Conference Agenda

The existence of physical closure phases in SAR interferometry implies the presence of different scatterering contributions with distinct phase histories [1]. So far, this fact has not been exploited explicitly in the retrieval algorithms: this is precisely what we are introducing in this work.

The first attempts to invert soil moisture variations from closure phases [2, 3] were structured as classical inversion problems starting directly from the observed closure phases, plus some coherence information. However, those kind of inversions tend to be very computationally expensive, especially if one wants to include all independent closure phases, which grow quadratically with the number of images. A fast approach was introduced by [4] but it is anyway based on processing directly the series of closure phases.

In this presentation I want to show a different approach to the inversion which is closely connected to the idea of having different scattering populations with their own phase history. We are going to see how to derive multiple phase measurements for each multilooking window.

This is achieved by multiple-reference interferometry. This proposal comprises two parts, one is trivial and the other much less so. The trivial part is that if we have two different reference images (let's call them z_a and z_b), we can simply derive two phase measurements for each acquisition by application of regular interferometric tools. We can generate two interferograms (e.g. φ_a and φ_b), each with one of the two references, and therefore measure two interferometric phases. This is going ot be repeated for each acquisition in the stack, indexed by "n".

φ_a(n) = angle ( <z_a^* y(n)> )

φ_b(n) = angle ( <z_b^* y(n)> )

What can we do with the different phase histories? In the case of soil moisture inversion, the difference of the two histories is expected to carry the soil misture variation information. For example, the moisture time series would be proportional to the phase difference, time by time:

mv(n) ∝ φ_b(n) - φ_a(n).

This is illustrated in the attached picture.

This difference of interferometric is almost a closure phase itself, considering the triplet z_a, z_b, and y(n). The only missing term is the interferometric phase between the references, which is constant and could also be set to zero by phase-rotation of one of the two references.

The difficult problem is identifying the two references in a way that the subsequent phase measurements fulfil the desired retrieval goal. For the soil moisture case we have developed a practical solution in [5]. We first solve the inversion problem on only three acquisitions (indexed by n, k, and h), chosen because they generate a large closure phase. We will therefore identify three moisture level for the three acquisitions (m_n, n_k, m_h).

After this, we proceed to identify the two references as two different linear combination of the three acquisitions that yield desired phase histories, i.e. phase histories that encode the moisture signal on those three acquisitions. To be more precise, the first phase history (φ_a(n), φ_a(k), φ_a(h)) is simply the result of phase linking, and it will be the basis for the generation of the first reference. The second phase history (φ_b(n), etc.) will deviate from the first proportionally to the identified moisture levels.

φ_b(n) = φ_a(n) + β m_n

and so on for indices "k" and "h".

The identification of the references follows from the solution of a simple linear problem [5]. This way, the two references should roughly correspond to two different layers in the soil, sinche the phase difference is by construction proportional to the moisture level and scatterers that experience more phase delay should logically sit relatively deeper in the soil. More details are going to be shown for the soil moisture retrieval problem. A similar problem, the retrieval of vegetation water content variations, has not been explored yet.

Apart from the particular solution described above, the problem of deriving the two references is open. One can try to tackle it trying to match a physical intuition depending on the problem at hand (as in the solution adopted for the soil moisture inversion) or from a more mathematical point of view, trying to find directly the references that can best explain the closure phase data, independently of any model.

An issue that affects this approach, as any interfeometric approach, is the obsolescence of the reference images. After a certian time it is likely thta new acquisitions are longer able to interfere coherencetly with the references, and one should design a way to update the references while limiting temporal drifts in the retrieved quantity.

[1] De Zan F., Zonno M., López-Dekker P. Phase inconsistencies and multiple scattering in SAR interferometry

IEEE Trans. Geosci. Remote Sens., 53 (2015), pp. 6608-6616

[2] De Zan F., Gomba G. Vegetation and soil moisture inversion from SAR closure phases: first experiments and results, Remote Sens. Environ., 217 (2018), pp. 562-572

[3] Karamvasis K., Karathanassi V. Soil moisture estimation from Sentinel-1 interferometric observations over arid regions, Comput. Geosci., 178 (2023), Article 105410

[4] Wig E., Michaelides R., Zebker H. Fine-resolution measurement of soil moisture from cumulative InSAR closure phase, IEEE Trans. Geosci. Remote Sens. (2023)

[5] De Zan, F. , Filippucci, P., Brocca L., Validation of high-resolution surface soil moisture time series retrieved by means of SAR interferometry, Remote Sensing of Environment, Volume 335, 2026, 115266

