# Improving Lake Level Prediction by Embedding Support Vector Regression in a Data Assimilation Framework

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}increasing from 0.975–0.982 to 0.998–0.999 and the RMSE decreasing from 0.436–0.159 m to 0.105–0.042 m. The prediction lead time also increased with the increase of continuous assimilation data. Further analysis of the assimilation model showed that when there was an assimilation cycle, the prediction remained stable for successive sets of two or more assimilated data, and the prediction lead time increased with successive assimilated data, from 4–8 days (one successive assimilation data) to 9–12 days (five successive assimilation data). Overall, this study found that the data assimilation framework can improve the prediction ability of data-driven models, with assimilated models having a smaller fluctuation range and higher degree of concentration than non-assimilated models. The increase in assimilated data will improve model accuracy as well as the number of days of prediction lead time when an assimilation cycle exists.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Collection

#### 2.2. Problem Formulation

_{t}is the water level at the site on day t; ${D}_{t\u2013j}^{i}$ (i = 1,…, N; j = m

_{i},…, n

_{i}) is the measured flow at river site #i on day t−j; L

_{t}

_{–j}(j = m

_{0},…, n

_{0}) is the water level at the site on day t−j.

#### 2.3. Support Vector Regression

#### 2.4. Unscented Kalman Filter

## 3. Results and Discussion

#### 3.1. Data Assimilation Model Prediction Results

^{2}, the root mean square error (RMSE), and the mean relative error (MRE):

^{2}varying from 0.975 (Yingtian) to 0.982 (Chenglingji) at different stations, the RMSE varying from 0.159 m (Xiaohezui) to 0.436 m (Yingtian), and the MRE in the range of 0.004 (Xiaohezui) to 0.013 (Yingtian). Among the three representative stations in Dongting Lake, Xiaohezui has the highest prediction accuracy, followed by Chenglingji, and Yingtian has the lowest, which is comparable to the error distribution of predictions obtained using the SVR model alone.

^{2}varies from 0.998 (Xiaohezui) to 0.999 (Chenglingji and Yingtian), the RMSE varies from 0.042 m (Xiaohezui) to 0.105 m (Yingtian), and the MRE varies from 0.001 (Xiaohezui) to 0.003 (Yingtian). The performance ranking results of the assimilation models for the different sites according to both the RMSE and MRE metrics are consistent with the previous results.

^{2}ranging from 0.949 (Chenglingji) to 0.984 (Xiaohezui) at different stations, the RMSE ranging from 0.103 (Xiaohezui) to 0.487 (Chenglingji), and the MRE in the range of 0.003 (Xiaohezui) to 0.017 (Chenglingji). Among the three representative stations in Dongting Lake, Xiaohezui has the best prediction accuracy, Yingtian has the second highest, and Xiaohezui has the lowest, which is equivalent to the error distribution of predictions produced using the SVR model alone.

^{2}ranges from 0.998 (Yingtian) to 0.999 (Chenglingji and Xiaohezui), RMSE ranges from 0.037 (Xiaohezui) to 0.116 (Yingtian), and MRE ranges from 0.001 (Xiaohezui) to 0.004 (Yingtian). It is worth mentioning that the phenomenon that the determination coefficient R

^{2}of the Xiaohezui model is slightly smaller than that of the models at the remaining two sites is related to the smaller range of water level fluctuations at these two sites.

#### 3.2. Further Model Testing

^{2}improved from 0.982 to 0.999 for Chenglingji, from 0.975 to 0.999 for Yingtian, and from 0.975 to 0.998 for Xiaohezui; Chenglingji’s RMSE decreased from 0.395 m to 0.068 m, Yingtian from 0.436 m to 0.105 m, and Xiaohezui from 0.159 m to 0.042 m, all of which significantly improved the model’s predictive capability in practical application scenarios. This data assimilation method is equally applicable to other artificial neural network (ANN) methods and can be extended by coupling them.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Map of the study area, showing (

**a**) its location and (

**b**) the Yangtze River–Dongting Lake water system. #1—Xiangtan, #2—Taojiang, #3—Taoyuan, #4—Shimen, #5—Gezhou Dam.

**Figure 2.**Time series of daily discharges of the (

**a**) Xiang River, (

**b**) Zi River, (

**c**) Yuan River, (

**d**) Li River, and (

**e**) Yangtze River.

**Figure 4.**Illustration of (

**a**) ε-insensitive loss function and (

**b**) support vector regression in the feature space.

Station | Dataset ^{a} | Minimum Value (m) | Maximum Value (m) | Mean Value (m) | Standard Deviation (m) |
---|---|---|---|---|---|

Chenglingji | Training | 20.21 | 33.40 | 25.66 | 3.95 |

Testing | 20.43 | 30.86 | 24.13 | 2.94 | |

Yingtian | Training | 21.21 | 33.67 | 26.69 | 3.66 |

Testing | 21.32 | 31.15 | 25.05 | 2.75 | |

Xiaohezui | Training | 27.89 | 34.93 | 29.99 | 1.68 |

Testing | 27.91 | 31.91 | 29.27 | 1.02 |

^{a}Training period: 2010 and 2012; testing period: 2009 and 2011.

Type | Source |
---|---|

Structural uncertainty | Insufficient degree of freedom of the approximator used |

Unreasonable input variable selection | |

Parameter uncertainty | Dependency of parameter values on data division |

Absence of representativeness of training samples | |

Difficulty in finding globally optimal parameters | |

Equifinality problem | |

Overfitting problem | |

Data uncertainty | Input and output measurement noise |

Lack of representativeness |

Station | SVR | SVR+UKF | ||||
---|---|---|---|---|---|---|

R^{2} | RMSE (m) | MRE | R^{2} | RMSE (m) | MRE | |

Chenglingji | 0.982 | 0.395 | 0.012 | 0.999 | 0.068 | 0.002 |

Yingtian | 0.975 | 0.436 | 0.013 | 0.999 | 0.105 | 0.003 |

Xiaohezui | 0.976 | 0.159 | 0.004 | 0.998 | 0.042 | 0.001 |

Station | SVR | SVR+UKF | ||||
---|---|---|---|---|---|---|

R^{2} | RMSE (m) | MRE | R^{2} | RMSE (m) | MRE | |

Chenglingji | 0.949 | 0.487 | 0.017 | 0.999 | 0.073 | 0.002 |

Yingtian | 0.961 | 0.412 | 0.016 | 0.998 | 0.116 | 0.004 |

Xiaohezui | 0.984 | 0.103 | 0.003 | 0.999 | 0.037 | 0.001 |

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**MDPI and ACS Style**

Wang, K.; Hu, T.; Zhang, P.; Huang, W.; Mao, J.; Xu, Y.; Shi, Y. Improving Lake Level Prediction by Embedding Support Vector Regression in a Data Assimilation Framework. *Water* **2022**, *14*, 3718.
https://doi.org/10.3390/w14223718

**AMA Style**

Wang K, Hu T, Zhang P, Huang W, Mao J, Xu Y, Shi Y. Improving Lake Level Prediction by Embedding Support Vector Regression in a Data Assimilation Framework. *Water*. 2022; 14(22):3718.
https://doi.org/10.3390/w14223718

**Chicago/Turabian Style**

Wang, Kang, Tengfei Hu, Peipei Zhang, Wenqin Huang, Jingqiao Mao, Yifan Xu, and Yong Shi. 2022. "Improving Lake Level Prediction by Embedding Support Vector Regression in a Data Assimilation Framework" *Water* 14, no. 22: 3718.
https://doi.org/10.3390/w14223718