Landslide displacement forecasting using deep learning and monitoring data across selected sites

Lorenzo Nava ORCID: orcid.org/0000-0002-2327-8721¹,
Edoardo Carraro²,
Cristina Reyes-Carmona³,
Silvia Puliero¹,
Kushanav Bhuyan¹,
Ascanio Rosi¹,
Oriol Monserrat⁴,
Mario Floris¹,
Sansar Raj Meena¹,
Jorge Pedro Galve³ &
…
Filippo Catani¹

7525 Accesses
1 Altmetric
Explore all metrics

Abstract

Accurate early warning systems for landslides are a reliable risk-reduction strategy that may significantly reduce fatalities and economic losses. Several machine learning methods have been examined for this purpose, underlying deep learning (DL) models’ remarkable prediction capabilities. The long short-term memory (LSTM) and gated recurrent unit (GRU) algorithms are the sole DL model studied in the extant comparisons. However, several other DL algorithms are suitable for time series forecasting tasks. In this paper, we assess, compare, and describe seven DL methods for forecasting future landslide displacement: multi-layer perception (MLP), LSTM, GRU, 1D convolutional neural network (1D CNN), 2xLSTM, bidirectional LSTM (bi-LSTM), and an architecture composed of 1D CNN and LSTM (Conv-LSTM). The investigation focuses on four landslides with different geographic locations, geological settings, time step dimensions, and measurement instruments. Two landslides are located in an artificial reservoir context, while the displacement of the other two is influenced just by rainfall. The results reveal that the MLP, GRU, and LSTM models can make reliable predictions in all four scenarios, while the Conv-LSTM model outperforms the others in the Baishuihe landslide, where the landslide is highly seasonal. No evident performance differences were found for landslides inside artificial reservoirs rather than outside. Furthermore, the research shows that MLP is better adapted to forecast the highest displacement peaks, while LSTM and GRU are better suited to model lower displacement peaks. We believe the findings of this research will serve as a precious aid when implementing a DL-based landslide early warning system (LEWS).

Algorithms for intelligent prediction of landslide displacements

Article 16 June 2020

A novel method based on deep learning model for national-scale landslide hazard assessment

Article 07 July 2023

Exploring time series models for landslide prediction: a literature review

Article Open access 05 September 2024

Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Introduction

Every year, landslides, a major global geohazard, result in a tremendous number of fatalities and economic damage (Froude and Petley 2018). Predicting future landslide evolution is critical for risk assessment and the design of reliable early warning systems for landslides produced by external triggers such as rainfall, reservoir and groundwater fluctuations, earthquakes, and anthropogenic activities (Aleotti and Chowdhury 1999). It can be difficult to predict how landslides will behave in the future because their progression typically does not adhere to a linear pattern. Several external elements (above all, rainfall, and water level reservoir variations) coordinate and impact landslide future displacements with varying magnitudes and intensities. Physical-based and data-driven techniques are the two main approaches for forecasting landslide displacement (Huang et al. 2017). The physical-based models mainly use creep theory, laboratory tests, and physical characteristics determined in situ to predict the landslide behavior. However, data-driven models are more widely used due to their straightforward methodology, precise predictions, lower costs, and scalability (Corominas et al. 2013). Recent breakthroughs in landslide displacement forecasting have demonstrated that artificial intelligence (AI) and, in particular, deep learning techniques are cutting edge. By accounting for contributing factors in addition to landslide displacement data, these approaches may accurately predict future velocity.

Landslides at the Three Gorges Reservoir have been investigated and utilized as benchmarks for the implementation, evaluation, and development of numerous AI-based techniques for landslide displacement forecasting (Yao et al. 2015). Several machine learning (ML) models have been used to this end such as artificial neural networks (ANN) (Du et al. 2013), support vector machines (SVM) (Zhu and Hu 2012; Zhou et al. 2016; Zhu et al. 2017; Wen et al. 2017; Miao et al. 2018; Ma et al. 2020; Wang et al. 2020, 2022; Han et al. 2021; Zhang et al. 2021), Gaussian process (Liu et al. 2014), and extreme learning machine (ELM) (Lian et al. 2015; Cao et al. 2016; Huang et al. 2017; Zhou et al. 2018a; Wang et al. 2019). The authors quite often used influencing factors in these situations which include previous landslide displacements, prior rainfall information, water level of reservoirs, and water level variations. In addition, Li et al. (2019) included a wavelet analysis-Volterra filter model (chaotic WA-Volterra model) based on chaos theory in SVM. The WA-Volterra model separates the high- and low-frequency components of cumulative displacement data. Chaos theory was used to recreate the spatial structure of each frequency, which was then used as input into the model. His paper investigates the possibility of chaotic characteristic identification of landslide displacements to be employed in machine learning.

