Time series modeling of water level at Sulaiman Station, Klang River, Malaysia - Galavi, Hadi (2010)
The temporal and spatial flow in rivers represents the total response of a watershed and is affected by every hydrological event occurs in the watershed. The important point in planning and management of water projects is to achieve accurate estimation of river stage and flow. Among the two major approaches for modeling and forecasting hydrologic events, the empirical or black-box models have received more attention than the physical based models by hydrologists. Among the empirical models the Autoregressive Integrated Moving Average (ARIMA) models which have been conventionally used for hydrologic modeling and the Adaptive Neuro-Fuzzy Inference System (ANFIS) as a data driven model were used in this study to investigate their effectiveness in forecasting the river flows. The Klang River is one of the important urban rivers in Malaysia and is the subject of this research. A total of 3012 daily average water level measurements (2002 – 2010) of the river were used in this study. The number of inputs for both models is selected based on the Autocorrelation function (ACF) and the Partial Autocorrelation Function (PACF). The best ARIMA model is selected based on the minimum corrected Akaike Information Criterion (AICC) statistic obtained among the several possible ARIMA models. An ARIMA(3,1,3) model was found to be the appropriate ARIMA model for the modelling of the selected case study. A Subtractive Clustering Method was used in the fuzzy inference system to determine the optimal number of Membership Functions (MF) and rules. Using the cross validation method the best training subset is selected to train the ANFIS model based on that dataset. The estimation of parameters of the model is accomplished using the hybrid learning algorithm consisting of standard neural network backpropagation algorithm and least squares method. Among the several structures of ANFIS model examined, the model with four membership functions for the model inputs and output, Guassian membership function for the fuzzification, four rules for the fuzzy inference engine, and trained using hybrid algorithm was selected as the best constructed ANFIS model. The performance of the models, ANFIS and ARIMA models, was compared based on established statistical performance measures. Results show the superiority of the ANFIS model over the ARIMA model with interestingly better overall index of 1.514 against 1.108. However, the database of ARIMA model when became updated with each prediction step showed that results were dramatically better than the simple ARIMA model with 0.48 improvement in overall index. The updated ARIMA model showed very close results to those of the ANFIS model with overall index of 1.588 and 1.514, respectively. Overall, the updated ARIMA model in terms of overall index measure outperforms the ANFIS model for prediction of average water level, but not in the prediction of an exact time a day. Both models based on the obtained results (below one percent mean absolute percentage error) are appropriate models for the modelling and forecasting of Klang River water level. These models can be applied to the other case studies with model calibration in terms of the available dataset.