This paper presents an analysis of a coupled ocean-atmosphere model used to study ENSO (El Niño–Southern Oscillation). Our interest here is in the growth of initial error: that is, the predictability of ENSO. The analysis proceeds by constructing a linear model that optimally fits the behavior of the original nonlinear coupled model. By construction, this approximate linear model has only a few degrees of freedom. Because the linear model is so much smaller than the original, it is possible to understand it in much finer detail, indirectly offering insight into the properties and behavior of the original model. As it turns out, even linear models with only a few degrees of freedom can have rather elaborate and surprising short-term error behavior. It has been shown that if a system is not self-adjoint that there is a possibiliiy of error growth in a mode completely unrelated to the classic nation of a fastest growing linearly unstable mode. This holds for simple linear models as well. The work he... Abstract This paper presents an analysis of a coupled ocean-atmosphere model used to study ENSO (El Niño–Southern Oscillation). Our interest here is in the growth of initial error: that is, the predictability of ENSO. The analysis proceeds by constructing a linear model that optimally fits the behavior of the original nonlinear coupled model. By construction, this approximate linear model has only a few degrees of freedom. Because the linear model is so much smaller than the original, it is possible to understand it in much finer detail, indirectly offering insight into the properties and behavior of the original model. As it turns out, even linear models with only a few degrees of freedom can have rather elaborate and surprising short-term error behavior. It has been shown that if a system is not self-adjoint that there is a possibiliiy of error growth in a mode completely unrelated to the classic nation of a fastest growing linearly unstable mode. This holds for simple linear models as well. The work he...