Groundwater Level Prediction for Landslides Using an Improved TANK Model Based on Big Data

Abstract

Geological conditions and rainfall intensity are two primary factors that can induce changes in groundwater level, which are one of the major triggering causes of geological disasters, such as collapse, landslides, and debris flow. In view of this, an improved TANK model is developed based on the influence of rainfall intensity, terrain, and geological conditions on the groundwater level in order to effectively predict the groundwater level evolution of rainfall landslides. A trapezoidal structure is used instead of the traditional rectangular structure to define the nonlinear change in a water level section to accurately estimate the storage of groundwater in rainfall landslides. Furthermore, big data are used to extract effective features from large-scale monitoring data. Here, we build prediction models to accurately predict changes in groundwater levels. Monitoring data of the Taziping landslide are taken as the reference for the study. The simulation results of the traditional TANK model and the improved TANK model are compared with the actual monitoring data, which proves that the improved TANK model can effectively simulate the changing trend in the groundwater level with rainfall. The study can provide a reliable basis for predicting and evaluating the change in the groundwater state in rainfall-type landslides.

1. Introduction

The occurrence of major earthquakes, such as the Wenchuan earthquake (2008, in Sichuan, China), Lushan earthquake (2013, in Sichuan, China), and Jiuzhaigou earthquake (2017, in Sichuan, China) caused catastrophic casualties and property losses, as well as drastic changes in the surrounding geological environment, which can act as a trigger for the subsequent occurrence of mountain disasters [1,2,3]. These geological changes often go undetected. One of the primary external triggering factors leading to landslides is rainfall; for example, at 10:00 a.m. on 10 July 2013, Sanxi Village, Zhongxing Town, Dujiangyan City, Sichuan Province, was affected by extreme heavy rain and a high-level landslide occurred. At 19:00 on 4 August 2015, part of the rock mass on the right side of the Taziping landslide in Hongse Village, Hongkou Township (Longchi Town), Dujiangyan City was transformed into a slope debris flow blocking the road, and the landslide volume was about 60,000 square meters. On 4 August 2015, there was only 1.9 mm of rainfall, and there was a full saturation state of banded water near the slip zone. The landslide in Xinmo Village, Songpinggou, Maoxian County, on 24 June 2017, occurred in a no-rain or low-rain environment. Sudden short-term heavy rainfall or long-term continuous rainfall can result in an increase in groundwater levels and an increase in the pore water pressure of soils and rocks. A sudden variation in the groundwater level is one of the important factors affecting the stability of the slope [4]. Groundwater usually participates in the water–rock (soil) interaction through physical, chemical, mechanical, and other ways. It plays a major role in the evolution of geological bodies; however, it may also be detrimental and contribute to the occurrence of geological disasters to some extent [5]. This necessitates the estimation of the groundwater level of the slope in the area of concern. However, the measurement of the groundwater level in landslides is time-consuming and expensive due to the complex and highly non-linear natures of dynamic groundwater fluctuation and the geological conditions and structures of landslide composition. Therefore, it is necessary to establish a reasonable hydrological model to estimate the stability of landslides under the influence of groundwater.

The majority of the existing landslide warning approaches adopt statistical methods, based on which early warning models of rainfall intensity–duration relationship are established [6,7,8,9,10,11]. However, such warning models can only reflect the possibility of landslide occurrence under certain rainfall characteristics (previous rainfall, rainfall intensity, duration, etc.). Furthermore, it is difficult to fully consider the influence of hydrological processes in small basins, such as rainfall infiltration and runoff accumulation, on landslide initiation. Accurate rainfall data are required for the construction of a reliable landslide warning system. With the development of hydrological models, several mature hydrological production and confluence models, such as SWAT (Soil and Water Assessment Tool) and SCS (Soil Conservation Service), are being adopted to simulate and study the fluctuation mechanics of groundwater levels [12,13,14,15]. Therefore, through the application of the long-term hydrological monitoring data of the Taziping landslide, the Python language was used to build the logic framework of the hydrologic dynamic balance of the improved TANK model. Rapid, effective, and accurate prediction of the groundwater level was achieved by the optimization and management of several influential parameters including permeability coefficient, lateral flow coefficient, and initial water level height. Based on the simulation results of this model, an effective and fast landslide groundwater level prediction model can be established to predict the potential landslide risk in advance.

