# A Comparative Analysis of Multiple Machine Learning Methods for Flood Routing in the Yangtze River

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Comparative ML Models

#### 2.1.1. Support Vector Regression

#### 2.1.2. Gaussian Process Regression

#### 2.1.3. Random Forest Regression

#### 2.1.4. Multilayer Perceptron

_{j}) can be calculated by the following equation.

_{i}is the output value of the ith node in the previous layer, w

_{ij}is the weight from the ith node in the previous layer to this node, θ

_{j}is the bias of this node and f denotes the activation function.

#### 2.1.5. Long Short-Term Memory

_{t}) can be computed by the following equations.

_{t}and h

_{t}

_{-1}are, respectively, the outputs of the current and prior LSTM cells. F

_{t}is the forgetting gate output of the current LSTM cell. I

_{t}is the input gate output of the current LSTM cell. O

_{t}is the output gate output of the current LSTM cell. G

_{t}is the candidate state set of the current LSTM cell. C

_{t}is the state of the current LSTM cell. x

_{t}is the input datum of the current LSTM cell. w

_{Fx}, w

_{Ix}, w

_{Gx}, w

_{Ox}, w

_{Fh}, w

_{Ih}, w

_{Gh}and w

_{Oh}are the weights of the current LSTM cell. b

_{Fx}, b

_{Ix}, b

_{Gx}, b

_{Ox}, b

_{Fh}, b

_{Ih}, b

_{Gh}and b

_{Oh}are the biases of the current LSTM cell. σ and tanh denote the sigmoid function and hyperbolic tangent function, respectively. ∗ denotes the Hadamard product.

#### 2.1.6. Gated Recurrent Unit

_{t}) can be computed by the following equations.

_{t}and h

_{t}

_{-1}are, respectively, the outputs of the current and prior GRU cells. R

_{t}is the reset gate output of the current GRU cell. U

_{t}is the update gate output of the current GRU cell. K

_{t}is the candidate set of the current GRU cell. x

_{t}is the input datum of the current GRU cell. w

_{Rx}, w

_{Ux}, w

_{Kx}, w

_{Rh}, w

_{Uh}and w

_{Kh}are the weights of the current GRU cell. b

_{Rx}, b

_{Ux}, b

_{Kx}, b

_{Rh}, b

_{Uh}and b

_{Kh}are the biases of the current GRU cell.

_{t}and U

_{t}are first obtained using Equations (8) and (9), respectively, based on the input data of the current GRU cell and the output of the prior GRU cell. Secondly, K

_{t}is obtained using Equation (10) based on the input data and reset gate output of the current GRU cell and the output of the prior GRU cell. Lastly, h

_{t}is obtained using Equation (11) based on the update gate output and the candidate set of the current GRU cell and the output of the prior GRU cell [48]. It can be seen from Figure 1 that the GRU possesses a simpler structure compared to the LSTM. Consequently, it facilitates a faster training rate than the LSTM. Therefore, the GRU has been widely used in the field of artificial intelligence, especially in processing long time series.

#### 2.2. Experimental Methods

#### 2.2.1. Data Normalization

_{t}is the normalized value of the data at time t; x

_{t}is the value of the original datum from the training dataset or the testing dataset at time t; and x

_{max}and x

_{min}are the maximum and minimum values of the original data from the training dataset, respectively.

#### 2.2.2. Efficiency Criteria

_{t}and S

_{t}are, respectively, the observed and simulated values at time t; $\overline{O}$ and $\overline{S}$ are, respectively, the average values of the observed and simulated values; T is the number of O

_{t}; and SD

_{O}and SD

_{S}are the standard deviations of the observed and simulated values, respectively. SD

_{O}and SD

_{S}can be respectively defined using the following equations.

#### 2.2.3. Taylor Diagram

_{0}is the maximum correlation attainable and is identified as 0.9999 in this paper. For any given SD

_{S}, TSS increases monotonically with increasing R; for any given R, TSS increases as SD

_{S}approaches SD

_{O}. The larger the TSS of the model, the better the model performance is.

