Introduction

Permafrost, an essential climatic variable of the cryosphere, is defined as a layer of soil or rock that remains at or below 0°for at least two consecutive years1,2,3. It covers approximately 25% of the Earth’s land surface4,5. Although the Arctic holds the majority of the area with continuous permafrost landscapes, mountain regions such as the Himalayas and the Qinghai‒Tibet Plateau (QTP) also present significant permafrost6,7. The Himalayan permafrost situated in areas such as Ladakh, Uttarakhand, and Himachal Pradesh is characterized by discontinuous and sporadic patches influenced by steep topography, elevation and microclimatic variations1,8,9,10. These permafrost areas, which are less studied than their arctic counterparts, are crucial for sustaining regional water resources and maintaining ecosystem stability. Previous studies have confirmed the presence of permafrost in the Himalayas via a combination of field surveys and remote sensing techniques11,12,13,14,15,16,17,18,19. The studies have considered active rock glaciers, ice-cored moraines, and talus slopes as geomorphological indicators of permafrost occurrence20.

Permafrost is extremely sensitive to climate change and often considered as a key indicator of shifting climatic conditions21,22,23,24. With rising temperatures and accelerated thawing, permafrost poses a severe threat to Himalayan communities and infrastructure 25,26,27. Recent projections indicate that the increase in permafrost degradation in the region could significantly influence local hydrological and geomorphic changes, such as increased rockfalls, landslides, and ground subsidence28,29,30,31,32,33. Degradation also poses a serious threat to the ecological process; livelihoods of indigenous mountainous community and engineering structures present in the area. Unlike Arctic regions, the permafrost in the Himalayas is highly sensitive to climatic fluctuations due to the relatively low ground ice content and steep gradients, which further increase the region’s vulnerability29,30,34,35,36.

Recent advances in remote sensing technologies, particularly interferometric synthetic aperture radar (InSAR),InSAR have made InSAR of critical importance in monitoring permafrost degradation at global and regional scales37,38,39. The detection of surface deformation associated with permafrost subsidence using InSAR techniques, such as differential interferometric synthetic aperture radar (D-InSAR), persistent scatter InSAR (PS-InSAR), and small baseline subset InSAR (SBAS-InSAR), differ in their capabilities in monitoring permafrost subsidence39,40,41. D-InSAR uses pairs of radar images to measure ground displacement and is usually affected by temporal and spatial decorrelation in areas with dynamic surface changes or dense vegetation42. PS-InSAR addresses some of these limitations by analyzing coherent scatterers such as bridges, buildings or rocks over a time series of radar images43. This technique enhances precision in urban areas or areas with less vegetation but is less effective in rugged terrain and snow mountains, such as those in the Himalayas44,45,46. PS-InSAR is less effective in these areas due to the irregular and sparse distribution of persistent scatterers. Similarly, SBAS-InSAR focuses on minimizing temporal decorrelation by using small temporal and spatial baselines in interferogram generation, making it more suitable for deformation mapping47. However, permafrost degradation is a slow-moving process and is difficult to monitor with pairs of radar images. MT-InSAR has emerged as a key tool for monitoring slow-moving processes such as permafrost subsidence48,49. It integrates long time series of radar images to capture surface deformation more accurately than other methods do.

Recent studies have demonstrated the effectiveness of InSAR in identifying surface deformation in permafrost regions like the QTP and Alaska using data from Envisat, ALOS, TerraSAR-X, and Sentinel-1 satellites50,51,52,53,54,55. Himalayan permafrost is not immune to degradation trends observed by QTP and Alaska. Despite this advancement, the application of MT-InSAR for permafrost degradation monitoring in the Himalayas remains rare. Although several studies have mapped the extent of permafrost over the Himalayas, studies related to permafrost-induced subsidence are relatively scarce. Therefore, to understand permafrost degradation across the Himalayan region, this study utilized MT-InSAR techniques to analyze the spatial and temporal advancement of permafrost degradation-induced subsidence over a Himalayan village. By analyzing climatic variables and local geology, this study aims to provide a comprehensive understanding of the degradation process affecting a village and its surrounding areas.

Study area

Lindur village is situated in the northwestern part of the Lahaul and Spiti districts of Himachal Pradesh (Fig. 1). The village covers an area of 43.09 hectares and is situated at an average elevation of 3328 m from the mean sea level. According to the 2011 census, the village comprises a small village/hamlet in Lahaul Tehsil in Lahaul and Spiti District of Himachal Pradesh, India, and it comes under Gohrma Panchayat. It is located 31 km northwest from District headquarters Keylong and 182 km from the state capital Shimla. In Lindur village, children aged 0–6 years account for 4.17% of the total population, with a total of 3 children in this age group. The village has an average sex ratio of 946, which is below the Himachal Pradesh state average of 972. However, the child sex ratio in Lindur is 2000, compared to the state average of 909. The literacy rate in Lindur village is lower than the state average, standing at 69.57% in 2011, while Himachal Pradesh had a literacy rate of 82.80%. In Lindur, male literacy is 77.78%, whereas female literacy is 60.61%. (Census 2011).

