Severe thunderstorms cause significant economic and human damage in the US, so understanding their spatial structure is critical for risk assessment. Traditional studies have examined either the temporal evolution of marginal extremes or spatial dependence without considering temporal covariates. This work fills the gap by introducing a model where the spatial dependence of extremes changes over time under the influence of seasonality and El Niño. It stands apart: neighboring works on dark energy or neutrino tomography are thematically distant, but the archive also contains studies of the civilization cycle and exoplanet mountains, which also address variability in climate parameters.
The authors use NARR reanalysis data from 1979 to 2015, calculating monthly maxima of CAPE, SRH, and PROD on a 1°×1° grid over a region that includes Tornado Alley. For modeling, they employ a fractional Brown–Resnick field where the range parameter depends on ENSO and month via a tensor product of radial cubic splines and cyclic P-splines. Parameter estimation is performed using pairwise likelihood, and marginal distributions are first fitted separately at each grid point. To check the adequacy of max-stability, a bootstrap test based on the Anderson–Darling statistic is developed, and for model selection, a criterion called CLICb is proposed, which accounts for uncertainty in marginal estimates.
The model demonstrates good out-of-sample performance. The range parameter is minimal in summer for all variables and regions, and maximal in winter and spring. During El Niño, range increases for PROD in the northeastern and southeastern regions, for CAPE in eastern regions, and for SRH in northern regions. During La Niña, range increases are observed for PROD in the northeastern region and for CAPE in eastern regions. For example, for SRH in region 2 (north), range increases by about 20–30% during El Niño compared to the neutral phase. This means that extreme thunderstorm environments become more spatially extensive, that is, they cover a larger area.
This work shows for the first time that the spatial dependence of thunderstorm environment extremes is not static but is driven by large-scale atmospheric signals. This differs from previous studies that focused on marginal distributions or assumed constant dependence. The proposed method can be extended to other climate variables and regions, as well as to include additional covariates such as the North Atlantic Oscillation.
Further development may include spatially non-stationary dependence models that allow parameters to vary smoothly within a region rather than dividing it into homogeneous zones. Also promising is the study of other atmospheric signals, such as the Madden–Julian oscillation, and the inclusion of time as a covariate to identify climate trends. Local likelihood could be applied for more flexible fitting.
The results can improve risk assessment for severe thunderstorms in the US, especially for seasonal forecasting that accounts for the El Niño phase. The methodology is useful for analyzing spatial extremes in hydrology, finance, and ecology.
The next step could be applying the model to other regions of the world and including additional atmospheric indices. It is also important to test the robustness of the findings on longer data records and with other reanalysis products.
This work links the unresolved problem of non-stationary spatial dependence of extremes with large-scale climate variability. This opens the way to more accurate modeling of rare events under a changing climate, where classical stationarity assumptions may be violated.
The range parameter for PROD in the northeastern US during a strong El Niño can increase by nearly a factor of two compared to the neutral phase, meaning that thunderstorm systems can cover an area comparable to several states.
In Kim Stanley Robinson's novel 'Forty Signs of Rain', climate models predict extreme weather events, and the accuracy of such predictions depends on accounting for global oscillations like El Niño.