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Atmospheric correction for interferometric synthetic aperture radar technique

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Atmospheric Correction for InSAR Technique

Atmospheric Correction for InSAR Technique is a set of different methods to remove artifact displacement from an Interferogram caused by the effect of weather variables such as humidity, temperature, and pressure. ​“Corrections”​ ​for​ ​this​ ​unwanted​ ​signal​ ​are​ ​an​ ​important​ ​stage​ ​of​ ​InSAR​ ​data processing in many study areas because the displacement result of Interferometric synthetic aperture radar (InSAR) can become inaccurate by 10-14cm if relative humidity differs by 20%. Overall, atmospheric correction methods can be divided into two categories: a) Using Atmospheric Phase Screen (APS) statistical properties and b) Using auxiliary (external) data such as GPS measurement, multi-spectral observations, local meteorological models, and Global Atmospheric Models[1].

Interferometric synthetic aperture radar (InSAR) can provide accurate (millimeter-level) ground displacement fields for large areas over hundreds of kilometers. This technique uses two SAR images of the same area acquired at different times to measure surface motion. Nevertheless, the result of InSAR in interferogram form includes actual displacement and other effects. Hence, these other effects must be calculated and removed from interferograms to achieve an accurate result. These effects include phase decorrelation, orbital errors, topographic residuals, phase-unwrapping errors, imperfect simulation of the imaging geometry, and extra path delay caused by microwave signal propagation through the atmosphere. There are several methods to remove all these noises except atmospheric effects with high accuracy. Thus, a significant challenge for the InSAR community remains atmospheric artifacts, and consequently, atmospheric delays cannot be ignored since they are often comparable or even much greater in magnitude than geophysical signals.

Advantages: On the other side, atmospheric noise might​ have​ ​some​ ​value for​ atmospheric​ ​research in Meteorology. The main advantage of InSAR maps of Precipitable Water Vapor (PWV) is their high spatial resolution (up to 20 m for C-band sensors) if compared with GNSS and other spaceborne passive sensors. The low temporal resolution of the InSAR PWV times series is the main disadvantage of this technique when seen from the side of meteorologists. However, these characteristics made the assimilation of InSAR maps of PWV into NWMs interesting for meteorologists only when studying [2].

Atmospheric noise

In radar satellites, microwave signals are reflected off a persistent scatter in a target area, and their two-way travel time is measured by satellites. Water vapor in the troposphere and free electrons in the ionosphere affect the propagation of microwave signals through the atmosphere because the different refractive index in these layers affects the speed of propagation.

File:Ionosphere Troposphere dGNSS 0.png
Ionospheric and Tropospheric effects on electromagnetic wave propagation[3]

Ionosphere

Ionospheric phase noise, which occurs more apparent with larger wavelengths, such as P or L-band radars, is a consequence of variations in free electron density in the 100-1000 km altitude along the travel path. Among radar satellites, L-band SARs (λ=23 cm), such as ALOS 1/2 and the future US-India NISAR mission because of their wavelength, are more subjected to ionospheric delays than C-band SARs (λ=5.6 cm), such as ERS 1/2, Envisat, and the RADARSAT. Therefore, the impact of the ionospheric contribution on the C and X bands SAR data is small and usually negligible [4]. There are a couple of methods to remove the Ionospheric noise artifact:

1) Using auxiliary data like GNSS

2) Ionospheric weather models

3) Using azimuth shift[5]

4) Split-spectrum methods[6]

An example of atmospheric artifacts in the interferogram of Tenerife, Spain[7]

Troposphere

The troposphere is the lower layer of the atmosphere, with up to 90% of the atmosphere's water vapor. A height of 1.4 km from the ground surface contains 50% of the water vapor mass, and both on the global and local scales, most of the world's weather takes place in this layer [8]. Therefore, the tropospheric path delays are caused by differences in temperature, atmospheric pressure, and the water vapor in the lower part of the atmosphere. Microwave atmospheric delay is a sum of the turbulent and vertical stratified components. The turbulent component can affect flat and mountainous terrains and is usually highly correlated in space and uncorrelated in time. On the other hand, the vertical stratified component with a high correlation to topography only influences areas with topography variations, such as hills or mountains. [9][10]. Although the tropospheric effect is regarded as noise in the InSAR community, it has great advantages in meteorology and enables scientists to predict and model water vapor in the troposphere. The propagationtion delay of electromagnetic waves of radar satellites in the troposphere will be explained in the following in terms of meteorology and the InSAR community.

