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  • View in gallery

    Polarization differences at 85.5 GHz plotted vs average 85.5-GHz radiances over (a) ocean and (b) land surfaces. TMI observations are plotted as points (nonraining areas) and open circles (raining areas). Diamonds represent radiative transfer simulations for atmospheres containing oriented, aspherical liquid and ice-phase precipitation. Dashed lines are approximate curves representing purely stratiform and purely convective precipitation conditions

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    Imagery of a mesoscale convective system near the Cape Verde Islands in the North Atlantic on 12 Sep 1999. (a), (b) The convective area 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

  • View in gallery

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

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

  • View in gallery

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

  • View in gallery

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

  • View in gallery

    Scatterplots of coincident instantaneous convective area fraction estimates at 0.5° resolution from the TMI and PR over (a) ocean and (b) land surfaces. A solid line indicating “perfect agreement” of estimates, and dashed lines indicating 50% error, are included for reference

  • View in gallery

    Monthly mean estimates of convective area percentage at 5° resolution from the TMI and PR for Feb 1998. Note that only TMI convective fraction estimates within the PR swath are included in the monthly average. For comparison, rain depths derived from the TMI (TRMM 2A12 algorithm) and PR (TRMM 3A25 algorithm) are shown in the third and fourth panels, respectively. Again, TMI monthly rain depths are derived only from TMI observations within the PR swath

  • View in gallery

    Scatterplot of 5° resolution, monthly mean convective area percentage estimates from the TMI and PR for Feb 1998. A solid line indicating perfect agreement of estimates is included for reference

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

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  • a Joint Center for Earth Systems Technology, University of Maryland, Baltimore County, Baltimore, and NASA Goddard Space Flight Center, Greenbelt, Maryland
  • | b The Aerospace Corporation, Los Angeles, California
  • | c Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado
  • | d Naval Research Laboratory, Monterey, California
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Abstract

Observational and modeling studies have revealed the relationships between convective–stratiform rain proportion and the vertical distributions of vertical motion, latent heating, and moistening in mesoscale convective systems. Therefore, remote sensing techniques that can be used to quantify the area coverage of convective or stratiform rainfall could provide useful information regarding the dynamic and thermodynamic processes in these systems. In the current study, two methods for deducing the area coverage of convective precipitation from satellite passive microwave radiometer measurements are combined to yield an improved method. If sufficient microwave scattering by ice-phase precipitation is detected, the method relies mainly on the degree of polarization in oblique-view, 85.5-GHz radiances to estimate the fraction of the radiometer footprint covered by convection. In situations where ice scattering is minimal, the method draws mostly on texture information in 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, instantaneous, 0.5°-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 precipitation radar (PR). TMI convective area fraction estimates are low-biased relative to PR estimates, with TMI–PR correlation coefficients of 0.78 and 0.84 over ocean and land surfaces, respectively. TMI monthly average convective area percentages in the Tropics and subtropics from February 1998 are greatest along the intertropical convergence zone and in the continental regions of the Southern (summer) Hemisphere. Although convective area percentages from the TMI are systematically lower than those derived from the PR, the monthly patterns of convective coverage are similar. Systematic differences in TMI and PR convective area percentages do not show any clear correlation or anticorrelation with differences in retrieved rain depths, and so discrepancies between TRMM version-5 TMI- and PR-retrieved rain depths are likely due to other sensor or algorithmic differences.

Corresponding author address: Dr. William Olson, Joint Center for Earth Systems Technology and NASA Goddard Space Flight Center, Code 912, Greenbelt, MD 20771. olson@agnes.gsfc.nasa.gov

Abstract

Observational and modeling studies have revealed the relationships between convective–stratiform rain proportion and the vertical distributions of vertical motion, latent heating, and moistening in mesoscale convective systems. Therefore, remote sensing techniques that can be used to quantify the area coverage of convective or stratiform rainfall could provide useful information regarding the dynamic and thermodynamic processes in these systems. In the current study, two methods for deducing the area coverage of convective precipitation from satellite passive microwave radiometer measurements are combined to yield an improved method. If sufficient microwave scattering by ice-phase precipitation is detected, the method relies mainly on the degree of polarization in oblique-view, 85.5-GHz radiances to estimate the fraction of the radiometer footprint covered by convection. In situations where ice scattering is minimal, the method draws mostly on texture information in 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, instantaneous, 0.5°-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 precipitation radar (PR). TMI convective area fraction estimates are low-biased relative to PR estimates, with TMI–PR correlation coefficients of 0.78 and 0.84 over ocean and land surfaces, respectively. TMI monthly average convective area percentages in the Tropics and subtropics from February 1998 are greatest along the intertropical convergence zone and in the continental regions of the Southern (summer) Hemisphere. Although convective area percentages from the TMI are systematically lower than those derived from the PR, the monthly patterns of convective coverage are similar. Systematic differences in TMI and PR convective area percentages do not show any clear correlation or anticorrelation with differences in retrieved rain depths, and so discrepancies between TRMM version-5 TMI- and PR-retrieved rain depths are likely due to other sensor or algorithmic differences.

