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

TL;DR

This paper introduces a two-stage statistical framework that combines sparse observational data and dense simulation outputs to improve the estimation of spatial extreme sea levels along the U.S. coast, demonstrating significant accuracy gains.

Contribution

The paper develops a novel fusion method using a linear model of coregionalization to integrate observations and simulations for spatial extreme value analysis.

Findings

35% reduction in 100-year return level RMSE

Fusion improves spatial extrapolation accuracy

Method implemented in R package evfuse

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.