Layers of troposphere and amount of water vapor in each altitude
Amount of water vapor in each altitude of the troposphere. Around 90% of water vapor is contained in the troposphere and 50% of which is between the earth's surface up to about a height of 1.4 km


  • In terms of Interferometry (InSAR)

From the InSAR side, signal delay caused by variations of tropospheric properties in space and time is the source of major challenges for interferometry. Tropospheric perturbation, caused by the differences in relative humidity, temperature, and pressure in the lower part of the troposphere between two acquisitions, can lead to additional fringes of up to 15–20 cm on interferograms [11]. The atmospheric artifacts on InSAR measurements span a broad spectrum from short-wavelength to long-wavelength. For example, a slow-moving weather system may cause a long-wavelength signal, which represents a ramp on the interferogram. This is the most dominant error source in interferograms with a large spatial extent and may be difficult to distinguish from other long-wavelength errors such as the orbital ramps, ocean tide loading, and solid earth tides[12]. On the other hand, the short wavelength signal can be caused by rapidly changing local atmospheric turbulence and the stratified component related to local topography.

Schematic resolution comparison of InSAR and GPS for a large area
Schematic resolution comparison of InSAR and GPS for a large area

In terms of Meteorology, tropospheric delay interestingly can be regarded as a useful tool for Meteorology purposes. Traditional methods for measuring water vapor include using a) Meteorological stations, b) Radiosonde, c) Spectrometer, and d) GPS. Recently, InSAR has been recognized as a promising tool for generating high-resolution maps of atmospherical precipitable water vapor temporal changes (ΔPWV) from the propagation delay of radar signals in the atmosphere [13]. Although InSAR temporal sampling of atmosphere properties is coarser than the GPS, the main advantage of InSAR PWV maps is their high spatial resolution of up to a few meters [14]. Therefore, meteorological scientists combine GPS and InSAR data (atmospheric part) to increase their models' temporal and spatial resolution [15].

Tropospheric correction methods

A phase delay through the troposphere can be characterized by the refractivity. This delay can be divided into two components: Dry delay and Wet delay. The dry delay, which is related to the pressure of dry air and temperature, and the wet delay, which is mainly related to the water vapor content present in the troposphere [16].

Figure 4. Schematic representation of the electromagnetic waves delays in tropospheric based on dry and wet components. Zenith Total Delay (ZTD) correspond to total delay, Zenith Wet Delay (ZWD) corresponds to Wet delay and Zenith Hydrostatic Delay (ZHD) is related to Dry delay of troposphere.
Schematic representation of the electromagnetic waves delays in tropospheric based on dry and wet components. Zenith Total Delay (ZTD) correspond to total delay, Zenith Wet Delay (ZWD) corresponds to Wet delay and Zenith Hydrostatic Delay (ZHD) is related to Dry delay of troposphere.

where N is the atmosphere refractivity and can be calculated using the atmospheric parameters as follows:

where P indicates total atmospheric pressure, T is the temperature and e is the partial pressure of water vapor. The coefficients k1 =77.689 ± 0.009 K/hPa, k2 = 71.2952 ± 1.3 K/hPa, and k3 = 3.75463 × 105 ± 0.0076 × 105 K2/hPa are called refractivity constants [17].

where dtropo is the tropospheric delay (1-way), θ the incidence angle, λ the radar wavelength. The dry component is correlated with the topography due to the pressure variation with height, and it can reach 2.3–2.4 m in the zenith direction (zenith hydrostatic delay (ZHD)). Due to the temporal and spatial stability of the dry constituents of the atmosphere, we can ignore the dry component. The wet component (zenith wet delay (ZWD)) represents about 10% of the total delay (varying approximately between 20 and 300 mm) regards the water content motion and turbulent mixing.