Groundwater withdrawal for irrigation is a major cause of land subsidence. In addition to creating hazard for infrastructure, this downward vertical displacement can also be a sign of reduced aquifer storage capacity, hindering long-term water sustainability. Ground leveling and GNSS measurements have shown that such subsidence affects the agricultural plain of Thessaloniki, Greece. However, the spatial coverage of ground measurements are limited, especially over the agricultural lands. Satellite Synthetic Aperture Radar interferometry (InSAR) provides a powerful means of measuring such deformation with high spatial resolution, however, variations in the backscattering properties of the surface, driven by changes in vegetation or soil moisture over cultivated areas, introduce decorrelation. Spatial filtering techniques, such as multilooking, can improve the signal-to-noise ratio in agricultural terrains but the resulting filtered signal contains a cumulative phase error that may bias the deformation estimates. This bias manifests at the interferogram level as a systematic non-zero closure phase over closed loops of multilooked interferograms, also referred to as « fading signal ».

Based on 5 years of Sentinel-1A/B images (2017-2022), we focus on characterizing the closure phase over agricultural plains of Thessaloniki, before looking at actual deformation estimates. The CORINE Land Cover (Copernicus, ESA) is used to classify crop types and select reference urban grounds. We first show that coherence and the rate of closure phase accumulation of short baseline triplets on agriculture are anti-correlated with a coefficient of about -0.4 and a marked seasonality. Time series of Normalized Difference Vegetation Index (NDVI) computed from Sentinel-2 multispectral images show similar behavior to the fading signal. We further demonstrate that phase errors accumulate more rapidly over irrigated fields and fruit trees. By extracting seasonal patterns and comparing them with the crop cycles in the Thessaloniki region, we find that the error exhibits a seasonal component following crop growth stages.

Seasonal error related to plant growth affects preferentially interferograms with short temporal baselines. It tends to "fade" when considering interferograms with a longer time span, but those exhibit lower coherences. This fading signal induces velocity biases in the deformation time series derived from the interferograms, which takes the apparence of subsidence and is related to the amplitude of the cumulated closure phase. In order to untangle signal from bias, we compare time series computed from interferogram networks of different connectivities on selected land covers. Vertical velocities of the order of a few centimeters per year inferred from short-baseline networks can decrease down to a few millimeters per year when the processed network contains long baselines. Finally, to evaluate the computed unbiased deformation, we compare our time series of deformation to the European Ground Motion Service (EGMS) products and to ground-truth data.

References :

* C. Loupasakis, ‘An overview of the land subsidence phenomena occurring in Greece, triggered by the overexploitation of the aquifers for irrigation and mining purposes’, Proc. IAHS, 382, pp. 321–326, 2020

* F. De Zan, M. Zonno, and P. Lopez-Dekker, “Phase inconsistencies and multiple scattering in SAR interferometry,” IEEE Trans. Geosci. Remote Sens., vol. 53, no. 12, pp.6608–6616, 2015

* H. Ansari, F. De Zan, and A. Parizzi, ‘Study of systematic bias in measuring surface deformation with SAR interferometry,’ IEEE Trans. Geosci. Remote Sens., vol. 59, no. 2, pp. 1285–1301, 2021.

* Y. Yuan, M. Kleinherenbrink, and P. Lopez-Dekker, ‘On Crop Growth and InSAR Closure Phases’, IEEE Trans. Geosci. Remote Sensing, vol. 62, pp. 1–12, 2024

Water management for irrigation is an essential activity especially in agricultural areas or where water is scarce. Water storage in the soil affects the vapour transpiration but also its heat storage capacity, its thermal conductivity and the energy separation between latent and sensible heat fluxes. From a hydrological perspective, soil moisture links the partitioning of rainfall into runoff and infiltration and therefore it has an important role in several ecological applications as flood forecasting, crop yield expectation, meteorological prediction, erosion and slope failure forecasting, water reservoir management, etc.

Most of the soil moisture models describe only the bare soil response. In a real scenario, the presence of bare soil is not common as most of the time some kind of vegetation may be found on top. In order to reduce the amount of vegetation responses in addition to the soil moisture estimation longer wavelength can be used. In this study we like to explore the polarimetric and interferometric response of the BIOMASS mission, which operates in P band wavelength.

