# Flood Forecasting Using Hybrid LSTM and GRU Models with Lag Time Preprocessing

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## Abstract

**:**

## 1. Introduction

#### 1.1. The Flood Prediction Models and Lag Time Preprocessing

#### 1.2. Contribution

## 2. Materials and Methods

#### 2.1. The Correlation of Water Level, Discharge and Precipitation

#### 2.2. The Water Level Lag Time between Each Station

#### 2.3. Theoretical Background of the Models and Performance Metrics

#### 2.3.1. STA-LSTM Model

#### 2.3.2. STA-GRU Model

#### 2.4. Performance Metrics

- RMSE emphasizes large errors by squaring the differences, making the model sensitive to significant deviations in predicting flood quantities, thus ensuring robustness and accuracy. The formula of RMSE is given as$$RMSE=\sqrt{\frac{1}{n}\sum _{i=1}^{n}{({O}_{i}-{P}_{i})}^{2}}$$
- MAE assigns equal weight to each error, aiding in evaluating the model’s average predictive precision in general scenarios. The MAE can be represented by the following equation$$MAE=\frac{{\sum}_{i=1}^{n}|{O}_{i}-{P}_{i}|}{n}$$
- R-square offers a measure of how well the model explains the variability in flood flow, where higher R-square values indicate better capability to account for observed fluctuations, enhancing the model’s interpretability and reliability. R-square is defined by$${R}^{2}=1-\frac{{\sum}_{i=1}^{n}{({O}_{i}-{P}_{i})}^{2}}{{\sum}_{i=1}^{n}{({O}_{i}-{\tilde{O}}_{i})}^{2}}$$

