Optimal Evolutionary Window for the Nonlinear Local Lyapunov Exponent

Abstract

The impact of the length of the evolutionary window (EW) on the estimation of the predictability limit of the Lorenz-63 model using the nonlinear local Lyapunov exponent (NLLE) method is studied. The structure of the initial errors and error growth dynamics are analyzed. It is found that there exists an optimal EW, at which the estimated predictability limit is closest to its theoretical value. With a shorter EW, the predictability limit is underestimated, while at longer EWs it is overestimated. The optimal EW is approximately equal to the decorrelation time of the system. A preliminary explanation for this link, based on the loss of information from the initial state, is given.