Markov chain random field kriging for estimating extreme precipitation at unevenly distributed sites

Abstract

Delineating a homogeneous region is a standard procedure for rainfall frequency analysis in predicting precipitation in ungauged basins (PUB) in vast unpopulated areas. However, for data about the extreme weather events measured at stations that are asymmetrically distributed, the use of conventional regionalization techniques for forecasting is challenging. Vast depopulated zones, such as high-mountain catchment areas, basins, and swamps, are rich in features that influence precipitation, but they contain few stations. Hence, data from the populated area must be used to estimate data for the unpopulated areas. Accordingly, this study developed a novel spatial imputation approach for simulating spatial precipitation over a planar grid. In this approach, the Markov chain random field (MCRF) technique is used to estimate the parameters of the stochastic process of ungauged sites at all grid points from versatile juxtapositional directions. The probability learning-based MCRF approach differs from most traditional interpolation approaches, which may fail in unevenly distributed situations. After completing the training, the predicted precipitation in the mountainous areas was validated through a third-party dataset. Despite the quality of third-party data, our accuracy is confirmed both in standard metric and visual inspections. The normalized root mean square errors between the predicted values and the validation values were below 0.321, demonstrating that the MCRF step can effectively estimate the precipitation at unevenly distributed sites.