1 Introduction

Slope movements, as prevalent geological hazards in mountainous regions globally, pose significant risks to human life and infrastructure (Metternicht et al. 2005). These events often result in fatalities within settled regions and cause extensive damage to affected areas. One of the primary triggers for such movements is precipitation. The frequency and intensity of extreme rainfall events are increasing due to global warming, leading to a rise in catastrophic slope failures (Gariano and Guzzetti 2016). Their kinematics are often complex, and characterized by transient changes in velocity and acceleration. Catastrophic failures typically begin with slow-moving processes, that can rapidly accelerate when triggered by factors such as rainfall, earthquakes, volcanic activity, etc., resulting in significant damage and loss (Lacroix et al. 2020; Wang et al. 2023; Wang et al. 2024; Xia et al. 2023; Zhou et al. 2022, 2024). Although it may be difficult to prevent slope movements, scientifically based early warning and comprehensive analyses of the dynamics before and after events can significantly help mitigate related risks. These measures encompass slope stability assessment and correlation analyses between acceleration in creep and triggering factors, facilitating a proactive approach to risk reduction (Kilburn and Petley 2003).

Synthetic Aperture Radar (SAR) and optical satellite remote sensing are promising in the detection of slope instabilities and for continuous monitoring of slope deformation due to their regular acquisitions, wide field of view, and relatively low cost. Optical satellites have enormous synergistic potential for slope failure inventory mapping due to their rich spectral and spatial features (Behling et al. 2016). However, acquiring near real-time cloud-free images is challenging during catastrophic failures as slope instabilities more frequently occur in mountainous regions and during the rainy seasons (Plank et al. 2016). In addition, there are limitations for accurately retrieving ground deformation related to slope activity using cross-correlation analysis of optical data. This arises due to the effective pixel size (e.g., ground pixel), as well as illumination conditions and changes in the ground surface that may induce partial or complete loss of coherence between image pairs (Leprince et al. 2007; Debella-Gilo and Kääb 2011; Travelletti et al. 2012). Compared to optical sensors, active SAR sensors have a longer wavelength to penetrate clouds and fog and are almost completely independent of weather conditions and sunlight. Differential Interferometric SAR (DInSAR) technology using a pair of two SAR images that are acquired at two different times from nearly identical orbital positions has been widely used for ground motion monitoring related to different types of geohazards (Motagh et al. 2008; Intrieri et al. 2018; Dai et al. 2020; Tomás et al. 2014; Lu et al. 2019). Advanced multi-temporal InSAR (MTI) techniques such as persistent scatterer interferometry (PSI) and small baseline subset (SBAS) (Ferretti et al. 2001; Hooper et al. 2004, 2007, 2012) extend the capabilities of DInSAR technique to assess ground deformation during the life cycle of landslides by utilizing multiple SAR acquisitions in time (Wasowski and Bovenga 2014; Dong et al. 2018; Wang et al. 2023; Xia et al. 2023). The launch of the C‑band Sentinel‑1 satellite in 2014 has significantly enhanced the availability of free satellite Synthetic Aperture Radar (SAR) images, which has drawn increased interest from worldwide researchers in studying slope deformation and instability dynamics (Haghshenas Haghighi and Motagh 2017; Dai et al. 2020; Solari et al. 2019; Intrieri et al. 2018; Barra et al. 2016; Vassileva et al. 2023). InSAR measurements from a single orbital track are limited by geometric distortions such as foreshortening, layover, and shadow effects. Moreover, differential interferometric measurements only provide a one-dimensional (1D) projection of a three-dimensional (3D) surface deformation field into the line-of-sight (LOS) direction from the ground to the satellite (Colesanti and Wasowski 2006). These limitations are challenging for accurately evaluating the detailed kinematics of slow-moving slopes (Casagli et al. 2023). However, existing multi-sensor and multi-track SAR data in the C, X, and L bands can help us better investigate slope instability kinematics (Herrera et al. 2013; Xia et al. 2023). The L‑band SAR data have shown great performance in investigating slope kinematics in vegetated regions due to their capability for deeper penetration (Lu and Kim 2021). Moreover, they can resolve relatively large displacement due to their long wavelength (Strozzi et al. 2005). The X‑band SAR data with high spatial (1–3 m) and temporal resolutions (11 days) provide us with more spatiotemporal information on the ground surface (Herrera et al. 2011; Motagh et al. 2013; Haghshenas Haghighi and Motagh 2017). The currently operational C‑band SAR data onboard Sentinel‑1 are freely available with an extensive archive, providing data for a wide range of applications. Interferometric measurements from different orbital tracks and satellites help us obtain the 2‑D or quasi-3‑D surface deformations field, which helps correct for geometric distortions and perform deeper geophysical investigation (Bechor and Zebker 2006; Fuhrmann and Garthwaite 2019; Hu et al. 2014; Xu et al. 2022).

