Uncertainty Analysis of Artificial Intelligence Models in Forecasting River Flow (Case Study: Karun River)

Document Type : Research Article


1 Graduate Student, Water Engineering Department, Faculty of Civil and Surveying Engineering, Graduate University of Advanced Technology, Kerman, Iran

2 Department of Water Engineering, Faculty of Civil and Survey Engineering, Graduate University of Advanced Technology, Kerman

3 Assistant Professor, Department of Ecology, Institute of Science and High Technology and Environmental Science, Graduate University of Advanced Technology, Kerman, Iran


An accurate estimation of the discharge flow of natural streams plays a key role in irrigation planning, the design of bridges embedded in waterways, the management of reservoirs and dams, and the design of flood-warning systems. In recent decades, several studies have been conducted using artificial intelligence (AI) to accurately estimate the flow. Despite the proven accuracy level of AI methods, in many cases, there are uncertainties that occur for a variety of reasons. Insufficient knowledge of these uncertainties in the flow modeling process can have irreversible effects. In this research, monthly flow data, measured from Armand hydrometric station, located in Karun River basin, during a-28 year period (from 1980 to 2008) were used. First, the Thomas and Fiering method was used to generate flow series data and consider them as input variables. Then, flow forecast modeling was performed by three AI methods, namely Model Tree (MT), Gene Expression Programming (GEP), and Multivariate Adaptive Regression Spline (MARS). Statistical indicators such as correlation coefficient (R) and Root Mean Square Error (RMSE) were used to evaluate the accuracy of the models. In terms of the training stage, the MARS model with R=0.839 and RMSE=28.624 m3/s performed better than the other two models. Additionally, in the testing stage, the MT model with R=0.784 and RMSE=34.441 m3/s showed a more appropriate performance than other models. The Monte Carlo simulation method was used to calculate the uncertainty of the models, so the results showed that the r-factor parameter, which was the average width of the confidence band in the MT model, was equal to 1.67, indicating a lower and more optimal number compared to MARS (1.92) and GEP (2.025) models. Moreover, the usability of the statistical criterion for quantifying uncertainty, (known as 95PPU) indicated that the GEP model with 95PPU of 64% was selected as a more appropriate percentage than MARS (61%) and MT-M5 (55%). 


Main Subjects

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