Bred vectors and forecast error in the NASA coupled general circulation model

In this study, we examined the characteristic and relationship between bred vector and the one-month forecast error in order to explore potential applications to use the bred vector as initial coupled ensemble perturbations for ensemble forecasting. Our results indicate that the one-month forecast error and the bred vectors share many common characteristics in the SST and subsurface temperature structure in both space and time. Our results indicate that the one-month forecast error in NSIPP CGCM is dominated by dynamical errors whose shape can be captured by bred vectors. Such agreement is especially good when the BV growth rate is large. At the peak of ENSO episodes the growth rate and error growth are low, in agreement with Cai et al (2003). Our results suggest the potential impact from using the bred vector to represent the features of forecast error, such as initial ensemble perturbations for capturing the uncertainties related with seasonal-to-interannual variability. Due to the heavy computational cost of CGCM, the operational ensemble size is limited. Therefore, using bred perturbations should allow small ensembles to perform efficiently by projecting the perturbation evolution on the seasonal-to- interannual associated features. In addition, the ability of bred vectors to detect the month to month forecast error variability should allow the oceanic data assimilation scheme with simple covariance having monthly flow-dependent variations in the SST and subsurface. Our preliminary results show that the mean correlation length estimated from bred vector and one-month forecast error have much shorter zonal scales than what has been prescribed in the OI scheme. If these shorter scales are used within the OI system, it may cause the analysis corrections to over-emphasize small scale structures. In stead, it is possible to use a hybrid background error covariance that combines the standard OI background error correlation with information on the "errors of the month" provided by the bred vectors. Experiments with a Quasi-Geostrophic model suggest that this approach can attain a level of accuracy comparable to 4D-Var, at a very low computational cost (Yang et al, 2005).