The total LOS single path tropospheric delay dLLOS (z) at an elevation z is the integral of the air refractivity between the surface elevation z and an elevation of reference zref and is modeled as [18] :

where θ is the local incidence angle, Rd = 287.05 J.kg−1.K−1 and Rv = 461.495 J.kg−1.K−1 are respectively the dry air and water vapor specific gas constants, gm is a weighted average of the gravity acceleration between z and zref, P is the dry air partial pressure in Pa, e is the water vapor partial pressure in Pa, and T is the temperature in K.

Since there is no accurate technique that could determine the total refractivity on the same spatial scale and temporal sampling as the interferogram itself, various methods have been developed to account for the atmospheric contribution within interferograms.

Time series (PS - SBAS)

One of the approaches used to mitigate tropospheric effects on InSAR measurements has been stacking/filtering. Interferogram stacking increases the signal-to-noise ratio of time-correlated/time-independent signals without any external information [19][20][21]. The other advantage of this method is independent on external data and straightforward to implement.

Limitation: For time series analysis approaches such as PS and SBAS, a large dataset has to be processed and this method only can reduce turbulent part of troposphere noise and signals of interest may be incorrectly removed.

Estimated tropospheric delay from GNSS

GNSS operates in the microwave portion of the electromagnetic spectrum similar to SAR technique and both measurements are affected by the atmospheric delay. In addition, both provide geodetic measurements with comparable accuracy. Using of both techniques simultaneously can lead to improvements in the atmospheric disturbances as well as for the cross-validation or integration of displacement measurements [22][23].

Limitation: Interpolation of zenith delay measurements from ground-based GPS. Requires dense GPS network but GPS stations are still sparsely distributed or even absent in many regions as well as this method only samples troposphere in the vicinity of individual GPS sites. Additionally, some GPS datasets are still not freely available to the public.

Satellite spectrometers

Spectrometer measurements are Satellite-based observations from space allow estimating the atmospheric water vapor by band ratios in the near-infrared spectrum. This method has a relatively high spatial resolution to calculate the turbulent component of the atmospheric disturbance [24].

Limitation: Requires collocated sensors and cloud-free conditions and only available in daytime. Time differences between radar and PWV data can be regarded as limitation [25].

Numerical weather models (ERA-I, ERA5, MERRA1, MERRA2)

Advantage of this method is insensitive to the presence of clouds and Global/regional/ local coverage. By using the ERA, uncertainty in ZWD in high latitudes (> 30∘), reach 1-2 cm, while uncertainty in low latitudes (< 30∘), is about 2-6 cm. Most of studies reported varying degrees of success for using this method [26].

Limitation: The low spatial resolution and the original mismatch in time between the model and the SAR acquisition do not permit addressing the turbulent component that takes place at lower Spatio-temporal scales. Moreover, complex data processing can be regarded as disadvantage of this method.

Phase based empirical: (i) linear correction (ii) power-law correction

The correlation analysis between interferometric phases and/or topography solves for the topography-correlated or stratified component. In other words, the correlation between range change in the LOS direction of InSAR and topography are related to the path length traveled by the electromagnetic wave. Estimation of linear and power-law relationships between the interferometric phase and the topography can be used to remove stratified parts of the troposphere. To estimate the stratified APS more accurately, recent improvements have been made by analyzing phase-elevation relationship with a multiple-regression model [27].

Limitation: The main limitation of these model related methods is that other phase terms (e.g., turbulent atmospheric artifacts, deformation related phase, decorrelation noise) can influence the estimate of the coefficient that relates phase with elevation. This method ignores the spatial variability of tropospheric signals and can be easily biased by orbit and topographic errors [28].

