Chaos: The Lorenze Attractor

Chaos in Predictive Sciences.
Forecasting model developers, practicing engineers and scientists are frequently required to provide solutions to projects that involve some form of prediction, whether it is provision of weather forecasts, flood forecasts or simulation of hydrologic/ hydraulic design parameters. In most of these projects one has to deal with uncertainties from a variety of sources. One source of uncertainty, especially in atmospheric-land surface hydrologic systems is the chaotic-random nature of atmosphere-hydrology processes. The chaotic phenomena in many cases is caused by the incomplete knowledge of the of the system including initial conditions. Errors in the initial conditions of a system have the potential to grow with time in a manner that can make long-term prediction unreliable. This is a phenomenon referred to as the butterfly effect and can typically be defined by differential equations specific to the prediction system under investigation. Although unduly complex at times, analysis of chaos dynamics can be used to effectively assess the sensitivity of a prediction tool to changes or perturbations in initial conditions of a prediction system. The application of chaos theory remains mainly in the realm of research, but literature is replete with discussion of this approach. Here we show an interesting animation of a hypothetical chaotic system developed via matlab/python scripting.