Structure of the stable manifold for a two-dimensional, chaotic map. Black dots are points on the model attractor and red line is the local structure of the stable manifold - all points on the stable manifold collapse to the same point as they are integrated forward in time. The colors are a representation of the distance between a point in the space and a specified model trajectory. Note that the stable manifold lies in the minimum of this cost function space. (Courtesy of Prof. Jim Hansen.)
Forecasting is the ultimate form of model validation. But even if a perfect model is in hand, imperfect forecasts are likely. This course will cover the factors that limit our ability to produce good forecasts, will show how the quality of forecasts can be gauged a priori (predicting our ability to predict!), and will cover the state of the art in operational atmosphere and ocean forecasting systems.
Special software is required to use some of the files in this course: .m.