Bayesian hierarchical model for bias-correcting climate models

Abstract. Climate models, derived from process understanding, are essential tools in the study of climate change and its wide-ranging impacts. Hindcast and future simulations provide comprehensive spatiotemporal estimates of climatology that are frequently employed within the environmental sciences community, although the output can be afflicted with bias that impedes direct interpretation. Post-processing bias correction approaches utilise observational data to address this challenge, although they are typically criticised for not being physically justified and not considering uncertainty in the correction. This paper proposes a novel Bayesian bias correction framework that robustly propagates uncertainty and models underlying spatial covariance patterns. Shared latent Gaussian processes are assumed between the in situ observations and climate model output, with the aim of partially preserving the covariance structure from the climate model after bias correction, which is based on well-established physical laws. Results demonstrate added value in modelling shared generating processes under several simulated scenarios, with the most value added for the case of sparse in situ observations and smooth underlying bias. Additionally, the propagation of uncertainty to a simulated final bias-corrected time series is illustrated, which is of key importance to a range of stakeholders, such as climate scientists engaged in impact studies, decision-makers trying to understand the likelihood of particular scenarios and individuals involved in climate change adaption strategies where accurate risk assessment is required for optimal resource allocation. This paper focuses on one-dimensional simulated examples for clarity, although the code implementation is developed to also work on multi-dimensional input data, encouraging follow-on real-world application studies that will further validate performance and remaining limitations. The Bayesian framework supports uncertainty propagation under model adaptations required for specific applications, providing a flexible approach that increases the scope of data assimilation tasks more generally.