Many studies have shown that slow-moving slopes exhibit transient velocity variations that correlate with rainfall patterns, with increased velocity generally corresponding to periods of high rainfall (Hu et al. 2020; Dille et al. 2021; Tang et al. 2023). Correlation and coherence analysis between displacement time-series and hydrogeological triggering factors is crucial for investigating slope destabilization processes (Xia et al. 2024). Tomás et al. (2014) used wavelets to interpret InSAR time-series ground deformation data and found that the Huangtupo slope (China) is affected by an annual displacement periodicity controlled by rainfall (Tomás et al. 2016). Haghshenas Haghighi and Motagh (2016) demonstrated that the 1‑year frequency observed in the wavelet result of the InSAR time series is generally absent from the rainfall wavelet spectrum from 2004 to 2010 in the Taihape landslide (New Zealand), except for a short period between 2007 and 2009, indicating no strong correlation with rainfall variation (Haghshenas Haghighi and Motagh 2016). Vassileva et al. (2023) utilized wavelet analysis to explore the correlation between slope displacement and precipitation, suggesting that the primary kinematic motion of the Hoseynabad‑e Kalpush (Iran) landslide is not ruled by seasonal precipitation instead influenced by changes in water levels at a nearby reservoir (Vassileva et al. 2023). Xia et al. (2024) utilized wavelet analysis to interpret periodic displacement features in the Huangtupo landslide associated with rainfall and found a continuity at a period of 365 days, with precipitation preceding seasonal displacement by approximately 12 days (Xia et al. 2024). Similarly, Fan et al. (2024) used the wavelet analysis and found a time lag of approx. 19–27 days between rainfall and seasonal displacement for the loess landslides in the Ili Valley (Fan et al. 2024).

In this paper, we aim to characterize the slope kinematics of the Joshimath landslide-prone slope in India. Joshimath, a town in the Chamoli district of the Uttarakhand state in Northern India, is located in a mountainous region within the Western Himalayas known for its tectonic activity (Yang et al. 2023). The instability within the Joshimath hill complex has a significant historical trajectory, with reported instances dating back to at least 1978 (Gahalaut et al. 2023). Since early 2010, Indian researchers have emphasized the urgent need for proactive measures to mitigate the escalating risks posed by ground deformation, debris displacement, and anthropogenically caused increasing pressure resulting from building activities (Bisht and Rautela 2010). However, by the end of 2022 and the beginning of 2023, the situation suddenly became extremely volatile as wide cracks opened up on the roads and many houses developed large cracks with their foundations sinking in the ground (Sreejith et al. 2024). Consequently, people were evacuated to safer locations. The Joshimath slope instability complex has been having a strong impact on livelihoods, transportation, infrastructure, and the economy, and thus, many research works are currently undergoing to study related processes and effects of this long-term ongoing slope destabilization.

Bera et al. (2023) utilized artificial intelligence and Geographic Information Systems (GIS) and identified Joshimath as a region with high susceptibility to slope instabilities (Bera et al. 2023). Yang et al. (2023) utilized ascending and descending Sentinel‑1 SAR data and assessed ground deformation in the Joshimath area for the period between January 2020 and January 2023 before the destabilization crisis using the SBAS method. Their findings showed that the slope instabilities are characterized by slow movements over a period of 3 years before the 2023 crisis, with annual deformation rates ranging from −92.4 to 105.2 mm/yr in the vertical direction and −107.9 to 99.7 mm/yr in the E‑W direction (Yang et al. 2023). Sati et al. (2023) analyzed the possible causes and consequences of slope instabilities in Joshimath using historical geological, and climatic records, and concluded that unplanned infrastructure development, lack of adequate drainage, and excavation of roads through unstable debris slopes influence the dynamics of slope destabilization (Sati et al. 2023). Shankar et al. (2023) utilized the SBAS technique, employing Sentinel‑1 data from May 2019 to April 2023, to analyze ground deformation hazards in the region. Their study revealed the maximum displacement of 69.1 mm/yr for the 2019–2023 time period (Shankar et al. 2023). Sreejith et al. (2024) investigated the kinematics of the Joshimath hillslope complex using ascending Sentinel‑1 and ALOS-1/2 data and found that the velocity of deformation increased from −22 mm/yr during 2004–2010 to −325 mm/yr during 2022–2023 (Sreejith et al. 2024).

However, the previous studies mentioned above did not perform a longer-term deformation history analysis of the Joshimath hillslope complex with more than two tracks of SAR data, nor did they provide an in-depth analysis regarding the influence of climatic and geological factors in promoting slope instabilities. Additionally, they did not investigate the spatiotemporal changes in deformation patterns before and after the destabilization crisis in January 2023. To further investigate the slope destabilization processes within the Joshimath hillslope complex, we analyze the ground deformation for different periods before and after the 2023 destabilization crisis using a variety of SAR data, including Sentinel‑1, ALOS‑2, and TerraSAR‑X. The Multi-temporal InSAR (MT-InSAR) technique of the small baseline subset (SBAS) method is applied to derive displacement time-series in the line-of-sight (LOS) direction from the satellite to the ground. Subsequently, InSAR-based measurements of ground deformation from different orbits are inverted to retrieve displacements in East-West (E–W), and Up–Down (U–D) directions. Clustering analysis for 2‑D displacement fields is implemented to investigate the spatiotemporal changes in deformation patterns before and after the 2023-crisis. Finally, the relation between transient changes in slope kinematics and daily precipitation is analyzed using the Wavelet transform to investigate whether changes in seasonal rainfall influence slope destabilization processes.

