The representation of the analysis effect in three error simulation techniques

Three error simulation techniques are compared formally, in particular regarding their representation of the analysis step. The associated results are moreover examined for the Aladin-France limited-area model, which is coupled with the Arp`ege global model. It is first shown that the analysis error equation involves the same operators as the analysis equation. This implies that the analysis ensemble approach is appropriate, as the analysis equation is used to transform the background and observation dispersions into the analysis dispersion. By contrast, the standard NMC method relies essentially on the analysis increment equation, which contributes to a large extent to the excessive emphasis on the large-scale structures. The so-called lagged NMC method is shown to be closely related to the Arp`ege/Aladin model differences. The analysis ensemble approach gives error spectra that are intermediate between those of the two other methods. This is in agreement with the representation of the initial and lateral boundary uncertainties, in a way that is consistent with the influence of the analysis equation and with the short forecast ranges.