Empirical modeling of unsteady flows

In this work we demonstrate the utility of stochastic empirical models. Linear stochastic models have been successful at reproducing responses to forcing of large-scale atmospheric flow. However, the linear forms of the models reach their limit on highly nonlinear problems. It is shown here that for simple low dimensional problems, a quadratically nonlinear empirical model is successful at reproducing a chaotic attractor. In addition, empirical models can be used to diagnose the important dynamics of a flow system and identify the essential terms to include in a forward dynamical model. Once the empirical model has been built, it can then be used to diagnose the underlying dynamics.