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This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Interferometric Synthetic Aperture Radar (InSAR) is a powerful technology for observing the Earth surface, especially for mapping the Earth's topography and deformations. InSAR measurements are however often significantly affected by the atmosphere as the radar signals propagate through the atmosphere whose state varies both in space and in time. Great efforts have been made in recent years to better understand the properties of the atmospheric effects and to develop methods for mitigating the effects. This paper provides a systematic review of the work carried out in this area. The basic principles of atmospheric effects on repeat-pass InSAR are first introduced. The studies on the properties of the atmospheric effects, including the magnitudes of the effects determined in the various parts of the world, the spectra of the atmospheric effects, the isotropic properties and the statistical distributions of the effects, are then discussed. The various methods developed for mitigating the atmospheric effects are then reviewed, including the methods that are based on PSInSAR processing, the methods that are based on interferogram modeling, and those that are based on external data such as GPS observations, ground meteorological data, and satellite data including those from the MODIS and MERIS. Two examples that use MODIS and MERIS data respectively to calibrate atmospheric effects on InSAR are also given.

Synthetic Aperture Radar (SAR) Interferometry, commonly referred to as InSAR, IFSAR or SARI, is a synthesis of the SAR and the interferometry techniques [

Significant progress has been made in further developing InSAR technology in the past two decades with the availability of a vast amount of globally covering SAR images from, e.g., ERS, Radarsat, JERS, Envisat, ALOS and TerraSAR sensors and with a wide range of applications of the technology (e.g., [

InSAR technology, however, has also limitations. One of the most intractable is the effect of the atmosphere (mainly the troposphere and the ionosphere) on repeat-pass InSAR. It is well known that electromagnetic waves are delayed (slowed down) when they travel through the troposphere. The effect often introduces significant errors to repeat-pass InSAR measurements. Massonnet

Contrary to the effects of the troposphere, the ionosphere tends to accelerate the phases of electromagnetic waves when they travel through the medium. The zenith ionospheric range error is proportional to the total electron content (TEC) in the ionosphere. For example, for C-band SAR, a TEC of 1 × 10^{16} m^{-2} causes a phase shift of about half a cycle [

InSAR can be classified into across- and along-track interferometry according to the interferometric baseline formed, or single- and repeat-pass interferometry according to the number of platform passes involved. Two antennas are mounted on the same platform in along-track interferometry and a single platform pass suffices [

The geometrical configuration of repeat-pass SAR interferometry is illustrated in _{1} and _{2}, measured at the two platform positions to a ground point are:
_{1} and _{2} are the slant ranges and

Under the far field approximation, one gets

When assuming a surface without topographic relief as illustrated in _{0} is the look angle. If topographic relief is present, the look angle will differ from _{0} by

The aforementioned process of topography reconstruction is based on the assumption that the imaged surface is stationary during the acquisitions. The interferometric phase in repeat-pass interferometry in fact measures any ground displacement in addition to topography. DInSAR is the technique to extract displacement signature from a SAR interferogram over the acquisition period. In

The displacement will introduce a variation of interferometric phase which is proportional to Δr:

To map the ground deformation between two SAR acquistions, the topographic contribution must be removed. According to the ways to remove the topographic contribution, three types of DInSAR configuration can be distinguished: (1) two-pass plus external DEM, (2) three-pass, and (3) four-pass. In two-pass plus external DEM formulation, a SAR interferogram (topographic interferogram thereinafter) is simulated based on the DEM and the imaging geometry of the “real” interferogram (deformation interferogram thereinafter) and is removed from the deformation interferogram. However, in three-pass and four-pass formulations, both the topographic and the deformation interferograms are generated from SAR images. The only difference between them is that in three-pass interferometry, one image is shared by both the topographic and the deformation interferograms. The two-pass plus external DEM and three-pass and four-pass configuration DInSAR can be expressed as:
_{d}_{t}

The interferometric phase in

Atmospheric artifacts in SAR interferograms are mainly due to changes in the refractive index of the medium. These changes are mainly caused by the atmospheric pressure, temperature and water vapor. In most cases, the spatial variations of pressure and temperature are not large enough to cause strong, localized phase gradients in SAR interferograms. Their effects are generally smaller in magnitude and more evenly distributed throughout the interferogram when comparing with that of the water vapor, and sometimes difficult to be distinguished from errors caused by orbit uncertainties [

Clouds are formed when the water vapor in the air condenses into visible mass of droplets or frozen crystals. Clouds are divided into two general categories, layered and convective. These are named stratus clouds and cumulus clouds respectively. The liquid water content in the stratiform clouds is usually low so that they do not cause significant range errors to SAR signals. The liquid water content in the cumulus clouds can however range from 0.5 to 2.0 g/m^{3} and cause zenith delays of 0.7 to 3.0 mm/km [

