# Further analysis of singular vector and ENSO predictability in the Lamont model—Part II: singular value and predictability

## Authors

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- Received:
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DOI: 10.1007/s00382-009-0728-z

- Cite this article as:
- Cheng, Y., Tang, Y., Jackson, P. et al. Clim Dyn (2010) 35: 827. doi:10.1007/s00382-009-0728-z

## Abstract

This is the second part of the 148 years (1856–2003) singular vector analysis, as an extension of part I (Cheng et al. 2009 Clim Dyn, doi:10.1007/s00382-009-0595-7), in which a fully physically based tangent linear model has been constructed for the Zebiak-Cane model LDEO5 version. In the present study, relationships between the singular values and prediction skill measures are investigated for the 148 years. Results show that at decadal/interdecadal time scales, an inverse relationship exists between the singular value (S1) and correlation-based skill measures whereas an in-phase relationship exists between the S1 and MSE-based skill measures. However, the S1 is not a good measure or predictor of prediction skill at shorter time scales such as the interannual time scale and for individual prediction. To explain these findings, S1 was decomposed into linear perturbation growth rate (L1) and linearized nonlinear perturbation growth rate (N1), which are controlled by the opposite underlying model dynamical processes (the linear warming and the nonlinear cooling). An offsetting effect was found between L1 and N1, which have opposite contributions to the S1 (i.e., S1 ≈ L1 − N1). The “negative” perturbation growth rate −N1 (denoted as NN1) probably is the consequence of the unrealistic nonlinear cooling in the LDEO5 model. Although the correlations of the actual prediction skill to both the L1 and the NN1 are good, their opposite signs lead to a weak relationship between S1 and actual prediction skill. Therefore, either L1 or N1/NN1 is better than S1 in measuring actual prediction skill for the LDEO5 model.