Numerical weather models (ERA5)

Here, we aim to explain ERA5 data with more details because of advantages of this data relative to others methods. Freely available Global Atmospheric Models (development of the numerical weather prediction) can provide accurate and higher resolution parameters for characterizing the atmosphere state, such as ERA5 data generated using Copernicus Climate Change Service Information. Hence, these methods are promising and practical techniques for atmospheric noise mitigation. The ERA5 is a global atmospheric model calculated by the European Center for Medium‑Range Weather Forecast (ECMWF) based on the assimilation of different input datasets. It provides several meteorological parameters, including pressure, temperature, and relative humidity at hourly intervals at a grid of 70 km (0.25 degrees) spatial resolution and 37 vertical intervals from sea level up to 50 km.

Figure 5. ERA5 data in 37 pressure levels and each grid has 16 parameters (Table 1)
Figure 5. ERA5 data in 37 pressure levels and each grid has 16 parameters (Table 1)

In this method, the zenith path delay is estimated first, and then delay along the Line-of-Sight (Z-LOS) direction is obtained geometrically by considering the incidence angle [29]. Once atmospheric phase delays are integrated along a zenithal path on the grid points using Equation, a cubic spline interpolation in the vertical direction and a bilinear interpolation in the horizontal one is performed to obtain the phase delays for the entire SAR scene from the sparse grid points. Once having the ZTD along the vertical direction, the cosine of the incidence angle is accounted for by back-projecting the result to the LOS direction [30]. Thus, we calculate in first image t1 and second image t2 by using equation and then subtracts these phases to achieve .

After that, by subtracting it from the original unwrapped interferogram we can remove the tropospheric effect from interferogram.

Name Variable Name Variable
divergence d specific_cloud_liquid_water_content clwc
fraction_of_cloud_cover cc specific_humidity q
geopotential z specific_rain_water_content crwc
ozone_mass_mixing_ratio o3 specific_snow_water_content cswc
potential_vorticity pv temperature t
relative_humidity r u_component_of_wind u
specific_cloud_ice_water_content ciwc v_component_of_wind v
vertical_velocity w vorticity vo

Table 1. Variables of ERA5 data

Conclusion

Tropospheric effects can limit the accuracy of InSAR measurements and cause misunderstanding in the interpretation of the geophysical processes. For instance, an error of 0.10–0.14 m for land surface deformation monitoring and possibly 80–290 m for topography mapping may be introduced by a 20% relative humidity change [31]. Thus, properly characterizing this noise remains a challenge and reduces the ability of researchers to take full advantage of the available InSAR time series.

1- Different methods correct for different components of the troposphere and no method is exclusive the best in reducing tropospheric delays. In other words, the different tropospheric correction techniques all have their own limitations, and are not always sensitive to the same component of the tropospheric delay. For example, GPS-derived corrections performed comparably well when and where data was available and elevation-phase dependence is a more useful metric for areas of high relief and less effective in areas of low relief. Thus, rather than opting for a single method, jointly invert for tropospheric properties such different technique constrains each other, this will require relative weighting, quality measure of methods

2- Global measurements of tectonic/volcanic deformation need global atmospheric corrections. Although, ECMWF based on atmospheric reanalysis data provides a global data, low spatial resolution of it regarded as drawback. In order to optimally utilize InSAR atmospheric correction methods and to avoid potential uncertainty caused, it is urgent to develop a generic assessment method without the use of ‘ground truth’ to evaluate the atmospheric correction performance.