Deep belief networks, LSTM-based architectures, gated recurrent unit neural networks (GRU), and other DL techniques have recently been employed in landslide displacement predictions (Yang et al. 2019; Xing et al. 2019; Li et al. 2020; Zhang et al. 2021; Guo et al. 2022). The relationship between landslide displacement and the primary triggering elements, for instance, was examined by Yang et al. (2019). In his paper, the periodical displacement was predicted using an LSTM model that considers the most crucial historical conditioning parameters. The LSTM model can gather insights from previous deformation time steps and create relationships between landslide conditions at different times. The results demonstrated that the LSTM model performs better than the SVM techniques. Wang et al. (2022) tested various ML models, including particle swarm optimization (PSO)-extreme learning machine (PSO-ELM), PSO-kernel extreme learning machine (PSO-KELM), PSO-support vector machine (PSO-SVM), PSO-least-squares support vector machine (PSO-LSSVM), and LSTM. Their research found that LSTM and PSO-ELM performed superior single predictions, but PSO-KELM and PSO-LSSVM yielded higher mean accuracies across cases.

Although there is a large body of research that suggests methodologies for landslide forecasting in extremely unique study cases such as the Three Gorges Reservoir landslides, few studies have used ML to estimate landslide displacement in different geographical, geological, and hydrogeological contexts. Based on historical data from landslides, rainfall, and groundwater, a new Random Forest-based technique for forecasting landslide velocity was proposed by Krkač et al. (2017) in the largest landslide in the Republic of Croatia. The landslide velocity was modeled using the expected daily groundwater levels predicted by using the historical daily precipitation data. Lastly, Zhu et al. (2017) compared and evaluated the performances of two different configurations of LSSVMs in a rainfall-sensitive slow-moving landslide located in the Sichuan Province, China.

This literature review shows that despite a significant amount of literature addressing the prediction capabilities of various ML-based algorithms and approaches for landslides in the Three Gorges Reservoir, there are few studies in which ML is utilized to the same end for study cases located in diverse places. However, in the world, a huge number of landslides are located outside reservoir contexts. Several critical slow-moving landslides are not located in reservoirs, and their behavior is particularly sensitive to rainfall events. Lastly, so far, the authors often evaluate the performances of ML algorithms to the performance of a single DL model (usually LSTM). However, several DL models are suited and employed successfully in a wide range of time series forecasting tasks.

In this paper, the abovementioned research gaps are addressed by evaluating, comparing, and discussing the predictive capabilities of seven state-of-art DL algorithms, in four study cases that differ in terms of geographical location, influencing factors, geological settings, time step dimensions, and measurement sensors.

Case studies and materials

Sant’Andrea and Lamosano landslides are both located in the Dolomites, an area of the Southern-Eastern Italian Alps, in the Province of Belluno (Veneto Region, NE Italy), in Perarolo di Cadore and Chies D’Alpago municipalities, respectively. The Baishuihe landslide is located in Three Gorges Reservoir in the Hubei province, Central China. The El Arrecife landslide is located within the western slope of the Rules Reservoir, in the Granada province (Southern Spain) (see Fig. 1).

Sant’Andrea landslide

The Sant’Andrea landslide affects the left-hand slope of the valley, overlooking the Boite river course, in the area just upstream of the Perarolo village (Fig. 2). The position of the landslide poses a significant risk to the inhabitants since a potential collapse of the unstable mass could result in temporary damming on the Boite river, which can cause flooding of the downstream area. The maximum temperature is 15 °C, while the minimum is − 7 °C. Several surveys were conducted over several years to gather spatially distributed information on the geological characteristics of the landslide area. The distribution of lithological units, in particular, was performed by combining information gathered from on-site surveys as well as geological and geotechnical investigations (Brezzi et al. 2021). The Sant’Andrea landslide is a 30-m-thick deposit of clay-calcareous debris composed of heterogeneous materials with different grain sizes and geotechnical characteristics. The debris mass slides across the weathered part of the bedrock composed of a dolomitic lithology and folded layers rich in anhydrides and gypsum.

