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To mitigate the impacts associated with adverse weather conditions, meteorological services issue weather warnings to the general public. These warning systems rely heavily on forecasts issued by underlying prediction systems. When deciding which prediction system(s) to utilise when constructing warnings, it is important to compare systems in their ability to forecast the occurrence and severity of extreme weather events: if a warning system has access to more accurate forecasts for extreme weather, then it has the potential to generate more useful warnings. However, evaluating forecasts for extreme events is known to be a challenging task. This is exacerbated further by the fact that high-impact weather often manifests as a result of several confounding features, a realisation that has led to considerable recent research on so-called compound weather events. Both univariate and multivariate methods are therefore required to evaluate forecasts for high-impact weather. In this work, we review weighted verification tools, which allow particular outcomes to be emphasised during forecast evaluation, and demonstrate how these can be used to verify forecasts for compound weather events. We compare different approaches to construct weighted scoring rules, and exploit recent developments to apply these scores in a multivariate setting. Additionally, we leverage existing results on weighted scores to introduce weighted probability integral transform (PIT) histograms, allowing forecast calibration to be assessed conditionally on particular outcomes having occurred. To illustrate the practical benefit afforded by these weighted verification tools, they are applied to forecasts for extreme heat events issued by the Swiss Federal Office of Meteorology and Climatology (MeteoSwiss). Extreme heat events are defined in terms of MeteoSwiss heat warning criteria, and these verification methods therefore assess the forecasts' potential to generate useful weather warnings. |
