Multi-Band Differential SAR Interferometry for Snow Water Equivalent Retrieval over Alpine Mountains

Abstract

Snow water equivalent (SWE) can be estimated using Differential SAR Interferometry (DInSAR), which captures changes in snow depth and density between two SAR acquisitions. However, challenges arise due to SAR signal penetration into the snowpack and the intrinsic limitations of DInSAR measurements. This study addresses these issues and explores the use of multi-band SAR data to derive SWE maps in alpine regions characterized by steep terrain, small spatial extent, and a potentially heterogeneous snowpack. We first conducted a performance analysis to assess SWE estimation precision and the maximum unambiguous SWE variation, considering incidence angle, wavelength, and coherence. Based on these results, we selected C-band Sentinel-1 and L-band SAOCOM data acquired over alpine areas and applied tailored DInSAR processing. Atmospheric artifacts were corrected using zenith total delay maps from the GACOS service. Additionally, sensitivity maps were generated for each interferometric pair to identify pixels suitable for reliable SWE estimation. A comparative analysis of the C- and L-band results revealed several critical issues, including significant atmospheric artifacts, phase decorrelation, and phase unwrapping errors, which impact SWE retrieval accuracy. A comparison between our Sentinel-1-based SWE estimations and independent measurements over an instrumented site shows results fairly in line with previous works exploiting C-band data, with an RSME in the order of a few tens of mm.

1. Introduction

Snow cover is the main component of the cryosphere, and knowledge of its properties, such as thickness, water equivalent, and freeze/thaw conditions, is relevant for the study of the global water cycle and the climate system [1,2]. Snow represents a natural water reservoir, and its seasonal changes influence freshwater availability, particularly in mountainous and high-latitude areas. In this context, the water content obtained by melting a sample of snow, known as snow water equivalent (SWE), is a relevant parameter for understanding the hydrological cycle, managing water resources, and predicting natural hazards such as floods and droughts. SWE retrieval through traditional ground-based methods is accurate but limited in both space and time. On the contrary, remote sensing has demonstrated its unique ability to provide estimations at a large scale and high temporal frequency [3]. Passive microwave sensors were largely exploited in the past, thanks to their wide coverage capability, but they suffer from coarse resolution and reduced accuracy in forested and mountainous regions [4,5]. Optical satellite imagery acquired under cloud-free conditions can provide high-resolution snow cover information but does not support SWE retrieval.

At basin scale, hydrologic models generally regard ≈ 10–15% of the seasonal maximum storage as the upper bound for “acceptable” SWE error. A benchmark example is the evaluation of the NOAA-NOHRSC Snow Model at five Colorado headwater catchments, which achieved a root-mean-square difference of 0.073 m against a mean peak SWE of 0.694 m (≈11%); the authors concluded that this fell within the noise of field observations and was therefore operationally adequate [6].

When individual measurement techniques are compared with this envelope the spread is wide. Manual snow-tube and pit methods—still the reference standard—show absolute uncertainties from ∼2 kg m⁻² to >50 kg m⁻² and mean bias errors up to 26%, depending on sampler diameter and protocol [7]. Among automated in situ sensors, the WMO-SPICE intercomparison reported root-mean-square error (RMSE) SWE values of 8–24 mm (≈5–15%) for the weighing SSG1000 scale, rising to 30–43 mm (∼30–35%) for the passive gamma CS725 [8]. Passive microwave satellite products still incur larger errors: the prototype AMSR-E algorithm of Kelly et al. gives global seasonal snow depth errors of 13.7–22.1 cm—equivalent to roughly 30–70 mm SWE or 15–150% relative error depending on accumulation [9].

Compared to radiometers, Synthetic Aperture Radar (SAR) is potentially able to provide SWE estimations at high resolution, independently from daylight and in any weather conditions [10]. The estimation of SWE can be performed by exploring the SAR backscattering coefficient through physically based inversion algorithms that model the interaction of the radar signal with the snowpack, mainly at the air–snow and the snow–ground interfaces, depending on the SAR frequency and snow conditions [11]. The use of the differential interferometric SAR (DInSAR) phase for estimating SWE changes was proposed for the first time by Guneriussen et al. in 2001 [12]. A detailed introduction to this method is presented in the next section, while here we just recall the criticalities related to both the penetration of the SAR signal into the snowpack and the nature of interferometric measurements: (i) SWE retrieval is possible only for dry snow of uniform density; (ii) only temporal SWE variations can be measured, and absolute SWE values can be derived if a reference value is available; (iii) phase aliasing limits the maximum measurable SWE variation; (iv) undesirable phase components related to residual topography, atmospheric inhomogeneities, and orbital errors increase the estimation uncertainty; and (v) the physical structure of the resolution cell defines both the characteristics of the backscattered signal and the noise affecting the interferometric phase (estimated through the interferometric coherence).

As a result of these several limitations, despite being proposed over two decades ago, DInSAR-based SWE estimation still does not provide reliable large-scale monitoring. Specifically, temporal decorrelation—caused by factors such as rain, wind, and temperature fluctuations—is particularly problematic for most current spaceborne SAR sensors due to their wavelengths and revisit times. Recently, this issue was investigated by using a multi-band ground-based interferometric SAR sensor under controlled test site conditions, observing critical DInSAR phase decorrelation occurring even after a few hours at short wavelengths, negatively impacting SWE estimation accuracy [13]. SWE estimations exploiting spaceborne C-band Sentinel-1 (S1) data show an accuracy between 6 mm and 13 mm, but these results were obtained under controlled conditions in flat terrain [14,15,16]. Studies are lacking that assess SWE estimation accuracy by using spaceborne repeat-pass InSAR data in more complex mountainous environments, where the error level is expected to increase due to phase decorrelation and variable snow characteristics.

This work first revisits some of the main challenges related to SWE estimation and explores the potential of using multi-band SAR data to derive SWE maps over alpine regions characterized by steep topography, limited spatial extent, and potentially heterogeneous snowpack conditions (Section 2). Then, a theoretical analysis is carried out to evaluate the performance of DInSAR-based SWE estimation at X-, C-, and L-bands (Section 3). Specifically, we assess both the estimation precision and the maximum SWE variation that can be measured unambiguously as functions of incidence angle, radar wavelength, and interferometric coherence. Building on the insights gained from this analysis, in Section 4 we describe a dedicated DInSAR processing chain tailored to improve SWE retrieval. This approach aims to minimize temporal decorrelation and effectively remove atmospheric and orbital artifacts. The processing strategy is applied to datasets acquired by C-band S1 and L-band SAOCOM satellites, with scenes selected based on the performance criteria defined earlier. The two study areas are located in Val Senales and Valle d’Aosta, in northern Italy. The SWE estimates obtained from both C- and L-band data were further refined using precision-based masking.

The resulting maps are then analyzed in terms of their spatial distribution and temporal evolution (Section 5), highlighting both the potential and limitations of DInSAR-based SWE estimation in complex alpine environments. A final comparison of the DInSAR results with ground truth and model-derived data collected over an instrumented test site within the observed area is attempted. Point-based analysis reveals reasonable agreement in SWE difference estimation, although the many assumptions and error sources clearly indicate the need to further investigate procedures to synergistically include other methodologies, in order to better constrain some of the factors that condition SWE retrieval.

