Catastrophic disasters afflicting human society are often triggeredby tsunamis, earthquakes, widespread flooding, and weather andclimate events. As human populations increasingly move intogeographic areas affected by these earth system hazards, forecastingthe onset of these large and damaging events has become increasinglyurgent. In this paper we consider the fundamental problem offorecasting in complex multi-scale earth systems when the basicdynamical variables are either unobservable or incompletelyobserved. In such cases, the forecaster must rely on incompletelydetermined, but "tunable" models to interpret observablespace-time patterns of events. The sequence of observable patternsconstitute an apparent pattern dynamics, which is related to theunderlying but hidden dynamics by a complex dimensional reductionprocess. As an example, we examine the problem of earthquakes, whichmust utilize current and past observations of observables such asseismicity and surface strain to produce forecasts of futureactivity. We show that numerical simulations of earthquake faultsystems are needed in order to relate the fundamentally unobservablenonlinear dynamics to the readily observable pattern dynamics. Wealso show that the space-time patterns produced by the simulationslead to a scale-invariant hierarchy of patterns, similar to othernonlinear systems. We point out that a similar program ofsimulations has been very successful in weather forecasting, inwhich current and past observations of weather patterns areroutinely extrapolated forward in time via numerical simulations inorder to forecast future weather patterns.
展开▼
