An Approach to Estimate the Areal Rain-Rate Distribution from Spaceborne Radar by the Use of Multiple Thresholds

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  • a NASA/Goddard Space Flight Center, Greenbelt, Maryland
  • | b Hughes STX Corporation, Lanham, Maryland
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Abstract

Estimates of rain rate derived from a spaceborne weather radar will be most reliable over an intermediate range of values. At light or heavy rain rates, where the signal-to-noise ratios are degraded either by small values of the backscattered power or by large attenuation, the accuracy will be poor. In forming an area average of the rain rate, an alternative to the averaging of the high-resolution estimates, irrespective of their individual accuracies, is a multiple threshold approach. The method is based on the fact that the Fractional area above a particular rain-rate threshold Rj is related to the cumulative distribution of rain rates evaluated at Rj. Varying the threshold over the effective dynamic range of the radar yields the cumulative distribution function over this range. To obtain the distribution at all rain rates, a lognormal or gamma test function is selected such that the mean-square error between the test function and the measured values is minimized. Once the unknown parameters are determined, the first-order statistics of the areawide rain-rate distribution can be found. Tests of the method with data from the SPANDAR radar provide comparisons between it and the single threshold and the direct averaging approaches.

Abstract

Estimates of rain rate derived from a spaceborne weather radar will be most reliable over an intermediate range of values. At light or heavy rain rates, where the signal-to-noise ratios are degraded either by small values of the backscattered power or by large attenuation, the accuracy will be poor. In forming an area average of the rain rate, an alternative to the averaging of the high-resolution estimates, irrespective of their individual accuracies, is a multiple threshold approach. The method is based on the fact that the Fractional area above a particular rain-rate threshold Rj is related to the cumulative distribution of rain rates evaluated at Rj. Varying the threshold over the effective dynamic range of the radar yields the cumulative distribution function over this range. To obtain the distribution at all rain rates, a lognormal or gamma test function is selected such that the mean-square error between the test function and the measured values is minimized. Once the unknown parameters are determined, the first-order statistics of the areawide rain-rate distribution can be found. Tests of the method with data from the SPANDAR radar provide comparisons between it and the single threshold and the direct averaging approaches.

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