Efficient Estimation of Spatial-Temporal Extremes in Climate Data Using Bayesian Hierarchical Models

Project Abstract

Efficient estimation of spatial-temporal extremes in climate data is essential for robust risk assessment and climate adaptation planning. This study develops a Bayesian hierarchical modeling framework to jointly analyze extreme precipitation and temperature events across spatially distributed monitoring networks, incorporating temporal nonstationarity, anisotropic dependence, and non-Gaussian characteristics. We introduce a flexible hierarchical structure that combines a latent Gaussian field for spatial dependence with a non-stationary temporal component to capture evolving climate regimes. Spatial random effects are modeled via a continuous Gaussian Markov random field (GMRF) with a Matérn covariance, implemented using the integrated nested Laplace approximation (INLA) for scalable inference in large datasets. For extremes, we adopt a peak-over-threshold (POT) approach based on generalized Pareto distributions, allowing thresholds to vary spatially and temporally through covariate-informed link functions. The dependence between multiple climate variables and locations is captured through a joint multivariate extreme value framework built atop a copula-based augmentation, enabling accurate estimation of joint exceedance probabilities and tail dependencies. We address nonstationarity by incorporating covariates such as elevation, land cover, storm tracks, and large-scale climate indices (e.g., ENSO, SAM) into both marginal and dependence parameters, thereby enhancing predictive performance under climate change scenarios. Model selection and validation employ cross-validation, proper scoring rules, and posterior predictive checks, emphasizing calibration, sharpness, and tail accuracy. We compare the proposed hierarchical Bayesian approach against traditional frequentist and simpler Bayesian models, highlighting improvements in out-of-sample tail risk estimation, regional transferability, and uncertainty quantification. The methodology is demonstrated on a continental-scale dataset of daily precipitation and temperature observations spanning multiple decades, enriched with reanalysis-driven covariates to extend temporal coverage. Our results reveal spatially heterogeneous extremes with pronounced nonstationarity and evolving dependence structures, which are not adequately captured by stationary models. The posterior distributions provide coherent uncertainty quantification for return levels, spatial risk maps, and joint exceedance probabilities, facilitating risk-informed decision-making for infrastructure design, flood management, and climate resilience planning. Computational efficiency is achieved via a combination of dimension reduction for the latent field, robust priors to regularize sparse extremal data, and scalable approximation techniques, enabling practical application to high-resolution gridded datasets. Sensitivity analyses assess the impact of threshold choice, covariate specification, and prior settings on inference and predictions. The study contributes a versatile Bayesian framework for accurate, interpretable, and computationally feasible estimation of spatial-temporal extremes in climate data, with transferable components suitable for other environmental variables and settings where tail risk assessment is critical.

Project Overview

What This Project Is About

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A plain-language overview of how scientists study extreme climate events by looking at the biggest values in weather data over space and time. The project combines simple ideas about data patterns with a flexible modeling approach to better estimate rare but important events, like heatwaves or heavy rainfall, across regions and time periods.

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The Problem It Addresses

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Climate data often shows that extreme events are rare and vary across places and years, making them hard to predict with standard methods. This project tackles the challenge of estimating how large extremes can be in different locations and times, using a model that learns from many data sources at once to improve accuracy and uncertainty quantification.

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Objectives of the Project

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1. Explain what spatial-temporal extremes are in simple terms.
2. Understand how Bayesian hierarchical ideas help borrow strength across places and times.
3. Develop a basic model that can handle data from multiple weather stations or grids.
4. Assess how well the model estimates extreme values and their uncertainty.
5. Provide practical guidance for interpreting results in real-world climate studies.

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What You Will Do Step by Step

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1. Review basic concepts of extremes and Bayesian thinking at a plain level.
2. Collect or simulate climate data with known extremes for testing.
3. Build a simple hierarchical model that links data across locations and times.
4. Estimate model parameters using approachable computational tools.
5. Check accuracy by comparing to standard methods and through simple diagnostics.
6. Interpret the results and discuss practical implications for risk assessment.

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Expected Outcome

A clear, easy-to-use framework for estimating the size of extreme climate events across space and time, with readable uncertainty estimates and guidance for interpreting results in policy or planning contexts.