A comparison of quadratic regression and artificial neural networks for the estimation of quantiles at ungauged sites in regional frequency analysis

Abstract

The study illustrates application of Regional Flood Frequency Analysis (RFFA) using Annual Maximum Peak Flows (AMPF) of eleven gauging sites of various streams of Khyber-Pakhtunkhwa, Pakistan. Assumptions associated to recorded data at various sites have been validated through various statistical tests. The discordancy measure indicates that there is no discordant site in the cluster of eleven sites. Heterogeneity measure based on l-moments confirms that the group of eleven sites is definitely homogeneous. Criterion of |Z - Dist| statistic and L-moment ratio diagram show that Generalized Pareto (GPA) distribution is the best fitted regional distribution of the study region. Regional flood quantiles for various return periods have been estimated using the quantile function of GPA distribution. Artificial Neural Networks (ANN) and Quadratic Regression (QR) model with robust estimation method have been used for the estimation of quantiles at ungauged sites. Model evaluation criteria’s (error comparison of predicted values) suggested that estimated quantiles through ANN are accurate relative to quadratic regression. Historical comparison shows that the quantiles estimated through index flood method and ANN are closely related to the highest recorded values of AMPF at each corresponding site for shorter as well as longer return periods.