A Scalable Bayesian Spatiotemporal Model for Water Level Predictions Using a Nearest Neighbor Gaussian Process Approach

Obtaining accurate water level predictions is essential for water resource management and implementing flood mitigation strategies. Several data‐driven models can be found in the literature. However, there has been limited research with regard to addressing the challenges posed by large spatio‐temporally referenced hydrological datasets, in particular, the challenges of maintaining predictive performance and uncertainty quantification. Gaussian Processes (GPs) are commonly used to capture complex space‐time interactions. However, GPs are computationally expensive and suffer from poor scaling as the number of locations increases, due to required covariance matrix inversions. To overcome the computational bottleneck, the Nearest Neighbor Gaussian Process (NNGP) introduces a sparse precision matrix providing scalability without compromising its inferential capabilities. In this work, we introduce an innovative model in the hydrology field, specifically designed to handle large datasets consisting of a large number of spatial points across multiple hydrological basins, with daily observations over an extended period. We investigate the application of a Bayesian spatiotemporal NNGP model to a rich dataset of daily water levels of rivers located in Ireland. The dataset comprises a network of 301 monitoring stations situated in various basins across Ireland, measured over a period of 90 days. The proposed approach allows predictions of water levels at future time points, as well as the prediction at unobserved locations through spatial interpolation. Furthermore, the Bayesian approach provides the benefits in terms of uncertainty propagation and quantification, which are of considerable importance to the hydrology field. Our findings demonstrate that the proposed model outperforms competing scalable approaches in terms of accuracy and precision. Moreover, the proposed model enables predictions across a broader range of water bodies with minimal trade‐off in predictive performance.