GAM-STTD: a spatiotemporal tropospheric delay correction model for time-series InSAR in complex mountainous regions

Slow-moving landslides are an important erosional geomorphic process that shape hillslopes and transport large amounts of sediment material to river channels. They may have potentially catastrophic consequences for infrastructure and human life. Identifying the spatiotemporal pattern of hillslope deformation is essential for understanding the kinematic evolution of hillslope failure and mitigating associated hazards. InSAR (Interferometric Synthetic Aperture Radar) is an effective geodetic method for mapping landslide deformation with high spatiotemporal resolution and precision, especially where direct access to the hillslope areas is difficult.The study area in the south-central Andes is characterized by steep climatic and topographic gradients. The low-elevation eastern foreland areas with dense vegetation cover change to semi-arid and arid, near-vegetation-free high-elevation areas. InSAR phase estimation and landslide mapping in such a complex region can be affected by spatial and temporal variations of soil moisture, vegetation cover, and atmospheric regime.  In this study, we extract InSAR time series from the C-band ascending and descending track of Sentinel-1A/B data acquired between 2014 and 2022 and the L-band ascending track of ALOS1 PALSAR data acquired between 2006 and 2011 in the south-central Andes of northwest Argentina. We compare Sentinel deformation time series and maps derived from the linear small baseline subset technique with different numbers of connections in sequential interferogram formation with non-linear phase inversion techniques. We assess the phase bias contribution of short-temporal baseline interferograms for the time series analysis and propose several correction techniques tailored to this study area. Statistical and weather based models are used to reduce the impact of tropospheric delay on the deformation signal, especially during convective events controlled by the South American Monsoon and the large fluctuation of topographic relief effects on the tropospheric phase delay. We investigate the difference between tropospheric correction methods. We further implement a double-difference filter with different local and regional spatial filters to reduce the tropospheric delay on the InSAR time series. After additional filtering steps to remove further ionospheric noise in the time series, we identify the landslide spatial extent and their dynamic through spatial analyses.  Our results reveal multiple landslides, including three transitional bodies with downslope velocities of 5-10 cm/yr that demonstrate the importance of carefully filtering InSAR time series for slow-moving landslide detection.  

Slow-moving landslides in high-mountain regions pose a significant natural hazard and are capable of delivering large sediment volumes to the fluvial system. Time series analysis of Interferometric Synthetic Aperture Radar (InSAR) allows us to identify unstable and potentially dangerous areas prone to landsliding, but this technique also helps quantify seasonal dynamics for predicting landslide behavior.Our study in the Eastern Cordillera of the Argentine Andes focuses on enhancing InSAR's reliability for landslide mapping. This region is characterized by moisture changes along the topographic gradient across the orogen and seasonal variability associated with the South American Summer Monsoon. We extract InSAR time series data from Sentinel-1A/B's C-band (2014-2022) and ALOS1 PALSAR's L-band (2006-2011). Tropospheric delay is caused by atmospheric turbulence and vertical stratification changes. These delays can introduce significant errors in deformation measurements, thus impacting the quality of maps portraying landslide deformation rates. To address this problem, we apply various correction techniques, ranging from spatial and temporal filtering to water-vapor estimation from an atmospheric model. Fading signal noise, another challenge caused by multi-looking and short temporal baselines in the Small Baseline Subset (SBAS) technique, additionally compromises InSAR time series accuracy. We investigate the pattern and magnitude of fading signals in landslide areas using Small Baseline Subset (SBAS) with different neighboring connections and non-linear phase inversion methods, such as the Eigenvalue Decomposition-based Maximum Likelihood (EMI), Eigenvalue Decomposition (EVD), and the Phase Triangulation Algorithm (PTA).Our research evaluates both statistical methods and Global Atmospheric Models for correcting tropospheric delays and fading signal noise. We explore statistical methods, such as double-difference filtering and corrections based on phase elevation, for different spatial windows, including individual catchments, moving windows, and adaptive window sizes. The efficiency of these methods varies with the environmental and topographic conditions in the orogen. Both stratified and turbulent components of the troposphere, along with fading signal noise, can significantly influence tropospheric delay and time series quality. In the context of the factors that influence deformation signals and the combined array of methods to obtain robust measurements, we can identify the spatial and temporal characteristics of slow-moving landslides and assess the different impacts on rate changes.