Corresponding author address: Dr. William Olson, Joint Center for Earth Systems Technology and NASA Goddard Space Flight Center, Code 912, Greenbelt, MD 20771. olson@agnes.gsfc.nasa.gov

Introduction

Understanding the complex interaction of convective cloud systems and their environment has been a major objective of meteorological research for many years. The latent heat release and vertical transports of sensible heat, moisture, and momentum by convective systems have a strong effect on the large-scale circulations in which they are embedded, whereas large-scale radiative and dynamical processes can change the stability characteristics of the atmosphere, thereby enhancing or suppressing convective activity. The large-scale flow can also influence the organization of convection and the nature of the vertical transports by convective systems.

In numerical weather prediction models and general circulation models, which currently have grid resolutions on the order of 100 km, convective processes are highly parameterized, and the accuracy of simulations based upon these models depends upon an adequate representation of convection and mesoscale effects at subgrid scale. An explicit description of the mesoscale organization of convection in model simulations requires relatively high grid resolution; simulated convective organization and transports can still be sensitive to the physical parameterizations employed.

Over the last half-century, several field campaigns have provided data needed for a better understanding of convective systems and their effects. These campaigns have focused observations from surface instruments, rawinsondes, radar, and aircraft sensors over regions spanning areas of about 100 000 km2 and periods up to several months in order to gather information pertaining to the microphysics, kinematics, organization, and environmental impact of convective systems. Although much has been learned from these campaigns, a more large-scale, long-term perspective can be gained through satellite remote sensing of cloud properties, especially over oceanic regions where long-term monitoring by other methods is generally unfeasible. Such observations could be used to track climatological variations in convective organization and transports and provide a means for validating cloud properties and effects simulated by numerical prediction models.

The capability of satellite passive microwave sensors to provide quantitative precipitation estimates is now well established (see Ebert et al. 1996; Smith et al. 1998). Over oceans, passive microwave rain estimates are possible because there is a fairly direct physical relationship between the path-integrated water content of rain along the sensor line of sight and the upwelling radiances measured by the sensor at frequencies less than ∼40 GHz. Passive microwave observations can be used to infer other cloud and precipitation properties such as ice-phase precipitation amount or to describe the organization of convective systems. However, these uses of the data have received much less attention.

Regarding organization, the basic structure of a convective system can be described in terms of the proportion and distribution of convective and stratiform rainfall within the system (Houze 1989). Previous observational and modeling studies have established the relationships between convective–stratiform rain proportion 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 that yield the area coverage of convective or stratiform rainfall within a sensor footprint may ultimately provide useful information regarding the dynamic and thermodynamic processes in these systems.

In the current study, two methods for estimating the area coverage of convective precipitation within a footprint of the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) are combined to create an improved technique that emphasizes the strengths of both methods. In section 2, the two methods and their merger are described. Applications of the combined method to TMI observations of individual convective systems are presented in section 3, including statistics of intercomparisons with convective area estimates from the TRMM precipitation radar (PR). Monthly estimates of convective area percentage over the Tropics and subtropics from both TMI and PR are presented in section 4. A summary and discussion are included in section 5.

Methods

Texture-based convective area fraction

It is commonly known (Zipser 1977; Leary and Houze 1979; Houze 1993) that stratiform precipitation regions are associated with relatively weak updrafts and downdrafts while convective regions are associated with more vigorous, turbulent updrafts and downdrafts. According to mass continuity arguments, a change in vertical velocity must be associated with a change in the horizontal mass field. It is therefore assumed that substantial horizontal gradients of precipitation (and likewise gradients of microwave radiances) characterize convective regions. The texture-based method empirically relates the horizontal variation of microwave radiances to the fraction of the TMI footprint area covered by convective precipitation.

Based on data from the Tropical Ocean and Global Atmosphere Coupled Ocean–Atmosphere Response Experiment (TOGA COARE), Hong et al. (1999) tested several indices, derived from passive microwave radiance measurements, for separating convective and stratiform rain areas. In that study a convective–stratiform index (CSI) was developed that combined the local maximum variation and relative magnitude of radiances from the 19.35-, 37.0-, and 85.5-GHz horizontal polarization channels of TMI. Formally,
i1520-0450-40-9-1577-e1
Here, TBυp and TBυp-back are the microwave radiance and background “clear-air” radiance, respectively, at frequency υ and polarization p. The variable VMυp is the local maximum variation of a measured radiance with respect to its neighbors. At 85.5 GHz, the local maximum variation is defined as,
i1520-0450-40-9-1577-e4
and at 19.35 and 37.0 GHz, the local maximum variation is
i1520-0450-40-9-1577-e5
In (4) and (5), the subscript j refers to any of the eight neighboring TMI footprints surrounding the footprint being analyzed. The local maximum variation is used here because the relatively low resolution of the satellite microwave observations may smear emission or scattering gradients in any particular direction.

Since convection is generally associated with heavy precipitation, the relative magnitude of the radiance with respect to a background radiance is added to the CSI [third term on the right-hand side of (1) and second term on the right-hand side of (2)]. The background radiance is defined as the average of clear-air radiances from the eight neighboring TMI footprints surrounding the footprint being analyzed. Over ocean, a footprint is classified as clear air if the mean cloud water content below the freezing level, retrieved using the algorithm of Karstens et al. (1994), is less than 0.06 g m−3. Over land, clear-air footprints are identified based upon the screening algorithm described in Adler et al. (1994) and Huffman et al. (1995). Since the background radiance is an average of neighboring clear-air radiances, it has a stabilizing effect on the relative magnitude. Therefore, the addition of the relative magnitude to CSIe and CSIs helps to temper these indices in situations where the VM are corrupted by a single bad radiance measurement among the neighboring footprints.

