Upper-tail correction of multivariate synthetic environmental series using annual maxima

Reliable risk assessment of environmental systems often relies on long, multivariate synthetic time series produced by sampling, stochastic simulators and/or fast emulators. In practice, such simulations may reproduce bulk behavior and dependence reasonably well, yet misrepresent marginal upper tails, biasing estimates of rare, high-impact events. This short communication presents an annual maxima (AM)-centric, marginal post-processing method that (i) tests whether a correction is needed by comparing simulated AM to a target AM distribution based on historical records; and (ii) if needed, anchors simulated AM to target quantiles and propagates that adjustment to the full time series via a monotone interpolation that preserves ranks. Because the procedure preserves the empirical copula, rank-based dependence and copula-based tail dependence are retained, while marginal tails are aligned with the target. The method is intended as a lightweight safeguard against marginal tail misrepresentation in synthetic risk simulations, avoiding unnecessary complexity or retraining of the underlying generator. An application to climate-based wave simulations for Santoña (Spain) illustrates the approach and provides diagnostics for tail fit, bulk preservation, and dependence stability, showing that the method corrects return levels while minimally altering the time series.