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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:Satte0301.tif
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]

File:Tenn09.tif
An example of atmospheric artifacts in the interferogram of Tenerife, Spain[7]. This image shows the correlation between height and displacement clearly.

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 InSAR rechnique. 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 noise in form of fringes up to 15–20 cm on interferograms [11]. The atmospheric artifacts on InSAR results 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. Generally, tropospheric signal can be diveded into two parts: space and time.

Tropospheric artifact Space Systematic Stratified
Stochastic Turbulent
Time Systematic Seasonal
Stochastic Nonseasonal
File:Reflection0010013s.tif
These figures show the correlation between the signal delay and altitude in two points( p and q ) with different hight at t1(date of image one) and t2(date of image two). The signal reflected from q would have more delay because the amount of water vapor near the surface is very high and subject to more variation in t2 [13].
  • Vertical stratification: Vertical stratification can cause differential delay contributions where the topography of a study area is characterized by significant changes such as hills or mountains. In other words, this part is a longer-scale topography-correlated (tens of km) component, introduced by lateral variation of pressure, temperature, and relative humidity.
  • Turbulence: Turbulent mixing consist of a short-scale (few km) component and is not directly correlated with topography and affects both flat terrains and higher altitude terrains.
  • File:Tene.jpg
    Popocatepetel, Mexico, 2014-2017 summit displacement and seasonal effect during 2016 (Amelung presentation, InSAR Meteorology Miami 2018[14]).
    Seasonal (systematic) effect : Variation of moisture content of the atmosphere during different seasons may impose an artifact and bias the InSAR displacement time series. The large number of SAR acquisitions will not redice the velocity bias necessarily [15]. Nonetheless, the stratified tropospheric delay correction can mitigate the effects of the seasonal delay[16][17].

In terms of Meteorology

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 [18]. Although InSAR temporal sampling (6 days) of atmosphere properties is coarser than the GPS (15 min), the main advantage of InSAR PWV maps is its high spatial resolution of up to a few meters (20 m) [19]. Therefore, meteorological scientists combine ​traditional​ ​GPS​ ​tomography​ ​of​ ​atmosphere with InSAR data (atmospheric part) to increase their models' temporal and spatial resolution [20].

File:Ppt file Seminar 28.jpg
Schematic resolution comparison of InSAR and GPS for a large area

Tropospheric correction methods

The phase delay through the troposphere can be characterized by the refractivity (N).

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. 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 [21].

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 [22].

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)). Nonetheless, due to the temporal and spatial stability of the dry constituents of the atmosphere in long time, this component does not regarded as big challange. On the contrary, although the wet component (zenith wet delay (ZWD)) represents about 10% of the total delay (varying approximately between 20 and 300 mm), it is regarded as the significant challange because of the water content motion and turbulent mixing.

Therefore, the total LOS single path tropospheric delay dLLOS (z) at an elevation z is the integral of the air refractivity (wet and dry components) between the surface elevation z and an elevation of reference zref and is modeled as [23] :

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 mesure for the atmospheric contribution within interferograms. In the following a couple of methods are introduced to mitigate tropospheric artifact from interfrograms:

Time series methods such as Persistent Scatter (PS) and Small Baseline Subset (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 [24][25][26]. 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 moslty can reduce turbulent part of troposphere noise and signals of interest may be incorrectly removed. Thus, this method cannot be implemented only for one interferogram.

Estimated tropospheric delay from GNSS

GNSS uses microwave portion of the electromagnetic spectrum similar to SAR technique and both measurements are affected by the atmospheric delay and both provide geodetic measurements with comparable accuracy. Therefore, using interpolating GNSS observation (ِdense GNSS network) to estimate tropospheric delay can be a more accurate strategy to correct InSAR observations[27].

Limitation: Interpolation of zenith delay measurements requires dense GPS network in the study area 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. Moreover, GPS datasets are still not freely available to the public in the many areas in the world.

Satellite Spectrometers (MERIS and MODIS)

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 [28].

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 [29]. Moreover, Spectrometer measurements only produce an estimate for the wet component of the delay.

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 [30]. Nonetheless, ​ERA-interim​​, and ERA5​ ​​global​ ​re-analysis​ ​models​ ​ are popular​ ​models​ ​​​provided​ ​by​ ​the​ ​European​ ​Center​ ​for​ ​Medium-Range​ ​Weather Forecasting​ ​(ECMWF)​ ​and​ ​the​ ​​HRES​ ​ECMWF​ ​forecast​ ​model.​ ​Moreover, the​ ​GACOS​ ​project​ ​aims​ ​to refine​ ​information​ ​from​ ​HRES​ ​with​ ​GNSS​ ​zenith​ ​delays​ ​if​ ​available.

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 the interferometric phase and topography can recognize the amount of topography-correlated (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 [31].

Limitation: The main limitation of these model 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 [32].

Numerical weather models (ERA5)

Freely available Global Atmospheric Models such as ERA5 data are generated using Copernicus Climate Change Service Information developed for numerical weather prediction. These models can provide accurate and high-resolution parameters for characterizing the atmosphere state. Therefore, these methods are promising and practical techniques for atmospheric noise mitigation in InSAR technique. 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. Several meteorological parameters are provided, such as pressure, temperature, and relative humidity, at hourly intervals with a horizontal resolution of 0.25 degrees and a vertical resolution of 37 intervals from sea level 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)

This method estimates the zenith path delay first and then calculates the delay along the Line of Sight (LOS) direction geometrically by considering the incidence angle, [33] though in some recent studies, LOS delays are calculated directly. In order to obtain the phase delays for the entire SAR scene from the sparse grid points, cubic spline interpolation in the vertical direction and bilinear interpolation in the horizontal direction are performed. Once the atmospheric phase delays are integrated along a zenithal path on the grid points using the Equation. 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 [34]. Thus, after calculation in first image t1 and second image t2, and subtraction of the original interferogram (), the effect of atmospheric noise can be removed.

File:A342d.jpg
Atmospheric correction across the Tenerife
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

Available packages for atmospheric correction

Terrain: TRAIN – is developed to include the current state of the art tropospheric correction methods into the default InSAR processing chain [35].

PyAPS: This python 3 module estimates differential phase delay maps due to the stratified atmosphere for correcting radar interferograms[36].

RAiDER: RAiDER-tools is a package in Python which contains tools to calculate tropospheric corrections for Radar using a raytracing implementation[37].

GACOS: GACOS utilizes the Iterative Tropospheric Decomposition (ITD) model to separate stratified and turbulent signals from total tropospheric delays, and generate high spatial resolution zenith total delay maps to be used for correcting InSAR measurements and other applications[38][39][40]

ICAMS: An open-source module in python for InSAR troposphere Correction using global Atmospheric Models that consider the Stochastic spatial properties of the troposphere (ICAMS)[41].

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 [42]. 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

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  33. ^ 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)
  34. ^ 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)
  35. ^ 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)
  36. ^ 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)
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  39. ^ Yu, Chen; Li, Zhenhong; Penna, Nigel T. (2018-01-01). "Interferometric synthetic aperture radar atmospheric correction using a GPS-based iterative tropospheric decomposition model". Remote Sensing of Environment. 204: 109–121. doi:10.1016/j.rse.2017.10.038. ISSN 0034-4257.
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