Nonlinear estimation of short time precipitation using weather radar and surface observations

Abstract

Rain gauges are the foundation in hydrology to collect rainfall data, however, gauge observations alone are limited at representing the complete rainfall distribution. On the other hand, weather radar can provide complete rainfall distribution at high temporal and spatial resolution, yet concerns about the biases in radar rainfall estimates hamper the direct use of radar data in hydrological applications. Thus, merging radar measurements and rain gauge observations for surface precipitation estimation, by exploiting the strength and minimizing the weaknesses of each method, is in an area of active research. Among all the sources of errors of radar rainfall estimates, the uncertainty in the relationship between radar reflectivity Z and rainfall rate R, namely the Z-R relationship, is regarded as a massive source of uncertainty. There is a whole branch of studies on delivering an accurate Z-R relationship based on different drop size distributions, rainfall regimes and geographical locations. The focus of this study is not to derive an accurate Z-R relationship, but to correct the radar rainfall estimates by the available surface observations nonlinearly. Specifically, radar data are used in the relative magnitudes, as a quantile map to indicate the spatial pattern of precipitation. A marginal distribution function is generated based on surface observations and the collocated radar quantiles, whereby the quantile map can be transformed to a precipitation map. It is a common practice to construct radar-gauge pairs by assuming vertical and instant falling of the hydrometeors onto the ground. Obviously, the assumption is invalid on many occasions, as it ignores a significant fact that it takes time for the hydrometeors to reach the ground and during the descending, the hydrometeors are very likely to be drifted by the wind, especially with a large measurement height and with the existence of snow. The effect of wind drift can result in great discrepancy of radar and gauge data if the vertical collocation is assumed, especially for domains of small size and for events with convective behavior. To tackle this, a method to quantify the wind effect is proposed and the result of the quantification is integrated in surface precipitation estimation. The spatial pattern of precipitation changes along the vertical distance. The change in the spatial pattern can be induced by many factors, such as uniform movement of the field, further development of precipitation below the radar measurement height, evaporation, nonuniform movement of the field, etc. The quantification scheme for the wind effect proposed in this study considers an overall migration of the field. It is assumed that the entire field moves uniformly with a single vector. The other factors causing the vertical variation of the spatial pattern cannot be captured by the scheme. To remediate the situation, random changes in the spatial pattern are allowed. Two conditional simulation methods, random mixing and phase annealing, are employed to generate realizations of surface precipitation.