## 3. Case Study

^{2}, which makes it the third-largest river in the world and the first in China. Above Yichang are the upper reaches of the Yangtze River with a main stream length of over 4500 km and a drainage area of 1 million km

^{2}. From Yichang to Hukou are the middle reaches of the Yangtze River with a main stream length of over 950 km and a drainage area of 0.68 million km

^{2}. Below Hukou are the lower reaches of the Yangtze River with a main stream length of over 930 km and a drainage area of 0.12 million km

^{2}. In this paper, two reaches with complex water systems are selected as case studies to compare and analyze the applicability of different ML methods for flood routing in the Yangtze River. The first case study is a reach in the valley from Cuntan Station to the Three Georges Reservoir (TGR) with a main stream length of over 650 km, which is located at the end of the Upper Yangtze River and characterized by a long distance, a large river bottom drop, a deep canyon, rapid flow and many tributaries, which increases the difficulty of inflow forecasting of the TGR. A schematic diagram of the Yangtze River and hydrological stations is shown in Figure 2.

^{3}) significantly enhances the flood control capacity of the Yangtze River in the Middle and Lower reaches, and the flood control standard of the downstream Jingjiang reach has risen from once every ten years to once every one hundred years. Cuntan Station and Wulong Station are the main control hydrological stations for the inflow hydrograph prediction of the TGR, and Zhicheng Station, Shashi Station and Chenglingji Station are the main flood control stations of the downstream Jingjiang reach. Therefore, the inflow hydrograph prediction of the TGR and the water level hydrograph prediction of Shashi Station for flood routing in the Yangtze River are scientific problems with important academic significance and engineering application value, which play an important role in guaranteeing the flood control security of the Jingjiang reach of the Yangtze River as well as China’s energy security.

^{2}, and the drainage areas above Cuntan Station and Wulong Station are about 867,000 and 88,000 km

^{2}, respectively. The drainage areas above Yichang Station, Zhicheng Station and Shashi Station are over 1.0055, 1.0241 and 1.0320 million km

^{2}, respectively. According to the location relationship between these stations, the daily average discharge series of Cuntan Station and Wulong Station are used for inflow prediction of the TGR so as to consider the influence of the discharge from the Wu River, and the daily average discharge series of Yichang Station and the daily average water level series of Zhicheng Station are used for water level prediction of Shashi Station so as to consider the influence of the discharge from the Qing River.

## 4. Results and Discussion

#### 4.1. Experimental Conditions

#### 4.2. The Inflow Hydrograph Prediction of the TGR

^{2}characterizes the accuracy of the linear fit equation. The larger the R

^{2}is, the more the data points are concentrated on both sides of the linear fit line. The closer the slope of the linear fit line is to 1 and the closer the intercept is to 0, the better the linear fit line matches the ideal fit line, and the better the simulated inflows and the observed inflows of the TGR are matched. Therefore, the slope of the linear fit line of the GRU model is closest to 1, and the linear fit line of the GRU model is more in line with the ideal fit line than those of the other ML models, which means that the simulated inflows of the TGR of the GRU model are closest to the corresponding observed inflows. In order to analyze the distribution pattern of the simulated inflow errors of the TGR of the different ML models, violin plots of the simulated inflow errors by different ML models during the testing period are shown in Figure 5.

^{3}/s), Q2 (from 10,000 to 20,000 m

^{3}/s), Q3 (from 20,000 to 30,000 m

^{3}/s), Q4 (from 30,000 to 40,000 m

^{3}/s), Q5 (from 40,000 to 50,000 m

^{3}/s), Q6 (from 50,000 to 60,000 m

^{3}/s), Q7 (from 60,000 to 70,000 m

^{3}/s) and Q8 (greater than 70,000 m

^{3}/s), and the ribbon diagram of the MAPEs for inflow hydrograph prediction of the TGR by the models during the testing period is shown in Figure 6. For the inflow of the TGR from 30,000 to 50,000 m

^{3}/s, namely, discharge interval Q4 and Q5, all models had a larger MAPE, around 10%. The GPR and RFR models had relatively poor MAPEs for larger inflow, the SVR model had a poor MAPE for a smaller inflow, and the MLP, LSTM and GRU models had relatively better MAPEs for smaller and larger inflows. Overall, the GRU model had a smaller MAPE.

#### 4.3. The Water Level Hydrograph Prediction of Shashi Station

^{3}/s (the obtained MAPE is around 10%), which may be related to the long distance from Cuntan Station to the TGR and the influence of many small tributaries with no observation data for this river.

