Spatial Approach of Peaks‐Over‐Thresholds in Trend Detection of Extremes

ABSTRACT In this study, recent trends in extreme temperatures and rainfall are evaluated using the statistical theory of extreme values, in a non‐stationary context. We extend the non‐stationary pointwise threshold exceedances approach to spatial threshold exceedances. The temporal evolution of the extremes is handled pointwise by the peaks‐over‐threshold approach. First, evolution of the parameters of the distribution of exceedances and the intensity of extreme event occurrences for several meteorological variables are described as functions of time. Then, the spatial dependence structure attached to threshold exceedances is integrated using generalized ‐Pareto processes in a non‐stationary framework. In addition to better taking spatial dependence into account, our method allows us to simulate spatial exceedance processes at different dates and predict non‐stationary return levels at desired times by extrapolating the trends identified in the marginal distributions and the estimated dependence structure. Our approach is applied to temperature and rainfall data in Burkina Faso.