Spatio-temporal model estimation and imputation of rainfall networks

High-quality observational data is essential for monitoring, modelling, and understanding climate patterns. Precipitation data serves as a primary input for various climate products such as climate normals and gridded products; however, careful preprocessing of raw data is required before going forward with any further analysis. This includes steps such as quality control and climate homogenisation, as well as the imputation of missing values. Missing data can greatly limit both the spatial and temporal coverage of a rainfall monitoring network, and it may introduce bias into the climate products derived from this data if the missingness is not properly addressed. However, the imputation of large networks faces several challenges, such as high-dimensional data, extensive gaps in observations, and significant computational costs when fitting imputation models. This thesis introduces several new imputation methods designed to address these challenges associated with large rainfall networks. The proposed techniques span multiple statistical areas, including regression-based methods alongside spatio-temporal modelling methods using likelihood-based and deep learning approaches. Many of these methods specifically address missing data, aiming to mitigate bias and uncertainty in estimated values associated with missingness. In comparison to other methods in the literature, the methods developed here are shown to perform favourably in several validations conducted on monthly rainfall totals collected by the Irish network from 1981-2010.