Atmospheric Phase Screen Research Articles

Atmospheric Phase Screen in GEO-SAR: Estimation and Compensation

We study the impact of atmospheric turbulence, specifically the wet tropospheric delay, in that synthetic aperture radar (SAR) with very long integration time, from minutes to hours, and wide swaths, such as the geosynchronous or geostationary SAR. In such systems, the atmospheric phase screen (APS) cannot be assumed frozen in time as for Low Earth Orbit or airborne SARs nor constant in space as for the ground-based SAR. The impact of space–time turbulence on SAR focusing is quantitatively assessed, and a novel focusing method that integrates APS estimation and compensation is proposed. Performances are evaluated as a function of SAR parameters, mainly the wavelength, based on a parametric model of the APS variogram, and results achieved by a simulating realistic scenario are shown.

Atmospheric turbulence phase screen modeling method based on sub-bands division and multirate sampling

The phase screen method is a well-established approach to analyze the effects of atmospheric turbulence in free space optical (FSO) communication and astronomical imaging system. Owning to the variation of atmospheric turbulence, low complexity modeling is required. Meanwhile, low frequency power should be compensated to overcome shortcomings of classical methods. The method based on sub-bands division and multirate sampling is proposed to solve these problems, and analytic formulas of the model is derived correspondingly. Simulation results are provided to show that our method overperforms the existing methods when both computational complexity and power compensation are taken into account. Furthermore, the proposed method is flexibly in operating which could be used to simulate the base phase screen of time-varying atmospheric turbulence.

Sentinel-1A/B imagery for terrain deformation monitoring: a strategy for Atmospheric Phase Screening (APS) estimation

This work focus on terrain deformation monitoring by means of C-band Synthetic Aperture Radar (SAR) Sentinel-1A/B imagery exploiting the Persistent Scatterer Interferometry (PSI) technique. The deformation monitoring strategy described in this article is related to a specific monitoring scenario where a relatively small urban area is potentially affected by deformation and its surroundings are stable. In the case study considered in this work, the scenario corresponds to an area of potential subsidence induced by underground water pumping covering an area of interest with a radius of approximately 1 km. The proposed monitoring strategy takes advantage of the specific scenario at hand and, in particular, of the availability of stable areas in the vicinity of the area potentially affected by ground deformation, to estimate the Atmospheric Phase Screen (APS), i.e. signal propagation delay caused by the Earth’s atmosphere, in an attempt to minimize the underestimation of the deformation rate.

PsInSAR based land subsidence estimation of Burgan oil field using TerraSAR-X data

Oil extraction over the years has increased tremendously resulting in land subsidence, which is a slow and gradual process and has long-term effects on ecohydrology and climate. For efficient measurement of land subsidence phenomenon due to oil extraction, an advanced PsInSAR technique was used in this study which overcame the obstacles such as temporal and geometrical decorrelation, phase delay due to atmospheric variation. The primary objective of the present study is to investigate the potential of PsInSAR technique to estimate total land subsidence in Burgan oil field, Kuwait, on a multitemporal scale from 2008 to 2011. A total of 26 datasets TerraSAR-X interferometric datasets were acquired from 31st January 2008 to 4th February 2011. Permanent Scatter Candidates (PSC) were selected based on amplitude stability index. Atmospheric Phase was estimated and removal of Atmospheric Phase Screen was carried using ensemble coherence. To measure the displacement between 31st January 2008 and 4th February 2011, a spatio-temporal displacement map was generated and overlaid on Google Earth to mark the areas of oil wells in Burgan oil field where subsidence has taken place. The total amount of subsidence was obtained from Integrated Cumulative Displacement Map, the value of which was estimated to be 10mm/year and an average of 25–30mm per 3 years. The land subsidence outcome of this study for three-years times was compared with already existing literature based results to show the potential of PsInSAR for subsidence mapping due to oil extraction. PsInSAR technique for land subsidence monitoring showed significant improvement in results after correcting for the atmospheric phase errors.

Monitoring Alpine glacier surface deformations with GB-SAR

ABSTRACTWe present methods and results from interferometric data processing of a long-lasting survey campaign monitoring the Planpincieux glacier, located on the Italian side of the Mont Blanc, using a ground-based synthetic aperture radar (GB-SAR). Monitoring a European Alpine glacier during the winter, when the meteorological conditions are highly variable, presents some difficulties in radar data interpretation. The main issues to tackle in interferometric processing are unwrapping errors and high amplitude dispersion (DA), mainly due to the high velocity and dielectric heterogeneity of the backscattering surface. To improve the reliability of the results, a coherence-driven pixel-selection criterion for identifying the glacier area and a simple approach to reduce possible unwrapping errors in interferograms with low coherence are here proposed. The development of a new 2D polynomial regression model, as a function of elevation, for atmospheric phase screen (APS) estimation is also discussed. A comparison with the results obtained with a vision-based approach gave showed good agreement.

