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Michael R. Farrar, Eric A. Smith, and Xuwu Xiang

Abstract

The impact of spatial resolution enhancement on estimates of tropical typhoon rainfall based on SSM/1 (Special Sensor Microwave/Imager) measurements is evaluated with six different microwave precipitation retrieval algorithms. Passive microwave estimates of rainfall are susceptible to errors from nonhomogeneous beam filling. The SSMIX ground footprints for the 19-, 22-, and 37-GHz channels have considerable overlap, and thus deconvolution techniques can be applied to enhance spatial resolution of measurements at those frequencies. The authors utilize a Backus-Gilbert matrix transform approach to accomplish the deconvolution so as to minimize noise amplification, as suggested by Stogryn. The deconvolution scheme is evaluated in terms of its impact on rain rates throughout the life cycles of seven tropical cyclones that occurred during the 1987 hurricane and typhoon season. The evaluation was performed on a single-frequency emission-based algorithm, a single- frequency scattering-based algorithm, two multiple-frequency statistical regression algorithms, and two physical inversion-based profile algorithms. While rainfall patterns detected by all algorithms were qualitatively enhanced by accentuating rainfall gradients and other smaller-wale features, quantitative responses to the deconvolution process were quite different for each algorithm. Furthermore, each of the algorithms, which uses its own distinct scientific approach, exhibits its own distinct properties in retrieving the rainfall patterns and in recovering the storm domain-averaged rain rates. The rain rates derived from the single-frequency emission algorithm were consistently increased by application of the deconvolution procedure. Time-and space-averaged rain rates were elevated by approximately 5%–6% due to the nonlinear relationship of rain rate to brightness temperature. On the other hand, rain rates from the single-frequency scattering algorithm were consistently reduced, with the time-space-averaged reduction between 10% and 20%. This effect is not algorithm related but is due to alteration of noise properties of the two polarized 37-GHz channels introduced during the deconvolution process. The multiple-frequency algorithms have more complex responses to deconvolution. Although instantaneous rain rates can be changed quite significantly by these methods, differences between deconvolved and raw time-space-averaged rain rates are small compared to the single-channel algorithms because the pixel-scale differences tend to be of a more random nature (positive and negative changes instead of consistent bias). However, it appears that the profile methods can undergo the greatest improvement to instantaneous rain rates after deconvolution is applied because they use perturbative inversion procedures rather than fixed brightness temperature-rain rate relationships.

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Bradley M. Muller, Henry E. Fuelberg, and Xuwu Xiang

Abstract

Radiative transfer simulations are performed to determine how water vapor and nonprecipitating cloud liquid water and ice particles within typical midlatitude atmospheres affect brightness temperatures T B's of moisture sounding channels used in the Advanced Microwave Sounding Unit (AMSU) and AMSU-like instruments. The purpose is to promote a general understanding of passive top-of-atmosphere T B's for window frequencies at 23.8, 89.0, and 157.0 GHz, and water vapor frequencies at 176.31, 180.3 1, and 182.31 GHz by documenting specific examples. This is accomplished through detailed analyses of T B's for idealized atmospheres, mostly representing temperate conditions over land. Cloud effects are considered in terms of five basic properties: droplet size distribution, phase, liquid or ice water content, altitude, and thickness. Effects on T B of changing surface emissivity also are addressed. The brightness temperature contribution functions are presented as an aid to physically interpreting AMSU T B's.

Both liquid and ice clouds impact the T B's in a variety of ways. The T B's at 23.8 and 89 GHZ are more strongly affected by altostratus liquid clouds than by cirrus clouds for equivalent water paths. In contrast, channels near 157 and 183 GHz are more strongly affected by ice clouds. Higher clouds have a water impact on 157- and 183-GHz T B's than do lower clouds. Clouds depress T B's of the higher-frequency channels by suppressing, but not necessarily obscuring, radiance contributions from below. Thus, T B's are less closely associated with cloud-top temperatures than are IR radiometric temperatures. Water vapor alone accounts for up to 89% of the total attenuation by a midtropospheric liquid cloud for channels near 183 GHz. The Rayleigh approximation is found to be adequate for typical droplet size distributions; however, Mie scattering effects from liquid droplets become important for droplet size distribution functions with modal radii greater than 20 µm near 157 and 183 GHz, and greater than 30–40 µm at 89 GHz. This is due mainly to the relatively small concentrations of droplets much larger than the mode radius. Orographic clouds and tropical cumuli have been observed to contain droplet size distributions with mode radii in the 30–40-µm range. Thus, as new instruments bridge the gap between microwave and infrared to frequencies even higher than 183 GHz, radiative transfer modelers are cautioned to explicitly address scattering characteristics of such clouds.

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Eric A. Smith, Harry J. Cooper, Xuwu Xiang, Alberto Mugnai, and Gregory J. Tripoli

Abstract

A cloud-radiation model is used to investigate the relationship between emerging microwave brightness temperatures (T B's) and vertically distributed mixtures of liquid and frozen hydrometeors as a means to establish the framework for a hybrid statistical-physical rainfall retrieval algorithm. The focus in this study is on the microwave characteristics of an intense hailstorm in which cold-rain microphysics dominate the precipitation process. The T B calculations exhibit a high degree of intercorrelation across a wide frequency range (15–128 GHz) due to the pervasive influence of large ice particles on attenuation of upwelling radiation emerging from the rain layers. When the radiative emission source is near blackbody, fluctuations of the mixing ratios of ice particles are wholly responsible for the T B variations, as opposed to fluctuations in the cloud-or raindrop mixing ratios. Supercooled cloud drops, suspended in the graupel layers, can exert influence on the T B's but only at the higher frequencies. Emission by the large ice particles themselves becomes an important radiative source to the emerging T B's at the top of the atmosphere as the graupel-mixing ratios increase and effectively block the radiative sources from within the liquid layers.

