Enforcing Calibration in Ensemble Postprocessing

Desirable attributes of probability forecasts are maximal sharpness, consistent with calibration ("reliability"). The usual procedure of optimizing ensemble-postprocessing parameters by minimizing a proper scoring rule such as the continuous ranked probability score or the "ignorance" (i.e., negative log-likelihood) does not guarantee the necessary calibration condition, potentially compromising the value of the resulting forecasts to users. The calibration condition can be enforced by including a miscalibration penalty in the loss function to be minimized in parameter estimation. The procedure is illustrated using ensemble forecasts for minimum temperatures and windspeeds, postprocessed using member-by-member algorithms.