Surface Motion and Structural Instability Monitoring of Ming Dynasty City Walls by Two-Step Tomo-PSInSAR Approach in Nanjing City, China

Spaceborne Multi-Temporal Synthetic Aperture Radar (SAR) Interferometry (MT-InSAR) has been a valuable tool in mapping motion phenomena in different scenarios. Recently, the capabilities of MT-InSAR for risk monitoring and preventive analysis of heritage sites have increasingly been exploited. Considering the limitations of conventional MT-InSAR techniques, in this study a two-step Tomography-based Persistent Scatterers (PS) Interferometry (Tomo-PSInSAR) approach is proposed for monitoring ground deformation and structural instabilities over the Ancient City Walls (Ming Dynasty) in Nanjing city, China. For the purpose of this study we utilized 26 Stripmap acquisitions from TerraSAR-X and TanDEM-X missions, spanning from May 2013 to February 2015. As a first step, regional-scale surface deformation rates on single PSs were derived (ranging from −40 to +5 mm/year) and used for identifying deformation hotspots as well as for the investigation of a potential correlation between urbanization and the occurrence of surface subsidence. As a second step, structural instability parameters of ancient walls (linear motion rates, non-linear motions and material thermodynamics) were estimated by an extended four-dimensional Tomo-PSInSAR model. The model applies a two-tier network strategy; that is, the detection of most reliable single PSs in the first-tier Delaunay triangulation network followed by the detection of remaining single PSs and double PSs on the second-tier local star network referring to single SPs extracted in the first-tier network. Consequently, a preliminary phase calibration relevant to the Atmospheric Phase Screen (APS) is not needed. Motion heterogeneities in the spatial domain, either caused by thermal kinetics or displacement trends, were also considered. This study underlines the potential of the proposed Tomo-PSInSAR solution for the monitoring and conservation of cultural heritage sites. The proposed approach offers a quantitative indicator to local authorities and planners for assessing potential damages as well as for the design of remediation activities.

Characterisation and improvement of the structure function estimation for application in PSI

Numerical Weather Prediction (NWP) is becoming state of the art for the compensation of atmospheric effects in InSAR and especially in PSI. The structure function (variogram) estimated on the InSAR data and on the NWP data is a required statistical characteristic and very useful in the processing of the data. For example, the structure function (typically the semivariogram) estimated on InSAR data is fundamental for the Kriging of the atmospheric phase screen (APS) based on irregular PSI estimates. The required parameters are the nugget, the range and the slope of the structure function. The practical implementation has shown that the NWP predicted structure function and the InSAR estimated structure function based on the conventional semivariogram equation do not match. Straightforward explanations are wrongly estimated APSs due to an insufficient number of interferograms or hindcasts that fail to capture the turbulent water vapour signal. However, in this paper we explain the effects of noise in interferograms and coarse resolution in the NWP on the conventional structure function estimation resulting in the observed mismatch. In order to avoid the mismatch, an alternative implementation based on wavelets is suggested and demonstrated using real Sentinel-1 data. We show that the wavelet based structure function estimation outperforms the conventional structure function estimation based on a variogram. Application of the proposed structure function alternative based on NWP data are the master selection, the estimation of the effective NWP data resolution, and a statistical consistency check of the estimated InSAR APS. To support the understanding, we demonstrate the effects of noise and resolution using simulated fractals. An application of the proposed wavelet based structure function estimation is the estimation of the effective NWP data resolution, which is demonstrated using the same Sentinel-1 data test case.

Unwrapping-free interpolation of sparse DInSAR phase data: experimental validation

ABSTRACTIn multi-temporal applications of synthetic aperture radar (SAR) interferometry, differential phase contributions due to atmospheric inhomogeneities, estimated over sparse points, have to be interpolated and removed from the regular-grid interferograms in order to highlight the phase stability of more image pixels, which then add to the available data to infer useful information about terrain displacements or other phenomena of interest. Interpolation is usually done on the phase data after a phase unwrapping (PU) operation. In a previous work, we considered the alternative interpolation step applied directly to the complex phasor derived from the wrapped phase, thus bypassing the error-prone sparse PU operation. In this article, the performances of the proposed methodology are evaluated over atmospheric phase screen (APS) data estimated from a previous processing through persistent scatterers interferometry (PSI) methods. The original persistent scatterer (PS) population is reduced by thresholding their inter-image coherence values, and then further subsampled randomly in a rectangle inside a detected subsidence bowl. Both the classical and the proposed interpolation procedures are applied to the subsampled APS phase values. The interpolated fields are then removed from the rest of the PS, and the residual phase values are compared in terms of inter-image coherence. Results confirm that interpolating complex phasors, thus avoiding PU, gives results equivalent to the standard procedure in good sampling conditions. Moreover, when point sparsity induces phase aliasing, thus hindering the PU operation, the proposed method allows to better recover phase information over unsampled pixels, improving the final results of the PSI processing.

