InSAR Theory and Techniques (1)

An accurate measurement of the content of water vapor in the atmosphere is a key requirement for the weather forecasting and climate research. Since water vapor affects the microwave signal propagating in the atmosphere by a high temporally and spatially variable delay, precise determination of water vapor content is also essential for remote sensing applications of global navigation satellite systems (GNSS) and interferometric synthetic aperture radar (InSAR). Although water vapor contributes to less than 10% of the total neutrospheric delay, this delay is considered as a significant source of limitation in InSAR and GNSS applications.  That is because water vapor content is highly variable in time and space, which makes the corresponding delay not easily modeled. The time delay caused by water vapor, called wet delay, can be related to the precipitable water vapor (PWV) content along the signal path and hence can be exploited to provide information at its content in the atmosphere.

Over the past twenty years, repeat-pass spaceborne InSAR has widely been used as a geodetic technique to generate maps of the Earth's topography and to measure the Earth's surface deformation. In this paper, we present InSAR, particularly Persistent Scatterer InSAR (PSI), as a meteorological tool to derive maps of the water vapor content in the atmosphere. Atmospheric water vapor corresponds to a phase shift in the interferogram, which if successfully separated from other phase components provides useful information about its distribution.

 PSI produces PWV difference maps of a high spatial density that are inverted to retrieve partial PWV maps at each SAR acquisition time. The PWV components eliminated during the PSI data processing can be reconstructed based on external data sources. If the master image is selected such that the atmospheric variations are spatially smooth, then the topography-dependent PWV is reduced during the PSI data processing. The long wavelength PWV cannot be distinguished from the orbital ramps and hence, this component is also missing in the retrieved maps. Based on external data, GNSS in our study, these components can be modeled.   

 We present a new method to reconstruct the missing components using the PWV estimated from the GNSS phase observations. The method is applied to build maps of the absolute PWV by combining data from InSAR and GNSS over the region of Upper Rhine Graben in Germany and France. We used data from ten GNSS sites distributed within and close to the SAR image. The sites do not have to be dense, but they should be well distributed within the image. This is important to observe different neutrospheric effects over the entire SAR image.

 Comparing the PWV maps derived using our method with these maps measured by the near infrared sensor MERIS (MEdium Resolution Imaging Spectrometer), the results show strong spatial correlation between the maps with RMS values of less than 1 mm. We also compared the derived maps with PWV maps simulated by numerical atmospheric models. The correlation between the maps varies due to the variable accuracy of the model output maps. Sometimes, a bias is observed between the model data and our results. Continuous grids of PWV are then produced by applying the kriging geostatistical interpolation technique that takes the benefit of the spatial correlations between the PWV observations.  

Introduction

SAR Interferometry with stacks has already shown its potential in identifying permanent scatterers, in processing decorrelating targets, mitigating atmospheric delays, etc., but we believe that there is still potential for retrieving information on the scattering environment which has not been extensively studied yet. In particular interferometric stacks can reveal systematic phase inconsistencies which are not detectable in single interferograms, challenging any simple interpretation of the interferometric phase and associated coherence. The explanation of such inconsistencies requires more complex propagation models than the one based on a simple delay.

Phase inconsistencies

Phase inconsistencies are residuals accumulated in a closed chain of interferograms in which each image is used once as a slave and then as a master in the following interferogram. The simplest case requires three images and three interferograms: Int_1,2, Int_2,3, Int_3,1. If the interferograms are averaged spatially, the phase of their product (Int_1,2*Int_2,3*Int_3,1) might differ from zero (with statistical significance), revealing a complex scattering mechanism with more than one coherent contribution to the interferogram.

This phenomenon was illustrated and described in [1], along with some possible explanations, among which a revisitation of volumetric scattering in presence of normal baseline. In this presentation we want to focus on a different effect, namely on the role of liquid water in creating differential delays. In both cases the basic explanation of phase inconsistencies is the simultaneous presence of different scattering mechanisms that experience different delay variations in different acquisitions. The difference lies in the cause of the delay: for the tomographic setting the differential delays come from the geometry. For the water-delay hypothesis the delay would be caused by the variation of water content in some propagation medium.

