Modern global variational data assimilation systems require the specification of statistics of background error at all resolved scales from the tidal scales upwards. A convenient way to calculate the statistics is from a sample of global fields which have statistical properties similar to those of background error. A common approach (introduced by Parrish and Derber (1992) and consequently dubbed the "NMC method" by some authors) is to use differences between short-range forecasts of different lengths, but which verify at the same time.

In this paper, an alternative approach to the calculation of background error statistics is presented. An ensemble of analyses is run. For each member of the ensemble, the observations are perturbed by the addition of random noise with the statistical characteristics of observation error. Differences between ensemble members' background fields provide a surrogate for the required sample of fields of background error. Background error statistics calculated using the new method differ significantly from those calculated using the NMC method, and were found to produce a significant improvement when implemented in the ECMWF analysis system.

The theoretical justification for the analysis ensemble method will be discussed, and the main characteristics of the implied statistics of background error will be presented.