Glacier retreats, along with associated geomorphological and periglacial processes, can significantly impact hiking infrastructure and have consequences for the local tourism industry, which heavily depends on high-altitude mountaineering. Interferometric Synthetic Aperture Radar (InSAR) time-series techniques, such as the Small Baseline Subset (SBAS) method, have gained considerable attention for analysing surface deformation and slope instability. InSAR utilises phase information to measure time-series surface deformations with sub-centimetre accuracy.The primary objective of this study is to identify and measure surface deformation and slope instability using InSAR, and to investigate the potential impacts on selected alpine huts in high mountain regions in Austria. We use time-series Sentinel-1 data and open-source software, including the InSAR Scientific Computing Environment (ISCE) tool for SAR data processing and the Miami InSAR Time-series software in PYthon (Mintpy) for SBAS analysis. By integrating the InSAR results, slope units derived from a high-resolution digital elevation model (DEM), and alpine infrastructure locations, we identify areas showing significant deformation rates. The initial results provide insights into the slope instabilities and surface deformation that may affect alpine infrastructure. The results highlight the potential of advanced InSAR time-series analysis for monitoring surface deformation in highly dynamic alpine landscapes, where increasing natural hazards, such as landslides, necessitate improved natural hazard and risk management. Future steps include discussion and validation of the results in collaboration with experts from alpine associations.

Time-series InSAR ground deformation monitoring: Atmospheric delay modeling and estimating

<p>Tropospheric delays are the main source of error when measuring ground displacements using InSAR. Increasingly, global atmospheric models (GAMs), e.g., ERA5 and MERRA2 reanalysis data, are used to reduce tropospheric signals in InSAR deformation observations. However, due to the coarse spatial resolution of current GAMs (~10s of kilometers), it is still challenging to obtain tropospheric corrections for high-resolution InSAR data (~10s of meters). Here we present an advanced GAM-based correction method, aimed at improving InSAR geodesy, that incorporates spatial stochastic models of the troposphere in the corrections. We first estimate stochastic models of the tropospheric parameters (temperature, pressure, and partial pressure of water vapor) at different GAM altitude layers and we then interpolate the parameters according to the correlation between pixels of interest and the GAM grid locations (3D). The interpolation accounts for spatial variabilities of the tropospheric random field, instead of subjectively using an inverse distance method or using a local spline function, which are commonly used in current GAM-correction methods. We also estimate the integral of the tropospheric delays along the satellite line-of-sight (LOS) direction directly, instead of calculating the projected zenith-delays, because the troposphere is not purely stratified. Our new method can easily be applied using any of the present GAMs; here we implemented it with the latest ECMWF ERA5 reanalysis outputs. We validate the new method for both interferograms and time-series analysis products (deformation velocities and time-series solutions), using hundreds of the Sentinel-1 images over the island of Hawaii from 2015 to 2020. The results show that the average standard deviation of non-deforming interferograms reduces from 2.55 cm to 1.91 cm when applying the new method, compared with standard deviations of 2.47 cm (PyAPS), 2.44 cm (d-LOS), and 2.10 cm (GACOS), after using three common GAM correction methods. In addition, the new method improves most (87%, i.e., 243 out of 280) of the interferograms, while only about half (52%, 53%, and 66%) are improved by the earlier correction methods. The results demonstrate the importance of considering (1) tropospheric stochastic models in GAM-corrections, (2) horizontal heterogeneities when estimating the LOS delays, and (3) tropospheric delays when mapping long-wavelength or small-magnitude deformation using InSAR.</p>

