Interpretation of spatio-temporal variation of precipitation from spatially sparse measurements using Bayesian compressive sensing (BCS)

Precipitation might change rapidly and vary spatially, therefore, knowledge on spatio-temporal variation of precipitation plays a pivotal role in water resources management, hydrogeological hazard and risk assessment, and city resilience enhancement. However, precipitation monitoring data are collected through a limited number of precipitation stations in practice, and they are often sparse and discontinuous, particularly in spatial domain. Furthermore, regional precipitation data exhibits characteristics of seasonality, periodicity and highly non-stationarity on a long-time scale. Therefore, it is challenging to obtain a spatio-temporal variation of precipitation with high spatial resolution from monitoring data measured at a limited number of precipitation stations. To address these challenges, this study develops a non-parametric spatio-temporal Bayesian compressive sensing (ST-BCS) method for interpolation of spatio-temporally varying, but sparsely measured precipitation data in the spatial domain. The proposed method is able to not only provide precipitation interpolation results with high spatial resolution from a limited number of monitoring stations, but also quantify the associated interpolation uncertainty simultaneously. In addition, ST-BCS is directly applicable to the non-stationary spatio-temporal meteorological data. Furthermore, real precipitation datasets are established to benchmark different spatio-temporal interpolation methods. The benchmarking results show that the proposed ST-BCS method performs well and outperforms the spatial BCS method.