. method distinguishes convective andstratiform regions based upon an examination of thelocal vertical and horizontal structure of the PR re-flectivity data. The vertical PR profile is examined todetermine whether a bright band of reflectivity, nor-mally associated with stratiform precipitation, is pre-sent. In the horizontal, the reflectivities in neighboringPR footprints are analyzed using a modified version ofthe method of Steiner et al. (1995) to identify con-vective centers. The vertical and horizontal analysesare combined to classify each PR footprint as convec-tive, stratiform, or indeterminate. Since the PR dataresolve precipitation spatial structure at a higher ver-tical resolution (0.25 km) and horizontal resolution(4.4 km) than the TMI data, the PR convective–strat-iform classification is considered to be a reliable ref-erence in the current study.

In order to more directly compare the relatively highresolution PR convective–stratiform classification toconvective area fraction estimates from the TMI, aweighted average of the PR-classified footprints in theneighborhood of a given TMI footprint is performed.Following Hong et al. (1999), a PR convective areafraction is defined by,

f 5 g PRCS g , (11)O OPR j j j@j j

where

1, convective PR classificationPRCS 5 (12)j 50, otherwise

is based upon the Awaka et al. (1998) PR classification,and

2 2g 5 exp[2ln(2)r /r ]j j 0 (13)

is a Gaussian weighting factor. Here, rj is the distancein kilometers between a PR footprint (indexed by j) andthe specified TMI footprint, and the summation in (11)is over all PR footprints within 2.5r0 of the TMI foot-


print. A value of r0 equal to 3.5 km leads to PR con-vective area fraction estimates that are comparable inresolution to the TMI estimates.

In Fig. 2, note that in regions of strong scattering at85.5 GHz (radiance depressions in Fig. 2c), both thetexure- and polarization-based TMI methods identify theconvective bands associated with the tropical system,as depicted in the PR classification (Fig. 2d). However,the weaker bands near 15.08N, 28.08W, and near 14.08N,30.08W produce less ice scattering and are more clearlydepicted by the texture-based method. In this case, localmaxima of emission at 19.35 and 37.0 GHz [see (1)]and local radiance minima due to scattering at 85.5 GHz[see (2)] help to identify the bands, whereas the polar-ization of the weakly scattered radiances provides littleinformation.

In Fig. 3, TRMM observations of another convectivesystem over the tropical North Atlantic on 1 October1998 are presented. Although the TMI 85.5-GHz im-agery reveals a large area of ice scattering in the boxbounded by 8.08N and 10.08N, 26.08W and 28.08W,much of this area is classified as stratiform by the PRmethod (see Figs. 3c,d). The TMI texture-based methodindicates a distribution of convection (Fig. 3a) thatmainly follows the pattern of scattering at 85.5 GHz,exaggerating the extent and proportion of convectionwithin the box. The TMI polarization-based method alsooverestimates the extent of convection, but the bias withrespect to the PR is less (Fig. 3b). Conversely, the TMItexture-based method underestimates the convectivecoverage associated with the 85.5-GHz scattering fea-ture near 12.08N, 30.08W, whereas convective fractionestimates from the polarization-based method are closerto the PR estimates.

In this example, the polarization-based method gen-erally yields less biased estimates of convective areafraction in regions of significant ice scattering. Texture-based estimates of convective fraction tend to vary inproportion to the depression of 85.5-GHz radiances inscattering regions, even if these scattering depressionsare produced by ice-phase precipitation that has beendetrained into stratiform regions. In stratiform regions,the polarization of ice-scattered 85.5-GHz radiances canbe significant, leading to a better discrimination usingthe polarization-based method. However, if ice scatter-ing is weak, as it is in the rainband near 11.08N, 30.58Win Fig. 3, then 85.5-GHz polarization data are less use-ful, and gradients of emission and scattering must beanalyzed to identify convection (Fig. 3a). The polari-zation-based method is also sensitive to noise and scan-to-scan gain variations in the 85.5-GHz data. For ex-ample, the streak of anomalous convective fraction es-timates with an endpoint near 9.58N, 28.08W in Fig. 3bis associated with a gain jump affecting the 85.5-GHzdata along one scan line.

