In this paper, the use of nonlinear nearest trajectory based on phase space reconstruction along with several data-driven methods, including two types of perceptron artificial neural networks with Levenberg–Marquardt (ANN-LM) and particle swarm optimization learning algorithms (ANN-PSO), adaptive neuro-fuzzy inference system (ANFIS) and gene expression programming for forecasting suspended sediment concentration (SSC) dynamics in streamflow is studied. The nonlinearity of the series was tested using the method of surrogate data at 0.01 significance level as well as correlation exponent method. The proper time delay is calculated using the average mutual information function. Obtained results of different models are compared using root mean square error (RMSE), Pearson's correlation coefficient (PCC) and Nash–Sutcliffe efficiency with logarithmic values (Eln). Of the applied nonlinear methods, ANFIS generates a slightly better fit under whole daily SSC values (the least amount of RMSE = 10.5 mg/l), whereas ANN-PSO shows superiority based on the Eln criterion (the highest amount of Eln = 0.885). According to the non-parametric Mann–Whitney test, all data-driven models represent the same forecasted results and are significantly superior to the nearest trajectory-based model at the 99% confidence level.
- correlation exponent
- particle swarm optimization
- perceptron neural network
- river flow data
- univariate time series
- First received 20 April 2016.
- Accepted in revised form 15 August 2016.
- © IWA Publishing 2016