The closure phase, which is a circular summation of the phases of the three multilooked interferograms, comprises a geophysical component and phase noise. In agricultural regions of southern Spain, encompassing both open crop fields and greenhouses, the closure phases constructed from Sentinel-1 acquisitions consistently exhibit positive signatures. The evolution of these observations appears to be related to the phenological stages of plants, as evidenced by crop calendars. Moreover, the signatures of closure phases stand out as a potential indicator of vegetation development under dense vegetation conditions when compared with coherence and normalized radar cross section (NRCS). Two existing models, one based on dielectric variation in the subsurface and another on volume scattering combined with perpendicular baselines, do not explain observed time series. Therefore, the presence of these positive closure phases implies the existence of supplementary factors contributing to closure phases associated with plant development. In this context, we explore two potential factors: variations in dielectric properties within crop canopies and the line-of-sight (LoS) motion of crops. These factors are considered to establish connections between temporal changes in vegetation parameters and observed closure phase signatures. Regarding the first factor, we characterize the crop canopies using the dielectric constant of an equivalent medium, thereby capturing changes in wave propagation within the canopies due to leaves and vertical stalks' development throughout the crop growth stages. We then model their contributions to closure phases in a manner analogous to an existing soil moisture model. Using realistic vegetation parameters derived from in situ measurements, this forward model generates synthetic data comparable in magnitude to the observations. As for the second factor, we propose an additional contributing mechanism to closure phases - skewed motion in the radar LoS direction induced by plant growth. This motion model is mathematically verified under a small-motion approximation. Both the models offer valuable insights into the origins of geophysical closure phases.

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Earth Explorer 10 mission Harmony will consist of two satellites that fly in formation with Sentinel-1. It will operate as a multistatic radar in which Sentinel-1 transmits signals and all three satellites receive signals from different lines-of-sight. To prepare for Harmony and other possible future bistatic missions, transforms are derived to map the ocean-wave spectrum into bistatic synthetic aperture radar (SAR) spectra. The SAR mapping follows the standard derivation using the multidimensional characteristic function, but with adjustments for the modulation transfer functions compared to the monostatic case. This article focuses on the SAR modulations caused by velocity bunching as it is the dominant distortion mechanism. We argue that a multistatic system, such as Harmony, leads to an inversion that constrains the real aperture radar (RAR) response on a scene-by-scene basis. A benefit of having additional receivers for wave spectra estimation is that the three lines-of-sight enable to capture a larger fraction of the wave spectrum. Improvements are especially expected in high wind speed conditions such as tropical cyclones, where large energetic surface motions strongly deteriorate the (azimuth) resolution of the SAR data. Enhanced directional wave spectral characteristics will further help to improve the interpretation of the new bistatic Harmony high-resolution scatter and Doppler combined directional measurements.

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The EarthExplorer 10 mission Harmony by the European Space Agency ESA, scheduled for launch around 2029–2030, consists of two passive C-band synthetic-aperture-radar companion satellites flying in a flexible constellation with one Sentinel-1 radar satellite as an illuminator. Sentinel-1 will serve as transmitter and receiver of radar waves, and the two Harmonys will serve as bistatic receivers without the ability to transmit. During the first and last year of the 5-year mission, the two Harmony satellites will fly in a cross-track interferometric constellation, such as that known from TanDEM-X, about 350 km ahead or behind the assigned Sentinel-1. This constellation will provide 12-day repeat DEMs, among other regions, over most land-ice and permafrost areas. These repeat DEMs will be complemented by synchronous lateral terrain displacements from the well-established offset tracking method. In between the cross-track interferometry phases, one of the Harmony satellites will be moved to the opposite side of the Sentinel-1 to form a symmetric bistatic “stereo” constellation with ±~350 km along-track baseline. In this phase, the mission will provide opportunity for radar interferometry along three lines of sight, or up to six when combining ascending and descending acquisitions, enabling the measurement of three-dimensional surface motion, for instance sub- and emergence components of ice flow, or three-dimensional deformation of permafrost surfaces or slow landslides. Such measurements would, for the first time, be available for large areas and are anticipated to provide a number of novel insights into the dynamics and mass balance of a range of mass movement processes.