Fig. 1
Fig. 1
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The study area map (a) Himachal Pradesh administrative boundary (b) Elevation map of the Lahaul and Spiti District (Image source: SRTM DEM) (c) Crack Location in Lindur village (Image Source: Sentinel 2 (Data acquisition: 3 November 2023), ESA Copernicus) (This map is generated using ArcGIS Pro 3.2.2, Licensed to School of Civil and Environmental Engineering, IIT Mandi).

The region lies in the rain shadow of the GHR (Great Himalayan Range), resulting in low annual rainfall ranging in between 10 to 40 cm. This makes a dry valley with characteristics of a cold desert. Snowfall in the area varies from less than 1 m to as much as 6 m, with higher altitudes experiencing greater amounts. In winter, the temperature at Keylong ranges from -100 C to + 100 C and in summer, the temperature ranges from 70 to 230C56.

Geology

The study area is situated near the Tandi syncline and Shikar Beh nappe of Haimanta formation that has thick sequence of unmetamorphosed to less metamorphosed sedimentary rocks, from the Precambrian-Cambrian era (Fig. 2). The Tandi Syncline, is a large-scale synformal fold containing Permian to Jurassic Tethyan metasediments, formed during a NE-directed nappe stacking event and characterized by an overturned limb with thrust imbricates57. The Tandi Group represents a sequence of predominantly carbonate rocks that are underlain by chlorite phyllite and overlies Precambrian-Eocambrian Batal Formation of the Haimanta Group58. The Shikar Beh Nappe is the Eocene aged thrusting towards the NE, reaching amphibolite facies conditions in the lower part of the Chandra basin59. The amplitude of the Shikar Beh nappe estimated between the hinge of the Tandi syncline and frontal part located in the Baralacha La region is approximately 50 km, however the frontal part of this nappe has been eroded59,60,61.

Fig. 2
Fig. 2
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(Modified from59).

Geological Map of the NW Himalaya showing the location of Lindur village situated in the Haimanta formation and its tectonic settings

This region is situated between South Tibetan Detachment System (STDS) in the northeast and Main Central Thrust (MCT) in the southwest (Fig. 2). The greenschist to granulite grade metamorphic rocks along with migmatites are situated between the MCT and the STDS throughout the Himalaya. These exposures are separated from the overlying low-grade to unmetamorphosed Tethyan Himalayan Sequence (THS) by segments of the STD system, locally referred to as the Sangla detachment and Zanskar shear zone57.

Data used

In this study, we used ESA Sentinel-1 images for the analysis of deformation pattern and ERA5 data for climatological observation. The C- band interferometric synthetic aperture radar (InSAR) data obtained from the Copernicus Sentinel-1 mission, launched by the European Space Agency (ESA) in 2014. The Data are downloaded from NASA’s Alaska Satellite Facility Data Archive and Communications Center (ASF-DACC). The Interferometric wide (IW) swath mode and VV polarization mode are used in this study. The spatial resolution is 5 m in the range direction and 20 m in the azimuth direction. We downloaded the Sentinel data from April 2022 to September 2023 along the ascending orbit track as proposed by62. Using this dataset, we generated interferometric pairs with 4 nearest acquisitions in time and the highly noisy interferogram was dropped from the analysis. The main sources of data noise in interferogram pairs are vegetation, heavy monsoon and snow cover. However, in our study area the primary correlation noise is due to the thick snow cover during winters. The highest phase noise was observed during the winter season (October–March), and for those interferograms with longer temporal baselines as suggested by62. Considering the high correlation noise during the winter we could not perform the seasonal displacement over the study area. Therefore, we analysed the interferogram covering a time span of seven months, from April 2022 to September 2022 as presented in Table 1.

Table 1 Sentinel 1A imagery acquisition date, orbit, path, and perpendicular base line.
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The study also analyzed climatic influences related to the permafrost degradation over the study area using the ERA5 reanalysis data from the European Centre for Medium-Range Weather forecasts (ECMWF) from 1950 to 2024. ERA5 offers hourly climate variables at 0.250 × 0.250 spatial resolution63. The ground observation daily temperature data at Keylong, Lahaul and Spiti was obtained from October 2022 to October 2023 to validate the ERA5 data. Climatic variables such as temperature and precipitation were used in this study to investigate potential correlations between climatic factors and observed surface deformation.

Methodology

The methodology of this study is broadly divided into four sections (Fig. 3). In the first section, we have collected data from various sources. In the second stage ISCE framework was used to compute the interferogram stack. In third stage the displacement time series map was obtained using time series analysis. Finally in the fourth stage a permafrost probability map is prepared by considering rock glaciers as a proxy for the presence of permafrost and climatological data are used to observe potential correlations with the ground deformation rate.

Fig. 3
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Methodology chart showing the MT-InSAR technique by EZ-InSAR for land deformation map and validation using permafrost probability map, temperature data, precipitation data, and field observations.

