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Comparison of Water Quality Time-series Using Statistical Tests Based on Power Spectrum

Published by the American Society of Agricultural and Biological Engineers, St. Joseph, Michigan www.asabe.org

Citation:  Paper number  022147,  2002 ASAE Annual Meeting . (doi: 10.13031/2013.10406) @2002
Authors:   Kevin M. Brannan, Saied Mostaghimi
Keywords:   Water Quality, Statistical Analysis, Watershed, Nonpoint Source Pollution

Two common properties of water quality time-series weaken the power of many currently available statistical tests. These two properties are serial correlation and high levels of variance. When applying these statistical tests, an effort is made to reduce or remove these properties to increase the power of the test. In this paper, three statistical tests that focus on the serial correlation and variance of water quality time-series are discussed. The tests are based on the power spectrum estimates of time-series. The power spectrum describes the variance (power) distribution of a timeseries over a range of frequencies. Two of the power spectrum tests use forms of the Kolmogorov- Smirnov and Anderson-Darling tests to evaluate the statistical significance of any differences identified between the power spectrum estimates. The theory behind the tests is discussed, along with the Type I and II error rates. Results from the comparison of observed water quality time-series are presented to demonstrate the applicability of the power spectrum tests to the investigation of nonpoint source pollution at a watershed scale.

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