The landslide activity shows an interplay of phases with slow displacements and accelerations that are primarily triggered by prolonged and intense rainfall. The characterization of the complex hydrogeological setting within the landslide was made possible by the information that was provided regarding the distribution of the geological units, which aids the interpretation of its behavior. Two circulation systems have been recognized within the unstable mass (Brezzi et al. 2021): a shallow groundwater flows in the upper layers of the debris deposits, whereas a deep one involves the upper part of the bedrock, mainly composed of altered and fractured gypsum. However, the role of water seems to be the main triggering factor of slope instability. On the one hand, the water circulations during the rainfall events cause the acceleration of the displacements. On the other hand, the active and deep circulation, coming from the upper part of the slope, induces slow displacements also in dry periods. This dynamic is related to the physical and chemical interaction between water and gypsum components of the upper part of the bedrock, as well as in the surficial debris layers, influencing the mechanical properties of rock mass (Brezzi et al. 2021). Hydration processes cause plastic rheology of the weak gypsum lithology, which drives the creep-like behavior of the unstable mass and the wide slope instability. Moreover, the dissolution induces an increase in the number of voids, resulting in the development of karst cavities and millimeter- to centimeter-thick microcrack net both in the bedrock and in the altered gypsum of the fractured part. Consequently, the water circulation in the landslide area makes the mechanical behavior of the gypsum lithology of the bedrock quite unpredictable, leading to the hazard of a sudden collapse of the unstable mass.

The Sant’Andrea landslide has been monitored using a topographic system since the end of 2013. This system is composed of a robotic total station (RTS) and several reflective targets installed on the unstable slope (Fig. 2). The implementation of the RTS targets was prompted by the evolution of landslides as various regions demonstrated deterioration of the stability conditions over time. The P4 target was chosen for this study because it has a 4-year displacement time series and is situated in an area affected by significant displacements. Figure 3 illustrates the daily differential displacement that was recorded by the P4 target during the period 2014–2019. The increase in the displacement rate is strongly related to rainfall events and, as previously stated, the duration of the rainfall also affects the landslide activity. The original measured time step dimension is 1 h. However, we decide to use daily frequency since it offers benefits such as reduced noise, as daily data can smooth out short-term fluctuations, data aggregation, providing a higher-level overview of data patterns, and improved computational efficiency, as there are fewer data points to process. Lastly, being the forecasting range equal to one time step, daily forecasts are more relevant for decision-making and planning compared to hourly forecasts, which may be subject to short-term fluctuations and may not be as useful.

Lamosano landslide

The Lamosano landslide is located in the local village of Lamosano, in the Chies D’Alpago municipality (Fig. 4). This slope instability involves the area where several buildings have been built in the past, causing structural damages observed in recent years. The maximum temperature is 20 °C, while the minimum is − 1 °C. The Lamosano landslide is classified as a rotational slow-moving landslide and its volume was estimated to be roughly 4.5 × 10⁶ m³, currently moving toward a WSW direction (Teza et al. 2008). Although a comprehensive characterization of the landslide is not available yet, the geological materials involved in the movement are mostly schistose clayey marls (upper layer of the bedrock), a grayish sandstone (lower layer of the bedrock), and a detrital cover of sandy gravel deposits (Pieraccini et al. 2006).

The landslide activity shows an interaction of phases with slow displacements and accelerations that, as previously described also for the Sant’Andrea case, are primarily triggered by prolonged and intense rainfall. As reported in Fig. 5, these peaks of intense rainfall are related to changes in the horizontal displacement component detected by the InSAR remote sensing technique.

In this study, the landslide was monitored by using the C-band Sentinel-1 horizontal component from 30 March 2015 to 8 February 2020. Time series were extrapolated after processing 229 ascending and 249 descending images through the Small Baseline Subset (SBAS) algorithm (Berardino et al. 2002) in Sarscape software. We considered the horizontal component because it exhibits the most evident step-like movements related to rainfall events. Moreover, horizontal displacement is the moving component that has the most implications for the element at risk in the area. The time step dimension of the modeled time series is 11 days. This frequency is the smallest available for the selected landslide using the above-described InSAR processing method.