On the Phase Calibration by Multisquint Analysis in TOPSAR and Stripmap Interferometry

The availability of accurate trajectory information is paramount for the processing and exploitation of synthetic aperture radar (SAR) data. Considering the particular case of spaceborne SARs designed for repeat-pass interferometric applications, errors in the trajectory translate into phase artifacts that affect the interferometric performance. In this paper, we propose a model-based procedure to calibrate the trajectories of spaceborne SAR systems by the multisquint (MS) phase. The technique allows to estimate the along and the derivative of across track geometric errors. The geometric model of the InSAR phase is derived as a function of positioning errors and the MS phase model as derivative of the InSAR phase geometric model, with respect to the squint angle. We perform a sensitivity analysis of the model in order to define which geometric errors can be estimated by the MS phase, justifying the assumption that the MS phase is very poorly affected by the atmospheric phase screen. We particularly concentrate on the TOPSAR acquisition mode, where the phase is very sensitive to geometric errors. We start from the classical two-image case and then consider the extension to the multibaseline case. Experimental results obtained by processing of interferometric pairs acquired by the Sentinel-1A sensor are reported.

Multi-technique approach to rockfall monitoring in the Montserrat massif (Catalonia, NE Spain)

Montserrat Mountain is located near Barcelona in Catalonia, in the northeast of Spain, and its massif is formed by conglomerate interleaved by siltstone/sandstone with steep slopes very prone to rockfalls. The increasing number of visitors in the monastery area, reaching 2.4 million per year, has highlighted the risk derived from rockfalls for this building area and also for the terrestrial accesses, both roads and the rack railway. A risk mitigation plan has been launched, and its first phase during 2014–2016 has been focused largely on testing several monitoring techniques for their later implementation. The results of the pilot tests, performed as a development from previous sparse experiences and data, are presented together with the first insights obtained. These tests combine four monitoring techniques under different conditions of continuity in space and time domains, which are: displacement monitoring with Ground-based Synthetic Aperture Radar and characterization at slope scale, with an extremely non-uniform atmospheric phase screen due to the stepped topography and atmosphere stratification; Terrestrial Laser Scanner surveys quantifying the frequency of small or even previously unnoticed rockfalls, and monitoring rock block centimetre scale displacements; the monitoring of rock joints implemented through a wireless sensor network with an ad hoc design of ZigBee loggers developed by ICGC; and, finally, monitoring singular rock needles with Total Station.

Simulating large atmospheric phase screens using a woofer-tweeter algorithm.

We describe an algorithm for simulating atmospheric wavefront perturbations over ranges of spatial and temporal scales spanning more than 4 orders of magnitude. An open-source implementation of the algorithm written in Python can simulate the evolution of the perturbations more than an order-of-magnitude faster than real time. Testing of the implementation using metrics appropriate to adaptive optics systems and long-baseline interferometers show accuracies at the few percent level or better.

Atmospheric phase screen correction in ground-based SAR with PS technique.

Ground-based synthetic aperture radar (GBSAR) is a powerful tool used in monitoring structures, such as bridges and dams. However, despite the extremely short range of GBSAR interferometry, the atmosphere effects cannot be neglected. The permanent scatterer technique is an effective operational tool that utilizes a long series of SAR data and detects information with high accuracy. An algorithm based on the permanent scatterer technique is developed in accordance with the phase model used in GBSAR interferometry. In this study, atmospheric correction is carried out on a real campaign (Geheyan Dam, China). The atmosphere effects created using this method, which utilizes SAR data, can be reduced effectively compared to when plumb line data are used.

