It is now well established that the atmospheric system leading to instantaneous weather is chaotic. Studies using the most sophisticated models available demonstrate that if Global Circulation Models perfectly simulated the atmosphere the predictability of weather variables would approach zero for forecasts beyond two weeks. Through their dependence on the atmosphere, hydrologic systems are likely to be chaotic. Attempts to quantify the chaotic nature of hydrologic systems have relied on calculations of the Correlation Dimension (Dc) for given time series using a procedure called Correlatron Integral Analysis (CIA). If Dc is non-integer then the dimension is fractal and the time series is likely to be chaotic.

Unfortunately, my assessment of reported CIAs in geosciences showed that the great majority of claims of chaos are unfounded because of a lack of data and/or the failure to apply various numerical constraints that are commonly overlooked when doing CIA analysis. Of the successful CIAs, most fail to find any low dimensionl attractor.

To assess the chaotic nature of hydrologic systems, I have worked with some of the longest, highest quality hydrologic time series available. I have also used all of the necessary and appropriate numerical constraints in an easy to follow procedure for carrying out CIA. The results of this research were presented at the recent 16th Annual Hydrology Days meeting held at Fort Collins, CO in 1996. Based on comments received during that conference and in subsequent thorough peer reviews, I improved the work and published a paper in the journal Advances in Water Resources.

A copy of the paper can be downloaded by clicking HERE

Or send e-mail to: gpast@ucdavis.edu

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Links related to chaos mathematics

• Exploring Chaos and Fractals
• Chaos Book References
• Chaos Visualizations

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last updated 01/22/00