DEM Error Correction in InSAR Time Series

The Interferometric Synthetic Aperture Radar (InSAR) technique has been widely used to obtain the ground surface deformation of geohazards (e.g., mining subsidence and landslides). As one of the inherent errors in the interferometric phase, the digital elevation model (DEM) error is usually estimated with the help of an a priori deformation model. However, it is difficult to determine an a priori deformation model that can fit the deformation time series well, leading to possible bias in the estimation of DEM error and the deformation time series. In this paper, we propose a method that can construct an adaptive deformation model, based on a set of predefined functions and the hypothesis testing theory in the framework of the small baseline subset InSAR (SBAS-InSAR) method. Since it is difficult to fit the deformation time series over a long time span by using only one function, the phase time series is first divided into several groups with overlapping regions. In each group, the hypothesis testing theory is employed to adaptively select the optimal deformation model from the predefined functions. The parameters of adaptive deformation models and the DEM error can be modeled with the phase time series and solved by a least square method. Simulations and real data experiments in the Pingchuan mining area, Gaunsu Province, China, demonstrate that, compared to the state-of-the-art deformation modeling strategy (e.g., the linear deformation model and the function group deformation model), the proposed method can significantly improve the accuracy of DEM error estimation and can benefit the estimation of deformation time series.

High-resolution synthetic aperture radar (SAR) data are widely used for disaster monitoring. To extract damaged areas automatically, it is essential to understand the relationships among the sensor specifications, acquisition conditions, and land cover. Our previous studies developed a method for estimating the phase noise of interferograms using several pairs of TerraSAR-X series (TerraSAR-X and TanDEM-X) datasets. Atmospheric disturbance data are also necessary to interpret the interferograms; therefore, the purpose of this study is to estimate the atmospheric effects by focusing on the difference in digital elevation model (DEM) errors between repeat-pass (two interferometric SAR images acquired at different times) and single-pass (two interferometric SAR images acquired simultaneously) interferometry. Single-pass DEM errors are reduced due to the lack of temporal decorrelation and atmospheric disturbances. At a study site in the city of Tsukuba, a quantitative analysis of DEM errors at fixed ground objects shows that the atmospheric effects are estimated to contribute 75% to 80% of the total phase noise in interferograms.

The Dead Sea water‐level has been dropping at an exceedingly increasing rate since 1960, and between 1993 and 2001, the interval of the InSAR data examined in this study, it has dropped at an average rate of 0.88 m per year. Such a water‐level change could potentially give rise to a resolvable lithospheric rebound and regional uplift, with spatial extent and amplitude that are controlled by the effective mechanical properties of the crust and upper mantle combined. We measure that deformation for the years 1993 to 2001, using 149 short baseline interferograms made of 31 ERS‐1 and ERS‐2 Synthetic Aperture Radar (SAR) images and continuous GPS data from the Survey of Israel recorded between 1997 and 2011. The uplift rate at the Dead Sea is small (up to 4 mm/year), and the basin topography is almost a mirror of the displacement, introducing a strong trade‐off between uplift and stratified atmosphere noise. To overcome this complication, we impose a linearity constraint on the satellite to ground Line Of Sight (LOS) phase changes based on the steady uplift observed by a continuous GPS station in the area of interest, and simultaneously solve for the LOS change rate, Digital Elevation Model (DEM) errors and the elevation‐phase correlation. While the LOS rate and DEM errors are solved for each pixel independently, the elevation‐phase correlation is solved for each SAR acquisition independently. Using this approach we separated the stratified atmospheric delay from the ground displacement. We observed a regional uplift around the Dead Sea northern basin, with maximum uplift close to the shorelines, and diminishing to zero by the Mediterranean coast. We modeled the effect of water load changes using a homogeneous elastic half‐space, and found a good agreement between modeled and observed ground displacements using elastic properties that are compatible with seismic and gravity data down to a depth of 15 km below the Dead Sea basin, suggesting that the response of the crust to the sea level drop is controlled mainly by the elastic properties of the upper‐crust immediately below the Dead Sea basin.