Permafrost mapping

To quantify the probability of permafrost occurrence in the selected study area, this study utilized the most effective machine learning model suggested by13. The methodology for mapping permafrost using rock glaciers as proxies through a random forest machine learning model by integrating climatological and topographical variables to map permafrost occurrence. The process begins with the collection of rock glacier inventories generated through onscreen visual interpretation and digitization of rock glacier boundaries. We selected only intact rock glaciers to increase the model performance and probability of permafrost existence. Furthermore, 70% of the rock glaciers were considered in the training samples, and the remaining 30% were considered in the testing samples. Similarly, the key climatological and topographical variables are derived from the available remote sensing data. This study selected eight conditioning factors, such as slope, aspect, elevation, curvature, mean annual land surface temperature (MA-LST), the mean annual normalized difference snow index (MA-NDSI), the mean annual normalized difference water index (MA-NDWI), and lithology, for permafrost mapping. The RF algorithm is a robust and nonlinear ensemble machine learning algorithm trained on labeled datasets to predict permafrost occurrence over the study area. The model’s performance was assessed through the area under the curve (AUC-ROC).

Time series deformation mapping

We used EZ-InSAR, an open-source toolbox for deformation mapping in the study region. The workflow for time series analysis is divided into three different blocks: (i) InSAR data preparation, (ii) ISCE processing, and (iii) time series analysis. These workflow blocks are accessible within the toolbox through three main sections in the user interface. The toolbox comes with a graphical user interface (GUI), has a progress bar for each InSAR processing step and shows the progress status and next steps during the data processing.

InSAR data preparation

Sentinel-1 InSAR data were searched and downloaded using the SAR data preparation module within the EZ-InSAR toolbox. A KML file of the selected study area was exported from Google Earth to define a search zone for the data search. After defining the study area, filtering keywords such as satellite name, path number, satellite direction (ascending or descending), and the desired time span were applied to search the Sentinel-1 SAR archive via the Alaska Satellite Facility (ASF) API. Once the provided data list has been verified, the EZ-InSAR toolbox can automatically download the SAR data. Prior to the interferogram computation, a DEM encompassing the study area was downloaded. For this purpose, the Copernicus 1 arc-second DEM was downloaded from Amazon Web Services in GeoTIFF format, and the spatial resolution of the DEM was 30 m.

ISCE processing

The InSAR Scientific Computing Environment (ISCE) framework developed by the Natural Geohazard Research Group at University College Dublin (UCD) under Eoghan Holohan, was used for interferogram generation and phase unwrapping64,65. The ISCE software package is a hierarchical package that combines shell and python scripts, is specifically designed to perform several tasks related to interferogram generation. These include creating a stack of coregistered SLC images, generating interferogram stacks without phase unwrapping and producing stacks of unwrapped interferograms. The interferometry module of EZ-InSAR provides an option to choose between “SLC stack” or “Unwrapped interferogram stack”, depending on the user requirements, whether the user wants to perform the time series analysis via the StaMPS or MintPy time series processor. In this study, we selected the Unwrapped Interferogram stack option for time series analysis in the MintPy processor. EZ_InSAR provides eleven steps to generate the unwrapped interferogram. The steps are unpack_topo_reference, unpack_secondary_slc, average_basline, fullBirst_geo2rdr, fullBurst_resample, extract_stack_valid_region, merge_reference_secondary_slc, generate_burst_igram, merge_burst_igram, filter_coherence and unwrap.

SBAS time series analysis

The workflow for InSAR time series analysis in this study follows the Miami InSAR time series software in Python (MintPy) approach to covert unwrapped interferogram stacks into displacement time series66. This workflow consists of two main stages: (i) correcting unwrapping errors and inverting the raw phase time series and (ii) adjusting for phase contributions from various sources to derive the displacement time series. The process begins with initializing the MintPy processor for time series analysis. The phase-unwrapped interferograms generated by the ISCE framework are registered to a common SAR acquisition for Earth curvature and topographic corrections. To address outliers caused by unwrapping errors in coherent pixels, a network modification step is employed as an optional feature in MintPy. This step eliminates interferograms with spatially averaged coherence values below a predefined threshold value. Although the processor provides other approaches for network modifications, such as thresholds for temporal and spatial baselines, the maximum number of connections per acquisition and the exclusion of precise interferograms from a particular acquisition. Similarly, the reference point was selected on the basis of the conditions suggested by66. The reference point is situated in an area based on prior field verification and following three conditions: the point should be in a coherent area, in an area with low atmospheric disturbance and at the same elevation as the area of interest.

Furthermore, to ensure temporal consistency in a redundant interferogram network, the integer ambiguities of unwrapped interferometric phases can be mathematically represented for each pixel as follows66:

$$CU+\left(C\Delta \varnothing -wrap\left(C\Delta \varnothing \right)\right)/(2\pi ) =0$$
(1)

Here, C is a T × M design matrix that accounts for all possible interferogram triplets, and U is the M × 1 vector representing the integer cycle numbers necessary for maintain phase consistency. where \(\Delta \varnothing\) denotes the unwrapped interferometric phase and wrap is the operation used to wrap the phase to its principal value within [-π, π]. This equation can sometimes be ill-posed when T < M (fewer triplets than interferograms), meaning that a unique solution is not guaranteed. Regularization techniques are employed to overcome this limitation, favoring solutions that are both sparse and small in magnitude. This approach utilized least squares optimization, commonly known as the least absolute shrinkage and selection operator (LASSO). The LASSO optimization objective function is expressed as follows:

$$\widehat{U}=argmin\parallel CU+C\Delta \varnothing -wrap(C\Delta \varnothing ))/(2\pi ){\parallel }_{2}+\alpha \parallel U{\parallel }_{1}$$
(2)

where the α regularization parameter and α = 0.01, determined through simulation or empirical testing, balance the trade-off between the L1 and L2-norm terms.

