Merging Radar and Rain Gauge Data by Using Spatial–temporal Local Weighted Linear Regression Kriging for Quantitative Precipitation Estimation

Merging radar and rain gauge data is an important means of obtaining precipitation products with high accuracy and high spatial-temporal resolution. However, due to the change of the raindrop size distribution itself and the uncertainty of the radar observational data, it is an indisputable fact that A and b in the Z-R (radar reflectivity factor (Z) to rainfall rate (R)) relationship are complex functions of space and time, which has a great influence on the accuracy of radar-rain gauge quantitative precipitation estimation (QPE). In this study, in an effort to further improve the accuracy of radar-rain gauge QPE, spatial-temporal local weighted linear regression (STLWLR) and its corresponding regression kriging (STLWLRK) are proposed for merging radar and rain gauge data for QPE, for which the maximum number of Z-R pairs in the spatial-temporal neighborhood N, the spatial-temporal distance transformation parameter mu, and the specified threshold C of |e/s| are three key parameters. Specifically, cases that occurred on Hainan Island and the cross-validation mode were used to calibrate the three key parameters and to evaluate the two methods with the relative mean absolute error (RMAE) and bias as evaluation indicators. The results show that compared with the real-time-adjusted Z-R relationship (AZR) scheme and the two-step calibration technique of radar QPE (the AID scheme), STLWLR and STLWLRK with optimization parameters could further improve the accuracy of radar-rain gauge QPE. For 10-fold crossvalidation of the cases occurring on Hainan Island from 1 May to 31 October 2018 and for 1-hr, 3-hr, 6-hr, 12-hr, and 24-hr time scales, the RMAE of STLWLRK decreased by 6.3%, 8.4%, 8.4%, 8.2%, and 7.9%, respectively, compared with that of the AID scheme. The results also show that increasing time scale could reduce the error of radar-rain gauge QPE for different methods. As STLWLR is based on solid geography, mathematics, and radar meteorology and has been tested by a large number of cases, STLWLR and its optimization parameters should have certain universality. Overall, compared with traditional methods, STLWLRK is a more robust, easier to implement, more accurate, and less computationally expensive method.