## 3. Results and Discussion

#### 3.1. Description of Validation Case

#### 3.2. Discussion of Results

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Jalili Pirani, F.; Najafi, M.R. Multivariate analysis of compound flood hazard across Canada’s Atlantic, Pacific and Great Lakes coastal areas. Earths Future
**2022**, 10, e2022EF002655. [Google Scholar] [CrossRef] - Lin, H.; Mo, R.; Vitart, F.; Stan, C. Eastern Canada flooding 2017 and its subseasonal predictions. Atmosphere-Ocean
**2019**, 57, 195–207. [Google Scholar] [CrossRef] - Ebtehaj, I.; Bonakdari, H. A reliable hybrid outlier robust non-tuned rapid machine learning model for multi-step ahead flood forecasting in Quebec, Canada. J. Hydrol.
**2022**, 614, 128592. [Google Scholar] [CrossRef] - Zadeh, S.M.; Burn, D.H.; O’Brien, N. Detection of trends in flood magnitude and frequency in Canada. J. Hydrol. Reg. Stud.
**2020**, 28, 100673. [Google Scholar] [CrossRef] - Taraky, Y.M.; Liu, Y.; McBean, E.; Daggupati, P.; Gharabaghi, B. Flood risk management with transboundary conflict and cooperation dynamics in the Kabul River Basin. Water
**2021**, 13, 1513. [Google Scholar] [CrossRef] - Burn, D.H.; Whitfield, P.H. Changes in floods and flood regimes in Canada. Can. Water Resour. J./Revue Can. Resour. Hydriques
**2016**, 41, 139–150. [Google Scholar] [CrossRef] - Saurav, K.; Shrestha, S.; Ninsawat, S.; Chonwattana, S. Predicting flood events in Kathmandu Metropolitan City under climate change and urbanisation. J. Environ. Manag.
**2021**, 281, 111894. [Google Scholar] - Lin, J.; Zhang, W.; Wen, Y.; Qiu, S. Evaluating the association between morphological characteristics of urban land and pluvial floods using machine learning methods. Sustain. Cities Soc.
**2023**, 99, 104891. [Google Scholar] [CrossRef] - Ward, P.J.; de Ruiter, M.C.; Mård, J.; Schröter, K.; Van Loon, A.; Veldkamp, T.; von Uexkull, N.; Wanders, N.; AghaKouchak, A.; Arnbjerg-Nielsen, K.; et al. The need to integrate flood and drought disaster risk reduction strategies. Water Secur.
**2020**, 11, 100070. [Google Scholar] [CrossRef] - Nguyen, H.D.; Fox, D.; Dang, D.K.; Pham, L.T.; Viet Du, Q.V.; Nguyen, T.H.T.; Dang, T.N.; Tran, V.T.; Vu, P.L.; Nguyen, Q.H.; et al. Predicting future urban flood risk using land change and hydraulic modeling in a river watershed in the central Province of Vietnam. Remote. Sens.
**2021**, 13, 262. [Google Scholar] [CrossRef] - Kumar, V.; Azamathulla, H.M.; Sharma, K.V.; Mehta, D.J.; Maharaj, K.T. The state of the art in deep learning applications, challenges, and future prospects: A comprehensive review of flood forecasting and management. Sustainability
**2023**, 15, 10543. [Google Scholar] [CrossRef] - Bubeck, P.; Otto, A.; Weichselgartner, J. Societal impacts of flood hazards. In Oxford Research Encyclopedia of Natural Hazard Science; Oxford University Press: Oxford, UK, 2017. [Google Scholar]
- Shah, A.A.; Ajiang, C.; Gong, Z.; Khan, N.A.; Ali, M.; Ahmad, M.; Abbas, A.; Shahid, A. Reconnoitering school children vulnerability and its determinants: Evidence from flood disaster-hit rural communities of Pakistan. Int. J. Disaster Risk Reduct.
**2022**, 70, 102735. [Google Scholar] [CrossRef] - Jonkman, S.N. Global perspectives on loss of human life caused by floods. Nat. Hazards
**2005**, 34, 151–175. [Google Scholar] [CrossRef] - Emerton, R.E.; Stephens, E.M.; Pappenberger, F.; Pagano, T.C.; Weerts, A.H.; Wood, A.W.; Salamon, P.; Brown, J.D.; Hjerdt, N.; Donnelly, C.; et al. Continental and global scale flood forecasting systems. Wiley Interdiscip. Rev. Water
**2016**, 3, 391–418. [Google Scholar] [CrossRef] - Cloke, H.L.; Pappenberger, F. Ensemble flood forecasting: A review. J. Hydrol.
**2009**, 375, 613–626. [Google Scholar] [CrossRef] - Moore, R. Real-time flood forecasting systems: Perspectives and prospects. Floods Landslides Integr. Risk Assess.
**1999**, 147–189. [Google Scholar] - Acharya, A.; Prakash, A. When the river talks to its people: Local knowledge-based flood forecasting in Gandak River basin, India. Environ. Dev.
**2019**, 31, 55–67. [Google Scholar] [CrossRef] - Kaur, B.; Szentimrey, Z.; Binns, A.D.; McBean, E.A.; Gharabaghi, B. Urban flood susceptibility mapping using supervised regression and machine learning models in Toronto, Canada. In Proceedings of the AGU Fall Meeting Abstracts, Online, 17 December 2020; Volume 2020, p. NH012-07. [Google Scholar]
- Borga, M.; Anagnostou, E.; Blöschl, G.; Creutin, J.D. Flash flood forecasting, warning and risk management: The HYDRATE project. Environ. Sci. Policy
