Uncertainty and Accuracy Analysis of Longitudinal Dispersion Coefficient Estimation Methods in Rivers

In recent years much attention has been paid to the environment, especially river and lake pollution. Rivers and streams are usually receiving the outlet of sewage systems which may cause pollutant levels to rise. Pollutant dispersion is a key element in water quality modeling and the longitudinal dispersion coefficient is an important factor in stream pollution modeling due to its effect on pollutant mixing intensity. Various methods proposed to estimate longitudinal dispersion coefficient in natural streams based on different procedures and different set of data. The performance of the methods presented in previous research is mainly based on precision indices that alone cannot be used as a comprehensive index for comparing different methods.

In this study, in order to evaluate the performance of different methods, a combination of uncertainty criteria along with accuracy indexes were considered. First, the interval analysis approach was used to evaluate the uncertainty of different methods such as Deng et al. (2001), Kashefipour and Falconer (2002), Sahin (2014), Zeng and Huai (2014), M5 and Gene Expression methods. For ± 10% uncertainty in the independent parameters of estimating dispersion coefficient, for all 164 measured data, the probability bands of computational longitudinal dispersion coefficient was obtained for the 6 estimator methods. Then, by comparing the actual measured values with the position of the computational uncertainty bands, 10 uncertainty and accuracy indices were calculated for each estimator method. To determine the most appropriate method for estimating longitudinal dispersion coefficient with less relative uncertainty and greater relative accuracy, weighting was performed on 10 uncertainty-accuracy indices using the G1 weighting method, and then the performance of the methods was evaluated by three multi-criteria decision models including CUI, TOPSIS and VIKOR.

Based on the results, the M5 tree model has the lowest containing ratio among all methods and also has the lowest band, while the Kashefipour and Falconer (2002) model has the highest containing ratio and band values. In addition, for all methods except the method of Deng et al. (2001), the parameter of average deviation amplitude decreases with increasing containing ratio. Among the methods used, the M5 tree model has the lowest CR and the highest D. Based on the uncertainty and accuracy analysis, the method of Deng et al. (2001) was better than other methods and then the equation presented by Zeng and Huai (2014) with CUI = 0.717 had the best performance. The two data-driven methods of the M5 and GE are also ranked next. The results of TOPSIS method are completely in accordance with CUI method and there is no difference between the two methods. According to the VIKOR method, the two methods of Deng et al. (2001) and Zeng and Huai (2014) performed the best, followed by data-driven models. The only difference between the results of the VIKOR model and the two CUI and TOPSIS methods is the ranking of the two data-driven methods, so the GE model is more efficient than the M5 model in VIKOR method.

The results of the three multi-criteria decision-making methods were close to each other and in all the methods, the mathematical model of Deng et al. (2001) and the empirical model of Zeng and Huai (2014) were more efficient than the other methods. It is important to note that the uncertainties of decision-making models have not been examined in this study and the purpose of the present uncertainty study has been to quantify the inherent uncertainties of the methods and relationships for estimating the longitudinal dispersion coefficient.