#### 4.4. Performance Comparison among Three Deep Learning Models with Different Time Lags for Flood Routing

## 5. Conclusions

- (1)
- The ML models were verified as effective and efficient in obtaining accurate flood hydrographs in river flood routing with fewer data (e.g., only flows and water levels that are daily measured). Therefore, the ML models could be widely used for flood routing in complex natural rivers. However, it is important to note that not all ML models were equally effective in flood routing, as some may overfit during the training phase.
- (2)
- The deep learning models, including the MLP, LSTM and GRU models, were more efficient than the SVR, GPR and RFR models. The GRU model, in particular, outperformed the others in almost all efficiency criteria, including MAPE, RMSE, NSE, TSS and KGE. The reductions in MAPE and RMSE were significant, with at least 7.66% and 3.80% for the first case study and 19.51% and 11.76% for the second case study during the testing period.
- (3)
- The model that had higher accuracy may necessitate a longer training time, but the GRU exhibited a faster training rate than the LSTM. Although the training times of the LSTM and GRU were longer than those of the other models, the GRU’s training times were, respectively, 32.19% and 26.14% shorter than those of the LSTM for the two case studies due to its simpler structure and more effortless convergence.
- (4)
- The time lag in flood routing determined the number of input variables of the models, which in turn may have affected the accuracy of flood routing. As a result, the accuracy of flood routing gradually increased and then slightly decreased as the time lag increased for the MLP, LSTM and GRU models. Interestingly, the GRU model performed better than the MLP and LSTM models for different time lags.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Akbari, R.; Hessami-Kermani, M.R.; Shojaee, S. Flood Routing: Improving Outflow Using a New Non-linear Muskingum Model with Four Variable Parameters Coupled with PSO-GA Algorithm. Water Resour. Manag.
**2020**, 34, 3291–3316. [Google Scholar] [CrossRef] - Kang, L.; Zhou, L.; Zhang, S. Parameter Estimation of Two Improved Nonlinear Muskingum Models Considering the Lateral Flow Using a Hybrid Algorithm. Water Resour. Manag.
**2017**, 31, 4449–4467. [Google Scholar] [CrossRef] - Zhang, S.; Kang, L.; Zhou, L.; Guo, X. A new modified nonlinear Muskingum model and its parameter estimation using the adaptive genetic algorithm. Hydrol. Res.
**2017**, 48, 17–27. [Google Scholar] [CrossRef] - Yuan, X.; Wu, X.; Tian, H.; Yuan, Y.; Adnan, R.M. Parameter Identification of Nonlinear Muskingum Model with Backtracking Search Algorithm. Water Resour. Manag.
**2016**, 30, 2767–2783. [Google Scholar] [CrossRef] - Kim, D.H.; Georgakakos, A.P. Hydrologic routing using nonlinear cascaded reservoirs. Water Resour. Res.
**2014**, 50, 7000–7019. [Google Scholar] [CrossRef] - Jeng, R.I.; Coon, G.C. True Form of Instantaneous Unit Hydrograph of Linear Reservoirs. J. Irrig. Drain. Eng.
**2003**, 129, 11–17. [Google Scholar] [CrossRef] - Dhote, P.R.; Thakur, P.K.; Domeneghetti, A.; Chouksey, A.; Garg, V.; Aggarwal, S.P.; Chauhan, P. The use of SARAL/AltiKa altimeter measurements for multi-site hydrodynamic model validation and rating curves estimation: An application to Brahmaputra River. Adv. Space Res.
**2021**, 68, 691–702. [Google Scholar] [CrossRef] - Singh, R.K.; Kumar Villuri, V.G.; Pasupuleti, S.; Nune, R. Hydrodynamic modeling for identifying flood vulnerability zones in lower Damodar river of eastern India. Ain Shams Eng. J.