After solving for \(\widehat{U}\), the corrected unwrapped interferometric phase is computed as:

$$\Delta {\varnothing }_{c}=\Delta \varnothing +2\pi .round(\widehat{U})$$
(3)

Here, the round operator rounds \(\widehat{U}\) to the nearest integer, ensuring consistency in the phase data. The methods improve the efficiency of phase unwrapping by mitigating inconsistencies, specifically in areas with sparse coherence and following advanced regularization approaches67. Similarly, the raw phase time series is determined by minimizing the residual interferometric phase \(\Delta {\varphi }_{\varepsilon }\). The temporal coherence \({\gamma }_{temp}\) is subsequently calculated via the following equation68:

$${\gamma }_{temp}=\frac{1}{M}|{H}^{T}\text{exp}[j(\Delta \varphi -A\widehat{\varphi }]|$$
(4)

Here, j represents the imaginary unit, and H is an M × 1 column vector filled with one. A denotes a threshold for temporal coherence, which is applied to identify pixels suitable for reliable network inversion. The coherence threshold was iteratively varied between 0.4 and 0.7 to obtain the most optimal value. We observe that when the value is less than 0.7 there was high noise in temporal coherence near the river valley. Therefore, we kept the coherence threshold of 0.7 to get the reliable pixel. The location of reference point with the geo temporal coherence value show in the supplementary fig. S1.

Tropospheric delay correction was conducted using global atmospheric models (GAMs). The relative double path tropospheric delay at \({t}_{i}\) between a specific pixel p and a reference pixel is expressed as follows:

$${\widehat{{\varphi }^{i}}}_{tropo}\left(p\right)=\left(\delta {L}_{p}^{i}-\delta {L}_{p}^{1}\right)\frac{4\pi }{\lambda }-\left(\delta {L}_{ref}^{i}-\delta {L}_{ref}^{1}\right)\frac{4\pi }{\lambda }$$
(5)

Here, i \(\epsilon\) [1…N], \(\delta {L}_{x}^{i}\) represents the integrated absolute single path tropospheric delay at \({t}_{i}\) for pixel x in meters, measured in the satellite line-of sight (LOS) direction (with \(\delta {L}_{p}^{1}\) for \({t}_{1}\)), and \(\lambda\) is the radar wavelength in meters. Climatic datasets such as ERA-5 and ERA-Interim from ECM-EWF, NARR from NOAA and MRRA from NASA were utilized via PyAPS software69,70.

The topographic phase residual due to DEM errors is estimated on the basis of its proportional relationship with the temporal baseline over time71. Traditional methods typically employ a cubic temporal deformation model, which is unable to accurately capture high-frequency displacement signals caused by events such as earthquakes, volcanic eruptions and landslides. To address this limitation, Yunjun et al.66 included step functions, following the method provided by72, allowing for permanent displacement offsets and general polynomial modeling with a user-defined polynomial order (\({N}_{poly})\). The DEM error (\({z}_{\varepsilon })\) for each pixel is modeled as:

$${\widehat{\varphi }}^{i}-{{\widehat{\varphi }}^{i}}_{tropo}=\left(\frac{{B}_{\perp }^{i}}{rsin\left(\theta \right)}{z}_{\varepsilon }+\sum_{k=0}^{{N}_{poly}}{c}_{k}{\left({t}_{i}-{t}_{1}\right)}^{k}/k!+\sum_{l\epsilon {I}_{s}}{s}_{l}H\left({t}_{i}-{t}_{l}\right)\right)\frac{-4\pi }{\lambda }+{\varphi }_{resid}^{i}$$
(6)

where i \(\epsilon\) [1, …N], \({B}_{\perp }^{i}\) is the perpendicular baseline at time \({t}_{i}\) relative to the reference time \({t}_{1}\). r is the slant range, and \(\theta\) is the incidence angle. H (\({t}_{i}-{t}_{l})\) is a Heaviside step function centered at specific times \({t}_{l}\), corresponding to displacement jumps. \({z}_{\varepsilon }\), \({c}_{k}\) and \({s}_{l}\) are unknown parameters determined by minimizing the \({L}^{2}\) norm of the residual phase time series \({\varphi }_{resid}={[{\varphi }_{resid}^{1}, \dots , {\varphi }_{resid}^{N} ] }^{T}\). Examples of design matrices and numerical solutions using least square estimation are provided in the supplementary section of66.

Furthermore, the residual phase \({(\widehat{\varphi }}_{resid})\) derived from the DEM error equation as a byproduct serves as an indicator of the noise level in the InSAR time series. The noise level for each SAR acquisition is quantified by computing the root mean square (RMS) of the residual phase, expressed as:

$${RMS}^{i}=\sqrt{\frac{1}{{N}_{\Omega }}\sum_{p\epsilon\Omega }{\left({{\widehat{\varphi }}^{i}}_{resid}\left(p\right).\frac{\lambda }{-4\pi }\right)}^{2}}$$
(7)