Using interferometric synthetic aperture radar (InSAR) to observe slow ground deformation can be challenging due to many sources of error, with tropospheric phase delay and unwrapping errors being the most significant. While analytical methods, weather models, and data exist to mitigate tropospheric error, most of these techniques are unsuitable for all InSAR applications (e.g., complex tropospheric mixing in the tropics) or are deficient in spatial or temporal resolution. Likewise, there are methods for removing the unwrapping error, but they cannot resolve the true phase when there is a high prevalence (>40%) of unwrapping error in a set of interferograms. Applying tropospheric delay removal techniques is unnecessary for C-band Sentinel-1 InSAR time series studies, and the effect of unwrapping error can be minimized if the full dataset is utilized. We demonstrate that using interferograms with long temporal baselines (800 days to 1600 days) but very short perpendicular baselines (<5 m) (LTSPB) can lower the velocity detection threshold to 2 mm y−1 to 3 mm y−1 for long-term coherent permanent scatterers. The LTSPB interferograms can measure slow deformation rates because the expected differential phases are larger than those of small baselines and potentially exceed the typical noise amplitude while also reducing the sensitivity of the time series estimation to the noise sources. The method takes advantage of the Sentinel-1 mission length (2016 to present), which, for most regions, can yield up to 300 interferograms that meet the LTSPB baseline criteria. We demonstrate that low velocity detection can be achieved by comparing the expected LTSPB differential phase measurements to synthetic tests and tropospheric delay from the Global Navigation Satellite System. We then characterize the slow (~3 mm/y) ground deformation of the Socorro Magma Body, New Mexico, and the Tampa Bay Area using LTSPB InSAR analysis. The method we describe has implications for simplifying the InSAR time series processing chain and enhancing the velocity detection threshold.

(English) Spaceborne radar interferometry (InSAR) has shown significant advantages in extracting surface deformation information of landslides. However, the steep terrain, dense vegetation coverage, and rapidly changing meteorological conditions in complex reservoir areas pose substantial challenges to the application of time-series InSAR technology for landslide deformation detection and dynamic monitoring. Therefore, achieving reliable, efficient, and high-precision InSAR-based landslide deformation detection and dynamic updates in complex mountainous regions has become a research hotspot in the fields of radar remote sensing and engineering geology. This paper addresses the aforementioned challenges and conducts theoretical algorithm development and applied research, with the main research contents and contributions including the following: 1) InSAR Applicability Estimation Method for Landslide Detection.2) Sequential Optimization Method for Distributed Scatterer Polarimetric Interferometric Phase. 3)Tropospheric Delay Phase Correction for Mountainous InSAR Considering Spatial Heterogeneity. 4) Automatic Detection and Dynamic Cataloging Method for Large-Scale Active Landslides Using InSAR. (Català) La interferometría de radar espacial (InSAR) ha demostrado ventajas significativas en la extracción de información de deformación de la superficie de los deslizamientos de tierra. Sin embargo, el terreno escarpado, la cobertura de vegetación densa y las condiciones meteorológicas rápidamente cambiantes en áreas de reservorios complejos plantean desafíos sustanciales para la aplicación de la tecnología InSAR de series temporales para la detección de deformaciones de deslizamientos de tierra y el monitoreo dinámico. Por lo tanto, lograr una detección de deformaciones de deslizamientos de tierra confiable, eficiente y de alta precisión basada en InSAR y actualizaciones dinámicas en regiones montañosas complejas se ha convertido en un foco de investigación en los campos de la teledetección por radar y la geología de ingeniería. Este documento aborda los desafíos antes mencionados y lleva a cabo el desarrollo de algoritmos teóricos e investigación aplicada, con los principales contenidos y contribuciones de investigación que incluyen lo siguiente: 1) Método de estimación de aplicabilidad de InSAR para detección de deslizamientos de tierra. 2) Método de optimización secuencial para fase interferométrica polarimétrica de dispersor distribuido. 3) Corrección de fase de retardo troposférico para InSAR montañoso considerando heterogeneidad espacial. 4) Método de detección automática y catalogación dinámica de deslizamientos activos a gran escala mediante InSAR. (Español) L'interferometria de radar a l'espai (InSAR) ha mostrat avantatges significatius en l'extracció d'informació de deformació superficial dels esllavissaments. No obstant això, el terreny costerut, la densa cobertura de vegetació i les condicions meteorològiques que canvien ràpidament a les zones complexes de l'embassament suposen reptes substancials per a l'aplicació de la tecnologia InSAR de sèries temporals per a la detecció de deformacions d'esllavissades i el seguiment dinàmic. Per tant, aconseguir una detecció de deformacions de lliscament de terra fiable, eficient i d'alta precisió basada en InSAR i actualitzacions dinàmiques en regions muntanyoses complexes s'ha convertit en un punt d'investigació en els camps de la teledetecció de radar i la geologia de l'enginyeria. Aquest treball aborda els reptes esmentats anteriorment i realitza el desenvolupament d'algorismes teòrics i la investigació aplicada, amb els principals continguts i contribucions de recerca que inclouen els següents: 1) Mètode d'estimació d'aplicabilitat InSAR per a la detecció d'esllavissades.2) Mètode d'optimització seqüencial per a la fase interferomètrica polarimètrica de dispersió distribuïda. 3) Correcció de la fase de retard troposfèrica per a InSAR muntanyós tenint en compte l'heterogeneïtat espacial. 4) Mètode de detecció automàtica i catalogació dinàmica per a esllavissades actives a gran escala mitjançant InSAR. espanya