Due to the propagation delay of radar signals, in repeat-pass SAR interferometry systems, the phase measurements corresponding to _{1} and Δ_{2} are atmospheric propagation delays of radar signals corresponding to the first and the second acquisitions. This gives the interferometric phase

It is obvious from _{1} − Δ_{2}) that causes errors in InSAR measurements. If the atmospheric profiles remain the same at the two acquisitions, the relative tropospheric delay will disappear. In addition, if Δ_{1} − Δ_{2} =

The influences of the atmosphere induced phase errors on repeat-pass topographic and two-pass surface deformation measurements are straightforward [_{ϕ}_{h}_{Δ}_{r,two}

Assuming the same standard deviation _{ϕ}_{d} ϕ_{t}^{T}

A SAR interferogram is a superposition of information on the topography, the surface deformation between the two SAR acquisitions, the differential atmospheric propagation delays between the two SAR acquisitions, and various noise (e.g., [

Radon transform is the projection of image intensities along a radial line at a specified angle. A single Radon transform is a mapping of an image from two dimensions to one dimension where the image intensities collapse to a profile. Radon transform is therefore a tool to investigate anisotropy in images since systematic intensity variations in a particular direction will be visible as a profile [

Hanssen [

The Radon transform of atmospheric signals showed varying degrees of anisotropy. For example, the first transform (

It is important to examine the Gaussianity of atmospheric signals in SAR interferograms as different processing strategies must be applied for Gaussian and non-Gaussian signals. There are a number of hypothesis tests to study whether a signal is Gaussian or non-Gaussian. The Jarque-Bera test is based on classical measures of skewness and kurtosis and it examines whether the sample skewness and kurtosis are unusually different from their expected values [

The spectrum of atmospheric signals in a SAR interferogram reveals the energy distribution of the atmospheric effects at different spatial scales. Two-dimensional (2D) FFT is generally used to estimate the 2D power spectra of atmospheric signals. As the power spectra derived can be very noisy, the one-dimensional (1D) rotationally averaged power spectra are usually calculated from the 2D power spectra and used to study the energy distribution of atmospheric signals (e.g., [

Goldstein

The power law spectral characteristics of the atmospheric signals are very useful. For example, Ferretti

The power law can be described by

The 3D Kolmogorov tropospheric turbulence can occur within the region of up to several kilometers in elevation, usually referred to as the effective height of the wet troposphere. The LOS ranges of space-borne SAR systems are much larger than the effective height. The wet tropospheric delays can be therefore typically modeled as 2D turbulence [

The power exponent is an important parameter for estimating to what extent the atmospheric effects can be determined and removed with the help of external data. The accumulated energy of the atmospheric signals can be estimated based on the information for different scales by integrating the atmospheric power over the spatial frequencies. The spatial scales corresponding to 90% of the energy thus computed for the four interferograms mentioned above are 0.82, 1.01, 0.94, and 0.29 km, respectively [

Using ground meteorological data to calibrate tropospheric delays in radio ranging has been well documented [

The difficulties in using meteorological data to correct atmospheric effects on InSAR include mainly the poor accuracy of the atmospheric delays estimated from empirical tropospheric models and the usually very sparse distribution of meteorological stations.

The advances in GPS meteorology have enabled accurate estimation of tropospheric delays from GPS observations [

Considering the power law nature of the atmospheric noise, Williams

The research results in [

There are many GPS networks around the world operated in continuous mode. If GPS observations prior to and after SAR acquisitions are available, they can also contribute to the correction of atmospheric effects on InSAR. Onn [

The various methods proposed to date that use GPS observations to correct InSAR atmospheric effects differ primarily in the algorithms used to generate atmospheric delay maps from the spatially sparse GPS atmospheric delay measurements. Therefore, the accuracy of the corrections depends on how much atmospheric delays can be retrieved at the unsampled locations from the sparse GPS measurements. With the gradual increase in the density of GPS networks around the world, the method should become more and more useful.

Numerical meteorological modeling is an essential tool in atmospheric research. Numerical meteorological modeling can be carried out on global, regional or mesoscale. The global and regional numerical meteorological models are usually too coarse to model atmospheric effects on InSAR. The mesoscale numerical models can have a continuous time scale and a horizontal spatial scale of a few kilometers, and are therefore suitable for InSAR atmospheric correction. Integrated water vapor content along the radar paths can be retrieved from such models and used to calibrate atmospheric effects on InSAR.

