Measuring Displacement Errors with Complex Wavelets

Abstract

Abstract When highly resolved precipitation forecasts are verified against observations, displacement errors tend to overshadow all other aspects of forecast quality. The appropriate treatment and explicit measurement of such errors remains a challenging task. This study explores a new verification technique that uses the phase of complex wavelet coefficients to quantify spatially varying displacements. Idealized and realistic test cases from the MesoVICT project demonstrate that our approach yields helpful results in a variety of situations where popular alternatives may struggle. Potential benefits of very high spatial resolutions can be identified even when the observational dataset is coarsely resolved itself. The new score can furthermore be applied not only to precipitation but also variables such as wind speed and potential temperature, thereby overcoming a limitation of many established location scores. Significance Statement One important requirement for a useful weather forecast is its ability to predict the placement of weather events such as cold fronts, low pressure systems, or groups of thunderstorms. Errors in the predicted location are not easy to quantify: some established quality measures combine location and other error sources in one score, others are only applicable if the data contain well-defined and easily identifiable objects. Here we introduce an alternative location score that avoids such assumptions and is thus widely applicable. As an additional benefit, we can separate displacement errors into different spatial scales and localize them on a weather map.