Observation Representativeness Error

NWP models simulate the atmospheric state on a given model grid, thereby principally
limiting the representation of atmospheric phenomena to scales larger than the grid point
distance. However, in addition such models generally filter away small-scale phenomena (of
several grid lengths) in order to avoid numerical instability of the discrete numerical model
equations, which also prevents upscale error growth originating from the relatively uncertain
small scales. Moreover, data assimilation systems act as so-called
low pass filters on the information provided by the observations, thereby essentially
rejecting observed information on scales smaller than the typical error structure of the NWP
model (background error covariance). So, observations do generally not affect the spectrum
of NWP model scales, but rather replace error variance with observed (true) variance. As a
consequence the simulated atmospheric state by NWP models is a smooth representation of
the true atmospheric state, lacking atmospheric variance in particular on the smallest
(turbulent) scales.

Based on wind energy spectra we demonstrate that global models generally not well resolve spatial scales below about 150-250 km, i.e., about 10-15 times the model grid size. Comparison of spectra from models and observations enables to quantify the observation representativeness error variance, a crucial component to give correct weight to observations in data assimilation.