BAYESIAN HIERARCHICAL AND MULTILEVEL MODELS FOR PREDICTING THE IMPACT OF CLIMATE CHANGE ON ENVIRONMENTAL SYSTEMS WITH UNCERTAINTY QUANTIFICATION

Abstract

Climate change exerts profound, nonlinear impacts on environmental systems ranging from sea-level rise and coastal flooding to shifts in species distributions, hydrological cycles, and ecosystem services yet predictive modeling is hampered by deep uncertainties in climate forcings, parameterizations, initial conditions, and socio-economic scenarios. Bayesian hierarchical and multilevel models provide a principled framework for addressing these challenges by explicitly partitioning and propagating uncertainty across spatial, temporal, and process scales. This review synthesizes recent advances in Bayesian hierarchical modeling (BHMs) and multilevel/hierarchical structures for climate impact assessment, emphasizing: (i) Gaussian process and spatial random effects models for downscaling coarse-resolution climate projections; (ii) multilevel latent process formulations that integrate mechanistic sub-models with observational data hierarchies; (iii) hierarchical Bayesian calibration of complex process-based simulators (e.g., hydrological, ecological, and ice-sheet models) via Markov chain Monte Carlo (MCMC), variational inference, and Hamiltonian Monte Carlo; (iv) uncertainty quantification through full posterior inference, credible intervals, and probabilistic forecasts; and (v) multifidelity emulation and active learning strategies to reduce computational cost. Applications span sea-level rise projection, compound flooding risk, species range shifts under RCP/SSP scenarios, watershed hydrology, and extreme event attribution. These approaches consistently outperform deterministic or frequentist alternatives in capturing tail risks, propagating structural uncertainties, and providing decision-relevant probabilistic outputs. Key challenges computational scalability for high-dimensional posteriors, model discrepancy, non-Gaussian likelihoods, and integration of diverse data sources are addressed through scalable approximations (INLA, EP, variational Bayes), discrepancy modeling, and hybrid physics-informed techniques. The convergence of Bayesian hierarchical methods with modern computational statistics positions them as indispensable tools for robust, uncertainty-aware climate impact prediction and adaptation planning.