Spatial Distance Metrics for Verification of Precipitation

<p>Precipitation is an essential meteorological variable affecting the biosphere and human societies. At the same time, the precipitation is notoriously difficult to predict and verify. Two new spatial distance metrics for verification of precipitation are presented. The aim was to develop measures that would provide a good and meaningful approximation of the displacement of precipitation events in the two fields. An estimate of spatial displacement is very appealing for forecast interpretation because it is easy to understand and mimics how humans tend to judge fields by eye. Contrary to most other distance metrics, the new metrics do not require thresholding and can thus be used to analyze binary and non-binary (e.g., continuous or multi-level) fields. The analysis of comparisons with idealized geometric fields showed that the new metrics provide a good and meaningful approximation of the displacement in situations with a single displaced event. Typically, the estimate of displacement was better than the results provided by most other metrics that were also analyzed. For situations with multiple events, the measure&#8217;s behavior was not inconsistent with a subjective evaluation. The analysis also showed that the measures are not overly sensitive to noise, their results are directly related to the actual displacements of events, and that the events with a larger magnitude have a bigger influence on the resulting value. The analysis of ECMWF precipitation forecasts over Europe and North Africa confirmed that the new metrics provide a meaningful approximation of the displacement in real-world situations. The uncertainty of the mean value of the metric can be estimated via statistical parameters linked to the width of the distribution. The trend and its statistical significance can be determined using an appropriate variant of the Mann-Kendall test, which properly accounts for the autocorrelation present in the time series. The source codes for efficient calculation of the metrics were published in a freely accessible repository.</p>