The Tangent Linear Model and Adjoint of a Coupled Ocean-Atmosphere Model and Its Application to the Predictability of ENSO

The authors compute the conditional nonlinear optimal perturbations (CNOPs) of an intermediated coupled ocean-atmosphere model, and compare them with linear singular vectors (LSVs). In the case of annual cycle being basic state, there exist not only CNOPs but also local CNOPs, which are respectively significantly different from the corresponding LSVs. Physically we find that these CNOPs (local CNOPs) tend to be more probably than LSVs in developing into El Nino (La Nina) events. In the case of an ENSO cycle being basic state, CNOP represents the initial error that has the largest effect on ENSO prediction at prediction time. It is shown that the optimal growth of initial errors superposed on ENSO cycle is potentially modulated by annual cycle and ENSO cycle.