2 Geographical and geological setting

Joshimath, covering approximately 2500 km2, is among the six geological blocks in the Chamoli district of Uttarakhand (N 30° 33ʹ 07ʺ, E 79° 33ʹ 40ʺ), and is located atop ancient glacial debris. The Joshimath hillslope complex sits on the intersection of the Main Central Thrust 1, 2, and 3, which are the intra-crustal fault lines, where the Indian Plate has pushed under the Eurasian Plate along the Himalayas (Tripathi et al. 2023; Yang et al. 2023; Shankar et al. 2023; Sati et al. 2023). Surrounded by the Dhauliganga River and the Alaknanda River (Fig. 1), the hillslope complex is mainly oriented towards the north and northeast direction, with slopes ranging from 10 to 30 degrees, at an altitude of approximately 1600 meters (Fig. 2). The climate in Joshimath is generally characterized as cool temperate, with annual average precipitation of around 1000 mm, and approximately 500 mm of rainfall occurring during the summer season (Sati et al. 2023). Joshimath hillslope complex sits atop a glacial moraine, which consists of distinct ridges or mounds of debris laid down by a glacier thickly covering the solid rocks underneath (Sati et al. 2023). These sediments have voids mainly caused by fluvial-erosional processes, resulting in extreme instability of these slopes. Fig. 1 shows the lithology underlying the glacial deposits of the Joshimath hillslope complex, mainly composed of Gneiss, Kyanite Shale, Quartzite, and Silicate Calc. Gneiss is characterized by strong foliation, with weak zones distributed along these planes. These weak zones can serve as pathways for water infiltration, leading to increased pore pressure and decreased stability, and thus contributing to slope destabilization. Kyanite, a sedimentary rock primarily comprised of clay minerals, is prone to fracturing due to weathering and erosion. Water infiltration along fractures can lead to slope failures. Silicate shale refers to shale with a higher concentration of silicate minerals, which can significantly impact its strength and stability. The water infiltration in areas rich in Silicate shale may potentially trigger slope failures (Castro et al. 2020).

Fig. 1
figure 1

Lithology map of Joshimath and surroundings. The data originated from Bhukosh, a platform serving as the gateway to all geoscientific data managed by the Geological Survey of India. URL:https://bhukosh.gsi.gov.in/Bhukosh/MapViewer.aspx

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Fig. 2
figure 2

Hillshade map, slope map, aspect map, and contour map derived from TanDEM‑X DEM acquired on March 05, 2016 covering the Joshimath hillslope complex

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The slope movements have been triggered by an incessant rainfall in the region over the past few years, which deposited more water on the surface (Tripathi et al. 2023; Yang et al. 2023; Shankar et al. 2023). However, due to the unavailability of solid rocks underneath, the water seeped into the soil and loosened it from within. With the top surface of the soil already gone due to intense construction, the region has remained on the edge. Nearly all houses, major hotels, and roads are riddled with massive cracks and fissures (Tripathi et al. 2023; Yang et al. 2023; Shankar et al. 2023). Leaning buildings are scattered throughout Joshimath. The city remained tranquil and conducted business as usual until the final months of 2022 when natural forces began to resist, prompting residents to take action. Cracks began to appear in their homes and other man-made structures throughout the city. This crisis period caused no fatalities or injuries but destroyed >1000 houses and many people had to be evacuated for fear of further slope instabilities (Tripathi et al. 2023; Yang et al. 2023; Shankar et al. 2023; Sati et al. 2023).

3 Data and methodology

The workflow for data processing and the main steps comprising this framework are illustrated in Fig. 3. This section provides a detailed explanation of the methodologies involved. Firstly, we employed the MTI technique to derive line-of-sight (LOS) displacements from Sentinel‑1, ALOS‑2, and TerraSAR‑X data, which helped us assess slope instability from 2015 to 2024. Then, active deformation identification (ADI) involving spatial clustering and temporal segmentation is applied to detect significant deformation areas and trend changes in the time-series of ground deformation data. Subsequently, a 2‑D decomposition method is utilized to decompose LOS motions into east-west and vertical components, allowing for a better understanding of the deformation regime related to instability. Here, the north-south component is disregarded as the sensor is not sensitive to the deformation in the N‑S direction (Motagh et al. 2017). Finally, the average displacement time-series from main deformation clusters is derived to investigate its relationship with precipitation using wavelet. Overall, the used methodology provides helps us to gain a more detailed understanding of slope instability dynamics in the study area.

Fig. 3
figure 3

Methodology framework

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3.1 Multi-temporal InSAR (MT-InSAR)

This study exploits C‑band Sentinel‑1 SAR, X‑band TerraSAR‑X SAR, and L‑band ALOS‑2 SAR images for the MTI analysis. The detailed features of the data are shown in Table 1. The detailed temporal distribution of the SAR data is shown in Fig. S2. We collected 361 ascending and descending Sentinel‑1 SAR images from the European Space Agency (ESA) for this study covering the period from 2017 to 2024. Moreover, 23 ALOS‑2 SAR images in Stripmap mode between March 2015 and December 2022 from the Japan Aerospace Exploration Agency (JAXA), and 32 TerraSAR‑X SAR images in Spotlight mode between February 2023 and March 2024 from the German Aerospace Center (DLR) were utilized for deformation analysis before and after the 2023 slope destabilization crisis in Joshimath, respectively. The pixel spacings in slant range and azimuth directions of Sentinel‑1, ALOS‑2, TerraSAR‑X images are 2.3 m × 14.0 m, 1.6 m × 2.2 m and 0.91 m × 1.25 m, respectively. In this study, the small baseline subsets (SBAS) method as implemented in the StaMPS/MTI software (Hooper 2008) was utilized to derive the LOS deformation from a stack of SAR images. Firstly, the acquired SAR images are co-registered and cropped to the study region. Next, differential interferograms are generated using the repeat-pass method implemented in GAMMA software with topographic phase components being removed using 12‑m resolution TanDEM‑X DEM. The network of small baseline interferograms was generated (Wegnüller et al. 2016). The network of interferograms for different datasets is shown in Fig. S3 in the supplementary materials. For the SBAS analysis in StaMPS/MTI, the amplitude difference dispersion with a threshold of 0.6 over time is utilized to select stable candidates for further time-series analysis (Hooper et al. 2012). Then unwrapping was performed based on the 3D unwrapping approach with a 50 m resampling grid spacing. The threshold standard deviation was set to 1.2 in this study to filter out noisy pixels caused by signal contributions from neighboring ground resolution elements. For the remaining parameters, the default settings provided by the StaMPS/MTI were utilized. It is worth noting that, the accuracy of surface displacement derived from InSAR measurements is significantly influenced by the spatiotemporal variations in atmospheric water vapor, which can introduce errors as the atmospheric effects are mixed with the displacement (Yu et al. 2018). Spatially correlated atmospheric errors can be effectively mitigated using linear regression method (Hooper et al. 2012). However, the seasonal rainfall in Joshimath possibly introduces temporally correlated atmospheric effects, which should not be neglected (Haghighi and Motagh 2019). Therefore, we utilized a regional climate model, GACOS (Generic Atmospheric Correction Online Service), to mitigate atmospheric effects (Yu et al. 2018).

