# A Multiple Model Approach for Flood Forecasting, Simulation, and Evaluation Coupling in Zhouqu County

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Flood Control Simulation and Dispatching System

## 3. Flood Forecasting Method Based on MOCSCDE

#### 3.1. Model Theory

_{2}is generated by subtracting the evapotranspiration E from the rainfall P. In the permeable area, the runoff R

_{2}is calculated using the Horton infiltration formula and the distribution curve of drainage capacity after deducting the evapotranspiration E from the rainfall. The total runoff for the basin is obtained as R = R

_{1}+ R

_{2}. The slope confluence of each unit area is computed using either a linear reservoir or a lag algorithm, while the river confluence is computed using the Muskingen piecewise continuous algorithm. The principle of the Shanbei model is illustrated in Figure 2.

#### 3.2. Model Parameters and Calibration Method

_{m}, FB, f

_{0}, f

_{c}, K, B, CS, L are included.

_{m}:

_{0}, generally θ

_{m}= 60~80 mm.

_{0}:

_{0}= 1.0~2.0 mm/min.

_{c}:

_{0}, generally f

_{c}= 0.3~0.5 mm/min.

_{0}, generally K = 0.04~0.05/min.

_{i}is the i-th objective function. The objective functions are as follows:

_{i}denotes the i-th observed value, and ${\widehat{Q}}_{i}$ is the i-th forecasting value. In the process of solving the above objectives by the MOCSCDE algorithm, the parameters that need to be customized are mainly as follows:

_{i}

^{C}(i = 1, 2, …, NC) obtained by each complex search in SK, NPC; the size of the set of non-inferior individuals P obtained by the whole population optimization calculation in SK, NP; evolutionary interval NM generations of history knowledge, HK; among these, HK is used to record the process of algorithm evolution calculation. In this paper, HK is used to preserve the degree of difference between individuals in the population P and to determine whether to use the Cauchy variation threshold ε or Cauchy’s coefficient of variation η.

**Step 1**: Initialize the (population space) PS and generate (belief space) BS by extracting knowledge information according to PS;

**Step 2**: According to Pareto ranking results of individual groups, the groups can be divided into NC Complexes;

**Step 3**: The evolutionary calculus of variation, crossover, selection, and so on is carried out for each Complex separately and based on (Situational Knowledge) SK during evolution, (Normative Knowledge) NK, and (History Knowledge) HK to guide. Every evolutionary computation generation, update the P

_{i}

^{C}(i = 1, 2, …, NC).

**Step 4**: After each Complex evolves NBS generation, mix all Complexes, and update P and NK in SK;

**Step 5**: Update HK after every evolution NM generation;

**Step 6**: Determine whether the maximum evolutionary algebra Max is reached; if not, jump to Step 2; if so, jump to Step 7;

**Step 7**: The evolution is over, and the calculation result is output.

## 4. Flood Risk and Disaster Estimation

#### 4.1. Flood Risk Estimation

#### 4.2. Flood Disaster Estimation

_{ij}represents the original related social–economic unit value of the jth disaster-affected body of the ith computing unit. η

_{jk}represents the loss rate, which is the combination of the j-type disaster-affected-body and the k-level water depth. α

_{i}represents the state of the computational grid. When i = 1, it means that we pay attention to the land use type to compute the loss; when i = 0, it indicates that the land use type of the region is other.

## 5. Experiment

#### 5.1. Study Area

^{2}. The terrain slopes high from the northwest to the southeast, featuring a landscape of overlapping mountains, gorges, and rugged terrain. Zhouqu County is situated in the Jialing River Basin within the South Qinling Mountains, characterized by a typical high mountain and canyon topography, with steep slopes, deep valleys, sparse vegetation, and severe soil erosion.

#### 5.2. Experimental Settings

#### 5.2.1. Datasets

#### 5.2.2. Evaluation Metrics

_{i}represents the true value, and ${\hat{y}}_{i}$ represents the predicted value.

