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. © 2022, Science Press. All right reserved.