**2020**, 11, 1035–1046. [Google Scholar] [CrossRef] - Chatterjee, C.; Förster, S.; Bronstert, A. Comparison of hydrodynamic models of different complexities to model floods with emergency storage areas. Hydrol. Process.
**2008**, 22, 4695–4709. [Google Scholar] [CrossRef] - Cho, M.; Kim, C.; Jung, K.; Jung, H. Water Level Prediction Model Applying a Long Short-Term Memory (LSTM)-Gated Recurrent Unit (GRU) Method for Flood Prediction. Water
**2022**, 14, 2221. [Google Scholar] [CrossRef] - Jeong, J.; Park, E. Comparative applications of data-driven models representing water table fluctuations. J. Hydrol.
**2019**, 572, 261–273. [Google Scholar] [CrossRef] - Zhang, Z.; Zhang, Q.; Singh, V.P. Univariate streamflow forecasting using commonly used data-driven models: Literature review and case study. Hydrol. Sci. J.
**2018**, 63, 1091–1111. [Google Scholar] [CrossRef] - Niu, W.J.; Feng, Z.K.; Feng, B.F.; Min, Y.W.; Cheng, C.T.; Zhou, J.Z. Comparison of Multiple Linear Regression, Artificial Neural Network, Extreme Learning Machine, and Support Vector Machine in Deriving Operation Rule of Hydropower Reservoir. Water
**2019**, 11, 17. [Google Scholar] [CrossRef][Green Version] - Zhang, J.; Xiao, H.; Fang, H. Component-based Reconstruction Prediction of Runoff at Multi-time Scales in the Source Area of the Yellow River Based on the ARMA Model. Water Resour. Manag.
**2022**, 36, 433–448. [Google Scholar] [CrossRef] - Yan, B.; Mu, R.; Guo, J.; Liu, Y.; Tang, J.; Wang, H. Flood risk analysis of reservoirs based on full-series ARIMA model under climate change. J. Hydrol.
**2022**, 610, 127979. [Google Scholar] [CrossRef] - Lian, Y.; Luo, J.; Xue, W.; Zuo, G.; Zhang, S. Cause-driven Streamflow Forecasting Framework Based on Linear Correlation Reconstruction and Long Short-term Memory. Water Resour. Manag.
**2022**, 36, 1661–1678. [Google Scholar] [CrossRef] - Ebrahimi, E.; Shourian, M. River Flow Prediction Using Dynamic Method for Selecting and Prioritizing K-Nearest Neighbors Based on Data Features. J. Hydrol. Eng.
**2020**, 25, 04020010. [Google Scholar] [CrossRef] - Dehghani, R.; Babaali, H.; Zeydalinejad, N. Evaluation of statistical models and modern hybrid artificial intelligence in the simulation of precipitation runoff process. Sustain. Water Resour. Manag.
**2022**, 8, 154. [Google Scholar] [CrossRef] - Rahbar, A.; Mirarabi, A.; Nakhaei, M.; Talkhabi, M.; Jamali, M. A Comparative Analysis of Data-Driven Models (SVR, ANFIS, and ANNs) for Daily Karst Spring Discharge Prediction. Water Resour. Manag.
**2022**, 36, 589–609. [Google Scholar] [CrossRef] - Yaseen, Z.M.; Sulaiman, S.O.; Deo, R.C.; Chau, K.-W. An enhanced extreme learning machine model for river flow forecasting: State-of-the-art, practical applications in water resource engineering area and future research direction. J. Hydrol.
**2019**, 569, 387–408. [Google Scholar] [CrossRef] - Zhu, S.; Luo, X.; Xu, Z.; Ye, L. Seasonal streamflow forecasts using mixture-kernel GPR and advanced methods of input variable selection. Hydrol. Res.
**2019**, 50, 200–214. [Google Scholar] [CrossRef] - Desai, S.; Ouarda, T.B.M.J. Regional hydrological frequency analysis at ungauged sites with random forest regression. J. Hydrol.
**2021**, 594, 125861. [Google Scholar] [CrossRef] - Wang, W.; Jin, J.; Li, Y. Prediction of Inflow at Three Gorges Dam in Yangtze River with Wavelet Network Model. Water Resour. Manag.