Table 1 Basic parameters of SAR images in this study
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3.2 Active deformation identification (ADI)

Active deformation identification (ADI) includes two key steps of spatial clustering and temporal segmentation to identify significant deformation areas and their trend changes during specific periods (Mirmazloumi et al. 2022). In this study, we first used the K‑Means method to identify clusters that represent significant deformation zones related to slope instabilities (Kanungo et al. 2002). If multi-orbit data are available for the same period, the intersection of the detected clusters is regarded as the final cluster. The clusters detected for the pre-crisis period in Joshimath are regarded as reference clusters, for which post-crisis instability was analyzed for comparison. Subsequently, the extracted time series from each cluster were analyzed with piecewise linear regression to identify segments with constant velocity and detect significant trend changes. The method proposed by Jekel and Venter (2019) was employed (Jekel and Venter 2019), with constraints of a velocity change of ±10 mm/y and a minimum segment duration of 60 days (Vassileva et al. 2023).

3.3 2-D deformation decomposition from multi-sensor Mt-InSAR results

Having obtained MTI results in LOS direction from various SAR satellites and in different orbits, we can derive ground deformation in east-west (E-W), north-south (N-S), and vertical directions \(d_{E}\), \(d_{N}\), and \(d_{U}\) using the following equation (Gamelin et al. 2009):

$$\begin{aligned}{}&{}\begin{bmatrix}\cos(\theta_{1})&-\sin(\theta_{1})\cdot\sin(a_{1})&-\sin(\theta_{1})\cdot\cos(a_{1})\\ \cos(\theta_{2})&-\sin(\theta_{2})\cdot\sin(\alpha_{2})&-\sin(\theta_{2})\cdot\cos(a_{2})\\ \cos(\theta_{3})&-\sin(\theta_{3})\cdot\sin(\alpha_{3})&-\sin(\theta_{3})\cdot\cos(a_{3})\\ \end{bmatrix}\begin{bmatrix}d_{U}\\ d_{E}\\ d_{N}\end{bmatrix}\\{}&{}=\begin{bmatrix}d_{\operatorname{LOS}_{1}}\\ d_{\operatorname{LOS}_{2}}\\ d_{\operatorname{LOS}_{3}}\\ \end{bmatrix}\end{aligned}$$

where d represents displacement, \({\operatorname{LOS}_{\text{1,2,3}}}\) are SAR data in different orbits. \(\theta\) and \(\alpha\) are the inclination angle and the heading angle, respectively. Before the 2023 destabilization crisis, Sentinel‑1 ascending, Sentinel‑1 descending, and ALOS‑2 ascending data are utilized, while after the 2023 crisis, Sentinel‑1 ascending, Sentinel‑1 descending, and TSX ascending data are employed for decomposition. In theory, using observations from three independent systems can be used to solve for three unknowns, i.e., deformation in E‑W, N‑S, and vertical directions. However, the SAR sensor is not sensitive to the deformation in the N–S direction since the satellite heading angle is near that direction, leading to artificial exaggeration. Thus, the N–S component is usually ignored in resolving three-dimensional velocity (Fuhrmann and Garthwaite 2019; Xia et al. 2023). In this study, we decompose LOS deformation in the E–W and vertical directions using three tracks by ignoring the N–S component and solving the above equation by the Least Squares (LS) method (Fuhrmann and Garthwaite 2019; Hu et al. 2014; Xia et al. 2023). To perform 2D decomposition, it is essential to first align the time series of the multi-orbit data. First, we use the combined acquisition times from various data sources as the reference time set. Each orbit’s data is then resampled to align with the reference time set. The resampled data is interpolated to fill in any missing values using the least squares method. Moreover, it is necessary to transform the multi-orbit LOS-based results to a common spatial grid because the locations of the detected pixels in each orbit are different. To achieve this, we use the pre-crisis ALOS‑2 and the post-crisis TSX results as the base layer for decomposition, as both have significantly more measurement points compared to the Sentinel‑1 data. For each pixel in the ALOS‑2 or TSX data, the pixels with the minimum Euclidean distance within a 30 m radius in the Sentinel‑1 data have been regarded as the corresponding common pixel. If more than one point has the same minimum distance, they are all considered as common pixels, and their average value is taken as the value of this common pixel.

3.4 Correlation analysis between displacement and precipitation using Wavelet Transform

Cross Wavelet Transform (XWT) analysis and Wavelet Transform Coherence (WTC) analyses are valuable tools in signal processing and time series analysis to explore the relationship between the two time series in both the time and frequency domains. The primary focus of XWT analysis is to assess the strength of a shared cycle between the two time series under investigation.

$$\mathrm{XWT}_{x_{1}x_{2}}(p,t)=\mathrm{S}\left(C_{x_{1}}^{*}(p,t)C_{x_{2}}(p,t)\right)$$

where \({x_{1}}\) and \({x_{2}}\) are two considered time series, C refers to the continuous wavelet transforms at scales (or periods) p and time t, the symbol * is the complex conjugate, and S refers to a smoothing operator in time and scale (Torrence and Webster 1999).