2. DInSAR-Based SWE Retrieval

In this section we introduce the relationship between the DInSAR phase and SWE, with the aim of clearly defining the assumptions behind its derivation and the consequent application constraints. SWE can be defined based on snow depth $Z_s$ and the ratio between snow density and the density of water, the latter being a known constant equal to 1 g/cm³$:$

$$\mathrm{S}\mathrm{W}\mathrm{E}={\displaystyle \frac{{\rho }_s}{{\rho }_w}}{Z}_s.$$

(1)

According to the standard DInSAR theory, the interferometric phase is related to the difference $\Delta R$ between the two-way paths from the SAR sensor to the target on the ground during the two acquisitions:

$$\Delta \mathrm{\Phi }={\displaystyle \frac{4\pi }{\lambda }}\Delta R,$$

(2)

where $\lambda$ is the SAR wavelength.

In order to derive the DInSAR phase contribution coming from a snowpack on the ground, we refer to Figure 1, where the SAR signal path ($R+dR$) for a reference acquisition in snow-free conditions and the SAR signal path ($R_s+{dR}_s$) for an acquisition in the presence of a snowpack of height $Z_s$ and density ${\rho }_s$ are sketched, covering an area on the ground with local slope $\alpha$ with respect to the horizontal plane. Since the distance between the SAR sensor and the common wavefront is the same ($R_s=R$) in the two acquisitions, the optical path length difference due to snow is $\Delta R_s=n_s·{dR}_s-dR$, where $n_s=\sqrt{\epsilon }$ is the snow refraction index, and both ${dR}_s$ and $dR$ can be formulated as functions of ${\Delta Z}_s$ and the incidence angles ${\theta }_s$ and $\theta$ with respect to the local normal to the ground. According to these definitions, in the case of a reference acquisition without snow (${{\Delta Z}_s=Z}_s$), the relationship in (2) becomes the following [12]:

$$\Delta {\mathrm{\Phi }}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}}^0=-{\displaystyle \frac{4\pi }{\lambda }}{Z}_s·\left(\cos \theta -\sqrt{\epsilon -{\sin }^2\theta }\right).$$

(3)

This is a general relationship that holds as long as $\epsilon$ (and thus $n_s$) is constant along the propagation path, which means that the snowpack is homogeneous. In this case, or by assuming that the dielectric inhomogeneities (such as density variations or the presence of ice lenses) are much smaller than $\lambda$, we can neglect volume scattering, which could reduce penetration depth and decorrelate the interferometric phase. In order to express (3) as a function of SWE, we need to introduce the additional, fundamental hypothesis that the snowpack consists of dry snow. Under this hypothesis, the absorption of the microwave signal is negligible (${\epsilon =\epsilon }_r+i·{\epsilon }_i\approx {\epsilon }_r$), allowing for penetration depths ranging from a few meters at 16 GHz to approximately 100 m at 1 GHz. As a result, SAR backscattering primarily originates from the ground surface beneath the snowpack. Within this frequency range, the SAR signal delay due to the propagation within the snowpack depends only on ${\epsilon }_r$; for dry snow, this is independent from frequency and depends only on snow density ${\rho }_s$: for instance, for ${\rho }_s<0.4{\displaystyle \frac{\mathrm{g}}{{\mathrm{c}\mathrm{m}}^3}}$, ${\epsilon }_r\simeq 1+1.6·{\rho }_s+1.8·{\rho }_s^3$ [17]. As a consequence, in dry snow conditions it is possible to express (3) as a function of ${\rho }_s$ instead of $\epsilon$. The most useful formulation is proposed in the work by Leinss et al. (2015) [18] and is based on the following approximation, which is valid for all possible snow densities and for a wide range of incidence angles ($\theta \in \left[0, 60°\right]$):

$$\left(\cos \theta -\sqrt{\epsilon -{\sin }^2\theta }\right)\approx -{\displaystyle \frac{{\rho }_s}{{\rho }_w}}{\displaystyle \frac{\beta }{2}}\left(1.59+{\theta }^{5/2}\right),$$

(4)

where $\beta$ is a numerical parameter, whose optimal value can be computed as a function of $\theta$ and ${\rho }_s$ by minimizing the RMSE of the difference between the two members of (4). This optimal $\beta$ value ranges between 0.92 and 1.05 for an RMSE below 3% [18]; using $\beta =1$ in (4) leads to a maximum RMSE below 10% for $\theta <50°$. By using (4), the DInSAR phase in (3) becomes the following:

$$\Delta {\mathrm{\Phi }}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}}^0={\displaystyle \frac{2\pi }{\lambda }}\beta \left(1.59-{\theta }^{5/2}\right)Z_s{\displaystyle \frac{{\rho }_s}{{\rho }_w}}.$$

(5)

Finally, by assuming the general case in which a snowpack is present in both interferometric acquisitions, and it changes in depth ($\Delta Z_s$) and/or density ($\Delta {\rho }_s$), the DInSAR phase can be written as a function of SWE variation ($\Delta \mathrm{S}\mathrm{W}\mathrm{E}$) derived from (1):

$$\Delta {\mathrm{\Phi }}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}}={\displaystyle \frac{2\pi }{\mathrm{\lambda }}}\beta \left(1.59-{\theta }^{5/2}\right)\left(\Delta Z_s{\displaystyle \frac{{\rho }_s}{{\rho }_w}}+Z_s{\displaystyle \frac{{\Delta \rho }_s}{{\rho }_w}}\right)={\displaystyle \frac{2\pi }{\lambda }}\beta \left(1.59+{\theta }^{5/2}\right)\Delta \mathrm{S}\mathrm{W}\mathrm{E}.$$

(6)

The linearized relation (6), which also holds for a snowpack consisting of an arbitrary number of layers with different densities [18], can be inverted to derive $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimations starting from DInSAR phase measurements:

$$\Delta \mathrm{S}\mathrm{W}\mathrm{E}={\displaystyle \frac{{\widehat{\Delta \mathrm{\Phi }}}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}}}{\beta ·\frac{2\pi }{\lambda }\left(1.59+{\theta }^{5/2}\right)}},$$

(7)

where ${\widehat{\Delta \mathrm{\Phi }}}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}}$ is the estimation of the DInSAR phase component related to the SWE variation that occurred between the two interferometric acquisitions. 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.

3. Performance Analysis

This section presents a performance analysis of DInSAR-based SWE estimation, which specifically investigates the precision and the maximum SWE variation measurable unambiguously as a function of incidence angle, wavelength, and interferometric coherence.

The quality of $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimates through (7) depends on both the approximation limits of relation (4) and on the reliability of the ${\widehat{\Delta \mathrm{\Phi }}}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}}$ measurement. Indeed, the DInSAR phase $\Delta \mathrm{\Phi }$ can be modeled as follows [19]:

$$\Delta \mathrm{\Phi }=\Delta {\mathrm{\Phi }}_{\mathrm{d}\mathrm{e}\mathrm{f}}+\Delta {\mathrm{\Phi }}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}}+\Delta {\mathrm{\Phi }}_{\mathrm{a}\mathrm{t}\mathrm{m}}+{ϵ}_{\mathrm{o}\mathrm{r}\mathrm{b}}+{ϵ}_{\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{o}}+{ϵ}_{\mathrm{P}\mathrm{U}}+{ϵ}_{\mathrm{n}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{e}},$$

