基于矩阵分解的降水时空插值方法

Spatiotemporal interpolation method of rainfall based on matrix decomposition

为了提高基于雨量站网观测值估算降水空间分布的精度,同时考虑降水的时序发展趋势和站点空间分布,将传统的插值方法(反距离权重法、普通克里金法)和Funk矩阵分解(Funk-SVD)模型结合,提出了一种基于矩阵分解的插值方法,并采用黄河流域小浪底到花园口区间2009—2012年多场降水的日观测数据进行了精度检验。结果表明,通过与Funk-SVD模型结合,反距离权重法和普通克里金法在平均绝对误差、百分误差等评价指标上的精度提升均超过15%,改善效果在周围站点分布不均匀或降水量很大的情况下尤为明显,可以大幅度减少传统方法在降水插值过程中的估计误差,提升空间估算的精度。

To improve the estimation accuracy of rainfall spatial distribution based on the gauge network,an interpolation method is proposed based on the matrix factorization.By combining the traditional interpolation methods,including the inverse distance weighting(IDW)method and the ordinary Kriging(OK)method,and the Funk-SVD model,this method considered the temporal development of precipitation and the spatial distribution of gauges.The daily observation data of rainfall events from 2009 to 2012 between Xiaolangdi and Huayuankou were selected for the accuracy test.The results show that through combining with the Funk-SVD model,the estimation errors of the IDW and OK can be reduced over 15%in terms of MAE and PERC,and the improvement is especially obvious when the surrounding stations are unevenly distributed,or the rainfall is heavy.The proposed method can greatly reduce the estimation error of traditional methods in the precipitation interpolation process and help improve the accuracy of spatial estimation.