^{2}):

#### 5.2.3. Implementation Details

#### 5.3. Results and Discussion

_{m}, K, and CS. the parameters before and after model optimization are shown in Table 1, the statistical indicators of the simulation results of the Shanbei model before and after the parameter optimization are shown in Table 2.

_{m,}, and K show a decreasing trend, and CS shows an upward trend. The remaining parameter values remain unchanged.

^{2}increases from 0.9 to 0.96 at the beginning, an increase of 0.06, and the increase rate is 6.67%.

^{2}decreases from 0.96 in Shanbei model to 0.89 in the LSTM model, decreasing by 7.29%. For the XAJ model, the MRE has increased by 13.16%. Moreover, the MAE increases from 5.16 in the proposed model to 6.03 in the XAJ model, and the R

^{2}decreases from 0.96 in Shanbei model to 0.90 in LSTM model, decreasing by 6.67%.

^{2}is the largest, and the prediction accuracy is also the highest, which indicates that the Shanbei model has the best prediction effect. The main reason is that the Shanbei model is a physically driven model, which can simulate the physical process of rainfall and flow well and has high accuracy in application in small watersheds. For the XAJ model, it is a lumped hydrological model, which can generalize the hydrological process of the basin or the transformation process of rain and flood into several key links such as runoff and confluence [38]. The model has few parameters, and the calibration is relatively easy. After the model parameters are verified, the prediction accuracy is high, but it cannot describe the spatial variation information of the hydrological physical process. As for the LSTM model, it is the data-driven model, which completely depends on the accuracy of historical data and has low accuracy when there is a certain amount of data error or insufficient data.