(8)

where $\Delta {\mathrm{\Phi }}_{\mathrm{d}\mathrm{e}\mathrm{f}}$ is related to the ground displacement occurring between the two acquisitions, and $\Delta {\mathrm{\Phi }}_{\mathrm{a}\mathrm{t}\mathrm{m}}$ is related to the delay difference in the microwave signal propagation in the atmosphere; the remaining terms are treated as random phase contributions: ${ϵ}_{\mathrm{o}\mathrm{r}\mathrm{b}}$ and ${ϵ}_{\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{o}}$ are related to processing errors due to uncertainties affecting, respectively, orbital parameters and a digital elevation model (DEM), ${ϵ}_{\mathrm{P}\mathrm{U}}$ is related to phase unwrapping (PU) errors (more on PU in the following), and ${ϵ}_{\mathrm{n}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{e}}$ is the term related to the intrinsic noise characteristics of the resolution cell, which affect SAR backscattering. By assuming that (i) the displacement that occurred on the ground between the two SAR acquisitions is negligible ($\Delta {\mathrm{\Phi }}_{\mathrm{d}\mathrm{e}\mathrm{f}}\simeq 0$), and (ii) the atmospheric term $\Delta {\mathrm{\Phi }}_{\mathrm{a}\mathrm{t}\mathrm{m}}$ has been modeled and filtered out, apart from a residual component ${ϵ}_{\mathrm{a}\mathrm{t}\mathrm{m}}$, the DInSAR phase component related to the SWE variation results in the following:

$${\widehat{\Delta \mathrm{\Phi }}}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}}=\Delta {\mathrm{\Phi }}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}}+{ϵ}_{\mathrm{a}\mathrm{t}\mathrm{m}}+{ϵ}_{\mathrm{o}\mathrm{r}\mathrm{b}}+{ϵ}_{\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{o}}+{ϵ}_{\mathrm{P}\mathrm{U}}+{ϵ}_{\mathrm{n}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{e}}.$$

(9)

According to this framework, the $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimation derived from Equation (7) is affected by residual processing errors (${ϵ}_{\mathrm{a}\mathrm{t}\mathrm{m}}+{ϵ}_{\mathrm{o}\mathrm{r}\mathrm{b}}+{ϵ}_{\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{o}}+{ϵ}_{\mathrm{P}\mathrm{U}}$) and by the phase noise affecting the target backscattering (${ϵ}_{\mathrm{n}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{e}}$), which can be estimated using interferometric coherence.

The first term is generally a non-negligible SAR phase contribution, due to the pixel-to-pixel variation in the thickness of the atmosphere crossed by the SAR signal [19], which is greater for sites with strong topographic variations. This phase term may vary significantly between SAR acquisitions and thus give rise to differential phase contributions which, if unaccounted for, may mask the sought signal, either displacements or SWE. Several approaches have been developed to model DInSAR atmospheric phase signals, including those based on numerical weather models [20,21], GNSS measurements, or passive satellite sensors or those using multi-temporal InSAR (MTInSAR) techniques [22]. However, defining a reference value for ${ϵ}_{\mathrm{a}\mathrm{t}\mathrm{m}}$ is challenging, as it depends heavily on atmospheric conditions, scene characteristics, and the specific method used. For a DInSAR interferogram, the expected ${ϵ}_{\mathrm{a}\mathrm{t}\mathrm{m}}$ can be expressed as a function of the two-way travel path delay standard deviation (${\sigma }_{\mathrm{a}\mathrm{t}\mathrm{m}}^{2\Delta R} \approx$1 cm, wavelength-independent). MTInSAR techniques enable the most accurate and robust atmospheric contribution estimation, which also scales inversely with the number $N_I$ of independent interferograms in the stack. DInSAR-based SWE estimation, instead, typically relies on single interferograms, so atmospheric correction is performed through spatial phase filtering, possibly supported by auxiliary atmospheric records derived by external tools. The resulting theoretical atmospheric phase error thus falls within the range ${\displaystyle \frac{2\pi }{\lambda }}\left[{\displaystyle \frac{1}{N_I}},1\right]·1 \mathrm{c}\mathrm{m}$, although clearly unmodeled residuals can be expected.

The phase residual term ${ϵ}_{\mathrm{o}\mathrm{r}\mathrm{b}}$ arises from inaccuracies in the orbital records [23], which affect DInSAR processing by introducing errors in the baseline estimation and generating phase ramps. The latter can be estimated and removed by using polynomial fitting. For most recent satellite missions, ${ϵ}_{\mathrm{o}\mathrm{r}\mathrm{b}}$ can generally be neglected thanks to the high precision of their orbital records. However, significant artifacts caused by orbital errors may still affect the DInSAR phase in certain cases, e.g., as reported in the processing of SAOCOM data [24,25].

The phase topographic residual term, ${ϵ}_{\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{o}}$, is related to errors in the digital elevation model (DEM) and is proportional to the perpendicular baseline. It can be mitigated by either using interferograms with small baselines or by estimating and correcting it through MTInSAR techniques.

Finally, to model the noise level related to the backscattering of the target, we refer to the case of a distributed target and use the closed-form relation between the interferometric phase standard deviation of single-look data (number of looks $N_L=1$) and the interferometric coherence $\gamma$, proposed by Bamler et al. [26]:

$${ϵ}_{\mathrm{n}\mathrm{o}\mathrm{i}\mathrm{s}\mathrm{e}}=\sqrt{{\displaystyle \frac{{\pi }^2}{3}}-\pi ·\arcsin \gamma +{(\arcsin \gamma )}^2-0.5·{\mathrm{L}\mathrm{i}}_2\left({\gamma }^2\right)},$$

(10)

where ${\mathrm{L}\mathrm{i}}_2$ is Euler’s dilogarithm, defined as follows:

$${\mathrm{L}\mathrm{i}}_2\left(x\right)={\sum }_{k=1}^{\mathrm{\infty }}{\displaystyle \frac{x^k}{k^2}}.$$

By combining (7), (9), and (10), an expression for the $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimation error can be derived, valid for any coherence value and for $N_L=1$, with the approximation ${ϵ}_{\mathrm{o}\mathrm{r}\mathrm{b}}={ϵ}_{\mathrm{t}\mathrm{o}\mathrm{p}\mathrm{o}}={ϵ}_{\mathrm{P}\mathrm{U}}={ϵ}_{\mathrm{a}\mathrm{t}\mathrm{m}}\simeq 0$ [27,28]:

$${ϵ}_{\Delta \mathrm{S}\mathrm{W}\mathrm{E}}={\displaystyle \frac{\sqrt{\frac{{\pi }^2}{3}-\pi ·\arcsin \gamma +{\left(\arcsin \gamma \right)}^2-0.5·{\mathrm{L}\mathrm{i}}_2\left({\gamma }^2\right)}}{\beta ·\frac{2\pi }{\lambda }\left(1.59+{\theta }^{5/2}\right)}}.$$

(11)

Equation (11) allows us to evaluate reference values for the measurement error, for instance, by providing indications about the minimum theoretical limits, and thus helps in defining the minimum measurable $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$. Figure 2 shows the trend in ${ϵ}_{\Delta \mathrm{S}\mathrm{W}\mathrm{E}}$ as a function of coherence, computed according to (11) for different values of $\theta$ and for $\beta =1$. Plots (a), (b), and (c) refer, respectively, to SAR measurements in the X- ($\lambda$ = 33 mm), C- ($\lambda$ = 56 mm), and L ($\lambda$ = 235 mm)-bands. As expected, the $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ error decreases as coherence increases and wavelength decreases.

