In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B
SIMULATED RAIN RATE EFFECTS ON SAR INTERFEROGRAMS
A. Elmzoughi 1 , R. Abdelfattah 1,2 and Z. Belhadj 1
1 URISA, École Supérieure des Communications, Tunis, Route de Raouède Km 3.5, 2083, Tunisia .
2 Département ITI, Telecom Bretagne, Institut TELECOM, CS 83818 - 29238 Brest Cedex 3 - France
Email: riadh.abdelfattah@supcom.rnu.tn and ziad.belhadj@supcom.rnu.tn
Commission TC VII
KEY WORDS: InSAR, Atmospheric effects, Interferograms, Signal delay.
ABSTRACT:
In this paper we discuss influence of the rain rate on SAR interferograms. Calculations of the path delay for different rain rate intensities
was made by considering a physical model for the rain drops and applying the Rayleigh approximation. The calculations do not include
estimations of the delay due to the melting layer of precipitations and due to the precipitating cloud above the melting layer since they
could be neglected. On simulated examples of interferograms considering perfectly flat areas, we show that there is a strong increase
in a propagation delay associated with rain rate and that, the rain can induce a considerable propagation delay of several centimeters.
1 INTRODUCTION: INTERFEROMETRY AND
ATMOSPHERIC EFFECTS
ERS1 and ERS2 provide 2D measurements of the earth surface
with a high resolution of 4x20 m. The phase value of every
resolution cell is defined as a superposition of the term which
corresponds to the geometric distance, a term which corresponds
to propagation effects, xp pr0 p, and the term which represents the
scattering within the resolution cell. By creating an interfero-
gram, effectively the phases corresponding to two measurements
are subtracted from each other and if objects within resolution
cells did not move and did not change from one acquisition to
the other, the differential phase is mainly defined by the propaga
tion effects and the difference in observation geometries. Further
more, if a reference elevation model is available one can remove
the topographic phase component. The remaining phase would
fully be determined by the propagation through the ionosphere,
Aipiono, and atmosphere, Aip a tm (Zebker et al., 1994):
A'ijjprop ~~ ^Tpiono + A Ipatm
— A'lpiono 4" (A'fihydr 4“ Alfiwet 4“ A 1 )'pliquid)
(1)
Indeed, the atmospheric component in its turn depends on hydro
static part, propagation through the dry atmosphere, wet delay,
propagation through water vapor and liquid part, caused by prop
agation through volume filled with liquid droplets.
The hydrostatic and ionospheric parts are dominating the delay
signal, but they hardly vary over the interferogram and may easily
be removed from the rest of the signal. The wet part, caused
by propagation throw a volume filled with liquid particles, have
a stochastic spatial behavior and therefore it is more difficult to
compensate for them (Moissev et al., 2002).
In this paper we will discuss influence of rain on the atmospheric
phase delay. Calculations of the path delay for different rain rate
intensities was made by considering a physical model for the rain
drops and applying the Rayleight approximation. Then in order
to illustrate our study, some interferograms were generated and
discussed.
2 SIMULATED SIGNAL DELAY INDUCED BY THE
RAIN DROPS
2.1 The physical model
For radar applications there is a great agreement that raindrops
can be well approximated by oblate spheroids (Nelson and Gokhale,
1972) characterized by their axis ratio e. In the literature, a great
number of theoretically derived relations between the axis ratio
and the equivolume sphere diameter D were derived (Imai, 1950)
(Spilhaus, 1948). Most of these relations are describing the equi
librium shape (shape of the rain drop in absence of perturbation).
However, the derived axis ratio from a linear fit to the wind-tunnel
data of Pruppacher and Beard (Pruppacher and Beard, 1970) rep
resents a very useful one:
e = 1.03 - 0.062 x D. (2)
The Drop Size Distribution (DSD) represents the number of par
ticles that have the same equivalent diameter and noted N(D)
located in a volume of Ira 3 . Based on extensive measurements,
Marshall and Palmer proposed a single-parameter negative expo
nential relation in (Marshall and Palmer, 1948):
N(D) = 8000 x exp(— A D), (3)
where the spherical equivalent diameter D is in mm and A is the
parameter of the exponential distribution function which can be
related to the rain rate throw the following equation:
A = 4.1/i? 0 ' 21 , (4)
where R is given in mm/hr.
An other important physical parameter for the rain drops is their
complex dielectric constant since it is related to transmission, ab-
sorbtion and backscattering phenomenons. It depends principally
in the exiting wavelength (water activity) and the temperature.
Evaluated for a wavelength of 5.6 cm (which corresponds to the
ERS 1/2 wavelength) and at 10°c the dielectrical constant can be
approximated by (Marshall and Palmer, 1948):
e ~ 70 + 30i (5)