To take advantage of the relative strengths of the tex-ture- and polarization-based methods for estimatingconvective area fraction, the estimates from each meth-

od are combined in inverse proportion to their expectederror variances at a given location. The combined es-timate of the convective area fraction within a TMIfootprint is given by

( f /var ) 1 ( f /var )CSI CSI POL POLf 5 , (14)COM (1/var ) 1 (1/var )CSI POL

where varCSI and varPOL are the error variances of thetexture- and polarization-based estimates of convectivefraction, respectively. This is the minimum variance es-timate described by Daley (1991).

The error variance of texture-based convective frac-tion estimates is derived from applications of the methodto synthesized TMI data. The synthesized TMI data aregenerated from TOGA COARE radar-measured rain dis-tributions, as described in Hong et al. (1999). An error,in this context, is the difference between the TMI tex-ture-based estimate of the convective area fraction andthe ‘‘true’’ convective fraction derived from a convec-tive–stratiform classification of the generating TOGACOARE radar data [see Short et al. (1997) for a de-scription of the convective–stratiform classificationmethod]. An analysis of these errors indicates greateruncertainty in convective fraction estimates when thereis a mixture of convective and stratiform precipitationwithin the radiometer footprint. Estimates of convectivefraction have less uncertainty when the radiometer foot-print is in the midst of a largely convective or stratiformregion. An empirical fit to the error variances of texture-based convective fraction estimates is given by

2var 5 g 1 g CSI 1 g CSI ,CSI 0 1 2 (15)

where g 0, g1, and g 2 are 0.246 653, 6.667 3 1023, and24.762 3 1025, respectively. In (15), intermediate val-ues of CSI indicate mixed convective and stratiformprecipitation within the radiometer footprint, and lowand high values indicate more uniform conditions.

The error of polarization-based convective area frac-tion estimates is primarily a function of the 85.5-GHzscattering depression. From (8), the error variance of aconvective fraction estimate is

2 2{2POL 1 [(aPOL) /2]}varstrat TB85var 5POL 4POLstrat

1 var , (16)f

where varTB85 is the variance of noise in the TMI 85.5-GHz radiance measurements (assumed to be 1 K2), andvarf is the error variance of the polarization-based es-timate in the absence of noise (approximately 0.1). Ifthe ice-scattering depression at 85.5 GHz is small, thenthe expected polarization difference in stratiform re-gions, POLstrat, is also small, and the error variance inthis limit is inversely proportional to . Therefore,4POLstrat

errors in polarization-based estimates of convective areafraction are expected to be large where ice scattering isweak.


FIG. 4. TMI 85.5-GHz polarization differences plotted vs average85.5-GHz radiances over (a) ocean and (b) land surfaces. The averageconvective area fraction derived from the PR in TMI 2-K polarizationdifference and 5-K average radiance intervals is plotted as a differentsymbol. Dashed lines are approximate curves representing purelystratiform and purely convective precipitation conditions.

d. Modification for overland applications

In applications of the combined texture–polarizationmethod over land and coastal regions, the interpretationof CSIe is ambiguous because microwave emission fromprecipitation is often indistinguishable from the rela-tively strong surface emission in these regions. There-fore, although (14) is formally applied over all surfaces,over land and coastal regions the weight ws in (3) is setequal to 1; that is, the texture-based convective areafraction estimate is only a function of the scatteringindex CSIs.

3. Applications to TMI observations

a. Signatures of convective area fraction in TMIobservations

Before direct comparisons of TMI and PR estimatesof convective area fraction are considered, the scatteringand polarization signatures of convective coverage areexamined. Plotted in Figs. 4a and 4b are the mean PRconvective area fraction estimates corresponding topairs of TMI 85.5-GHz average radiance (abscissa) andpolarization difference (ordinate) over ocean and landsurfaces, respectively. The plots are derived from thesame sets of TMI observations shown in Figs. 1a and1b, here collocated with nearly coincident PR obser-vations. Since Fig. 4 is provided primarily for illustra-

tion, no parallax correction is applied in the collocationprocedure. For comparison, the purely stratiform andpurely convective lines from the polarization-based con-vective area fraction method are superimposed on thedata.

