Extreme precipitation often occurs simultaneously at several stations, amplifying damage. Classical spatial extremes models rely on block maxima (e.g., annual) and ignore daily records. Nearby in the archive are studies on extreme value analysis, noise reduction in spectra, and quantum systems, but direct neighbors on spatial precipitation extremes are scarce. This work fills the gap by offering a way to use all available data without complex multivariate threshold models.
The authors developed a two-step procedure. In the first step, for each station separately, a generalized extreme value (GEV) distribution is fitted to daily data using a point process that accounts for exceedances over a threshold. Spatial dependence is ignored at this step, making estimates of marginal parameters robust to misspecification of dependence. In the second step, fixing the marginal parameters, they estimate spatial dependence parameters from block maxima by maximizing a pairwise likelihood. A profile method is used for optimization, and standard errors are obtained by block bootstrap over years.
In simulations, the two-step method showed lower mean squared error for all marginal parameters compared to pairwise likelihood based on block maxima alone. The relative efficiency of the latter ranged from 23% to 95% depending on the parameter and the level of dependence. For the shape parameter, which determines the tail of the distribution, efficiency was particularly low (as low as 45%). When applied to data from 35 stations in California over 55 years, the method detected a significant El Niño effect at 22 stations versus 14 for the traditional approach. Confidence intervals for joint 50-year return levels narrowed by 27–51%.
This work differs from neighboring studies by being the first to systematically combine daily data and block maxima in a two-step estimation framework for spatial max-stable processes. This improves estimation accuracy without complicating the model or requiring multivariate thresholds. The method is simple to implement and intuitive for practitioners, facilitating its adoption in hydrology and climatology.
Possible directions include improving threshold selection for the point process, using the r largest order statistics instead of all exceedances, and comparing with multivariate threshold methods in terms of the robustness-efficiency trade-off. Extending the approach to spatio-temporal models is also promising.
The method can improve risk assessment for floods and co-occurring extreme events in insurance, urban planning, and emergency management.
The next step could be adapting the method to other regions and data types, as well as developing automatic threshold selection based on quantile regression.
In extreme value statistics, the choice of threshold for threshold methods and the proper handling of dependence in multivariate data remain open questions. This work sidesteps the multivariate threshold problem but does not solve threshold selection in the first step. This connects it to an active research area on robust estimation of distribution tails.
The joint 50-year return level for the station pair Napa and Winters at a Southern Oscillation Index value of -1 was about 10–15 cm of precipitation per day, depending on the estimation method.