This performance analysis can be used to (i) preliminarily assess the suitability of a SAR dataset’s radiometric and geometric characteristics based on the required precision for $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimation; (ii) identify pixels where $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimation is reliable, based on coherence values; and (iii) provide the expected minimum theoretical error for each $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ measurement. In practice, the latter constitutes the minimum measurable $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ value. However, due to the characteristics of the interferometric phase, a limit on the maximum $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ measurable without ambiguity also exists. In fact, interferometric phase measurements are limited to the principal interval $[-\pi ,+\pi ]$ (wrapped); thus PU is required to derive absolute phase values before computing $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ through (7) [19]. The absolute interferometric phase can be unambiguously reconstructed from its principal value through the integration of its gradient, only if phase aliasing can be assumed to be absent, i.e., if the constraint $\left|\Delta {\mathrm{\Phi }}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}}\right|<\pi$ can be assumed. This constraint on the phase gradient translates into a maximum SWE variation (${\Delta \mathrm{S}\mathrm{W}\mathrm{E}}_{\mathrm{M}\mathrm{A}\mathrm{X}}$) which can be measured unambiguously. The latter can be expressed as a function of wavelength and incidence angle [27,28]:

$${\Delta \mathrm{S}\mathrm{W}\mathrm{E}}_{\mathrm{M}\mathrm{A}\mathrm{X}}={\displaystyle \frac{\lambda }{2\beta \left(1.59+{\theta }^{5/2}\right)}}.$$

(12)

Figure 3 shows the ${\Delta \mathrm{S}\mathrm{W}\mathrm{E}}_{\mathrm{M}\mathrm{A}\mathrm{X}}$ values computed for incidence angles ranging between 10° and 60° and for wavelengths relative to the X-, C-, and L-bands (in blue, red, and yellow, respectively). As expected, performance improves—i.e., larger SWE variations can be measured unambiguously—as wavelength increases, while it slightly decreases with increasing incidence angles for a given wavelength. Indeed, the L-band is the most robust with respect to phase aliasing, leading, for example, to a maximum measurable SWE variation of about 6 cm for $\theta =35°$, which is the typical value of the incidence angle at the center of the SAR beam for many sensors.

Note that the above limit for unambiguous phase gradients is valid in the case of both temporal and spatial gradients. In fact, in order to apply relation (2), a continuous spatial phase field has to be retrieved for each interferogram; this is obtained by spatially integrating the interferometric fringes corresponding to the phase jumps due to the wrapping within the principal interval. This PU operation in two dimensions can be particularly tricky [29]. As the absence of phase aliasing conditions cannot be ascertained empirically but only assumed as an a priori constraint, both spatial and temporal PU inevitably gives rise to residual PU errors, which have to be considered in the total error budget (9), although their impact on the results is difficult to quantify.

A feasibility analysis of this kind has been carried out on the Teufelsegg site, a location sited within the Val Senales test site area, equipped with in situ instrumentation and monitored for snow parameters [30], by exploiting the multi-frequency SAR dataset made up of L-band SAOCOM, C-band S1, and X-band COSMO-SkyMed (CSK) images. Between September 2021 and February 2022, independent SWE measurements were available from a permanent in situ station. Figure 4 shows the $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ (black) and $\mathrm{S}\mathrm{W}\mathrm{E}$ (green) time series, together with the ${\Delta \mathrm{S}\mathrm{W}\mathrm{E}}_{\mathrm{M}\mathrm{A}\mathrm{X}}$ values computed for the SAOCOM (yellow lines), S1 (orange lines), and CSK (light blue lines) SAR datasets. ${\Delta \mathrm{S}\mathrm{W}\mathrm{E}}_{\mathrm{M}\mathrm{A}\mathrm{X}}$ was computed by using the incidence angle values specific for each dataset over the Teufelsegg site and reported in the table on the right of the figure. The SAOCOM dataset is potentially able to catch all the SWE variations that occurred at that site, while for both S1 and CSK, some variations lead to aliased DInSAR phase values. Of course, $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ measurement accuracy also depends on the time interval between SAR acquisitions, so a short revisit time improves performance. Related to this issue, the S1B failure that occurred on 23 December 2021, by doubling the revisit time, negatively impacts the SWE estimation for the following period; this situation was recently restored to a period of 6 days after the successful launch of the S1C spacecraft.

Ground topography also impacts the performance of DInSAR-based SWE. First, the slope and orientation (aspect) angles of the ground surface determine the likelihood of layover and shadowing, which strongly degrade interferometric measurements. Second, relation (7) depends on the local incidence angle, which in turn depends on both the slope and aspect of the terrain. This dependency was leveraged by Eppler et al. (2022) [31] with the aim to perform $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimation by exploiting topographic variations. Here, we just investigate the sensitivity of the DInSAR phase to $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ with respect to the local slope $\alpha$. Figure 1 shows the incidence angles $\theta$ and ${\theta }^{\prime }$ computed with respect to the local slope $\alpha$ and the horizontal plane, respectively. The incidence angle $\theta$ can be computed as a function of ${\theta }^{\prime }$, $\alpha$, and slope orientation with respect to the SAR sensor: $\theta {=\theta }^{\prime }\pm \alpha$ where + is for the slope oriented away from the SAR sensor (backslope geometry) and − for the slope oriented to the SAR sensor (foreslope geometry as in Figure 1). By reformulating (6) as a function of ${\theta }^{\prime }$ and $\alpha$, we derive the following:

$$\Delta {\mathrm{\Phi }}_{\mathrm{s}\mathrm{n}\mathrm{o}\mathrm{w}}={\displaystyle \frac{2\pi }{\lambda }}\beta \left[1.59+{\left({\theta }^{\prime }\pm \alpha \right)}^{{\displaystyle \frac{5}{2}}}\right]\Delta \mathrm{S}\mathrm{W}\mathrm{E}.$$

(13)

According to (13), the DInSAR phase sensitivity to $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ improves for backslope geometries. This suggests that SAR datasets acquired from ascending orbits should be selected to investigate sites located on east-facing slopes and from descending orbits for sites on west-facing slopes.

In summary, the performance analysis outlined above was carried out by neglecting phase contributions coming from ground displacements and atmosphere and processing errors and by deriving a relationship between $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ precision and DInSAR phase coherence, incidence angle, and wavelength. This is useful for assessing the reliability of both the radiometric and geometric characteristics of a SAR dataset to perform SWE estimation. The results indicate that higher-frequency (like X-band) SAR data allow for the accurate retrieval of $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ (see Figure 2) but are very sensitive to phase aliasing (see Figure 3) and more affected by decorrelation due to changes in the liquid water content in the snow volume. On the contrary, lower-frequency signals (C- or L-band SAR) are more robust against phase aliasing and decorrelation but provide less accurate $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimations. Thus, the optimal radar frequency and sampling interval to be used for a specific measurement may be chosen according to the expected $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ (evaluated, e.g., from the amount of snowfall between two acquisitions) and to the weather conditions, as increasing air temperatures or rainfall could change the liquid water content in snow and cause interferometric phase decorrelation. The C-band data acquired by S1 are promising, thanks to the short revisit time, which potentially limits temporal decorrelation and allows dense time series to be processed. However, the mountainous alpine areas investigated in this work typically present unfavorable conditions for interferometric coherence, as we will demonstrate in the following by providing examples of time series of coherence values derived from both C- and L-band data. Finally, to relax the phase aliasing constraint, split-band approaches [32,33] could be adopted, which require wideband SAR data as those provided in the X-band by the CSK and CSK Second Generation constellations. However, due to decorrelation, these high-frequency data are not ideal for performing interferometric analysis on the alpine areas selected for this work, which are critical even for the C- and L-bands.

4. Data Selection and DInSAR Processing

4.1. Test Sites and Data Selection

The selected test sites are both in northern Italy, one in Val Senales (Trentino Alto Adige Region, located in the eastern part of South Tyrol) and another in the Valle d’Aosta Region (Western Italian Alps; see Figure 5).

The Val Senales study area (latitude 46.739N, 10.780E, Figure 5a) is characterized by high variability in terms of altitude (ca. 900 to 3600 m a.s.l.), presents permafrost-covered areas (e.g., the Lazaun rock glacier), and is usually covered by snow from November to May [34]. As mentioned, the Teufelsegg ground station is located in a neighborhood close to the test site location [30].

