SNOW MASS RETRIEVAL BY MEANS OF SAR INTERFEROMETRY

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1 SNOW MASS RETRIEVAL BY MEANS OF SAR INTERFEROMETRY Helmut Rott (1), Thomas Nagler (1), Rolf Scheiber (2) (1) ENVEO, Environmental Earth Observation OEG, Exlgasse 39, A-6020 Innsbruck, Austria (2) Microwaves and Radar Institute, German Aerospace Center (DLR), Oberpfaffenhofen, D-82230, Germany ABSTRACT The feasibility for retrieving the mass of snow on ground (the snow water equivalent, SWE) by means of repeat-pass SAR interferometry has been investigated. Because the SAR signal of ground covered by dry snow is dominated by backscatter from the snow/ground interface, the differential phase shift due to propagation in the snow can be directly related to SWE. The factors of relevance for coherence of snow covered areas were studied by theoretical modeling and analysis of repeat pass SAR data, showing that the C-band coherence often deteriorates rapidly in case of snow fall whereas coherence is much better preserved at L-band. Case studies on SWE retrieval are presented for 3-day repeatpass ERS SAR data of the Austrian Alps and 4-month repeat-pass L-band airborne SAR data of Oberpfaffenhofen. The investigations confirm the potential of repeat-pass InSAR data for mapping SWE with high spatial detail, suggesting clear preference for L-band. For fully assessing the InSAR capabilities for SWE retrieval, dedicated experiments with co-located, spatially detailed field measurements need to be carried out. 1 INTRODUCTION Spatially distributed information on the mass of snow on ground (the snow water equivalent, SWE) is a key parameter for hydrology and water management in mountainous basins and high latitudes and for climate research. Because of the high spatial variability of SWE, in-situ point measurements are not a suitable basis for estimating areal SWE. Presently no remote sensing method exists which enables reliable observation and mapping of SWE in complex terrain. Retrieving SWE from SAR backscattering data, for example, suffers from the insensitivity of long wavelengths (L- and C-band) to dry winter snow, whereas at short wavelength the snow metamorphic state becomes important [1]. On the other hand, the interferometric phase shift in snow due to differences in the propagation constant relative to the atmosphere offers a direct method for retrieving SWE, as first proposed by Guneriussen et al. [2]. In order to assess the capability of InSAR for SWE mapping, we studied the coherence behaviour of snow covered areas and analysed ERS SAR repeat pass data sets of the Austrian Alps. Information on the capability of L-band for SWE retrieval was obtained from an airborne repeat pass SAR experiment. 2 INSAR RETRIEVAL OF SNOW WATER EQUIVALENT The mass of snow on ground, the snow water equivalent (SWE), is a basic hydro-meteorological variable. SWE is the amount of water that would be obtained if a snowpack is completely melted. It may be specified as equivalent depth of water [mm] or as mass deposited on a unit surface area [kg/m 2 }: SWE = <ρ s > d s (1) Where ρ s is snow density and d s is the depth of the snow pack. < > denotes the mean value over the snow pack. The propagation of radar waves in snow is governed by the complex permittivity which is strongly dependent on the liquid water content. The penetration depth d p at the wavelength in free space λ 0 can be estimated from the real ε and imaginary ε parts of the complex permittivity according to: λ0 ε d p = (2) 2 π ε ε of dry snow at C- and L-band is of the order of to , whereas ε depends only on snow density [3]: 3 s = ρs 1.86ρs (3) ε + Proc. of FRINGE 2003 Workshop, Frascati, Italy, 1 5 December 2003 (ESA SP-550, June 2004) 46_rott

2 where ρ s is specified in [g/cm 3 ]. This results in a typical penetration depth of dry winter snow of d p 20 m at C-band and d p > 50 m at L-band [1] [4]. The dielectric losses of wet snow, on the other hand, are large and the typical penetration depth of wet snow with liquid water of several per cent by volume is of the order of few centimetres only. The InSAR SWE retrieval algorithm exploits the large penetration depth in dry snow, taking into account that the main contribution of backscattering from ground covered by dry winter snow stems from the ground surface. Assuming that the radar return from ground covered with a layer of dry snow comes from the ground/snow interface, the repeat-pass interferometric phase φ of an unmoving pixel consists of the following contributions: φ + = φ flat + φtopo + φatm + φsnow φnoise (4) where φ flat and φ topo are the phase differences due to changes of the relative distance satellite-target for flat earth and for topography, respectively, φ atm results from changes in atmospheric propagation, and φ noise is phase noise. φ snow is the two-way propagation difference in the snow-pack relative to air. If volume scattering in the snow pack is neglected, which is very small at C-band and lower frequencies, φ snow can be interpreted in terms of SWE. Fig. 1 illustrates the difference of the geometric path of the radar in air versus the path with a snow layer present: R = R s ( R a + R r ). Fig. 1. Propagation path of radar wave in snow. For calculating the phase shift in snow, the different propagation constants between