where i = [1, …, N], which represents the SAR acquisition index. where \({{\widehat{\varphi }}^{i}}_{resid}\left(p\right)\) is the residual phase for pixel p at time \({t}_{i}\). \(\Omega\) is a set of reliable pixels chosen based on temporal coherence during the network inversion process. \({N}_{\Omega }\) is the total number of reliable pixels in \(\Omega\). \(\lambda\) is the radar wavelength. Since long-wavelength phase components in \({{\widehat{\varphi }}^{i}}_{resid}\) are typically difficult to assess precisely, noise evaluation focuses on short-wavelength phase variation66. To isolate short wavelength noise, a quadratic phase ramp is removed from the residual phase of each acquisition before calculating the Root Mean Square Error (RMSE)66,73,74. After calculating the RMSE, we excluded the noisy SAR data and selected the best optimal reference date. Furthermore, the average velocity v is calculated as the slope of the best fitting line to the displacement time series using the equation \({\varphi }_{dis}^{i}.\frac{\lambda }{-4\pi }=v.{t}_{i}+c, i=1,\dots ., N\), where c is an unknown offset constant.

ERA-5 analysis

The ERA-5 reanalysis datasets were obtained from the ECMWF75. These datasets were utilized to analyze the temperature and precipitation trends in the study area. The focus was on understanding how air temperature and precipitation patterns along with their combined effects contribute to crack formation. We used ERA5-Land Daily Aggregated data, which has a spatial resolution of 11 km and spans from 1950 to 2024, to produce time series plots for temperature and precipitation. To understand the historical trends, this study used the Mann‒Kendall test, linear regression and Theil‒Sen analysis76,77,78,80.

Results

InSAR deformation

Using the MT-InSAR technique, we obtained the surface deformation area in the selected study region. The displacement results span from April 2022 to September 2022. The observed ground movement velocities are shown in Fig. 4a. The velocity map highlights the region with significant surface movement, expressed in centimeter per year (cm/year). The velocity map clearly indicates substantial surface displacement of 7.914 cm/year in the toe region of the elongated rock glacier present in that area. The negative velocity values indicate movement toward the sensor (i.e., uplift), and positive values indicate movement away from the sensor (i.e., subsidence). The subsidence area is most likely linked with the thawing of permafrost or soil compaction due to the melting of underground ice. In contrast to the subsidence area, the neighboring area experiences surface displacement close to zero. The transection line from the top of the rock glacier to the reiver showing an increasing subsidence rate from 0 to 7.914 cm/ year (Fig. 4b). Furthermore, the standard deviation map (Fig. S2a) quantifies the reliability of the measurements, showing higher uncertainties of 0.02 m/year. Uncertain areas are present along the river valley and areas with steep terrain, which is caused mainly by low radar signal coherence. Lindur village, which is situated in a region with lower standard deviation values, has robust and reliable displacement estimates.

Fig. 4
Fig. 4
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(a) Map showing the observed permafrost deformation rates in cm/year. (b) Displacement rate variation along the transection line extending form the rock glacier to the river.

The intercept map representing the initial displacement values at the start of the observation period shows minor variation ranging from approximately -0.02 to 0.01 m (Fig. S2b). The residual map represents signal noise after applying the linear model to the time series data, revealing that the residue is less than -0.01 m, which indicates that the linear model effectively captures the deformation trends (Fig. S2c). Similarly, the obtained intercept value map reveals low uncertainties (< 0.003 m) across most of the study area (Fig. S2d). The highest intercept value was observed in the area where the velocity was at its maximum. Furthermore, the spatiotemporal evolution of deformation patterns across the village is shown in Fig. 5. The time series map shows that the displacement rapidly increases from the summer season until the beginning of winter, indicating that subsidence is attributed to the thawing of permafrost during the summer season.

Fig. 5
Fig. 5
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Displacement time series observed form April 2022 to September 2022 over the study area, showing temporal variation in surface movement.

Permafrost area

The permafrost probability map for the study area was prepared via the random forest (RF) machine learning method. The obtained probability values of permafrost occurrence were further divided into three classes, namely, low, moderate, and high, on the basis of the natural break classification (Fig. 6b). The map shows that areas with elevations greater than 3800 have a probability of permafrost occurrence. There is very little permafrost in the habitat region of the village. Similarly, the agricultural area and the NE region of the village have the highest probability of permafrost occurrence. On the other hand, as we considered rock glaciers as proxies for permafrost presence, the results revealed very high permafrost occurrence over rock glaciers and adjacent areas. The evaluation of the model for permafrost modeling over the study region revealed an AUC-ROC score of 0.93. Furthermore, the high probability zone of permafrost area was compared with the land deformation map and found that the high probability zone are associated with the high deformation zones (Fig. 6a).

Fig. 6
Fig. 6
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(a) Map showing Land deformation rate (cm/year) over Lindur village and nearby area, black boxes representing significant deformation regions (i) Lindur village (ii) Rock glacier (iii) Talus slope with high permafrost probability (iv) area with moderate permafrost probability. Rock glacier boundaries are shown in red colour. (b) Permafrost probability map with low, moderate, and high probability of permafrost. The black boxes represent deformation areas with a significant deformation rate that gives a spatial relationship between deformation and permafrost occurrence.