**2011**, 14, 834–844. [Google Scholar] [CrossRef] - Nauman, C.; Anderson, E.; Coughlan de Perez, E.; Kruczkiewicz, A.; McClain, S.; Markert, A.; Griffin, R.; Suarez, P. Perspectives on flood forecast-based early action and opportunities for Earth observations. J. Appl. Remote. Sens.
**2021**, 15, 032002. [Google Scholar] [CrossRef] - Lawford, R.; Prowse, T.; Hogg, W.; Warkentin, A.; Pilon, P. Hydrometeorological aspects of flood hazards in Canada. Atmosphere-Ocean
**1995**, 33, 303–328. [Google Scholar] [CrossRef] - Alfieri, L.; Salamon, P.; Pappenberger, F.; Wetterhall, F.; Thielen, J. Operational early warning systems for water-related hazards in Europe. Environ. Sci. Policy
**2012**, 21, 35–49. [Google Scholar] [CrossRef] - Merz, B.; Kuhlicke, C.; Kunz, M.; Pittore, M.; Babeyko, A.; Bresch, D.N.; Domeisen, D.I.; Feser, F.; Koszalka, I.; Kreibich, H.; et al. Impact forecasting to support emergency management of natural hazards. Rev. Geophys.
**2020**, 58, e2020RG000704. [Google Scholar] [CrossRef] - Jain, S.K.; Mani, P.; Jain, S.K.; Prakash, P.; Singh, V.P.; Tullos, D.; Kumar, S.; Agarwal, S.; Dimri, A. A Brief review of flood forecasting techniques and their applications. Int. J. River Basin Manag.
**2018**, 16, 329–344. [Google Scholar] [CrossRef] - Kim, G.; Barros, A.P. Quantitative flood forecasting using multisensor data and neural networks. J. Hydrol.
**2001**, 246, 45–62. [Google Scholar] [CrossRef] - Brocca, L.; Melone, F.; Moramarco, T. Distributed rainfall-runoff modelling for flood frequency estimation and flood forecasting. Hydrol. Process.
**2011**, 25, 2801–2813. [Google Scholar] [CrossRef] - Toth, E.; Brath, A.; Montanari, A. Comparison of short-term rainfall prediction models for real-time flood forecasting. J. Hydrol.
**2000**, 239, 132–147. [Google Scholar] [CrossRef] - Hapuarachchi, H.; Wang, Q.; Pagano, T. A review of advances in flash flood forecasting. Hydrol. Process.
**2011**, 25, 2771–2784. [Google Scholar] [CrossRef] - Yin, D.; Xue, Z.G.; Bao, D.; RafieeiNasab, A.; Huang, Y.; Morales, M.; Warner, J.C. Understanding the role of initial soil moisture and precipitation magnitude in flood forecast using a hydrometeorological modelling system. Hydrol. Process.
**2022**, 36, e14710. [Google Scholar] [CrossRef] - Li, Y.; Grimaldi, S.; Walker, J.P.; Pauwels, V.R. Application of remote sensing data to constrain operational rainfall-driven flood forecasting: A review. Remote. Sens.
**2016**, 8, 456. [Google Scholar] [CrossRef] - Piadeh, F.; Behzadian, K.; Alani, A.M. A critical review of real-time modelling of flood forecasting in urban drainage systems. J. Hydrol.
**2022**, 607, 127476. [Google Scholar] [CrossRef] - Taraky, Y.M.; Liu, Y.; Gharabaghi, B.; McBean, E.; Daggupati, P.; Shrestha, N.K. Influence of headwater reservoirs on climate change impacts and flood frequency in the Kabul River Basin. Can. J. Civ. Eng.
**2022**, 49, 1300–1309. [Google Scholar] [CrossRef] - Oruh, J.; Viriri, S.; Adegun, A. Long short-term memory recurrent neural network for automatic speech recognition. IEEE Access
**2022**, 10, 30069–30079. [Google Scholar] [CrossRef] - Li, W.; Kiaghadi, A.; Dawson, C. Exploring the best sequence LSTM modeling architecture for flood prediction. Neural Comput. Appl.
**2021**, 33, 5571–5580. [Google Scholar] [CrossRef] - Kumar, A.; Bhatia, A.; Kashyap, A.; Kumar, M. LSTM Network: A Deep Learning Approach and Applications. In Advanced Applications of NLP and Deep Learning in Social Media Data; IGI Global: Hershey, PA, USA, 2023; pp. 130–150. [Google Scholar]
- Iparraguirre-Villanueva, O.; Guevara-Ponce, V.; Ruiz-Alvarado, D.; Beltozar-Clemente, S.; Sierra-Liñan, F.; Zapata-Paulini, J.; Cabanillas-Carbonell, M. Text prediction recurrent neural networks using long short-term memory-dropout. Indones. J. Electr. Eng. Comput. Sci.