air and snow have to be taken into account in addition to the differences in the geometric path. A uniform layer of snow with the depth, d s, accumulating in the time between the acquisition of the two SAR images of an interferogram, causes the following phase shift [2]: 4π 2 φ snow = d s cosθi ε s sinθi (5) λ i Assuming the relation between snow density and the permittivity, ε, according to Eq. 3, the dependence of the interferometric phase on SWE can be approximated by a linear relation for ρ s 500 kg/m 3. For an incidence angle θ i = 23 the phase shift due to a change of SWE is [2]: 4π φ snow = SWE (6) λi This means that at the ERS wavelength one fringe is equivalent to 32.5 mm SWE, and for L-band (λ = 24 cm, θ i = 23 ) one fringe corresponds to SWE = 138 mm. 3 COHERENCE OF SNOW COVERED SURFACES A critical issue for the application of InSAR to SWE retrievals is the temporal decorrelation. The total coherence is governed by the following main factors: γ total = γthermal. γsurface. γ volume. γ temporal (7)

3 γ thermal depends on the signal-to-noise ratio, which is usually high for ground covered by dry snow, so that this contribution to decorrelation of snow covered ground is small. For a volume scattering medium, the wave number shifts in slant range and in vertical direction have to be considered, expressed in Eq. 7 by the terms γ surface and γ volume. Model calculations, carried out with the expression for volume decorrelation derived by Hoen and Zebker [5], show that at C- and L-band γ volume is significantly smaller than γ surface, even for a snow pack of several metres depth. The main reason for decrease of coherence of repeat pass SAR data of snow covered areas is temporal decorrelation due to changes of the snow pack caused by: (1) surface melt, (2) snow fall, (3) snow drift (wind erosion and deposition). Because we consider dry snow for SWE retrieval, the first factor is of no relevance. The other two factors, snow fall and snow drift result in changes of the structure and roughness of the snow-surface at sub-pixel scale, and consequently change the propagation path in the snow pack of the radar return from each surface elements. For estimating these effects, we derived an expression for temporal decorrelation of ground covered by dry snow, following the formulation developed by Zebker and Villasenor [6] for volume scattering media such as forests. We assumed that the radar return comes from the rough snow/ground interface and that the phase delay in the snow pack δφ snow is statistically unrelated to the position of a scattering element in a radar resolution cell and has the probability density function p(δφ snow ). In this case the cross-correlation of the two radar signals of an interferogram can be expressed by: V exp[ iδφ ] p( δφ ) d( δφ ) * 1 V2 = σ snow snow snow (8) Because a uniform snow layer does not cause any decorrelation, only the differential phase delay due to non-uniform snow accumulation or erosion needs to be considered. According to Eq. 5 the phase delay depends on the radar wavelength and permittivity. Assuming that δz s depends on the roughness of the snow surface, δφ snow can be described by a Gaussian probability distribution, resulting in the following expression for temporal decorrelation: π 2 2 γ temporal = exp σ z cosθi ε sinθi (9) 2 λ0 where σ z is the standard deviation of the geometric path length through the snow pack. With this equation we calculated the decorrelation for C-band (5.3 GHz) and L-band (1.2 GHz) in dependence of surface roughness, assuming a rough ground surface and a perfectly flat snow surface after snow fall (Fig. 2). Fig. 2. Model calculations of decorrelation due to variation of the path length in snow at C- and L-band. The model calculation in Fig. 2 represent an upper limit for decorrelation in dependence of the path length through a snow pack at sub-pixel scale because statistical independence between roughness of the ground surface and the snow surface was assumed. The calculations are shown for three different snow densities, where 100 kg/m 3 is the typical

4 density of fresh snow falling without much wind, whereas 300 kg/m 3 is the mean density of dry winter snow in the Alps. Surfaces in Alpine terrain, which are a prime target for SWE retrieval, are characterized by surface roughness and undulations over a wide range of scales. Field measurements of surface roughness for radar backscatter modelling were usually made over distances of 1 to 2 m (see e.g. [7]), thus neglecting the roughness at metre-scale which is important in mountainous terrain. At ERS SAR pixel scale ground surface roughness variability is of the order several centimetres, whereas the snow surfaces are usually much smoother, resulting in small-scale changes of φ snow. The model calculations indicate that decorrelation due to snow fall and snow drift is a major problem at C-band, whereas at L-band much better temporal phase stability can be expected. This is confirmed by the analysis of ERS tandem data, where the coherence decreases significantly in case of snow fall or snow drift even within one day [8]. We found a similar behaviour in a time series of 3-day repeat pass ERS-1 data from January to March 1994, acquired over the Austrian Alps (track 044, frame 2650, covering western Styria and the southern part of Upper Austria). 