Application of Fuzzy Logic Techniques in Estimating the Regional Index Flow for Michigan

Abstract

Knowledge of flow dynamics within streams is not only helpful in determining applications, such as water withdrawals, but is also a driving force in a watershed for other components, such as nutrients, dissolved oxygen, and ecological health. With increased pressure on water resources, along with growing attention to climate change and anthropogenic activity, the ability to accurately predict extreme conditions continues to be invaluable to decision makers and watershed managers. Our objective was to explore new concepts and to identify robust techniques for estimating the index water yield and subsequently the index flow for ungauged streams in the state of Michigan. Four different modeling methods (multiple linear regression, fuzzy regression, fuzzy expert, and adaptive neuro-fuzzy inference system, or ANFIS) were evaluated using 10-fold cross-validation. A combination of statistical and graphical analyses confirmed the advantages of 10-fold cross-validation in selecting the best model while avoiding overfitting or generating unexplained values such as outliers. Results showed that the fuzzy expert method was the best and most robust prediction model. Further evaluation revealed that the ANFIS model preserved many attributes of the data set, at the expense of overfitting and generating unexplained values such as outliers.