2. Landslide Situation and Monitoring

2.1. Taziping Landslide

The Taziping landslide is a slope landform that was created by mid-mountain structural erosion and is on the right bank of the Baisha River in Longchi Town, Dujiangyan City, Sichuan Province. The 5.12 magnitude Wenchuan earthquake led to the formation of an irregularly shaped semi-elliptical slope with a sliding body area of 8.03 × 10⁴ m² and a sliding body height of 363 m. The lithology of the slide body is comprised of gravel fragments, the surface is covered with silty clay and gravel, the landslide is generally 20 to 25 m thick, and the volume is about 116 × 10⁴ m³. The front edge of the landslide is adjacent to the residential part of Hongjiamiao Dam, the rear edge wall is at the top of the ridge, and the edge of the landslide is bounded by the west gully and the east gully. The landslide is characterized by its longitudinal length of 530 m passing through an axial plane and an average width of 145 m, as shown in Figure 1.

After the earthquake, the Taziping slope was deformed by rainwater infiltration. There was visible downward dislocation deformation in the contact zone between the rear edge of the landslide and the loose landslide accumulation body, as well as visible deformation at the western boundary of the landslide. Numerous gullies were created in the fault and dislocation deformation of the landslide as a result of the loose structure of the landslide following the earthquake, along with the action of rainfall and intermountain confluence.

2.2. Formation Lithology

The primary outcrop strata in and around the study area include quaternary landslide deposits, colluvial and residual slope deposits, and Proterozoic Sinian volcanic formations. The distribution of stratigraphic lithology and permeability parameters in the study area are shown in

Table 1. Characteristics and permeability coefficients of different rock formations in the study area [16,17,18].

Rock Strata (from New to Old)	Distribution Position and Characteristics	Permeability Coefficient (cm·s−1)
Quaternary colluvium	It is mainly distributed in the upper part of the study area and is mainly composed of stone and gravel.	6 × 10−2~1.8 × 10−1
Landslide deposit	A small amount of surface yellow–brown and gray–brown silty clay with debris, while the lower gravel is mainly distributed in the landslide area.	1 × 10−6~1 × 10−4
Residual slope deposit	The bottom and center portions of the mountain are primarily made of silty clay gravel, whereas the perimeter of the study area is primarily made up of blocks of stone and gravel. However, the thickness of these substances is not uniform.	1 × 10−6~1 × 10−4
Proterozoic Sinian volcanic group	The layer consists of brown and gray–green andesite. The drilling revealed that the weathered crust of andesite is a thick, blocky structure, fully exposed to weak weathering, and that the rock mass varies from broken to relatively complete, the structural plane is developed, and the fracture is developed.	8 × 10−7~3 × 10−2

.

2.3. Monitoring Device Layout

The Taziping landslide monitoring and early warning system utilizes a variety of instruments and equipment that are positioned at various locations in the Taziping landslide (see Figure 2a,b) to monitor and warn of the occurrence and progression of landslides in real time. The monitoring and early warning system mainly includes an automatic rain gauge, hole pressure gauge, surface inclinometer, data collector, and wireless transmission devices.

3. TANK Model Construction and Improvement

At present, many scholars use numerical simulation to manage groundwater [19]. The TANK model (tank or black box model) is a conceptual runoff model proposed by Sugawara (1972) [20]. It generalizes the rainfall runoff process into a simple relationship between water storage and runoff in a basin, without considering vegetation, geology, topography, weathering, and other factors of each slope. Its basic principle is to define rainwater infiltration and runoff production as functions of the water storage capacity of the basin, and to calculate and simulate the processes of infiltration, runoff production, and confluence of the basin by varying the water storage depth of the tank, the discharge of the measuring hole and the bottom hole, and other parameters [21,22,23,24,25]. The water tank is equipped with lateral and bottom discharge holes. The model includes three typical types [26]: a simple single-tank TANK model, a multi-tank series model for surface runoff [27], and a multi-tank parallel model for a horizontal water supply [28].

TANK models based on optimization methods are capable of delivering predictions of high accuracy with limited data. In the present study, Python3.8 software is used to conduct sample training based on the multi-tank series model of runoff to study the variation law of groundwater level under different rainfall conditions. Accordingly, a simple-structured TANK model with fewer parameters is developed, which is capable of self-learning with changes in dry and wet cycles of rainfall, thereby improving the accuracy and reliability of the landslide groundwater level prediction.

