# A New Spatial Distance Metric for Verification of Precipitation
## 4 Discussion and Conclusions  
In this study, a new spatial distance metric for precipitation is presented. The new metric is meant to be used by meteorologists and atmospheric scientists who want to compare or evaluate the predictive skill of multiple numerical weather prediction models or determine if a newer version of the same model has a better predictive skill than the older version. In order to determine if the model possesses some minimal measure of skillfulness, the metric can also be evaluated for the model's forecasts and the corresponding persistence forecasts, and the results compared. Figure 7: Analysis of time-series of ECMWF precipitation forecasts. Monthly (solid line) and yearly (dash-dotted line with circles) averages of PSD values for the 6-h precipitation accumulations (0000–0600 UTC) in the period 2007–2014. Contrary to most other distance metrics, the PSD does not require thresholding (although it can still be used if one wishes to) and can thus be used to analyze binary and non-binary (e.g., continuous or multi-level) fields. Similar to other distance measures, it provides a global estimate of spatial distance, a single value related to the spatial distribution of all events present in the two fields (as opposed to providing a different value for each individual event). The analysis of 23 comparisons with idealized geometric fields showed that the new metric provides a good and meaningful approximation of the displacement in situations with a single displaced event. Typically the estimate of displacement provided by PSD was better than the results provided by most other metrics. For situations with multiple events, the measure's behavior was not inconsistent with a subjective evaluation. The analysis also showed that the measure is not overly sensitive to noise, its 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 metric provides a meaningful approximation of the displacement in real-world situations. If a sequence of fields is analyzed, the uncertainty of the mean PSD value can be estimated via statistical parameters linked to the width of the distribution (e.g., standard deviation, 10 and 90 percentile). 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 value of the new metric can be calculated efficiently via the use of Fast-Fourier-Transform-based convolution and the Bisection method. A python code package for efficient calculation of the PSD value is freely available. In the end, it is important to acknowledge that spatial displacement is only one type of forecast error [3]. It is thus always necessary to simultaneously use multiple metrics that can analyze different aspects of forecast performance. One example is the bias, which is a useful complementary measure to the PSD since it ignores the differences in the spatial distribution of precipitation and only compares the precipitation sums in the two fields. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app12084048/s1](https://www.mdpi.com/article/10.3390/app12084048/s1)]([https://www.mdpi.com/article/10.3390/app12084048/s1](https://www.mdpi.com/article/10.3390/app12084048/s1)), Section S1 includes a detailed description of how the new metric was devised, Section S2 provides a description of the comparisons with idealized geometric fields. Ref. [17] is cited in supplementary material. Conceptualization, G.S. ; methodology, G.S. ; software, G.S. ; validation, G.S. ; formal analysis, G.S. ; investigation, G.S. ; resources, G.S. ; data curation, G.S. ; writing--original draft preparation, G.S. ; writing--review and editing, G.S. ; visualization, G.S. ; supervision, G.S. ; project administration, G.S. ; funding acquisition, G.S.