Baishuihe landslide

The Baishuihe landslide affects the right-hand slope of the Yangtze valley, in the Three Gorges Reservoir. Figure 6 reports the main topographical features of this slope instability. The highest elevation of the landslide boundary is 297 m a.s.l., with the crack acting as the rear barrier to the less unstable area (Song et al. 2020). The frontal edge is immersed in water, and its elevation is approximately 120 to 130 m a.s.l., which is always 145 m below the Yangtze river water level in the reservoir. The landslide measures 500 m in length from north to south and 430 m in width from east to west, encompassing an area of 215,000 m² with an average depth of around 30 m. The main sliding inclination is 20° and the volume has been estimated at 6.45 million m³ (Li et al. 2010). The landslide body is mainly composed of silty clay and gravelly soil, which appear alternately and its thickness ranges from 7.5 to 37.7 m. The slip surface is mainly composed of gravel-containing or breccia-containing silty clay; in addition, some parts are full of breccia and clay. The thickness of the failure zone varies from 0.2 to 1.3 m with an average thickness of 0.7 m (Yang et al. 2019).

The landslide is located in the subtropical monsoon climate zone, which is characterized by substantial rainfall and distinct seasons. The maximum temperature is 42 °C instead the minimum is − 8.9 °C (Song et al. 2020), where the average temperature ranges between 17 and 19 °C. June through September is the flood season; instead, October to May is considered the non-flood season. When persistent and intense rainfall events occur during the flood season, the landslide deforms significantly. Consequently, precipitations can be considered one of the major factors triggering the deformation of the Baishuihe landslide. Moreover, the water level in the reservoir fluctuates periodically every year. Usually, the reservoir water level is maintained at about 175 m in November and December. From early January to May, the water level gradually drops from 175 to 145 m; during this period, the deformation of the Baishuihe increases (see Fig. 7). In June and July, the reservoir water level is at a low level which fluctuates slightly to about 145 m. Then, the reservoir water level begins to rise gradually at the end of July and early August. From October on, the water level rises again, and, at the same time, the velocity of the Baishuihe deformation slows down (Keqiang et al. 2008; Li et al. 2010; Miao et al. 2021). Likewise, the water level is an indispensable factor when studying the activity of the Baishuihe landslide.

Since June 2003, the Baishuihe landslide has been monitored by six manual GNSS monitoring stations, named XD-01, XD-02, XD-03, XD-04, ZG93, and ZG118 respectively (Li et al. 2008). The locations of the monitoring stations are reported in Fig. 6 and these allow a wide characterization of the landslide displacements. Middle and posterior areas of the landslide are the most unstable (Li et al. 2010). As shown respectively in Figs. 6 and 7, ZG118 has been utilized in this study for its comprehensive data. In addition, station ZG118 demonstrates a notable deformation with the longest time series and a considerably greater displacement. The time step dimension of the modeled time series is 1 month. This frequency is the highest available for the selected landslide.

El Arrecife landslide

The El Arrecife landslide affects the slope directly overlooking the Rules Reservoir. This landslide has been recently identified and characterized by Reyes-Carmona et al. (2021, 2020). It is classified as a translational landslide with a sliding surface dipping 21° toward N120°E, parallel to the mean orientation of the slope, while the landslide’s foot is affected by several smaller-scale rotational slides. The landslide involves an area of 473.107 m², with a mean thickness of 31.1 m, and a volume of 14.7 million m³, which makes the El Arrecife to be considered an extremely large landslide (see Fig. 8). Its most notable feature is that it lacks well-defined landslide morphologies (e.g., large head scarps or lateral scarps) and is difficult to identify in the landscape. Furthermore, geological variables such as lithology and geological structure contribute to the formation of the El Arrecife landslide. The slope is composed of phyllites, which are coarse-grained metamorphic rocks with a planar fabric and a low friction angle. Because of these characteristics, the slope has a high potential for instability and landsliding. As the landslide is situated near a reservoir, it poses a threat not only to the reservoir itself but also to other facilities (such as highways, viaducts, and powerlines) and the local inhabitants. Due to its translational nature, it is impossible to rule out the possibility of a critical acceleration of the entire landslide mass and a catastrophic failure of the slope. If an impulse wave is generated and the reservoir’s dam is breached, resulting in a downstream flash flood, this scenario would have catastrophic implications. Despite this, it is more likely that the smaller-scale rotating slides at the base of the landslide may cause greater damage to other infrastructures, such as the N-323 National Road, which crosses the El Arrecife landslide.