4 CASE STUDY FOR INTERFEROMETRIC SWE RETRIEVAL To derive SWE from an interferogram, φ snow has to be separated from the other phase contributions shown in Eq. 4. The topographic phase can be calculated if a very accurate DEM and precision orbits are available. However, the quality of DEMs in mountain areas is usually not sufficient for accurate simulation of a topographic phase image. Therefore we used one-day or three-day ERS repeat pass data without snowfall or from the summer season to retrieve φ topo, and applied differential processing to separate φ snow and φ topo. If available, it is advisable to use several image pairs with different baseline for deriving the topographic phase, applying the multi-baseline approach [9]. Accurate correction of the atmospheric phase screen in single InSAR pairs requires spatially detailed information on the atmospheric propagation conditions (in particular water vapour) which is usually not available. Therefore we estimated the errors for SWE retrievals if the differences of φ atm in the two SAR images are neglected. Because the SWE retrieval method works only for dry snow, atmospheric temperatures and water vapour content should be rather low. We calculated the atmospheric phase shifts for winter conditions, using radiosonde measurements from Austrian stations. The typical winter case would introduce an atmospheric phase delay dφ atm 0.2 rad over an altitude range of 1000 m, corresponding to SWE = 1mm. Maximum values for the atmospheric phase error under winter conditions should be below 5 mm. This magnitude of error is not relevant for snow hydrology applications. More important can be errors in the topographic phase, caused by baseline errors. However, if precise orbit data are available and the SWE analysis is carried by differential processing at regional scale, these errors are small. Fig. 3. InSAR analysis for a section of the ERS image track 044, frame 2650, over the Zeltweg region, Styria. (a) repeat pass interferogram 25 to 31 January 1994, superimposed to an amplitude image. (b) Map of SWE (colour coded) obtained by differential processing. Areas with decorrelation are in grey (amplitude image only).

5 The SWE retrieval applies differential processing to obtain the phase shift due to snow accumulation in the interferometric time interval, as explained above. At least one reference point with zero or known snow accumulation in that period is needed to derive a SWE map from φ snow. In order to reduce errors introduced by phase noise, inaccuracies of baselines and small scale variability of accumulated snow at measurement sites, it is recommendable to use several reference stations. In the 3-day repeat pass data set of the Austria Alps from winter 1994 we identified two repeat pass pairs, which covered a period of substantial snow fall and comparatively low temperatures, qualifying as candidates for interferometric SWE retrieval. In both cases large parts of the images decorrelated, as to be expected from the analysis of coherence effects of snow fall presented above. Only unforested surfaces in valleys were sufficiently coherent to enable differential interferometric analysis. Fig. 3 shows an example of such an analysis for Zeltweg in the Mur valley (Styria) and its surroundings. In the 6-day repeat pass interferogram 25 to 31 January 1994 (Fig. 3a) fringes are evident in the lower parts of the valleys, whereas on the forested mountain slopes the signal decorrelates. This interferogram includes the phase contributions of topography and the snow pack, and possible atmospheric contributions. According to the baseline of B n = 42 m, one fringe corresponds to 220 m of altitude. Fig. 3b shows a map of SWE for the coherent areas, calculated from φ snow according to Eq. 6. The topographic phase was subtracted by means of differential processing, using the 3- day repeat pass interferogram of February 1994 (B n = 77 m) without snowfall. The analysis reveals an altitude increase of SWE from close to zero in the city of Zeltweg (altitude 650 m) to about 10 mm in the open countryside at the bottom of the valleys and about 20 mm on the slopes at about 850 m elevation and above. The precipitation measurements of the three stations (Zeltweg 3 mm, Seckau 10 mm, Oberzeiring 26 mm), confirm qualitatively the altitude gradient of SWE. However, the number of stations is not sufficient for quantitative validation. 5 SNOW-INDUCED PHASE SHIFTS IN L-BAND AIRBORNE SAR DATA Quantitative investigation of the interferometric phase shift in a snow pack was possible with repeat pass airborne SAR data which had been acquired by E-SAR of DLR for vegetation studies [10] [11]. The three repeat pass scenes used for this analysis were acquired at L-band, polarimetric mode, with high resolution (pulse bandwidth 100 MHz) at two dates: two repeat passes within half an hour on 22 October 2002 when the site was snow free, and a third pass on 20 February 2003 when the ground was covered by dry snow. Fig. 4. (a) Amplitude image of the airport at Oberpfaffenhofen, corner reflectors are surrounded by yellow circles. (b) and (c) detailed view of the interferograms, VV polarisation of the image pairs acquired on 22/22 October 2002 and on 22 October 2002/20 February 2003, with colour coded phase.