The final index, CSI, is a weighted sum of the emission and scattering indices [see (3)]. The weighting factor ws increases with the relative amount of scattering in the microwave footprint:
i1520-0450-40-9-1577-e6
Therefore, the horizontal variation of the 85.5-GHz ice-scattering depression mainly determines CSI when significant ice is present, whereas the horizontal variation of emission at 19.35 and 37.0 GHz mainly determine CSI when little ice is present.
Hong et al. (1999) demonstrated that as sensor resolution degrades, the likelihood of observing a mixture of convective and stratiform rainfall within the sensor footprint increases. Over 6 km × 6 km areas, which are about 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 covers 30% to 70% of the total area) was about 30%, based upon an analysis of TOGA COARE shipboard radar data. The contribution from mixed regions increased to about 50% for 12 km × 12 km areas, which are comparable to the footprints of the highest-resolution Special Sensor Microwave Imager (SSMI) channels. Therefore, instead of classifying TMI footprints as convective or stratiform, these authors related CSI to the fraction of the footprint area covered by convective rainfall (hereinafter, the convective area fraction) by matching the cumulative distribution of convective area fractions derived from the TOGA COARE shipboard radar data to the cumulative distribution of synthesized TMI CSI measurements. The resulting empirical relationship is well-approximated by
i1520-0450-40-9-1577-e7
Readers are referred to Hong et al. (1999) for a more detailed description of the texture-based convective–stratiform separation method.

Polarization-based convective area fraction

An alternative formula for convective area fraction is suggested by the analyses of SSMI observations by Spencer et al. (1989) and Heymsfield and Fulton (1994a,b). These authors found significant differences, on the order of 5 K or greater, between the vertically and horizontally polarized 85.5 GHz radiances in stratiform precipitation regions over land, whereas regions of strong convection were nearly unpolarized at 85.5 GHz. Although the physical basis of these polarization differences has not been verified, the aforementioned authors hypothesized that aspherical, precipitation-sized ice particles such as snow or aggregates would tend to become oriented as they fall through the relatively weak updrafts or downdrafts of stratiform regions, resulting in preferential scattering in the horizontal polarization. The more vigorous, turbulent updrafts of convective regions would cause ice hydrometeors to lose any preferred orientation, leading to similar scattering signatures in both polarizations.

Turk and Vivekanandan (1995), Petty and Turk (1996), and Schols et al. (1997) more recently performed microwave radiative transfer calculations for clouds of oriented, aspherical ice hydrometeors and found polarization differences exceeding 5 K at 85 GHz, supporting the earlier hypothesis. Roberti and Kummerow (1999) obtained similar polarization differences based upon Monte Carlo radiative simulations. Their results suggest that in addition to ice particle orientation, the relative amounts of asymmetric snow and more spherical graupel in convective and stratiform precipitation regions could contribute to the observed polarization differences. A greater abundance of oriented, asymmetric snow particles in stratiform regions yielded polarization differences greater than 10 K at 85 GHz, while a greater abundance of spherical graupel in convective regions produced polarization differences less than 5 K.

In Olson et al. (1999) the approximately inverse relationship between 85.5-GHz polarization difference and convective fraction was utilized to constrain retrievals of precipitation 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 convective area fraction within the TMI footprint.

In Fig. 1, TMI-observed 85.5-GHz polarization differences are plotted versus average 85.5-GHz radiances. These observations are derived from TMI overpasses of 10 organized convective systems over ocean (Fig. 1a) and nine systems over land (Fig. 1b), sampled from the first three years of the TRMM mission. Organized convective systems, such as squall lines and tropical cyclones, are selected here because they generally produce microwave scattering by ice-phase precipitation at 85.5 GHz and are often characterized by significant proportions of convective and stratiform precipitation. It follows that these systems best illustrate the relationships between microwave polarization difference and scattering; relationships that form the foundation of the polarization-based method for estimating convective area fraction. TMI data from all footprints in the swath segments containing the convective systems are plotted in Fig. 1; that is, precipitation-free footprints have not been filtered.

Overlaid on the TMI observations of Fig. 1 are radiative-transfer-model-simulated 85.5-GHz polarization differences and average radiances for atmospheres containing layers of rain, cloud, and ice-phase precipitation. The model atmosphere is characterized by tropical profiles of temperature and water vapor, and a layer of nonprecipitating cloud liquid water with a water content of 0.5 g m−3 between 1- and 6-km altitude is assumed. Embedded in this atmosphere is a homogeneous rain layer between the surface and 4 km. The equivalent rain rate of the rain layer is varied in steps from 0 to 50 mm h−1. For each rain rate, the thickness of a capping graupel layer is varied between 0 and 8 km, and the equivalent water content of graupel within the layer is assumed to be equal to the rain water content. Raindrops are assumed to be oblate spheroidal, the oblateness increasing with equivalent spherical volume diameter. Graupel particles are conical in shape, with a constant density of 0.6 g cm−3. Both rain and graupel are oriented such that the long axes of the particles are parallel to the earth's surface. Calculations of the upwelling radiances at 53.4° incidence (close to the 52.8° incidence angle of the TMI) are performed using a polarized multistream radiative transfer method (Evans and Stephens 1991). Because the earth's surface is entirely obscured by absorbing cloud water in the rain-free model atmosphere at 85.5 GHz, only overocean radiative calculations are considered in the intercomparisons of Fig. 1. Details of the radiative modeling can be found in Turk and Vivekenandan (1995), and Petty and Turk (1996).