At the Valle D’Aosta site, two test areas are identified, named Torgnon and Cime Bianche (Figure 5e). The Torgnon experimental site (45.844N, 7.578E) is located at 2160 m a.s.l., and it is a subalpine, unmanaged pasture area, classified as intra-alpine with a semi-continental climate. The site is usually covered by snow from the end of October to late May. The Cime Bianche experimental site (45.920N, 7.694E) is located in the Valtournenche valley, at an altitude of 3100 m a.s.l. on a rather flat area, characterized by the presence of permafrost. The site is usually snow-covered from September to July and is often strongly impacted by wind [30,34].

Based on the indications coming from the performance analysis reported above, as well as from a literature review (e.g., [13]), we expect the C- and L-bands to be the most promising to mitigate some of the limitations associated with SWE estimation in the selected alpine study areas, characterized by steep topography, limited spatial extent, and heterogeneous snowpack conditions. Consequently, S1 C-band data were employed to leverage the constellation’s short revisit time, which is crucial for temporal monitoring. Complementarily, SAOCOM L-band data were utilized to exploit their longer wavelength, which is expected to enable deeper SAR signal penetration into the snowpack, enhance snow volume homogeneity, maintain suitable interferometric coherence, and reduce the likelihood of phase aliasing. Figure 5 shows the borders enclosing the areas on the ground covered by the interferometric pairs acquired over the two test sites by S1 (panels c and f) and SAOCOM (panels d and g). The captions within the panels in Figure 5 report dataset specifications, namely the number of images, acquisition geometry, orbit identification, and the time interval between the acquisitions.

4.2. DInSAR Processing

In the following, the processing chain tailored to produce SWE maps from SAR interferometric pairs is described. To optimize the retrieval of DInSAR information, a “cascaded” interferogram formation approach is adopted, in which each image is paired to the one acquired on the immediately subsequent date. This allows temporal decorrelation to be minimized and thus improves the estimation of SWE variations from one date to the next. The time sequence of absolute SWE values can be reconstructed by integration, using, e.g., an initial reference SWE value from external ancillary data.

For each interferometric pair, the DInSAR phase field is generated, removing the reference topography provided by the SRTM DEM. As mentioned, interferometric phase measurements are sensitive to atmospheric variations, particularly in mountainous sites, including variations in the tropospheric stratified delay. An example of such atmospheric artifacts can be seen in Figure 6, where the principal and unwrapped DInSAR phases are shown, respectively, in panels a and b. In this case, most of the observed phase spatial variations are due to atmospheric effects.

To reduce such unwanted effects, SAR interferograms can be corrected for atmospheric artifacts through various approaches and methodologies [35]. The most reliable algorithms exploit the statistical properties of the atmospheric signal in space and time, and in fact they were originally developed in the framework of multi-temporal SAR interferometry methods [36]. To deal with single interferometric pairs, such as in the present study, the best approach is to rely on model-based methodologies. Specifically, we exploited the Toolbox for Reducing Atmospheric InSAR Noise (TRAIN) [37], which is a collection of scripts and functions which helps in downloading, formatting, and applying different kinds of atmospheric corrections to SAR interferograms derived from models or public data services [38]. In particular, the Generic Atmospheric Correction Online Service for InSAR (GACOS) [39] provides free access to globally available zenith total delay (ZTD) maps generated on the fly through the processing of the high-resolution (HRES) forecast data from the European Centre for Medium-Range Weather Forecasts (ECMWF) model [21]. So, in our processing scheme, the ZTD maps from GACOS are downloaded and integrated within the DInSAR processing chain. This processing step also includes the estimation and removal of a phase ramp superimposed on the DInSAR phase field. This allows us to correct the final product in terms of possible phase components related to errors in the orbital parameters. An example of an evident phase ramp can be seen in Figure 7a, as further considered in the following section.

Phase unwrapping was performed by using the Statistical-cost, Network-flow Algorithm for Phase Unwrapping (SNAPHU) algorithm proposed by Chen et al. in 2001 [40]. Phase unwrapping is performed after removing the atmospheric signal component to reduce the probability of phase aliasing. An example of an unwrapped DInSAR phase corrected by atmospheric artifacts is shown in Figure 6c: the atmospheric pattern correlated with the topography, evident in the unwrapped DInSAR phase in panel b, is strongly reduced after atmospheric correction.

$\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ can now be computed pixel by pixel from the corrected interferogram by using (7). The incidence angle ${\theta }^{\prime }$ is derived according to the orbital parameters and to the SRTM digital elevation model (DEM). Moreover, for each interferometric pair, a sensitivity map ${ϵ}_{\Delta \mathrm{S}\mathrm{W}\mathrm{E}}$ is also created through (10), where the interferometric coherence is computed by using an estimation window of 11 pixels along the azimuth direction and 3 along the range direction.

Finally, to discard pixels unsuitable for performing a valuable SWE estimation, selection masks are generated. The first mask (${\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}}_{geo}$) is derived by combining geometrical information coming from orbits and topography to mask out pixels affected by layover and shadow. A second mask is derived by removing pixels for which the expected precision of SWE estimation is unreliable according to a coherence threshold ${\gamma }^{th}$:

$${\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}}_{\gamma }=\left\{\begin{array}{c}1 \mathrm{if} \gamma \ge {\gamma }^{th}\\ 0 \mathrm{otherwise}\end{array}\right. .$$

(14)

These two are then combined to derive a final $\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}={\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}}_{geo}\circ {\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}}_{\gamma }$, where $\circ$ is the Hadamard product.

The absolute SWE value at each time $t_j$ can be reconstructed from the cascaded time series of SWE differences by using a reference SWE value (${\mathrm{S}\mathrm{W}\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{f}}$) set according to ancillary data at $t_0$ and by integrating the $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimations computed along the stack, as in the following:

$$\mathrm{S}\mathrm{W}\mathrm{E}{(t}_j)={\mathrm{S}\mathrm{W}\mathrm{E}}_{\mathrm{r}\mathrm{e}\mathrm{f}}{(t}_0)+{\sum }_{i=1}^j\Delta \mathrm{S}\mathrm{W}\mathrm{E}\left(t_i-t_{i-1}\right).$$

(15)

This procedure assumes that the DInSAR phase fields in the stack are all calibrated with respect to a common reference target.

Figure 8 presents a scheme of the full processing chain developed for deriving DInSAR-based SWE maps, including the processing steps described above, where ${\Phi }_{APS,UW,Geo}$ is the geocoded unwrapped DInSAR phase before removing atmospheric artifacts, and ${\Phi }_{UW,Geo}$ is the geocoded unwrapped DInSAR phase after removing atmospheric artifacts. The sample maps on the right refer to an interferometric pair acquired by SAOCOM over the Val Senales test site.

5. Results and Discussion

A large dataset of 345 S1 images acquired between 2015 and 2022 over the Val Senales site was analyzed to assess the feasibility of leveraging the short revisit time of the S1 constellation for ΔSWE estimation. Specifically, we estimated the average coherence over an area around the Lazaun rock glacier (Figure 5b) for each cascaded interferogram, and based on this, we computed ${ϵ}_{\Delta \mathrm{S}\mathrm{W}\mathrm{E}}$ through the model in (11) to obtain an idea of the range of coherence values expected in our test site and, accordingly, of the expected SWE precision. Figure 9 shows the trends over time in this theoretical ${ϵ}_{\Delta \mathrm{S}\mathrm{W}\mathrm{E}}$. The vertical dashed lines correspond to the first of June (red) and to the first of October (blue) of each year. During autumn, winter, and early spring months, when snow is usually present, coherence is on average very low, leading to an expected precision of $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimations of about 7 mm. Late spring and summer months exhibit higher coherence values, and thus better theoretical accuracies, but of course this is mainly due to the absence of snow. Similar results are expected on the Val d’Aosta test site. This is in fact a general critical issue for general SWE estimation in mountainous areas.