Observations that support the role of liquid water in generating inconsistencies

In a previous work [3] we have shown that variations in soil moisture are able to explain phase inconsistencies observed over bare agricultural fields in L-band. Here we report additional observations with different frequency bands (C and P).

C-band InSAR data (ERS-1) show that some systematic inconsistencies persist on vegetated areas even when the geometrical baselines become relatively small, e.g. for height of ambiguities larger than 150m, so that the pure volumetric-tomographic explanation can be ruled out. For example this can be seen comparing figure 1 with figure 2 in the attached pdf, belonging to a dataset acquired over the region of Rome (Italy), and representing the phase inconsistencies for two different image triplets. In the first case the three baselines are relatively large and the heights of ambiguity are all below 60m. Volumetric effects are evident on Rome city center, which appears as a bluish region in the center right portion of the figure. In the second case the heights of ambiguities are much larger (always larger than 150m) and the volumetric effects in the city center disapppear completely. Now a clean, green area takes the place of the previous bluish signature. However, in other parts of the figure, positive or negative inconsistencies emerge, where in the other figure there were none or there was too much decorrelation.The independence of the trend with repect to the height of ambiguity and especially the fact that anomalies are observed on vegetated areas support the hypothesis that moisture (liquid water) is the cause of anomalous propation effects.

ESA's TropiScat experiment constitutes a very interesting dataset to study coherence and phase variations of antural targets, in the specific case of tropical forest. With one acquisition every 15 minutes for long periods of time and with its tomographic capability, TropiScat provided a valuable tool to study the short and long term dynamics of the low-frequency backscatter of the forest. We have processed tomographically the P-band data (400-600 MHz) tomographically and we have extrated sections at different heights The tomographic processing is intense, so this was done for selected time spans. Successively, the interferometric coherence was computed for each section ("layer"), taking as a reference the section at midnight of a given day. The magnitude of the coherence and the phase are plotted in figures 3 and 4 respectively for the HH polarization and in figures 5 and 6 for the VV polarization. From these results one can clarly see that the phase behaviour is different for different polarizations and for different layers. For lower layers there is limited phase variation with respect to higher layers. Particularly interesting are the linear trends during each night, with phases changing as much as 40 deg in the HH case for the 20m layer. Such phase variations correspond to about 3 cm away from the sensor if interpreted as physical displacements of the trees or branches, but can be also explained alternatively as a extra delays introduced by a thin layer of liquids of just a few millimeters (integrated in the line-of-sight), considering a relative dielectric constant of about 90 for water. This explanation seems reasonable considering the intense water-activity of plants in sapwood, which was measured directly in the past in the work of McDonald and colleagues (see [2]).

Seeing decorrelation as a coherent mechanism

This work is also an attempt to stress that temporal decorrelation can have a clear coherent character. Temporal coherence loss can be caused by the simulatenous presence of a few scattering contributions (even just two), if each of them has a different interferometric behaviour. This explains some intermittent coherent patterns observed in SAR temporal stacks and invites to consider coherence loss both as a signal and a disturbance.

Acknowledgment

The authors acknoledge ESA for the TropiScat and ERS-1 data.

References

 [1] De Zan, F., Zonno, M. and Lopez-Dekker, P. "Lack of triangularity in SAR Interferometric phases". Proceedings of European Conference on Synthetic Aperture Radar (EUSAR), pp. 854-857. 2014.

[2] McDonald, K., Zimmermann, R. and Kimball, J., "Diurnal and spatial variation of xylem dielectric constant in Norway Spruce (Picea abies [L.] Karst.) as related to microclimate, xylem sap flow, and xylem chemistry," Transactions on Geoscience and Remote Sensing, vol. 40 (9), pp. 2063-2082, Sep 2002.