Note first, in Fig. 1a the relatively large observed polarization differences, many greater than 20 K, that characterize cloud-free regions over the ocean. These polarization differences are due to the highly polarized emission from the ocean surface that is only partially absorbed by water vapor in a clear atmosphere. Clouds in the atmosphere strongly absorb the polarized surface emission, and thermal emission from the absorbing cloud droplets raises the observed upwelling radiances at 85.5 GHz. The transition from cloud-free to cloudy atmospheres creates the nearly vertical branch of plotted points corresponding to average 85.5-GHz radiances greater than 230 K in Fig. 1a.

A cloud liquid water vertical path exceeding about 1 kg m−2 renders the cloudy atmosphere almost completely absorbing, and nearly unpolarized blackbody emission close to the cloud-top temperature at the freezing level (273 K) is observed. This limit is confirmed by the radiative transfer model calculations, which indicate a maximum average radiance of 272.5 K with a 0.1-K polarization difference for an atmosphere containing only nonprecipitating cloud with a liquid water path of 2.5 kg m−2.

In precipitating clouds, weak microwave scattering by raindrops and stronger scattering by precipitation-sized ice particles reduce the upwelling cloud-top radiance by diverting the upwelling emission from lower levels. Note the congregation of observations along an approximate 45° diagonal line in Fig. 1a, indicating increasing 85.5-GHz polarization difference with decreasing average 85.5-GHz radiance. These observations generally correspond to stratiform areas in mesoscale convective systems. An empirical linear fit to these “purely stratiform” observations is shown in the figure. Also in Fig. 1a, the radiative transfer model simulations incorporating oriented ice hydrometeors exhibit a similar trend, with polarization differences generally increasing with decreasing average radiances. As scattering by ice-phase precipitation becomes very strong, and simulated average radiances fall below 160 K, the simulated polarization differences level off and then decrease. The TMI observations suggest that these modeled combinations of very-low-average radiance and large polarization difference do not occur naturally, likely because the large concentrations of ice-phase precipitation required can only be supported by strong, convective updrafts.

In contrast, radiative transfer simulations based upon atmospheres containing randomly oriented ice particles yield relatively small polarization differences. Haferman (2000; 2000, personal communication) calculated polarization differences less than 2 K at 85.5 GHz in radiances upwelling from optically thick clouds of precipitating ice. This limiting case is represented by the zero-polarization “purely convective” line in Fig. 1a. If it is assumed that TMI footprints at 85.5 GHz are essentially filled with precipitation but contain different proportions of convective and stratiform precipitation, then a combination of the partially polarized purely stratiform model radiances and nearly unpolarized purely convective model radiances within each TMI footprint could explain the scatter of observed 85.5-GHz average radiances and polarization differences that fall between these limits. The clustering of observations near the purely stratiform model curve is due to the greater frequency of occurrence of stratiform precipitation that also tends to fill the TMI 85.5 GHz footprints. Smaller-scale convective elements occur less frequently and may be mixed with stratiform precipitation within the sensor's field of view.

It is evident from Fig. 1b that over land, the polarization of 85.5-GHz radiances in rain-free areas is very low, but the relationship between average radiances and polarization differences at 85.5 GHz in precipitation regions is similar to that observed over ocean.

If it is assumed that TMI 85.5-GHz polarization differences are essentially zero in purely convective regions, and that they follow a quasi-linear relationship with average 85.5-GHz radiances in stratiform regions, then an estimate of the convective area fraction within the sensor footprint is given by
i1520-0450-40-9-1577-e8
where
i1520-0450-40-9-1577-e9
In the empirical linear relationship relating the polarization difference to the average 85.5-GHz radiance in stratiform regions, the constants a (−0.192) and b (52.4 K) have been adjusted to obtain a best fit with the cluster of TMI observations. Here, the broad assumption is that the footprint is completely filled with precipitation, such that the polarized (nearly unpolarized) emission from the ocean (land) surface does not contribute significantly to the total observed radiance. Given the oblique viewing angle of the TMI (52.8° angle of incidence) and the relatively small footprint of the 85.5 GHz channels (5 km × 7 km), this is not too unreasonable an assumption. However, small convective cells that only partially fill the TMI footprint over ocean (land) could lead to an underestimate (overestimate) of the convective area fraction.

One final note: plotted in Fig. 1 are several observations of negative polarization differences at 85.5 GHz over ocean and land surfaces. A physical basis for these observations is yet to be determined. In theory, negative polarization differences could be due to scattering by vertically oriented asymmetric ice particles, but measurement errors cannot be ruled out.

