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SAR interferometry with distributed satellites is a technique based on the exploitation of the interference pattern of two SAR images acq uired synchronously. The interferogram contains geometric, atmospheric, topographic and land defomation. This paper focuses on atmospheric effects on SAR interferometry, which shows theoretically that the relationship among ionosphere TEC and troposphere parameters such as temperature, relative humitdity and pressure with respect to slant rang changes. An atmospheric correction method is given in the end.

With the development and the maturity of SAR Interferometry technology, its accuracy is increasing largely and it is significant to study the factors which can lower the accuracy of SAR Interferometry technology [

According to the Fermat principle and Snell’s law in the basic theory of light propagation, the optical range ρ from satellite to ground point is formed as

where r_{0} is the center distance for a ground point (

Define N for the difference of atmospheric refractive index:

In a spherically symmetric layered medium, according to Snell law, a formula is given by

According to Saastamoinen model (1972) of the atmospheric refraction, the zenith delay of atmospheric refraction can be given by

where

According to Magnus’ empirical formula, the relationship between vapor pressure and relative humidity at the condition of air temperature T (˚C) can be expressed as

Due to variable insolation of the Sun the spatial distribution of the layers varies during the day. The impact of the state of the ionosphere on the propagation of waves is characterized by the Total Electron Content (E), where

The integral contains the total number of electrons that are included in a column with a cross-sectional area of 1 m^{2}, counted along the signal path ρ between the ground point P0 and the satellite S. The unit of measurement is the TECU (Total Electron Content Unit): 1TECU = 1 × 10^{16} el/m^{2}.

The ionosphere is a dispersive medium for radio waves. For the formula of dispersion (e.g. Davies, 1990) of the index of refraction, rearranging and neglecting higher order terms gives [

where the parameter a is a constant.

According to Equations (7) and (8), the ionosphere delay along the signal propagation path

That is to say, if we can get the E(TEC) along the signal propagation path, we can calculate the propagation delay directly.

The atmospheric refractive effect of Troposphere is independent of the frequency but is decided by the atmospheric temperature, pressure and humidity. Atmospheric refractive error of Troposphere includes the dry item and the wet item. Refraction error of Tropospheric atmosphere in zenith direction is about 2.0 - 2.7 m, which is computed approximately (

The inland distribution of distance error caused by Tropospheric atmosphere refraction, which is obtained by using the historical meteorological sounding data of 10 years, is shown in

From the above research on the inland distribution of distance error, we can get some conclusions as follow:

1) When the elevation of the satellite is above 30˚ (viewed from the ground), the distance error caused by Tropospheric atmosphere refraction is mostly less than 5.5 m.

2) The dry item of refractive error can be estimated accurately from the ground meteorological parameters due to its regular and steady changes. The wet item of refractive error is the main part of the residual error for refractive error correction due to its irregular changing with time and space.

3) The proportion changes of distance error caused by the wet item of the refraction vary with month and quadrillage obviously but do not vary with elevation.

The refractive error of Ionospheric atmosphere has a close relationship to systemic working frequency, degree of solar activity, etc. To take Haiko as an illustration, the changing of distance error caused by Ionosphere atmospheric refraction with solar activity and working frequency is shown in

By the analysis, we can get the following conclusion: when the frequency is in the X band and the elevation of the satellite is above 30˚ (viewed from the ground), the maximal distance error caused by Ionosphere atmospheric refraction is about 0.5 m, even in high solar activity years.

Distance errors caused by atmospheric refraction must be corrected to meet the accuracy demand of slant ranging in InSAR system with distributed satellites.

The overall technical process of distance error correction for atmospheric refraction is shown in

The key technoique mainly includes the following three aspects:

1) Methods of radio wave refraction correction.

2) Researches on profile model of global tropospheric refractive index.

3) Methods of system error calibration.

1) Refraction correction method of mapping function

In view of the high elevation of the system, we can use the refraction correction method of mapping function under the premise of the accuracy being not affected.

The method adopts a mapping function as the following form.

where

2) Profile model of global tropospheric refractive index

To achieve the global distance error correction for refraction, it is necessary to establish the profile model of global tropospheric refractive index. Firstly, a global range of refractive index profile model of statistical data is established by using a great deal of historical meteorological sounding data obtained from the global observation stations. Secondly, the statistical model is corrected afterwards to improve the precision of the profile model by using the measured refractive index of global.

3) System error calibration

Microwave radiometer, which has a good real-time performance, can observe automatically and continuously on atmospheric environment in all-weather conditions. And it can directly calculate the radio wave refraction error of the propagation path by measuring the atmospheric radiation brightness temperature of the propagation path. It is shown in the study that the accuracy of refraction correction can reach 2 cm in the elevation of above 100˚. Accordingly, the refractive error which calculated from the microwave radiometer measurement data can be considered as the total error caused by the radio environment.

The famous Marcor technique, which measures the additional time-delay integral of atmosphere on the path of radio wave propagation with ground-based microwave radiometer, gives distance error correction directly [

Due to the fact that the elevation of the satellite with distributed SAR is more than 30˚, ray bending effects can be ignored. Therefore, the distance error caused by atmospheric refraction can be formulated as follow.

where

Atmospheric refraction is the main one among the errors which influence the accuracy of the InSAR system. Distance errors caused by atmospheric refraction must be corrected to meet the accuracy demand of slant ranging in InSAR system with distributed satellites. Aiming at two satellites, error correction experiments were carried out in 2007 and 2008 by using the error correction method presented in the paper. The experiments have demonstrated that residual error is little and steady after using the distance error correction for atmospheric refraction. It shows that the method discussed in the paper is effective, which can mainly eliminate the distance precision loss caused by Troposphere atmospheric refraction and Ionosphere atmospheric refraction.

Further researches and experiments should be done in future to get a better atmospheric refraction model and a better error correction method.

Hu, G.J., Zhang, L., Li, G., Gong, H. and Qin, J.C. (2016) Research on Error Analysis and Correction Technique of Atmospheric Refraction for InSAR Measurement with Distributed Satellites. Journal of Computer and Communications, 4, 142-150. http://dx.doi.org/10.4236/jcc.2016.415014