Over either surface, there is a trend of increasingconvective area fraction, deduced from the PR, withdistance perpendicular to the purely stratiform line ofthe polarization-based method. However, for values ofconvective fraction exceeding 0.5 this trend becomesless well-defined, especially over land surfaces. It maybe inferred that the relationship between convective areafraction and 85.5-GHz radiances is indeed more com-plex than the graphical polarization-based techniquegiven by (8) suggests, and that the interpretation of 85.5-GHz scattering signatures using texture, as in (2), shouldhelp to improve estimates of convective fraction.

b. TMI–PR convective area fraction intercomparisons

In Fig. 5, the combined texture–polarization method,(14), is applied to TMI observations of precipitationsystems over ocean surfaces. The resulting TMI esti-mates of convective area fraction (left panels) are com-pared with nearly coincident PR estimates [right panels,from (11)]. The figure indicates a reasonable correlationbetween TMI and PR convective fraction estimates inthe larger-scale convective bands; however, a low biasof the TMI estimates relative to the PR estimates is alsoevident. In addition, because of the higher resolutionand finer sampling of the PR, smaller-scale convectivefeatures and isolated convective elements are sometimesdetected by the PR but not by the TMI. For example,convection near 17.58N, 139.58E in Fig. 5b, and near26.08N, 91.08W in Fig. 5f is identified using the PRmethod, but convection in the corresponding TMI im-ages is either weak or nonexistent.

As in the overocean applications, TMI and PR con-vective area fraction estimates over land are well-cor-related, with an apparent low bias of the TMI estimatesrelative to the PR (Fig. 6). The performance of the TMIcombined texture–polarization method over ocean andland surfaces is similar, even though information fromthe texture of microwave emission signatures, [(1)], isnot available in overland applications. The lack of emis-sion information may not be as critical a factor overland, where there is a greater probability that precipi-tation-sized ice particles are produced in convective re-gions due to generally greater atmospheric instabilityand stronger updrafts. Also for this reason, isolated con-vection may be more easily detected by the TMI overland; for example, convective cells near 1.08N, 67.08Win Figs. 6c and 6d. Over ocean or land, noise and gainvariations in the 85.5-GHz observations can lead to falseconvective signatures in the TMI analysis. For example,the TMI falsely identifies convection along a scan linenear 33.08N, 83.08W in Fig. 6a, where no convectionis found in the PR data (Fig. 6b).


FIG. 5. (left) TMI- and (right) PR-derived convective area fraction estimates for three different convective systems over the ocean. Lightshading indicates convective fractions between 0.0 and 0.3, moderate shading corresponds to convective fractions between 0.3 and 0.7, anddark shading indicates convective fractions between 0.7 and 1.0. Unshaded areas are rain-free or beyond the sensor observing area.


FIG. 6. Same as Fig. 5, but for convective systems over land.


FIG. 7. Scatterplots of coincident instantaneous convective areafraction estimates at 0.58 resolution from the TMI and PR over (a)ocean and (b) land surfaces. A solid line indicating ‘‘perfect agree-ment’’ of estimates, and dashed lines indicating 50% error, are in-cluded for reference.

TABLE 1. Statistics of collocated, instantaneous 0.58-resolution es-timates of convective area fraction from the TRMM TMI and PRover ocean and land surfaces. The samples contain 1374 and 823collocated estimates over ocean and land, respectively.

Surface BiasStd dev

of differenceCorrelationcoefficient

OceanLand

20.0220.02

0.060.07

0.780.84

Collocated TMI and PR convective area fraction es-timates from the 10 convective systems over ocean andnine convective systems over land (see Figs. 1 and 4)are plotted in Figs. 7a and 7b, respectively. Note thatthese estimates are spatially averaged over 0.58 3 0.58boxes to minimize data geolocation errors and representthe ratio of the convective area to the total area observedby the sensors within a given grid box, rather than theratio of the convective area to the raining area. Theformer definition allows a direct comparison of con-

vective area estimates without ambiguities introducedby differing estimates of the raining area from TMI andPR. Bivariate statistics of the collocated, box-averagedestimates are presented in Table 1. Although there isscatter in the plotted estimates over ocean or land, thereis also an obvious correlation between the estimates.The correlation coefficient of the TMI and PR estimatesis 0.78 over ocean and 0.84 over land surfaces. TheTMI convective fraction estimates are systematicallylower than the PR estimates, with a bias of 20.02 overocean or land. The standard deviations of the differencesbetween the TMI and PR estimates are 0.06 and 0.07over ocean and land, respectively.