**2023**, 29, 1758–1768. [Google Scholar] [CrossRef] - Hayder, I.M.; Al-Amiedy, T.A.; Ghaban, W.; Saeed, F.; Nasser, M.; Al-Ali, G.A.; Younis, H.A. An Intelligent Early Flood Forecasting and Prediction Leveraging Machine and Deep Learning Algorithms with Advanced Alert System. Processes
**2023**, 11, 481. [Google Scholar] [CrossRef] - Granata, F.; Di Nunno, F. Neuroforecasting of daily streamflows in the UK for short-and medium-term horizons: A novel insight. J. Hydrol.
**2023**, 624, 129888. [Google Scholar] [CrossRef] - Le, X.H.; Ho, H.V.; Lee, G.; Jung, S. Application of long short-term memory (LSTM) neural network for flood forecasting. Water
**2019**, 11, 1387. [Google Scholar] [CrossRef] - Boopathi, S. Deep Learning Techniques Applied for Automatic Sentence Generation. In Promoting Diversity, Equity, and Inclusion in Language Learning Environments; IGI Global: Hershey, PA, USA, 2023; pp. 255–273. [Google Scholar]
- Tabrizi, S.E.; Xiao, K.; Thé, J.V.G.; Saad, M.; Farghaly, H.; Yang, S.X.; Gharabaghi, B. Hourly road pavement surface temperature forecasting using deep learning models. J. Hydrol.
**2021**, 603, 126877. [Google Scholar] [CrossRef] - Li, J.; Yuan, X. Daily Streamflow Forecasts Based on Cascade Long Short-Term Memory (LSTM) Model over the Yangtze River Basin. Water
**2023**, 15, 1019. [Google Scholar] [CrossRef] - Zou, Y.; Wang, J.; Lei, P.; Li, Y. A novel multi-step ahead forecasting model for flood based on time residual LSTM. J. Hydrol.
**2023**, 620, 129521. [Google Scholar] [CrossRef] - Jia, P.; Cao, N.; Yang, S. Real-time hourly ozone prediction system for Yangtze River Delta area using attention based on a sequence to sequence model. Atmos. Environ.
**2021**, 244, 117917. [Google Scholar] [CrossRef] - Zhang, Y.; Gu, Z.; Thé, J.V.G.; Yang, S.X.; Gharabaghi, B. The Discharge Forecasting of Multiple Monitoring Station for Humber River by Hybrid LSTM Models. Water
**2022**, 14, 1794. [Google Scholar] [CrossRef] - Moishin, M.; Deo, R.C.; Prasad, R.; Raj, N.; Abdulla, S. Designing deep-based learning flood forecast model with ConvLSTM hybrid algorithm. IEEE Access
**2021**, 9, 50982–50993. [Google Scholar] [CrossRef] - Yao, Z.; Wang, Z.; Wang, D.; Wu, J.; Chen, L. An ensemble CNN-LSTM and GRU adaptive weighting model based improved sparrow search algorithm for predicting runoff using historical meteorological and runoff data as input. J. Hydrol.
**2023**, 625, 129977. [Google Scholar] [CrossRef] - Ding, Y.; Zhu, Y.; Feng, J.; Zhang, P.; Cheng, Z. Interpretable spatiotemporal attention LSTM model for flood forecasting. Neurocomputing
**2020**, 403, 348–359. [Google Scholar] [CrossRef] - Li, P.; Zhang, J.; Krebs, P. Prediction of flow based on a CNN-LSTM combined deep learning approach. Water
**2022**, 14, 993. [Google Scholar] [CrossRef] - Khorram, S.; Jehbez, N. A Hybrid CNN-LSTM Approach for Monthly Reservoir Inflow Forecasting. Water Resour. Manag.
**2023**, 37, 4097–4121. [Google Scholar] [CrossRef] - Yang, Y.; Xiong, Q.; Wu, C.; Zou, Q.; Yu, Y.; Yi, H.; Gao, M. A study on water quality prediction by a hybrid CNN-LSTM model with attention mechanism. Environ. Sci. Pollut. Res.
**2021**, 28, 55129–55139. [Google Scholar] [CrossRef] - Dehghani, A.; Moazam, H.M.Z.H.; Mortazavizadeh, F.; Ranjbar, V.; Mirzaei, M.; Mortezavi, S.; Ng, J.L.; Dehghani, A. Comparative evaluation of LSTM, CNN, and ConvLSTM for hourly short-term streamflow forecasting using deep learning approaches. Ecol. Inform.
**2023**, 75, 102119. [Google Scholar] [CrossRef] - Wu, Y.; Ding, Y.; Zhu, Y.; Feng, J.; Wang, S. Complexity to forecast flood: Problem definition and spatiotemporal attention LSTM solution. Complexity
**2020**, 2020, 7670382. [Google Scholar] [CrossRef] - Liu, Y.; Yang, Y.; Chin, R.J.; Wang, C.; Wang, C. Long Short-Term Memory (LSTM) Based Model for Flood Forecasting in Xiangjiang River. KSCE J. Civ. Eng.
**2023**, 27, 5030–5040. [Google Scholar] [CrossRef] - Shewalkar, A.; Nyavanandi, D.; Ludwig, S.A. Performance evaluation of deep neural networks applied to speech recognition: RNN, LSTM and GRU. J. Artif. Intell. Soft Comput. Res.