**2009**, 23, 2791–2803. [Google Scholar] [CrossRef] - Lee, W.J.; Lee, E.H. Runoff Prediction Based on the Discharge of Pump Stations in an Urban Stream Using a Modified Multi-Layer Perceptron Combined with Meta-Heuristic Optimization. Water
**2022**, 14, 99. [Google Scholar] [CrossRef] - Wunsch, A.; Liesch, T.; Broda, S. Groundwater level forecasting with artificial neural networks: A comparison of long short-term memory (LSTM), convolutional neural networks (CNNs), and non-linear autoregressive networks with exogenous input (NARX). Hydrol. Earth Syst. Sci.
**2021**, 25, 1671–1687. [Google Scholar] [CrossRef] - Peng, A.; Zhang, X.; Xu, W.; Tian, Y. Effects of Training Data on the Learning Performance of LSTM Network for Runoff Simulation. Water Resour. Manag.
**2022**, 36, 2381–2394. [Google Scholar] [CrossRef] - Wang, Q.; Liu, Y.; Yue, Q.; Zheng, Y.; Yao, X.; Yu, J. Impact of Input Filtering and Architecture Selection Strategies on GRU Runoff Forecasting: A Case Study in the Wei River Basin, Shaanxi, China. Water
**2020**, 12, 3532. [Google Scholar] [CrossRef] - Wang, Y.; Liu, J.; Li, R.; Suo, X.; Lu, E. Medium and Long-term Precipitation Prediction Using Wavelet Decomposition-prediction-reconstruction Model. Water Resour. Manag.
**2022**, 36, 971–987. [Google Scholar] [CrossRef] - He, R.; Zhang, L.; Chew, A.W.Z. Modeling and predicting rainfall time series using seasonal-trend decomposition and machine learning. Knowl. Based Syst.
**2022**, 251, 109125. [Google Scholar] [CrossRef] - Shabbir, M.; Chand, S.; Iqbal, F. A Novel Hybrid Method for River Discharge Prediction. Water Resour. Manag.
**2022**, 36, 253–272. [Google Scholar] [CrossRef] - He, X.; Luo, J.; Zuo, G.; Xie, J. Daily Runoff Forecasting Using a Hybrid Model Based on Variational Mode Decomposition and Deep Neural Networks. Water Resour. Manag.
**2019**, 33, 1571–1590. [Google Scholar] [CrossRef] - Ghasempour, R.; Azamathulla, H.M.; Roushangar, K. EEMD and VMD based hybrid GPR models for river streamflow point and interval predictions. Water Supply
**2021**, 21, 3960–3975. [Google Scholar] [CrossRef] - Zhang, X.; Duan, B.; He, S.; Wu, X.; Zhao, D. A new precipitation forecast method based on CEEMD-WTD-GRU. Water Supply
**2022**, 22, 4120–4132. [Google Scholar] [CrossRef] - Li, B.-J.; Sun, G.-L.; Liu, Y.; Wang, W.-C.; Huang, X.-D. Monthly Runoff Forecasting Using Variational Mode Decomposition Coupled with Gray Wolf Optimizer-Based Long Short-term Memory Neural Networks. Water Resour. Manag.
**2022**, 36, 2095–2115. [Google Scholar] [CrossRef] - Ye, S.; Wang, C.; Wang, Y.; Lei, X.; Wang, X.; Yang, G. Real-time model predictive control study of run-of-river hydropower plants with data-driven and physics-based coupled model. J. Hydrol.
**2023**, 617, 128942. [Google Scholar] [CrossRef] - Adnan, R.M.; Kisi, O.; Mostafa, R.R.; Ahmed, A.N.; El-Shafie, A. The potential of a novel support vector machine trained with modified mayfly optimization algorithm for streamflow prediction. Hydrol. Sci. J.
**2022**, 67, 161–174. [Google Scholar] [CrossRef] - Adnan, R.M.; Mostafa, R.R.; Kisi, O.; Yaseen, Z.M.; Shahid, S.; Zounemat-Kermani, M. Improving streamflow prediction using a new hybrid ELM model combined with hybrid particle swarm optimization and grey wolf optimization. Knowl. Based Syst.
**2021**, 230, 107379. [Google Scholar] [CrossRef] - Adnan, R.M.; Liang, Z.; Trajkovic, S.; Zounemat-Kermani, M.; Li, B.; Kisi, O. Daily streamflow prediction using optimally pruned extreme learning machine. J. Hydrol.
**2019**, 577, 123981. [Google Scholar] [CrossRef] - Yuan, X.; Chen, C.; Lei, X.; Yuan, Y.; Muhammad Adnan, R. Monthly runoff forecasting based on LSTM–ALO model. Stoch. Environ. Res. Risk Assess.
