The skill of probabilistic precipitation forecasts under observational uncertainties within the generalized likelihood uncertainty estimation framework for hydrological applications

A methodology for evaluating ensemble forecasts, taking into account observational uncertainties for catchment-based precipitation averages, is introduced. Probability distributions for mean catchment precipitation are derived with the Generalized Likelihood Uncertainty Estimation (GLUE) method. The observation uncertainty includes errors in the measurements, uncertainty as a result of the inhomogeneities in the rain gauge network, and representativeness errors introduced by the interpolation methods. The closeness of the forecast probability distribution to the observed fields is measured using the Brier skill score, rank histograms, relative entropy, and the ratio between the ensemble spread and the error of the ensemble-median forecast (spread-error ratio). Four different methods have been used to interpolate observations on the catchment regions. Results from a 43-day period (20 July-31 August 2002) show little sensitivity to the interpolation method used. The rank histograms and the relative entropy better show the effect of introducing observation uncertainty, although this effect on the Brier skill score and the spread-error ratio is not very large. The case study indicates that overall observation uncertainty should be taken into account when evaluating forecast skill.