Atmospheric correction in time-series SAR interferometry for land surface deformation mapping – A case study of Taiyuan, China

The dominant error source of Synthetic Aperture Radar Interferometry (InSAR) is atmospheric phase screen (APS), resulting in phase delay of the radar signal propagating through the atmosphere. The APS in the atmosphere can be decomposed into stratified and turbulent components. In this paper, we introduced a method to compensate for stratified component in a radar interferogram using ERA-Interim reanalysis products obtained from European Centre for Medium-Range Weather Forecasts (ECMWF). Our comparative results with radiosonde data demonstrated that atmospheric condition from ERA-Interim could produce reasonable patterns of vertical profiles of atmospheric states. The stratified atmosphere shows seasonal changes which are correlated with time. It cannot be properly estimated by temporal high-pass filtering which assumes that atmospheric effects are random in time in conventional persistent scatterer InSAR (PSI). Thus, the estimated deformation velocity fields are biased. Therefore, we propose the atmosphere-corrected PSI method that the stratified delay are corrected on each interferogram by using ERA-Interim. The atmospheric residuals after correction of stratified delay were interpreted as random variations in space and time which are mitigated by using spatial–temporal filtering. We applied the proposed method to ENVISAT ASAR images covering Taiyuan basin, China, to study the ground deformation associated with groundwater withdrawal. Experimental results show that the proposed method significantly mitigate the topography-correlated APS and the estimated ground displacements agree more closely with GPS measurements than the conventional PSI.

Robust Detection of Single and Double Persistent Scatterers in Urban Built Environments

In this paper, we develop a synthetic aperture radar (SAR) tomography-based persistent scatterer interferometry (Tomo-PSInSAR) method to detect single and double persistent scatterers (PSs) in urban built environments. By constructing a two-tier network, we can jointly detect single and double PSs with no need for preliminary removal of the atmospheric phase screen (APS) in the whole area. This technique is more applicable in high-rise built environments (e.g., Hong Kong) with cloudy and rainy weather, where there is much uncertainty when removing the APS. In the first-tier network, we aim to detect the most reliable single PSs (SPSs) by constructing a Delaunay triangulation network. To improve the robustness of estimation, we combine beamforming with an M-estimator for parameter estimation at the arcs and introduce a ridge estimator for network adjustment. In the second-tier network, we detect the remaining SPSs and all of the double PSs (DPSs) by constructing local star networks that use the SPSs detected in the first-tier network as reference points. To simplify the detection of DPSs, we employ a local maximum ratio method for extracting overlaid DPSs. Finally, 56 Hong Kong TerraSAR-X images are used to validate the Tomo-PSInSAR method.

Spin-up time research on the weather research and forecasting model for atmospheric delay mitigations of electromagnetic waves

Atmosphere causes distortions in the geometry and phases of synthetic aperture radar images denoted by the atmospheric phase screen (APS). Numerical weather models are beneficial in correcting these disturbances. After initialization, the models need time to derive a physical valid state. This is called the spin-up time, and it affects delay predictions. The positive impact of a 12-h spin-up time on delay mitigation has not yet been reported and is the objective of this paper. Hence, four independent experiments are considered, revealing the best accuracy in the case of 12-h predictions and showing the best consistency of spatial frequencies. First, global positioning system zenith path delay (ZPD) series are compared with model-predicted ZPD series, which reports a 28% reduction of the root mean squared error. Second, the absolute ranging technique as an application of the delay prediction reports a 21% standard deviation decrease of position estimates. Third, a comparison of spatial frequencies between APS predictions and interferograms shows a closer consistency using a 12-h rather than a 6-h spin-up time. Fourth, APS mitigation in interferograms as an application of APS prediction is twice as good with respect to the 12-h spin-up time as with the 6-h spin-up time.

Wide-Area Landslide Deformation Mapping with Multi-Path ALOS PALSAR Data Stacks: A Case Study of Three Gorges Area, China

In recent years, satellite synthetic aperture radar interferometry (InSAR) has been adopted as a spaceborne geodetic tool to successfully measure surface deformation of a few well-known landslides in the Three Gorges area. In consideration of the fact that most events of slope failure happened at places other than those famous landslides since the reservoir impoundment in 2003, focusing on a limited number of slopes is insufficient to meet the requirements of regional-scale landslide disaster prevention and early warning. As a result, it has become a vital task to evaluate the overall stability of slopes across the vast area of Three Gorges using wide-coverage InSAR datasets. In this study, we explored the approach of carrying out joint analysis of multi-path InSAR data stacks for wide-area landslide deformation mapping. As an example, three ALOS (Advanced Land Observing Satellite) PALSAR (Phased Array type L-band Synthetic Aperture Radar) data stacks of neighboring ascending paths covering the area along the Yangtze River from Fengjie to Zigui were analyzed. A key problem to be solved is the separation of the tropospheric signal from the interferometric phase, for which we employed a hybrid description model of the atmospheric phase screen (APS) to improve APS estimation from time series interferograms. The estimated atmospheric phase was largely correlated with the seasonal rainfall in the temporal dimension. The experimental results show that about 30 slopes covering total areas of 48 km2 were identified to be landslides in active deformation and should be kept under routine surveillance. Analyses of time series displacement measurements revealed that most landslides in the mountainous area far away from Yangtze River suffered from linear deformation, whereas landslides located on the river bank were destabilized predominantly by the influences of reservoir water level fluctuation and rainfall.

