The applicability of power spectral density techniques, Fourier series analysis, and linear regression to the mathematical modeling of river water temperature is demonstrated. Consideration is also given to the problem of estimating thermal inputs to rivers from man-made sources such as electrical power plants. First, power spectral density techniques are used in the time-series analysis of water temperature records which were taken from the Missouri River. Two spectral ranges are then studied from the standpoint of their applicability to (1) mathematical model building and (2) detection and identification of cyclic thermal inputs. Next, a Fourier regression fit to the time-series data is used to show that normal random variates having zero mean are obtained when the regression curve is extracted from the data. A 60-day prediction of daily-average water temperature is then made using a model which is based upon a polynomial regression fit to the fluctuating amplitudes of significant Fourier components. A final predictive model, which is based on the above analysis methods, is proposed.


Geosciences and Geological and Petroleum Engineering


United States. Office of Water Resources Research


The work upon which this publication is based was supported by funds provided by the United States Department of the Interior, Office of Water Resources Research, as authorized under the Water Resources Research Act of 1964.

James C. Maxwell, Principal Investigator
Project No. B-045-Mo.
Agreement No. 14-31-0001-3299
DATE: 7-1-70 thru 1-31-72
Completion Report - December 27, 1972

"This report is taken from a doctoral dissertation by the junior investigator, Dr. Leland Long" which can be found here.

Keywords and Phrases

Missouri River -- Temperature; Thermal pollution of rivers, lakes, etc. -- Missouri River

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Print OCLC #


Report Number


Document Type

Technical Report

Document Version

Final Version

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© 1972 University of Missouri--Rolla, All rights reserved.

Publication Date

27 Dec 1972