Uncertainty quantification of mean-areal radar-rainfall estimates

The most common rainfall measuring sensor for validation of radar-rainfall products is the rain gauge. However, the difference between area-rainfall a nd rain gauge point-rainfall estimates imposes additional noise in the rada r-rain gauge difference statistics, which should not be interpreted as rada r error. A methodology is proposed to quantify the radar-rainfall error var iance by separating the variance of the rain gauge area-point rainfall diff erence from the variance of radar-rain gauge ratio. The error in this resea rch is defined as the ratio of the "true" rainfall to the estimated mean-ar eal rainfall by radar and rain gauge. Both radar and rain gauge multiplicat ive errors are assumed to be stochastic variables, lognormally distributed, with zero covariance. The rain gauge area-point difference variance is qua ntified based on the areal-rainfall variance reduction factor evaluated in the logarithmic domain. The statistical method described here has two disti nct characteristics: first, it proposes a range-dependent formulation for t he 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 a t 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 r adar-rain gauge differences, depending on the radar grid size, the location of the sampling point in the grid, and the distance from the radar.