Fusing Sparse Observations and Dense Simulations for Spatial Extreme Value Analysis: Application to U.S. Coastal Sea Levels

2026-03-03

AI Summary

This study addresses the high uncertainty in estimating spatial extremes such as 100-year sea levels due to sparse observational networks, which hinders reliable risk mapping. To overcome this limitation, the authors propose a two-stage frequentist framework that integrates sparse in situ measurements with dense physically based simulations. First, nonstationary generalized extreme value (GEV) distributions are independently fitted at each observation site. Then, a linear model of coregionalization (LMC) is employed to jointly model the spatial processes of GEV parameters from multiple data sources. Crucially, the method enables estimation of cross-source correlations using spatially interlaced networks without requiring colocated observations, thereby facilitating effective information transfer. The approach substantially improves computational efficiency and, when applied to U.S. coastal data from 1979–2021, reduces the root mean square error (RMSE) of 100-year sea level estimates by 35% compared to using observations alone, while maintaining superior performance in extrapolated regions.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Estimating spatial extremes from sparse observational networks produces uncertain return level maps, but dense output from physics-based simulation models is often available as a complementary data source. We develop a two-stage frequentist frame-work for fusing observations and simulations. In Stage 1, generalized extreme value (GEV) distributions are fitted independently at each site, with a nonstationary location parameter where appropriate to accommodate observed trends. In Stage 2, the parameter estimates from all sources are modeled jointly as a high-dimensional spatial process through a linear model of coregionalization (LMC). Cross-source correlations, estimated from spatially interspersed networks without co-located sites, provide the mechanism for information transfer; an analytic gradient for the resulting likelihood keeps estimation computationally practical. We apply the framework to U.S. coastal sea levels over 1979-2021, fusing 29 NOAA tide gauge records with 100 ADCIRC hydrodynamic simulation sites. Leave-one-out cross-validation shows a 35% reduction in 100-year return level RMSE relative to a gauge-only model. Geographic block cross-validation confirms that fusion benefits persist under spatial extrapolation. The approach is implemented in the R package evfuse.

Problem

• spatial extremes
• sparse observations
• dense simulations
• extreme value analysis
• sea level

Innovation

• data fusion
• spatial extremes
• linear model of coregionalization
• generalized extreme value
• cross-validation