**2019**, 9, 235–245. [Google Scholar] [CrossRef] - Gao, S.; Huang, Y.; Zhang, S.; Han, J.; Wang, G.; Zhang, M.; Lin, Q. Short-term runoff prediction with GRU and LSTM networks without requiring time step optimization during sample generation. J. Hydrol.
**2020**, 589, 125188. [Google Scholar] [CrossRef] - Zhao, Z.; Yun, S.; Jia, L.; Guo, J.; Meng, Y.; He, N.; Li, X.; Shi, J.; Yang, L. Hybrid VMD-CNN-GRU-based model for short-term forecasting of wind power considering spatiotemporal features. Eng. Appl. Artif. Intell.
**2023**, 121, 105982. [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] - Pan, M.; Zhou, H.; Cao, J.; Liu, Y.; Hao, J.; Li, S.; Chen, C.H. Water level prediction model based on GRU and CNN. IEEE Access
**2020**, 8, 60090–60100. [Google Scholar] [CrossRef] - Hua, G.; Wang, S.; Xiao, M.; Hu, S. Research on the Uplift Pressure Prediction of Concrete Dams Based on the CNN-GRU Model. Water
**2023**, 15, 319. [Google Scholar] [CrossRef] - Hood, M.J.; Clausen, J.C.; Warner, G.S. Comparison of Stormwater lag times for low impact and traditional residential development 1. JAWRA J. Am. Water Resour. Assoc.
**2007**, 43, 1036–1046. [Google Scholar] [CrossRef] - Gericke, O.; Smithers, J. Direct estimation of catchment response time parameters in medium to large catchments using observed streamflow data. Hydrol. Process.
**2017**, 31, 1125–1143. [Google Scholar] [CrossRef] - Berne, A.; Delrieu, G.; Creutin, J.D.; Obled, C. Temporal and spatial resolution of rainfall measurements required for urban hydrology. J. Hydrol.
**2004**, 299, 166–179. [Google Scholar] [CrossRef] - Perdikaris, J.; Gharabaghi, B.; Rudra, R. Reference time of concentration estimation for ungauged catchments. Earth Sci. Res
**2018**, 7, 58–73. [Google Scholar] [CrossRef] - Langridge, M.; Gharabaghi, B.; McBean, E.; Bonakdari, H.; Walton, R. Understanding the dynamic nature of Time-to-Peak in UK streams. J. Hydrol.
**2020**, 583, 124630. [Google Scholar] [CrossRef] - Seyam, M.; Othman, F. The influence of accurate lag time estimation on the performance of stream flow data-driven based models. Water Resour. Manag.
**2014**, 28, 2583–2597. [Google Scholar] [CrossRef] - Adeyi, G.; Adigun, A.; Onyeocha, N.; Okeke, O. Unit hydrograph: Concepts, estimation methods and applications in hydrological sciences. Int. J. Eng. Sci. Comput.
**2020**, 10, 26211–26217. [Google Scholar] - Barbero, G.; Costabile, P.; Costanzo, C.; Ferraro, D.; Petaccia, G. 2D hydrodynamic approach supporting evaluations of hydrological response in small watersheds: Implications for lag time estimation. J. Hydrol.
**2022**, 610, 127870. [Google Scholar] [CrossRef] - Oliveira Santos, V.; Costa Rocha, P.A.; Scott, J.; Thé, J.V.G.; Gharabaghi, B. A New Graph-Based Deep Learning Model to Predict Flooding with Validation on a Case Study on the Humber River. Water
**2023**, 15, 1827. [Google Scholar] [CrossRef] - Elkurdy, M.; Binns, A.D.; Bonakdari, H.; Gharabaghi, B.; McBean, E. Early detection of riverine flooding events using the group method of data handling for the Bow River, Alberta, Canada. Int. J. River Basin Manag.
**2022**, 20, 533–544. [Google Scholar] [CrossRef] - Langridge, M.; McBean, E.; Bonakdari, H.; Gharabaghi, B. A dynamic prediction model for time-to-peak. Hydrol. Process.
**2021**, 35, e14032. [Google Scholar] [CrossRef] - Soltani, K.; Ebtehaj, I.; Amiri, A.; Azari, A.; Gharabaghi, B.; Bonakdari, H. Mapping the spatial and temporal variability of flood susceptibility using remotely sensed normalized difference vegetation index and the forecasted changes in the future. Sci. Total. Environ.
**2021**, 770, 145288. [Google Scholar] [CrossRef] - Maas, A.L.; Hannun, A.Y.; Ng, A.Y. Rectifier nonlinearities improve neural network acoustic models. In Proceedings of the 30th International Conference on International Conference on Machine Learning, Atlanta, GA, USA, 16–21 June 2013; Volume 30, p. 3. [Google Scholar]
- Zhang, Y.; Pan, D.; Van Griensven, J.; Yang, S.X.; Gharabaghi, B. Intelligent flood forecasting and warning: A survey. Intell. Robot.
**2023**, 3, 190–212. [Google Scholar] [CrossRef]

