Multi-band SAR Interferometry for snow water equivalent estimation over Alpine mountains

Snow cover is the main component of the cryosphere and the knowledge of its properties such as thickness, water equivalent, and freeze / thaw conditions, is relevant for the study of global cycle water and the climate system. The snow water equivalent (SWE) is the water content obtained from melting a sample of snow and can be defined according to the snowpack depth and density. Compared to optical sensors and radiometers, SAR is potentially able to provide SWE estimations at high resolution, independently from daylight and in any weather conditions. The estimation of SWE can be performed by exploring both the backscattering coefficient and the interferometric phase of SAR acquisitions. The SWE estimation through differential SAR interferometry (DInSAR) [1] is based on the change of interferometric phase induced by changes on both geometrical path and propagation velocity of the SAR signal due to different SWE conditions between the two interferometric acquisitions. By assuming that dielectric inhomogeneities are much smaller than wavelength, we can neglect the volume scattering. By further assuming that snowpack is made by dry snow, the absorption of the microwave signal is negligible. Under these hypotheses, the backscattered SAR signal comes from the ground surface under the snowpack and the signal time delay related to the snowpack depends just on the snowpack depth and density. So, the DInSAR phase can be approximated as a linear function of the SWE changes [2] (due to a change in snow depth and / or density) occurred between the two interferometric acquisitions. This linear relation between DInSAR phase and SWE changes, involves also the incident angle and the wavelength, and holds for a snowpack consisting of dry snow and an arbitrary number of layers each of uniform density. Of course, due to the differential nature of the DInSAR measurements both in space and time, only SWE changes can be measured. Absolute SWE values can be inferred either by assuming that one of the two interferometric acquisitions is snow free, or by using a reference SWE value coming from independent measurements. Moreover, the SWE estimation from DInSAR phase presents some critical aspects typical of the interferometric measurements: i) phase aliasing, which limits the maximum measurable SWE variation; ii) undesirable phase components related to residual topography, atmospheric signal, and orbital errors; iii) interferometric coherence, which depends on the scattering properties of the resolution cell. Recently, this last issue has been investigated by using a multiband interferometric SAR sensor under controlled test site, observing critical DInSAR phase decorrelation conditions occurring even after few hours at shorter wavelengths. [3]. Therefore, by all above considerations, the retrieval of SWE through DInSAR is feasible only under conditions of dry snow and spatial homogeneity of snowpack properties and is hindered by phase decorrelation, aliasing, and presence of spurious signals. In particular, temporal decorrelation is due to several concurrent causes such as rain, wind, and temperature changes, and it represents a very critical issue to be faced with most of wavelengths and revisit times of nowadays spaceborne SAR sensors. That's why, this approach, despite proposed more than two decades ago, does not yet allow reliable and operational SWE monitoring at large scale. This work revises some of the issues related to the SWE estimation, and experiments the use of multifrequency SAR data for deriving SWE maps over Alpine mountains trough both DInSAR-based and SAR backscattering-based algorithms. Case studies in Val Senales and Val d'Aosta (Italy) were investigated, characterised by critical settings such as steep topography, limited size, and potential spatial inhomogeneous snowpack. Preliminarily, we performed a theoretical analysis aimed at assessing the performance of DInSAR-based SWE estimation at X, C and L bands. By neglecting phase contributions coming from ground displacements, atmosphere and processing errors, the SWE variation can be related to DInSAR phase estimations, incident angle, and wavelength. This relation was used for assessing the precision of the DInSAR based SWE, showing that it decreases as incident angle and coherence increase and wavelength decreases. Moreover, it allowed to evaluate the impact of residual signals related the atmosphere, as well as orbital and topographic inaccuracies. Finally, by using the constraint needed to avoid interferometric phase aliasing, we derived for different values of wavelength and incident angle, the maximum SWE variation measurable unambiguously. This analysis is very useful for assessing the reliability of both radiometric and geometric characteristics of a SAR dataset to perform SWE estimation. The work illustrates example of this performance analysis carried out by exploring L, C and X bands and by set the parameters according to the datasets available for the processing in Val Senales. As expected, the L-band is the more robust with respect to the phase aliasing, leading to maximum measurable SWE variation of about 6 cm