Author(s): N. Hamdaoui; Y. K. Tung
Linked Author(s): Yeou-Koung Tung
Keywords: Partial Least Square; Regional hydrologic analysis; Principal component; Ordinary Least Square
Abstract: This paper elucidates the method of Partial Least Squares (PLS) and shows that PLS is an excellent tool for model discovery and has great potential in the fields of hydraulics and hydrology. PLS combines the capability of multiple linear regression, principal component analysis and canonical correlation analysis to develop predictive models from data. PLS is particularly advantageous when the number of independent variables is larger than the number of observation and/or the data is multi-collinear. PLS has been used in economics, finance, chemometrics, chemistry, medicine, psychology, and pharmaceutical science for model building from measured inputs, system characteristics and outputs. Surprisingly, it appears that PLS has not made its way to the fields of water resources engineering. Therefore, this article introduces the PLS to the water resources community and uses two examples to illustrate how PLS can be used to build predictive models. In the first example, synthetic data derived from the Darcy-Weisback relationship is used to illustrate the PLS's ability for model discovery under ideal condition (i.e., zero error). In the second example, the PLS method is applied to field of hydrologic regionalization to derive a predictive model for annual mean flood flow according to basin and rainfall characteristics. The superiority of the PLS-derived model is fully supported through cross-validation exercise.