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  • Author or Editor: S. Joseph Munchak x
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S. Joseph Munchak and Ali Tokay

Abstract

Observations of raindrop size distributions (DSDs) have validated the use of three-parameter distribution functions in representing the observed spectra. However, dual-frequency radar measurements are limited to retrieving two independent parameters of the DSD, thus requiring a constraint on a three-parameter distribution. In this study, disdrometer observations from a variety of climate regions are employed to develop constraints on the gamma distribution that are optimized for dual-frequency radar rainfall retrievals. These observations are composited by reflectivity, and then gamma parameters are fit to the composites. The results show considerable variability in shape parameter between regions and within a region at different reflectivities. Most notable is that oceanic regions exhibit maxima in shape parameter at 13.6-GHz reflectivities between 40 and 50 dBZ, in contrast to continental regions. The shape parameter and slope parameter of all composite DSDs are poorly correlated. Thus, constraints of a constant shape parameter or shape parameter–slope parameter relationship are inadequate to represent the observed variability. However, the shape and slope parameters are highly correlated at a given reflectivity. Constraints of a fixed shape parameter and relationships between a shape parameter m and slope parameter Λ, both of which are given as functions of 13.6-GHz reflectivity, are applied to retrieve rain rate, liquid water content, and mean mass diameter from the composites. The m–Λ relationships perform best at high reflectivity (dBZ 13.6 > 35), whereas the fixed shape parameter generally results in lower error at medium and low reflectivities (dBZ 13.6 < 35). All calculations have been made under the assumption that the reflectivity measurements have been corrected for attenuation.

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S. Joseph Munchak and Christian D. Kummerow

Abstract

Although zonal mean rain rates from the Tropical Rainfall Measuring Mission (TRMM) are in good (<10%) agreement between the TRMM Microwave Imager (TMI) and precipitation radar (PR) rainfall algorithms, significant uncertainties remain in some regions where these estimates differ by as much as 30% over the period of record. Previous comparisons of these algorithms with ground validation (GV) rainfall have shown significant (>10%) biases of differing sign at various GV locations. Reducing these biases is important in the context of developing a database of cloud profiles for passive microwave retrievals that is based upon the PR-measured profiles. A retrieval framework based upon optimal estimation theory is proposed wherein three parameters describing the raindrop size distribution (DSD), ice particle size distribution, and cloud water path (cLWP) are retrieved for each radar profile. The modular nature of the framework provides the opportunity to test the sensitivity of the retrieval to the inclusion of different measurements, retrieved parameters, and models for microwave scattering properties of hydrometeors. The retrieved rainfall rate is found to be strongly sensitive to the a priori constraints in DSD and cLWP; thus, these parameters are tuned to match polarimetric radar estimates of rainfall near Kwajalein, Republic of Marshall Islands. An independent validation against gauge-tuned radar rainfall estimates at Melbourne, Florida, shows agreement within 2%, which exceeds previous algorithms’ ability to match rainfall at these two sites. Errors between observed and simulated brightness temperatures are reduced and climatological features of the DSD, as measured by disdrometers at these two locations, are also reproduced in the output of the combined algorithm.

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Christopher R. Williams, V. N. Bringi, Lawrence D. Carey, V. Chandrasekar, Patrick N. Gatlin, Ziad S. Haddad, Robert Meneghini, S. Joseph Munchak, Stephen W. Nesbitt, Walter A. Petersen, Simone Tanelli, Ali Tokay, Anna Wilson, and David B. Wolff
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Christopher R. Williams, V. N. Bringi, Lawrence D. Carey, V. Chandrasekar, Patrick N. Gatlin, Ziad S. Haddad, Robert Meneghini, S. Joseph Munchak, Stephen W. Nesbitt, Walter A. Petersen, Simone Tanelli, Ali Tokay, Anna Wilson, and David B. Wolff
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Christopher R. Williams, V. N. Bringi, Lawrence D. Carey, V. Chandrasekar, Patrick N. Gatlin, Ziad S. Haddad, Robert Meneghini, S. Joseph Munchak, Stephen W. Nesbitt, Walter A. Petersen, Simone Tanelli, Ali Tokay, Anna Wilson, and David B. Wolff

Abstract

Rainfall retrieval algorithms often assume a gamma-shaped raindrop size distribution (DSD) with three mathematical parameters N w, D m, and μ. If only two independent measurements are available, as with the dual-frequency precipitation radar on the Global Precipitation Measurement (GPM) mission core satellite, then retrieval algorithms are underconstrained and require assumptions about DSD parameters. To reduce the number of free parameters, algorithms can assume that μ is either a constant or a function of D m. Previous studies have suggested μ–Λ constraints [where Λ = (4 + μ)/D m], but controversies exist over whether μ–Λ constraints result from physical processes or mathematical artifacts due to high correlations between gamma DSD parameters. This study avoids mathematical artifacts by developing joint probability distribution functions (joint PDFs) of statistically independent DSD attributes derived from the raindrop mass spectrum. These joint PDFs are then mapped into gamma-shaped DSD parameter joint PDFs that can be used in probabilistic rainfall retrieval algorithms as proposed for the GPM satellite program. Surface disdrometer data show a high correlation coefficient between the mass spectrum mean diameter D m and mass spectrum standard deviation σ m. To remove correlations between DSD attributes, a normalized mass spectrum standard deviation is constructed to be statistically independent of D m, with representing the most likely value and std representing its dispersion. Joint PDFs of D m and μ are created from D m and . A simple algorithm shows that rain-rate estimates had smaller biases when assuming the DSD breadth of than when assuming a constant μ.

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