Users of GIS are faced with the ongoing and difficult problem of estimating the validity of a GIS output given the uncertainty of the quality of digital mapped data. This research project examines the manner in which error from a digital elevation model (DEM) results in error in an estimate of a viewshed. The data set includes two DEMs for the same study area. A 10‐metre DEM serves as the control model to test a United States Geological Survey (USGS) DEM. The amount and spatial pattern of the error in the test DEM is determined by comparing it to the control DEM. A viewshed analysis is then performed at a set of 61 sites. After determining the relative accuracy of the viewsheds thus estimated, a causal model of viewshed error is developed, which links the sources of the DEM error with the error in the viewshed. The most important factor in DEM error is terrain roughness. The error in the viewsheds is a result of the error being propagated from the DEM, with landscape characteristics of the viewpoinr playing a role due to their effect on the error in the DEM. The conceptual path model developed sets the stage for a quancitative approach that will attempt to predict viewshed error from the landscape characteristics without direct knowledge of the error in the DEM.

This paper provides a error modeling and calibration method to the geolocation error problem arising in the generation of digital elevation model (DEM) via interferometr ic synthetic aperture radar (InSAR) technique. DEM error is divided into two parts, systematic error and random error, they are modeled respectively. The baseline error is of crucial importance in the systematic error, it causes a slowly changed height error in the azimuth and a small tilt in the ground range of the DEM, a 2-D polynomial function is used to fit the systematic height error. The corrected DEM is obtained by removing the systematic error from the raw DEM. Computer simulation results prove the availability of the method. Keywords: InSAR; DEM; height error modeling; baseline error; error calibration; GCPs; least-squares method 1. INTRODUCTION The InSAR technique is a very efficient tool for terrain he ight measurement by the interferometry of two or multiple SAR images which are acquired from two or multiple antennas with a slight look angle difference [1]. It can get the DEM of the Earth's surface quickly in all kinds of weather and day or night. DEM is of fundamental importance for a broad range of commercial and scientific applications. For example, many geoscience areas, like hydrology, glaciology, forestry, geology, oceanography, and land environment, require precise and up-to-date information about the Earth's surface and its topography. Nevertheless, in the process of DEM generation, the errors of the instrument, orbit, and processing parameters which have been used in the InSAR processing affect the accuracy of DEM significantly. TanDEM-X mission provides an example [2], The TanDEM-X mission is the first bistatic satellite synthetic aperture radar mission which is formed by flying TanDEM-X and TerraSAR-X in a closely controlled helix formation. The primary mission goal is the derivation of a high-precision global digital DEM according to High-Resolution Terrain Information (HRTI) level 3 accuracy. The finite precision of the baseline knowledge and uncompensated radar instrument drifts along with some other parameter errors introduce errors that may compromise the height accuracy requirements. To fulfill the its demanding requirements, a DEM calibration method which uses absolute height references and the information provided by adjacent interferogram overlaps is pr oposed to minimize th e residual height errors. It can be seen that the correction of systematic height errors in the DEM is necessary to achieve the specified accuracies [3-4]. In the future InSAR system, the required DEM accuracy will be more and more precise, therefore, the DEM calibration will play a more important role in the DEM post-processing. The main purpose of this paper is to describe the influe nces of the systematic error and obtain a more precise DEM by removing it from the overall DEM. Section 2 provides a brie f analysis of the total DEM height error, and classifies it into two groups, the systematic error and the random error. Section 3 sets up the models of systematic error especially the baseline error and presents a DEM calibration method. Sec tion 4 is the computer simulation results which prove the availability of the method. The paper concludes in Section 5.

Lanzhou is one of the cities with the higher number of civil engineering projects for mountain excavation and city construction (MECC) on the China’s Loess Plateau. As a result, the city is suffering from severe surface displacement, which is posing an increasing threat to the safety of the buildings. However, up to date, there is no comprehensive and high-precision displacement map to characterize the spatiotemporal surface displacement patterns in the city of Lanzhou. In this study, satellite-based observations, including optical remote sensing and synthetic aperture radar (SAR) sensing, were jointly used to characterize the landscape and topography changes in Lanzhou between 1997 and 2020 and investigate the spatiotemporal patterns of the surface displacement associated with the large-scale MECC projects from 2015 December to March 2021. First, we retrieved the landscape changes in Lanzhou during the last 23 years using multi-temporal optical remote sensing images. Results illustrate that the landscape in local areas of Lanzhou has been dramatically changed as a result of the large-scale MECC projects and rapid urbanization. Then, we optimized the ordinary time series InSAR processing procedure by a “dynamic estimation of digital elevation model (DEM) errors” step added before displacement inversion to avoid the false displacement signals caused by DEM errors. The DEM errors and the high-precision surface displacement maps between December 2015 and March 2021 were calculated with 124 ascending and 122 descending Sentinel-1 SAR images. By combining estimated DEM errors and optical images, we detected and mapped historical MECC areas in the study area since 2000, retrieved the excavated and filling areas of the MECC projects, and evaluated their areas and volumes as well as the thickness of the filling loess. Results demonstrated that the area and volume of the excavated regions were basically equal to that of the filling regions, and the maximum thickness of the filling loess was greater than 90 m. Significant non-uniform surface displacements were observed in the filling regions of the MECC projects, with the maximum cumulative displacement lower than −40 cm. 2D displacement results revealed that surface displacement associated with the MECC project was dominated by settlements. From the correlation analysis between the displacement and the filling thickness, we found that the displacement magnitude was positively correlated with the thickness of the filling loess. This finding indicated that the compaction and consolidation process of the filling loess largely dominated the surface displacement. Our findings are of paramount importance for the urban planning and construction on the Loess Plateau region in which large-scale MECC projects are being developed.