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Assessing the performance of interferometers and processing interferograms require accurate knowledge of the temporal lag, sensitivity, and spectral shift. While these parameters are well-defined for conventional interferometric configurations, their definition becomes opaque for complex configurations, such as bistatic systems with formation-flying satellites. According to the principle of diffraction tomography, each instrument samples a distinct region of the scattering surface’s Fourier domain. Using this principle, we introduce a wavenumber-domain method for calculating the temporal lag, spectral shift, and sensitivity to height of synthetic-aperture radar (SAR) interferometers. The method calculates interferometric parameters by aligning the ground-projected wavenumber support of the SAR images forming the interferogram. Although the wavenumber-support method agrees with the conventional geometric formulations of the temporal lag and sensitivity in geometrically simple cases, the two methods diverge in more complex geometries. We show that when the two SAR satellites fly in a close-formation or have lines of sight that are squinted with respect to the zero-Doppler direction, then the geometric formulations are inadequate and the wavenumber-support method is needed to accurately estimate the interferometric parameters.@en

The paper presents a novel concept of SwarmSAR for improving the azimuth resolution of fast-decorrelating targets such as ocean surfaces to generate high-resolution SAR images. The SwarmSAR concept consists of multiple simple nodes in a close formation cooperating in a MIMO-like fashion and illuminating a common footprint. Each individual node is basic but self-sufficient, guaranteeing decent target-resolving capabilities, even when operating individually. However, when operating in a MIMO-like fashion, they significantly improve the target resolution and imaging capabilities.In this paper, we promote an S-band SwarmSAR considering a simplified geometry for resolving a fast-decorrelating point target in the azimuth direction. The results demonstrated in this work show the superiority of distributed SwarmSAR architecture over traditional monostatic SAR systems in resolving fast-decorrelating targets, and provide insight into the potential of the concept for future SAR missions.

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Simultaneous multiangle spaceborne synthetic aperture radar (SAR) can provide spatially diverse SAR images of the same scene without time lags. Through differential SAR interferometry (D-InSAR), the system can extract accurate multidimensional deformations from the mixing differential tropospheric delay (DTD), which generally distorts deformation signals in single interferograms. This article focuses on the multidimensional deformation estimation by simultaneous multiangle spaceborne D-InSAR. A multichannel Wiener filter (MWF)-based multidimensional deformation and DTD joint estimation method is proposed in this article. The method can achieve optimal estimation accuracy and reduce the loss of scene details. It was first validated by the simulations based on the system parameters of the future European Space Agency (ESA) Harmony mission. Additionally, the method was confirmed through the utilization of the real TanDEM-X bidirectional (BiDi) SAR data acquired over two scenes in California, USA. We analyzed the performance of the method in the presence of multiple error sources and investigated the impact of different observation geometries on estimation performance. Finally, the results demonstrate the potential of simultaneous multiangle spaceborne D-InSAR in multidimensional deformation measurement. The proposed method is effective in achieving good estimation accuracy and spatial resolution preservation.

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Estimating sea surface height using cross-track interferometry (XTI) requires high sensitivity because the ocean surface signal is in the order of 10 cm. In addition, the interferometer requires a temporal delay of a few milliseconds to ensure the coherency of the moving ocean surface. We show that a squinted line of sight (LoS), in combination with a helix satellite formation, allows optimizing the effective perpendicular and along-track baselines to satisfy these conditions. This article presents a model to estimate the performance of a formation-flying cross-track interferometer with a squinted LoS. The tenth Earth Explorer, Harmony, which features two bistatic synthetic aperture radar (SAR) companions, and a theoretical system with one monostatic and one bistatic SAR are used as case studies. The standard deviation of the height estimate is 1-10 cm between 29° and 41° and increases to 30 cm at the far range (46°) at a wind speed of 5 ms-1. The power spectral density of the elevation shows that spatial scales of 47 km can be resolved. The performance improves at higher wind speeds due to higher backscattering. At a wind speed of 15 ms-1, the wavelengths from 27 to 11 km can be resolved, depending on the elevation spectrum. The performance over a 250-km swath enables the instantaneous estimation of the surface elevation at the submesoscales for the first time.

