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To mitigate the impacts associated with adverse weather conditions,meteorological services issue weather warnings to the general public. Thesewarnings rely heavily on forecasts issued by underlying prediction systems.When deciding which prediction system(s) to utilise to construct warnings, itis important to compare systems in their ability to forecast the occurrence andseverity of extreme weather events. However, evaluating forecasts for extremeevents is known to be a challenging task. This is exacerbated further by thefact that high-impact weather often manifests as a result of severalconfounding features, a realisation that has led to considerable research onso-called compound weather events. Both univariate and multivariate methods aretherefore required to evaluate forecasts for high-impact weather. In thispaper, we discuss weighted verification tools, which allow particular outcomesto be emphasised during forecast evaluation. We review and compare differentapproaches to construct weighted scoring rules, both in a univariate andmultivariate setting, and we leverage existing results on weighted scores tointroduce weighted probability integral transform (PIT) histograms, allowingforecast calibration to be assessed conditionally on particular outcomes havingoccurred. To illustrate the practical benefit afforded by these weightedverification tools, they are employed in a case study to evaluate forecasts forextreme heat events issued by the Swiss Federal Office of Meteorology andClimatology (MeteoSwiss).

Weighted verification tools to evaluate univariate and multivariate forecasts for high-impact weather events