The algorithms for 12-hourly probability of precipitation (POP12) and the deterministic, 6-hourly quantitative precipitation (QPF06) are described here. The procedure for POP12 is: (1) Populate cumulative distribution functions (CDFs) for forecast and analyzed to be used later in quantile mapping. Were every grid point processed without benefit of data from other points, 60 days of training data would likely be insufficient for estimating CDFs and adjusting the errors in the forecast. Accordingly, “supplemental” locations were identified for each grid point, and data from the supplemental locations were used to populate the forecast and analyzed CDFs used in the quantile mapping. (2) Load the ensemble from NCEP and Environment Canada deterministic and ensemble forecasts interpolated to ⅛-degree. (2) Using CDFs from the past 60 days of data, apply a stochastic quantile mapping procedure to the ensemble forecasts. (3) Generate probabilities from the ensemble relative frequency. (4) Spatially smooth the forecast using a Savitzky-Golay smoother, applying more smoothing in flatter areas.
The QPF06 algorithm is simpler: (1) Form a grand ensemble mean from the NCEP and Environment Canada deterministic and ensemble forecasts, again interpolated to ⅛-degree. (2) Quantile-map the mean forecast using CDFs of the ensemble mean and analyzed distributions. (3) Spatially smooth the field, similar to POP12.
Results for spring 2016 are provided demonstrating that the post-processing improves POP12 reliability and skill and the deterministic forecast bias while maintaining sharpness.