The statistical structure of short-range forecast errors as determined from radiosonde data

This paper analyses the statistical structure of the errors of the short-range wind forecasts used in the global data assimilation system at ECMWF, by verifying the forecasts against radiosonde data over North America. The kinematics of two-dimensional homogeneous turbulence is used to partition the perceived forecast errors into prediction errors which are horizontally correlated, and observational errors which are assumed to be horizontally uncorrelated. The theory further partitions the wind prediction errors into three components, viz. large-scale, rotational and divergent components, and provides a spectral description of the covariance and cross-covariance functions for stream function and velocity potential. The calculations also provide an estimate of the vertical error covariance matrices for prediction error and for radiosonde observational error, by which we mean the combined effects of instrumental error and errors of representativeness. The basic assumptions are that the forecast errors are h...