<p>Slow-moving landslides pose significant natural hazards to humans and infrastructure.  Analysis of Interferometric Synthetic Aperture Radar (InSAR) time series provide the opportunity to monitor unstable hillslopes in difficult to access terrains at large spatial scales.</p><p>The geological conditions and land cover of the eastern Central Andes in northwestern Argentina ranges from densely vegetated areas in the low elevation foreland at around 1000 metres to arid, vegetation free conditions at high elevations at about 6000 metres. The land cover has a significant impact on the spatial and temporal InSAR signal decorrelation and deformation estimation. In our study, we extract InSAR time series from Sentinel-1 ascending and descending data acquired between 2014 and 2021 using both linear small baseline technique and non-linear phase inversion techniques to have a better understanding of deformation rate estimation techniques for landslide detection in complex areas. We identified several landslides including three main translational bodies with areas exceeding 1 km<sup>2</sup> and downslope deformation rates in excess of 5-10 cm/yr. </p><p>Our study is influenced by ionospheric total electron content variation for the C band Sentinel-1 ascending phase observations. We applied the split range-spectrum technique to minimize the ionospheric contribution on the phase measurements. The tropospheric signal was estimated using both statistical approaches based on topography and weather models to reduce the effects of atmospheric water vapor during South American Monsoon activity. We explore the impact of topographic relief on tropospheric phase delay. We compared our deformation-rate estimates with a double-differencing time series with local and regional spatial filters to mitigate tropospheric noise and unwrapping problems in the time series. We take advantage of connected component analysis and hierarchical clustering approaches on the mean velocity from the double-difference time series and vertical component derived from the 3D decomposition of InSAR time series to map landslides with similar characteristics. Our results highlight the importance of the several processing parameters during InSAR time-series analysis and their sensitivity toward slow-moving landslide detection.</p>

Separating different sources of signal in Interferometric Synthetic Aperture Radar (InSAR) studies over large areas is challenging, especially between the long‐wavelength changes of atmospheric conditions and tectonic deformations, both correlated to elevation. In this study, we focus on the 2017–2018 slow slip event (SSE) in the Guerrero state (Mexico) where (1) the permanent GPS network has a low spatial density (less than 30 stations in an area of 300 300 km) with uneven distribution; (2) the tropospheric phase delays can be as high as 20 cm of apparent ground displacements, with a complex temporal evolution; (3) the tested global weather models fail to correct interferograms with enough accuracy (with residual tropospheric signal higher than the tectonic signal); and (4) the surface displacement caused by the seismic cycle shows complex interactions between seismic sequences and aseismic events. To extract the SSE signal from Sentinel‐1 InSAR time series, we test two different approaches. The first (parametric method) consists of a least squares linear inversion, imposing a functional form for each deformation or atmospheric component. The second uses independent component analysis of the InSAR time series. We obtain time series maps of surface displacements along the radar line of sight associated with the SSE and validate these results with a comparison to GPS. Combining those two approaches, we propose a method to separate atmospheric delays and tectonic deformation on time series data not corrected from atmospheric delays. From the extracted ground deformation maps, we propose a first‐order slip inversion model at the subduction interface during this SSE.