**2018**, 32, 2199–2212. [Google Scholar] [CrossRef] - Fang, Z.; Wang, Y.; Peng, L.; Hong, H. Predicting flood susceptibility using LSTM neural networks. J. Hydrol.
**2021**, 594, 125734. [Google Scholar] [CrossRef] - Lian, Y.; Luo, J.; Wang, J.; Zuo, G.; Wei, N. Climate-driven Model Based on Long Short-Term Memory and Bayesian Optimization for Multi-day-ahead Daily Streamflow Forecasting. Water Resour. Manag.
**2022**, 36, 21–37. [Google Scholar] [CrossRef] - Kilinc, H.C.; Haznedar, B. A Hybrid Model for Streamflow Forecasting in the Basin of Euphrates. Water
**2022**, 14, 80. [Google Scholar] [CrossRef] - Ikram, R.M.A.; Mostafa, R.R.; Chen, Z.; Parmar, K.S.; Kisi, O.; Zounemat-Kermani, M. Water Temperature Prediction Using Improved Deep Learning Methods through Reptile Search Algorithm and Weighted Mean of Vectors Optimizer. J. Mar. Sci. Eng.
**2023**, 11, 259. [Google Scholar] [CrossRef] - Zhang, F.; Kang, Y.; Cheng, X.; Chen, P.; Song, S. A Hybrid Model Integrating Elman Neural Network with Variational Mode Decomposition and Box–Cox Transformation for Monthly Runoff Time Series Prediction. Water Resour. Manag.
**2022**, 36, 3673–3697. [Google Scholar] [CrossRef] - Alizadeh, B.; Bafti, A.G.; Kamangir, H.; Zhang, Y.; Wright, D.B.; Franz, K.J. A novel attention-based LSTM cell post-processor coupled with bayesian optimization for streamflow prediction. J. Hydrol.
**2021**, 601, 126526. [Google Scholar] [CrossRef] - Noor, F.; Haq, S.; Rakib, M.; Ahmed, T.; Jamal, Z.; Siam, Z.S.; Hasan, R.T.; Adnan, M.S.G.; Dewan, A.; Rahman, R.M. Water Level Forecasting Using Spatiotemporal Attention-Based Long Short-Term Memory Network. Water
**2022**, 14, 612. [Google Scholar] [CrossRef] - Li, Y.; Wang, W.; Wang, G.; Tan, Q. Actual evapotranspiration estimation over the Tuojiang River Basin based on a hybrid CNN-RF model. J. Hydrol.
**2022**, 610, 127788. [Google Scholar] [CrossRef] - Zhou, S.; Song, C.; Zhang, J.; Chang, W.; Hou, W.; Yang, L. A Hybrid Prediction Framework for Water Quality with Integrated W-ARIMA-GRU and LightGBM Methods. Water
**2022**, 14, 1322. [Google Scholar] [CrossRef] - Xu, W.; Chen, J.; Zhang, X.J. Scale Effects of the Monthly Streamflow Prediction Using a State-of-the-art Deep Learning Model. Water Resour. Manag.
**2022**, 36, 3609–3625. [Google Scholar] [CrossRef] - Gong, Y.; Liu, P.; Cheng, L.; Chen, G.; Zhou, Y.; Zhang, X.; Xu, W. Determining dynamic water level control boundaries for a multi-reservoir system during flood seasons with considering channel storage. J. Flood Risk Manag.
**2020**, 13, e12586. [Google Scholar] [CrossRef] - Chao, L.; Zhang, K.; Yang, Z.-L.; Wang, J.; Lin, P.; Liang, J.; Li, Z.; Gu, Z. Improving flood simulation capability of the WRF-Hydro-RAPID model using a multi-source precipitation merging method. J. Hydrol.
**2021**, 592, 125814. [Google Scholar] [CrossRef] - Ping, F.; Jia-chun, L.; Qing-quan, L. Flood routing models in confluent and dividing channels. Appl. Math. Mech.
**2004**, 25, 1333–1343. [Google Scholar] [CrossRef] - Wang, K.; Wang, Z.; Liu, K.; Cheng, L.; Bai, Y.; Jin, G. Optimizing flood diversion siting and its control strategy of detention basins: A case study of the Yangtze River, China. J. Hydrol.
**2021**, 597, 126201. [Google Scholar] [CrossRef] - Chiang, S.; Chang, C.-H.; Chen, W.