Merger of techniques

Figures 2 and 3 illustrate the strengths and weaknesses of the texture-based (fCSI) and polarization-based (fPOL) methods for estimating the convective area fraction within a TMI footprint. A tropical convective system near the Cape Verde Islands was observed by the TMI on 12 September 1999, and the corresponding texture- and polarization-based convective fractions are displayed in Figs. 2a and 2b, respectively.

For comparison, TMI-observed 85.5-GHz radiances are shown in Fig. 2c, and convective area fraction estimates 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 and stratiform regions based upon an examination of the local vertical and horizontal structure of the PR reflectivity data. The vertical PR profile is examined to determine whether a bright band of reflectivity, normally associated with stratiform precipitation, is present. In the horizontal, the reflectivities in neighboring PR footprints are analyzed using a modified version of the method of Steiner et al. (1995) to identify convective centers. The vertical and horizontal analyses are combined to classify each PR footprint as convective, stratiform, or indeterminate. Since the PR data resolve precipitation spatial structure at a higher vertical resolution (0.25 km) and horizontal resolution (4.4 km) than the TMI data, the PR convective–stratiform classification is considered to be a reliable reference in the current study.

In order to more directly compare the relatively high resolution PR convective–stratiform classification to convective area fraction estimates from the TMI, a weighted average of the PR-classified footprints in the neighborhood of a given TMI footprint is performed. Following Hong et al. (1999), a PR convective area fraction is defined by,
i1520-0450-40-9-1577-e11
where
i1520-0450-40-9-1577-e12
is based upon the Awaka et al. (1998) PR classification, and
gjr2jr20
is a Gaussian weighting factor. Here, rj is the distance in kilometers between a PR footprint (indexed by j) and the specified TMI footprint, and the summation in (11) is over all PR footprints within 2.5r0 of the TMI footprint. A value of r0 equal to 3.5 km leads to PR convective area fraction estimates that are comparable in resolution to the TMI estimates.

In Fig. 2, note that in regions of strong scattering at 85.5 GHz (radiance depressions in Fig. 2c), both the texure- and polarization-based TMI methods identify the convective bands associated with the tropical system, as depicted in the PR classification (Fig. 2d). However, the weaker bands near 15.0°N, 28.0°W, and near 14.0°N, 30.0°W produce less ice scattering and are more clearly depicted by the texture-based method. In this case, local maxima 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 polarization of the weakly scattered radiances provides little information.

In Fig. 3, TRMM observations of another convective system over the tropical North Atlantic on 1 October 1998 are presented. Although the TMI 85.5-GHz imagery reveals a large area of ice scattering in the box bounded by 8.0°N and 10.0°N, 26.0°W and 28.0°W, much of this area is classified as stratiform by the PR method (see Figs. 3c,d). The TMI texture-based method indicates a distribution of convection (Fig. 3a) that mainly follows the pattern of scattering at 85.5 GHz, exaggerating the extent and proportion of convection within the box. The TMI polarization-based method also overestimates the extent of convection, but the bias with respect to the PR is less (Fig. 3b). Conversely, the TMI texture-based method underestimates the convective coverage associated with the 85.5-GHz scattering feature near 12.0°N, 30.0°W, whereas convective fraction estimates from the polarization-based method are closer to the PR estimates.

In this example, the polarization-based method generally yields less biased estimates of convective area fraction in regions of significant ice scattering. Texture-based estimates of convective fraction tend to vary in proportion to the depression of 85.5-GHz radiances in scattering regions, even if these scattering depressions are produced by ice-phase precipitation that has been detrained into stratiform regions. In stratiform regions, the polarization of ice-scattered 85.5-GHz radiances can be significant, leading to a better discrimination using the polarization-based method. However, if ice scattering is weak, as it is in the rainband near 11.0°N, 30.5°W in Fig. 3, then 85.5-GHz polarization data are less useful, and gradients of emission and scattering must be analyzed to identify convection (Fig. 3a). The polarization-based method is also sensitive to noise and scan-to-scan gain variations in the 85.5-GHz data. For example, the streak of anomalous convective fraction estimates with an endpoint near 9.5°N, 28.0°W in Fig. 3b is associated with a gain jump affecting the 85.5-GHz data along one scan line.

