Snow Water Equivalent (SWE) of dry snow derived from InSAR -theory and results from ERS Tandem SAR data

Snow Water Equivalent (SWE) of dry snow derived from InSAR -theory and results from ERS Tandem SAR data Tore Guneriussen, Kjell Arild Høgda, Harald Johnsen and Inge Lauknes NORUT IT Ltd., Tromsø Science Park, 95 Tromsø, Norway Tel: + 47 77 62 94, Fax: + 47 77 62 94 1, e-mail: tore@itek.norut.no www.itek.norut.no ABSTRACT In case of dry snow, only small changes (cm) in snow depth between two images pairs significantly increases the error in DEM generation due to the disturbance of the phase property, although no effects are observed on the coherence. Thus, the degree of coherence is not a sufficient parameter for estimating the expected error in DEM generation for snow covered areas. However, the phase disturbances is shown to be related to the Snow Water Equivalent (SWE). The relation between the snow water equivalent and the phase properties of the InSAR data is presented together with results from experiments using ERS-1 and ERS-2 tandem data. ERS tandem data together with high precision DEM is used demonstrate the impact of dry snow cover on InSAR, and how this can be used to derive information of SWE. KEY WORDS: SAR, InSAR, snow, Snow Water Equivalent INTRODUCTION Significant progress has been obtained during the last years in understanding the interaction of microwaves with snow and ground. Synthetic Aperture Radar (SAR) on ERS and RADARSAT have demonstrated the capabilities of detecting the extent of a wet snow cover in mountainous areas. However, the natural variation in scattering properties of ground and snow together with the relief effects gives rise to large variation in the backscattering which makes development of reliable automatic snow classification difficult. Only limited results on InSAR techniques applied to snow covered ground parameter estimation have so far been reported. Hagberg and Askne (1995) observed coherence values which they related to the temperature of the snow cover. Shi et al. (1997) evaluated the use of interferometric measurements, mainly the coherence from SIR-C/X- SAR data from the Mammoth Mountain (37 o N, 119 o W). Both the backscattering and the coherence from snow covered areas and snow free areas were considered. Coherence was found to be an easy way to map snow covered areas. An accuracy of better than 86% was achieved comparing the result with TM derived information as the ground truth. They found that both dry and wet snow can be mapped without topographic information. Strozzi et al. (1999) analyzed ERS tandem data over wet snow in Switzerland. They found that in the cases where the occurrence of wet snow could not be directly observed in the backscattering image the degree of coherence could easily be used to discriminate wet snow from bare ground. As a result of the wet snow metamorphism the scattering geometry changes and causes a large decrees of the degree of coherence. The reduction in coherence was confirmed by ground based scatterometer measurements. In this study we present an innovative approach to utilize InSAR techniques to derive information related to the Snow Water Equivalent (SWE) of dry snow cover. Results from analysis of 3 ERS tandem data are presented. The effect on the error in DEM derived from the Tandem data are shown to be related to the changes in snow properties. THEORY The interferogram or the phase difference image is obtained by a complex multiplication of the corresponding pixels of two repeat-pass images,: Imn (, ) = A 1 ( m, A 2 ( m, e iφ( m, where the complex pixel, ( m, of a SAR image can be written as an amplitude, A and phase term, Φ. Assuming now that one of the images is obtained over snow free ground, and the other acquired when the ground is covered with dry snow. Then the phase term in (1) represents the difference in phase shift caused by the two-way propagation of the radar signal to the ground plus one term Φ s representing the phase shift caused by the twoway propagation in the snow, plus one term Φ n, representing system, processing and a target noise given as: Φ( m, = 4π ---------- R( mn, ) + Φ + Φ λ s n rad where λ rad is the radar wavelength, and R is the difference slant-range vector from satellite to pixel ( m, on ground. The noise term, Φ n represents transmitter/ receiver path delay, atmospheric and ionospheric path delay, processing phase errors, system noise and target dependent phase term. (1) (2) Fringe 99, 1-12 Nov. 1999 Guneriussen et al. Page 1 of 5