-B. Comparison of Rainfall-Runoff Simulation between Support Vector Regression and HEC-HMS for a Rural Watershed in Taiwan. Water
**2022**, 14, 191. [Google Scholar] [CrossRef] - Roushangar, K.; Chamani, M.; Ghasempour, R.; Azamathulla, H.M.; Alizadeh, F. A comparative study of wavelet and empirical mode decomposition-based GPR models for river discharge relationship modeling at consecutive hydrometric stations. Water Supply
**2021**, 21, 3080–3098. [Google Scholar] [CrossRef] - Kumar, M.; Elbeltagi, A.; Pande, C.B.; Ahmed, A.N.; Chow, M.F.; Pham, Q.B.; Kumari, A.; Kumar, D. Applications of Data-driven Models for Daily Discharge Estimation Based on Different Input Combinations. Water Resour. Manag.
**2022**, 36, 2201–2221. [Google Scholar] [CrossRef] - Rezaie-Balf, M.; Nowbandegani, S.F.; Samadi, S.Z.; Fallah, H.; Alaghmand, S. An Ensemble Decomposition-Based Artificial Intelligence Approach for Daily Streamflow Prediction. Water
**2019**, 11, 709. [Google Scholar] [CrossRef][Green Version] - Acharya, U.; Daigh, A.L.M.; Oduor, P.G. Machine Learning for Predicting Field Soil Moisture Using Soil, Crop, and Nearby Weather Station Data in the Red River Valley of the North. Soil Syst.
**2021**, 5, 57. [Google Scholar] [CrossRef] - Khosravi, K.; Golkarian, A.; Tiefenbacher, J.P. Using Optimized Deep Learning to Predict Daily Streamflow: A Comparison to Common Machine Learning Algorithms. Water Resour. Manag.
**2022**, 36, 699–716. [Google Scholar] [CrossRef] - Xie, J.; Liu, X.; Tian, W.; Wang, K.; Bai, P.; Liu, C. Estimating Gridded Monthly Baseflow From 1981 to 2020 for the Contiguous US Using Long Short-Term Memory (LSTM) Networks. Water Resour. Res.
**2022**, 58, e2021WR031663. [Google Scholar] [CrossRef] - Li, Z.; Kang, L.; Zhou, L.; Zhu, M. Deep Learning Framework with Time Series Analysis Methods for Runoff Prediction. Water
**2021**, 13, 575. [Google Scholar] [CrossRef] - Nevo, S.; Morin, E.; Gerzi Rosenthal, A.; Metzger, A.; Barshai, C.; Weitzner, D.; Voloshin, D.; Kratzert, F.; Elidan, G.; Dror, G.; et al. Flood forecasting with machine learning models in an operational framework. Hydrol. Earth Syst. Sci.
**2022**, 26, 4013–4032. [Google Scholar] [CrossRef] - Anderson, S.; Radić, V. Evaluation and interpretation of convolutional long short-term memory networks for regional hydrological modelling. Hydrol. Earth Syst. Sci.
**2022**, 26, 795–825. [Google Scholar] [CrossRef] - Zhang, X.; Yang, Y. Suspended sediment concentration forecast based on CEEMDAN-GRU model. Water Supply
**2020**, 20, 1787–1798. [Google Scholar] [CrossRef] - Taylor, K.E. Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res. Atmos.
**2001**, 106, 7183–7192. [Google Scholar] [CrossRef] - Bai, T.; Wei, J.; Yang, W.W.; Huang, Q. Multi-Objective Parameter Estimation of Improved Muskingum Model by Wolf Pack Algorithm and Its Application in Upper Hanjiang River, China. Water
**2018**, 10, 14. [Google Scholar] [CrossRef][Green Version] - Dazzi, S.; Vacondio, R.; Mignosa, P. Flood Stage Forecasting Using Machine-Learning Methods: A Case Study on the Parma River (Italy). Water
**2021**, 13, 1612. [Google Scholar] [CrossRef] - Zhang, Y.; Yang, L. A novel dynamic predictive method of water inrush from coal floor based on gated recurrent unit model. Nat. Hazards
**2021**, 105, 2027–2043. [Google Scholar] [CrossRef] - Wang, J.; Cui, Q.; Sun, X. A novel framework for carbon price prediction using comprehensive feature screening, bidirectional gate recurrent unit and Gaussian process regression. J. Clean. Prod.
**2021**, 314, 128024. [Google Scholar] [CrossRef] - Park, K.; Jung, Y.; Seong, Y.; Lee, S. Development of Deep Learning Models to Improve the Accuracy of Water Levels Time Series Prediction through Multivariate Hydrological Data. Water
**2022**, 14, 469. [Google Scholar] [CrossRef]

