Edward N Lorenz discovered that chaos and unpredictability are hallmarks of even simple driven systems. Yet forecasting the onset and severity of extreme events in driven earth systems, such as hurricanes, landslides, earthquakes, flooding, and weather/climate events remains a pressing global need. The economic damages from the most severe of these events amount to annualized economic costs of many billions of dollars, and are also associated with great suffering associated with the loss of many thousands of human lives each year. In addition to the problems identified by Lorenz, predicting the future evolution of a variety of driven nonlinear earth systems is further complicated by the fact that their dynamical processes are 1) often not amenable to direct observation; and 2) are strongly multi-scale, so that length and time scales range from very much smaller and shorter than human perception, to very much larger and longer. An example of such an earth system is the atmosphere, in which, from a practical standpoint, it is impossible to measure the temperatures, pressures, and humidity at all locations at all times. Here turbulent processes span length scales from sub-meter length scales to thousands of km, and time scales extend from fractions of seconds to many thousands of years. Another example is earthquake fault systems, in which lengths associated with earthquakes range from centimeters to many hundreds of km. Similarly, time scales extend from the seconds associated with the slip process, to the thousands of years between recurring events on the same fault. In systems such as these, we can only observe the space-time patterns of extreme events, the large storms, climate events, earthquakes, and floods that are the inevitable consequences of the underlying dynamics. Using these space-time patterns, and whatever is known about the dynamics of these high-dimensional nonlinear earth systems, it often possible to construct numerical simulations that can be used to make predictions about the future space-time evolution of the system and the possible occurrence of extreme events. The accuracy of these predictions and forecasts is limited by the proximity and similarity of the model trajectory through state space, to that of the actual system. This problem can be approached through data assimilation techniques. In addition, the existence of flexible new Grid computing techniques made possible by the World Wide Web has opened new avenues for the realization of sophisticated, state-of-the-art numerical simulations. Thus our ability to forecast the extreme events of the future is limited by a range of issues originating from the dynamical process of interest, the space-time patterns we can observe, and the accuracy of the predictions that are desired.

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