In this topic we make an attempt to characterize ocean wave states by applying and extending a technique for identifying stochastic differential equations from measured data. A stochastic approach based on the theory of Markov processes is applied. With this analysis we achieve a characterization of the scale-dependent complexity of ocean waves by means of a Fokker-Planck equation, providing stochastic information on multi-scale processes.
We extend the stochastic cascade description by conditioning on the wave height value itself and find that the corresponding process is also governed by a Fokker-Planck equation and based on this we proposed a reconstruction method.
With this model we are able to generate complete new time series or model the next steps for a given sequence of data. The model itself is based on the joint probability density which can be extracted directly from given data, thus no estimation of parameters is necessary.