6 The investigation area is the campus of DLR including the local airport, where in two sub-areas 9 corner reflectors are permanently mounted. The corner reflectors were used for E-SAR calibration and therefore the snow accumulated inside of the trihedral reflectors had been removed before the image acquisition. In spite of snow cover in the second image, the coherence over the 4-month time span was sufficient for interferometric analysis. Figs. 4b and 4c show phase shifts of the corner reflectors relative to the snow covered meadows. Also buildings and roads reveal phase shifts. The average phase shift of the 9 corner reflectors amounted to 2.3 rad, with a standard deviation of 0.4 rad. The mean HH and VV polarized phase shifts differed only by 2 %. According to Eq. 6 a phase shift of 2.3 rad corresponds to SWE = 43 mm. No snow measurements are available directly from the site, but from Munich (snow depth d s = 12 cm) 25 km to the east and Landsberg (d s = 20 cm) 20 km to the west. The interferometrically retrieved SWE = 43 mm corresponds to d s = 14 cm, 17 cm, 21 cm for snow density of 300 kg/m 3, 250 kg/m 3, and 200 kg/m 3, respectively. Typical densities of metamorphic winter snow are in the range of 250 to 300 kg/m 3, which supports the conclusion that the observed phase shift is a measure of the accumulated snow. 6 CONCLUSION The analysis of InSAR data sets and model calculations confirm that the interferometric phase shift of repeat pass SAR data in a dry snowpack provides a physically based means for mapping the spatial distribution of the mass of snow on ground (the snow water equivalent, SWE). Temporal decorrelation due to differential phase delays at sub-pixel scale caused by snow fall or wind re-distribution of snow is the main limiting factor for application of this method. In C-band SAR data these effects often result to complete decorrelation even within time spans of a few days, whereas L-band is much less affected by temporal decorrelation. Because of better coherence and larger measurement range (lower 2 π ambiguity) L-band is preferable for interferometric SWE mapping than shorter wavelengths. For fully assessing and quantifying the InSAR capabilities for SWE retrieval, dedicated experiments with co-located, spatially detailed snow measurements are needed. ACKNOWLEDGEMENT The work was carried out within ESA/ESTEC Contract No /02/ NL/MM. The ERS SAR data were made available by ESA for ERS AO-3 Project No 239. Special thanks also to Mrs. Arundhati Misra of ISRO-SAC, who provided the differential processing of the E-SAR data in the frame of her guest stay at DLR. REFERENCES 1. Mätzler C., Applications of the interaction of microwaves with the natural snow cover, Remote Sensing Review, Vol. 2, , Guneriussen T., Høgda K.A., Johnson H. and Lauknes I., InSAR for estimating changes in snow water equivalent of dry snow, IEEE Trans. Geosc. Rem. Sens., Vol. 39(10), , Mätzler C., Microwave permittivity of dry snow. IEEE Trans. Geosc. Remote Sensing, Vol. 34(2), , Rott H., Sturm K. and Miller H.,. Active and passive microwave signatures of Antarctic firn by means of field measurements and satellite data, Annals of Glaciology, Vol 17, , Hoen E.W. and Zebker H.A., Penetration depths inferred from interferometric volume decorrelation observed over the Greenland Ice Sheet, IEEE Trans. Geosc. Rem. Sens., Vol. 38(6), , Zebker H.A. and Villasenor J., Decorrelation in Interferometric Radar Echos. IEEE Trans. Geosc. Rem. Sens., Vol. 30(5), , Floricioiu D. and Rott H., Seasonal and short-term variability of multifrequency, polarimetric radar backscatter of alpine terrain from SIR-C/X-SAR and AIRSAR data, IEEE Trans. Geosc. Rem. Sens., Vol.39(12), , Rott H. and Siegel A., Glaciological Studies in the Alps and in Antarctica Using ERS Interferometric SAR. ERS SAR Interferometry, Proc. of Fringe 96 Workshop, Zürich. Oct ESA SP 406, Vol. II, , Ferretti, A., Prati C. and Rocca F., Multibaseline InSAR DEM reconstruction: The wavelet approach, IEEE Trans. Geosc. Rem. Sens., Vol. 37, , Reigber A. and Scheiber R., Airborne differential SAR interferometry: first results at L-band, IEEE Trans. Geosc. Rem. Sens., Vol. 41(6), Misra A. and Scheiber R, Differential Interferometric SAR Processing of E-SAR Data, International Radar Symposium of India, paper no. 121, pp , Bangalore, Dec