To take advantage of the relative strengths of the texture- and polarization-based methods for estimating convective area fraction, the estimates from each method are combined in inverse proportion to their expected error variances at a given location. The combined estimate of the convective area fraction within a TMI footprint is given by
i1520-0450-40-9-1577-e14
where varCSI and varPOL are the error variances of the texture- and polarization-based estimates of convective fraction, respectively. This is the minimum variance estimate described by Daley (1991).
The error variance of texture-based convective fraction estimates is derived from applications of the method to synthesized TMI data. The synthesized TMI data are generated from TOGA COARE radar-measured rain distributions, as described in Hong et al. (1999). An error, in this context, is the difference between the TMI texture-based estimate of the convective area fraction and the “true” convective fraction derived from a convective–stratiform classification of the generating TOGA COARE radar data [see Short et al. (1997) for a description of the convective–stratiform classification method]. An analysis of these errors indicates greater uncertainty in convective fraction estimates when there is a mixture of convective and stratiform precipitation within the radiometer footprint. Estimates of convective fraction have less uncertainty when the radiometer footprint is in the midst of a largely convective or stratiform region. An empirical fit to the error variances of texture-based convective fraction estimates is given by
CSIγ0γ1γ22
where γ0, γ1, and γ2 are 0.246 653, 6.667 × 10−3, and −4.762 × 10−5, respectively. In (15), intermediate values of CSI indicate mixed convective and stratiform precipitation within the radiometer footprint, and low and high values indicate more uniform conditions.
The error of polarization-based convective area fraction estimates is primarily a function of the 85.5-GHz scattering depression. From (8), the error variance of a convective fraction estimate is
i1520-0450-40-9-1577-e16
where varTB85 is the variance of noise in the TMI 85.5-GHz radiance measurements (assumed to be 1 K2), and varf is the error variance of the polarization-based estimate in the absence of noise (approximately 0.1). If the ice-scattering depression at 85.5 GHz is small, then the expected polarization difference in stratiform regions, POLstrat, is also small, and the error variance in this limit is inversely proportional to POL4strat. Therefore, errors in polarization-based estimates of convective area fraction are expected to be large where ice scattering is weak.

Modification for overland applications

In applications of the combined texture–polarization method over land and coastal regions, the interpretation of CSIe is ambiguous because microwave emission from precipitation is often indistinguishable from the relatively strong surface emission in these regions. Therefore, although (14) is formally applied over all surfaces, over land and coastal regions the weight ws in (3) is set equal to 1; that is, the texture-based convective area fraction estimate is only a function of the scattering index CSIs.

Applications to TMI observations

Signatures of convective area fraction in TMI observations

Before direct comparisons of TMI and PR estimates of convective area fraction are considered, the scattering and polarization signatures of convective coverage are examined. Plotted in Figs. 4a and 4b are the mean PR convective area fraction estimates corresponding to pairs of TMI 85.5-GHz average radiance (abscissa) and polarization difference (ordinate) over ocean and land surfaces, respectively. The plots are derived from the same sets of TMI observations shown in Figs. 1a and 1b, here collocated with nearly coincident PR observations. Since Fig. 4 is provided primarily for illustration, no parallax correction is applied in the collocation procedure. For comparison, the purely stratiform and purely convective lines from the polarization-based convective area fraction method are superimposed on the data.

Over either surface, there is a trend of increasing convective area fraction, deduced from the PR, with distance perpendicular to the purely stratiform line of the polarization-based method. However, for values of convective fraction exceeding 0.5 this trend becomes less well-defined, especially over land surfaces. It may be inferred that the relationship between convective area fraction and 85.5-GHz radiances is indeed more complex than the graphical polarization-based technique given by (8) suggests, and that the interpretation of 85.5-GHz scattering signatures using texture, as in (2), should help to improve estimates of convective fraction.

TMI–PR convective area fraction intercomparisons

In Fig. 5, the combined texture–polarization method, (14), is applied to TMI observations of precipitation systems over ocean surfaces. The resulting TMI estimates of convective area fraction (left panels) are compared with nearly coincident PR estimates [right panels, from (11)]. The figure indicates a reasonable correlation between TMI and PR convective fraction estimates in the larger-scale convective bands; however, a low bias of the TMI estimates relative to the PR estimates is also evident. In addition, because of the higher resolution and finer sampling of the PR, smaller-scale convective features and isolated convective elements are sometimes detected by the PR but not by the TMI. For example, convection near 17.5°N, 139.5°E in Fig. 5b, and near 26.0°N, 91.0°W in Fig. 5f is identified using the PR method, but convection in the corresponding TMI images is either weak or nonexistent.

As in the overocean applications, TMI and PR convective area fraction estimates over land are well-correlated, with an apparent low bias of the TMI estimates relative to the PR (Fig. 6). The performance of the TMI combined texture–polarization method over ocean and land surfaces is similar, even though information from the texture of microwave emission signatures, [(1)], is not available in overland applications. The lack of emission information may not be as critical a factor over land, where there is a greater probability that precipitation-sized ice particles are produced in convective regions due to generally greater atmospheric instability and stronger updrafts. Also for this reason, isolated convection may be more easily detected by the TMI over land; for example, convective cells near 1.0°N, 67.0°W in Figs. 6c and 6d. Over ocean or land, noise and gain variations in the 85.5-GHz observations can lead to false convective signatures in the TMI analysis. For example, the TMI falsely identifies convection along a scan line near 33.0°N, 83.0°W in Fig. 6a, where no convection is found in the PR data (Fig. 6b).

Collocated TMI and PR convective area fraction estimates from the 10 convective systems over ocean and nine convective systems over land (see Figs. 1 and 4) are plotted in Figs. 7a and 7b, respectively. Note that these estimates are spatially averaged over 0.5° × 0.5° boxes to minimize data geolocation errors and represent the ratio of the convective area to the total area observed by the sensors within a given grid box, rather than the ratio of the convective area to the raining area. The former definition allows a direct comparison of convective area estimates without ambiguities introduced by differing estimates of the raining area from TMI and PR. Bivariate statistics of the collocated, box-averaged estimates are presented in Table 1. Although there is scatter in the plotted estimates over ocean or land, there is also an obvious correlation between the estimates. The correlation coefficient of the TMI and PR estimates is 0.78 over ocean and 0.84 over land surfaces. The TMI convective fraction estimates are systematically lower than the PR estimates, with a bias of −0.02 over ocean or land. The standard deviations of the differences between the TMI and PR estimates are 0.06 and 0.07 over ocean and land, respectively.