**Figure 12.**TSSs of the MLP, LSTM and GRU models for water level hydrograph prediction of Shashi Station during the testing period.

**Figure 3.**Taylor diagram depicting the performance of six ML models for inflow hydrograph prediction of the TGR.

**Figure 4.**The scatter plots of the simulated and observed inflows of the TGR by different ML models during the testing period.

**Figure 5.**Violin plots of the simulated inflow errors of the TGR by different ML models during the testing period.

**Figure 6.**Ribbon diagram of the MAPEs for inflow hydrograph prediction of the TGR by the models during the testing period.

**Figure 8.**Scatter plots of the simulated and observed water levels of Shashi Station by different ML models during the testing period.

**Figure 9.**Violin plots of the simulated water level errors of Shashi Station by different ML models during the testing period.

**Figure 10.**Ribbon diagram of the MAPEs for water level hydrograph prediction of Shashi Station by the models during the testing period.

Dataset | Model | MAPE (%) | RMSE (m ^{3}/s) | NSE | R | TSS | KGE | Time (s) |
---|---|---|---|---|---|---|---|---|

Training | LMM | 6.25 | 1834 | 0.9681 | 0.9858 | 0.9701 | 0.9370 | 7.969 |

SVR | 27.19 | 2348 | 0.9478 | 0.9898 | 0.9757 | 0.8506 | 0.057 | |

GPR | 6.28 | 1698 | 0.9727 | 0.9864 | 0.9721 | 0.9662 | 6.159 | |

RFR | 4.72 | 1171 | 0.9870 | 0.9935 | 0.9869 | 0.9852 | 8.992 | |

MLP | 5.12 | 1438 | 0.9804 | 0.9915 | 0.9811 | 0.9462 | 2.370 | |

LSTM | 5.58 | 1404 | 0.9813 | 0.9911 | 0.9820 | 0.9694 | 13.841 | |

GRU | 5.17 | 1401 | 0.9814 | 0.9909 | 0.9819 | 0.9837 | 9.386 | |

Testing | LMM | 6.48 | 2262 | 0.9429 | 0.9733 | 0.9463 | 0.9361 | \ |

SVR | 19.96 | 2301 | 0.9410 | 0.9858 | 0.9687 | 0.8720 | \ | |

GPR | 5.65 | 2044 | 0.9534 | 0.9766 | 0.9531 | 0.9612 | \ | |

RFR | 5.01 | 1889 | 0.9602 | 0.9800 | 0.9601 | 0.9691 | \ | |

MLP | 4.96 | 1763 | 0.9653 | 0.9842 | 0.9672 | 0.9436 | \ | |

LSTM | 5.21 | 1736 | 0.9664 | 0.9840 | 0.9682 | 0.9643 | \ | |

GRU | 4.58 | 1670 | 0.9689 | 0.9848 | 0.9697 | 0.9793 | \ |

Dataset | Model | MAPE (%) | RMSE (m) | NSE | R | TSS | KGE | Time (s) |
---|---|---|---|---|---|---|---|---|

Training | SVR | 1.65 | 0.67 | 0.9601 | 0.9908 | 0.9659 | 0.8796 | 0.014 |

GPR | 0.57 | 0.28 | 0.9932 | 0.9966 | 0.9932 | 0.9882 | 5.291 | |

RFR | 0.30 | 0.15 | 0.9979 | 0.9989 | 0.9979 | 0.9975 | 3.723 | |

MLP | 0.22 | 0.14 | 0.9983 | 0.9992 | 0.9984 | 0.9968 | 3.845 | |

LSTM | 0.23 | 0.15 | 0.9981 | 0.9991 | 0.9982 | 0.9985 | 11.912 | |

GRU | 0.24 | 0.14 | 0.9983 | 0.9993 | 0.9986 | 0.9943 | 8.798 | |

Testing | SVR | 2.64 | 1.02 | 0.9037 | 0.9918 | 0.9483 | 0.8237 | \ |

GPR | 0.99 | 0.39 | 0.9857 | 0.9966 | 0.9889 | 0.9358 | \ | |

RFR | 0.78 | 0.33 | 0.9899 | 0.9967 | 0.9918 | 0.9589 | \ | |

MLP | 0.41 | 0.17 | 0.9972 | 0.9992 | 0.9984 | 0.9869 | \ | |

LSTM | 0.42 | 0.18 | 0.9971 | 0.9991 | 0.9944 | 0.9937 | \ | |

GRU | 0.33 | 0.15 | 0.9980 | 0.9993 | 0.9985 | 0.9966 | \ |

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## Share and Cite

**MDPI and ACS Style**

Zhou, L.; Kang, L.
A Comparative Analysis of Multiple Machine Learning Methods for Flood Routing in the Yangtze River. *Water* **2023**, *15*, 1556.
https://doi.org/10.3390/w15081556

**AMA Style**

Zhou L, Kang L.
A Comparative Analysis of Multiple Machine Learning Methods for Flood Routing in the Yangtze River. *Water*. 2023; 15(8):1556.
https://doi.org/10.3390/w15081556

**Chicago/Turabian Style**

Zhou, Liwei, and Ling Kang.
2023. "A Comparative Analysis of Multiple Machine Learning Methods for Flood Routing in the Yangtze River" *Water* 15, no. 8: 1556.
https://doi.org/10.3390/w15081556