at incident angle of 35°. Thanks to this, it is potentially able to catch all the SWE variations measured by a permanent ground station, while for both C and X bands some variations would lead to aliased DInSAR phase values and so unreliable estimation. Of course, the SWE variation depends also on the time interval between SAR acquisitions, so that short revisit time improves the performance. About this, the Sentinel-1B failure occurred on 23.12.2021 by doubling will certainly negatively impact on the SWE estimation. According to the indications coming from the performance analysis as well as from a literature review, C and L band are the more promising to overcome some of the factors limiting the SWE estimation. For the present work a large dataset of Sentinel-1 data (345 Sentinel-1 SAR images acquired between 2015 and 2022 in Val Senales) were selected with the aim to explore the interferometric coherence over time and to exploit the short revisit time of the Sentinel-1 constellation for SWE estimation. SAOCOM data were also used, for taking advantage of the long L-band wavelength, which should guarantee SAR penetration into the snowpack, snow homogeneity, suitable values of interferometric coherence, and low probability of phase aliasing. Both Sentinel-1 and SAOCOM datasets were processed by adopting a "cascaded" interferogram formation approach, in which each image is paired to the one acquired in the next following date. This allows minimizing temporal decorrelation and estimating SWE changes from one date to the next. The time sequence of absolute SWE values was then reconstructed by integration and using a reference SWE value set by external data. Interferometric phase measurements are sensitive to atmosphere changes, in particular in mountainous sites due to the tropospheric stratified delay. This is due to the varying thickness of the atmosphere from pixel to pixel and is thus greater for sites with strong topographic variations, may vary significantly between acquisitions, and thus give rise to phase contributions, which may corrupt the SWE estimation. In order to identify and remove such atmosphere artifacts, we used the zenith total delay maps derived by the Generic Atmospheric Correction Online Service for SAR Inteferometry (GACOS) generated through processing of HRES-ECMWF model data. A stack of consecutive DInSAR phase fields, unwrapped and corrected by the atmospheric and orbital artifacts were generated and used to derive a stack of SWE change maps. In order to select pixels suitable for performing a valuable SWE estimation, a sensibility map was generated for each interferometric pair. First, the map combines geometrical information coming from orbits and topography in order to mask out pixels affected by layover and shadow. Then, by exploiting the model developed for the performance analysis, the minimum value of expected precision of SWE estimations is derived for each pixel. Finally, according to a coherence threshold, pixels for which the expected precision of SWE estimation is unreliable, are masked out in the sensitivity map. Both C-band Sentinel-1 and L-band SAOCOM datasets selected over the test cases were processes according to described processing strategy. The SWE estimations resulting from C- and L-band data were combined and analysed looking at their behavior in space and time. Moreover, the demonstrated sensitivity of X-band backscattering to SWE of dry snow [4] was also exploited to derive SWE estimations in the test areas, by processing Cosmo Sky-Med (CSK) data. Following the strategy outlined in [5], a retrieval algorithm based on Artificial Neural Networks (ANN) was implemented, having as input the CSK data at the available polarizations (HH and VV) along with the local incidence angle, on which the backscattering is greatly dependent in areas characterized by complex orography. The forest cover fraction is also considered as ancillary input of the algorithm, with the twofold scope to provide a threshold for masking out the dense forests in which the SWE retrieval is not feasible and to be used as ancillary input in the retrieval for compensating the effect of sparse forests on the CSK measurements. ANN output is the SWE parameter. The algorithm has been trained by using in-situ SWE measurements from ground stations, which have been integrated by distributed SWE values simulated by a nivological model, to make the training more representative of the observed conditions and to extend the generalization capabilities of the algorithm. The SWE estimations derived through this backscattering-based approach, may be fruitfully combined with those coming from the DInSAR approach with aim of: i) setting the reference SWE value needed to calibrate the DInSAR-based SWE measurements; ii) aiding the integration of SWE change values derived from the DInSAR approach; iii) supporting the analysis and validation of the DInSAR-based SWE measurements. Finally, where available, measurements from ground stations were also used the result analysis. The work describes some of the results obtained in the selected Alpine test sites, critically discusses advantages and limitations of the proposed approaches, and suggests possible future developments.