Introduction
Due to limited budgets and human resources for long-term monitoring, gathering observed discharge data from rivers in Iran is challenging. Novel flow estimation methods are valuable in this context. Developing accurate methods for estimating river flow is crucial due to direct discharge measurement limitations. On the other hand, indirect methods include hydrological and hydraulic models, the rating curve, and data-based models. These methods are cheaper and more accessible, but their accuracy depends on the input data quality and the model's complexity. This study evaluates and compares the performance of a multivariate power rating curve model (MPRC), classic rating curve model (CRC), the Shiono and Knight model (SKM), and adaptive neuro-fuzzy inference system (ANFIS) model for estimating streamflow time series. In addition to well-known hydraulic variables such as cross-sectional area, wetted perimeter, and free surface width, determining the mean flow velocity through isovel contours is also essential as input variables for the MPRC. A novel approach in the calibration and uncertainty analysis of the MPRC model by Markov Chain Monte Carlo (MCMC), using the ANFIS model instead of the MPRC model and comparing them with the CRC and SKM models, are the novelties of the present research.
Methodology
The MPRC model proposed by Maghrebi & Ahmadi (2017) requires not only hydraulic input variables such as cross-sectional area, wetted perimeter, and free water surface width but also the velocity parameter obtained from the isovel contours. Before model calibration using MCMC, effective parameters are identified through correlation analysis. The model is calibrated using the Markov Chain Monte Carlo (MCMC) method on a portion of the observed data from the Molasani Hydrometric Station on the Karun River. The advantage of this method is that it not only calibrates the model but also evaluates its uncertainty. In the next step, the Adaptive Neuro-Fuzzy Inference System (ANFIS) method is used with the mentioned input variables instead of using the multi-variable power model. The results of these two models are compared with the CRC and SKM models.
Results and Discussion
This study compares the accuracy of four models—MPRC, ANFIS, CRC, and SKM—in estimating streamflow. Also, the Maghrebi & Ahmadi (2017) approach, MPRC model, incorporates the following modifications:
• Feature Selection: A feature selection step is introduced before calibration and uncertainty analysis.
• Model Calibration: Station-specific data is used for calibration instead of laboratory data, enhancing the model's real-world accuracy and efficiency.
• Uncertainty Analysis: Calibration methods incorporating uncertainty analysis provide a better understanding of model limitations and more accurate flow estimates.
• Integration with Machine Learning Models: Integrating the modified model with machine learning models like ANFIS is explored. This enhances the model's potential for accurate flow estimation under diverse conditions.
Results demonstrate that the ANFIS model outperforms the other three models based on four metrics: Kling-Gupta efficiency (KGE), Scatter index (SI), Index of agreement (d), and Percent bias (PBIAS). The values of these criteria in the testing phase for ANFIS are equal to 0.988, 0.9%, 0.994, and 0.41%, respectively, which are much better than the MPRC, CRC, and SKM.
Conclusion
Overall, integrating the mentioned hydraulic variables with the ANFIS model can improve the accuracy of streamflow time series estimation. Also, this approach increased the efficiency and accuracy of the model proposed by Maghrebi & Ahmadi (2017).
Keywords
Isovel contours, machine learning, Markov chain Monte Carlo, river discharge, Shiono and Knight model