3.1. TANK Model

The rock strata in the study area comprises of andesite in three different weathering levels: fully weathered, strongly weathered, and moderately weathered, which form the three parts of the water storage area. During rainfall, part of the surface water flows down the slope, raising the water level in each rock layer as the intensity and duration of the rainfall increase. This water then flows along the cracks in the rock layers and merges with the runoff in the bottommost rock layer. The principle and the structure of the TANK model are shown in Figure 3 and Figure 4, respectively.

The principle of the model simulation is shown in the Supplementary File.

3.2. Improved TANK Model

The traditional rectangular TANK model cannot accurately reflect the nonlinear problems, such as a sudden increase in the water level caused by heavy rain and terrain changes, and, thus, does not comply with the physical significance. The topographic profile of the study area is obtained from the geological exploration report on the Taziping landslide (Figure 5 and Figure 6). It can be observed that the overall longitudinal section of the rainfall infiltration production convergence mode is trapezoidal rather than rectangular.

In such cases, the improved TANK model with a trapezoidal shape can reflect the nonlinear problem more accurately, as shown in Figure 7.

According to the principle of the improved TANK model and the mechanism of tank fluctuation, the calculation formulas can be expressed as follows:

$$a=1/\tan \theta$$

(1)

$$b=L_2+2ah$$

(2)

$$c=-L_1\times R$$

(3)

$$h_i={\displaystyle \frac{-b\pm \sqrt{b^2-4ac}}{2a}}$$

(4)

where $\theta$ is the angle between the long side of the trapezoid and the hypotenuse; $L_1,L_2$ are the long and short sides of trapezoids, respectively; $h$ is under the improved water tank (vertical rainfall height); $R$ is the rainfall intensity ($mm·h^{-1}$); $c$ mainly simulates the rainfall accumulated by cumulative rainfall intensity $R$ in contact with long side side $L_1$ at time t; $h_i$ is the groundwater accumulation height when the upper cumulative rainfall falls and the bottom water level section changes unevenly, showing a nonlinear change.

The improved TANK model can efficiently simulate physical problems [29] with reliable prediction results and provide a more valuable basis for relevant decisions. Therefore, the improved TANK model with trapezoidal properties is suggested to predict the water table.

4. Analysis and Verification of Prediction Results

4.1. Monitoring Data

The hydrologic data used in the present study were provided by the Chengdu Geological Environment Monitoring Station. The remote real-time monitoring and early warning system of the Taziping landslide was installed and debugged from May 2012 to December 2012. The monitoring data collected from 2013 to 2016 were analyzed to determine the hydrological change process of the entire Taziping landslide. Three pieces of monitoring equipment used to measure the pore pressure (groundwater level) were placed in the upper, middle, and lower parts of the study area, respectively. Since the groundwater level in the upper and middle parts was low and the variations were not large, monitoring data from the lower part were selected for the study.

Figure 8 shows the rainfall intensity and pore water pressure measured in the Taziping landslide from 2013 to 2016. As can be seen from the figure, the greater the rainfall intensity, the higher the pore water pressure and the greater the change in the groundwater level. The relationship between rainfall intensity and pore water pressure in the past four years shows that precipitation in the study area was concentrated from May to September, with the peak rainfall intensity of 224.8 mm·d⁻¹ on 9 July 2013, and the peak underground pore water pressure of 119.9 kPa on 10 July 2013.

4.2. Forecast Results

Through monitoring, a total of 150,343 pore water pressure data, 103,260 water level data, and 7407 rainfall intensity data were obtained, and the date–rainfall intensity–pore water pressure–groundwater level data were aligned through data processing. The pore water pressure (groundwater level), rainfall intensity, and permeability coefficients α and β (as listed in

Table 2. Parameter settings of training samples. The following shows the parameters required for the traditional TANK model and the improved TANK model, and then selects the optimal parameters for prediction through trial and error.