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Two air-sea interaction quantification methods are employed on synthetic aperture radar (SAR) scenes containing atmospheric-turbulence signatures. Quantification performance is assessed on Obukhov length L, an atmospheric surface-layer stability metric. The first method correlates spectral energy at specific turbulence-spectrum wavelengths directly to L. Improved results are obtained from the second method, which relies on a machine-learning algorithm trained on a wider array of SAR-derived parameters. When applied on scenes containing convective signatures, the second method is able to predict approximately 80% of observed variance with respect to validation. Estimated wind speed provides the bulk of predictive power while parameters related to the kilometer-scale distribution of spectral energy contribute to a significant reduction in prediction errors, enabling the methodology to be applied on a scene-by-scene basis. Differences between these physically based estimates and parameterized numerical models may guide the latter's improvement.

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In this article, our aim is to estimate synthetic aperture radar (SAR) observables, such as backscatter in VV and VH polarizations, as well as the VH/VV ratio, cross ratio, and interferometric coherence in VV, from agricultural fields. In this study, we use the decision support system for agrotechnology transfer (DSSAT) crop-growth simulation model to simulate parcel-level phenological and growth parameters for over 1500 parcels of silage maize in the Netherlands. The crop model was calibrated using field data, including silage maize phenological phases, leaf area index, and above-ground dry biomass (AGB). The simulations incorporate fine-resolution gridded precipitation data and soil parameters to model the interaction between soil-plant-atmosphere and genotype in DSSAT. The crop variables produced by DSSAT are then used as inputs to a support vector regression model. This model is trained to simulate SAR observables in 2017, 2018, and 2019, and its performance is evaluated using independent fields in each of these years. The results show a close fit between modeled and observed SAR C-band observables. The importance of vegetation variables in the estimation of SAR observables is assessed. The AGB showed significant importance in the estimation of backscatter. This study demonstrates the potential value of combining crop-growth simulation models and machine learning to simulate SAR observables. For example, the SVR model developed here could be used as an observation operator in an assimilation context to constrain vegetation and soil water dynamics in a crop-growth model.

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The Harmony satellite mission was recently approved as the next European Space Agency (ESA) Earth Explorer 10. The mission science objectives cover several applications related to solid earth, the cryosphere, upper-ocean dynamics and air–sea interactions. The mission consists of a constellation of two satellites, flying with the Copernicus Sentinel 1 (C or D) spacecraft, each hosting a C-band receive-only radar and a thermal infrared (TIR) payload. From an ocean dynamics/air–sea interaction perspective, the mission will provide the unique opportunity to observe simultaneously the signature of submesoscale upper-ocean processes via synthetic aperture radar and TIR imagery. The TIR imager is based on microbolometer technology and its acquisitions will rely on four channels: three narrow-band channels yielding observations at a ≃1 km spatial sampling distance (SSD) and a panchromatic (PAN, 8–12 (Formula presented.) m) channel characterized by a ≃300 m SSD. Our study investigates the potential of Harmony in retrieving spatial features related to sea surface temperature (SST) gradients from the high-resolution PAN channel, relying on top-of-atmosphere (TOA) observations. Compared to a standard SST gradient retrieval, our approach does not require atmospheric correction, thus avoiding uncertainties due to inter-channel co-registration and radiometric consistency, with the possibility of exploiting the higher resolution of the PAN channel. The investigations were carried out simulating the future Harmony TOA radiances (TARs), as well as relying on existing state-of-the-art level 1 satellite products. Our approach enables the correct description of SST features at the sea surface avoiding the generation of spurious features due to atmospheric correction and/or instrumental issues. In addition, analyses based on existing satellite products suggest that the clear-sky TOA observations, in a typical mid-latitude scene, allow the reconstruction of up to 85% of the gradient magnitudes found at the sea-surface level. The methodology is less efficient in tropical areas, suffering from smoothing effects due to the high concentrations of water vapor.

