Collado et al. (2026) Upper-tail correction of multivariate synthetic environmental series using annual maxima

Identification

• Journal: Stochastic Environmental Research and Risk Assessment
• Year: 2026
• Date: 2026-04-01
• Authors: Víctor Collado, Fernando J. Méndez, Roberto Mínguez
• DOI: 10.1007/s00477-026-03215-0

Research Groups

• Statistics department, Universidad Carlos III de Madrid, Getafe, Spain
• Geomatics and Ocean Engineering Group, ETSI Caminos, Canales y Puertos, Universidad de Cantabria, Santander, Spain

Short Summary

This paper presents an annual maxima (AM)-centric, marginal post-processing method to correct upper-tail misrepresentation in multivariate synthetic environmental time series, ensuring consistency with historical AM distributions while preserving rank-based dependence. The method is shown to effectively mitigate the overstatement of extreme event hazards in synthetic wave simulations, which would otherwise bias risk assessments.

Objective

• To develop a lightweight, model-agnostic marginal upper-tail correction method for multivariate synthetic environmental time series that ensures consistency of simulated annual maxima (AM) with a target historical AM distribution, while minimally perturbing the bulk behavior and preserving rank-based dependence.

Study Configuration

• Spatial Scale: Santoña, Spain (coastal location).
• Temporal Scale: Historical records (1979 to 2018, daily values), synthetic dataset (100 years, daily values).

Methodology and Data

• Models used:
  • Proposed method: AM-centric marginal post-processing with a test-if-needed gate and rank-preserving interpolation.
  • Extreme Value Theory (EVT): Generalized Extreme Value (GEV) distribution for annual maxima, Peaks-Over-Threshold (POT) model with Generalized Pareto Distribution (GPD) for exceedances.
  • Synthetic data generator: MUSCLE emulator (for wave height and peak period).
• Data sources:
  • Historical wave climate: CSIRO oceanographic database (CAWCR hindcast).
  • Synthetic data: Generated by MUSCLE emulator.

Main Results

• The method successfully corrects significant inflation of threshold exceedances in synthetic series, observed as approximately +73% for significant wave height ($Hs$) and +128% for peak period ($Tp$) relative to historical rates.
• Corrected synthetic annual maxima (AM) align coherently with the historical AM tail, preventing overestimation of hazard levels and return periods.
• The correction minimally alters the bulk of the distribution; empirical cumulative distribution functions (ECDFs) are virtually indistinguishable up to the 90th percentile.
• Rank-based dependence measures (Spearman's $\rho$, Kendall's $\tau$) are preserved by construction, and cross-variable tail co-movement diagnostics (e.g., conditional exceedance probabilities) remain essentially unchanged.
• Autocorrelation function (ACF) and partial autocorrelation function (PACF) vectors show minimal changes (e.g., Pearson correlation coefficient for 7-day lags: $r{ACF} = 0.9999$ for $Hs$, $r{ACF} \approx 1$ for $Tp$).

Contributions

• Introduces an AM-centric, conditional, and rank-preserving marginal post-processing method for multivariate synthetic environmental time series.
• Provides a lightweight, model-agnostic safeguard against marginal upper-tail misrepresentation in synthetic risk simulations, avoiding the need for complex retraining of underlying generators.
• Incorporates a "test-if-needed" gate based on a parametric bootstrap Cramér–von Mises (or Anderson–Darling) test to objectively determine if a correction is warranted, accounting for estimation uncertainty in the target AM law.
• Demonstrates the method's ability to correct return levels while preserving bulk behavior, temporal sequencing, and cross-variable rank dependence, crucial for reliable Monte Carlo risk analyses.

Funding

• R&D project “Algorithms for Stochastic Optimization Using Data-driven and Learning Analysis (ASTRAL)” (PID2023-151013NB-I00)
• R&D project “Towards a Digital TWIN for Physical and SocioEconomic Analysis of Coastal Systems (TWINPEACS:RISK)” (AIA2025-163820-C54)
• Project “SENSEI: Smart watEr NetworkS using artificial intEllIgence” (CNS2022-135472)
• HyBay (PID2022-141181OB-I00)
• Perfect-Storm (2023/TCN/003)
• CE4Wind (CPP2022-010118)
• MyFlood (PLEC2022-009362)
• (TWINPEACS:HYDRO)” (AIA2025-163820-C51)
• Environmental Security Technology Certification Program (ESTCP)
• Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.

Citation

@article{Collado2026Uppertail,
  author = {Collado, Víctor and Méndez, Fernando J. and Mínguez, Roberto},
  title = {Upper-tail correction of multivariate synthetic environmental series using annual maxima},
  journal = {Stochastic Environmental Research and Risk Assessment},
  year = {2026},
  doi = {10.1007/s00477-026-03215-0},
  url = {https://doi.org/10.1007/s00477-026-03215-0}
}