3- Compared with GPS data, InSAR is a promising technique to retrieve the water vapor product with global coverage and higher resolution. On the other hand, the InSAR technique can also provide potential enrichment of datasets used for research using numerical weather models, especially in very localized areas for turbulent atmosphere research. Even now, the latest suite of numerical weather prediction models has difficulty in accurately predicting meso- and micro-scale atmospheric dynamics, due mainly to computational discretization and observational scarcity. It is believed that atmospheric delays from InSAR can provide a promising observation dataset for weather data assimilation

See also

InSAR technique

Atmosphere of Earth

Meteorology

References

  1. ^ Hu, Zhongbo; Mallorquí, Jordi J. (2019-01). "An Accurate Method to Correct Atmospheric Phase Delay for InSAR with the ERA5 Global Atmospheric Model". Remote Sensing. 11 (17): 1969. doi:10.3390/rs11171969. ISSN 2072-4292. {{cite journal}}: Check date values in: |date= (help)CS1 maint: unflagged free DOI (link)
  2. ^ Mateus, Pedro; Catalao, Joao; Nico, Giovanni (2017-05). "Sentinel-1 Interferometric SAR Mapping of Precipitable Water Vapor Over a Country-Spanning Area". IEEE Transactions on Geoscience and Remote Sensing. 55 (5): 2993–2999. doi:10.1109/TGRS.2017.2658342. ISSN 0196-2892. {{cite journal}}: Check date values in: |date= (help)
  3. ^ "GPS Satellite Signals: Frequency and the Data Contained Within Them". www.brighthub.com. 2011-03-28. Retrieved 2022-10-23.
  4. ^ Gray, A. Laurence; Mattar, Karim E.; Sofko, George (2000-05-15). "Influence of ionospheric electron density fluctuations on satellite radar interferometry". Geophysical Research Letters. 27 (10): 1451–1454. doi:10.1029/2000GL000016.
  5. ^ Meyer, F.; Bamler, R.; Jakowski, N.; Fritz, T. (2006-10). "The Potential of Low-Frequency SAR Systems for Mapping Ionospheric TEC Distributions". IEEE Geoscience and Remote Sensing Letters. 3 (4): 560–564. doi:10.1109/LGRS.2006.882148. ISSN 1558-0571. {{cite journal}}: Check date values in: |date= (help)
  6. ^ Rosen, Paul A.; Hensley, Scott; Chen, Curtis (2010-05). "Measurement and mitigation of the ionosphere in L-band Interferometric SAR data". 2010 IEEE Radar Conference: 1459–1463. doi:10.1109/RADAR.2010.5494385. {{cite journal}}: Check date values in: |date= (help)
  7. ^ Hu, ZhongBo (2019). Atmospheric artifacts correction for insar using empirical model and numerical weather prediction models (http://purl.org/dc/dcmitype/Text thesis) (in Spanish). Universitat Politècnica de Catalunya (UPC). {{cite thesis}}: External link in |degree= (help)
  8. ^ Mateus, Pedro; Nico, Giovanni; Catalao, Joao (2015-12). "Uncertainty Assessment of the Estimated Atmospheric Delay Obtained by a Numerical Weather Model (NMW)". IEEE Transactions on Geoscience and Remote Sensing. 53 (12): 6710–6717. doi:10.1109/TGRS.2015.2446758. ISSN 0196-2892. {{cite journal}}: Check date values in: |date= (help)
  9. ^ Radar Interferometry. doi:10.1007/0-306-47633-9.
  10. ^ Xiao, Ruya; Yu, Chen; Li, Zhenhong; He, Xiufeng (2021-04). "Statistical assessment metrics for InSAR atmospheric correction: Applications to generic atmospheric correction online service for InSAR (GACOS) in Eastern China". International Journal of Applied Earth Observation and Geoinformation. 96: 102289. doi:10.1016/j.jag.2020.102289. {{cite journal}}: Check date values in: |date= (help)
