IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 1, NO. 2, APRIL

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1 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 1, NO. 2, APRIL Delta-K Interferometric SAR Technique for Snow Water Equivalent (SWE) Retrieval Geir Engen, Tore Guneriussen, and Øyvind Overrein Abstract This letter describes the concept of using delta-k technique on interferometric synthetic aperture radar (InSAR) data for deriving the snow water equivalent (SWE) of dry snow-covered ground by utilizing the presence of scatterers in both datasets. The main scattering contribution from a dry snow cover is from the snow ground interface. Thus, the interferometric phase of two SAR images, one with no snow and one with dry snow cover, contains information on the SWE. By performing a delta-k processing of the two SAR scenes followed by averaging, an estimation of the SWE can be achieved. The first step in the delta-k InSAR processing is to split the band into two nonoverlapping subfrequency band images. The resulting two subband images then contain two new carrier frequencies with a small delta frequency or delta-k separation. The next step is to multiply the two subband images together to obtain the delta-k image, one for summer and one for winter. Finally, the delta-k interferometric SAR image is generated by multiplying the two delta-k images from summer and winter together. In this letter, experimental results using European Remote sensing Satellite 1 (ERS-1) data from a summer and winter situation show that the delta-k phase can be estimated to a few degrees accuracy for an area of km 2 corresponding to an SWE accuracy of approximately 100 mm. Index Terms Interferometry, snow water equivalent (SWE), synthetic aperture radar (SAR). I. INTRODUCTION SNOW COVER has the largest area extent of any component of the cryosphere (the portions of the earth s surface where water is in a solid form), and most of the earth s snow-covered area is located in the Northern Hemisphere, where the mean snow-cover extent ranges from 46.5 million km in January to 3.8 million km in August [1]. The temporal variability is dominated by the seasonal cycle. However, changes in the annual spatial distribution of snow have been observed during the last decades related to the climate change [2]. The terrestrial cryosphere plays a significant role in the global climate, in climate response to global changes, and as an indicator of change in the climate system. However, a better understanding of the interactions and feedback of the land cryosphere system and their adequate parameterization within climate and hydrological Manuscript received May 15, 2003; revised November 8, The work was supported in part by the EC-EESD under FP 5 Contract EVG1-CT (EnviSnow) and in part by Norges forskningsråd through the project SnowMan. G. Engen and Ø. Overrein are with the NORUT Information Technology Ltd., N-0349 Oslo, Norway ( geir.engen@itek.norut.no; overrein@arp.no). T. Guneriussen is with the University of Tromsø, N-9037 Tromsø, Norway ( tore.guneriussen@adm.uit.no). Digital Object Identifier /LGRS models are still needed. 1 The amount and timing of snow-melt runoff from snow and glaciers is important information for management of water resources, including flood prediction and hydropower operations in many countries. Snow water equivalent (SWE) is considered to be a very important snow parameter for flood prediction and optimization of hydropower production. Earth observation techniques have proved to be powerful tools in deriving snow parameters. During the last years, significant progress has been achieved in understanding the interaction of microwaves with snow and ground [3]. In addition to the conventional backscattering analysis for the study of snow-covered ground, results confirm the potential of interferometric synthetic aperture radar (InSAR) techniques for snow parameter retrieval algorithms. Strozzi et al. [4] demonstrated the possibility of separating bare ground from wet snow using coherence analysis. Shi et al. [5] showed that using coherence measurements from repeat-pass InSAR data, both dry and wet snow can be mapped in alpine regions without requiring any topographic information. A new approach to retrieve information on the changes in SWE from InSAR analysis was introduced by Guneriussen et al. [6], [7]. Only small changes in the snow properties between European Remote sensing Satellite 1 and 2 (ERS 1/2) tandem interferometric SAR data were observed to change the interferometric phase. Ground measurements from the area showed that the ground was covered with 1 4 m dry snow and very limited (only a few millimeters at maximum) precipitation had occurred between the two acquisitions. Theoretically, it was shown that phase wrapping occurs for snow depth changes of 16.4 cm, which equals a SWE of 3.3 cm in case of snow density of 0.2 kg dm at 23 incidence angle. SWE mapping utilizing this technique with summer and winter images will normally not be possible due to temporal decorrelation, resulting in a complete loss of coherence. Also, the spatial variation of SWE between different InSAR pixels will reduce the coherence. In this letter, a delta-k interferometric SAR technique for deriving SWE of dry snow is proposed. The basic assumption behind this technique is the presence of scatterers in both datasets. In the winter image, the scatterer is observed through the snow cover. Even if the coherence for the interferometric pair is very low, the phase coherence for the scatterers present in both datasets will be high, allowing for accurate phase estimation. 1 See for World Climate Research Programme Climate and Cryosphere (CLIC) Project-Initial Science and Co-Ordination Plan X/04$ IEEE

