Nonlinear Modeling of Wave Runup on Sloping Beach

A new method of identifying nonlinear systems has been developed and applied to the wave runup process. The new method consists of estimating the parameters of the nonlinear system through the known relation between the correlation functions of the input and output records. The unknown function representing the nonlinear system is expanded into a series of Hermite polynomials. The output autocovariances are expressed in terms of the input autocorrelations and the unknown system function. This provides as many equations as there are autocovariance estimates. From these equations the parameters of the function representing the nonlinear system are estimated. The autocorrelations and spectral density have been computed by using the nonlinear model and compared with the actual autocorrelation and spectral density of the measured output. The predictions are reasonably close to the observations. Results presented indicate the possibility of representing the surf zone as a nonlinear system.