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Bred vectors and forecast errors in the NASA coupled general ...

Bred vectors and forecast errors in the NASA coupled general ...

ed perturbations. The

ed perturbations. The key to selecting the instability of interest is to use physically meaningful breeding parameters, i.e., the rescaling amplitude and rescaling time interval (Toth and Kalnay, 1993, 1997 and Peña and Kalnay, 2004). Peña and Kalnay (2004) derived bred vectors, singular vectors (SV) and Lyapunov vectors (LV) with experiments using fast and slow coupled Lorenz 3-variable models. Their idealized coupled system was designed to mimic a coupled system including a tropical ocean, and tropical and extratropical atmospheres. They demonstrated that breeding can be used to isolate the slow modes when choosing a slow variable to measure the growth of the perturbation and when using a long interval for the rescaling, allowing the fast extratropical weather noise to saturate. In contrast, SV and LV are swamped by the fast growing instabilities, since by being linear they are designed to capture the fastest growing instability of the system. The coupled breeding experiments of Cai et al. (2003) with a Cane-Zebiak intermediate coupled model, and of Yang et al. (2006) with the coupled general circulation model (CGCM) developed at NASA Goddard Space Flight Center gave very similar robust conclusions. In these breeding experiments, all the dynamical variables in both atmospheric and oceanic components are perturbed so that coupled nonlinear processes are naturally included. Both studies show that ENSO bred vectors and their growth rate are sensitive to the background ENSO evolution, and that the dominant fast growing mode in the SST appears in the eastern equatorial Pacific. Moreover, Yang et al. (2006) confirmed that the characteristics of bred vectors from two independently developed CGCMs (NASA and NOAA/NCEP) have a similar structure, not only in the tropical Pacific basin but also in the atmospheric ENSO-teleconnected region. These 6

findings suggest that the perturbations derived from breeding runs are representative of the coupled atmospheric and oceanic changes associated with the ENSO variability. Cai et al. (2003) also showed that using a pair of positive/negative BVs as the ensemble perturbations, the “spring barrier” † in ENSO forecast skill could be substantially reduced. Although the results of these studies were encouraging, the coupled breeding experiments were performed under a perfect model scenario. In this paper we extend the coupled breeding technique to a realistic scenario: performing breeding cycles in the NASA operational CGCM with real, noisy observations assimilated into the ocean component. The first goal in this study is to test whether BVs (representing the leading coupled instabilities) can be used to represent the structure of the short-range (about one month) coupled forecast error. If BVs turn out to be similar to forecast errors then they have potential for use in ensemble forecasting. Another goal in our study is to explore the potential to incorporate bred vectors with operational ocean data assimilation for better use of the observations. The current ocean data assimilation in the NASA operational system uses the optimal interpolation (OI) scheme. The background error covariance used in the OI scheme is a statistical estimation of the forecast error structure averaged in time and therefore it is flow-independent. A data assimilation scheme with a time-independent background error covariance may underestimate sudden changes of the background flow due to the dynamical instabilities. Advanced oceanic data assimilation schemes carrying flow-dependent error statistics, like ensemble ocean data assimilation (Evensen, 2003, Keppenne et al. 2002, 2003, 2005) or 4-dimensional variational analysis (4D-Var) † “Spring Barrier” is a common feature of a sudden drop of forecast skill for the forecasts that begin in the spring and pass through the summer. 7

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