Prediction

Abstract

Forecasting complex dynamical systems is one of the most important practical issues. This chapter starts by presenting the method of ensemble forecast, which adopts a probabilistic characterization of the model states utilizing a Monte Carlo-type approach. The two factors that determine the forecast results are the initial condition and the forecast model, which highlight the importance of data assimilation and appropriate modeling of complex systems, respectively. In addition to the correctness of the model, the useful information provided by the model beyond prior knowledge is also crucial for practical forecasts. To this end, the concept of internal predictability is introduced, which is quantified via information theory. The internal predictability and the statistical model error further allow for develo** practical guidelines for designing suitable forecast models. Next, the fluctuation-dissipation theory (FDT) is introduced to facilitate the prediction of model response to external perturbations, which outweighs direct methods in terms of computational efficiency and accuracy. Finally, an information criterion is introduced to find the direction of the perturbation that leads to the most sensitive change in the system. FDT can naturally be incorporated into the framework to facilitate the calculation significantly.