Nonlinear Regression Applied to Hydrologic Data

Abstract

An overview of nonlinear regression is presented based on the concept of model linearization and use of successive approximations in order to minimize the sum of squared residuals. The Marquardt method is proposed as a general tool for regression on nonlinear expressions. Using concepts from linear regression, it is possible to investigate the statistical behavior of model parameters and thus choose between competing models. To demonstrate the applicability of the method, intensity-duration-frequency (IDF) curves were constructed from point-precipitation data. Such curves are required for the design of urban drainage systems via the rational formula. The constructed IDF curves represent precipitation conditions at two urban areas in Southwestern Greece. The present approach can be very useful in many civil-engineering applications because it avoids the bias associated with logarithmic transformation of nonlinear expressions and subsequent application of linear regression. It can also be extended to a set of algebraic or differential equations for one independent variable.