Backscattering from a snow covered terrain depends on 1) sensor parameters which includes frequency, polarization and viewing geometry, and 2) snowpack and ground parameters which includes snow density, liquid water content, particle size and shape of water and ice, and surface roughness parameters. O 1 B x B y θ B x x 2 B z O 1 H z θ B ξ R 1 R g O 2 Figure 1. Geometry of repeat-pass interferometry where the radar wave is incident at θ i incidence angle with a dry snow cover with z depth is covering the ground giving rise to refraction. In the case of wet snow the scattering comes from the air snow interface and the snow phase, Φ s is simply a reduction in two-way path given as R= z/cosθ i. In the case of dry snow the backscattering is from the snow-ground interface and the snow phase represents difference between the two way propagation in snow and air given by: where k rad is the incoming radar beam vector, k s is the radar beam vector in snow, λ rad is the radar wavelength, θ i is the incidence angle, Φ s is the angle of refraction, z is the depth of snowcover and n is the refraction index. In dry snow the refraction index, n, is given as (Matzler 1996): n 2 = ε = 1 + 1, 6ρ + 1, 8ρ 3 (4) where ρ is the snow density and, ε is the dielectric constant (real part). For snow density in the -.6 g/cm 3 range, a linear approximation of (4) given as n= ε 1 +,85ρ can be substituted in (3), and the two way phase difference due to dry snow propagation is then given by: 4π 1 +, 85ρ Φ = S ---------- z 1 ------------------------ (5) λ rad cosθ s Figure 2 presents the two way phase delay using (5) with incidence angle of 23 o. The snow density is assumed to be.3g/cm 3. We observe that the phase wrapping at 23 o R 2 P z y z θ i ε(z) 4π Φ 2 S k R + 2k R ---------- z 1 n = = ------------- rad s s λ rad cosθ s n R θ s R s y (3) occurs for approximately 1 cm snow which equals a SWE of 3, cm. Phase (deg) 72 63 54 45 36 27 18 9 5 1 15 2 Snow depth (cm) Figure 2. Two way phase delay as function of snow depth derived using (5) with incidence angle of 23 o. Snow density is,3g/cm 3. In case of L band, which has a 4,5 time longer wavelength than C- band, the corresponding phase wrapping snow depth is 58 cm at nominal ERS incidence angle and the equivalent SWE is 17 cm. The phase difference at normal incidence i.e. θ i and θ s = inserted in (5), is given as: Φ = 2k z85ρ, = 17k, ρ z = 17k, SWE s rad rad rad (6) Thus we have a direct relation between the phase difference and SWE. However the phase sensitivity to changes in SWE is high. In case of nominal ERS incidence angle of 23 o, the relation is Φ = s 2k ( 3, z, 84SWE) rad (7) Thus, in case of d-insar the measured interferometric phase differential contains information directly related to the SWE of dry snow. RESULT AND DISCUSSION Three Tandem ERS data sets (11 and 12 March, 21 and 22 May, 3 and 31 July together with 21 Radarsat SLC data have been acquired from the Heimdalen areas during snow melt period in 1997. The Heimdalen area, Norway (61 o N, 9 o E) is a 128 Km 2 sub catchment to Vinstra river and cover altitudes from 153 to 1853 m. The area has moderate topography. More than 64% of the area have slopes less 1 o. Less than 8% of the area is affected by slopes more than 2 o, and 28% have slopes between 1-2 o. The main study area is above the treeline, which is approximately at 12 meter elevations, consists of mostly sparsely vegetated areas. Three in-situ measurements campaign were carried out (March, May and June) where measurements of snow temperature, snow density, snow grain size, and snow liquid water content were measured at more than 5 locations within the catchment. Mean snow depth, air temperature, and surface roughness were also measured. Air temperature data from meteorological stations within the study area q Fringe 99, 1-12 Nov. 1999 Guneriussen et al. Page 2 of 5