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This paper presents an approach to implement a forward model for Sentinel-1 copol and crosspol backscatter and coherence using crop bio-geophysical parameters namely leaf area index, biomass, canopy height, soil moisture and root zone moisture as inputs for the maize. These required input parameters are generated using Decision Support System for Agrotechnology Transfer (DSSAT), one of the state-of-the-art crop growth models. The predicted SAR signal is generated using Support Vector Regression (SVR) over all the maize fields in an agricultural region, Flevoland, Netherlands. The correlation between simulated signal and observed signal is evaluated.@en

Bistatic scattering from rough surfaces is typically approached through the analysis of the scattered field in the conventional H and V polarization basis, which coincides with the zenith and azimuth unit vectors in a spherical reference frame. This study delves into the impacts of different choices of the transmit and receive linear basis on the performance and design of a synthetic aperture radar (SAR) mission receive-only companion. This article formalizes the rotation of the scattered wave orientation at the antenna axes of the companion with respect to the transmitted one and introduces a novel set of linear polarizations, named principal polarizations, in transmit and receive, deemed more suited to represent the scattering mechanisms of rough surfaces. Such a set is defined by the polarization bases that maximize the radar cross section. It is shown that the theoretical estimates from the proposed geometrical framework provide a good agreement with analytical and numerical simulations, performed considering state-of-the-art numerical solutions. In addition, this article promotes the hypothesis that a bistatic radar configuration, defined through the conventional H and V linear basis, presents a strong similarity, from a target information retrieval standpoint, to a monostatic compact φ-pol mode, i.e., with the transmission of a linear polarization rotated by an angle φ. The rotation φ varies over the swath and as a function of satellite separation. For baselines of 250-300 km, such as those envisioned by the European Space Agency (ESA) Harmony Earth Explorer candidate, and for steep incidence angles, an equivalent π8-pol can be achieved for rough surfaces.

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Observations of wind and ocean surface velocity vectors by along-track interferometry (ATI) with the synthetic aperture radar (SAR) are not only important for direct applications but also to increase understandings of ocean upper layer mixing, air-ocean interactions, and mapping submesoscale (1-10 km) structures. An experimental bidirectional (BiDi) ATI acquisition mode of TanDEM-X observes with two squinted beams separated by an angle of approximately 13.2° in azimuth on the ground. The baseline is very short, and the along-track interferometric phase (ATI phase) of the ocean surface in the line-of-sight direction of the beams can be interpreted as a total Doppler velocity. The 2-D Doppler velocity field will thus include wind-wave detected motions. In this article, Doppler velocity fields acquired from this experimental acquisition mode are presented. The sequential retrieval of wind vector and total surface current vectors (TSCV) is demonstrated on the BiDi TanDEM-X data. The retrieval algorithm builds on existing geophysical model functions (GMFs) of normalized radar cross section (NRCS) and Doppler velocity. XMOD2 and a GMF based on the Elfouhaily ocean wave spectrum coupled with a Kirchhoff approximation (EOWS&KA) are used. The retrieved wind fields are generally consistent with the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-5. While the ATI phase errors are small, the retrieved TSCV field looks promising. Acquisitions were located at sea over the tip of the Novaya Zemlya in Russia and over an area near Tromso, Norway.

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This article describes the observation techniques and suggests processing methods to estimate dynamical sea-ice parameters from data of the Earth Explorer 10 candidate Harmony. The two Harmony satellites will fly in a reconfigurable formation with Sentinel-1D. Both will be equipped with a multi-angle thermal infrared sensor and a passive radar receiver, which receives the reflected Sentinel-1D signals using two antennas. During the lifetime of the mission, two different formations will be flown. In the stereo formation, the Harmony satellites will fly approximately 300km in front and behind Sentinel-1, which allows for the estimation of instantaneous sea-ice drift vectors. We demonstrate that the addition of instantaneous sea-ice drift estimates on top of the daily integrated values from feature tracking have benefits in terms of interpretation, sampling and resolution. The wide-swath instantaneous drift observations of Harmony also help to put high-temporal-resolution instantaneous buoy observations into a spatial context. Additionally, it allows for the extraction of deformation parameters, such as shear and divergence. As a result, Harmony's data will help to improve sea-ice statistics and parametrizations to constrain sea-ice models. In the cross-track interferometry (XTI) mode, Harmony's satellites will fly in close formation with an XTI baseline to be able to estimate surface elevations. This will allow for improved estimates of sea-ice volume and also enables the retrieval of full, two-dimensional swell-wave spectra in sea-ice-covered regions without any gaps. In stereo formation, the line-of-sight diversity allows the inference of swell properties in both directions using traditional velocity bunching approaches. In XTI mode, Harmony's phase differences are only sensitive to the ground-range direction swell. To fully recover two-dimensional swell-wave spectra, a synergy between XTI height spectra and intensity spectra is required. If selected, the Harmony mission will be launched in 2028.