**Figure 7.**Performance of the LSTM, GRU, CNNLSTM, CNNGRU, ConvLSTM, STA-LSTM, and STA-GRU models during training and validation error. (

**a**,

**c**,

**e**,

**g**,

**i**,

**k**,

**m**) Before lag time; (

**b**,

**d**,

**f**,

**h**,

**j**,

**l**,

**n**) After lag time.

Reference | Model Name | Applicable to Spatiotemporal Data | Maximum Prediction Duration | Model Performance |
---|---|---|---|---|

Liu et al. (2023) [55] | RNN | No | 12 h | $MSE=0.936$, $RMSE=0.124$ |

Dehghani et al. (2023) [53] | CNN | Yes | 6 h | $NSE=0.68$∼0.74 |

Liu et al. (2023) [55] | LSTM | No | 12 h | $MSE=0.942,RMSE=0.109$ |

Dehghani et al. (2023) [53] | ConvLSTM | Yes | 6 h | $NSE=0.965$∼0.986 |

Zhang et al. (2022) [46] | CNNLSTM | Yes | 24 h | $MAE=3.52,MSE=85.43$ |

Zhang et al. (2022) [46], Ding et al. (2020) [49] | STA-LSTM | Yes | 24 h | $MAE=2.88,MSE=63.92,{R}_{2}=0.78$∼0.96 |

