New Developments of the Intensity-Scale Technique within the Spatial Verification Methods Intercomparison Project

The intensity-scale verification technique introduced in 2004 by Casati, Ross, and Stephenson is revisited and improved. Recalibration is no longer performed, and the intensity-scale skill score for biased forecasts is evaluated. Energy and its percentages are introduced in order to assess the bias on different scales and to characterize the overall scale structure of the precipitation fields. Aggregation of the intensity-scale statistics for multiple cases is performed, and confidence intervals are provided by bootstrapping. Four different approaches for addressing the dyadic domain constraints are illustrated and critically compared. The intensity-scale verification is applied to the case studies of the Intercomparison of Spatial Forecast Verification Methods Project. The geometric and synthetically perturbed cases show that the intensity-scale verification statistics are sensitive to displacement and bias errors. The intensity-scale skill score assesses the skill for different precipitation intensities and on different spatial scales, separately. The spatial scales of the error are attributed to both the size of the features and their displacement. The energy percentages allow one to objectively analyze the scale structure of the fields and to understand the intensity-scale relationship. Aggregated statistics for the Storm Prediction Center/National Severe Storms Laboratory (SPC/NSSL) 2005 Spring Program case studies show no significant differences among the models' skill; however, the 4-km simulations of the NCEP version of the Weather Research and Forecast model (WRF4 NCEP) overforecast to a greater extent than the 2-and 4-km simulations of the NCAR version of the WRF (WRF2 and WRF4 NCAR). For the aggregated multiple cases, the different approaches addressing the dyadic domain constraints lead to similar results. On the other hand, for a single case, tiling provides the most robust and reliable approach, since it smoothes the effects of the discrete wavelet support and does not alter the original precipitation fields.