Developing precipitation intensity-duration-frequency (IDF) models using nonlinear minimization in R

Development of rainfall coefficients from Intensity-Duration-Frequency (IDF) models has been used in the United States at least since the 1970s. Rainfall coefficient development methods involve regression analysis to best fit a line through an observed set of rainfall depths at varying durations and frequency. IDF equations provide an advantage to engineers who wish to calculate intensities at varying durations. IDF models are constructed based on rainfall patterns and thus vary by geographic location. The IDF model used in the state of Texas is found in the Texas Department of Transportation’s (TxDOT) Hydraulic Design Manual. The IDF model is composed of e, b and d variables known as the Texas rainfall coefficients. The most recent method for developing the e, b and d rainfall coefficients in Texas was completed through the 0-6824-1 TxDOT project that employed an ordinary least squares (OLS) regression. The OLS method required analyst time to linearize a nonlinear equation. Linearization within this thesis refers to transforming a nonlinear equation into linear form. The OLS method developed rainfall coefficients using linear regression analysis, one-dimensional optimization and a predicted residual sum of squares error (PRESS) statistic. We decided to develop the coefficients directly through nonlinear minimization (NLM) to cut down on time and cost, and increase efficiency. In this thesis we present the background of intensity-duration-frequency models, the previous OLS method, the suggested NLM method, and a comparison of the results between the two methods in graphical and tabular form. We further discuss the adaptability, efficiency and regression fit of the two methods. In addition, we present two R scripts, created to develop coefficients for various forms of IDF models. R is an open source, statistical programming language and software. The first code accepts data for single rainfall stations, and the second code accepts data for an entire state based on frequency. Both codes use the nlm package in R to develop the IDF model. This thesis presents the code with a general guidance but it is not meant to be a tutorial.