A New Spatial Scale Decomposition of the Brier Score for the Verification of Probabilistic Lightning Forecasts

A scale decomposition of the Brier score for evaluating spatial probabilistic forecasts is presented. The technique is illustrated on the Canadian Meteorological Center lightning probabilistic forecasts. Probability forecasts of lightning rate for 3 hour time windows and 22 km spatial resolution are verified against lightning frequencies from the North American Lightning Detection Network on a domain encompassing Canada and the northern United States. Verification is performed for lightning rates exceeding different thresholds, to evaluate the forecast performance both for modest and intense lightning activity. Forecast and observation are decomposed into the sum of components on different spatial scales by performing a 2D Haar wavelet decomposition. Evaluation at different spatial scales is then performed by evaluating Brier score and skill score for each spatial scale component.