  11. ^ Bekaert, D.P.S.; Walters, R.J.; Wright, T.J.; Hooper, A.J.; Parker, D.J. (2015-12). "Statistical comparison of InSAR tropospheric correction techniques". Remote Sensing of Environment. 170: 40–47. doi:10.1016/j.rse.2015.08.035. {{cite journal}}: Check date values in: |date= (help)
  12. ^ Shirzaei, Manoochehr; Walter, Thomas R. (2011-11). "Estimating the Effect of Satellite Orbital Error Using Wavelet-Based Robust Regression Applied to InSAR Deformation Data". IEEE Transactions on Geoscience and Remote Sensing. 49 (11): 4600–4605. doi:10.1109/TGRS.2011.2143419. ISSN 1558-0644. {{cite journal}}: Check date values in: |date= (help)
  13. ^ Mateus, Pedro; Nico, Giovanni; Catalao, Joao (2014-12). "Maps of PWV Temporal Changes by SAR Interferometry: A Study on the Properties of Atmosphere's Temperature Profiles". IEEE Geoscience and Remote Sensing Letters. 11 (12): 2065–2069. doi:10.1109/LGRS.2014.2318993. ISSN 1545-598X. {{cite journal}}: Check date values in: |date= (help)
  14. ^ Mateus, Pedro; Nico, Giovanni; Catalao, Joao (2014-12). "Maps of PWV Temporal Changes by SAR Interferometry: A Study on the Properties of Atmosphere's Temperature Profiles". IEEE Geoscience and Remote Sensing Letters. 11 (12): 2065–2069. doi:10.1109/LGRS.2014.2318993. ISSN 1545-598X. {{cite journal}}: Check date values in: |date= (help)
  15. ^ Benevides, Pedro; Nico, Giovanni; Catalao, Joao; Miranda, P. M. A. (2016-02). "Bridging InSAR and GPS Tomography: A New Differential Geometrical Constraint". IEEE Transactions on Geoscience and Remote Sensing. 54 (2): 697–702. doi:10.1109/TGRS.2015.2463263. ISSN 0196-2892. {{cite journal}}: Check date values in: |date= (help)
  16. ^ Mateus, Pedro; Nico, Giovanni; Catalao, Joao (2015-12). "Uncertainty Assessment of the Estimated Atmospheric Delay Obtained by a Numerical Weather Model (NMW)". IEEE Transactions on Geoscience and Remote Sensing. 53 (12): 6710–6717. doi:10.1109/TGRS.2015.2446758. ISSN 0196-2892. {{cite journal}}: Check date values in: |date= (help)
  17. ^ Smith, Ernest; Weintraub, Stanley (1953-08). "The Constants in the Equation for Atmospheric Refractive Index at Radio Frequencies". Proceedings of the IRE. 41 (8): 1035–1037. doi:10.1109/JRPROC.1953.274297. ISSN 0096-8390. {{cite journal}}: Check date values in: |date= (help)
  18. ^ Berrada Baby, H.; Golé, P.; Lavergnat, J. (1988-11). "A model for the tropospheric excess path length of radio waves from surface meteorological measurements". Radio Science. 23 (6): 1023–1038. doi:10.1029/RS023i006p01023. {{cite journal}}: Check date values in: |date= (help)
  19. ^ Fattahi, Heresh; Amelung, Falk (2015-12). "InSAR bias and uncertainty due to the systematic and stochastic tropospheric delay". Journal of Geophysical Research: Solid Earth. 120 (12): 8758–8773. doi:10.1002/2015JB012419. ISSN 2169-9313. {{cite journal}}: Check date values in: |date= (help)
  20. ^ Hooper, Andrew; Zebker, Howard; Segall, Paul; Kampes, Bert (2004-12-16). "A new method for measuring deformation on volcanoes and other natural terrains using InSAR persistent scatterers: A NEW PERSISTENT SCATTERERS METHOD". Geophysical Research Letters. 31 (23). doi:10.1029/2004GL021737.
  21. ^ Berardino, P.; Fornaro, G.; Lanari, R.; Sansosti, E. (2002-11). "A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms". IEEE Transactions on Geoscience and Remote Sensing. 40 (11): 2375–2383. doi:10.1109/TGRS.2002.803792. ISSN 0196-2892. {{cite journal}}: Check date values in: |date= (help)
