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Jonathan P. Meagher and Ziad S. Haddad

Abstract

In this paper, an analytical treatment of the atmospheric remote sensing problem of determining the raindrop size distribution (DSD) with a spaceborne multifrequency microwave nadir-looking radar system is presented. It is typically assumed that with two radar measurements at different frequencies one ought to be able to calculate two state variables of the DSD: a bulk quantity, such as the rain rate, and a distribution shape parameter. To determine if this nonlinear problem can indeed be solved, the DSD is modeled as a Γ distribution and quadratic approximations to the corresponding radar–rain relations are used to examine the invertibility of the resulting system of equations in the case of two as well as three radar frequencies. From the investigation, it is found that for regions of DSD state space multiple solutions exist for two or even three different frequency radar measurements. This should not be surprising given the nonlinear coupled nature of the problem.

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Ziad S. Haddad, Jonathan P. Meagher, Stephen L. Durden, Eric A. Smith, and Eastwood Im

Abstract

The threat of flooding from landfalling tropical cyclones is a function of the local variation in rain rate and rain accumulation. To date, these have been inferred from single-frequency radar reflectivity measurements. However, the Tropical Rainfall Measuring Mission experience has confirmed that one of the main difficulties in retrieving rain profiles using a single-frequency radar is the unknown raindrop size distribution (DSD). A dual-frequency radar such as the one planned for the upcoming Global Precipitation Measurement (GPM) core satellite is expected to help sort out at least part of this DSD-induced ambiguity. However, the signature of precipitation at 14 GHz does not differ greatly from its signature at 35 GHz (the GPM radar frequencies). To determine the extent of the vertical variability of the DSD in tropical systems and to quantify the effectiveness of a dual-frequency radar in resolving this ambiguity, several different models of DSD shape are considered and used to estimate the rain-rate and mean-diameter profiles from the measurements made by Jet Propulsion Laboratory’s (JPL’s) airborne second generation precipitation radar (PR-2) over Hurricanes Gabrielle and Humberto during the Fourth Convection and Moisture Experiment (CAMEX-4) in September 2001. It turns out that the vertical structures of the rain profiles retrieved from the same measurements under different DSD assumptions are similar, but the profiles themselves are quantitatively significantly different.

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