2 58 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 1, NO. 2, APRIL 2004 Fig. 1. Radar geometry for winter and summer measurements. Previous radar has been related to SAR interferometry by Sarabandi [8]. He has developed an expression relating change in aspect angle for SAR interferometry and change in frequency for radar. The processing of the delta-k InSAR is performed by a carrier down-conversion technique before InSAR processing is applied to the data. The technique was first exploited in radar by Hagfors [9]. The new baseband carrier is chosen to avoid phase wrapping for normal snow situations. The relation between SWE and delta-k InSAR phase is presented in Section II. Section III briefly describes the SAR processing steps. Accuracy properties and method for estimation of local uncertainty is given in Section IV. Section V gives a description of the study area and the datasets applied in the analysis. The results are discussed in Section VI, while the conclusions are presented in Section VII. II. MATHEMATICAL DESCRIPTION The concept of the proposed delta-k interferometric SAR method is to relate changes in the delta-k InSAR phase to snow water equivalent (SWE). In a homogeneous dry snow cover, the main radar backscattering comes from the snow ground interface. The volume scattering component is small, as confirmed by several ground-based signature measurement campaigns [10]. Thus, in our case we consider dry snow to be a dielectric medium above the ground with no volume scattering contribution to the interferometric phase. Assume radar geometries for winter and summer as given in Fig. 1. The phase difference for one scatterer in the conventional interferometric image is given by where is the wavenumber, is the snow depth and is the refraction index. By splitting the radar band into two subbands with center wavenumbers and the delta-k interferometric phase is given as (2) where is the delta-k wavenumber. The dielectric constant for dry snow is independent of frequency in the range GHz. The real part is found to depend solely on the snow density and is given as [10]. A linear approximation of the dielectric constant for the density in the kg dm range [7] simplifies the delta-k InSAR phase to (1) (3) Fig. 2. Data float diagram of the delta-k InSAR technique. As times is equivalent with SWE we now have a relationship which relates the delta-k InSAR phase and SWE of dry snow. The equation implies that the delta-k InSAR phase integrates out the SWE of a snow pack also in the case of varying snow density. For incidence angles different from zero the delta-k InSAR phase is modified by the factor [7]. III. SIGNAL PROCESSING DESCRIPTION The data float diagram of the delta-k InSAR technique is illustrated in Fig. 2. One single look complex SAR image from summer, and one from winter, are used as input. The images are colocated to the same SAR geometry. The first step is to split the range frequency band into two parts with as little spectral leakage as possible. Each subband image will then have a new carrier frequency that is approximately the middle frequency in each subband. This results in the four new SAR images,,, and. Next step is to delta-k process the two images from summer by multiplying them together. The same is carried out on the two winter images. The two delta-k images and are then generated. Finally, he delta-k InSAR image is generated by multiplying the two delta-k images from summer and winter together. The band split approach has the consequence that delta-k InSAR resolution is reduced by a factor of 2 in range compared to conventional InSAR resolution. IV. ACCURACY AND RESOLUTION PROPERTIES The delta-k InSAR method utilizes scatterers observable in the two images (summer and winter). One SAR image pixel is a sum of many discrete scatterers. Delta-K InSAR processing is a multiplication of two colocated delta-k images pixel by pixel. Each delta-k image is a multiplication of two subband SAR images pixel by pixel. The sums of discrete scatterers from the subband images are multiplied together and the resulting delta-k image then consists of two kinds of phasors. The first kind is the phasors that are the discrete scatterers squared in amplitude and with phase dependent upon the delta-k wavenumber. The second kind is all the cross products of scatterers with amplitude dependent upon two different scatterers and phase depen-

