Dynamics of Prediction Errors under the Combined Effect of Initial Condition and Model Errors

The transient evolution of prediction errors in the short to intermediate time regime is considered under the combined effect of initial condition and model errors. Some generic features are brought out and connected with intrinsic properties. Under the assumption of small uncorrelated initial errors and of small parameter errors, the conditions of existence of a time at which the mean quadratic error reaches a minimum and of a crossover time at which the contribution of initial condition errors matches that of model errors are determined. The results are illustrated and tested on representative low-order models of atmospheric dynamics exhibiting bistability, saddle-point behavior, and chaotic behavior.