Scale issues in verification of precipitation forecasts

Precipitation forecasts from numerical weather prediction models are often compared to rain gauge observations to make inferences as to model performance and the "best" resolution needed to accurately capture the structure of observed precipitation. A common approach to quantitative precipitation forecast (QPF) verification is to interpolate the model-predicted areal averages (typically assigned to the center point of the model grid boxes) to the observation sites and compare observed and predicted point values using statistical scores such as bias and RMSE. In such an approach, the fact that the interpolated values and their uncertainty depend on the scale (model resolution) of the values from which the interpolation was done is typically ignored. This interpolation error, which comes from scale effects, is referred to here as the "representativeness error." It is a nonzero scale-dependent error even for the case of a perfect model and thus can be seen as independent of model performance. The scale dependency of the representativeness error can have a significant effect on model verification, especially when model performance is judged as a function of grid resolution. An alternative method is to upscale the gauge observations to areal averages and compare at the scale of the model output. Issues of scale arise here too, with a different scale dependency in the representativeness error. This paper examines the merits and limitations of both verification methods (area-to-point and point-to-area) in view of the pronounced spatial variability of precipitation fields and the inherent scale dependency of the representativeness error in each of the verification procedures. A composite method combining the two procedures is introduced and shown to diminish the scale dependency of the representativeness error.