Climatological observations

Lindur village is located in a remote region devoid of an operational weather station. The nearest weather station is situated in Keylong around 30 km away from the study area. The ground observation daily temperature data could only be obtained for one year i.e. from October 2022 to 2023. Due to short temporal availability of ground observation data ERA5 data was used to analyze the temperature and precipitation trend over the region. Before carrying out the detailed analysis of ERA5 data, it was validated from the ground observation data. It was observed that the coefficient of determination between the ERA-5 data and the observed data having 357 data points was 0.82 which indicates a strong correlation. Furthermore, the root mean square error (RMSE) and mean absolute error (MAE) were calculated as 4.15 and 3.17 °C, respectively (Fig. 7a,b). It is interesting to observe that ERA5 tends to underestimate the actual temperature data, but it follows a similar trend as that of observed data. Hence for long term temperature variation analysis ERA5 data was used.

Fig. 7
Fig. 7
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Comparison of observed and ERA5 temperature data. (a) Time series of observed (blue line) and ERA5 (orange line) temperature (°C) from October 2022 to December 2023. (b) Scatter plot of observed versus ERA5 temperature (°C), with a regression line (red) fitted to the data.

Upon analyzing the annual average air temperature trend along with its 10-year rolling average trend line, it is evident that the air temperature has steadily increased over time. In 1950, the annual average air temperature was −8.40 °C, and by 2024, it had risen to −5.87 °C. We also examined both the annual average precipitation trend and the annual accumulated precipitation trend, as shown in Fig. 8a,b. In 1950, the average precipitation was 5 mm, and the accumulated precipitation was 1840 mm. By 2024, the average precipitation had decreased to 3 mm, and the accumulated precipitation had decreased to 1110 mm. Figure 8 reveals that while the air temperature has shown a consistent upward trend, precipitation has followed a cyclic pattern. Initially, the air temperature and precipitation were inversely related, and the precipitation decreased as the air temperature increased. Later, both precipitation and air temperature increased for a period, followed by a decline in both variables. In the last decade, the trend has shown that air temperature has continued to rise, whereas precipitation has continued to decrease.

Fig. 8
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Plot showing the trends of (a) Annual average air temperature (°C) and annual average precipitation (mm) from 1950 to 2024, along with their 10-year rolling average trend lines. (b) Annual average air temperature (°C) and annual accumulated precipitation (mm) from 1950 to 2024, along with their 10-year rolling average trend lines.

For the annual average air temperature, the Mann‒Kendall test indicates a significant positive trend with a statistic of 0.36 and a very small p value (0.00), confirming that the trend is statistically significant, as shown in Table 2. The linear regression analysis revealed a positive slope of 0.02, indicating that the air temperature increased by approximately 0.02 °C per year, with a p value of 0.00, further confirming the significance of this increase. The R-squared value of 0.30 means that approximately 30% of the variation in air temperature is explained by time. Additionally, the Theil–Sen analysis reveals a smaller positive slope of 0.02, corresponding to a decadal rate of + 0.18 °C per decade, reinforcing the conclusion that air temperature increases over time. In contrast, the annual average precipitation showed no significant trend (Table 2). The Mann‒Kendall test yields a statistic of −0.14 and a p value of 0.12, which suggests a very weak negative trend, but it is not statistically significant. Similarly, the linear regression reveals a slight negative slope of −0.01, but with a p value of 0.09, this decrease is not statistically significant. The Theil-Sen analysis reveals an extremely small negative slope of 0.00 and a decadal rate of −0.00 mm per decade, which is practically negligible, indicating no meaningful change in the annual average precipitation. For annual accumulated precipitation, the Mann‒Kendall test yields a statistic of −0.06 and a p value of 0.46, further suggesting that there is no significant trend. The linear regression shows a negative slope of −1.19, indicating a small decrease in accumulated precipitation, but the p value (0.28) indicates that this trend is not statistically significant. The Theil-Sen analysis reveals a negative slope of -0.88 with a decadal rate of -8.85 mm per decade, suggesting a slight but insignificant decrease in accumulated precipitation over time.

Table 2 Statistical significance analysis of the annual average air temperature, annual average precipitation and annual accumulated precipitation trends was performed via the Mann‒Kendall test, linear regression and Theil‒Sen analysis.
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Field observations

During the field traverse, several indicators of ground instability in the form of cracks were observed across the study area. We observed the orientation of the beds are towards the riverbed and sub surface ice melting water flowing to the Jahlma nala river (Fig. 9a,b). Significant numbers of cracks were observed in the agricultural field, on the wall of houses, floor of the houses, across rock glacier, and along the slope indicating a substantial surface movement (Fig. 9c–e). The cracks are also present in residential buildings in horizontal, vertical and diagonal patterns, indicating structural stress. The crack clearly extends over a considerable length and varies in width, indicating a complex interplay of geological forces. The crack follows the natural contours along the rooting line of the rock glacier in both elevated and relatively flat terrain. Field measurements suggest that the depth and width of the crack are greater in the northern direction than in the southern direction. The village and its surrounding terrain are situated on loose, unsorted debris material supported by a clay matrix derived from the glacier present above the village (Fig. 9a). The soft composition of the sediments forming the hillslopes renders them susceptible to swift soil erosion, especially during intense rainfall events. Additionally, displaced fences and numerous drunken trees were found, with the tilt generally oriented in the southwest direction. The drunken tree, loose talus derived soil and rock glacier indicating the presence of permafrost in the region (Fig. 9f). After following the major cracks present in the village area, it was observed that the major crack has subsequent parallel smaller cracks.