5.1. Val Senales Test Site

The S1 and SAOCOM datasets selected for the Val Senales test site consist of ascending acquisitions, to maximize the DInSAR phase sensitivity to $\mathrm{S}\mathrm{W}\mathrm{E}$ changes for the dominantly eastward-facing rock glaciers present in the area [41]. The 31 S1 interferometric pairs listed in

Table 1. A list of the S1 interferometric pairs processed for deriving $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ maps in the Val Senales test site (Figure 5c).

Val Senales: Sentinel-1 (Ascending/Orb.117)
#	Satellite	Date 1 (ddmmyyyy)	Date 2 (ddmmyyyy)	Bt (Days)	Season *
1	S1A/S1B	20072021	26072021	6	S/S
2	S1B/S1A	26072021	01082021	6	S/S
3	S1A/S1B	01082021	07082021	6	S/S
4	S1B/S1A	07082021	13082021	6	S/S
5	S1A/S1B	13082021	31082021	18	S/S
6	S1B/S1A	31082021	06092021	6	S/S
7	S1A/S1B	06092021	12092021	6	S/S
8	S1B/S1A	12092021	18092021	6	S/S
9	S1A/S1B	18092021	24092021	6	S/A
10	S1B/S1A	24092021	30092021	6	A/A
11	S1A/S1B	30092021	06102021	6	A/A
12	S1B/S1A	06102021	12102021	6	A/A
13	S1A/S1A	12102021	24102021	6	A/A
14	S1A/S1B	24102021	30102021	6	A/A
15	S1B/S1A	30102021	05112021	6	A/A
16	S1A/S1B	05112021	11112021	6	A/A
17	S1B/S1A	11112021	17112021	6	A/A
18	S1A/S1B	17112021	23112021	6	A/A
19	S1B/S1A	23112021	29112921	6	A/A
20	S1A/S1B	29112021	05122021	6	A/A
21	S1B/S1A	05122021	11122021	6	A/A
22	S1A/S1B	11122021	17122021	6	A/A
23	S1B/S1A	17122021	23122021	6	A/W
24	S1A/S1A	23122021	04012022	12	W/W
25	S1A/S1A	04012022	16012022	12	W/W
26	S1A/S1A	16012022	28012022	12	W/W
27	S1A/S1A	28012022	09022022	12	W/W
28	S1A/S1A	09022022	21022022	12	W/W
29	S1A/S1A	21022022	05032022	12	W/W
30	S1A/S1A	05032022	17032022	12	W/W
31	S1A/S1A	17032022	29032022	12	W/SP

(*) A = autumn; W = winter; SP = spring; S = summer.

, selected from the stack of 345 scenes previously described, covering the years 2021 and 2022, were processed according to the chain described in the previous section and sketched in Figure 8. An example of the products derived is provided in Figure 6 for the interferometric pair 30.10.2021–24.10.2021, which is one of the few cases in which good coherence values occur during the autumn season. Panels a, b, and c show, respectively, the DInSAR phase, the unwrapped DInSAR phase, and the unwrapped DInSAR phase after the removal of atmospheric artifacts performed through GACOS. The coherence map is shown in panel d. The estimated $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ map is shown in panels e and h, masked by using, respectively, the layover and shadow mask (${\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}}_{geo}$) and the final mask ($\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}$) computed by using ${\gamma }^{th}=0.3$, a value suggested by several studies in the literature [42,43,44]. Thanks to the favorable coherence conditions, a good number of pixels is selected. The ${ϵ}_{\Delta \mathrm{S}\mathrm{W}\mathrm{E}}$ maps, also masked according to ${\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}}_{geo}$ and $\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}$, are shown, respectively, in panels f and i.

All the $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ products generated by processing the S1 interferometric pairs listed in Table 1 are shown in Figure 10, grouped by season. The coherence map derived from the same interferometric pair is reported below each $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ map. The $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ maps are masked by using the layover and shadow mask ${\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}}_{geo}$ instead of the full mask to avoid large voids in the maps. In fact, although the pairs acquired in summer and early autumn exhibit slightly less critical conditions, the pairs useful for $\mathrm{S}\mathrm{W}\mathrm{E}$ retrieval, involving autumn and winter acquisitions, are generally characterized by a widespread presence of low coherence values, which compromise the reliability of the DInSAR-based SWE estimations.

The interferometric processing of the SAOCOM dataset gave results exhibiting a generally lower quality. A likely cause is the known problems in the determination of SAOCOM orbital parameters [24,25], which hinder interferometric processing. An example of SAOCOM products derived through the algorithm on the Valle d’Aosta test site is reported in Figure 7: a roughly planar phase pattern, likely due to orbital errors, is clearly visible in panels a and b, showing, respectively, the wrapped and unwrapped DInSAR phases. The unwrapped DInSAR phase after the removal of atmospheric artifacts performed through GACOS is shown in panel c, which shows how satisfactory performance could be achieved in this case. The successfully processed SAOCOM scenes, acquired from March 2020 to September 2022, are listed in

Table 2. A list of the SAOCOM interferometric pairs processed for deriving $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ maps in Val Senales (Figure 5d).

Val Senales: SAOCOM (Ascending/VV)
#	Beam–Path/Row	Date 1 (ddmmyyyy)	Date 2 (ddmmyyyy)	Bt (Days)	Season *
1	S5–214/527	23112020	27022021	96	A/W
2	S5–214/527	27022021	16042021	48	W/SP
3	S5–214/527	16042021	03062021	48	SP/SP
4	S5–214/527	03062021	21072021	48	SP/S
5	S5–214/527	21072021	07092021	48	S/S
6	S5–214/527	07092021	02032022	176	S/W
7	S5–214/527	02032022	19042022	48	W/SP
8	S3–213/528	27102020	31012021	96	A/W
9	S3–213/528	31012021	20032021	48	W/SP
10	S3–213/528	20032021	07052021	48	SP/SP
11	S3–213/528	07052021	24062021	48	SP/S
12	S3–213/528	24062021	28092021	96	S/A

(*) A = autumn; W = winter; SP = spring; S = summer.

, and the corresponding $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimations are shown in Figure 11. As in Figure 10, the coherence map derived from the same interferometric pair is reported below each $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ map, and the $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ maps are masked by using the layover and shadow mask ${\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}}_{geo}$ instead of the full mask, to avoid large voids in the maps. Only a few interferograms, involving spring and summer acquisitions, show sufficient coherence values. $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimation is thus limited to the few sparse areas showing consistent coherence conditions through all the winter scenes.

5.2. Valle d’Aosta Test Site

At the Valle d’Aosta test site, $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimation was also attempted by processing the S1 and SAOCOM datasets in Figure 5f,g according to the processing steps described in the previous section and sketched in Figure 8.

The $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ maps generated by processing the S1 interferometric pairs listed in

Table 3. A list of the S1 interferometric pairs processed for deriving $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ maps in Valle d’Aosta (Figure 5f).