Note that these statistics are somewhat skewed by the relatively large number of low convective fraction estimates. For example, based upon the PR method the mean convective fraction over ocean is only 0.05. From Fig. 7, it appears that both the bias and standard deviation of differences increase with increasing convective area fraction, although the standard deviation expressed as a percentage may actually decrease with the convective fraction.

Monthly-mean estimates of convective area proportion

In addition to instantaneous TMI–PR comparisons, large-scale distributions of the convective area fraction are compared for the month of February 1998. Instantaneous convective area fraction estimates from the TMI and PR are averaged in 5° × 5° boxes over the month. As in the previous section, these convective fraction estimates represent the ratio of the convective area to the total area observed by the sensors. Distributions of mean convective area percentage from the TMI and PR are displayed in the first two panels of Fig. 8. For comparison, monthly rain depths derived from the TRMM version-5 TMI (2A12) and PR (3A25) algorithms are shown in the third and fourth panels, respectively. Note that only TMI convective area fraction and rain-rate estimates from footprints located within the PR swath contribute to the TMI convective percentages and rain depths in Fig. 8.

TMI convective area percentages are greatest in the intertropical convergence zone (ITCZ) and over the continental regions in the Southern (summer) Hemisphere. The South Pacific convergence zone, Gulf of Mexico, and midlatitude storm-track regions of the western Atlantic and western Pacific Oceans also exhibit significant values.

PR convective area percentages (second panel of Fig. 8) are generally greater than the TMI estimates, although the patterns of convective coverage are similar. At a given location, the PR convective area percentage is typically 0.5% greater than the corresponding TMI convective percentage (see also the scatterplot in Fig. 9). The most noticeable differences occur over the Northern (winter) Hemisphere oceans, where PR convective percentages exceed 0.5% widely, and TMI convective percentages are generally less than 0.5%. One possible explanation for these differences is the greater sensitivity of the PR to isolated convective cells over the ocean (see section 3b). Isolated convection over the ocean is sometimes not detected by the TMI because of the larger footprints of the instrument and the difficulty of discriminating precipitation polarization signatures from the polarized ocean background.

Despite the fact that TMI convective percentages are generally less than those derived from the PR, TMI rain depths are mostly greater than PR rain depths (see third and fourth panels of Fig. 8). Significant biases are seen in the ITCZ/Southern (summer) Hemisphere oceanic regions and tropical continental regions, where TMI rain depths are roughly 50% greater than corresponding rain depths from the PR. Elsewhere, TMI and PR rain depths are comparable in magnitude, and the overall monthly patterns are similar. The reasons for the systematic differences of TMI and PR rain depths are not obvious: the relationships between rainwater content and the signatures observed by the two instruments are very different, and the physical assumptions embodied in the respective algorithms are not the same. However, it appears that systematic TMI–PR differences in estimated convective area percentages do not show any clear correlation or anticorrelation with differences in retrieved rain depths, and therefore the discrepancies between TRMM version-5 TMI- and PR-retrieved rain depths are likely due to other sensor or algorithmic differences.

Concluding remarks

A method combining texture and polarization information from measurements of the TRMM Microwave Imager is used to estimate the fraction of the sensor footprint area covered by convective precipitation. Instantaneous estimates of convective area coverage from the TMI at 0.5° resolution are low-biased relative to precipitation radar estimates, with correlation coefficients of 0.78 and 0.84 over ocean and land surfaces, respectively. TMI monthly average convective area percentages in the Tropics and subtropics from February 1998 are greatest along the ITCZ and in continental regions of the Southern (summer) Hemisphere. Although convective area percentages from the TMI are systematically lower than those derived from the PR, the patterns of convective coverage from the TMI and PR are similar. Systematic differences in TMI and PR convective area percentages do not show any clear correlation or anticorrelation with differences in retrieved rain depths, and so the discrepancies between TRMM version-5 TMI- and PR-retrieved rain depths are likely due to other sensor or algorithmic differences.

The TMI combined texture–polarization method for estimating convective coverage is expected to perform best in situations where organized deep convection produces ice scattering at 85.5 GHz, since the 85.5-GHz channels have relatively high resolution (∼5 km), and both the texture- and polarization-based techniques may contribute to the combined estimate of convective fraction. However, shallow convection producing negligible ice scattering often occurs in tropical oceanic regions, and the combined method must then rely primarily on the gradients of liquid precipitation emission at 19.35 and 37.0 GHz to identify convection. These TMI channels have lower resolution (∼20 km at 19.35 GHz and ∼10 km at 37.0 GHz) than the 85.5-GHz channels, but shallow convective lines may still produce detectable gradients over ocean surfaces. On the other hand, shallow convective cells embedded within widespread stratiform rain are difficult to detect because the emission signatures 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 regarding shallow convection, and isolated convective cells (either shallow or deep) may not produce a discernable signal relative to ocean- or land-surface background radiances. In future validation studies, the aforementioned limitations of the combined method could be examined by sorting convective coverage estimates according to precipitation system type.

