# Forecasting Groundwater Level for Soil Landslide Based on a Dynamic Model and Landslide Evolution Pattern

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

#### 2.1. Quadratic Exponential Smoothing Model

_{t}

^{(1)}= aM

_{t − 1}+ (1 − a)V

_{t − 1}

^{(1)}

_{t}

^{(2)}= aV

_{t}

^{(1)}+ (1 − a)V

_{t − 1}

^{(2)}

_{t}and V

_{t−}

_{1}stand for the smoothed groundwater levels, and a is a constant, which can be called the smoothing coefficient [26]. M

_{t−}

_{1}is the measured groundwater level, and V

_{t}

^{(1)}and V

_{t}

^{(2)}can be acquired from the training data set; this method could be described as follows:

_{t + T}= a

_{t}+ r

_{t}T

_{t}= 2V

_{t}

^{(1)}− V

_{t}

^{(2)}

_{t}= a(V

_{t}

^{(1)}− V

_{t}

^{(2)})/(1 − a)

_{t + T}represents the forecasted groundwater level, and a

_{t}and r

_{t}are parameters in the model. Equations (1)–(5) indicate that the smoothing coefficient, or damping coefficient (a) has a large impact on the related calculations, and it may reflect an approximation of the forecasted values based on the available data [27].

#### 2.2. Effect of Smoothness Parameter on the Forecasted Value

_{i}represents the actual data, and Y

_{i}represents the forecasted value of the modeling process; ${X}^{\prime}$ and ${Y}^{\prime}$ represent the means of the two data types. The lower the MAE is, the lower the model error. Moreover, if R increases, the correlation between the modeled values and actual data increases, indicating an improvement in the model forecasting ability.

#### 2.3. Clustering Analysis

_{i}(i = 1, 2,…, N), p represents the value of the N, and it was given a random initial cluster center—c

_{e}(e =1, 2,…, K); it can be specified according to the actual needs. The K-means clustering algorithm alternately performs the following two steps [32]:

- (1)
- Identify the nearest central point for each sample point X
_{i}:$$\mathrm{e}=mi{n}_{e\in \left\{1,2,\dots ,K\right\}}d\left({c}_{e},{X}_{i}\right),e=1,2,\dots ,K$$ - (2)
- Calculate the means of the samples in each cluster. The mean vector will be the new center:$${c}_{e}=\frac{1}{{n}_{e}}{\displaystyle \sum}_{j=1}^{{n}_{e}}{X}_{j}^{\left(e\right)},e=1,2,\dots ,K$$

_{j}represents the value in cluster e, and j represents the serial number of the element in one cluster, the number of clustering elements in cluster e was set as n

_{e}. The above two steps are repeated until no samples or very few samples are assigned to different clusters. Note that the K-mean clustering algorithm uses K as the input parameter and divides the collection of N objects into K clusters [33]. Ultimately, the similarity within each cluster is high, and the similarity between different clusters is low. The K-means clustering method generally uses the mean square error as the clustering evaluation criteria; thus, the clustering result exhibits the minimum mean square error (Figure 1).

## 3. Characteristics of Groundwater Level in a Soil Landslide

## 4. Methods

#### 4.1. Division of Landslide Evolution

#### 4.2. Establishment of the Dynamic Evaluation Factors

## 5. Results

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**K-means clustering process. (

**a**) Defining the initial three cluster centers, (

**b**) Moving the cluster center to minimize the total mean square error, (

**c**) Forming the final cluster result.

**Figure 2.**Baijiabao landslide geological characteristics: (

**a**) Geological landscape, (

**b**) Profile map of the Baijiabao landslide. The surrounding area of the ground belongs to the Jurassic system.

**Figure 3.**The monitoring data of the reservoir water level, rainfall, temperature, and groundwater level in the Baijiabao landslide.

**Figure 5.**The deformation stage of the landslide. We use the relative displacement of ZG326 on the main sliding surface to identify each evolution stage: Compacting deformation (0.191 mm–14.132 m), integral displacement (16.122 mm–61.361 mm), and shear failure compaction (114.996 mm–191.358 mm).

C-1 | C-2 | C-3 | C-4 | C-5 | C-6 | |
---|---|---|---|---|---|---|

C-1 | 0 | |||||

C-2 | 0.02 | 0 | ||||

C-3 | 0.42 | 0.60 | 0 | |||

C-4 | 0.70 | 0.31 | 0.71 | 0 | ||

C-5 | 0.24 | 0.78 | 0.82 | 0.53 | 0 | |

C-6 | 0.79 | 0.13 | 0.53 | 0.82 | 0.35 | 0 |

^{1}C-1 – C-6 represent 6 clustering classes for monthly relative displacement.

Rainfall factor | Stage | Parameter |
---|---|---|

3.5–62.1 | Compacting deformation | 0.3 |

62.1–124.1 | Integral displacement | 0.5 |

124.1–151.1 | Integral displacement | 0.7 |

151.1–316 | Shear failure compaction | 0.9 |

Model | Mean Absolute Error | R |
---|---|---|

Dynamic Fixed | 0.053 0.363 | 0.929 0.327 |

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**MDPI and ACS Style**

Duan, G.; Chen, D.; Niu, R. Forecasting Groundwater Level for Soil Landslide Based on a Dynamic Model and Landslide Evolution Pattern. *Water* **2019**, *11*, 2163.
https://doi.org/10.3390/w11102163

**AMA Style**

Duan G, Chen D, Niu R. Forecasting Groundwater Level for Soil Landslide Based on a Dynamic Model and Landslide Evolution Pattern. *Water*. 2019; 11(10):2163.
https://doi.org/10.3390/w11102163

**Chicago/Turabian Style**

Duan, Gonghao, Deng Chen, and Ruiqing Niu. 2019. "Forecasting Groundwater Level for Soil Landslide Based on a Dynamic Model and Landslide Evolution Pattern" *Water* 11, no. 10: 2163.
https://doi.org/10.3390/w11102163