The WTC analysis assesses the alignment and similarity between two sequences by examining their periodic patterns and helps identify any shared periodicities or patterns that may exist across different time scales. The WTC of two time series is calculated using the following formula (Torrence and Webster 1999; Grinsted et al. 2004)

$$\mathrm{WTC}_{x_{1}x_{2}}(p,t)=\frac{\left|\mathrm{S}\left(C_{x_{1}}^{*}(p,t)C_{x_{2}}(p,t)\right)\right|^{2}}{\mathrm{S}\left(\left|C_{x_{1}}(p,t)\right|^{2}\right)\mathrm{S}\left(\left|C_{x_{2}}(p,t)\right|^{2}\right)}$$

where \({x_{1}}\) and \({x_{2}}\) are two investigated time series, and the other symbols are the same as the previous.

The temporal delay \(\Delta d\) between two investigated time series \({x_{1}}\) and \({x_{2}}\), could be derived using the below formula (Tomás et al. 2020):

$$\Delta d=\frac{\Delta\varphi\times P}{2\pi}$$

where \(\Delta\varphi\) denotes the angles of arrows (radian) and P refers to the interested wave period.

In this study, the Wavelet transform is used to analyze the time lag between daily precipitation and changes in the displacement rates within the hillslope. Wavelet analysis necessitates that the two input time-series data, i.e., InSAR displacement and precipitation, maintain a consistent interval frequency. InSAR data is based on a sensor-specific revisit cycle and is not available on a daily basis. To align the InSAR displacement time-series with the daily precipitation time-series on a common timeline, a linear interpolation method is used to fill in missing dates within the InSAR time series (Tomás et al. 2016).

Precipitation data from 2021 to 2023 were obtained from the IMD (India Meteorological Department) weather observatory at Joshimath, located within the affected hillslope zone (Sati et al. 2023). Additionally, rainfall data from three nearby observatories in Chamoli district and merged rainfall products from 2015 to 2021 were used for time-series analysis (Pai et al. 2014).

4 Results

4.1 Slope kinematics before the 2023 destabilization crisis

Figure 4a,b illustrate the LOS displacement rates from March 2017 to December 2022 for ascending and descending Sentinel‑1 data, respectively. Meanwhile, Fig. 4c depicts the corresponding measurements from ascending ALOS‑2 observations for the period between March 2015 and December 2022. Blue (positive values) represents motion towards the sensor, while red (negative values) represents motion away from the sensor. The red outline represents the boundary of the Joshimath hillslope complex, which was mapped from high-resolution TanDEM‑X DEM (12 m resolution). The reference point (79.5716N, 30.5337E) is selected to represent a stable position far away from the instable hillslope complex. We validated multi-orbit InSAR observations using a probability density function (PDF) approach and its derived statistical parameters (mean, standard deviation, RMSE (Root Mean Squared Error)) (Guo et al. 2022), finding that the residuals from multi-orbit data in the far field are statistically similar, as detailed in Fig. S1 and related explanations in the supplementary materials. The validation of InSAR observations against GPS data, as illustrated in Fig. S5 and explained in the supplementary materials, shows a high level of consistency. The observations from both Sentinel‑1 ascending and descending and ALOS‑2 ascending, comprise more than 50,000 measurement points. This large number of measurement points significantly enhances the assessment of instabilities within the Joshimath hillslope complex. Two unstable clusters can be discerned from ascending Sentinel‑1 data in Fig. 4a using the clustering method described in Sect. 3.2: The eastern cluster (purple area) and the middle cluster (pink area). The deformation in the eastern cluster (max LOS approx. −200 mm/yr) appears to be significantly larger than that in the middle cluster (max LOS of approx. −75 mm/yr). The western side of the hillslope complex does not show any significant deformation in this period. MTI results of the ascending ALOS‑2 data in Fig. 4c show a similar deformation pattern as Sentinel‑1 ascending with max LOS of −175m mm/yr for the eastern cluster and −40 mm/yr for the middle cluster. In contrast, Sentinel‑1 descending results in Fig. 4b show only minor deformations of up to −45 mm/yr in both the central and eastern regions. The Joshimath hillslope complex is oriented towards the northeast, as determined from the slope and aspect derived from DEM shown in Fig. 2. This slope direction is approximately aligned with the flight path of the Sentinel‑1 satellite in descending orbit, resulting in the descending data being less sensitive to slope motion (Notti et al. 2014; Darvishi et al. 2018). Figure. 5a–f illustrates the average cumulative displacement time series from the eastern and middle clusters in Fig. 4a for different SAR sensors. As seen in Fig. 5, during the whole observation period the Joshimath hillslope complex exhibits a continuous displacement in both deformation clusters (active deformation regions).

Fig. 4
figure 4

Average displacement rates in LOS direction using a ascending Sentinel‑1 data from March 2017 to December 2022, b descending Sentinel‑1 data from March 2017 to December 2022, and c ascending ALOS‑2 data from May 2015 to December 2022. The image background is from Planet Images. The red outline represents the boundary of the hillslope complex. Red (negative value) indicates movement away from the sensor, while blue (positive value) indicates movement towards the sensor

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Fig. 5
figure 5

Average cumulative displacement time-series in LOS direction: a S1 (Asc), East Cluster; b S1(Des), East Cluster; c ALOS-2(Asc), East Cluster; d S1 (Asc), Middle Cluster; e S1(Des), Middle Cluster; f ALOS-2(Asc), Middle Cluster. The blue bars represent daily precipitation. The red scatter points represent the cumulative displacement time-series in LOS

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4.2 Slope kinematics after the 2023 destabilization crisis

Figure 6a–c show post-crisis LOS velocities for ascending/descending Sentinel‑1, and ascending TerraSAR‑X, from January 2023 to March 2024. The positive values indicate movements towards the satellite, while negative values refer to movements away from the satellite. The two reference clusters identified before the crisis are used here to examine how instability evolves after the crisis. Similar to the pre-crisis analysis, the S1 ascending data shows significant deformation in both—the eastern cluster and the middle cluster, with maximum line-of-sight (LOS) displacements of approximately −370 and −210 mm/yr, respectively. Sentinel‑1 descending data also show instability in the same two clusters of Joshimath. However, compared to the ascending analysis, the descending observations reveal lower displacement rates; about −90 mm/yr for the middle cluster and −130 mm/yr for the eastern cluster. Significant deformation is also observed in both deformation clusters from TerraSAR‑X data, as depicted in Fig. 6c, with maximum deformation rates reaching up to −200 mm/yr.