TANK Model	Seepage Coefficient (cm·s−1)	Lateral Flow Coefficient (cm·s−1)	Short-Term Monitoring of Hole Height (m)	Long-Term Monitoring of Hole Height (m)
Traditional TANK model	1 × 10−4~1.8 × 10−1	1 × 10−6~1.8 × 10−1	5–15	10–60
Improved TANK model	1 × 10−4~1.8 × 10−1	1 × 10−6~1.8 × 10−1	5–15	10–60

) obtained as monitoring data were input as training samples into the two prediction models. The results obtained by dynamic recognition and learning by the program are shown in Figure 9.

Figure 9 shows that when the rainfall intensity is high or the rainfall duration is long, the traditional TANK prediction model can predict the growth trend and amplitude of groundwater level more accurately. When the rainfall intensity is low, the prediction model (marked as the red area in Figure 9) cannot simulate the fluctuation in the water level. The simulated and predicted groundwater level showed a significant lag compared to the monitored groundwater level due to the short machine learning time in the early stage and the medium and low rainfall. The prediction results revealed that the traditional TANK model for the prediction of the water level could not provide a prediction index with high accuracy, indicating that the traditional TANK model needs to be improved in order to achieve an accurate prediction.

Figure 10 shows the comparison between predicted groundwater levels and the observed groundwater levels using the improved TANK model. As shown in the figure, the improved TANK model can not only compensate for the delay observed with the traditional TANK model in predicting the groundwater level in the early stages, but it can also predict the groundwater level fluctuation caused by brief periods of low rainfall and heavy rainfall.

4.3. Comparison of Model Accuracy

In general, there are three categories of weather forecast based on duration, namely a short-term weather forecast (2 to 3 days), medium weather forecast (4 to 9 days), and long-term weather forecast (more than 10 to 15 days). The frequencies of these forecasts are 3 h and 24 h. Due to the long sequence of water level simulation, both TANK models have certain predictive abilities. Therefore, to verify the accuracy and prediction ability of the models, short-, medium-, and long-term weather forecasts were chosen as validation samples, and model sample training was carried out in accordance with the forecast frequency of rainfall every 3 h and 24 h.

Due to the issue of lagging in the prediction for early groundwater levels by the traditional TANK model, rainfall data from the rainy season of 2013 were used as the sample for comparing the model accuracy. Figure 11 presents the training and prediction results of the improved TANK model for short-term (7 July to 9 July), medium-term (7 July to 13 July), and long-term (7 July to 20 July) forecasts at a frequency of 3 h. It can be observed from the figure that the improved TANK model exhibited greater sensitivity in identifying rainfall factors, required less training time, and was capable of calculating water level changes in advance (23 June) with a trend similar to the results obtained from monitoring devices. On the other hand, the traditional TANK model could only provide accurate predictions under intense rainfall conditions.

To further compare the accuracy of the two models in predicting groundwater levels over a long period with multiple rainfall inputs, the two prediction models were trained using daily rainfall data for short-, medium-, and long-term forecasts. The reliability of the two prediction models was validated, and the results are shown in Figure 12. It can be observed from the figure that the longer the duration and frequency of the rainfall inputs, the closer the predicted results agree with the actual observations. When comparing the results provided by the models trained with a 3-h interval between 29 June to 9 July, the results from the improved TANK model agreed well with the actual observations. Between 11 July and 20 July, both the improved TANK model and the traditional TANK model produced results that were consistent with the observed values.

It is well known that different factors in the model can cause great uncertainty in the prediction of future groundwater levels. Therefore, there is a need to find an analytical method to screen scientifically significant options [30]. The calibration and evaluation of the two hydrological models were conducted using the data presented in Figure 11 and Figure 12, according to Equation (5). The Nash–Sutcliffe Efficiency (NSE) coefficient was adopted for the evaluation, which is commonly used to assess the performance of hydrological models in simulating results. The NSE coefficient ranges from negative infinity to 1, wherein a higher NSE value approaching 1 indicates better model performance and more reliable simulation results. When the NSE approaches 0, the overall simulation results are considered acceptable, although severe inaccuracies in the process simulation may exist. NSE values lower than 0 indicate an unreliable model. Therefore, in this study, NSE was chosen as the evaluation metric for the models, and is expressed as follows:

$$NSE=1-{\displaystyle \frac{{\displaystyle {\sum }_{t=1}^T{(Q_o^t-Q_m^t)}^2}}{{\displaystyle {\sum }_{t=1}^T{(Q_o^t-\overline{Q_o})}^2}}}$$

(5)

where $Q_o$ refers to the observed value; $Q_m$ refers to the simulated value; $Q^t$ represents a value at time t; and $\overline{Q_o}$ represents the total average of the observed value.

The NSE coefficient calculated for the two models is shown in

Table 3. Comparison of the accuracy of the two models.

Forecast Result
Accuracy	Forecasting model	Short-term (every 3 h)	Medium-term (every 3 h)	Long-term (every 3 h)	Short term (24 h)	Medium-term (24 h)	Long-term (24 h)
evaluation index
NSE	Traditional TANK model	0.82	0.88	0.86	0.79	0.90	0.88
	Improved TANK model	0.94	0.96	0.93	0.95	0.97	0.94

. It can be observed from the table that in terms of prediction accuracy, the improved TANK model consistently outperformed the traditional TANK model. Compared to the traditional model, the improved model showed an increase in NSE by 0.12, 0.08, and 0.03 for the forecast duration of 3 days, 7 days, and 14 days (every 3 h), respectively. However, when the forecast duration was 3 days, 7 days, and 14 days (24 h), the improved model exhibited an increase of 0.16, 0.07, and 0.06 in NSE, respectively, compared to the traditional model.

Based on different time periods and frequencies of received rainfall data, the prediction results of the two forecasting models indicated that as the forecasting period increased, the accuracy of the predictions initially increased and then decreased. Moreover, higher forecasting frequencies led to higher accuracy in the predictions. Furthermore, the improved TANK model consistently outperformed the traditional TANK model in terms of accuracy.

The traditional TANK model required a longer training time during the training process. It needed approximately two weeks’ worth of data to calculate the current water level accurately and to make reliable predictions. On the other hand, the improved TANK model required less training time. It generated accurate prediction results with only a few days’ worth of data, thereby reducing the dependence on previous data and enabling quick and accurate predictions.

The traditional TANK model could not generate results in advance and only aligned with the observed results, exhibiting noticeable fluctuations only under heavy rainfall conditions. However, the improved TANK model generated predictions on the water level trend in advance. It effectively addressed the delayed infiltration of the rainwater. It could also serve as an early warning system by assigning a warning threshold.

Overall, the improved TANK model offered the advantage of early prediction of water level trends, allowing for the effective prediction of rainfall-induced effects.

The improved TANK model provided higher accuracy, since it considers the non-uniform variation in the stored water in the rock layer over time as rainwater infiltrates. Specifically, when forecasting for short- (24 h), medium- (24 h), and long-term (24 h) periods, the improved TANK model outperformed the traditional model by 20.3%, 7%, and 6.8%, respectively.

For each hydrological model, heavy rainfall resulted in higher relative errors. The primary contributing factors may be the interaction between rainfall and surface runoff, as well as the delay for surface water to infiltrate the subsurface layers. During the prediction period, the relative error values of both TANK models also increased with the duration of the forecasted time. It is evident that the long-term prediction capability is a natural limitation for many hydrological models due to the complexity of certain hydrological processes. However, after refinement and optimization, the improved TANK model provided groundwater level predictions that were closer to the true observed values of groundwater storage than the traditional TANK model.

Therefore, considering the lithological characteristics of the Taziping landslide formation is a reasonable and reliable method to improve the TANK model.

5. Discussion

The model was validated using the groundwater level monitoring data collected from the Taziping landslide that occurred in 2015. The data validation period started on 15 January 2013, the day that the monitoring equipment was deployed. The improved TANK model was utilized to forecast the groundwater levels in the area after three years, and its accuracy was validated.

The modeling was performed using the flood season data from 21 July to 14 August 2015. The tank model was optimized based on this data, and its performance during sudden heavy rainfall events was observed. The predicted results of the improved TANK model are presented in Figure 13.

The results show that the improved TANK model that was trained on the monitoring data samples was capable of capturing the changing trend of groundwater levels based on the variations in rainfall. The improved TANK model not only accurately reflected the observed groundwater variations, but it also exhibited sensitivity to abrupt changes in rainfall intensity, immediately reflecting fluctuations in groundwater levels, especially from 29 July to 1 August. This demonstrates that the improved TANK model can react to training data with speed and accuracy, thus significantly reducing the time it takes to judge predictions.

