Bred Vectors of the Zebiak–Cane Model and Their Potential Application to ENSO Predictions

Ming Cai Department of Meteorology, University of Maryland at College Park, College Park, Maryland

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Eugenia Kalnay Department of Meteorology, University of Maryland at College Park, College Park, Maryland

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Zoltan Toth SAIC at Environment Modeling Center, National Centers for Environmental Prediction, Camp Springs, Maryland

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Abstract

The breeding method is used to obtain the bred vectors (BV) of the Zebiak–Cane (ZC) atmosphere–ocean coupled model. Bred vectors represent a nonlinear, finite-time extension of the leading local Lyapunov vectors of the ZC model. The spatial structure and growth rate of bred vectors are strongly related to the background ENSO evolution of the ZC model. It is equally probable for the BVs to have a positive or negative sign (defined using the Niño-3 index of the BV), though often there is a sign change just before or after an El Niño event. The growth rate (and therefore the spatial coherence) of the BVs peaks several months prior to and after an El Niño event and it is nearly neutral at the mature stage.

Potential applications of bred vectors for ENSO predictions are explored in the context of data assimilation and ensemble forecasting under a perfect model scenario. It is shown that when bred vectors are removed from random initial error fields, forecast errors can be reduced by up to 30%. This suggests that minimizing the projection of the bred vectors on the observation-minus-analysis field may be a beneficial factor to an operational forecast system. The ensemble mean of a pair of forecasts perturbed with positive/negative bred vectors improves the forecast skill, particularly for lead times longer than 6 months, substantially reducing the “spring barrier” for ENSO prediction.

Corresponding author address: Dr. Eugenia Kalnay, Department of Meteorology, University of Maryland at College Park, College Park, MD 20742. Email: ekalnay@atmos.umd.edu

Abstract

The breeding method is used to obtain the bred vectors (BV) of the Zebiak–Cane (ZC) atmosphere–ocean coupled model. Bred vectors represent a nonlinear, finite-time extension of the leading local Lyapunov vectors of the ZC model. The spatial structure and growth rate of bred vectors are strongly related to the background ENSO evolution of the ZC model. It is equally probable for the BVs to have a positive or negative sign (defined using the Niño-3 index of the BV), though often there is a sign change just before or after an El Niño event. The growth rate (and therefore the spatial coherence) of the BVs peaks several months prior to and after an El Niño event and it is nearly neutral at the mature stage.

Potential applications of bred vectors for ENSO predictions are explored in the context of data assimilation and ensemble forecasting under a perfect model scenario. It is shown that when bred vectors are removed from random initial error fields, forecast errors can be reduced by up to 30%. This suggests that minimizing the projection of the bred vectors on the observation-minus-analysis field may be a beneficial factor to an operational forecast system. The ensemble mean of a pair of forecasts perturbed with positive/negative bred vectors improves the forecast skill, particularly for lead times longer than 6 months, substantially reducing the “spring barrier” for ENSO prediction.

Corresponding author address: Dr. Eugenia Kalnay, Department of Meteorology, University of Maryland at College Park, College Park, MD 20742. Email: ekalnay@atmos.umd.edu

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