State dependent predictability: impact of uncertainty dynamics, uncertainty structure and model inadequacies

Abstract. The implications of state dependent, finite time error growth has been studied using singular values in a chaotic 2-dimensional map. Earlier studies have demonstrated the superiority of the singular values over the Lyapunov number in representing error growth over finite time scales, since they take state dependency into account. In this work, linearized error growth as given by singular values under operational constraints like non-isotropic initial uncertainty and model error is considered. It is demonstrated that the relevant singular values in the case of non-isotropic initial uncertainty are quite different from the isotropic case. The effect of model inadequacy on error growth is delineated.