An admitted weakness of the current study is the lack of independent ground validation data for evaluating remote sensing estimates of convective area coverage. The TRMM ground validation program will soon produce maps of convective–stratiform coverage based upon ground-based radar observations from stations at Melbourne, Florida; Houston, Texas; Kwajalein, Republic of the Marshall Islands; and Darwin, Australia. The authors will compare TMI and PR estimates of convective area fraction to the classification data from these sites in a future study; however, the classification of ground-based radar data is derived from an analysis of reflectivity magnitude and horizontal texture that may not always reflect the underlying dynamical variations associated with convective and stratiform precipitation.

Coinciding with a limited number of satellite overpasses are dual-Doppler radar observations collected during three of the TRMM field campaigns: the South China Sea Monsoon Experiment, the TRMM Large-scale Biosphere–Atmosphere campaign, and the Kwajalein Experiment. Analysis of these dual-Doppler observations will yield fields of vertical air motion that can be used to check the dynamical consistency of reflectivity-based convective–stratiform classification fields. Also, latent heating vertical structure, which is strongly correlated with vertical air velocity in precipitating clouds, can be estimated by combining dual-Doppler vertical velocities with thermodynamic data from coincident radiosonde observations. If agreement between TMI convective coverage estimates and dynamically-consistent, ground-based estimates can be achieved, then the prospects for estimating latent heating distributions from TMI data are much improved.

Acknowledgments

The authors thank Grant Petty and Jeffrey Haferman for helpful discussions regarding the radiative modeling of aspherical ice-phase precipitation and Gerald Heymsfield for his insights into the variation of microwave polarization signatures from organized convective systems. We also thank Edward Zipser for his careful review of our manuscript. This study was funded by the TRMM Science Program.

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Fig. 1.
Fig. 1.

Polarization differences at 85.5 GHz plotted vs average 85.5-GHz radiances over (a) ocean and (b) land surfaces. TMI observations are plotted as points (nonraining areas) and open circles (raining areas). Diamonds represent radiative transfer simulations for atmospheres containing oriented, aspherical liquid and ice-phase precipitation. Dashed lines are approximate curves representing purely stratiform and purely convective precipitation conditions

Citation: Journal of Applied Meteorology 40, 9; 10.1175/1520-0450(2001)040<1577:ATPMFE>2.0.CO;2

Fig. 2.
Fig. 2.

Imagery of a mesoscale convective system near the Cape Verde Islands in the North Atlantic on 12 Sep 1999. (a), (b) The convective area 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

Citation: Journal of Applied Meteorology 40, 9; 10.1175/1520-0450(2001)040<1577:ATPMFE>2.0.CO;2

Fig. 3.
Fig. 3.

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

Citation: Journal of Applied Meteorology 40, 9; 10.1175/1520-0450(2001)040<1577:ATPMFE>2.0.CO;2

Fig. 4.
Fig. 4.

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

Citation: Journal of Applied Meteorology 40, 9; 10.1175/1520-0450(2001)040<1577:ATPMFE>2.0.CO;2

Fig. 5.
Fig. 5.

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

Citation: Journal of Applied Meteorology 40, 9; 10.1175/1520-0450(2001)040<1577:ATPMFE>2.0.CO;2

Fig. 6.
Fig. 6.

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

Citation: Journal of Applied Meteorology 40, 9; 10.1175/1520-0450(2001)040<1577:ATPMFE>2.0.CO;2

Fig. 7.
Fig. 7.

Scatterplots of coincident instantaneous convective area fraction estimates at 0.5° resolution from the TMI and PR over (a) ocean and (b) land surfaces. A solid line indicating “perfect agreement” of estimates, and dashed lines indicating 50% error, are included for reference

Citation: Journal of Applied Meteorology 40, 9; 10.1175/1520-0450(2001)040<1577:ATPMFE>2.0.CO;2

Fig. 8.
Fig. 8.

Monthly mean estimates of convective area percentage at 5° resolution from the TMI and PR for Feb 1998. Note that only TMI convective fraction estimates within the PR swath are included in the monthly average. For comparison, rain depths derived from the TMI (TRMM 2A12 algorithm) and PR (TRMM 3A25 algorithm) are shown in the third and fourth panels, respectively. Again, TMI monthly rain depths are derived only from TMI observations within the PR swath

Citation: Journal of Applied Meteorology 40, 9; 10.1175/1520-0450(2001)040<1577:ATPMFE>2.0.CO;2

Fig. 9.
Fig. 9.

Scatterplot of 5° resolution, monthly mean convective area percentage estimates from the TMI and PR for Feb 1998. A solid line indicating perfect agreement of estimates is included for reference

Citation: Journal of Applied Meteorology 40, 9; 10.1175/1520-0450(2001)040<1577:ATPMFE>2.0.CO;2

Table 1.

Statistics of collocated, instantaneous 0.5°-resolution estimates of convective area fraction from the TRMM TMI and PR over ocean and land surfaces. The samples contain 1374 and 823 collocated estimates over ocean and land, respectively

Table 1.
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