Fig. 9
Fig. 9
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Field photographs showing the local geology and cracks (a) Slate bed orientation along the slope gradient (b) Subsurface ice melt water stream (c) Crack present across the rock glacier in NE direction of the village (d) Vertical cracks on the wall of a house (e) NNE-SSW trending transverse cracks observed in agricultural field (f) Drunken tree present on the slope.

Discussion

Permafrost-induced land subsidence is a critical consequence of climate change and is driven by the thawing of ground ice. In recent decades, there has been a significant rise in global temperature, which is a severe concern for permafrost present in high-latitude regions. On the Tibetan Plateau, several studies have reported land degradation due to permafrost degradation39,52,54. Similarly, via GPS interferometry81 reported significant interannual variations in surface deformation within the permafrost region of Alaska. Recently, in the Indian Himalayas, several studies reported that catastrophic events occurred in the Chamoli district of Uttarakhand in February 2021 with the degradation of permafrost14,82. However, there is no such study available in the Indian Himalayas that aims to understand the permafrost aspects of land subsidence and slope instability.

In this study, we used multitemporal interferometric synthetic aperture radar (MTInSAR) techniques to analyze the spatial and temporal evolution of ground subsidence in Lindur village of Himachal Pradesh caused by the degradation of permafrost in this region. The use of MTInSAR has proven to be a well-established method for monitoring the slow movement of ground. By leveraging radar imagery over extended periods, this method enables the detection of subtle deformation patterns with millimeter- to centimeter-scale accuracy. Thaw-induced subsidence is largely governed by thermal degradation and hydrological changes. Rising temperatures lead to increased soil moisture, and deeper thaw depths exacerbate subsidence. The results revealed that the village experienced a high rate of land subsidence, as shown in the map, and the subsidence rate was greater than 7.9 cm/yr in the northeastern direction of the village. Similar subsidence rates are observed in areas where the permafrost occurrence probability is high. Furthermore, we observed that there is a correlation between the air temperature and cumulative displacement (Fig. 10). The cumulative displacement is increasing when the temperature is increasing.

Fig. 10
Fig. 10
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Showing the displacement rate, cimulative displacement and air temperature from 04/04/2022 to 07/09/2022 over the rock glacier.

Field observations revealed that the exposed outcrop of slate beds was oriented along the slope gradient. The alignment of beds in the direction of slopes generates a slip surface, indicating a geological setting conducive to mass wasting processes such as subsidence and landslides. The joints present in the rock create a zone of weakness within the slate beds, which reduces cohesion and increases rock susceptibility to subsidence and landslides. The glacier melt water, seepage from irrigation channels and monsoon rain contribute to the surface tension crack. Surface tension cracks are developed during the dry period after a prolonged freeze and thaw cycle. Additionally, tectonic movements in the Himalayas might influence the land subsidence in the region. Lots of papers are carried out in the eastern part of the Himalaya, mainly focusing on Manipur, Arunachal and Sikkim, in addition to eastern Tibet83,84,85,86. However, such movements are not constrained in the Himachal section. The observation stations are mainly situated below the MCT line, and our study region is situated above the line. The eastern Himalayas is moving at a higher rate with a velocity of 20 mm/yr, whereas the western Himalayas is moving at a slower rate of 10 mm/yr 87. Reference88 also reported that the GPS velocity in the Zanskar Valley was observed at a rate of 4 mm/yr. Considering the tectonic movement, micro earthquake data reported by GSI from 1900 to 2023 within the 50 km radius of the Lindur village, it was observed that 1 larger earthquake (> M 7), 2 moderate earthquakes (> M 5), and 33 small earthquakes (5 > M > 3) have occurred in the region. Additionally, the well-known devastating Kangra earthquake of 1905 occurred around 75 km (aerial distance) away from the site in the SW direction. Also, there is no major active thrust passing near the study area and this region is situated on the southern side of STDS (South Tibetan Detachment System) on the High Himalayan slab. Metamorphism in the High Himalayan Slab, where the study area is located, is widely interpreted as the result of a regional Barrovian-type event that refers to the classic concept of progressive metamorphism under moderate pressure–temperature (P–T) conditions. It is typically associated with significant crustal shortening and thickening in the continental- continental collision orogeny, following the initial collision between the Indian and Asian plates around 54–50 Ma89,90,91. The earliest episode of crustal thickening that has been documented is the emplacement of the Shikar Beh antiformal nappe, which is also associated with the creation of the Tandi syncline60,92,93. This crustal thickening ended at 30–29 Ma as per the Monazite and garnet geochronology data61,91. Afterwards the cooling of the Higher Himalayan crystalline in this area happened between ~ 26–20 Ma (muscovite Rb–Sr and 40Ar/39Ar ages) and ~ 18–10 Ma (biotite 40Ar/39Ar and Rb–Sr ages) (Schlup et al., 201159,61).