Polarimetry can be used to define the scattering mechanisms and is able, when using decomposition methods to separate the ground and vegetation contribution. To perform this separation a physical model is employed and fully polarimetric data is needed in order to invert for the different involved parameters. It is worth mentioning that for extracting the ground response and the corresponding soil moisture, a significant degree of penetration into vegetation is required. For this reason, SAR soil moisture inversion has traditionally been investigated with L-band. In this study we use quad polarimetry in P band to investigate the sensitivity to bare soil and vegetated soil for soil moisture estimation [R1].

Differential SAR interferometry, a popular technique for measuring displacements of the Earth's surface, is potentially influenced by changes in soil moisture. Different mechanisms for this impact have been proposed, but its magnitude, sign and even presence remain poorly understood. In this study the dependence of the phase, the coherence magnitude as well as the phase triplets at different polarisation on soil moisture is investigated. In addition, the impact of vegetation is analysed [R2].

The main test site is located in Argentina, where massive ground measurements exists and a comparison with the SAOCOM derived soil moisture can be performed.

[R1] Hajnsek, I., Pottier, E., & Cloude, S. R. (2003). Inversion of surface parameters from polarimetric SAR. IEEE Transactions on Geoscience and Remote Sensing, 41(4), 727-744.

[R2] Zwieback, S., Hensley, S., & Hajnsek, I. (2015). Assessment of soil moisture effects on L-band radar interferometry. Remote Sensing of Environment, 164, 77-89.

Soil moisture (SM)—a fundamental geophysical variable in the energy, carbon, and water cycle—can be retrieved from the temporal interferometric phase measured by differential synthetic aperture radar interferometry (D-InSAR). Compared to C-band, L-band is especially well suited for SM estimation as a result of the deeper penetration depth and weaker susceptibility to temporal decorrelation [1]. This enables SM retrieval under vegetation. Two D-InSAR models have been proposed: De Zan et al. [2] models the scene with an infinite homogeneous soil volume and no surface scattering term, while Zwieback et al. [3] includes an adjustable soil profile combined with surface scattering weighted by the volume-to-surface ratio. Importantly, both models assume bare ground conditions. Zwieback et al. [3] treats the HH and VV polarizations separately, while De Zan et al. [2] notes that there is a small but negligible difference between the polarizations according to the volumeonly model. Both models are complemented by the use of closure phases (triplets) that reduce topographic and ionospheric effects on the interferometric phase.

Parameterization of Zwieback et al. [3] as part of global model inversion is a challenging task: (1) the phase is sensitive not only to SM but also to vegetation, the terrain, displacements, and atmospheric effects. Taking into account the exclusion of displacements and atmospheric effects using closure phases, vegetation remains the main source of uncertainty in SM estimation with effects on the interferometric HH-VV phase difference in L-band of up to 3 cm [4]; (2) the higher model complexity compared to De Zan et al. [2] requires careful handling of the optimization to ensure overdetermined equations. Still, this advance is backed by the transition to fully-polarimetric sensors that significantly enlarge the observation space, offering greater constraints for model inversion; (3) internal model ambiguities can arise from non-uniqueness in the inversion stemming from a multitude of parameters such as the volume-to-surface ratio, the soil profile, dielectric mixing models, surface roughness, incidence angle, and possible, not yet demonstrated, additional parameters for vegetation quantification.

The dominant challenge we tackle in this study is the vegetation-induced phase distortion in HH and VV polarization (1), which we address directly by extending the polarimetric approach of Zwieback et al. [3] to explicitly incorporate a vegetation contribution—drawing on the differential vegetation phase model introduced in Brancato and Hajnsek [5]. This includes-in addition to the vegetation parameters plant density, plant height, stalk density, and vegetation water content-a component that physically weighs the power of the soil and vegetation terms. The advancement also partially addresses challenges (2) and (3). The inversion of the proposed forward model will be tested on the recent airborne F-SAR AgriROSE-L 2025 dataset [6] using the D-InSAR closure phase and coherence time-series gathered from April 22 to July 23. Therefore, the data cover the majority of the vegetation growth period for most crops in very high spatial resolution (0.6 m in azimuth by 1.3 m in range) and temporal resolution (6 days). The analysis will focus on L-band and three fields (winter barley, winter wheat, and corn) around Puch in Germany. For these fields extensive in-situ SM and vegetation measurements have been performed that enable careful validation of the newly extended model.

The results will focus on quantifying model performance and correctly tuning model parameters as part of the global model inversion task to ensure unambiguous SM estimates. A sensitivity analysis and global soil moisture inversion for increasingly vegetated conditions will be conducted. Hence, this work contributes to an understanding of optimal model parameterization to estimate SM under various vegetation conditions using D-InSAR-only observables. This pathway is critical for fully utilizing quad-polarimetric missions, such as BIOMASS, NISAR, and ROSE-L, to obtain reliable SM products for climate, agriculture, and hydrological applications.