## 6. Conclusions

^{2}value of 0.96. In comparison, the XAJ model and LSTM model exhibit lower prediction accuracy evaluation metrics when compared to the optimized model. Our optimized model excels in simulating flood forecasts for Zhouqu, demonstrating remarkable performance. This achievement is highly commendable for the flood prevention department as it provides them with a reliable and precise prediction model. The main limitation of this study lies in the outdated theoretical mechanism of the model, as it is not the most recent flood forecasting model based on the latest theories. However, considering the circumstances of our research area, it was not feasible to use data-driven forecasting models with their required input and calibration conditions. Therefore, we employed the simple yet innovative SHANBEI model coupled with the MOCSCDE algorithm, which yielded satisfactory flood forecasting results. We consider this research outcome to hold significant importance for the study area, despite the limitation that our research approach cannot be directly applied in well-documented and moist basins.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Che, H.; Wang, J. Sparse Nonnegative Matrix Factorization Based on Collaborative Neurodynamic Optimization. In Proceedings of the 2019 9th International Conference on Information Science and Technology (ICIST), Hulunbuir, China, 2–5 August 2019; pp. 114–121. [Google Scholar]
- Xu, Y.; Wang, X.; Jiang, Z.; Liu, Y.; Zhang, L.; Li, Y. An Improved Fineness Flood Risk Analysis Method Based on Digital Terrain Acquisition. Water Resour. Manag.
**2023**, 37, 3973–3998. [Google Scholar] [CrossRef] - Xu, Y.; Jiang, Z.; Liu, Y.; Zhang, L.; Yang, J.; Shu, H. An Adaptive Ensemble Framework for Flood Forecasting and Its Application in a Small Watershed Using Distinct Rainfall Interpolation Methods. Water Resour. Manag.
**2023**, 37, 2195–2219. [Google Scholar] [CrossRef] - Burstein, O.; Grodek, T.; Enzel, Y.; Helman, D. SatVITS-Flood: Satellite Vegetation Index Time Series Flood Detection Model for Hyperarid Regions. Water Resour. Res.
**2023**, 59, e2023WR035164. [Google Scholar] [CrossRef] - Guo-wei, L. Definition and classification of non-structure measures for flood prevention. Adv. Water Sci.
**2003**, 14, 98. [Google Scholar] - Ye, J.; Wu, Y.; Li, Z.; Chang, L. Research and application of small and medium-sized flash flood forecasting methods in humid regions. Hehai Univ. Sci. (Ed.)
**2012**, 40, 615–621. [Google Scholar] - Zhang, J.; Na, L.; Zhang, B. Applicability of the distributed hydrological model of HEC-HMS in a small watershed of the Loess Plateau area. J. Beijing For. Univ.
**2009**, 31, 52–57. [Google Scholar] - Liu, Z.; Li, L.; Zhu, C.; Wu, J.; Dai, R. Comparative study of distributed hydrological models in flood forecasting. Hydropower Energy Sci.
**2006**, 2, 70–73. [Google Scholar] - Li, Z.; Hu, W.; Ding, J.; Hu, Y.; Wu, Y.; Li, J. Research on distributed hydrological model based on physical foundation and grid. J. Hydroelectr. Power
**2012**, 2, 5–13. [Google Scholar] - Javier, J.R.N.; Smith, J.A.; Meierdiercks, K.L.; Baeck, M.L.; Miller, A. Flash flood forecasting for small urban watersheds in the Baltimore metropolitan region. Weather. Forecast.
**2007**, 22, 1331–1344. [Google Scholar] [CrossRef] - Karpatne, A.; Ebert-Uphoff, I.; Ravela, S.; Babaie, H.A.; Kumar, V. Machine Learning for the Geosciences: Challenges and Opportunities. IEEE Trans. Knowl. Data Eng.
**2019**, 31, 1544–1554. [Google Scholar] [CrossRef] - Sainju, A.M.; He, W.; Jiang, Z. A Hidden Markov Contour Tree Model for Spatial Structured Prediction. IEEE Trans. Knowl. Data Eng.
**2022**, 34, 1530–1543. [Google Scholar] [CrossRef] - Singh Vijay, P.; Woolhiser David, A. Mathematical Modeling of Watershed Hydrology. J. Hydrol. Eng.
**2002**, 7, 270–292. [Google Scholar] [CrossRef] - Sahoo, R.; Zhao, S.; Chen, A.; Ermon, S. Reliable decisions with threshold calibration. Adv. Neural Inf. Process. Syst.
**2021**, 34, 1831–1844. [Google Scholar] - Shen, Y.; Wang, S.; Zhang, B.; Zhu, J. Development of a stochastic hydrological modeling system for improving ensemble streamflow prediction. J. Hydrol.
**2022**, 608, 127683. [Google Scholar] [CrossRef] - Chilkoti, V.; Bolisetti, T.; Balachandar, R. Investigating the role of hydrological model parameter uncertainties in future streamflow projections. J. Hydrol. Eng.
**2020**, 25, 05020035. [Google Scholar] [CrossRef] - Eidsvik, J.; Mukerji, T.; Bhattacharjya, D. Value of Information in the Earth Sciences: Integrating Spatial Modeling and Decision Analysis; Cambridge University Press: Cambridge, UK, 2015. [Google Scholar]
- Zhang, X.; Srinivasan, R.; Zhao, K.; Liew, M. Evaluation of global optimization algorithms for parameter calibration of a computationally intensive hydrologic model. Hydrol. Process.
