Geostatistical Based Models for the Spatial Adjustment of Radar Rainfall Data in Typhoon Events at a High-Elevation River Watershed

Abstract

Geographical constraints limit the number and placement of gauges, especially in mountainous regions, so that rainfall values over the ungauged regions are generally estimated through spatial interpolation. However, spatial interpolation easily misses the representation of the overall rainfall distribution due to undersampling if the number of stations is insufficient. In this study, two algorithms based on the multivariate regression-kriging (RK) and merging spatial interpolation techniques were developed to adjust rain fields from unreliable radar estimates using gauge observations as target values for the high-elevation Chenyulan River watershed in Taiwan. The developed geostatistical models were applied to the events of five moderate to high magnitude typhoons, namely Kalmaegi, Morakot, Fungwong, Sinlaku, and Fanapi, that struck Taiwan in the past 12 years, such that the QPESUMS’ (quantitative precipitation estimation and segregation using multiple sensors) radar rainfall data could be reasonably corrected with accuracy, especially when the sampling conditions were inadequate. The interpolated rainfall values by the RK and merging techniques were cross validated with the gauge measurements and compared to the interpolated results from the ordinary kriging (OK) method. The comparisons and performance evaluations were carried out and analyzed from three different aspects (error analysis, hyetographs, and data scattering plots along the 45-degree reference line). Based on the results, it was clearly shown that both of the RK and merging methods could effectively produce reliable rainfall data covering the study watershed. Both approaches could improve the event rainfall values, with the root-mean-square error (RMSE) reduced by up to roughly 30% to 40% at locations inside the watershed. The averaged coefficient of efficiency (CE) from the adjusted rainfall data could also be improved to the level of 0.84 or above. It was concluded that the original QPESUMS rainfall data through the process of RK or merging spatial interpolations could be corrected with better accuracy for most stations tested. According to the error analysis, relatively, the RK procedure, when applied to the five typhoon events, consistently made better adjustments on the original radar rainfall data than the merging method did for fitting to the gauge data. In addition, the RK and merging methods were demonstrated to outperform the univariate OK method for correcting the radar data, especially for the locations with the issues of having inadequate numbers of gauge stations around them or distant from each other.

Keywords

• radar rainfall data
• geostatistical models
• spatial interpolation
• regression kriging
• semivariogram