The landslide activity exhibits a linear movement pattern with small accelerations in the lower sector of the unstable area which are related to a decrease in the water level of the Rules Reservoir. Two slight accelerations were observed during two periods of water level decline from 2017 to 2019 (Reyes-Carmona et al. ), whereas times of no change or rise in the water level resulted in the movement stabilizing or not accelerating. In contrast, rainfall seems unrelated to landslide accelerations since it leads to reservoir filling and, thus, relative slope stabilization. Therefore, the reservoir’s water level variation is the only factor that triggers the movement of the El Arrecife landslide, as it has a greater effect on the movement than rainfall.

The landslide was first monitored through the InSAR technique from March 2015 to September 2018 (Reyes-Carmona et al. 2020). A mean surface ground displacement of 25 mm/year. and a maximum of 55 mm/year were observed, as well as a cumulative displacement of 10 cm during that period (approx. 3.5 years). Later, the InSAR monitoring has been also extended to 2014, providing the landslide activity from December 2014 to March 2020 and resulting in a mean displacement of up to 20 mm/year (Reyes-Carmona et al. 2021). Figure 9 reports a frame of the InSAR monitoring, from October 2016 to March 2020, in which the relationship between the landslide displacement and the reservoir water table is recognized. Additionally, a ground penetrating radar (GPR) study has been performed from 1997 to 2020, evidencing that the landslide has been active for the last 22 years: as a result, a vertical ground subsidence of up to 23 mm/year was estimated.

In this study, the landslide was monitored through the C-band Sentinel-1B satellite from 30 September 2015 to 13 March 2020. Time series with a temporal resolution of 12 days were extrapolated after processing 101 ascending orbit images by using the Parallel Small Baseline Subset (P-SBAS) algorithm (Casu et al. 2014) implemented in the European Space Agency’s (ESA) geohazards exploitation platform (GEP) (De Luca et al. 2015). The time step dimension of the modeled time series is 12 days. This frequency is the highest available for the selected landslide using the above-described InSAR processing.

Methodology

Data pre-processing

In reservoir landslide displacement prediction studies using machine learning, cumulative landslide displacement is frequently divided into a trend term and a periodic component (Du et al. 2013; Zhou et al. 2018b; Yang et al. 2019). In these cases, the evolutionary tendency of the landslide is represented by a so-called trend-term displacement, whereas a periodic-term displacement refers to variations in displacement due to periodic triggers. The two terms (trend and periodic displacements) are then forecasted independently, and the final expected cumulative displacement is produced by combining the two predictions. However, this method works on the assumption that the trend term is dependent just upon itself, and no external trigger influences it. However, depending on the decomposition strategy, this assumption might not always be true. Moreover, by removing level fluctuations in a time series and so decreasing trend and seasonality, differencing can help to stabilize the mean of a data series, and therefore, it helps to improve the prediction capabilities of data-driven models (Montesino Pouzols and Lendasse 2010). For this reason, we detrend both the displacement and reservoir water level time series by differencing. In detail, the value at the current time step is determined as the difference between the original observation and the observation at the previous time step. This is valid for all the timesteps, except the first of the series. By avoiding decomposition and opting for differencing as a detrending approach, the research aims to minimize potential uncertainties and complexities associated with decomposition strategies, while maintaining simplicity and effectiveness in trend removal from the landslide displacement time series data.

Deep learning algorithms

This paper evaluates seven cutting-edge deep learning architectures for time series forecasting and compares them. Among them, MLP, LSTM, GRU, and 1D CNNs are commonly used in several forecasting tasks. However, to the author’s knowledge, although 1D CNNs are quite common for several time series forecasting tasks (Kiranyaz et al. 2021), (Kiranyaz et al. 2021), such a model has never been used for landslide displacement forecasting. We decided to evaluate also the bidirectional LSTM since it has already been used for landslide displacement forecasting (Lin et al. 2022). Moreover, some configurations based on the combination of the abovementioned models are proposed. For instance, the 2xLSTM model is nothing but the combination of two LSTM layers. This configuration is expected to perform better than a single LSTM layer when dealing with complex problems. Another proposed model is the Conv-LSTM, which performs well in several time series forecasting tasks. Further details of the used models can be found in the Supplementary materials.