Note that these statistics are somewhat skewed by therelatively large number of low convective fraction es-timates. For example, based upon the PR method themean convective fraction over ocean is only 0.05. FromFig. 7, it appears that both the bias and standard de-viation of differences increase with increasing convec-tive area fraction, although the standard deviation ex-pressed as a percentage may actually decrease with theconvective fraction.

4. Monthly-mean estimates of convective areaproportion

In addition to instantaneous TMI–PR comparisons,large-scale distributions of the convective area fraction arecompared for the month of February 1998. Instantaneousconvective area fraction estimates from the TMI and PRare averaged in 58 3 58 boxes over the month. As in theprevious section, these convective fraction estimates rep-resent the ratio of the convective area to the total areaobserved by the sensors. Distributions of mean convectivearea percentage from the TMI and PR are displayed in thefirst two panels of Fig. 8. For comparison, monthly raindepths derived from the TRMM version-5 TMI (2A12)and PR (3A25) algorithms are shown in the third andfourth panels, respectively. Note that only TMI convectivearea fraction and rain-rate estimates from footprints locatedwithin the PR swath contribute to the TMI convectivepercentages and rain depths in Fig. 8.

TMI convective area percentages are greatest in theintertropical convergence zone (ITCZ) and over the con-tinental regions in the Southern (summer) Hemisphere.The South Pacific convergence zone, Gulf of Mexico,and midlatitude storm-track regions of the western At-


FIG. 8. Monthly mean estimates of convective area percentage at 58 resolution from the TMI and PR forFeb 1998. Note that only TMI convective fraction estimates within the PR swath are included in the monthlyaverage. For comparison, rain depths derived from the TMI (TRMM 2A12 algorithm) and PR (TRMM 3A25algorithm) are shown in the third and fourth panels, respectively. Again, TMI monthly rain depths are derivedonly from TMI observations within the PR swath.


FIG. 9. Scatterplot of 58 resolution, monthly mean convective areapercentage estimates from the TMI and PR for Feb 1998. A solidline indicating perfect agreement of estimates is included for refer-ence.

lantic and western Pacific Oceans also exhibit significantvalues.

PR convective area percentages (second panel of Fig.8) are generally greater than the TMI estimates, althoughthe patterns of convective coverage are similar. At agiven location, the PR convective area percentage istypically 0.5% greater than the corresponding TMI con-vective percentage (see also the scatterplot in Fig. 9).The most noticeable differences occur over the Northern(winter) Hemisphere oceans, where PR convective per-centages exceed 0.5% widely, and TMI convective per-centages are generally less than 0.5%. One possible ex-planation for these differences is the greater sensitivityof the PR to isolated convective cells over the ocean(see section 3b). Isolated convection over the ocean issometimes not detected by the TMI because of the largerfootprints of the instrument and the difficulty of dis-criminating precipitation polarization signatures fromthe polarized ocean background.

Despite the fact that TMI convective percentages aregenerally less than those derived from the PR, TMI raindepths are mostly greater than PR rain depths (see thirdand fourth panels of Fig. 8). Significant biases are seenin the ITCZ/Southern (summer) Hemisphere oceanic re-gions and tropical continental regions, where TMI raindepths are roughly 50% greater than corresponding raindepths from the PR. Elsewhere, TMI and PR rain depthsare comparable in magnitude, and the overall monthlypatterns are similar. The reasons for the systematic dif-ferences of TMI and PR rain depths are not obvious:the relationships between rainwater content and the sig-natures observed by the two instruments are very dif-ferent, and the physical assumptions embodied in the

respective algorithms are not the same. However, it ap-pears that systematic TMI–PR differences in estimatedconvective area percentages do not show any clear cor-relation or anticorrelation with differences in retrievedrain depths, and therefore the discrepancies betweenTRMM version-5 TMI- and PR-retrieved rain depths arelikely due to other sensor or algorithmic differences.

