Influence of hydrometeors on InSAR observations

Repeat-pass synthetic aperture radar interferometry is an important tool for measuring earth surface topography and/or surface deformations. These observations, however, are highly affected by the atmosphere. Therefore, an accurate description of atmospheric distortions is very important to improve an accuracy of interferometric measurements. In this paper we discuss influence of hydrometeors on the microwave propagation. On examples of two interferograms we show that there is a strong increase in a propagation delay associated with rain. To validate this observation we have used weather radar measurements to estimate contribution of rain droplets on the propagation path. It is shown that in some cases, a rain induced propagation delay can be of several centimeters. Keywords-SAR interferometry; raadiowave propagation; precipiation I. SAR INTERFEROMTRY AND ATMOSPHERIC PHASE DELAY The ERS-1,2 and ENVISAT SAR measurements provide a high resolution measurements of the earth surface. A phase value of every resolution cell is defined as a superposition of the term which corresponds to the geometric distance, ψgeo, a term which corresponds to propagation effects, ψprop, and the term which represents the scattering within the resolution cell, ψscat. By creating an interferogram, effectively the phases corresponding to two measurements are subtracted from each other ∆Ψ=∆Ψgeo +∆Ψprop+∆Ψscatt (1) 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 propagation effects and the difference in observation geometries. Furthermore, 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, ∆Ψiono, and atmosphere, ∆Ψatm: ∆Ψprop=∆Ψiono+∆Ψatm= =∆Ψiono+(∆Ψhydr+∆Ψwet+∆Ψliquid) (2) the atmospheric component in its turn depends on hydrostatic part, propagation through the dry atmosphere, wet delay, propagation through water vapor and liquid part, caused by propagation through volume filled with liquid droplets. The hydrostatic and ionospheric parts have the largest contribution to the total phase delay. A variability of these delays, however, have mainly a rather long wavelength as compared to the spatial extend of an interferogram and thus their contribution can easily be suppressed. The wet and liquid delays, on the other hand, contribute less to the total delay, but spatial behavior of these delays is more stochastic and therefore it is more difficult to compensate for them. In this article we will discuss influence of precipitation on the atmospheric phase delay. Moreover, we will illustrate our study by two comparisons of weather radar rain rate measurements to atmospheric phase delay observations as acquired by ERS-1,2 during the tandem mission in 1995-96. II. HYDROMETEORS CONTRIBUTION TO ATMOSPHERIC PHASE DELAY A. Signal delay induced by scattering in rain It was shown in [3, 5] that for the case of coherent propagation in rain the propagation phase delay, δ in mm/km, can calculated as (3) where k is the wave number (wavelength is 56 mm) , D is the equivolumic drop diameter, f(D) is the forward scattering amplitude in millimeters and N(D) is the drop size distribution given in mmm. Commonly the drop size distribution is assumed to have an exponential form [4] N(D)=N0exp(-ΛD) (4) where N0=8000 mmm and Λ=4.1/R (5) where R is the rain rate given in mm/hr. To estimate the scattering amplitude it is common to model the raindrops that are larger than 1 mm as oblate spheroids with the ratio of the horizontal to vertical axis e related to the equvolumic drop diameter D as [6] e=1.03-0.062 D (6) In this case using Rayleigh approximation [5] the scattered amplitude for h-polarized incidence wave can be calculated as: