**1. Introduction**

Landslides are a harmful environmental and geological phenomenon, occurring frequently worldwide [1,2]. They are gradually formed by the long-term interactions of both natural and human factors under specific geologic and geographic conditions. The occurrence of landslides is irreversible, and a severe landslide may induce a series of geological environmental disasters and form a disaster chain, posing severe threats to human life and built infrastructures [3]. Thus, analyzing and predicting geological hazards using monitoring data collected from various sources is essential to mitigate these severe devastations.

Time series landslide displacement, directly reflecting the deformation and stability of a slope, is the most critical dataset to understand landslide characteristics and infer its future development [4]. For instance, the Global Navigation Satellite System (GNSS),

**Citation:** Jiang, Y.; Luo, H.; Xu, Q.; Lu, Z.; Liao, L.; Li, H.; Hao, L. A Graph Convolutional Incorporating GRU Network for Landslide Displacement Forecasting Based on Spatiotemporal Analysis of GNSS Observations. *Remote Sens.* **2022**, *14*, 1016. https://doi.org/10.3390/ rs14041016

Academic Editors: Serdjo Kos, José Fernández and Juan F. Prie

Received: 12 January 2022 Accepted: 14 February 2022 Published: 19 February 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

measuring surface motion at a very high frequency and accuracy, is a powerful tool to help diagnose the progression of landslide movement. For this reason, these datasets enable deep-learning models to be trained for predicting the future state of surface deformation.

Deep-learning approaches, as suggested, are superior to traditional statistical methods in many applications, especially in time-series prediction [5,6]. Representative statistical models, such as multivariate regression models (MLR) [7], auto-regressive integrated moving average (ARIMA) [8], and others, are widely used for a single time series forecasting [8–12], while they neglect the potential relationship among multiple time series in the monitoring network under similar geological conditions. By comparison, deep-learning methods integrate various processing layers and produce abstract learning features and nonlinear dependencies from multidimensional datasets [6,11,13], making them sound alternatives in landslide displacement forecasting.

Given the outstanding performance in time-series forecasts, recurrent neural networks (RNN) and their variants [14], such as long short-term memory (LSTM) and gated recurrent unit (GRU), have achieved impressive results in the prediction of land displacements based on GNSS time-series data [9,10]. These models can solve the problems of nonlinear dynamic characteristics in complex time series, thus being particularly suitable to predict time-series landslide displacement. The workflows of these methods are approximately the same: select representative GNSS monitoring stations and plot the curve of displacement–time to analyze the deformation; next, the monitoring data of specific stations will be adopted for modelling one station by one station; as each displacement–time curve only shows the evolution characteristics of a single monitoring point, the model predictions only reflect the displacement behaviour of a single location.

However, landslide-displacement prediction is a spatiotemporal task because the evolution of the landslide process often exhibits spatial and temporal characteristics. The existing time-series forecast model only explores temporal features, ignoring the underlying spatial correlations. Thus, it is difficult to comprehensively assess the displacement changes of the entire monitoring system and reveal the future state of the landslide as a whole. Several studies have utilized convolutional neural networks (CNNs) to explore the spatial dependencies and build prediction models in traffic forecasting problems [6,15–17]. However, CNN-based models only consider the absolute distance relationship among stations in Euclidean space. Compared with CNN, graph convolutional networks (GCNs) can handle neighbourhood information in non-Euclidean spaces, providing a more feasible way to model spatial dependencies within a monitoring network [13,17,18].

Based on the problems mentioned above and inspired by current encouraging results in traffic forecasting problems, there is a need to combine GCN and RNN models to build a collaborative prediction model to capture spatial and temporal features for spatial–temporal forecast problems. However, displacement prediction of a landslide relies not only on historical GNSS measurements and the spatial correlations of the monitoring network but also on internal geological conditions and various external factors, such as hydrologic conditions [19–22], anthropogenic factors, etc. For example, in China's Three Gorges Reservoir area, many landslides are triggered and accelerated by seasonal precipitation and the fluctuation of reservoir water level [17,19]; thus, the impact factors in predicting landslide deformation are indispensable during modelling.

To the best of the authors' knowledge, there is currently no related work focusing on addressing the prediction of rainfall reservoir-induced landslide displacement from a holistic perspective combining the external incentive factors. Inspired by current encouraging results in traffic forecasting problems [13,18], we propose a novel deep-learning method named graph convolutional incorporating gated recurrent unit network (GC-GRU-N). In the GC-GRU-N, the monitored GNSS time-series displacements, the distance, and other external triggering factors are integrated to construct the GCN module handling the spatial dependency; the GRU module model's temporal dependence captures long-term dependencies by considering landslide displacement time series. This architecture is expected to inherit the merits from both GCN in extracting spatial dependencies and GRU in capturing

temporal correlation features. The main contributions are twofold. First, we have extended GCN for spatial data imputation in the GNSS network deployed on the landslides. Second, we introduce a graph deep-learning framework to predict landslide displacement in time and space.

### **2. Methods**

Landslide displacement forecasting is a spatiotemporal prediction task because the evolution of landslide movement often exhibits spatial and temporal characteristics. This paper proposes a deep-learning framework to predict the landslide displacement based on the spatiotemporal analysis of the time series monitoring data. This framework is expected to inherit the merits from both GCN in extracting spatial dependencies and GRU in capturing temporal correlation features.

The workflow is shown in Figure 1. According to the GNSS monitoring network structure and the obtained time-series datasets, pro-processing is conducted to obtain spatial and temporal attributes as the model inputs. Then, the GCN module is employed to handle spatial dependencies, while the GRU module is used to capture temporal dependencies. This paper uses tensorFlow2.1, Python3.6, and Matlab2020 to conduct the experiments and analysis.

**Figure 1.** The workflow of the proposed model.

#### *2.1. Study Area and Dataset*

Since the Three Gorges Reservoir (TGR) was used in 2003, the fluctuated water level has changed the rock and soil physical and mechanical properties around the reservoir [19]. Over 4200 landslides are distributed in this region, and the majority of these landslides show characteristics of multiple triggers and reactivations [4]. The Baishuihe landslide and the Shuping landslide (Figure 2) are two typical recurrence reservoir landslides that have attracted the concern of researchers for a long time. As shown in Figure 2, both landslides are located on the south bank of the Yangtze River and spread into the Yangtze River.

**Figure 2.** Location of the study area and the overall view of the two landslides.

The Shuping landslide has an elevation of between 65 m and 400 m and is about 650 m wide. It is a south–north-oriented slope with a gradient varying from 22◦ in the upper part to 35◦ in the lower part. The overall sliding mass is about 27 million m3 with a thickness of approximately 40–70 m [19]. According to the field investigation, this landslide is divided by a valley into two blocks (Figure 2).

While the maximal dimensions of the Baishui landslide in the north–south and east– west are 780 m and 700 m, respectively, it has a volume of about 12.6 million m3 with an average thickness of approximately 30 m [20]. The field investigation and monitoring data

have confirmed that the landslide has a relatively flat central part with more significant gradients in the upper and lower parts of the landslide. It can also be categorized as two blocks (Figure 2).

The two landslides were re-activated by the first impoundment of the TGR, and since then, visible cracks have gradually formed [19,20]. Two GNSS networks were deployed to study the displacement characteristics during landslide evolution (Figure 2). The displacement dataset was collected monthly by the Trimble GPS receiver with a plane accuracy of 5 ± 1 ppm. The measurements of the reservoir water level were collected daily by the water level indicator provided by the China Three Gorges Project Development Corporation. The precipitation observations were collected daily by the rain gauge provided by Zigui County Meteorological Bureau. These collected datasets (from July 2003 to March 2013 for the Baishuihe landslide; from September 2007 to May 2015 for the Shuping landslide) are presented in Figures 3 and 4. It can be inferred from Figures 3 and 4 that:


**Figure 3.** Monitoring data in time series of the Baishuihe landslide.

Thus, the seasonal characteristics of the evolution of the landslides are a joint effort of the precipitation and the fluctuation of reservoir water levels, with a period of about a year.