**2009**, 23, 430–441. [Google Scholar] [CrossRef] - Arsenault, R.; Poulin, A.; Côté, P.; Brissette, F. Comparison of stochastic optimization algorithms in hydrological model calibration. J. Hydrol. Eng.
**2014**, 19, 1374–1384. [Google Scholar] [CrossRef] - Huo, J.; Liu, L.; Zhang, Y. Comparative research of optimization algorithms for parameters calibration of watershed hydrological model. J. Comput. Methods Sci. Eng.
**2016**, 16, 653–669. [Google Scholar] [CrossRef] - Chu, W.; Gao, X.; Sorooshian, S. A solution to the crucial problem of population degeneration in high-dimensional evolutionary optimization. IEEE Syst. J.
**2011**, 5, 362–373. [Google Scholar] [CrossRef] - Chen, Y.; Li, J.; Xu, H. Improving flood forecasting capability of physically based distributed hydrological models by parameter optimization. Hydrol. Earth Syst. Sci.
**2016**, 20, 375–392. [Google Scholar] [CrossRef] - Deb, K.; Agrawal, S.; Pratap, A.; Meyarivan, T. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In Parallel Problem Solving from Nature-PPSN VI, Proceedings of the 6th International Conference, Paris, France, 18-20 September 2000; Springer: Berlin/Heidelberg, Germany, 2000; pp. 849–858. [Google Scholar]
- Guo, J.; Zhou, J.; Zou, Q.; Liu, Y.; Song, L. A novel multi-objective shuffled complex differential evolution algorithm with application to hydrological model parameter optimization. Water Resour. Manag.
**2013**, 27, 2923–2946. [Google Scholar] [CrossRef] - Zitzler, E.; Laumanns, M.; Thiele, L. SPEA2: Improving the Strength Pareto Evolutionary Algorithm; ETH Zurich, Computer Engineering and Networks Laboratory: Zurich, Switzerland, 2001; Volume 103. [Google Scholar]
- Li, C.; Han, Z.; Li, Y.; Li, M.; Wang, W.; Dou, J.; Xu, L.; Chen, G. Physical information-fused deep learning model ensembled with a subregion-specific sampling method for predicting flood dynamics. J. Hydrol.
**2023**, 620, 129465. [Google Scholar] [CrossRef] - Zhang, M.; Ding, D.; Pan, X.; Yang, M. Enhancing Time Series Predictors With Generalized Extreme Value Loss. IEEE Trans. Knowl. Data Eng.
**2023**, 35, 1473–1487. [Google Scholar] [CrossRef] - Binkowski, M.; Marti, G.; Donnat, P. Autoregressive convolutional neural networks for asynchronous time series. In Proceedings of the International Conference on Machine Learning, Stockholm, Sweden, 10–15 July 2018; pp. 580–589. [Google Scholar]
- Fu, S.; Zhong, S.; Lin, L.; Zhao, M. A Novel Time-Series Memory Auto-Encoder With Sequentially Updated Reconstructions for Remaining Useful Life Prediction. IEEE Trans. Neural Netw. Learn. Syst.
**2022**, 33, 7114–7125. [Google Scholar] [CrossRef] - Kang, S.; Yin, J.; Gu, L.; Yang, Y.; Liu, D.; Slater, L. Observation-Constrained Projection of Flood Risks and Socioeconomic Exposure in China. Earth’s Future
**2023**, 11, e2022EF003308. [Google Scholar] [CrossRef] - Awasthi, C.; Archfield, S.A.; Reich, B.J.; Sankarasubramanian, A. Beyond Simple Trend Tests: Detecting Significant Changes in Design-Flood Quantiles. Geophys. Res. Lett.
**2023**, 50, e2023GL103438. [Google Scholar] [CrossRef] - Shi, P.; Du Juan, J.M.; Liu, J.; Wang, J. Urban risk assessment research of major natural disasters in China. Adv. Earth Sci.
**2006**, 21, 170. [Google Scholar] - Altan, A.; Karasu, S.; Zio, E. A new hybrid model for wind speed forecasting combining long short-term memory neural network, decomposition methods and grey wolf optimizer. Appl. Soft Comput.
**2021**, 100, 106996. [Google Scholar] [CrossRef] - Mohamed, T.; Sayed, S.; Salah, A.; Houssein, E.H. Long Short-Term Memory Neural Networks for RNA Viruses Mutations Prediction. Math. Probl. Eng.
**2021**, 2021, 9980347. [Google Scholar] [CrossRef] - Sherstinsky, A. Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) network. Phys. D Nonlinear Phenom.
**2020**, 404, 132306. [Google Scholar] [CrossRef] - Wang, J.; Bao, W.; Gao, Q.; Si, W.; Sun, Y. Coupling the Xinanjiang model and wavelet-based random forests method for improved daily streamflow simulation. J. Hydroinformatics
**2021**, 23, 589–604. [Google Scholar] [CrossRef] - Wu, Y.; Xu, W.; Yu, Q.; Feng, J.; Lu, T. Hierarchical Bayesian Network Based Incremental Model for Flood Prediction. In MultiMedia Modeling, Proceedings of the 25th International Conference, MMM 2019, Thessaloniki, Greece, 8–11 January 2019; Springer: Cham, Switzerland, 2019; pp. 556–566. [Google Scholar]
- Zhou, Y.; Wu, Z.; Xu, H.; Wang, H.; Ma, B.; Lv, H. Integrated dynamic framework for predicting urban flooding and providing early warning. J. Hydrol.
**2023**, 618, 129205. [Google Scholar] [CrossRef]

