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Simple Derivation of the Nonuniform Beam Filling (NUBF) Bias Formula in Spaceborne Doppler Radar Measurements

The nonuniform beam filling (NUBF) bias in Doppler velocity measurements from a spaceborne precipitation radar is investigated. A simple derivation of the already-known formula that relates the bias to the along-track gradient of measured radar reflectivity in dBZ is shown. From the formula, the uncertainty of bias correction due to discretization is discussed. The error is shown to be proportional to the square of the spacing for discretization, and is related to the third moment of the distribution of the radar reflectivity convolved with the antenna pattern. The effectiveness of averaging is also shown from a simulation.