Ant colony optimization and genetic algorithm models for suspended sediment discharge estimation for gorgan-river, Iran

Suspended sediment transport by rivers is an important phenomenon in the science of sedimentation in river engineering. Empirical relations, such as sediment rating curves, are often applied to determine the average relationship between discharge and suspended sediment loads. These types of model generally underestimate or overestimate the amount of sediment. Notably, the direct measurement of sediment loads is very expensive to implement. Various models have been developed so far to identify the relationship between discharge and sediment loads. Most of the models, based on the regression method, have some restrictive assumptions. In recent years, some black box models based on artificial neural networks have been developed to overcome this problem. Therefore, it is still necessary to develop the model for the discharge-sediment relationship. New models based on artificial intelligence models, namely; Ant Colony Optimization (ACO) and Genetic Algorithm (GA) are now being used more frequently to solve optimization problems. Hence, the main purpose of this study was to apply ACO and GA in order to identify the relationship between stream flow discharge and suspended sediment discharge for estimation of sediment loads for the Nodeh Station at the Gorgan River in Iran. In this study, to identify the relationship between the suspended sediment discharge and flow discharge for each model, data from around 600 samples of suspended sediment discharge and flow discharge at Nodeh Station on the Gorgan River in Iran were used. Also, the daily flow discharge was used for the estimation of suspended sediment load for Nodeh station. After testing each model, the best relationship between suspended sediment discharge and flow discharge for all methods were found, and the suspended sediment load was estimated for Nodeh station from 1978-2008. The training and testing data sets were chosen based on the K-fold method of cross validation to find the optimal classifier. In the first part of this study, the sample data, which included suspended sediment discharge and flow discharge, were used as the inputs to the ant colony optimization and genetic algorithm models to identify the relationship between the suspended sediment discharge and flow discharge. Three methods based on the dividing of used data into monthly, seasonally and annually time bases were used by each model to identify the relationship between suspended sediment discharge and flow discharge for estimate the suspended sediment. Different input combinations of ACO and GA models (i.e. ACO1 and GA1: the suspended sediment estimation based on current discharge; ACO2 and GA2: the estimation of suspended sediment based on current and one day of previous discharges; and ACO3 and GA3: the suspended sediment estimation based on current, one and two-day of previous discharges) were chosen based on similar meteorological requirements to those of the suspended sediment equations included in this study. The accuracy of the ACO and GA models was also compared with the empirical model of the sediment rating curve (SRC) technique. The models were compared based on statistical criteria, namely; the Regression Coefficient (R2) and the Root Mean Square Error (RMSE). The results of the monthly method indicated that ACO model with inputs of current discharge (ACO1) model provided better performance as compared to the other ACO models. As seen from results for majority of related months (about 10 month) the ACO1 had the lowest RMSE and the highest R2. In this case, for example, in May, the RMSE and R2 values for the ACO1 model were 28.98 and 0.37, respectively. On the other hand, the RMSE and R2 for the ACO2 model were 50.48 and 0.38, respectively, and 31.80 and 0.11, accordingly for the ACO3 model. Also, the GA2 model was more accurate than the GA1 and GA3 models because from results for majority of related months (about 8 month) the GA2 had the lowest RMSE and the highest R2. For example in Aril, the RMSE and R2 values for the GA1 model were 117.83 and 0.68, respectively. On the other hand, the RMSE and R2 values for the GA2 model were 86.93 and 0.74, and as for the GA3 model, they were 130.2 and 0.63, correspondingly. The findings in this study showed that the performance of the GA model was inferior than the ACO and SRC techniques when the inputs of the GA, ACO and rating curve models comprised only the current discharge. As seen from the results, the ACO1 model approximated the corresponding of the observed suspended sediment values better than the rating curve and GA2 techniques. The GA2 also performed better than the SRC model. It was seen from the results that both the low and high sediment values and in general the overall shape of the sediment time series were closely approximated by the ACO1 for the monthly method. The ACO1, GA1 and SRC models were applied to identify the relationship between the suspended sediment discharge and flow discharge for annually and seasonally methods. For the annually method the result showed that the GA1 has good performance than sediment rating curve and ACO1 techniques. In this case the RMSE and R2 values for the ACO1 model were 14.06 and 0.79, respectively. On the other hand, the RMSE and R2 for the GA1 model were 10.47 and 0.79, respectively, and 16.59 and 0.73, accordingly for the SRC model. In addition, as for the seasonal suspended sediment estimation, it can be obviously seen from this result that the ACO1 model performed much better than the rating curve techniques for spring and winter. Conversely, the SRC model for summer and autumn is much better than ACO. Furthermore, it can be observed from Table 4.27 that the performance of the ACO1 model was much better than the GA1 techniques in summer and winter, while the GA1 was much better in spring and autumn. The comparison between the GA1 and SRC models showed that the GA1 model for spring had more accuracy than the SRC model. Conversely, the accuracy of the SRC model in summer, autumn and winter were much better than GA1. Comparison between the ACO1 model and SRC showed that the ACO1 model had more accuracy in spring and winter, whereas the accuracy of SRC in summer and autumn was better than ACO1. From these results, it can be concluded that GA1 for spring, SRC for summer and autumn and ACO1 for winter are good models for estimating suspended sediment using the seasonal method at Nodeh station. From the above-mentioned results, it can be concluded that the suspended sediment discharge had a good relationship with the current discharge for the ACO model and a good relationship with the current discharge and one-day previous discharge for the GA model, whereas there was a weak relationship between the two-day previous discharge and suspended sediment discharge for both ACO and GA. For the evolution of parameters a and b from SRC, GA1 and ACO1, their characteristics were explored using the monthly and seasonal methods