Multi-layer perceptron (MLP) (see Fig. S1)

The ANN model is one of the most widely used models that has been effectively utilized in various applications, including time series modeling and forecasting. The appeal of ANN models stems from extrapolating the underlying data flow without constraints on the model structure. Another notable aspect of ANNs is that they are universal approximators capable of accurately approximating a wide range of functions. In the literature, there are indeed a variety of ANN model architectures. Whereas ANNs have a similar structure, distinctions among different algorithms have been made based on how they are designed. The so-called multi-layer perceptron (MLP), a three-layer feed-forward network (input, hidden, and output), is the most widely used ANN architecture for time series forecasting (Khashei and Hajirahimi 2019).

Recurrent neural networks (RNNs)

Three types of RNNs are used in this research, namely long short-term memory (LSTM), gated recurrent unit (GRU), and bidirectional LSTM. Traditional neural networks are fully linked to the input-implicit-output layer. There is no connection between the positions in the sequences. As a result, time series prediction cannot be performed using a standard neural network (Chen and Chou 2012). The recurrent neural network (RNN), which enables feedback in the networks (Sak et al. 2014), retains the prior knowledge and applies it to the current output computation.

LSTM (see Fig. S2): A unique variety of RNNs called LSTM neural networks may successfully address the issue of “gradient explosion” (Hochreiter and Schmidhuber 1997). The forgetting gate, input gate, and output gate of the LSTM assure data discovery and long-term memory. The three gate functions offer a reliable nonlinear control mechanism for the input and deletion of control information. Following forward propagation, the backpropagation through time (BPTT) method transfers the accumulated error back in time and determines the gradient of error-associated parameters. Finally, the stochastic gradient descent method updates the weights and thresholds. Two architectures, the first with one LSTM layer and the second with two LSTM layers (2xLSTM), are evaluated.

Bidirectional LSTM (see Fig. S4): Even though the LSTM model fixes the gradient vanishing issue with RNNs, it can only learn knowledge from the past and cannot consider future data. Concerning the training phase, landslide motion is connected to both past and future displacement information, which may be used as a supplement while training the model since the causes impacting it is repeated in time. Architecture-wise, Bi-LSTM has forward and backward LSTM layers. The backward LSTM extracts forthcoming data regarding the current time step while in the opposite direction from the forward LSTM model, which leverages the current time step to retrieve past information. The Bi-LSTM architecture has been utilized effectively in several forecasting applications, such as solar radiation (Peng et al. 2021), well log (Shan et al. 2021), and tourism demand (Kulshrestha et al. 2020).

GRU (see Fig. S3): Recurrent unit is an RNN variation that performs better while being more streamlined (Cho et al. 2014; Zhao et al. 2018). The GRU is similar to a long short-term memory (LSTM) with a forget gate, but it has fewer parameters since it eliminates an output gate. GRU outperformed LSTM on specific tasks such as audio modeling, voice signal modeling, and natural language analysis (Ravanelli et al. 2018).

1D convolutional neural network (Conv) (see Fig. S5)

Convolutional neural networks (CNNs), a subset of ANNs, are widely used in a wide range of applications, such as image and video recognition, image classification, and natural language processing. CNN utilizes filters of comparable form to the data processed and dependent on the shape of the data. Because time series (Gamboa 2017) are one-dimensional data, 1-dimensional CNNs (Amarasinghe et al. 2017; Kiranyaz et al. 2021) are used for the landslide displacement forecasting task. A conv1D layer’s output sequence is shorter than its input sequence. This is corrected by padding the input sequence with zeros at both ends, also known as the same padding. A filter is moved over the input sequence using a Conv1D layer. One stride means that the filter is moved across the input sequence one step at a time. This is the first research in which a 1D convolutional-based architecture is used to forecast landslide displacement.

Conv-LSTM model (see Fig. S6)

The Conv-LSTM model used in this research is composed of one 1D convolutional layer, two LSTM layers, and one dense hidden layer. In this model, the feature extraction of the input data is performed by a CNN layer; then, the output values are fed to the LSTM and Dense layers to predict the landslide displacement with the extracted feature data. The combination between CNN and LSTM achieved the highest prediction accuracies in several forecasting tasks (Xue et al. 2019; Lu et al. 2020; Livieris et al. 2020). However, this is the first research in which a Conv-LSTM architecture is used to forecast landslide displacement.

