International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004
Figure 8. Power spectrum of differential atmospheric signals in
the Hong Kong study region. The dashed lines follow a slope of
-83.
10* :
C^
4 V 1 Na
E (0 A.
s hé
: 3
o 0° N
i 1 E
g =
o X
a. No
10° ™
10 à
10° 10” 10° 10° 10°
Wavenumber (cycle/km)
Figure 9. Power spectrum of differential atmospheric signals in
the New South Wales study region. The dashed lines follow a
slope of —8/3.
The power spectra of the differential atmospheric delays in all
the three areas on the whole follow the power law, which is
commonly associated with the Kolmogorov turbulence
(Tatarski, 1961). The results are in good agreement with those
presented by Hanssen (1998, 2001). The dashed lines in the
diagrams are the - 8/3 power law values. The power law
index varies with the scales slightly, which is consistent with
the turbulence behavior of such phenomena as integrated water
vapor (Ruf and Beus, 1997), and the wet delays in radio
ranging. >
The power law spectral property of the atmospheric signals is
very useful. For example, Ferretti et al (1999) takes advantage
of the particular spectral (or frequency) characteristics to
estimate the noise and atmospheric effects powers for each
interferogram and based on the results develop method to
combine the resulted SAR DEMs by means of a weighted
average in wavelet domain instead of the simple average;
Ferretti et al (2000) utilize the frequency characteristic to
design filters to separate atmospheric effects from nonlinear
subsidence; Williams et al. (1998) however conclude based on
spectral analysis that the low-frequency (long-wavelength)
components of atmospheric effects have the largest amplitude,
and therefore the sparse external data, such as GPS and
meteorological data, can be used to calibrate such effects: Li et
al. (2004) incorporate the power law nature in designing
algorithms to integrate CGPS and meteorological data for
atmospheric effects mitigation.
Though in all of the areas the power spectra follow the power
law, the absolute powers of differential atmospheric delays are
different. Examining the power at the frequency of 1 km in
Figure 7, 8, and 9, we know clearly that the power decreases in
an order Hong Kong > New South Wales > Shanghai. This
ranking order indicates to certain extent the severeness of the
atmospheric effects in these areas. In flat areas, only the
turbulent mixing process of the troposphere will affect the
InSAR measurements, whilst in mountainous areas both
turbulent mixing and vertical stratification will affect InSAR
measurements. The effects of vertical stratification may even
become dominant in areas with high mountains (Hanssen,
2001). While the Hong Kong study area is mountainous,
Shanghai and New South Wales study areas are quite flat. For
example, in the Shanghai study area, the standard deviation of
ground variations is less than 5 m; the ground roughness of
New South Wales is larger than that of Shanghai, but on the
whole it is reasonably flat. Therefore it could reasonably be
expected that the Hong Kong study area is more severely
affected by the atmosphere than the New South Wales area and
that the New South Wales area is more severely affected than
the Shanghai area. However. it should be noted that the results
are obtained for normal weather conditions. Under extreme
conditions, such as thunderstorms and heavy showers, the
results may vary.
6 Conclusions
The atmospheric effects on InSAR measurements in two areas
of southern China and one area of Australia have been studied.
The results show that in all the three areas the atmospheric
signatures show strong anisotropy though with quite different
patterns. The Hinich tests in the three areas invariably reveal
that the atmospheric signatures are non-Gaussian, rather than
being Gaussian as commonly assumed. Further spectral
analysis shows that the approximate power law distribution
holds for all the three study areas though with different
strengths. Further study will focus on the impact of the results
on InSAR measurements and parameter estimation.
Acknowledgements: The work presented was partially
supported by grants from the Research Grants Council of the
Hong Kong Special Administrative Region, China (Project No.:
PolyU 5064/02E) and the Australian Research Council. The
images are provided by European Space Agency under the
Category 1 User project (AO-1227).
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