Abstract
The problem of system identification from input-output data continues to be a challenge in all aspects of hydrology. In this study, cumulants are proposed as tools for determining the relevant information contained in output data. A method for computing cumulants in terms of moments is proposed using ideas from combinatorics theory. This method was applied to effluent concentration data from soil-column studies. Analyzing effluent concentration data from soil columns is the most common laboratory method for calculating solute transport properties. The ratios of cumulants to moments for various orders were computed using physically realistic examples and actual experimental results. The use of cumulants in determining deviation from Gaussianity and providing an estimate of the useful orders of moments was also investigated. It was concluded that cumulants provide a useful analytical tool for guiding the determination of model choice.
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