The model used has the advantage of storage-first dynamics, which allowed for a quick initial reaction followed by a slower response, to predict the rise in water levels in advance (from 3 August to 7 August) during the time of intense rainfall in July and August. This resulted in more rapid predictions and an early warning system.

The data feedback was accurate in terms of prediction accuracy, and the improved TANK model demonstrated excellent performance in predicting results. The accuracy (NSE) of the improved TANK model in short-, medium-, and long-term forecasts was all greater than 0.5, regardless of whether 3-h cumulative rainfall or 24-h hourly rainfall was included (as shown in

Table 4. Accuracy of the 2015 flood season model under two conditions.

Forecast Results of Flood Season in 2015
Accuracy	Forecasting model	Flood season (every 3 h)			Flood season (24 h)
evaluation index
NSE	Improved TANK model	Short-term	Metaphase	Long-term	Short-term	Metaphase	Long-term
		0.61	0.73	0.71	0.6	0.76	0.74

). And, from the table, we can find that the NSE prediction results (3-h cumulative rainfall or 24-h hourly rainfall) in the flood season are the most accurate in the medium-term forecast, which are 0.11, 0.02, 0.16, and 0.02 higher than the short-term and long-term, respectively. The prediction accuracy for the 2015 flood season was lower compared to the 2013 predictions. This may be due to the absence of or minimal rainfall in the early stages of the intense rainfall period in 2015, resulting in some calibration errors in the learning process. It shows that the quality of monitoring data has a huge impact on the prediction of the model, and a part of the data in the early stage is needed to make the model form the correct initial water level, so as to improve the accuracy of subsequent predictions. However, in the work of laying the detection equipment, the laying time is not fixed, so the initial water level setting will be inaccurate, resulting in the unstable prediction effect. However, during the flood season from July to August, the predictions made by the improved TANK model under different time periods (as shown in Figure 13) aligned well with the observed results, demonstrating excellent overall performance. It proves the importance of the prediction model for the accuracy of the initial water level in the previous precipitation simulation, and by comparing the data of 2013, it is not difficult to find that the 24-h hourly rainfall model has better a predictive power. All in all, this proves that the improved TANK model can effectively enhance prediction accuracy.

6. Conclusions

The present study proposes an improved TANK model that considers various factors, such as precipitation, surface runoff, rainfall infiltration, and lithological characteristics, to rapidly forecast short-term groundwater levels. The model was applied to investigate the groundwater level variations in the Taziping landslide. The main conclusions are as follows:

(1) The traditional TANK model was modified from a rectangular shape to an inverted trapezoidal shape with a storage rate that starts fast and slows down over time based on the topography and hydrological characteristics of the Taziping landslide. This modification enabled the modified TANK model to dynamically learn and predict water level changes from an unknown initial level to an improved tank water level that grows with time based on the rainfall data. The water level change in the TANK model is mostly linear, which does not accord with the physical significance. The improved TANK model can follow the infiltration process of real soil.

(2) The improved TANK model required a shorter training time and exhibited increased sensitivity in identifying groundwater level changes caused by moderate to small rainfall intensities. The predicted trends agreed well with the monitored data obtained from the field.

(3) The improved TANK model provided higher accuracy than the traditional TANK model for short-, medium-, and long-term forecasts, with improvements in prediction accuracy (NSE) ranging from 6.8% to 20.3%. The improvement in short-term prediction is the largest after the improvement of the short-term forecast in the 3-h cumulative rainfall mode. The NSE coefficient increased by 0.12, followed by the medium-term forecast, which increased by 0.08, and the long-term forecast had the lowest improvement of only 0.07, but the medium-term forecast had the highest NSE coefficient of 0.96, which had the best prediction effect, and the NSE coefficient increased by 0.16 after the improvement of the short-term forecast in the 24-h hourly rainfall mode, followed by the medium-term forecast, which increased by 0.07, and the long-term forecast had the lowest improvement of 0.06. As with the 3-h cumulative rainfall model, the medium-term forecast has the best effect, and the NSE coefficient is as high as 0.97. It overcame the limitation of the traditional TANK model, which included a long training time and the generation of predictions that were accurate only during heavy rainfall periods.

The proposed improved TANK model presents significant potential for practical applications as an easy-to-use tool for forecasting groundwater levels and assures early prediction of potential landslide disasters.