Valle d’Aosta: Sentinel-1 (Ascending/Orb.88)
#	Satellite	Date 1 (ddmmyyyy)	Date 2 (ddmmyyyy)	Bt (Days)	Season *
1	S1A/S1A	24062021	06072021	12	S/S
2	S1A/S1B	06072021	12072021	6	S/S
3	S1B/S1A	12072021	18072021	6	S/S
4	S1A/S1B	18072021	24072021	6	S/S
5	S1B/S1A	24072021	30072021	6	S/S
6	S1A/S1B	30072021	05082021	6	S/S
7	S1B/S1A	05082021	11082021	6	S/S
8	S1A/S1B	11082021	17082021	6	S/S
9	S1B/S1A	17082021	23082021	6	S/S
10	S1A/S1B	23082021	29082021	6	S/S
11	S1B/S1A	29082021	04092021	6	S/S
12	S1A/S1B	04092021	10092021	6	S/S
13	S1B/S1A	10092021	16092021	6	S/S
14	S1A/S1B	16092021	22092021	6	S/A
15	S1B/S1A	22092021	28092021	6	A/A
16	S1A/S1B	28092021	04102021	6	A/A
17	S1B/S1A	04102021	10102021	6	A/A
18	S1A/S1B	10102021	16102021	6	A/A
19	S1B/S1A	16102021	22102021	6	A/A
20	S1A/S1B	22102021	28102021	6	A/A
21	S1B/S1A	28102021	03112021	6	A/A
22	S1A/S1B	03112021	09112021	6	A/A
23	S1B/S1A	09112021	15112021	6	A/A
24	S1A/S1B	15112021	21112021	6	A/A
25	S1B/S1A	21112021	27112021	6	A/A
26	S1A/S1B	27112021	03122021	6	A/A
27	S1B/S1A	03122021	09122021	6	A/A
28	S1A/S1B	09122021	15122021	6	A/A
29	S1B/S1A	15122021	21122021	6	A/A
30	S1A/S1A	21122021	02012022	12	A/W
31	S1A/S1A	02012022	20220114	12	W/W
32	S1B/S1A	14012022	26022022	12	W/W
33	S1A/S1A	26022022	07022022	12	W/W
34	S1A/S1A	07022022	19022022	12	W/W
35	S1B/S1A	19022022	03032022	12	W/W
36	S1A/S1A	03032022	25032022	12	W/W
37	S1A/S1A	25032022	27032022	12	W/SP

(*) A = autumn; W = winter; SP = spring; S = summer.

are shown in Figure 12, grouped by season as in Val Senales. Again, the coherence map derived from the same interferometric pair is reported below each $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ map. Similarly to the Val Senales test site, the maps show generally low coherence, except for the interferometric pairs acquired in summer and early autumn.

Concerning the interferometric processing of SAOCOM data, we experimented with the same issues reported for the SAOCOM datasets on the Val Senales test site. Figure 7, already presented, shows products derived from the interferometric pair 27.06.2021–14.08.2021. The coherence map is sketched in panel d. The estimated $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ map is shown in panels e and h masked by using, respectively, the layover and shadow mask (${\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}}_{\mathrm{g}\mathrm{e}\mathrm{o}}$) and final mask ($\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}$) computed by using ${\gamma }^{th}=0.3$. Despite the interferometric pair being obtained from L-band images acquired during the summer season, several low-coherence areas are visible. The list of all SAOCOM interferometric pairs successfully processed over this test site is reported in

Table 4. A list of the SAOCOM interferometric pairs processed for deriving $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ maps in Valle d’Aosta (Figure 5g).

Valle d’Aosta: SAOCOM (VV)
#	Beam–Path/Row	Date 1 (ddmmyyyy)	Date 2 (ddmmyyyy)	Bt (Days)	Season *
Ascending
1	S4–216/527	13112020	31122020	48	A/W
2	S4–216/527	31122020	17022021	48	W/W
3	S4–216/527	17022021	06042021	48	W/SP
4	S4–216/527	06042021	24052021	48	SP/SP
5	S4–216/527	24052021	11072021	48	SP/S
6	S4–216/527	11072021	28082021	48	S/S
7	S4–216/527	28082021	15102021	48	SP/A
8	S4–216/527	15102021	04022022	112	A/W
9	S4–216/527	04022022	24032022	48	W/SP
10	S4–216/527	24032022	11052022	48	SP/SP
11	S4–216/527	11052022	14072022	64	SP/S
12	S4–216/527	14072022	08092022	56	S/S
13	S4–216/527	08092022	10102022	32	S/A
Descending
1	S4–113/75	23032021	10052021	48	SP/SP
2	S4–113/75	10052021	27062021	48	SP/S
3	S4–113/75	27062021	14082021	48	S/S
4	S4–113/75	14082021	01102021	48	S/A
5	S4–113/75	01102021	17102021	16	A/A
6	S4–113/75	17102021	13052022	208	A/SP
7	S4–113/75	13052022	30062022	48	SP/S
8	S4–113/75	30062022	18092022	80	S/S
9	S4–113/75	18092022	20102022	32	S/A
10	S4–113/75	20102022	05112022	16	A/A

(*) A = autumn; W = winter; SP = spring; S = summer.

and refers to images acquired from both ascending and descending orbits. For each interferogram, Figure 13 shows the $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ map masked by using ${\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{k}}_{\mathrm{g}\mathrm{e}\mathrm{o}}$ and, below each, the corresponding coherence. As in previous cases, the interferometric pairs involving autumn and winter acquisitions, which are useful for SWE measurements, generally show low coherence, thus representing a challenge for DInSAR-based $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimation.

At this test site, the two experimental stations of Cime Bianche and Torgnon are located within or close to the SAR acquisitions areas (see Figure 5f,g), providing in situ measurements useful for attempting calibration and comparison activities. In situ $\mathrm{S}\mathrm{W}\mathrm{E}$ measurements were available on the Torgnon experimental site from the automated stations installed by the Regional Environmental Protection Agency (ARPA) of Valle d’Aosta. Moreover, $\mathrm{S}\mathrm{W}\mathrm{E}$ estimations were available at 3 h timesteps from EURAC Research—Institute for Earth Observation, by running the one-dimensional SNOPACK model [45]. This is a model developed by the WSL Institute for Snow and Avalanche Research SLF, which uses data from automatic weather stations to simulate main snow parameters including $\mathrm{S}\mathrm{W}\mathrm{E}$ [46,47].

Only the DInSAR-based $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ products derived from S1 interferometric pairs were exploited, taking advantage of the large number of estimations performed at time intervals of 6/12 days. The temporal baselines exhibited by the SAOCOM data were considered too large to allow for meaningful comparisons in this case. We selected the S1 acquisitions corresponding to the presence of snow cover according to in situ observations. Starting from the $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ estimations, we derived, for each acquisition date $t_n,$ the $\mathrm{S}\mathrm{W}\mathrm{E}$ value according to (15) and using reference $\mathrm{S}\mathrm{W}\mathrm{E}$ values at $t_0$ derived either by the in situ measurements or by the model, according to their availability. Figure 14 shows, respectively, in panels (a) and (b), the time series of $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ and $\mathrm{S}\mathrm{W}\mathrm{E}$, derived from DInSAR, in situ measurements, and the SNOPACK model. As expected, due to the unfavorable coherence conditions, the likely presence of unwrapping errors, and residual signals from strong atmospheric artifacts not properly removed, the DInSAR-based $\mathrm{S}\mathrm{W}\mathrm{E}$ estimations exhibit non-negligible differences with respect to both independent records over this particular site. The RMSE values computed with respect to in situ measurements and model outcomes are 20.2 mm and 22.4 mm for $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$ and 50.2 mm and 68.6 mm for SWE, respectively. The RMSE values are higher for SWE than for the differential $\Delta \mathrm{S}\mathrm{W}\mathrm{E}$; this is likely caused by residual errors in the spatial and/or temporal PU. In fact, aliasing conditions due to, e.g., strong SWE variations cannot be ruled out, which are also worsened by the low-coherence conditions.