The Digital Elevation Model (DEM) can be created using airborne Light Detection And Ranging (LIDAR), Image or Synthetic-Aperture Radar (SAR) mapping techniques. The direct georeferencing of the DEM model is conducted using a GPS/inertial navigation system. The airborne mapping system datasets are processed to create a DEM model. To develop an accurate DEM model, all errors should be considered in the processing step. In this research, the errors associated with DEM models are investigated and modeled using Principal Component Analysis (PCA) and the least squares method. The sensitivity analysis of the DEM errors is investigated using PCA to define the significant GPS/inertial navigation data components that are strongly correlated with DEM errors. Then, the least squares method is employed to create a functional relationship between the DEM errors and the significant GPS/inertial navigation data components. The DEM model errors associated with airborne mapping system datasets are investigated in this research. The results show that the combined PCA analysis and least squares method can be used as a powerful tool to compensate the DEM error due to the GPS/inertial navigation data with about 27% in average for DEM errors produced by the direct georeferenced airborne mapping system.

Previous evaluations of viewshed analyses have raised concerns about the accuracy and repeatability of the process. Digital elevation model (DEM) errors, the limited spatial resolution of DEMs, and differing algorithms employed by different GIS packages have all been suggested as possible sources for inaccuracy and non‐repeatability. This study compared a field surveyed viewshed to predicted viewsheds generated using a variety of software packages and DEM databases, some of which contained known amounts of error. We found that each of the factors suggested by previous authors contributes to errors in predicted viewsheds. DEM errors contribute most to the discrepancies between surveyed and predicted viewsheds, and the majority of their negative impact occurred at very low levels of DEM error. Differing algorithms used by different GIS packages also contribute significantly to surveyed/predicted viewshed discrepancies, but more importantly, result in predicted viewsheds that disagree with one other, thereby confounding comparisons of results generated with differing software systems. Finally, the spatial resolution of DEMs also has a significant effect on the degree of agreement between surveyed and predicted viewsheds, but the magnitude of this effect is not as great as are the effects produced by DEM errors.

Digital Elevation Model (DEM) errors tend to be spatially correlated, inevitably affecting DEM-based topographic change detection. Traditional topographic change detection methods often ignore the spatial distribution of the DEM error. This paper aims to develop a workflow that considers the spatial autocorrelation of the error in topographic change detection. Firstly, the DEM of Difference (DoD) is obtained from two-period DEMs, and the Monte Carlo method is employed to evaluate the Spatially Distributed Errors (SDE) in DEMs. Secondly, DoD errors are calculated by propagation based on spatially distributed DEM errors. At the same time, its spatial distribution is quantified using the semi-variance function. Finally, topographic changes (erosion, deposition, and net changes) are calculated based on the spatial distribution analysis and significance detection. The results in two small catchments indicate that DEM errors are spatially correlated, increasing the volume calculation errors. However, using Standard Deviation of Errors (SDE) instead of Root Mean Square Error (RMSE) can effectively reduce the sensitivity of the detection results in the significance threshold. When the significance threshold increases from 68% to 95%, the observations loss using the spatially distributed error is 4.67% −6.92% lower than that using the RMSE. The level of detection has little impact on the net topographic change and significantly influences gross erosion and deposition. In particular, the use of level of detection can effectively reduce the misclassification of erosion or deposition in stable topography areas. The proposed method can be effectively utilized in various applications like surface deformation monitoring, erosion monitoring, and sediment transport assessment.

