Accounting for representativeness in the verification of ensemble forecasts

Spatial variability of 2 m temperature, 10 m wind speed, and daily precipitation is analysed to characterize
to what extent measurements at a single location are representative of averages over a larger area. Characterization of representativeness error is made in probabilistic terms using parametric approaches, namely by fitting a normal, a truncated normal, and a censored shifted gamma distribution to observation measurements for the 3 weather variables of interest, respectively. Distribution parameters are estimated with the help of high-density network observational datasets. These results serve as a basis for accounting for representativeness error in ensemble verification. Uncertainty associated with the scale mismatch between forecast and observation is accounted for by applying a perturbed ensemble approach before the computation of scores. For all 3 variables investigated, verification results presented here quantify the large impact of representativeness error on forecast reliability and skill estimates.