Assessing models for estimation and methods for uncertainty quantification for spatial return levels

The return level estimation is an essential topic in studying spatial extremes for environmental data. Recently, various models for spatial extremes have emerged, which generally yield different estimates for return levels, given the same data. In the meantime, several approaches that obtain confidence intervals (CIs) for return levels have arisen, and the results from different approaches can also largely disagree. These pose natural questions for assessing different return level estimation methods and different CI derivation approaches. In this article, we compare an array of popular models for spatial extremes in return level estimation, as well as three approaches in CI derivation, through extensive Monte Carlo simulations. Our results show that in general, max-stable models yield return level estimates with similar mean squared error, and the spatial generalized extreme value model also provides comparable estimates. The bootstrap method is recommended for max-stable models to compute the CI, and the profile likelihood CI works well for spatial generalized extreme value. We also evaluate the methods for return level interpolation at unknown spatial locations and find that kriging of marginal return level estimates performs as well as max-stable models.