Fig. 6
figure 6

Average displacement rates in LOS direction using a ascending Sentinel‑1 data, b descending Sentinel‑1 data, c ascending TerraSAR‑X data from January 2023 to March 2024. The image background is a Planet image. The red outline represents the boundary of the Joshimath hillslope complex. Red (negative value) indicates movement away from the sensor, while blue (positive value) indicates movement towards the sensor

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Figure 7a–c show the estimated average cumulative displacement time series after the crisis for the two deformation clusters (see Fig. 4a). In ascending Sentinel‑1 data from January 2023 to March 2024, the eastern cluster and middle cluster show a cumulative LOS displacement of approximately −400 and −180 mm, respectively, Similarly, in the ascending TerraSAR‑X observation, these accumulations amount to approximately −50 and −200 mm, respectively. However, in the descending Sentinel‑1 data, the average cumulative displacement is less; approximately −65 and −105 mm for the eastern and middle clusters, respectively.

Fig. 7
figure 7

Average cumulative displacement time-series in LOS direction for the east (red dots) and middle clusters (blur dots) in a Sentinel‑1 ascending, b Sentinel‑1 descending and c TerraSAR‑X data

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4.3 2-D displacement decomposition

Figure 8 illustrates the distribution of E‑W and vertical deformation for the pre-crisis and post-crisis periods. In the E–W displacement direction, positive values indicate motion towards the East, whereas negative values represent motion towards the West. Similarly, for the vertical displacement direction, positive values correspond to upward motion, while negative values indicate downward motion. As seen in Fig. 8, during the pre-2023 crisis period, horizontal deformation dominates the instability in the eastern part as the largest displacement in E‑W direction of up to 65 mm/yr is greater than the vertical displacement of up to −45 mm/yr. Similarly, during the post-2023 crisis period, horizontal deformation continues to dominate, with E‑W displacement increasing up to 100 mm/yr and vertical displacements amounting up to −75 mm/yr. In the middle part, maximum velocities in both directions—E‑W and vertical—are almost equal for the pre-2023 crisis period. However, during the post-2023 crisis period, vertical deformation dominates the instability (‑60 mm/yr for maximum vertical deformation rate versus 40 mm/yr of EW deformation rate).

Fig. 8
figure 8

2‑D displacement results, covering the period from March 2017 to March 2024, in a, c vertical and b, d E–W directions within the Joshimath hillslope complex

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5 Discussion

5.1 Multi-sensor InSAR survey to assess slope instabilities

Utilizing multi-sensor and multi-temporal InSAR results from advanced MT-InSAR technique enables a comprehensive assessment of slope instabilities occurring within the Joshimath hillslope complex. As depicted in Fig. 4a, both middle and eastern clusters show a significant long-term deformation pattern obtained from data of ascending Sentinel‑1 and ALOS‑2 orbits. The displacement direction of these clusters moves away from the sensor in results obtained from descending Sentinel‑1 data, indicating either subsidence or westward movement. However, the westward movement is impossible because the slope is facing east-north (see Fig. 2 and Fig. S.4). Therefore, the results derived from descending Sentinel‑1 data mainly represent the subsidence component of slope deformation. In comparison, the results derived from the corresponding ascending data show slow movement away from the sensor, indicating both subsidence and eastward movement. The difference between ascending and descending results is due to the orientation of the slope with respect to satellite acquisition geometry. The main direction of slope movements is approximately perpendicular to the looking direction of descending Sentinel‑1, thus making the slope deformation not contribute significantly to the LOS observations in the descending results. A possible 3D relationship between the slope geometry and Sentinel‑1 ascending and descending SAR views is shown in Fig. S4. The integration of observations from ascending and descending orbits suggests that both subsidence and eastward motion contribute to the overall slope instability kinematics. Compared with Sentinel‑1, ALOS‑2 offers a higher spatial density of measurement points to evaluate active deformation areas within the Joshimath hillslope complex. The L‑band SAR sensor onboard ALOS‑2 enables deeper penetration and higher coherence in interferometric measurements. However, the lower temporal resolution of ALOS‑2 limits its ability to precisely detect transient deformation events.

LOS deformation velocities can be projected to slope velocities for the assessment of slope deformation intensity and activity. According to Cigna et al. (2013), the measurement points characterized by slope velocities of less than 16 mm/year are classified as Extremely Slow (ES), while slope velocities ranging from 16 mm/yr to less than 1.6 m/yr are classified as Very Slow (VS) (Cigna et al. 2013). The slope velocities derived from ascending Sentinel‑1 and ALOS‑2 are shown in Fig. 9a,c, with corresponding intensity of activity illustrated in Fig. 9b,d, respectively. The results indicate that the entire hillslope complex can be categorized into either ES or VS velocity classes. However, the results reveal a distinct spatial variation in intensity within the hillslope complex. Specifically, the middle and eastern parts of this area mainly exhibit VS movements, whereas other areas are characterized by ES velocities. These findings suggest that future investigations should prioritize the middle and eastern parts of Joshimath hillslope complex, which are potentially at higher risk.