[3] De Zan, F., Parizzi A., Prats-Iraola, P. and Lopez-Dekker, P., "A SAR interferometric model for soil moisture", Transactions on Geoscience and Remote Sensing, vol. 52 (1), pp. 418-425, Jan 2014.

Propagation (chiefly, atmospheric and ionospheric) effects are thedominant source of noise in radar interferograms, and the mainobstacle to measuring low-amplitude deformation signals. We present acomputationally efficient method for estimating and removing radarphase delays due to propagation effects. The method takes advantage ofthe fact that the atmospheric phase delays have common contributionsin interferograms that share a common scene. Therefore one canevaluate atmospheric phase screens by stacking appropriately choseninterferograms centered on a given acquisition date. We use aniterative procedure in which the atmospheric contributions are firstcrudely estimated for all shared scenes, and ranked according to thenoise level. We then perform a common-scene stacking, starting withthe noisiest scenes. Estimated phase screens are subtracted from therespective interferograms in the subsequent processing steps. Theprocedure is repeated until the estimated phase screens vary by lessthan the prescribed threshold. We use geocoded unwrappedinterferograms in our analysis, however the method should be alsoapplicable in case of wrapped interferograms and/or in the radarcoordinates. Tectonic contributions are essentially excluded from theevaluation of atmospheric phase screens if deformation is steady state(secular), or quasi-steady (slowly varying transients). We demonstratethe feasibility of the proposed method by inverting a synthetic dataset, and by comparing atmosphere-corrected InSAR data to independentGPS data. The method performs best in case of temporally dense SARcatalogs with regular and frequent data acquisitions, such as theanticipated data from the new and upcoming InSAR missions (Sentinel-1,ALOS-2, NISAR etc.). We also demonstrate the method performance usingavailable data from the past InSAR missions acquired over the EasternCalifornia Shear Zone. We use ERS-1/2 and ENVISAT data from thedescending tracks 399 and 170 spanning a time period between 1992-2010to derive the mean line-of-sight (LOS) velocity fields, as well astime series of LOS displacements for several points of interest. Theestimated atmospheric phase screens are subtracted from the data priorto stacking for the mean LOS velocities, or computing time series. Wefocus on several areas where previous studies have suggested anomalousdeformation signals. In particular, we find that subsidence around theCoso geothermal plant (the second largest geothermal production sitein the US) has persisted at a nearly constant rate over the period ofobservations (1992-2010). The average subsidence rate at Coso is about2 cm/yr. We also observe subsidence around Harper Lake, most likelydue to compaction caused by water pumping, at an average rate of 1cm/yr. The Harper Lake area is covered by both tracks, and we find anexcellent agreement between data from each track. The find a localizedLOS velocity gradient across the Blackwater Fault of about 1 mm/yrover 3-5 km using data from track 170, consistent with findings ofPeltzer et al. (2001) who used data from the same track spanning 8years between 1992-2000. However, data from the neighboring track 399do not show a similar LOS velocity pattern, implying that the dataprecision are of the order of 1 mm/yr, and that the inferreddeformation due to the Blackwater fault may be due to residualnoise. Finally, we investigate deformation across the Hunter MountainFault, where a similar secular deformation anomaly was inferred fromInSAR data from track 442, and attributed to interseismic slip rate of5 mm/yr and an anomalously shallow locking depth of 2 km (Gourmelen etal. 2011). Our analysis of data from the overlapping track 170 doesnot reveal a step in secular LOS velocity across the Hunter MountainFault. The atmospheric phase corrections result in a significantreduction in the data scatter in time series of the radarline-of-sight displacements. 

