The use of structure functions and spectra from numerical model output to determine effective model resolution

The effective model resolution of three numerical weather prediction (NWP) models is determined from analyses of spatial structure functions and spatial spectra. In this paper, the effective resolution is defined as the dimensions of the rectangular spatial filter that describes the net effect of all of the NWP model's numerical filtering and smoothing effects. These effects are determined by comparison of spatial statistics of the NWP model output with statistical climatologies derived from aircraft data for the upper troposphere and lower stratosphere. The comparisons are based on both spatial structure functions and spatial spectra. The structure function approach has fewer assumptions and fewer numerical artifacts. Accurate estimates of NWP effective model resolution require a robust climatology of the spatial statistics, which are a function of latitude and location, such as over mountainous regions. An artifact in the climatology of the velocity statistics resulting from mountain waves is identified from NWP model output and corroborated with research aircraft data, which has not been previously observed in global statistical climatologies.