Situation | Serial Number | Parameter | Reference Parameter Value | Lower Limit | Upper Limit |
---|---|---|---|---|---|

Before parameter optimization | 1 | KC | 0.6 | 0.5 | 1.0 |

2 | θ_{m} | 80 | 60 mm | 80 mm | |

3 | FB | 0.5 | 0 | 1 | |

4 | f_{0} | 1.8 | 1 mm/min | 2 mm/min | |

5 | f_{c} | 0.4 | 0.3 mm/min | 0.5 mm/min | |

6 | K | 0.05 | 0.04/min | 0.05/min | |

7 | B | 4 | 0 | 5 | |

8 | CS | 0.5 | 0.1 | 1.0 | |

9 | L | 2 | 1 | 5 | |

After parameter optimization | 1 | KC | 0.55 | 0.5 | 1.0 |

2 | θ_{m} | 70 | 60 mm | 80 mm | |

3 | FB | 0.5 | 0 | 1 | |

4 | f_{0} | 1.8 | 1 mm/min | 2 mm/min | |

5 | f_{c} | 0.4 | 0.3 mm/min | 0.5 mm/min | |

6 | K | 0.04 | 0.04/min | 0.05/min | |

7 | B | 4 | 0 | 5 | |

8 | CS | 0.7 | 0.1 | 1.0 | |

9 | L | 2 | 1 | 5 |

**Table 2.**The statistical indicators of the simulation results of Shanbei model before and after parameter optimization.

Accuracy Indicators | MAE | MRE | R^{2} | |
---|---|---|---|---|

Conditions | ||||

Before parameter optimization | 6.16 | 8.62% | 0.90 | |

After parameter optimization | 5.16 | 7.60% | 0.96 |

Accuracy Indicators | MAE | MRE | R^{2} | |
---|---|---|---|---|

Model Category | ||||

XAJ | 6.03 | 8.60% | 0.90 | |

LSTM | 10.26 | 9.50% | 0.89 |

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**MDPI and ACS Style**

Li, Y.; Liu, Y.; Liu, X.; Shen, C.
A Multiple Model Approach for Flood Forecasting, Simulation, and Evaluation Coupling in Zhouqu County. *Water* **2023**, *15*, 4246.
https://doi.org/10.3390/w15244246

**AMA Style**

Li Y, Liu Y, Liu X, Shen C.
A Multiple Model Approach for Flood Forecasting, Simulation, and Evaluation Coupling in Zhouqu County. *Water*. 2023; 15(24):4246.
https://doi.org/10.3390/w15244246

**Chicago/Turabian Style**

Li, Yongfeng, Yi Liu, Xiaoming Liu, and Chao Shen.
2023. "A Multiple Model Approach for Flood Forecasting, Simulation, and Evaluation Coupling in Zhouqu County" *Water* 15, no. 24: 4246.
https://doi.org/10.3390/w15244246