Short-Term Peak Flow Rate Prediction and Flood Risk Assessment Using Fuzzy Linear Regression

Abstract

A fuzzy linear regression (FLR) method is proposed that uses real-time data to accurately predict daily peak flow rate for the Bow and Elbow Rivers in southern Alberta. FLR model performance was compared to a non-fuzzy, error-in-variables model (EIV). Mean daily flow rate, with a delay of one, two, three or seven days was used as the independent variable. In implementing the FLR, a unique hybrid modelling approach was devised that treated peak flow rate as probabilistic and mean daily flow rate as possibilistic. Three gauge errors, 5%, 10% and 20%, were tested and compared to quantify uncertainty in observed flow rate. The research proposed a new method of computing the exceedance probability of peak flow rate using fuzzy numbers. NSE, PBIAS and RSR and a proposed rating system were used to evaluate and compare the methods. Two different calibration schemes were used, including a quasi-real time system. The tests demonstrated that FLR with a one day lag was a very good predictor of peak flow rate and outperformed EIV for two stations on the Bow River. A test dataset from the floods of June 2013 in Calgary was used for risk assessment. The FLR results demonstrated higher flexibility and sensitivity to the flood as it approached Calgary. The fuzzy method was able to capture the peak flow rate for the majority of the high flow rate days, while the EIV model was unable to predict this data within the 95% confidence interval.

Keywords: floods, fuzzy linear regression, peak flow, risk analysis, uncertainty analysis