Water vapor is the most variable of the major constituents of the atmosphere, playing an important role in many atmospheric processes over a wide range of temporal and spatial scales. It is basically concentrated in the troposphere, the atmosphere layer where the most important phenomena related to weather occur. The spatial distribution of water vapor plays a critical role in the vertical stability of the atmosphere, the distribution of clouds and rainfall and in the structure and evolution of atmospheric storm systems. Recently, it has been demonstrated that maps of the temporal variations of the Precipitable Water Vapour spatial distribution can be obtained by SAR interferometry [1]. The high spatial resolution and the almost daily updating of the InSAR Precipitable Water Vapour maps make them of interest to study variations of the local concentrations of water vapor, not possible with current measurement techniques which give information on water vapor distribution only at a coarse scales. This property could be important for numerical forecasting procedures (e.g. those based on the 3DVAR and 4DVAR analysis). In fact, these procedures could take advantage from the availability of high resolution maps of Precipitable Water Vapour to provide more accurate precipitation forecasts and open interesting perspectives for nowcasting applications. In this work we present a generalization of the Small Baseline approach to estimate the temporal evolution of Precipitable Water Vapour (ΔPWV) maps obtained by multiple time-series of SAR images acquired over the same area by different satellites. Interferograms are corrected for Digital Elevation Model and orbit errors and unwrapped. The unwrapping procedure introduces an arbitrary constant in the ΔPWV estimate. The ΔPWV maps derived by SAR interferometry are calibrated using data acquired by the GPS network to estimate this constant. Furthermore, the comparison of InSAR and GPS estimates of ΔPWV helps to check errors in SAR interferometric processing due to the use of incorrect satellite orbits and to verify that SAR interferometric phase is only related to atmospheric phenomena and not to terrain deformation. At each station, the temporal difference of the PWV measured by GPS at the acquisition times of the two SAR images is computed. This quantity is compared to the ΔPWV estimated by InSAR and the calibration constant K is determined by minimizing a cost function. The problem of ΔPWV estimation is formulated as a constrained linear least-square problem with linear constraints. The ΔPWV spatial has a poor temporal correlation and a good spatial correlation.

The temporal evolution of the PWV is modeled by constraining at a given time the differences between ΔPWV values in adjacent pixels to be in a given interval.

The modeled PWV maps are compared to InSAR ΔPWV maps and PWV profiles estimated by a network of GPS receivers and to the maps derived by numerical weather models.  The proposed methodology has been applied to time-series of ENVISAR-ASAR (C-band), TerraSAR-X.  and Cosmo-Sky-Med (X-band).

[1] P. Mateus, G. Nico, J. Catalao, “Can spaceborne SAR interferometry be used to study the temporal evolution of PWV?”, Atmospheric Research, 119, 70-80, 2013.

Many of the recent and upcoming spaceborne SAR systems (ALOS-2, SAOCOM, NISAR (all L-band), BIOMASS (P-band)) are operating at the L-band or P-band frequency range. The choice of lower center frequencies has a number of advantages especially for InSAR applications. These include deeper penetration into vegetation, higher coherence, and higher sensitivity to soil moisture.

While low-frequency SARs are undoubtedly beneficial for a number of earth science disciplines, their signals are susceptive to path delay effects in the ionosphere. Many recent publications indicate that the ionosphere can have detrimental effects on InSAR image quality, coherence and phase. It has also been shown that the magnitude of these effects strongly depends on the time of day and geographic location of the image acquisition as well as on the coincident solar activity. Hence, in order to provide realistic error estimates for geodetic measurements derived from L-band and P-band InSAR, an error model needs to be developed that is capable of describing ionospheric noise.

With this paper, we present a global ionospheric error model that is currently being developed in support of NASA’s future L-band SAR mission NISAR, but can be equally applied to support other low-frequency SAR missions. The system is based on a combination of empirical data analysis and modeling input from the ionospheric model WBMOD, and is capable of predicting ionosphere-induced SAR phase noise as a function of space and time. The error model parameterizes ionospheric noise using a power spectrum model and provides the parameters of this model in a global 1x1 degree raster. From the power law model, ionospheric errors in deformation estimates can be calculated.