3 ENGEN et al.: DELTA-K INSAR TECHNIQUE FOR SWE RETRIEVAL 59 Fig. 3. Scatterers appearing in either summer or winter images. Fig. 5. Rotated axis system. For calculation of the uncertainty of the angle a rotation has to be carried out multiplying the complex pixels within the averaged local area by. Fig. 5 describes a Cartesian axis system rotated so the axis is directed along the local mean vector. The Gaussian function in the new axis system becomes (4) Fig. 4. Natural corner reflectors in stone visible in both summer and winter images. dent upon the carrier wavenumber. The phasors of the first kind are the information (signal) and the phasors of the second kind are the noise. Multiplying the two delta-k images from summer and winter respectively produces cross cross product noise in each resolution cell. The noise discussed so far is present in the Delta-K InSAR image assuming that all scatterers are seen both in summer and winter SAR images. Normally some scatterers present in the summer image may not be present in the winter image, and vice versa. This is caused by refraction in the snow. For ERS 1/2, the nominal incidence angle varies, e.g., between 20 and 26, giving a refraction angle deviation of about 7 from the incidence angle. Fig. 3 illustrates how a flat stone can be visible only in the summer image. The signal in the main lobe is not propagating in the radar receiver direction. Smaller stones with the effective aperture of some tens of centimeters may have a large beamwidth that makes them visible both in summer and winter image. Also, natural corner configurations in stone will be visible in both summer and winter images. A typical configuration is illustrated in Fig. 4. A simple analytical expression for the pixel noise statistics is hard to derive. The problem will be solved by a different approach. Gaussian statistics in the complex resulting image can be achieved if sufficient pixels are averaged in accordance with the central limit theorem requirements. A number of 100 pixels in the averaging is more than sufficient. Any correlation between the pixels in the resampled delta-k InSAR image is also reduced significantly. Then the real and imaginary part of the pixels can be handled with the statistical mean, standard deviation and cross correlation properties. They describe a rotated Gaussian function shifted in the space spanned by the real and imaginary part of the complex-numbered pixels. The phase gives the local SWE average of the number of pixels within the averaged area. This will also give the Cramer Rao lower bound limit for. where is the standard deviation for the real part, is the standard deviation for the imaginary part, and is the mean of the real part. The normalized covariance and mean of the imaginary part will then be zero. The expression gives the local phase uncertainty. The method is dependent upon resampling by pixel averaging of the image so Gaussian statistics is obtained and no spatial pixel correlation is left. It is important to avoid that the signal vectors influence the estimate. For a delta-k frequency of about 10 MHz and zero baseline, the signal vectors may theoretically have a roughly estimated phase standard deviation with the real axis of about 15 to 20 due to snow variations of 1 4 m.for most cases the noise vectors have been observed to introduce a phase standard deviation extremely higher than this (more than 100 ). For the resampling, a weighting with the magnitude of each pixel is suggested. The local signals in each pixel will then contribute equally to the resulting phase estimate. V. STUDY AREA AND DATASET For verification of the method data from ERS-1/2 taken over Heimdalen is used. The summer data is taken 30. July 1997 and the winter data is taken March 12, The ERS data are from the western part of Norway. The Heimdalen area, Norway (61 N, 90 E), is a 128 km subcatchment to Vinstra river and covers altitudes from 1053 to 1853 m. The area has moderate topography. More than 64% of the area has slopes less than 10 Less than 8% of the area is affected by slopes more than 20 and, 28% has slopes between 10 to 20 The main study area is above the tree line, which is approximately at 1200-m elevations and consists of mostly sparsely vegetated areas. Three in situ measurements campaigns 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 50 locations within the catchment. Mean snow depth, air temperature, and surface roughness were also (5)

4 60 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 1, NO. 2, APRIL 2004 Fig. 6. (Upper left) Elevation map of Heimdalen. (Upper right) Intensity map of the delta-k InSAR dataset of Heimdalen taken by ERS-1. (Lower left) Delta-K InSAR phase standard deviation map for km areas averaged in 5-km steps. (Lower right) Delta-K InSAR phase map of Heimdalen. measured. Air temperature data from meteorological stations at 1060 m within the study area 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 m. Data from a nearby meteorological station showed that only small (a few millimeters) snowfall occurred between March 12 and 15. Normally, 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 whole area was covered with partly wet snow. In June, the field was partly covered with wet snow. An external DEM with 5 5m spatial resolution and a height standard deviation of 1 m was also available. Three Tandem ERS datasets (March 12 and 13, May 21 and 22, July 30 and 31) have been acquired from the Heimdalen area during snow-melt period in VI. EXPERIMENTAL VERIFICATIONS ERS-1 data from March 12 and July 30 are presented in Fig. 6. Delta-K wavenumber for ERS-1 equals , and 1 step in the delta-k InSAR phase corresponds to SWE of 68 mm. The baseline is close to zero (maximum 14 m). An elevation map of Heimdalen is given to the upper left where the blue fields are water. The plot to the upper right gives an intensity map of the delta-k InSAR dataset with resample factor of 125. The white lines follow the steep sides of the mountains and man-made objects in the valleys. The dynamics in the plot is about 100 db because four images are multiplied together, giving rise to four times more dynamics in decibels than just one SAR image has. Magnitude normalization