Atmospheric water vapour constitutes the primary source of delay errors in time-series InSAR. Even after implementing conventional spatiotemporal filtering and GACOS-based atmospheric correction, residual errors persist, compromising deformation monitoring accuracy. Consequently, using Tianjin as the study area. Sentinel-1A SAR imagery and PS-InSAR technique are utilized to derive time-series land subsidence information, following prior atmospheric correction via GACOS. By integrating observational data from 15 GNSS station, a systematic analysis is conducted on the residual atmospheric effects remaining in post-GACOS time-series InSAR deformation results. Furthermore, leveraging ERA5 PWV datasets, correction models tailored to residual atmospheric error in time-series InSAR across different weather scenarios are developed, with the aim of enhancing the accuracy of time-series InSAR-based deformation monitoring. Results show that residual effects persist in the time-series InSAR deformation results after GACOS-based atmospheric correction under rainfall, haze, and snowfall conditions. Rainfall in summer induces the most significant atmospheric residual error on InSAR deformation accuracy, with impacts of up to 8 mm. In contrast, haze and snowfall in autumn, winter, and spring have smaller effects on deformation accuracy than those during the rainy season, approximately 2 mm. A significant negative correlation exists between the atmospheric residual error of time-series InSAR during rainfall, haze, and snowfall events and the ΔPWV over the same periods. Moreover, the correlation coefficients are all greater than −0.85. Subsequently, using the 11 GNSS and ERA5 Δ PWV data, a time-series InSAR atmospheric residual error model was constructed via the linear regression method. Then, based on the results of the 4 GNSS and the precise levelling measurements of the two engineering projects, the reliability of the model was verified. After model correction, the deformation accuracy of time-series InSAR is better than 1 mm.

Despite the many applications of time series interferometric synthetic aperture radar (TS-InSAR) techniques in geophysical problems, error analysis and assessment have been largely overlooked. Tropospheric propagation error is still the dominant error source of InSAR observations. However, the spatiotemporal variation of atmospheric effects is seldom considered in the present standard TS-InSAR techniques, such as persistent scatterer interferometry and small baseline subset interferometry. The failure to consider the stochastic properties of atmospheric effects not only affects the accuracy of the estimators, but also makes it difficult to assess the uncertainty of the final geophysical results. To address this issue, this paper proposes a network-based variance–covariance estimation method to model the spatiotemporal variation of tropospheric signals, and to estimate the temporal variance–covariance matrix of TS-InSAR observations. The constructed stochastic model is then incorporated into the TS-InSAR estimators both for parameters (e.g., deformation velocity, topography residual) estimation and uncertainty assessment. It is an incremental and positive improvement to the traditional weighted least squares methods to solve the multitemporal InSAR time series. The performance of the proposed method is validated by using both simulated and real datasets.