In Polar Regions, our error model relies on a statistical analysis of ionospheric-phase noise in a large number of SAR data from previous L-band SAR missions such as ALOS PALSAR and JERS-1. The focus on empirical analyses is due to limitations of WBMOD in high latitude areas. Outside of the Polar Regions, the ionospheric model WBMOD is used to derive ionospheric structure parameters for as a function of solar activity. A cross validation of both model components show good correspondence, indicating that data-driven and WBMOD-based error calculations can be used together to calculate error characteristics on a global scale. The power spectrum descriptors provided by the model are converted to ionospheric phase screens from which image, coherence, and phase distortions in SAR data can be derived.

We introduce the concept of the error model and provide examples of global error maps calculated for the missions, ALOS-2 and NISAR. For NISAR, we also propagate ionospheric phase errors to errors in line-of-site deformation estimates assuming simple multi-temporal stacking algorithms. We also provide results of a model validation analysis that was conducted over equatorial and polar regions and compare model predictions to observed image and phase distortions.

For Interferometric Synthetic Aperture Radar (InSAR) the atmosphere forms one of the largest sources of error when it comes to the extraction of small-magnitude long-wavelength tectonic signals, and this remains a major problem for analysis of Sentinel-1 data. Spatio-temporal variation of water vapour, pressure and temperature in the troposphere is the main cause of these noise terms, introducing apparent differential path delays in interferograms of up to 15 cm in extreme cases. Several correction techniques have been applied in the past that rely on external data from weather models, GPS or spectrometer data, but these are typically limited by the lower spatial resolution or availability of the auxiliary data.

Alternatively, time-series InSAR techniques and filtering of the interferometric phase in space and time can be applied, but separating atmospheric delays from non-linear deformation is challenging. Another method, which can be applied to individual interferograms, is to estimate the correlation between interferometric phase and topography, either in a non-deforming area or using a frequency band insensitive to deformation. While this method can be successful for small areas, it does not account for spatial variation of atmospheric properties, which can be significant across regions larger than 100 km. While the slope relating phase and topography can be reliably estimated for subregions, the intercept cannot, as it is biased by the presence of unrelated signals. The intercept cannot, however, be neglected, as the mean height of each subregion typically varies, leading to a different intercept for each window.

We have developed a new power-law representation of the topographically-correlated phase delay that can be applied locally and which is able to account for these spatial variations in atmospheric properties (Bekaert et al., in review, JGR). We estimate the power law from sounding data to fit altitudes of up to 4 km, as this includes most of the topography range in our/most regions of interest. We also constrain the power-law by specifying the height above which the relative tropospheric delays are approximately zero. To ensure that tectonic deformation is not mapped into the atmospheric correction, we solve for the power law function in a frequency band insensitive to deformation.

While all methods have their advantages and disadvantages, it is unclear whether or not one method consistently outperforms the others. Here we present a statistical comparison of ENVISAT interferograms over Mexico and Italy for different tropospheric correction methods including (1) spectrometer observations from MERIS and MODIS, (2) weather model outputs from ERA-I at 75 km spatial resolution and the WRF model run at up to 5 km resolution, and from (3) phase-based estimation methods including the conventional linear method and our new power-law method. As MERIS is operated simultaneous with the SAR onboard ENVISAT it describes the correct atmospheric state, and is therefore used as reference in our study. Being limited by cloud cover our statistical analysis covers respectively 60% and 55% of our datasets for Mexico and Italy. We found that none of the methods exclusively perform best in reducing tropospheric InSAR signals. MERIS loses its simultaneous acquisition advantage when applied to other SAR sensors.

The selection of the appropriate correction technique therefore remains specific for your region of study, and so as part of this work we will be releasing a tropospheric correction toolbox that includes all the presented methods in a common processing frame.

References:

Bekaert et al., A spatially-variable power-law tropospheric correction technique for InSAR data, in review JGR