Coastal managers require reliable spatial data on the extent and timing of potential coastal inundation, particularly in a changing climate. Most sea level rise (SLR) vulnerability assessments are undertaken using the easily implemented bathtub approach, where areas adjacent to the sea and below a given elevation are mapped using a deterministic line dividing potentially inundated from dry areas. This method only requires elevation data usually in the form of a digital elevation model (DEM). However, inherent errors in the DEM and spatial analysis of the bathtub model propagate into the inundation mapping. The aim of this study was to assess the impacts of spatially variable and spatially correlated elevation errors in high-spatial resolution DEMs for mapping coastal inundation. Elevation errors were best modelled using regression-kriging. This geostatistical model takes the spatial correlation in elevation errors into account, which has a significant impact on analyses that include spatial interactions, such as inundation modelling. The spatial variability of elevation errors was partially explained by land cover and terrain variables. Elevation errors were simulated using sequential Gaussian simulation, a Monte Carlo probabilistic approach. 1,000 error simulations were added to the original DEM and reclassified using a hydrologically correct bathtub method. The probability of inundation to a scenario combining a 1 in 100 year storm event over a 1 m SLR was calculated by counting the proportion of times from the 1,000 simulations that a location was inundated. This probabilistic approach can be used in a risk-aversive decision making process by planning for scenarios with different probabilities of occurrence. For example, results showed that when considering a 1% probability exceedance, the inundated area was approximately 11% larger than mapped using the deterministic bathtub approach. The probabilistic approach provides visually intuitive maps that convey uncertainties inherent to spatial data and analysis.

Abstract. In this paper, we present a method for using the estimated precipitable water (PW) to mitigate atmospheric phase delay in order to improve the accuracy of land-deformation assessment with differential interferometric synthetic aperture radar (DInSAR). The phase difference obtained from multi-temporal synthetic aperture radar images contains errors of several types, and the atmospheric phase delay can be an obstacle to estimating surface subsidence. In this study, we calculate PW from external meteorological data. Firstly, we interpolate the data with regard to their spatial and temporal resolutions. Then, assuming a range direction between a target pixel and the sensor, we derive the cumulative amount of differential PW at the height of the slant range vector at pixels along that direction. The atmospheric phase delay of each interferogram is acquired by taking a residual after a preliminary determination of the linear deformation velocity and digital elevation model (DEM) error, and by applying high-pass temporal and low-pass spatial filters. Next, we estimate a regression model that connects the cumulative amount of PW and the atmospheric phase delay. Finally, we subtract the contribution of the atmospheric phase delay from the phase difference of the interferogram, and determine the linear deformation velocity and DEM error. The experimental results show a consistent relationship between the cumulative amount of differential PW and the atmospheric phase delay. An improvement in land-deformation accuracy is observed at a point at which the deformation is relatively large. Although further investigation is necessary, we conclude at this stage that the proposed approach has the potential to improve the accuracy of the DInSAR technique.

We analysed the sensitivity of a decision tree derived forest type mapping to simulated data errors in input digital elevation model (DEM), geology and remotely sensed (Landsat Thematic Mapper) variables. We used a stochastic Monte Carlo simulation model coupled with a one‐at‐a‐time approach. The DEM error was assumed to be spatially autocorrelated with its magnitude being a percentage of the elevation value. The error of categorical geology data was assumed to be positional and limited to boundary areas. The Landsat data error was assumed to be spatially random following a Gaussian distribution. Each layer was perturbed using its error model with increasing levels of error, and the effect on the forest type mapping was assessed. The results of the three sensitivity analyses were markedly different, with the classification being most sensitive to the DEM error, than to the Landsat data errors, but with only a limited sensitivity to the geology data error used. A linear increase in error resulted in non‐linear increases in effect for the DEM and Landsat errors, while it was linear for geology. As an example, a DEM error of as small as ±2% reduced the overall test accuracy by more than 2%. More importantly, the same uncertainty level has caused nearly 10% of the study area to change its initial class assignment at each perturbation, on average. A spatial assessment of the sensitivities indicates that most of the pixel changes occurred within those forest classes expected to be more sensitive to data error. In addition to characterising the effect of errors on forest type mapping using decision trees, this study has demonstrated the generality of employing Monte Carlo analysis for the sensitivity and uncertainty analysis of categorical outputs that have distinctive characteristics from that of numerical outputs.

