Uncertainty quantification of mean-areal radar-rainfall estimates

Abstract

The most common rainfall measuring sensor for validation of radar-rainfall products is the rain gauge. However, the difference between area-rainfall and rain gauge point-rainfall estimates imposes additional noise in the radar-rain gauge difference statistics, which should not be interpreted as radar error. A methodology is proposed to quantify the radar-rainfall error variance by separating the variance of the rain gauge area-point rainfall difference from the variance of radar-rain gauge ratio. The error in this research is defined as the ratio of the 'true' rainfall to the estimated mean-areal rainfall by radar and rain gauge. Both radar and rain gauge multiplicative errors are assumed to be stochastic variables, lognormally distributed, with zero covariance. The rain gauge area-point difference variance is quantified based on the areal-rainfall variance reduction factor evaluated in the logarithmic domain. The statistical method described here has two distinct characteristics: first, it proposes a range-dependent formulation for the error variance, and second, the error variance estimates are relative to the mean rainfall at the radar product grids. Two months of radar and rain gauge data from the Melbourne, Florida, WSR-88D are used to illustrate the proposed method. The study concentrates on hourly rainfall accumulations at 2- and 4-km grid resolutions. Results show that the area-point difference in rain gauge rainfall contributes up to 60% of the variance observed in radar-rain gauge differences, depending on the radar grid size, the location of the sampling point in the grid, and the distance from the radar.