  22. ^ Bonforte, Alessandro; Ferretti, Alessandro; Prati, Claudio; Puglisi, Giuseppe; Rocca, Fabio (2001-08). "Calibration of atmospheric effects on SAR interferograms by GPS and local atmosphere models: first results". Journal of Atmospheric and Solar-Terrestrial Physics. 63 (12): 1343–1357. doi:10.1016/S1364-6826(00)00252-2. {{cite journal}}: Check date values in: |date= (help)
  23. ^ Onn, F.; Zebker, H. A. (2006). "Correction for interferometric synthetic aperture radar atmospheric phase artifacts using time series of zenith wet delay observations from a GPS network". Journal of Geophysical Research. 111 (B9): B09102. doi:10.1029/2005JB004012. ISSN 0148-0227.
  24. ^ Li, Zhenhong; Fielding, Eric J.; Cross, Paul; Muller, Jan-Peter (2006). "Interferometric synthetic aperture radar atmospheric correction: Medium Resolution Imaging Spectrometer and Advanced Synthetic Aperture Radar integration". Geophysical Research Letters. 33 (6): L06816. doi:10.1029/2005GL025299. ISSN 0094-8276.
  25. ^ Bekaert, D.P.S.; Walters, R.J.; Wright, T.J.; Hooper, A.J.; Parker, D.J. (2015-12). "Statistical comparison of InSAR tropospheric correction techniques". Remote Sensing of Environment. 170: 40–47. doi:10.1016/j.rse.2015.08.035. {{cite journal}}: Check date values in: |date= (help)
  26. ^ Jolivet, R.; Grandin, R.; Lasserre, C.; Doin, M.-P.; Peltzer, G. (2011-09). "Systematic InSAR tropospheric phase delay corrections from global meteorological reanalysis data: CORRECTING INSAR WITH ERA-INTERIM". Geophysical Research Letters. 38 (17): n/a–n/a. doi:10.1029/2011GL048757. {{cite journal}}: Check date values in: |date= (help)
  27. ^ Bekaert, D. P. S.; Hooper, A.; Wright, T. J. (2015-02). "A spatially variable power law tropospheric correction technique for InSAR data". Journal of Geophysical Research: Solid Earth. 120 (2): 1345–1356. doi:10.1002/2014JB011558. ISSN 2169-9313. {{cite journal}}: Check date values in: |date= (help)
  28. ^ Fattahi, Heresh; Amelung, Falk (2015-12). "InSAR bias and uncertainty due to the systematic and stochastic tropospheric delay". Journal of Geophysical Research: Solid Earth. 120 (12): 8758–8773. doi:10.1002/2015JB012419. ISSN 2169-9313. {{cite journal}}: Check date values in: |date= (help)
  29. ^ Jolivet, R.; Grandin, R.; Lasserre, C.; Doin, M.-P.; Peltzer, G. (2011-09). "Systematic InSAR tropospheric phase delay corrections from global meteorological reanalysis data: CORRECTING INSAR WITH ERA-INTERIM". Geophysical Research Letters. 38 (17): n/a–n/a. doi:10.1029/2011GL048757. {{cite journal}}: Check date values in: |date= (help)
  30. ^ Jolivet, R.; Grandin, R.; Lasserre, C.; Doin, M.-P.; Peltzer, G. (2011-09). "Systematic InSAR tropospheric phase delay corrections from global meteorological reanalysis data: CORRECTING INSAR WITH ERA-INTERIM". Geophysical Research Letters. 38 (17): n/a–n/a. doi:10.1029/2011GL048757. {{cite journal}}: Check date values in: |date= (help)
  31. ^ Zebker, Howard A.; Rosen, Paul A.; Hensley, Scott (1997-04-10). "Atmospheric effects in interferometric synthetic aperture radar surface deformation and topographic maps". Journal of Geophysical Research: Solid Earth. 102 (B4): 7547–7563. doi:10.1029/96JB03804.
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