Strong relationships are found between the emerging T B's and various rain parameters, but these correlations are misleading in that the T B's are largely controlled by fluctuations in ice-particle mixing ratios, which in turn are highly correlated to fluctuations in liquid-particle mixing ratios. This does not negate the use of empirically based brightness-temperature-rain-rate (T B-RR) algorithms as useful tools for estimating precipitation (i.e., graupel particles ultimately fall out as rain), but it does point to a basic problem that remote-sensing methodology must address. More specifically, the hydrometeor profiles used for T B-RR algorithms must not be specified in an ad hoc fashion. It is argued that a cloud model can overcome the ad hoc assumptions.

It is shown that the lowest SSM/I frequency (19 GHz) is actually a better estimator of columnar ice water content than the highest frequency (85 GHz). This is because both cloud-water emission and multiple scattering by ice particles are more prevalent at 85 GHz than at 19 GHz (which tends to be mostly influenced by single scattering). As a consequence, 85 GHz is much more sensitive to the configurational details of the vertical distribution of large ice particles and to the presence of supercooled cloud drops within the lower ice layers.

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Eric A. Smith, F. Joseph Turk, Michael R. Farrar, Alberto Mugnai, and Xuwu Xiang

Abstract

This study presents research in support of the design and implementation of a combined radar–radiometer algorithm to be used for precipitation retrieval during the Tropical Rainfall Measuring Mission (TRMM). The combined algorithm approach is expected to overcome various difficulties that arise with a radar-only approach, particularly related to estimates of path-integrated attenuation (PIA) along the TRMM radar beam. A technique is described for estimating PIA at the 13.8-GHz frequency of the TRMM precipitation radar (PR) from 10.7-GHz brightness temperature T B measurements obtained from the TRMM microwave imager. Because the PR measures at an attenuating frequency, an independent estimate of PIA is used to constrain the solution to the radar equation, which incorporates effects of attenuation propagation along a radar beam. Through the use of variational or probabilistic techniques, the independent PIA calculations provide a means to adjust for errors that accumulate in estimates of range-dependent rain rates at progressively increasing range positions from radar reflectivity vectors. The accepted radar approach for obtaining PIA from ocean-viewing radar reflectivity measurements is called the surface reference technique, a scheme based on the difference in ocean surface cross sections between cloud-free and raining radar pixels. This technique has encountered problems, which are discussed and analyzed with the aid of coordinated aircraft radar (Airborne Rain Mapping Radar) and radiometer (Advanced Microwave Precipitation Radiometer) measurements obtained during the west Pacific Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment in 1993. The derived relationship expressing 13.8-GHz PIAs as a function of 10.7-GHz T B’s is based on statistical fitting of many thousands of radiative transfer (RTE) calculations in which the relevant physical and radiative parameters affecting transmission, absorption, and scattering in a raining column and the associated emission-scattering properties of the wind-roughened ocean surface are systematically varied over realistic range intervals. The results demonstrate that the T B–PIA relationship is stable, with a dynamic range up to about 8 dB. The RTE calculations are used to examine the relative merits of different viewing configurations of the radar and radiometer, and the associated uncertainty variance as the viewing configuration changes, since PIA uncertainty is an important control factor in the prototype TRMM combined algorithm.

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Giulia Panegrossi, Stefano Dietrich, Frank S. Marzano, Alberto Mugnai, Eric A. Smith, Xuwu Xiang, Gregory J. Tripoli, Pao K. Wang, and J. P. V. Poiares Baptista

Abstract

Precipitation estimation from passive microwave radiometry based on physically based profile retrieval algorithms must be aided by a microphysical generator providing structure information on the lower portions of the cloud, consistent with the upper-cloud structures that are sensed. One of the sources for this information is mesoscale model simulations involving explicit or parameterized microphysics. Such microphysical information can be then associated to brightness temperature signatures by using radiative transfer models, forming what are referred to as cloud–radiation databases. In this study cloud–radiation databases from three different storm simulations involving two different mesoscale models run at cloud scales are developed and analyzed. Each database relates a set of microphysical profile realizations describing the space–time properties of a given precipitating storm to multifrequency brightness temperatures associated to a measuring radiometer. In calculating the multifrequency signatures associated with the individual microphysical profiles over model space–time, the authors form what are called brightness temperature model manifolds. Their dimensionality is determined by the number of frequencies carried by the measuring radiometer. By then forming an analogous measurement manifold based on the actual radiometer observations, the radiative consistency between the model representation of a rain cloud and the measured representation are compared. In the analysis, the authors explore how various microphysical, macrophysical, and environmental factors affect the nature of the model manifolds, and how these factors produce or mitigate mismatch between the measurement and model manifolds. Various methods are examined that can be used to eliminate such mismatch. The various cloud–radiation databases are also used with a simplified profile retrieval algorithm to examine the sensitivity of the retrieved hydrometeor profiles and surface rainrates to the different microphysical, macrophysical, and environmental factors of the simulated storms. The results emphasize the need for physical retrieval algorithms to account for a number of these factors, thus preventing biased interpretation of the rain properties of precipitating storms, and minimizing rms uncertainties in the retrieved quantities.

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