before resampling has been carried out because of the high dynamics. The delta-k InSAR phase standard deviation (STD) map is given to the lower left. A window of pixels (10 10 km) is used in the estimate where water pixels are masked out. The estimates have been taken over the study area with 5-km step. The best areas show STD down to subdegrees. Large areas have STD around 2 to 4 and some small areas reach 10 STD. The high STD areas are at elevations around m. This is likely areas with much bush/forest vegetation. Low STD is found in areas above the tree line and in the valleys. The plot to the lower right shows mapping of the corresponding mean phase of the STD map to the lower left. The phase spans from about 14 to about 6 corresponding to SWE variations of about 1360 mm, which is normal for the snow variation in the study area. The phase is not absolute calibrated since the coregistration is based upon magnitude correlation. The height effects are not compensated for in the delta-k InSAR data, however the height effects are negligible. The delta-k phase due to height differences is in this case from simulations, using

5 ENGEN et al.: DELTA-K INSAR TECHNIQUE FOR SWE RETRIEVAL 61 Fig. 7. (Left) Phase versus height. The data points are delta-k InSAR phase with STD lower than 2.0 (Right) Elevation map with the areas having delta-k InSAR phase STD of 2.0 and higher masked. satellite trajectory parameters, geometry and the available DEM, estimated to be lower than 1.5 all over the study area. This is due to the small baseline. Fig. 7 addresses the possibility of seeing any height correlation with snow. The data points in the plot to the left are phase versus height. The data points are delta-k InSAR phase estimates with STD lower than 2.0 The data points show a trend with a phase STD of about 2 In the plot to the right, the elevation map is shown with the areas having delta-k InSAR phase STD of 2.0 and higher masked. Again this shows that the areas with lowest STD are lying at high altitudes and in the valleys. Atmospheric effects may also contribute to the noise as the refraction index of the atmosphere and ionosphere is not homogeneous in space and time. The variation in the atmospheric conditions has been shown to result in time variation in fringes for Mt. Etna (3300 m). Measurements show from fringes [11], which is severe for ordinary InSAR measurements. However, the error in delta-k InSAR phase caused by variations in atmospheric conditions is assumed to be much less than the variation observed due to the SWE (less than 1 when assuming a K to delta-k wavenumber reduction factor of about 500). VII. CONCLUDING REMARK A new approach for estimating SWE of dry snow-covered ground from spaceborne InSAR data utilizing a delta-k InSAR principles is presented. First the theoretical relation between delta-k interferometric phase and SWE is presented. As the dielectric constant of snow is solely dependent of the snow density the interferometric phase contains information of the SWE of the snow pack. The processing steps of the delta-k approach are presented and the statistical accuracy estimates are given. Experimental verification of the method using ERS data from a summer and winter situation shows that the delta-k InSAR phase can be estimated to a few degrees accuracy for an area of km corresponding to roughly a SWE accuracy of 100 mm. Further studies will be performed in order to optimize spatial resolution and the performance of this method for operational snow mapping. In particular, the accuracy of the method for Envisat and Radarsat will be explored. ACKNOWLEDGMENT The authors wish to thank the staff at Norut IT, in particular E. Malnes and I. Lauknes, for scientific discussions, coordination, and help with data processing. REFERENCES [1] D. A. Robinson, K. F. Dewey, and R. R. Heim, Global snow cover monitoring: An update, Bull. Amer. Meteorol. Soc., vol. 74, pp , [2] M. Serreze et al., Observational evidence of recent change in the northern high-latitude, Clim. Change, vol. 46, no. 1-2, pp , [3] M. Hallikainen, J. Pulliainen, J. Praks, and A. Arslan, Progress and challenges in radar remote sensing of snow, in Proc. Retrieval of Bioand Geophysical Parameters from SAR Data for Land Applications Conf., Sheffield, U.K., Sept [4] T. Strozzi, U. Wegmuller, and C. Matzler, Mapping wet snowcovers with SAR interferometry, Int. J. Remote Sens., vol. 20, no. 12, pp , [5] J. Shi, J. Dozier, and S. Hensley, Mapping snow cover with repeat pass synthetic aperture radar, in Proc. IGARSS, Singapore, 1997, pp [6] T. Guneriussen, H. Johnsen, and I. Lauknes, Snow cover mapping capabilities using RADARSAT standard mode data, Can. J. Remote Sens., vol. 27, pp , [7] T. Guneriussen, K. A. Høgda, H. Johnsen, and I. Lauknes, InSAR for estimation of changes in snow water equivalent of dry snow, IEEE Trans. Geosci. Remote Sensing, vol. 39, pp , Oct [8] K. Sarabandi, 1k Radar equivalent of interferometric SARs: A theoretical study for determination of vegetation height, IEEE Trans. Geosci. Remote Sensing, vol. 35, pp , Sept [9] T. Hagfors, Some properties of radio waves reflected from the moon and their relation to the lunar surface, J. Geophys. Res., vol. 66, no. 3, [10] C. Matzler, Microwave permittivity of dry snow, IEEE Trans. Geosci. Remote Sensing, vol. 34, pp , Mar [11] D. Massonnet and K. L. Feigl, Radar interferometry and its application to changes in the earth s surface, Rev. Geophys., vol. 36, pp , 1998.