Estimating the scaling of rain rate moments from radar and rain gauge

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Abstract

[1] Rain rate is a physical parameter that is only defined over some spatial or spatial-temporal integration volume. The moments of rain rate fields calculated from measurements derived from integration volumes of the same shape and a range of sizes are commonly used as a summarizing statistic of the rain rate process. Ranges of scales are known as stochastically scaling, either simple or multiscaling, when the moments are a power law of integration volume size. The identification of scaling ranges provides information about the dominant physical processes leading to rain rate variation and allow simulation models to be devised. The spatial moment scaling statistics of rain fields have been estimated from radar data many times. In this paper, three real and potential problems with the reported statistics are identified; that is, the existence of moments is not verified, the effects of interpolation have not been considered and the inhomogeneity introduced by variation in radar sample volume with range has been ignored. Radar data from the Chilbolton CAMRa radar in the UK are analyzed, and the existence of positive moments of all orders is demonstrated. An algorithm has been implemented for the calculation of moments from spatially averaged rain data on a regular polar grid. The resulting moments are consistent with cosited rain gauge data and show smooth variation across the scales considered, 300 m to 10 km and 10 s to 6 hours. The resulting moments are well approximated by two multiscaling ranges with a scale break around 3 km or 300 s.

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