Abstract
The suspended sediment load transported by rivers can be estimated using various methodologies, including those based on artificial intelligence. In this study, we employed the Long Short-Term Memory (LSTM) model to estimate the suspended sediment concentration in the Mississippi River, United States of America. The input variables for the LSTM model included river discharge, water depth, suspended sediment load, and flow velocity. To enhance the model's performance, the input data and initial parameters were optimized using the Red Fox Optimization (RFO) algorithm, resulting in a super-optimized LSTM model (SLSTM-RFO) developed through a two-phase optimization process. Additionally, sediment load estimations were conducted using alternative models, specifically the Artificial Neural Network (ANN) and Generalized Regression Neural Network (GRNN) models. The performance of these models was assessed using five performance indicators, the correlation coefficient (R2), root mean square error (RMSE), mean absolute error (MAE), Nash and Sutcliffe efficiency (NS), and RMSE observations standard deviation ratio (RSR), demonstrating that the SLSTM-RFO model significantly outperformed the other models. Specifically, the SLSTM-RFO yielded improved estimation results, achieving reductions in error (RMSE) of 73.30%, 81.50%, and 82.56% compared to the LSTM, ANN, and GRNN models, respectively.
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Data availability
Datasets are derived from public resources and are available in the USGS Water Data for the Nation (https://waterdata.usgs.gov/nwis).
Abbreviations
- ANN :
-
Artificial Neural Network
- GRNN :
-
Generalized Regression Neural Network
- LSTM :
-
Long Short-Term Memory
- MAE :
-
Mean Absolute Error
- NS :
-
Nash-Sutcliffe efficiency
- PI :
-
Performance Indicator
- Q :
-
Discharge
- R 2 :
-
Correlation Coefficient
- RFO :
-
Red Fox Optimization
- RMSE :
-
Root Mean Square Error
- RNN :
-
Recurrent Neural Network
- RSR :
-
RMSE observations standard deviation ratio
- SLSTM-RFO :
-
Super-Optimized Long Short-Term Memory based on Red Fox Optimization
- SM-LSTM :
-
Smoothing Long Short-Term Memory
- SSL :
-
Suspended Sediment Load
- USA :
-
United States of America
- USGS :
-
United States Geological Survey
- V :
-
Velocity
- WL :
-
Water Level
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Acknowledgements
Mohammad Mahdi Malekpour would like to thank the University of Bremen and the Martin-Luther-University Halle-Wittenberg (both in Germany) for letting him complete the research as a guest scientist.
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All authors contributed to the study conception and design. Data collection, preparation, and analysis were performed by Mohammad Mahdi Malekpour and Kourosh Qaderi. Working on LSTM and ANN model and the optimization process by the RFO algorithm were performed by Mohammad Mehdi Ahmadi, Mohammad Mahdi Malekpour, and Marcello Gugliotta. Working on GRNN model were performed by Mahmoud Mohammad Rezapour Tabari. The first draft of the manuscript was written by Mohammad Mahdi Malekpour and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
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Communicated by: Hassan Babaie
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Malekpour, M.M., Ahmadi, M.M., Gugliotta, M. et al. Estimation of suspended sediment load utilizing a super-optimized deep learning approach informed by the red fox optimization algorithm. Earth Sci Inform 18, 286 (2025). https://doi.org/10.1007/s12145-025-01801-4
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DOI: https://doi.org/10.1007/s12145-025-01801-4