The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: The wind field

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 horizontally homogeneous and that the observational errors are horizontally uncorrelated. Several important results are found. The wind prediction errors are comparable in magnitude with the wind observation errors. The prediction errors are dominated by the synoptic scales, but there is a substantial large scale wind error which reverses phase between the stratosphere and troposphere. The synoptic scale errors are largely non-divergent in the troposphere. There are good grounds for increasing the resolution of the analysis system, both in the horizontal and the vertical, over North America and other data-rich regions.