References
[1] T. Schmidt et al., “Comprehensive quality assessment of satellite-and model-based soil moisture products against the COSMOS network in Germany,” Remote Sensing of Environment, vol. 301, p. 113 930, 2024.

[2] F. De Zan, A. Parizzi, P. Prats-Iraola, and P. L´opez-Dekker, “A SAR interferometric model for soil moisture,” IEEE Transactions on Geoscience and Remote Sensing, 2013.

[3] S. Zwieback, S. Hensley, and I. Hajnsek, “A polarimetric first-order model of soil moisture effects on the dinsar coherence,” Remote Sensing, vol. 7, no. 6, pp. 7571–7596, 2015.

[4] S. Zwieback and I. Hajnsek, “Influence of vegetation growth on the polarimetric zero-baseline DInSAR phase diversity—implications for deformation studies,” IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 5, pp. 3070–3082, 2016.

[5] V. Brancato and I. Hajnsek, “Analyzing the influence of wet biomass changes in polarimetric differential SAR interferometry at L-band,” IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 11, no. 5, pp. 1494–1508, 2018.

[6] H. I. Schauer, N. Basargin, and I. Hajnsek, “Airborne L-band soil moisture retrieval over agricultural areas in preparation for ESA ROSE-L mission,” 2025.

In this study, we explore the relationships among closure phases, soil moisture, and vegetation water content. The existing soil moisture models, which consider only soil moisture variations, fail to explain the observed temporal signal in the closure phase. The core premise of our experiment is that phase decorrelation is influenced by variations in both soil moisture and vegetation water content, rather than solely by soil moisture variations. If this hypothesis holds, closure phases could offer valuable insights into changes in vegetation water content. Building on this theoretical framework, we analyse the relationships among closure phases, soil moisture, and land-cover types (e.g., maize, tomato, forest, urban, and bare soil). For this purpose, regression techniques are employed, in which the interferometric phase observables are expressed as functions of soil moisture, and the closure phase is described as a function of vegetation indices used as proxies for vegetation cover and water content variability within vegetation. In this research, we use multiple datasets, including Sentinel-1 SAR images, Sentinel-2 and Landsat multispectral images, PRISMA hyperspectral images and two soil moisture sensor networks. The ARM facility in Oklahoma, U.S., the FCUL site in the Lisbon region, Portugal, and an experimental farm in the province of Bari, Italy, are used as case studies. All three case studies are agricultural areas with crops, pasture, and bare soil. Closure phases are constructed from three successive acquisitions with the shortest temporal lag (6 days in Lisbon and Bari, 12 days in Oklahoma) to minimize coherence loss. After that, images are multilooked with an 8x32 window. The impact of varying the size of the multilook window on the closure phase estimation was assessed. For each soil moisture station, time series of multilooked phase triplets and spatial averaged coherence, NDVI and NDWI are computed, using the same kernel. We observe that soil moisture is positively correlated with the closure phases, although in some stations the correlation is negative, an outcome consistent with spatially variable scattering regimes (surface-dominated versus volume/vegetation-dominated contributions) and suggesting that land cover and canopy state mediate the direction and magnitude of the closure-phase response. The inverse behavior is observed with the vegetation index; in this case, the correlation is negative. The highest correlation values (80%-90%) are observed in maize parcels, which can be explained by increased volume scattering. Although tomato can reach very high NDVI and NDWI values, the correlation is very low (between 0.1 and 0.3), possibly due to its low height of about 30 to 40 cm. We have also observed that the best correlation values are obtained when the maximum difference in the vegetation index is used across the 3 dates used for the closure-phase computation. A sensitivity analysis of the implemented soil moisture models is carried out to provide an interpretation of the linear relationship between InSAR-measured and modelled phase triplets. It is studied the model behavior for different ranges of soil moisture and phenological stages.

References:

[1] E. Wig, R. Michaelides, H.A. Zebker, “Fine-resolution measuremet of soil moisture from cumulative InSAR closure phase”, IEEE Transactions on Geoscience and Remote Sensing, 62, 5212315, 2024.

[2] N.C. Mira, J. Catalão, G. Nico “On the mitigation of phase bias in SAR interferometry applications: a new model based on NDWI”, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 17, 3850-3859, 2024.