Statistical analysis of water temperature residuals

Water temperature residuals, which are taken as the difference between the daily average water temperature (Missouri River, Boonville, Missouri) and the Fourier series regression fit to the data points, are analyzed. A 1-yr record length is used as a base period. The Kolmogorov-Smirnov test is used to determine, for a given number of extracted harmonics, the sample size required to yield a set of normal random variates with mean zero. It is also shown that with only the fundamental harmonic removed, a sample size of at least 180 is required to yield a sample average residual of less than 0.2°F. When the fundamental and higher order harmonics are removed, this sample size is reduced considerably.