Full text: Papers accepted on the basis of peer-reviewed abstracts (Part B)

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)
	        
Waiting...

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.