A Spatial and Spatiotemporal Statistical Downscaling Model for Combining Spatially Misaligned Maximum Temperature Data Using R‐INLA

Africa is one of the most vulnerable regions to climate change. However, studying climate change and its impacts in Africa is very scarce due to the limited availability and access to climate data. Although weather stations provide accurate climate measurements, they are sparse and unevenly distributed across Africa and suffer from large proportions of missingness over space and time. Physical climate model output presents another source of climate gridded data that cover large and dense spatial and temporal domains at a certain resolution, but not at smaller scales. Physical climate model data do not account for uncertainty in the data and hence tend to exhibit bias compared to in‐situ observations. In an attempt to enhance the accuracy of climate model outputs and the spatial coverage of in‐situ data, simulated climate model data are statistically calibrated against real measurements from weather stations. This paper presents a statistical downscaling framework for combining in‐situ maximum temperature observations from weather stations across the Nile Basin countries with gridded data simulated from a regional climate model (RCM) across the same study region. To account for the spatial misalignment between the two datasets and the uncertainty from the two data sources and propagate it to predictions, a spatially varying coefficients (SVCs) coregionalization model is employed. This model assumes a joint distribution between the covariate (simulated model output) and the response (in‐situ observations) and allows for a spatially varying relationship between the observed and simulated data across the study region. The proposed model is fitted under a hierarchical Bayesian framework using integrated nested Laplace approximation (INLA) coupled with a stochastic partial differential equations (SPDEs) approach. To allow for future predictions, the model has also been extended to account for the temporal structure in spatiotemporal data. By comparing the model predictions against predictions from a global coregionalization model, as well as a generalized additive model (GAM) and an ordinary spatial interpolation (kriging) model relying only on one source of data, the proposed model proved to be relatively better.