Fig. 9
figure 9

Slope displacement: a ascending Sentinel‑1 for Mar.2017–Dec.2022 and its b intensity of activity, c ascending ALOS‑2 May.2015–Dec.2022 and its b intensity of activity

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5.2 Long-term movements versus episodes of accelaration

The long-term deformation analysis at Joshimath hillslope complex indicates that this slope has been moving at least for more than eight years (see Fig. 5). To further analyze long-term displacement trends, we explored trends and transient events from the average displacement time series in the two clusters using the method described in Sect. 3.3, with results being depicted in Fig. 10. The overall deformation signal plotted in Fig. 10 does not show a significant correlation with the pattern of precipitation in the region. However, two episodes of accelerations are found in the temporal pattern of deformation in both—the eastern and middle clusters. In ascending Sentinel‑1, the first acceleration occurred on Aug 21, 2019, where the deformation rate increased by 20% and 63% in the east cluster and middle cluster, respectively. The second acceleration occurred on Oct 25, 2021, when the deformation further accelerated by around 4 times and 1.4 times in the east cluster and middle clusters, respectively (see Fig. 10a,b). Two episodes of accelerations also are found in the temporal pattern of deformation in descending Sentinel‑1. The first occurred on October 2, 2019, with deformation accelerating 1.6 times and 2.8 times in the eastern and middle clusters, respectively. The second acceleration occurred on Nov 02, 2021, when the velocities in eastern and middle clusters increased 3.3 times and 1.7 times, respectively (see Fig. 10c,d). These observations align with the findings of Sreejith et al. (Sreejith et al. 2024). However, our findings contrast with those from Shankar et al., who reported an initial rapid acceleration starting in November 2022 (Shankar et al. 2023). ALOS‑2 data was not analyzed here due to a limited number of multi-temporal data acquisitions, which restricts detailed trend analysis.

Fig. 10
figure 10

Pre-failure average displacements time-series for the main clusters: a S1 (Asc), East Cluster; b S1 (Asc), Middle Cluster; c S1 (Des), East Cluster; d S1 (Des), Middle Cluster. Red circles are average values; shaded areas represent standard deviation; black, green and red dashed lines depict piecewise segmentation models. The blue histogram represents daily precipitation, while annual cumulative precipitation is shown in the grey curves. The purple vertical black dotted line marks the date of the flood that occurred on 07 Feb 2019

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Overall, the above analysis suggests that the Joshimath hillslope complex was already experiencing destabilization before the 2023 crisis in the form of very slow-moving displacements. Note that although a flood event occurred in the Rishiganga and Dhauliganga rivers on 7 January 2021, which was triggered by a snow avalanche and rockslide approx. 30 km east and upstream of Joshimath town (Singh et al. 2022; Pandey et al. 2022; Gahalaut et al. 2023), no immediate acceleration response to this event was observed in any of the data analyzed in this study (the flood event is marked in the Fig. 1d). However, more detailed investigations need to be carried out in order to further analyze the possibility for a time lag between flood events and related accelerations in slope deformation.

To better investigate the correlation between changes in displacement rates and precipitation, we applied wavelet analysis to the displacement time-series in vertical and E‑W directions for the clusters and precipitation data, as shown in Fig. 11 and 12, respectively. From the results, no similar continuity at the period of 365 days was found in either XWT or WTC, which indicates that no continuity correlation between seasonal precipitation and changes in deformation trend from Mar.2017 to Nov.2022 in the frequency domain. However, XWT and WTC reveal a common similar continuity at the period of 192 days in both—the vertical and E‑W components—for both—the middle and eastern clusters. The derived wavelet phase angle, as depicted in Fig. 11 and 12, shows an average angle of around 30 degrees. This suggests a positive correlation between precipitation and the displacement time series (east and middle clusters) over a 192-day period, with precipitation leading to these displacements by around 16 days in 2019. The time lag was estimated by the method described in Sect. 3.4. In addition, XWT reveals a high coherence at the period of 356 days during the 2021–2022 period. However, the corresponding exact time lag cannot be reliably determined due to phase arrows that change randomly over time. The possible explanation is that the second acceleration that occurred on Oct.25 2021 is not only triggered by rainfall but maybe also by other factors, such as discharge, groundwater flow, anthropogenic factors, etc. From the wavelet analysis, no annual continuity correlation between precipitation and acceleration was found for the whole observation period with only a 192-day cycle in 2019 and a 365-day cycle during 2021–2022. This possibly indicates that the acceleration during these three years may be influenced to a certain extent by periods of extreme precipitation, while the overall transient behavior in other years showed no correlation at all with rainfall in the frequency domain.

Fig. 11
figure 11

Analysis of E‑W displacement time-series and daily precipitation from March 2017 to December 2022. a Average E‑W displacement time-series for the eastern cluster, with corresponding b XWT and c WTC for correlation analysis with daily precipitation (blue bars in (a)). d Average E‑W displacement time-series for the middle cluster, with corresponding e XWT and f WTC for correlation analysis with daily precipitation (blue bars in (d)). In XWT and WTC, the cross-wavelet power and magnitude-squared coherence are revealed, and the relative time lag and degree of correlation are shown as arrows. A coarse contour at the 5% significance level in comparison to red noise is presented. Edge pseudo-effects outside the cone of influence (COI) might take place. The phase arrows (black arrows) indicate the phase relationship between two time series, where right-pointing arrows signify in-phase, left-pointing arrows denote anti-phase, downward arrows indicate X leading Y by 90 degrees, and upward arrows represent Y leading X by 90 degrees

