Reduced Order Probabilistic Prediction of Rogue Waves in One-Dimensional Envelope Equations

Abstract

We describe a method for prediction of rogue waves in the one-dimensional Nonlinear Schrodinger and Modified Nonlinear Schrodinger equations. This method is based on distinguishing the unstable wave groups likely to generate rogues out of a complex background field. After a careful study of the evolution of isolated wave groups, we then apply an automatic scale selection algorithm to pick out these individual wave groups that will trigger the formation of rogue waves. We demonstrate the skill of our scheme for Reduced Order Prediction of Extremes (ROPE), predicting rogues well in advance of their formation with low rates of false positives/negatives.