Station No. | Average Lag Time (h) | Euclidean Distance (km) |
---|---|---|

02HB025 | 5 | 13.9 |

02HB018 | 7 | 27.6 |

02HB001 | 8 | 37.9 |

02HB031 | 9 | 41.9 |

02HB013 | 12 | 44.7 |

Hourly | Algorithm | RMSE | MAE | ${\mathit{R}}^{2}$ |
---|---|---|---|---|

6 | LSTM | 0.0623 | 0.0309 | 0.9001 |

6 | GRU | 0.0589 | 0.0278 | 0.9107 |

6 | CNNLSTM | 0.0620 | 0.0292 | 0.9012 |

6 | CNNGRU | 0.0573 | 0.0275 | 0.9158 |

6 | ConvLSTM | 0.0513 | 0.0243 | 0.9323 |

6 | STA-LSTM | 0.0503 | 0.0229 | 0.9385 |

6 | STA-GRU | 0.0464 | 0.0228 | 0.9445 |

12 | LSTM | 0.0939 | 0.0435 | 0.7734 |

12 | GRU | 0.0911 | 0.0431 | 0.7865 |

12 | CNNLSTM | 0.0954 | 0.0481 | 0.7660 |

12 | CNNGRU | 0.0931 | 0.0433 | 0.7780 |

12 | ConvLSTM | 0.0864 | 0.0408 | 0.8080 |

12 | STA-LSTM | 0.0833 | 0.0407 | 0.8106 |

12 | STA-GRU | 0.0832 | 0.0405 | 0.8125 |

24 | LSTM | 0.1332 | 0.0757 | 0.5461 |

24 | GRU | 0.1255 | 0.0658 | 0.5971 |

24 | CNNLSTM | 0.1322 | 0.0673 | 0.5528 |

24 | CNNGRU | 0.1262 | 0.0652 | 0.5925 |

24 | ConvLSTM | 0.1241 | 0.0641 | 0.6061 |

24 | STA-LSTM | 0.1227 | 0.0631 | 0.6143 |

24 | STA-GRU | 0.1220 | 0.0625 | 0.6181 |

Hourly | Algorithm | RMSE | MAE | ${\mathit{R}}^{2}$ |
---|---|---|---|---|

6 | LSTM | 0.0456 | 0.0243 | 0.9466 |

6 | GRU | 0.0520 | 0.0290 | 0.9304 |

6 | CNNLSTM | 0.0482 | 0.0299 | 0.9402 |

6 | CNNGRU | 0.0499 | 0.0272 | 0.9359 |

6 | ConvLSTM | 0.0405 | 0.0213 | 0.9578 |

6 | STA-LSTM | 0.0399 | 0.0203 | 0.9590 |

6 | STA-GRU | 0.0382 | 0.0199 | 0.9646 |

12 | LSTM | 0.0644 | 0.0353 | 0.8935 |

12 | GRU | 0.0643 | 0.0351 | 0.8936 |

12 | CNNLSTM | 0.0677 | 0.0372 | 0.8821 |

12 | CNNGRU | 0.0652 | 0.0324 | 0.8907 |

12 | ConvLSTM | 0.0631 | 0.0332 | 0.8974 |

12 | STA-LSTM | 0.0553 | 0.0318 | 0.9214 |

12 | STA-GRU | 0.0526 | 0.0291 | 0.9288 |

24 | LSTM | 0.1165 | 0.0600 | 0.6525 |

24 | GRU | 0.1150 | 0.0607 | 0.6637 |

24 | CNNLSTM | 0.1178 | 0.0575 | 0.6453 |

24 | CNNGRU | 0.1154 | 0.0569 | 0.6592 |

24 | ConvLSTM | 0.1134 | 0.0550 | 0.6713 |

24 | STA-LSTM | 0.1052 | 0.0548 | 0.7164 |

24 | STA-GRU | 0.1039 | 0.0534 | 0.7232 |

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**MDPI and ACS Style**

Zhang, Y.; Zhou, Z.; Van Griensven Thé, J.; Yang, S.X.; Gharabaghi, B.
Flood Forecasting Using Hybrid LSTM and GRU Models with Lag Time Preprocessing. *Water* **2023**, *15*, 3982.
https://doi.org/10.3390/w15223982

**AMA Style**

Zhang Y, Zhou Z, Van Griensven Thé J, Yang SX, Gharabaghi B.
Flood Forecasting Using Hybrid LSTM and GRU Models with Lag Time Preprocessing. *Water*. 2023; 15(22):3982.
https://doi.org/10.3390/w15223982

**Chicago/Turabian Style**

Zhang, Yue, Zimo Zhou, Jesse Van Griensven Thé, Simon X. Yang, and Bahram Gharabaghi.
2023. "Flood Forecasting Using Hybrid LSTM and GRU Models with Lag Time Preprocessing" *Water* 15, no. 22: 3982.
https://doi.org/10.3390/w15223982