On the validity of empirical power laws |
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| Authors: | B C Kenney |
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| Institution: | (1) National Hydrology Research Institute, 11 Innovation Boulevard, S7N 3H5 Saskatoon, Saskatchewan, Canada |
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| Abstract: | Empirical power laws are frequently used to relate parameters in complex hydrological and hydrometeorological processes. The validity of power laws relating two parameters with a common variable may be compromised by spurious influences of the common variable. Theoretical results are presented that allow both the spurious self-correlation coefficient and the slope of a spurious self-correlation to be determineda priori. Raising a common variable to a higher power in either parameter amplifies the spurious effects.Power law regression equations are not single-valued analytical functions and must not be treated as such. Because of the strong influence of a common variable on the correlation coefficient, the transfer of a common variable from one side of a power-law regression equation to another (by cross-multiplying) may severely distort the results. Examples from lake hydrology are presented. |
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| Keywords: | Hydrological processes power laws spurious self-correlation lake hydrology |
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