Training strategy and optimization

Present and past landslide displacement information and its triggers might influence future displacements through nonlinear relationships. In this research, we use seven DL models to forecast one single displacement time step in the future by showing the model n past time steps (look back) of both displacement and trigger variables. Several look-back windows (3, 5, 7, 9, 12) are evaluated for all the abovementioned models across all four case studies, to define the best one for each study case. A visual scheme of the approach is shown in Fig. 10.

The displacement time series are divided into 80% and 20% for training and testing, respectively. Twenty percent of the training set is used to monitor the model performances during training, as well as to create checkpoints (save model weights) corresponding to the lower validation loss. The division is performed temporally, meaning that the training set is the oldest, followed by the validation set, and finally the test set. All sets are further divided into small chunks of time series, having the length of the look-back value plus the ground truth of the predicted step. Meaning that if the look back is set equal to 3, the chunks’ length is four time steps. Huber loss was used as the loss function (Holland and Welsch 1977; Huang and Wu 2021). The Huber loss combines and optimizes both the mean square error (MSE) and mean average error (MAE), and it is defined as follows:

$${L}_{\delta }\left(y, f\left(x\right)\right)= \left\{\begin{array}{lr}\frac{1}{2}{(y-f(x))}^{2} & \mathrm{for}\;\left|y-f\left(x\right)\right|\le \delta ,\\ \delta \left|y-f\left(x\right)\right|- \frac{1}{2}{\delta }^{2} & \mathrm{otherwise}.\end{array}\right.$$

(1)

where $\delta =1$.

Therefore, for loss values greater than $\delta$, MAE is used, while for lower loss values MSE is used. We reduce the importance of outliers by using the MAE for bigger loss values, which nevertheless results in a well-rounded model. At the same time, we preserve a quadratic function close to the center by using the MSE for the smaller loss values. The number of training epochs is set to 1000, while, to reduce tuning time, an early stopping strategy is used to stop the training when the validation loss does not decrease after 20 subsequent epochs. For each architecture, weights are automatically saved in the epoch corresponding to the lowest validation loss value.

Furthermore, the appropriate combinations of hyper-parameters must be used while training such deep learning models to optimize the model and deliver the best results. As a result, we iteratively train the model using a variety of combinations of batch sizes (9, 18, 36, 74, 144), learning rates (10e-3, 5e-3, 10e-4, 5e-4, 10e-5, 5e-5) and the number of layer nodes (8, 16, 32, 64, 128, 256). Therefore, for each architecture, we train 180 different hyperparameter combinations per each look back, for a total of 900 combinations per architecture.

The process is built in Python programming language. All experiments were executed on a Windows operating system computer with a 3rd Gen Ryzen Threadripper 3990X CPU and NVIDIA RTX 3090 GPU with 10,496 CUDA cores.

Model evaluation

After model training, the prediction models must be evaluated on an unseen test dataset. The prediction performance is estimated using root mean squared error (RMSE) (2), normalized RMSE (NRMSE) (3), and coefficient of determination (R²) (17), which are defined as follows:

$$RMSE=\sqrt{\frac{{\sum }_{i=1}^{N}{({P}_{i}-{M}_{i})}^{2}}{N}}$$

(2)

$${R}^{2}={\left[\frac{{\sum }_{i=1}^{N}\left({M}_{i}-\overline{M }\right)\bullet \left({P}_{i}-\overline{P }\right)}{\sqrt{{\sum }_{i=1}^{N}{\left({M}_{i}-\overline{M }\right)}^{2}\bullet {\sum }_{i=1}^{N}{\left({P}_{i}-\overline{P }\right)}^{2}}}\right]}^{2}$$

(3)

where P and M stand for the predicted and measured displacements, respectively. $\overline{M }$ is the mean of observed values and $\overline{P }$ refers to the average of the predicted displacements. The number of samples is represented by N.

The R² statistic evaluates the connection between measured and predicted values. The RMSE displays the difference between actual and predicted values. An effective model has a low value of RMSE and a high value of R².

Landslide displacement forecasting

Landslides outside artificial reservoir contexts

As stated above, few studies in which ML approaches are applied for landslide displacement forecasting outside reservoir contexts exist. In this section, we show the forecasting results of two rainfall-triggered slow-moving landslides. In those cases, the main factor that influences the landslide displacement is the groundwater level, that, in turn, is further conditioned by rainfall. Since for both cases groundwater level time series are not available, just rainfall is used as a triggering factor.