ON THE VALIDITY OF EMPIRICAL POWER LAWS

Empirical power laws are frequently used to relate parameters in compl ex hydrological and hydrometeorological processes. The validity of pow er laws relating two parameters with a common variable may be compromi sed by spurious influences of the common variable. Theoretical results are presented that allow both the spurious self-correlation coefficie nt and the slope of a spurious self-correlation to be determined a pri ori. Raising a common variable to a higher power in either parameter a mplifies the spurious effects. Power law regression equations are not single-valued analytical functions and must not be treated as such. Be cause of the strong influence of a common variable on the correlation coefficient, the transfer of a common variable from one side of a powe r-law regression equation to another (by cross-multiplying) may severe ly distort the results. Examples from lake hydrology are presented.