at 16 meters have been available. At several locations temperature loggers were deployed for measurement of snow temperature during the snow melt period. The field was covered with dry snow in March 15, with a depth of the snow cover in the range 1-4 meters. Snow melt starts in mid May and the snow starts to become wet in the lower parts of the area. During the field campaign in mid May the area was covered with partly wet snow. In June the field was partly snow covered with wet snow. A geocoding and calibration processing was applied tot he Radarsat and ERS data using an external DEM with 5x5m high resolution with a height standard deviation of 1m was used (Johnsen et al., 1998). Fig. 3 presents the geocoded and recalibrated Radarsat and ERS backscattering images from 11 June, 12 March and 31 July, respectively. Nedre Heimdalvatn located in the middle of the images. The ERS backscattering image from March where the area is covered with dry snow is to some extent similar to the July data.figure 4 presents the temporal backscattering coefficient derived from ERS and RADARSAT S1-S2 data from Area 1, Heimdalen, during snow melt period 1997. From the snow temperature measurements at station 5 (see ffigur 3) at 12 meter altitude, we find (not shown here) that the snow temperature reach o C in mid May. From the backscattering data, we observe a decrease corresponding to the onset of snow melt in end of April and beginning of May. From the temperature data and the field measurements we find that the snow is wet in mid May and June. Thus, at these times surface scattering is the main scattering component from the snow. We observe a decrease in backscattering corresponding to the melt onset as observed by the snow temperature loggers. s1-s2 A (Area1) s6-s7 A (Area1) -5 o (db) -1-15 -2-25 2.5. Figure 4. Temporal backscattering coefficient derived from ERS (triangle) and RADARSAT S1-S2 (square) Area 1, Heimdalen. Figure 3. Geocoded and fully calibrated SAR data from Heimdalen area, 1997. From top ERS 12 March, ERS 31 July and, Radarsat 11 June. Squares indicates the field sites. In June the ground was partly covered with wet snow, we clearly see the difference between wet snow (dark) and bare ground. The positions of some of the field sites are also shown. We clearly observe the lake Øvre and All interferometric processing of ERS-1/2 and Radarsat SAR data were performed using EarthView INSAR version 1.2 software from Atlantis Scientific Inc. The interferometric pairs were coregistered with a typical fit in the order of.1 pixels. A interferogram was generated and filtered for baseline decorrelation, flat earth phase, and azimuth spectral overlap. The phase unwrapping was performed with the patented Iterative Disk Masking algorithm. ERS-1/2 data were used to generate a DEM from unwrapped phase by the use of one control point with known height. The resulting products, master SAR image, generated DEM and coherence image, were all geocoded and resampled to a common map projection. Differential INSAR processing was performed using an external DEM which was slant range converted and coregistered to the master SAR image with an accuracy better than.1 pixels. The coregistration was done Fringe 99, 1-12 Nov. 1999 Guneriussen et al. Page 3 of 5

applying control points between a simulated SAR image and the master SAR image. This coregistered external DEM is used to remove all topographic phase, and a slant range change image is produced. The coherence images from the March and July tandem acquisition are presented in figure 5. We observe that the area close to the lakes have low coherence while the area south of the lake have high coherence. The whole area is snow covered with snow depth 1-5 meter in March. The snow situation changed between the 11 and 12 March tandem acquisition. The temperature is around/below freezing. However, strong wind was recorded on 11 and 12 March, thus a redistribution of snow is likely to have occurred. In the July data we observe a high coherence except from the area near the water. o (db) Coherence,9,8,7,6,5,4,3,2,1-2 -4-6 -8-1 -12-14 -16-18 -2 2.5. 2.5. a1 a2 a3 a4 a1 a2 a3 a4 Figure 6. a) Backscattering values derived from ERS data from Area 1-4. b) Coherence values derived from Area 1-4. Figure 5. Coherence image from top) ERS 11 and 12 March and, bottom) 31 31 July tandem acquisition, respectively. Figure 6 present the backscattering coefficient and the coherence values from the March, May and the July ERS Tandem acquisitions derived from Area 1-4. In May we have low backscattering coefficient and a decreased degree of coherence. Thus, we observe a change in coherence which is related to the change in surface characteristics due to melting processes. A similar low coherence was observed by Strozzi el al. (1999) and explained to be a result of the wet snow metamorphism changing the scattering geometry. Figure 7 present the contour plot of the error in the InSAR DEM versus coherence for March and July tandem acquisitions. The SAR derived DEM has been compared to the external DEM. We observe that in March the spread in error is high, even in cases