A quantile calibration method for producing economically valuable probabilistic weather forecasts of continuous variables

A quantile calibration method is presented as a general approach for producing calibrated probabilistic weather forecasts of continuous variables. This method separates the task of modeling forecast uncertainty from the act of ensuring the statistical consistency of the probabilistic forecast. Perfecting the first step concentrates the probability distribution, while the latter performs statistical calibration.

The method takes any suitable probability distribution and uses a calibration function to relabel raw cumulative probabilities into calibrated cumulative probabilities. The pre-calibrated distribution can be created in a variety of ways that attempt to describe the uncertainty of the ensemble. The method can be applied to bounded mixed-discrete variables such as relative humidity. The advantage of the method is that it does not need to assume a particular distribution of the ensemble uncertainty, such as being normally distributed, in order to ensure proper probabilistic calibration. Instead, this uncertainty distribution is measured directly.

The method is tested on surface temperature and relative humidity forecasts, using a number of different uncertainty models. Fourteen ensemble forecasts and their corresponding observations at 34 locations in British Columbia, Canada were tested. When compared to a climatological reference forecast, the method produces economically more valuable forecasts over a range of decision-making thresholds and cost/loss ratios, and have better continuous ranked probability scores. It was found that for surface temperature forecasts, dressing each ensemble member with a Gaussian kernel worked best. For relative humidity forecasts a weighted ranks method worked best.-->