面向稀疏降水站点的套合各向异性贝叶斯地统计估计研究

由于形成过程中各种影响因素在不同尺度上的运行和相互作用,降水的空间变异普遍是发生在多尺度上地理过程叠加后的结果。建立较好地反映该动力学过程的多尺度复杂空间模型对于区域降水变量估计和空间分析是很有必要的,尤其是面向稀疏监测区域。贝叶斯地统计模型具有多尺度结构化建模的能力,提供了一种可以融合观测值(含有误差的外在实现)、未知变量、先验信息和复杂数据模型(隐藏的真实过程)的统计推断框架。鉴于降水现象在尺度和各向异性上的叠加特征,本研究将基于贝叶斯和地统计的理论和方法探讨二维随机场中存在的套合各向异性分解估计的可行性,并在对每个独立组分贡献定量计算的基础上,进一步分析和挖掘套合各向异性模型在降水插值中的应用潜力。结果表明:通过贝叶斯方法,稀疏数据中叠置的多尺度性和多方向性通过地统计套合模型可以得到有效的分解;复杂套合模型估计具有向下兼容简单套合模型的能力;套合各向异性协方差结构的使用对于区域降水插值的精度提升具有明显作用。

Bayesian Geostatistical Modelling for Precipitation Data with Nested Anisotropy Measured at Sparse Reference Stations

Spatially continuous precipitation data are important data input in hydrological simulation in a watershed, hydrological modeling of land surface, eco-environmental sensitivity evaluation, comprehensive investigation and zoning of geographical environment, and so on. These data are often interpolated from the discrete observations of monitoring points. However, due to the operations and interactions of the underlying physical processes on different scales, the spatial variations of precipitation are generally viewed as a result of the superposition of different geographical processes on multiple scales and directions. The multi-scale, multi-direction natures of geographical processes determine the weights between spatial points, which have an important impact on spatial interpolation. Therefore, it is necessary to establish a multi-scale and multi-direction spatial model to better reflect the dynamic process for regional precipitation estimation and spatial analysis, especially in sparse monitoring areas. Bayesian geostatistical models have the ability of multi-scale and multi-direction modeling and provide a scalable statistical inference framework by integrating observations (external implementation with errors), unknown variables, prior information, and complex dynamical models (real processes). In view of the superposition phenomena of precipitation on scales and directions, this study explored the possibility of decomposition estimates for the sparse data with nested anisotropy based on Bayesian and geostatistical methods to accurately determine the contribution of each independent component. We also further demonstrated the application potential of this model in precipitation interpolation. The results showed that, firstly, the nested anisotropy and multi-scale properties hidden in the sparse data could be well estimated by the Bayesian and geostatistical methods applied in the four random simulations with nested structures using a Fourier integration method. The more complex the model was, the more difficult the estimation was and the stronger the uncertainty was, and the convergence and estimation accuracy could be improved by introducing some prior information. The interpolation accuracy of the heterogeneous models was better than that of the models with simple isotropy or anisotropy. And also the more complex the covariance structure of the data was, the more obvious the improvement effect was. Secondly, complex structures had the ability of downward compatibility with simple structures, but simple structures did not have the ability of upward compatibility with complex structures. Finally, based on the interpolation results, the nested model played an obvious role in improving the accuracy of regional precipitation interpolation, which was about 10% higher than the estimation accuracy of the two basic models. Compared with the two basic structures, the method in this study not only identified two kinds of superposition information but also obtained the contributions of the two components, with a contribution ratio close to 1:1.