Date of Award
Doctor of Philosophy (PhD)
Chin Y. Kuo
Inconsistent results have been obtained from previous experiments which have applied linear multiple regression techniques to remote sensing data for quantification of water quality parameters. The objective of this investigation is to define optical physics and/or environmental conditions under which the linear multiple regression should be applicable. To achieve this objective, an investigation of the signal response equations is conducted and the concept is tested by application to both analytical test cases and actual remote sensing data from a laboratory under controlled conditions.
Investigation of the signed response equations shows that the exact solution for a number of optical physics conditions is of the same form as a linearized multiple regression equation, even if nonlinear contributions are made by such factors as surface reflections atmospheric constituents, or other water pollutants. Limitations on achieving this type of solution are defined. Since the exact solution is in the form of a linear multiple regression equation, application of multiple regression techniques to remote sensing and ground truth data is viewed as a calibration of the exact solution to account for daily variations in background constituents.
Least-squares and statistical concepts for performing the multiple regression analysis are examined. A test for evaluating the applicability of least-squares techniques to a particular set of data is defined and criteria for selection of "good" data are established.
From analytical test case results, it is concluded that constituents with linear radiance gradients with concentration may be quantified from signals which contain nonlinear atmospheric and surface reflection effects for both homogeneous and non-homogeneous water bodies provided accurate data can be obtained and nonlinearities are constant with wavelength. It is also concluded that statistical parameters must be used which give an indication of bias as well as total squared error to insure that an equation with an optimum combination of bands is selected for utilization.
From application to laboratory data, it is concluded that the effect of error in upwelled radiance measurements is to reduce the accuracy of the least-squares fitting process and to increase the number of points required to obtain a satisfactory fit. The problem of obtaining a multiple regression equation that is extremely sensitive to error is discussed. It is also concluded that the linearized multiple regression is applicable in situations in which some types of optical interaction occur between constituents.
The result of this investigation is an increased understanding of technique limitations, mathematical requirements, ground truth requirements, and error effects which should aid in the obtaining of consistent results from future remote sensing experiments.
Whitlock, Charles H..
"Fundamental Analysis of the Linear Multiple Regression Technique for Quantification of Water Quality Parameters From Remote Sensing Data"
(1977). Doctor of Philosophy (PhD), dissertation, Civil/Environmental Engineering, Old Dominion University, DOI: 10.25777/e4xs-ag13