非Kolmogorov大气湍流随机相位屏模拟

The methods of power spectrum, Zernike polynomial and Fractal used to generate atmospheric phase screens with the non-Kolmogorov statistics were introduced. Based on the three methods, non-Kolmogorov turbulent phase screens were simulated. Phase structure functions were calculated and compared with the theoretical results. In addition, the accuracy and efficiency of different methods were also analyzed. It shows that phase screen created by FFT method has the drawback of lacking low frequency, by adding subharmonics the phase screen can be compensated which also leading to the decreasing of simulation efficiency; phase screen created by Zernike polynomial method has the drawback of lacking high frequency, by using much more orders of Zernike polynomials the phase screen can be compensated which also leading to the decreasing of simulation efficiency; phase screen created by Fractal method is relatively good at both low and high frequency and the simulation efficiency is also high. In addition, the number of subharmonics and the order of Zernike polynomials under same condition of accuracy are related to the power law of non-Kolmogorov turbulent spectrum. As the spectral power law increases, the number of subharmonics increase and the order of Zernike polynomials decrease, and phase screens created by fractal method are more accurate.

非Kolmogorov大气湍流随机相位屏模拟

The methods of power spectrum, Zernike polynomial and Fractal used to generate atmospheric phase screens with the non-Kolmogorov statistics were introduced. Based on the three methods, non-Kolmogorov turbulent phase screens were simulated. Phase structure functions were calculated and compared with the theoretical results. In addition, the accuracy and efficiency of different methods were also analyzed. It shows that phase screen created by FFT method has the drawback of lacking low frequency, by adding subharmonics the phase screen can be compensated which also leading to the decreasing of simulation efficiency; phase screen created by Zernike polynomial method has the drawback of lacking high frequency, by using much more orders of Zernike polynomials the phase screen can be compensated which also leading to the decreasing of simulation efficiency; phase screen created by Fractal method is relatively good at both low and high frequency and the simulation efficiency is also high. In addition, the number of subharmonics and the order of Zernike polynomials under same condition of accuracy are related to the power law of non-Kolmogorov turbulent spectrum. As the spectral power law increases, the number of subharmonics increase and the order of Zernike polynomials decrease, and phase screens created by fractal method are more accurate.

Computationally efficient autoregressive method for generating phase screens with frozen flow and turbulence in optical simulations.

We present a sample-based, autoregressive (AR) method for the generation and time evolution of atmospheric phase screens that is computationally efficient and uses a single parameter per Fourier mode to vary the power contained in the frozen flow and stochastic components. We address limitations of Fourier-based methods such as screen periodicity and low spatial frequency power content. Comparisons of adaptive optics (AO) simulator performance when fed AR phase screens and translating phase screens reveal significantly elevated residual closed-loop temporal power for small increases in added stochastic content at each time step, thus displaying the importance of properly modeling atmospheric "boiling". We present preliminary evidence that our model fits to AO telemetry are better reflections of real conditions than the pure frozen flow assumption.

Using several monitoring techniques to measure the rock mass deformation in the Montserrat Massif

Montserrat Mountain is located near Barcelona in Catalonia, at the north-east corner of Spain, and its massif is formed by conglomerate interleaved by siltstone/sandstone with steep slopes very prone to rock falls. The increasing visitor's number in the monastery area, reaching 2.4 million per year, has pointed out the risk derived from rock falls for this building area and also for the terrestrial accesses, both roads and rack railway. A risk mitigation plan is currently been applied for 2014-2016 that contains monitoring testing and implementation as a key point. The preliminary results of the pilot tests carried out during 2014 are presented, also profiting from previous sparse experiences and data, and combining 4 monitoring techniques under different conditions of continuity in space and time domains, which are: displacement monitoring with Ground-based Synthetic Aperture Radar and characterization at slope scale, with an extremely non uniform atmospheric phase screen because of the stepped topography and atmosphere stratification; Terrestrial Laser Scanner surveys quantifying frequency for unnoticed activity of small rock falls, and monitoring rock block displacements over 1cm; monitoring of rock joints with a wireless net of sensors; and tentative surveying for singular rocky needles with Total Station.