5.3. Final Remarks

The devised processing chain is effective in producing SWE measurements over alpine glaciers, provided that data are carefully selected and assumptions are fulfilled. Based on the performance analysis presented and already discussed in Section 3, we could expect that C- and L-band data present less critical challenging factors limiting SWE estimation such as phase decorrelation, phase aliasing, the presence of artifacts coming from orbital and topographic errors, unreliable phase unwrapping, and residual atmospheric signals, with respect to higher-frequency data such as those of the X-band, especially in mountainous areas.

Our results corresponding to C-band S1 and L-band SAOCOM data seem to fulfill these expectations. Nevertheless, challenges arise even for these data. Specifically, for both datasets, temporal decorrelation represents a very critical issue. This phenomenon, which can generally be due to several concurrent causes such as rain, wind, or temperature changes [13], affects most current spaceborne SAR sensors in fact, with their different operating wavelength and revisit time characteristics, when applied to studies in mountainous areas. In view of these general challenges, S1 data can be used with the aim of exploiting the constellation’s short revisit time in order to maximize the temporal coherence, while SAOCOM data may be preferred for taking advantage of their longer L-band wavelength, which should guarantee deeper SAR penetration into the snowpack and higher apparent snow homogeneity, entailing lower volume decorrelation and a lower probability of phase aliasing.

The developed processing strategy consists of generating interferometric pairs with the smallest temporal baselines to minimize temporal decorrelation effects. Then, each pair is processed according to both standard DInSAR and ad hoc procedures, such as atmospheric phase removal by leveraging auxiliary products such as in the GACOS service and the generation of reliability masks by using the products of the performance analysis. In spite of this optimized approach, our results show that interferometric pairs involving autumn and winter acquisitions, which are useful for SWE retrieval, are generally characterized by a widespread presence of low coherence values, often leading to unreliable DInSAR-based SWE estimations.

Nevertheless, a comparison between our DInSAR-based SWE estimations and independent measurements shows results fairly in line with previous works exploiting C-band data. Specifically, the RMSE for ΔSWE computed from S1 data, with respect to model predictions or in situ measurements over a single test site area, shows a value of about 20 mm, which is close to the 13 mm obtained by using S1 data over a flat area [14] and between the values obtained by using a ground-based InSAR sensor on a flat area under controlled conditions, namely 17 mm and 38 mm for, respectively, 6 and 12 days of separation between acquisitions [13].

The following factors should be considered to understand and, possibly, correct the problems affecting DInSAR-based SWE inference, especially in mountainous environments. First, the highly variable topography does not guarantee sufficiently homogeneous snowpack properties, thus affecting the spatial averaging needed to filter out noise and residual artifacts from the DInSAR phase. Second, over particularly steep areas, residual topographic and atmospheric artifacts are both more pronounced and frequent than in flat terrain. Finally, on land cover types typical of mountainous settings (forests and vegetation), phase temporal decorrelation occurs at shorter revisit times and persists at longer wavelengths with respect to experimental conditions encountered in other applications, thus corrupting the quality of the final estimations. The last two issues may lead to phase gradients (both in space and time) beyond the aliasing limit, causing unwrapping errors and inaccuracies in SWE estimations.

Hence, in order to overcome these limitations, further developments are needed to synergistically include other methodologies able to support the processing steps and constrain some of the factors conditioning retrieval.

6. Conclusions

This work consists of an attempt to assess the estimation of DInSAR-based SWE on mountainous alpine areas. The retrieval of SWE through spaceborne DInSAR was investigated through a theoretical review of the physical principles underlying the technique, which allows us to assess the impact of both radiometric and geometric parameters involved in SAR data acquisition. According to the results of the analysis, performance is expected to increase for a decreasing wavelength of the carrier radar signals in terms of the minimum error in the measurement of SWE temporal variations, besides an increasing trend with increasing InSAR coherence. An additional improvement effect is found to be due to increasing local incidence angles. The analysis thus leads us to expect tighter constraints on temporal baselines for higher-frequency sensors, e.g., operating in the C-band, in order to contain temporal decorrelation and to select ascending acquisition geometries for east-facing slopes and descending ones for west-facing slopes for current satellites in sun-synchronous orbit. Operating wavelength also impacts on the maximum DInSAR phase values which can be measured unambiguously, so L-band data are expected to give more reliable estimates in this respect as, at longer wavelengths, phase differences corresponding to a given snowpack depth give rise to fewer phase wrapping jumps. Shorter wavelengths such as those used in X-band data, despite their higher sensitivity to SWE changes, are more sensitive to both temporal decorrelation and aliasing conditions, which may lead to larger PU errors and thus to final unreliable estimations [13].

Based on these analyses, we developed a processing chain tailored to maximize performance for the retrieval of SWE from DInSAR data over alpine areas. The methodology was applied to C-band S1 and L-band SAOCOM image time series acquired over two test sites located in the Italian Alps, namely Val Senales (Piedmont Region) and Valle d’Aosta. Over both test sites, the method produced fairly reliable SWE variation maps, properly masked to discard low-coherence, shadow, and layover areas. Comparisons with in situ SWE measurements available over the Valle d’Aosta test site gave results in line with previous works.

The main advantages of the proposed methodology are the following:

• Ad hoc MTInSAR processing is tailored to minimize processing errors and optimize critical steps such as atmospheric phase correction, performed via model zenith delay maps obtained from the GACOS service and phase unwrapping.
• The methodology involves the masking of areas exhibiting insufficient coherence as well as spring–summer acquisitions, which are irrelevant to SWE retrieval.

Both aspects are confirmed to reduce the impact of errors and thus produce reliable SWE maps with high resolution and large area coverage. Nevertheless, limits still exist, which can be summarized as follows:

• Several assumptions are involved in the estimation of the SWE values from the DInSAR phase; some of these assumptions, such as the state of snow (dry/wet) and its homogeneity, are not verifiable a priori on the ground over large areas, especially in steep topography conditions.
• In spite of the ad hoc procedure, some processing errors, such as those involved in spatial and temporal phase unwrapping or in the modeling and compensation of atmospheric phase artifacts, are difficult to quantify or predict.
• Retrieval over only relevant areas, i.e., those covered by snow in winter periods, is still plagued by generally low-coherence conditions.

Considering all the above-mentioned results and limitations, it can be concluded that DInSAR-based SWE retrieval still requires further assessment work in mountainous areas. In particular, more experiments, possibly over larger areas, are expected to shed more light on the best ground conditions to be sought for optimal performance. Potential strategies to be investigated for reducing inaccuracies are listed as follows:

• Including SAR sensors operating at different wavelengths will probably give more insight into some of the critical issues discussed in the present work. To this aim, a relevant role should be played by future missions such as ROSE-L [48], which will acquire L-band data in combination with S1, or the NISAR mission, which will operate in the L- and S-bands [49]. Both these missions will provide acquisitions at different wavelengths with a short revisit time.
• The integration of other techniques is expected to bring some benefit. For instance, the identification of areas suitable (in terms of snow coverage and status) for DInSAR-based SWE retrieval through optical or other passive sensors may help focus processing on cases where the assumptions needed by the DInSAR-based approach are likely fulfilled, thus constraining efforts and reducing inaccuracies. Also, SWE estimations obtained by exploiting X-band SAR intensity, rather than phase [28,50], may be adopted in DInSAR-based SWE retrieval to better support phase unwrapping and the evaluation of absolute SWE values.