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A wide-swath synthetic aperture radar (SAR) image is known to be achievable by merging multistatic aliased data that is collected with an appropriate along track displacement. However, in terms of both flexibility requirements like potentiality of both along track and cross track interferometry and design requirements like orbital safety etc., a cross track baseline is not only demanded but also unavoidable. In this work, two methods are proposed in order to merge SAR data to recover the Doppler spectrum unambiguously for the non zero cross track baseline case. The algorithms are compared and validated by simulating an azimuth invariant multistatic SAR satellite constellation. The results are promising in terms of dealing with long cross track baselines.@en

A recent publication claims that closure phases in SAR interferometry bear no relationship to physical changes of the scatterer, but only to the statistical properties of the averaged pixels. We disprove this claim with a simple counterexample and remind the reader of cases in which closure phases indicate a clear physical content, including the exploitation of closure phases in other fields.

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Distributed SAR systems provide imaging capabilities that cannot be achieved by traditional monolithic satellites, thanks to the multiple angles and times of observation. In this paper the opportunities offered by a swarm of small satellite nodes operating in S-Band are discussed. The nodes fly in a close formation and operate in MIMO mode. All the $N$ satellites transmit and receive the $N$ pulses at the same time, following a Frequency Division Multiplexing (FDM) scheme. The work focuses in particular on the impact of the cross-track baselines on the resolution and on the quality of the signal reconstructed from the $N^{2}$ channels. A first iteration of a distributed target processor based on adaptive frequency and channel treatment is hence proposed with the aim of effectively accounting for the slope-induced spectral shifts.@en

Tropospheric delays are one of the main contributors to the interferometric phase in synthetic aperture radar (SAR) interferometry. When the phase contributions from surface deformation, topography, and ionospheric delays are negligible or known, the interferogram can be used to estimate the differential tropospheric delay (DTD), which can help to improve tropospheric delay predictions from weather models and in situ measurements. In conventional repeat-pass interferometric SAR (InSAR), however, the estimation of the DTD can still be significantly hindered by baseline errors. In addition, a single interferogram provides only relative DTDs, as the delays can be retrieved up to an unknown offset. To address such issues, this article presents a method for the estimation of DTDs on large scales by using repeat-pass simultaneous multi-angle SAR systems. Complementary simultaneous observations of the correlated troposphere from multiple angles are used to retrieve estimates of the absolute DTD and, at the same time, to mitigate the effect of baseline knowledge errors. Finally, a performance evaluation is presented for the Harmony Earth Explorer 10 candidate mission. A centimeter-level absolute accuracy and a submillimeter-level relative accuracy of the DTD estimation are achieved under the multistatic Harmony case when at least one companion satellite has an inter-satellite distance longer than 300 km to provide enough sensitivity.

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Multiple CubeSat altimeters can work independently or corporately to form altimeter constellations. Different configurations of the constellations can acquire distinguished advantages: improved spatial/temporal sampling and high cross-track resolution, which will be helpful for observations of oceanic small-scale structures and weather forecasting. Compared to single conventional altimeters, CubeSat altimeter constellations may achieve better performances with lower costs. To fully understand these systems, this article focuses on the performance analysis and methodology for CubeSat altimeter constellations. Besides the typical analyses of the resolution, revisit, and absolute sea surface height (SSH) accuracy, the performance analysis was conducted by considering the characteristics of multiple measurements provided by CubeSat altimeter constellations. Local and global spatial sampling performances are investigated for various constellations and compared by sampling density and swath size. Moreover, relative SSH accuracy is introduced and evaluated based on the spatial structure functions of errors to effectively evaluate the measurement performance. Related system requirements on power, delta-v, etc., to achieve the performance are also discussed, which ensures that the analysis fits the boundary conditions of implementation. Finally, different concepts of the CubeSat altimeter constellations are compared, where their limitations and possible solutions are also discussed.

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Using a combination of multi-directional SAR and TIR measurements, the Harmony Earth Explorer 10 mission candidate will provide high resolution simultaneous measurements of surface stress, surface currents SST and wave spectra over oceans, 3-D deformation vectors over solid Earth, and time-series of surface elevation changes over volcanic areas and land ice masses. This will serve a series of science objectives aimed at better understating multi-scale processed and feedbacks in the Earth System.@en