5. Concluding remarks

A method combining texture and polarization infor-mation from measurements of the TRMM MicrowaveImager is used to estimate the fraction of the sensorfootprint area covered by convective precipitation. In-stantaneous estimates of convective area coverage fromthe TMI at 0.58 resolution are low-biased relative toprecipitation radar estimates, with correlation coeffi-cients of 0.78 and 0.84 over ocean and land surfaces,respectively. TMI monthly average convective area per-centages in the Tropics and subtropics from February1998 are greatest along the ITCZ and in continentalregions of the Southern (summer) Hemisphere. Al-though convective area percentages from the TMI aresystematically lower than those derived from the PR,the patterns of convective coverage from the TMI andPR are similar. Systematic differences in TMI and PRconvective area percentages do not show any clear cor-relation or anticorrelation with differences in retrievedrain depths, and so the discrepancies between TRMMversion-5 TMI- and PR-retrieved rain depths are likelydue to other sensor or algorithmic differences.

The TMI combined texture–polarization method forestimating convective coverage is expected to performbest in situations where organized deep convection pro-duces ice scattering at 85.5 GHz, since the 85.5-GHzchannels have relatively high resolution (;5 km), andboth the texture- and polarization-based techniques maycontribute to the combined estimate of convective frac-tion. However, shallow convection producing negligibleice scattering often occurs in tropical oceanic regions,and the combined method must then rely primarily onthe gradients of liquid precipitation emission at 19.35and 37.0 GHz to identify convection. These TMI chan-nels have lower resolution (;20 km at 19.35 GHz and;10 km at 37.0 GHz) than the 85.5-GHz channels, butshallow convective lines may still produce detectablegradients over ocean surfaces. On the other hand, shal-low convective cells embedded within widespread strat-iform rain are difficult to detect because the emissionsignatures of convective and stratiform rain are similar[Hong et al. (1999)]. Over land, the 19.35- and 37.0-GHz channels provide little relevant information re-garding shallow convection, and isolated convectivecells (either shallow or deep) may not produce a dis-cernable signal relative to ocean- or land-surface back-ground radiances. In future validation studies, the afore-mentioned limitations of the combined method could be


examined by sorting convective coverage estimates ac-cording to precipitation system type.

An admitted weakness of the current study is the lackof independent ground validation data for evaluatingremote sensing estimates of convective area coverage.The TRMM ground validation program will soon pro-duce maps of convective–stratiform coverage basedupon ground-based radar observations from stations atMelbourne, Florida; Houston, Texas; Kwajalein, Re-public of the Marshall Islands; and Darwin, Australia.The authors will compare TMI and PR estimates ofconvective area fraction to the classification data fromthese sites in a future study; however, the classificationof ground-based radar data is derived from an analysisof reflectivity magnitude and horizontal texture that maynot always reflect the underlying dynamical variationsassociated with convective and stratiform precipitation.

Coinciding with a limited number of satellite over-passes are dual-Doppler radar observations collectedduring three of the TRMM field campaigns: the SouthChina Sea Monsoon Experiment, the TRMM Large-scale Biosphere–Atmosphere campaign, and the Kwa-jalein Experiment. Analysis of these dual-Doppler ob-servations will yield fields of vertical air motion thatcan be used to check the dynamical consistency of re-flectivity-based convective–stratiform classificationfields. Also, latent heating vertical structure, which isstrongly correlated with vertical air velocity in precip-itating clouds, can be estimated by combining dual-Doppler vertical velocities with thermodynamic datafrom coincident radiosonde observations. If agreementbetween TMI convective coverage estimates and dy-namically-consistent, ground-based estimates can beachieved, then the prospects for estimating latent heat-ing distributions from TMI data are much improved.

Acknowledgments. The authors thank Grant Petty andJeffrey Haferman for helpful discussions regarding theradiative modeling of aspherical ice-phase precipitationand Gerald Heymsfield for his insights into the variationof microwave polarization signatures from organizedconvective systems. We also thank Edward Zipser forhis careful review of our manuscript. This study wasfunded by the TRMM Science Program.

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A Texture-Polarization Method for Estimating Convective