Mixed extreme wave climate model for reanalysis databases

TL;DR

The paper addresses the mismatch between wave reanalysis data and instrumental records in extreme-value analysis for offshore and coastal design. It introduces a mixed extreme-value framework where the annual reanalysis maximum $X$ is extended with a conditional difference $Y|X$ modeled as normal, producing the instrumental maximum $Z=X+Y$, with $F_Z(z)$ computed via numerical integration. By allowing $f_X$ to be a GEV or Pareto-Poisson and modeling $f_{Y|X}$ through heteroscedastic regression, the approach merges information from both data sources to yield more reliable and narrower return-period estimates. The method is validated through simulation and a Bilbao case study, showing reduced uncertainty and better alignment with instrumental data, thereby enhancing practical risk assessment for offshore structures.

Abstract

Hindcast or wave reanalysis databases (WRDB) constitute a powerful source with respect to instrumental records in the design of offshore and coastal structures, since they offer important advantages for the statistical characterization of wave climate variables, such as continuous long time records of significant wave heights, mean and peak periods, etc. However, reanalysis data is less accurate than instrumental records, making extreme data analysis derived from WRDB prone to under predict design return period values. This paper proposes a mixed extreme value model to deal with maxima, which takes full advantage of both (i) hindcast or wave reanalysis and (ii) instrumental records, reducing the uncertainty in its predictions. The resulting mixed model consistently merges the information given by both kinds of data sets, and it can be applied to any extreme value analysis distribution, such as generalized extreme value, peaks over threshold or Pareto-Poisson. The methodology is illustrated using both synthetically generated and real data, the latter taken from a given location on the northern Spanish coast.

Figures (5)

• Figure 1: Instrumental and reanalysis significant wave height records for Bilbao buoy location.
• Figure 4: Diagnostic plots for the GEV fit related Bilbao site reanalysis maxima (${\hbox{\boldmath $x$\unboldmath}}^{\rm max}$): i) PP plot, ii) QQ plot, iii) autocorrelation function, and iv) partial autocorrelation function.
• Figure 5: Diagnostic plots for the regression fit related Bilbao site $({\hbox{\boldmath $x$\unboldmath}}^{\rm max},{\hbox{\boldmath $y$\unboldmath}})$: i) data pairs, mean values, upper and lower bounds for both expected values and predicted response, ii) normal probability plot of studentized residuals, iii) autocorrelation function of studentized residuals , and iv) partial autocorrelation function of studentized residuals.
• Figure 6: Diagnostic plots for the GEV fit related Bilbao site instrumental maxima (${\hbox{\boldmath $x$\unboldmath}}^{\rm max}$): i) PP plot, ii) QQ plot, iii) autocorrelation function, and iv) partial autocorrelation function.
• Figure 7: Annual return period values from: i) reanalysis data, ii) instrumental data, iii) reanalysis GEV fitted model, iv) instrumental GEV fitted model, and v) reanalysis and instrumental fitted model. For the models 95% confidence bands are also plotted.