Time series interferometric synthetic aperture radar (TS-InSAR) has been a powerful tool for monitoring land surface deformation over the last two decades. Atmospheric effects cause large-scale delays in InSAR observations, which is one of the difficulties facing deformation calculations from differential InSAR and time-series InSAR. Currently, the atmospheric delay is derived mainly from auxiliary data from sources such as the global navigation satellite system (GNSS) and moderate-resolution imaging spectroradiometry (MODIS), but GNSS data are limited by the sparse distribution of observation stations. MODIS data may also not temporally match SAR image acquisition, which leads to low accuracy in atmospheric phase correction. This article presents a decomposition method to remove the atmospheric delay. We consider the atmospheric phase to be caused by the combined changes in spatial position and elevation. Therefore, quadtree segmentation is applied to divide the topographic units, and we improve the drift function of universal kriging by adding an elevation component. We then interpolate the whole atmospheric phase space from reliable sampling points estimated by the coherence coefficient. Using Sentinel-1 data, we test the proposed method in discriminating and monitoring a mining subsidence area in Shanxi Province and compare the results with the results from interferometric point target analysis and the network-based variance-covariance estimation method. The results demonstrate that the proposed method is superior to existing methods for the detection of deformation inverted from TS-InSAR.

Interferometric Synthetic Aperture Radar (InSAR) is capable of detecting crust deformation. However, the accuracy is limited by spatiotemporal changes in the lower troposphere. In this paper, we constructed a periodic zenith total delay negative exponential function (PZTD-NEF) model of atmospheric spatiotemporal variation characteristics based on ERA-5 data to alleviate the temporal oscillation bias introduced by tropospheric delay and improve the accuracy of time series InSAR (TS-InSAR) inversion of surface deformation. We evaluated the model’s performance using the phase standard deviation (STD), atmospheric delay correlation coefficient with topography and the spatial structure function. The results were compared with a linear topography-dependent empirical model, generic atmospheric correction online service (GACOS) and ERA-5 methods. Our method reduces the STD of the phase of 83% of the interferograms by 12.8%. For vertical stratification delay correction, the correlation between the proposed method and the Linear, GACOS, and ERA-5 reached 0.734, 0.708, and 0.729, respectively. We found that accounting for spatiotemporal variation characteristics of tropospheric delay can alleviate the seasonal oscillations of vertical stratification delay and improve the accuracy of the deformation time series solution by 40.04%. We also used the Kunming continuous operation reference station system (KMCORS) to verify the displacement results of our method.

One of difficulties in measuring the ground deformation using SAR interferometry is the atmospheric phase screen (APS). Severe stratified APS could occur in mountain region. Thus APS could compromise the accuracy of the ground deformation estimated by SAR interferometry in stratovolcano. Since the stratified APS is correlated with the elevation, both ground deformation and APS error are indistinguishable. In order to improve the accuracy of the ground deformation and estimate the accurate APS involved in SAR interferogram, the effective algorithm is necessary which reflect the properties of APS in space and time. In this research we proposed a time-series approach combined with the weather prediction model. The main concept about APS is that the severe stratified APS usually occur in mountain region correlating with elevation and has the seasonality, while the turbulent APS has a random process in time and space. On basis of these temporal and spatial properties, we applied the troposphere-corrected time-series interferometry and successfully extracted both APS and estimated the better ground deformation results than a conventional time-series analysis.

ABSTRACTRecent researches have illustrated with the image tracking method that Ordos, China is suffering from a significant drop in earth surface level. However, such method can lead to bias in terms of its accuracy. In this paper, land displacement in Ordos between 8 January 2007 and 19 January 2011 was mapped using L-band ALOS Phased Array type L-band Synthetic Aperture Radar (PALSAR) data. Twenty PALSAR images were utilized to generate both Differential Synthetic Aperture Radar Interferometry (DInSAR) and time-series InSAR (TS-InSAR) results. Several locations in the eastern Ordos experiencing rapid land subsidence were identified. The subsidence rates ranging from −30 mm year−1 to 30 mm year−1 were measured in line-of-sight direction. The comparison between TS-InSAR and DInSAR results, although showing good agreement in general, reveals some gaps in time-series map near Qu Jia Liang coalmine mainly due to sudden changes within the four-year period. DInSAR result was exploited to fill these gaps after removing the tropospheric stratification phase delay and the verification step was conducted over the relatively stable region identified by TS-InSAR analysis. At last, the refined DInSAR result was converted into time-series velocity map and superimposed to TS-InSAR outcome to generate a final product.