Spatially localized dimensionality reduction for storm surge analysis: a Non-negative Matrix Factorization framework for imputation, bias correction, and surrogate modeling

Accurate characterization of storm surge hazards relies on high-fidelity hydrodynamic simulations and coastal sensor networks that together generate massive, high-dimensional datasets; yet these resources frequently suffer from incomplete spatial coverage, sparse observational records, and high dimensionality. Traditional dimensionality reduction techniques, such as Principal Component Analysis (PCA), cannot natively accommodate missing data and produce abstract global modes that lack explicit spatial localization. This study presents a novel data-driven framework based on Non-negative Matrix Factorization (NMF) to address these operational challenges in storm surge modeling and risk assessment. Unlike global decomposition methods, NMF decomposes surge fields into additive, spatially localized patterns, enabling native handling of missing values through mask-constrained optimization. The framework's utility is demonstrated through three proof-of-concept applications using the US Army Corps of Engineers' North Atlantic Coast Comprehensive Study (NACCS) storm surge database. For imputation, missing data is recovered with high accuracy; for synthetic bias correction, bias is significantly reduced by projecting sparse high-fidelity data onto dense low-fidelity fields; for surrogate modeling, NMF achieves predictive accuracy comparable to PCA while providing location-specific reduced dimensions. These results establish NMF's effectiveness not only as a dimensionality reduction technique, but also as a practical spatially interpretable tool for coastal modelers to manage incomplete data and enhance the reliability of storm surge risk assessments.