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Fig. 12
figure 12

Analysis of vertical displacement time-series and daily precipitation from March 2017 to December 2022. a Average vertical displacement time-series for the eastern cluster, with corresponding XWT b and WTC c analysis correlating with daily precipitation. d Average vertical displacement time-series for the middle cluster, with XWT e and WTC f analyses of their correlation with precipitation. In XWT and WTC, the cross-wavelet power and magnitude-squared coherence are revealed, and the relative time lag and degree of correlation are shown as arrows. A coarse contour at the 5% significance level in comparison to red noise is presented. Edge pseudo-effects outside the cone of influence (COI) might take place. The phase arrows (black arrows) indicate the phase relationship between two time series, where right-pointing arrows signify in-phase, left-pointing arrows denote anti-phase, downward arrows indicate X leading Y by 90 degrees, and upward arrows represent Y leading X by 90 degrees

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5.3 Changes in instability kinematics before and after the 2023 crisis

Significant changes in spatial and temporal patterns of instability are observed between pre- and post-crisis, offering important insights into the evolution of deformation kinematics within the Joshimath hillslope complex. All SAR data acquired after the 2023 destabilization crisis allow the derivation of a higher density of measurement points as the basis for analyzing the evolution of post-crisis slope deformation (see Fig. 4 and 6). This increase in density is attributed to the enhanced temporal coherence of the SAR time series within the Joshimath hillslope complex, since the observation period shortened from around 6 years for the pre-crisis period to 1.3 years for the post-crisis period. Moreover, the used TerraSAR‑X data acquired in spotlight mode has a resolution of around 0.9 × 1.2 m in range and azimuth directions, respectively, which helps in maintaining good coherence throughout the time series over moderately vegetated terrain despite the shorter wavelength of the X‑band compared to the C‑band of Sentinel‑1. The specifics of the TerraSAR‑X data enable the retrieval of a significantly increased number of measurement points forming an enhanced basis for effective deformation analysis.

Compared to the long-term deformation kinematics, results derived for the period between Nov.2021 and Dec.2022, for the eastern and middle clusters show significant changes in their respective deformation rates compared to after the crisis. For example, in the eastern cluster, the deformation rate in the Sentinel‑1 ascending data shows a significant decrease of approximately 53.62%, while the middle cluster experiences an increase of approximately 28.51% (see Fig. 7 and 10). On the other hand, the deformation rate in the Sentinel‑1 descending data revealed an increase in the eastern cluster by approximately 13.04%. Meanwhile, the middle cluster showed a substantial increase of approximately 95.35% (see Fig. 7 and Fig. 10). In addition, we found that after the 2023 crisis, the displacement within the middle cluster continued to increase, reaching 1.3 times its previous level from January 2023 to July 2023, before stabilizing thereafter. However, the displacement within the eastern cluster continues to exhibit a linear increase across the whole time series.

The changes in the 2‑D spatial deformation patterns help in gaining a better understanding of the spatiotemporal evolution of the Joshimath hillslope complex before and after the 2023 crisis. Within the eastern cluster, horizontal deformation dominates both—the pre- and post-crisis periods—with E‑W displacements increasing from 65 mm/yr during the pre-crisis period to 100 mm/yr during the post-crisis period(a 54 % increase), while vertical displacements increase from −45 to −75 mm/yr (a 67% increase) between the two periods. For the middle cluster, the pre-crisis velocities are similar in both—vertical and E‑W directions, but in the post-crisis period the vertical deformation dominates with vertical velocities reaching −60 mm/yr, surpassing the E‑W velocities of 40 mm/yr.

6 Conclusions

We developed a methodological framework to investigate spatiotemporal characteristics of slope instabilities within the Joshimath hillslope complex using multi-sensor interferometric measurements from Sentinel‑1, ALOS‑2, and TerraSAR‑X satellites. The long-term multi-temporal InSAR-based deformation analysis for the time period before the destabilization crisis in January 2023 indicates that slope displacement had occurred at Extremely-Slow (ES) and Very-Slow (VS) velocities, at least for more than eight years before the 2023 crisis occurred. Using the K‑means clustering method, we identified two main clusters characterized by active deformation within the hillslope complex, namely the eastern and middle clusters, where deformation occurred at an average rate of −85 and −65 mm/yr, respectively, between Mar.2017 and Dec.2022. InSAR time-series analysis also has revealed two episodes of accelerations in ground displacement derived for August 21, 2019 and November 02, 2021 from Sentinel‑1 observations, both are attributed to periods of extreme rainfall. With the exception of these two extreme events, the overall slope kinematics does not show any dependency on changes in precipitation, which has been revealed by statistical analysis using wavelet transform. Decomposition of multi-temporal InSAR measurements obtained by three different SAR sensors from ascending and descending orbits for a 1.3 year time period after the 2023 destabilization crisis, suggests that in the eastern deformation cluster, horizontal deformation dominates the slope instabilities which increased significantly compared to the pre-crisis period, whereas for the middle cluster, vertical deformation became more dominant during the post-crisis period. These results show that multi-sensor and multi-temporal interferometric measurements derived from satellite-based SAR observations are a powerful tool for analyzing slope deformation with a high degree of spatial and temporal detail. The ese results contribute to a detailed spatiotemporal assessment of changing risks related to the 2023 destabilization crisis. Moreover, they contribute to the reconstruction of the destabilization history within the Joshimath hillslope complex with the goal of developing and implementing measures for mitigating the risk for people living in this intensively used area. Future research should focus on obtaining reliable data on the volume changes of landslides, the geometry of the slip surface and its variations, and the correlation between groundwater level changes and deformations to gain a deeper understanding on the mechanisms of slope instability at Joshimath.