Benefit Assessment of Using Bred Vectors for ENSO Prediction

The breeding method (Toth and Kalnay, 1993) is used to obtain the bred vectors of the Cane-Zebiak atmosphere-ocean coupled (CZ) model. The bred vectors are the proxies of the time varying leading local Lyapunov's vectors of the CZ model.

The spatial structure and growth rate of the bred vectors are strongly related to the background ENSO evolution of the CZ model. The bred vectors of the CZ model tend to have largest growth rate several months prior to and after an El Nino event. At the mature stage of an El Nino event, the growth rate of bred vector is slightly negative. Accordingly, the spatial structure of the bred vectors is more when the growth rate is lager. It is equally probable for the bred vectors to have either a positive or a negative Nino-3 index regardless the sign of the background Nino-3 index.

The applications of using the bred vectors for ENSO predictions have been explored in two contexts: data assimilation and ensemble forecasts. It has been argued that the errors in data assimilation are made primarily of growing errors that resemble to bred vectors because a data assimilation cycle, in essence, behaves like a breeding cycle (Toth and Kalnay, 1994). We demonstrate that by removing bred vectors from initial error fields consisting of random maps, the ENSO forecast errors can be reduced as much as 30% and the “spring barrier” for ENSO prediction is less noticeable. We argue that within a data assimilation cycle, together by removing “systematic dynamic errors” inherited in data assimilation, this reduction of errors would accumulate to an even larger value. The ensemble forecasts with a pair of “positive/negative” bred vectors lead to an improved forecast skill, particularly at a forecast lead time longer than 6 months.