Wadge

The near-IR water vapor products provided by the Moderate Resolution Imaging Spectroradiometer (MODIS) have a spatial resolution of 1 km× 1 km (at nadir) and an accuracy of 5-10% [

Li

Considering that all data interpolators unavoidably suffer from smoothing effects [

The MODIS PWV measurements however are sensitive to the presence of clouds as noted earlier, which limits significantly the use of MODIS PWV in cloudy regions. In addition, systematic biases in space borne MODIS PWV measurements may exist and need to be calibrated with more accurate PWV measurements (e.g., GPS PWV).

The MERIS onboard the Envisat satellite allows for global retrieval of PWV every three days, with two near infrared water vapor channels. It therefore can acquire water vapor data simultaneously with the Advanced SAR (ASAR). Its PWV measurements have a resolution as high as 300 m and accuracy higher than that of MODIS [

Li

Using the Los Angeles area as an example, Li

There are mainly two types of correlation analysis adopted to reduce atmospheric effects on InSAR. The first type analyzes the correlation between interferograms, and the second the correlation between atmosphere-induced interferometric phases and elevation. Sarti

Beauducel

Chaabane

The method of correlation analysis is advantageous in that no external data are needed. The method however strongly depends on the correlations between the deformations and between the atmospheric signals in different interferograms. Weak correlation may lead to insufficient atmospheric effect reduction.

The atmospheric signature in a SAR interferogram can be determined with the pair-wise logic method [

PSInSAR is a relatively new interferometic processing method [

Stacking is a method that reduces the atmospheric effects on InSAR by averaging independent SAR interferograms. Assuming that atmospheric effects are uncorrelated between the interferograms, averaging

We have in this section looked through the various existing methods for mitigating the atmospheric effects on InSAR measurements. It should however be pointed out that in principle an optimal integration of some of the methods should yield the best results.

Atmospheric effects are one of the limiting error sources in repeat-pass InSAR measurements. They can introduce errors of over ten centimeters to ground deformations and of several hundred meters to DEMs measured with the conventional DInSAR method when considering the typical baseline geometries used. Studies have shown that atmospheric signals in SAR interferograms are anisotropic and non-Gaussian in distribution. The spectra of the atmospheric signals follow a power law distribution with the power exponent very close to -8/3. Various methods have been developed for mitigating the atmospheric effects on InSAR measurements based on external data such as ground meteorological observations, GPS data, satellite water vapor products such as those from MERIS and MODIS, and results from numerical meteorological modeling. These methods are typically able to reduce the atmospheric effects by about 20-40 percents. The other methods developed for mitigating the atmospheric effects are mainly based on simple data analysis or numerical solutions, including the pair-wise logic, the stacking, the correlation analysis, and the PSInSAR methods. Each of the methods developed has its pros and cons. The most suitable method should be chosen considering the number of SAR scenes acquired, the method used for InSAR processing, the atmospheric conditions (e.g., cloud conditions) and the external data available. Despite the progress already made in the research, further studies are still necessary in the area to develop more effective methods for the mitigation of the atmospheric effects.

The work presented was supported by the Research Grants Council of the Hong Kong Special Administrative Region (Project Nos.: PolyU 5157/05E and PolyU 5161/06E), the National Science Foundation of China (Project Nos.: 40774003 and 40404001), the Hong Kong Polytechnic University (Project No.: G-YX48), the National High-Tech. Program of China (Project No.: 2006AA12Z156), and West China 1:50000 Topographic Mapping Project. Some of the images used were provided by the European Space Agency under a Category 1 User Project (AO-4458, 4914).

Interferometric geometry (from Li

Geomtry of DInSAR.

Radon transform of atmospheric signals in SAR pairs acquired on: (a) 19 and 20 February, 1996, (b) 25 and 26 March, 1996, (c) 3 and 4 June, 1996, and (d) 16 November and 21 December, 1999 (from Li

Power spectra of atmospheric signals for SAR pairs acquired on: (a) 19 and 20 February, 1996, (b) 25 and 26 March, 1996, (c) 3 and 4 June, 1996, and (d) 16 November and 21 December, 1999. (from Li

Atmospheric path delay corrections for interferometric pair of 29 July 2000 and 18 August 2001 over Los Angeles basin, South California. (a) original interferogram (deformation field has been modeled with GPS observations and removed from the interferogram); (b) interferogram corrected using MODIS data. (from Li [

Atmospheric path delay correction for interferometric pair of 30 April 2006 and 11 March 2007 over Hong Kong area. (a) original interferogram; (b) interferogram corrected using MERIS data.