The STDS, located in the northern margin of the Higher Himalayan Sequence (HHS) in the Himalaya is a ductile to brittle shear zone that dips top-to-the-northeast-down along the northern margin of the Higher Himalayan Sequence (HHS) in the Himalaya (57,94, Searle, 201095,96,97). Further, the STDS evolved as a proto-tectonic terrane boundary, that grew from the latest Neoproterozoic to uppermost Cretaceous in the Tethyan Basin thus accumulating around 10 km thick sediments. The fault system was reactivated during the Cenozoic, followed by the continuous movement from the earliest Miocene (23.68 ± 0.94 Ma) to abruptly ceasing in early Middle Miocene (13.30 ± 0.30 Ma) for nearly 10 myr95. This indicates that the activity along the STDS has ceased in the Neogene and the quaternary period. Thus, it seems that the effect of neo-tectonic movement in the deformation observed in this location seems very less.

The relationship between climate change and permafrost degradation is a critical process with widespread environmental and societal impacts. Climate change, driven by rising global temperatures causes permafrost to thaw. As temperature increases the active layer of permafrost thaw, and deeper frozen layers begin to melt leading to land degradation98. This degradation leads to significant landscape change including land subsidence and slope instability99. To understand the impact of local climatic conditions over the years, this study utilized temperature and precipitation data obtained from ERA-5. The analysis revealed that the annual temperature in the study area is rising at a rate of 0.02 °C/year. Although precipitation also showed a decreasing trend, the rate of decline was not statistically significant. Similar findings regarding temperature increases were reported by100. In a related study101 found a significant decrease in annual average snowfall in Keylong and Udaipur, with rates of 11.1 cm/yr and 5.3 cm/year, respectively, from 1982 to 2017 and 1975–2016. They also reported a slight increase in average annual temperature at a rate of 0.0006 °C per year. The rise in temperature and decrease in precipitation in the form of snow and rain are the primary reasons for the permafrost thaw and melting of ground ice leading to ground subsidence in this region. Furthermore, as precipitation is most prominent during the monsoon season in the Indian Himalayas, which lasts from June to the end of September, we analyzed the monthly average precipitation trends for June, July, August, and September (Fig. S3). Similarly, we examined the monthly average air temperature trends for the same months (Fig. S4). Both figures visualize the 4-year and 10-year rolling average trends for precipitation and air temperature, providing a clearer picture of the short term and long-term patterns in these variables. Precipitation trends reveal a clear and statistically significant increase in June, suggesting more rainfall at the start of the monsoon season. However, July to September does not show significant trends in precipitation (Fig. S3). Air temperature trends show consistent and significant warming during June, July, and August, indicating a rise in temperature during the monsoon months, whereas September shows no significant increase (Fig. S4), suggesting stabilization at the end of the monsoon.

Conclusion

In this study, we analyzed the cause of land subsidence in Lindur village of Himachal Pradesh. For this purpose, we use the SBAS-InSAR technique with Sentinel-1A images from April 2022 to September 2022. The results revealed significant subsidence rates ranging from −6.8 cm/year to 7.9 cm/year. High subsidence areas are dominated by areas where the probability of permafrost occurrence is high, conversely the negative deformation rates in high-elevation regions indicate snow accumulation. The cumulative displacement over the seven months was 16 cm, showing a significant land deformation in the region. From the observation of the deformation pattern and its association, it is evident that the area proxies to permafrost such as rock glaciers and talus slope have a high value of deformation rate indicating the degradation of permafrost in the study area.

Furthermore, the study depicted that a combination of climatic and geological factors influences land subsidence in Lindur village. The analysis of the ERA-5 temperature and precipitation data revealed a significant increase in the annual temperature at a rate of 0.02 °C per year. Similarly, a reduction in snow accumulation in winters and increase in monsoon precipitation was over the region. The rise in temperatures leads to the melting of permafrost is a primary reason for subsidence. Increase rain fall in monsoon exacerbates permafrost melting due to its higher thermal conductivity and percolation of water to the ground. Moreover, field observations indicated that the slate beds are orientated along the gradient slope, jointed rock formations and rock glacier movement further accelerated the ground deformation and slope instability.

This study highlights the importance of more detailed studies into the interaction of climatic, geological and hydrological factors that drive permafrost thaw and land subsidence in the Indian Himalayas. The quantified deformation rates and identified vulnerable areas provide crucial information for developing targeted mitigation strategies and early warning systems. Finally, these measures can contribute to improved disaster preparedness and risk management for the residents of mountainous regions.

Limitations and future scope

This study provides a comprehensive understanding into permafrost melt-induced subsidence in the study region despite over limitations. One of the primary limitations of the study is that it is considered only a single season from April to September 2022. This restricts the analysis of seasonal variations in permafrost melt-induced subsidence. The decision to consider only a single seasonal variation is due to the limited ground penetration capability of C-band SAR data. C-band SAR data has shorter wavelengths and limited penetration ability through snow reduces the temporal coherence. This limitation affects the accuracy of deformation measurements85,86,102. Another limitation is the absence of below-ground temperature data over the study region and the absence of subsurface validation, such as the use of ground penetrating radar (GPR). The use of ground observation data and the use of the GRP could increase the reliability of deformation mapping by providing critical subsurface insights.

To address these limitations, future research in the Himalayas should focus on multiple seasonal and interannual analyses to provide a comprehensive understanding of how permafrost melts and how subsidence evolves over time. The incorporation of L-band SAR data would help overcome penetration challenges during snow cover periods and enhance deformation mapping accuracy. Additionally, integrating GPR and below-ground temperatures can provide critical validation of SAR-based observations.