Extended Abstract

used to deform the forecast field to match the obser vations. Two fields areconstructed: a displacement error field DIS obs (x,y) equal to the magnitude of thedisplacement vector, and an amplitude error field AMP obs (x,y) defined as the rootmean square (RMS) difference between t he observation field and the morphedforecast field. Both fields are set to zero wherever the observation field is zero, sothat errors are only defined wher e an obser ved feature is present. A nonzero valueof DIS obs (x,y) at the location of an observed feat ure implies that there was a forecastfeature within the maximum sea rch distanc e, while a zero value means either aperfect location forecast or that no feature was forecast within the maximum searchdistance. These two possibilit ies are distinguished by the amplitude error, which willbe large for a missed feature.Similarly, one can ask for each forecast feature how well it corresponds to theobservations in amplitude and location. For this, displacement and amplitude errorfields for the forecast space error, DIS fct (x,y) and AMP fct (x,y) can be constructed bymorphing the observation field onto the forecast field. In this case a large amplitudeerror for a feature where the di splacement error is zero in dicates a false alarm, i.e.something was forecast, but nothing was observed within the maximum searchdistance. Note that false alarms were not treated correctly by the FQM defined inKeil and Craig (2007), which applied the image matcher only in observation space.For many applications, it is not su fficient to have separate amplitude anddisplacement errors; a single measure of forecast quality is required. Beforecombining the two components, the displacement error fi eld is normalised by themaximum search distance D max , while the amplitude error field is normalised by acharacteristic intensity I 0 chosen to be typical of t he amplitude of the observedfeatures. A nalogously to t he computation of the amplit ude error the characteristicintensity I 0 is chosen to be the R MS amplitude of the observed field. Howeve r, thechoice of I 0 depends on the application. For compar ing forecast quality over largedatasets the characteristic intensity I 0 could be specified by a climatological rain rate,for instance.The normalisation is based on the princi ple that, for an observed feature withthe characteristic amplitude, a f orecast displaced by the distanc e D max giv es thesame error as a miss plus a false alarm, i.e. no forecast feature is found within adistance D max , but rather there are two unrelated errors in widely s eparated regions.The final displacement -amplitude score, DAS, is defined as the average of the twonormalised components:DAS DISDAMPmaxI 0 .The DAS values are bounded from below by ze ro (for a perfect forecast), and willtypically take values of order one, alt hough there is no upper limit. A value of onewould result from a forecast with the correct amplitude, but an average position errorof D max , or a forecast with the correct position with an RMS amplitude error of I 0 , or acombination of both types of error.3. DAS performance for geometric ICP casesIn the intercomparison project (ICP) of spatial verification measures there arethree different sets of test cases (Ahije vych et al. 2009) on which DAS has beenapplied. For geometric case 5 (forecast feat ure much larger in size, displac ed but-206-