Efficient Likelihood and Machine‐Learning Models for Spatiotemporal Rainfall Estimation and Imputation

A common challenge in modelling spatiotemporal precipitation data is the high computational costs associated with high‐dimensional data sets. In addition, frequent missing entries can severely impact data quality, but imputing missing values can enhance a rainfall network's ability to generate accurate climate reports and produce informative models. We present and outline a likelihood‐based imputation approach designed to greatly improve computational efficiency when modelling large spatiotemporal rainfall data. This method uses a spatiotemporal model fitted through Maximum Likelihood Estimation with the Expectation‐Maximisation algorithm, where multiple covariance functions with varying complexity have been explored. Additional techniques, such as the block composite likelihood and a block Toeplitz decomposition algorithm, are also applied to significantly reduce the method's computational burden. A second approach, Spatiotemporal DeepKriging, was also investigated. This method applies a Deep Neural Network model with spatiotemporal basis functions as input features to effectively capture dependencies in the data. It scales well computationally for large data sets, and various basis functions have been explored. Both methods were compared to previously established regression‐based imputation methods, namely Elastic‐Net Chained Equations (ENCE) and Multiple Imputation by Chained Equations with Direct Use of Regularised Regression (MICE DURR). All methods were applied to monthly precipitation totals from an Irish rainfall network of 474 stations. Both ENCE and MICE DURR achieved the highest imputation accuracy for 10‐fold cross‐validation; though this advantage largely disappears when validating under temporal or spatiotemporal gaps. In addition, unlike ENCE and MICE DURR, both the likelihood‐based method and DeepKriging fit a global spatiotemporal model, improving interpretability and supporting prediction beyond station locations.