The accuracy of a digital elevation model (DEM) is at stake, critically affecting the success of DEM applications. One important issue of DEM research concerns those factors that touch the generated DEM accuracy. The relationship between DEM error and the sampling density is still a worthy question, especially for nonlinear interpolations. This research comparatively analyzes the qualitative and quantitative relationship between the sampling density and DEM error by both bilinear and bicubic interpolation methods. First, the qualitative relationships between the DEM error and the sampling density for both bilinear interpolation and bicubic interpolation models are investigated based on convergence analysis. Second, the quantitative relationships between the DEM error and the sampling density are further derived by means of the numerical approaches. Here the model error is specified by its right upper bound of the truncated error function, with the sampling density as its variable. Third, experimental studies, involving both mathematical and real DEM surfaces, are conducted to verify the foregoing theoretical findings. The theoretical derivations and experimental studies both demonstrate that the DEM quality by a bicubic interpolation method, in terms of model error, is superior to the counterpart generated by a bilinear interpolation method under the assumption of the original sample data being error-free. The new findings about the model errors for bicubic interpolated DEM, together with the previous work on bilinear interpolated DEM drawn from an earlier study, form a full picture depicting the model errors of an interpolated DEM surface. These results can serve as a guideline for interpolation model selection regarding the practical DEM production.

Abstract. The primary step in all timeseries interferometric synthetic aperture radar (T-InSAR) algorithms is the phase unwrapping step to resolve the inherent cycle ambiguities of interferometric phases. In areas with a high spatio-temporal deformation gradient, phase unwrapping fails due to the aliasing problem, and so it can result in an underestimation of deformation signal. One way to handle this problem is to use the so called Small-Baseline Subset (SBAS) algorithms; in these algorithms, by using only small-baseline interferograms – hence interferograms with small deformation gradients – the chance of unwrapping error gets reduced. However, due to more number of the used interferograms, SBAS method is computationally more expensive and more time-consuming compared to algorithms that exploit Single-Master (SM) stacks. Moreover, the existence of sufficiently small temporal baseline interferograms is not guaranteed in all SAR stacks. In this paper, we propose a new method to take advantage of short temporal baseline interferograms but effectively using SM approach. We treat the phase unwrapping step as a Bayesian estimation problem while the prior information, required by the Bayesian estimator, is extracted from few short coherent interferograms that are unwrapped separately. Results from the proposed approach and a case study over the southwest of Tehran, with a high subsidence rate (reaching to 25 cm/year), demonstrates that utilizing the proposed method overcomes the aliasing problem and produces the results equal to the conventional SBAS results, while the proposed method is computationally much more efficient than SBAS.

Terrain survey with traditional photogrammetry is often difficult in western China, such as Qingzang tableland at an average height of 5000 m above sea level and the southwest China area with cloudy weather. To resolve western terrain mapping, the first Chinese single-pass airborne Interferometric Synthetic Aperture Radar (InSAR) system was successfully developed by the Institute of Electronics, Chinese Academy of Sciences (IECAS) in 2004. The main objective of this article is to examine and evaluate the performance of the airborne SAR system through interferometric processing and error analysis. First, the article describes how high-precision digital elevation models (DEMs) are derived from the airborne dual-antenna (single-pass) InSAR data. In order to improve the precision, the antenna eccentricity correction and parameter calibration with the least square method (LSM) are proposed. Based on the airborne dual-antenna InSAR bore-sight model, this article summarizes the primary factors that influence the accuracy of DEMs in data processing, and analyses the errors induced by these factors. Then, the global positioning system (GPS)/inertial measurement unit (IMU) data, acquired and stored by the position and orientation system (POS), is used for analysing the quantitative relationships among the platform height, baseline length, baseline angle, look angle and DEM error. The experimental data used are airborne dual-antenna X-band InSAR data, and the measured ground control points (GCPs) are used to validate the accuracy of the DEM. The evaluation results in terms of the standard deviation (SD) and the average mean error (AME) are derived by comparing the reconstructed InSAR DEM with the reference GCPs. The AMEs of the X-direction, the Y-direction and the height are up to 2.078, 9.149 and 1.763 m, respectively. The SDs of the X-direction, the Y-direction and the height are up to ±1.379, ±0.764 and ±1.086 m, respectively. These results agree with the previously calculated quantitative errors. The error value of the Y-direction seems too large, a possible result of system errors. In general, the airborne dual-antenna InSAR system initially meets the requirements of 1:50 000 terrain mapping in western China.