where the coherence is high. Also notice that the error occurs at regular intervals which corresponding to multiples of the phasewrapping. As previously shown, only small changes in the snow height (cm) will result in a phase shift which will transform to error in height estimates. In this tandem dataset the fringe frequency is related to approximately 1 meters. Thus, snow redistribution in the order of few cm will introduce error in the estimated DEM. The observed height error versus coherence show a multimodal distribution for coherence above.8 with a separation between the peaks corresponding to 2π phase error. In the July data we observe a much smaller spread in the error. Thus, the height error distribution is related to spatial changes in snow height in the order of a few cm between the 11 March and 12 March acquisitions. On the other hand, in case of bare ground (June data) the DEM error is much less and show no multi-modal distribution as shown in Figure 7b. Fringe 99, 1-12 Nov. 1999 Guneriussen et al. Page 4 of 5

the possibility for unambiguous SWE estimation in the range -3 meters from InSARdata. Multi temporal processing techniques may be used to overcome some of these problems. The potential for utilizing L-band data and higher incidence angle data to overcome these limitations must be further investigated. a) b) Figure 7. Contour plot of distribution of error in DEM versus degree of coherence for a) March and b) July acquisition. A differential InSAR experiment was performed for the same data sets using the external DEM combined with the tandem acquisitions. Figure 8 presents the contour plot of the differential height versus coherence for the March and July acquisition. We observe a significantly higher spread in the March data than in the June data, even for the same high degree of coherence. These results are basically the same as shown in Figure 7. a) b) Figure 8. Contour plot of distribution of differential height in DEM versus degree of coherence for a) March and b) July acquisition, respectively. CONCLUSION A theory for describing relationship between SWE of dry snow and the observed phase difference in d-insar data is presented. The dielectric constant of dry snow results in phase difference which is related to the snow depth and density. A snow density of.3g/cm 3 gives a phase wrapping at 23 o incidence angle for approximately 1 cm snow which equals a SWE of 3, cm. Experimental results using tandem SAR data over a dry snow cover show high degree of coherence. The height error in the DEM and differential DEM, support the presented theory. The snow is redistributed due to strong wind between the 11 and 12 March tandem acquisition, and the observed differences in the DEM and the d- InSAR are related to changes in the SWE. It is shown how InSAR can be used for estimation of changes in the SWE of dry snow. Phase wrapping occurs for SWE of approximately 3 cm, which currently limits REFERENCES Bambler, R., and Hartl, P., 1998, Synthetic aperture radar interferometry, Inverse Problems, Vol 8, no 4, R1-R54. O. Hagberg, L.M.H. Ulander, J. Askne, 1995, Repeatpass SAR interferometry over forested terrain, IEEE Trans. on Geoscience and Rem. Sensing, 33(2), 331-339. Johnsen, H.,Lauknes, I., and Guneriussen T., 1998, Geometric and Radiometric Calibration of Synthetic Aperture Radar Imagery Acquired in Alpine Regions- Spaceborne and Airborne, Norut It report IT431/32-98 (www.itek.norut.no/snowtools). Matzler, C., 1996, Microwave Permittivity of Dry Snow, IEEE Trans. Geosci. Remote Sensing, vol. 34, No 2, pp 573-581. Shi, J, Dozier, J., and Hensley, S., 1997, Mapping snow cover with Repeat Pass Synthetic Aperture Radar, IEEE Proceedings of IGARSS 97, ISBN--783-3839-, pp. 628-63. Strozzi T., Wegmuller, U. Matzler C., 1998, Using Repeat SAR Interferometry for Mapping of Wet snow Cover, IEEE Proceedings of IGARSS 98, ISBN-- 783-446-5. ACKNOWLEDGMENT This work was carried out within SNOWTOOLS, an Environment and Climate project funded by Commission of the European Community Contract no ENV4- CT96-34, Norwegian research Council, ENFO, Statkraft and Norwegian Water and Energy administration. Some work was also funded by GIN. Many thanks to all members of the field team at Heimdalen, in particular the SINTEF team lead by Sjur Kolberg. The RADAR- SAT data have been acquired as part of the ADRO project no 172. RADARSAT data are Canadian Space Agency 1997. ERS data acquired from Eurimage 1999. Fringe 99, 1-12 Nov. 1999 Guneriussen et al. Page 5 of 5