Atmosphere/Ionosphere

Propagation delay of the microwave signals through the ionosphere causes distortions in the repeat pass Interferometric Synthetic Aperture Radar (InSAR) interferograms. The dispersive medium of ionosphere for microwave signals, allows separating the ionospheric phase delay from non-dispersive interferometric phase components through a range split-spectrum technique. Although the performance of the technique has been evaluated for limited number of InSAR pairs, it has not been applied on InSAR stacks. We present a new algorithm to estimate a time-series of ionospheric phase delay using a stack of SAR acquisitions. The time-series of ionospheric phase delay can be used to compensate the InSAR displacement time-series and can be also used to evaluate the spatio-temporal variation of the relative Ionosphere’s Total Electron Content (TEC). 

We apply the new algorithm to several stacks of L-band SAR acquisitions in Ecuador, Chile, Alaska and California. Our analysis of the time-series of ionospheric delay reveals maximum temporal variation of more than 1m of delay over ~400 km in Ecuador and Chile with spatial variations in both short and long spatial wavelengths of hundreds of meters to tens of kilometers. In contrast the time-series of the ionospheric delay in California shows smaller temporal variations of ~10 cm over ~100 km with large spatial wavelengths of tens to hundreds of kilometers. Using the estimated time-series of ionospheric delay we correct the InSAR displacement time-series covering the 2007 M7.7 Tocopilla earthquake in Chile, and Mw 8.8 2010 Maule earthquake and demonstrate how the corrected InSAR time-series reveals the ground displacement due to the earthquakes. Our analysis reveals that the ionospheric delay correction reduces the uncertainty of InSAR displacement timeseries from few 10s of centimeters to few centimeters in regions with significant TEC variations such as Ecuador and Chile. The correction can significantly improve the uncertainty of InSAR velocity fields from 10s of cm/yr before correction to few mm/yr after the correction.

Differential synthetic aperture radar interferometry (DInSAR) has been proved to be a very powerful technique for measuring large-scale land de-formations with centimeter to millimeter accuracy along the line-of-sight direction. Their high accuracy is achieved in correspondence of high phase quality of interferograms without noise. However, in real cases, the differences in humidity, temperature and pressure between two acquisitions causes additional fringes on differential interferograms, which is known as atmospheric phase screen (APS). Previous studies [Hanssen, 2001] show that the APS can be categorized into stratification and turbulence components mixing. In the situation of stratification atmospheric delay, in some cases, the phase delay correlates with topographic variations, while in the turbulent phase delay situation, the spatial correlation length typically can be described by the slope of its power spectral density based on Kolmogorov’s theory. Both these atmospheric artefacts could distort differential interferograms severely. Mitigating APS is one of the largest challenges in DInSAR community. Recently, a number of methods have been exploited and developed to dedicate to atmospheric compensation. They can be classified in three categories.

The classical approaches in time series analysis take advantage of the properties of the interferometric phase. Turbulent atmospheric phase artefacts are highly correlated in space, but they can be assumed to be uncorrelated in time. At the same time, the phase terms associated to deformation present a higher temporal correlation and a lower spatial correlation. Thus, the phase terms coming from atmospheric artefacts can be estimated and partially removed from the interferometric phase with different spatial and temporal filters [Ferretti et al., 2001,Berardino et al., 2002]. However, without prior information of the atmospheric artefacts and/or the deformation signal characteristics, it is difficult to determine the shape and length of the temporal filter optimally. In order to optimize the filtering approaches, some researchers have tried to obtain statistical properties of atmospheric artefacts as a prior from auxiliary data (such as Numerical Weather Prediction (NWP) products [Gong et al., 2015]). It has been proved that this is an alternative method to mitigate the atmospheric artefacts. These filtering methods are simple and effective in case of turbulent atmospheric delay.

Other techniques use auxiliary data sets such as meteorological models and multispectral remote sensing data. The APS delay in each individual interferogram can be mitigated using data about atmosphere state from MERIS data, MODIS data [Mateus et al., 2013, Li, 2005], GPS [Wadgeet al., 2002, Onn and Zebker, 2006, L ofgren et al., 2010] or forecast products from NWP [Perissin et al., 2009, Perissin et al., 2011, Adam et al., 2011]. However, the main limitation of this technique is the lack of available water vapor data at the presence of cloud areas and on the corresponding date of acquisition. In cloudy areas, weather research and forecasting (WRF) models have been used for predicting atmospheric conditions. However, the accuracy of the predicted water vapor contents depends on the quality of the models and their input data [Jung et al., 2014].

Another kind of techniques considers that APS is related to topography [Beauducel et al., 2000], which can happen in mountainous areas. Stratification APS contribution in interferograms can be modelled by analyzing the phase-elevation relationship with a linear model [Cavali ́e et al.,2007, Elliott et al., 2008, Doin et al., 2009, Lin et al., 2010, Adam, 2014]. To estimate the stratification APS more accurately, recent improvements have been made by analysing phase-elevation relationship with a multiple-regression model [Iglesias et al., 2014]. In addition, a power law model has also been applied to remove tropospheric APS, which accounts for the spatial variation of the tropospheric properties [Bekaert et al., 2015]. The main limitation of these model related methods is that other phase terms (e.g. turbulent atmospheric artefacts, deformation related phase) usually influence the estimation of the coefficient of the stratification APS. In practice, permanent scatterers are usually elaborately selected to calculate the coefficient in order to reduce the impact of other phase terms. Although such attempt can be more effective to some extent [Chaabane et al., 2007], the influence of turbulent atmospheric artefacts can not be neglected. In the case of stratification APS and turbulent APS are mixed, current phase-elevation based methods may obtain an incorrect coefficient estimation and lead to severe phase biases.

In this paper, we present an improved linear model-based technique that takes into account the influence of turbulent atmospheric phase for correcting tropospheric phase delays. In addition, as the coefficient may not be constant in one interferogram convering a large area, segmentation related issues are also studied. The strategy proposed in this paper utilizes the phase difference between selected high quality pixels to estimate the coefficient of a linear model, which is a Linear Model Method Resisting Turbulent Atmosphere Delay(LMMRTA). The realization of the LMMRTA is presented below. Considering the situation with turbulent APS, i.e. the observation consists of stratification APS and turbulent APS components. If stratification APS component correlates with topography, and turbulent component is spatially correlated, adjusting a linear model with the observation phase directly will obtain the incorrect coefficient. However, if we use the differential phase between pixel i and pixel j as a new observation phase, it would be beneficial to cancel the turbulent APS partially by adjusting the LMMRTA to the new observation phase. As in previous research, it indicates that the turbulent atmospheric artefacts correlate spatially. The correlation level depends on the distance of different links between pixels. Therefore, when estimating the coefficient of stratification APS, the influence of turbulent component can be weakened partially by weighting the observation phase. To be more specific, for pixel i and j with short distance, as the turbulent condition of each pixel is similar, the turbulent difference is close to zero, while for pixels with larger distance, the turbulent APS may be totally uncorrelated, the impact of the turbulent difference have to be considered. Based on this concept, an appropriate covariance matrix involving correlation length would be beneficial to weight the new observation phase. Utilizing the APS covariance, a more accurate coefficient of the linear model can be estimated.

The algorithm presented in this paper allows a more robust estimate of the stratified atmospheric delay from SAR interferograms with turbulent delay situations. The improvements of the proposed method are validated first with simulated data. In real case, our algorithm is cross validated using atmospheric delay estimated from NWP in the mountainous area of Tenerife island (Spain) with Envisat and Sentinel-1 data. The following aspects are discussed to demonstrate the performance of the algorithm. (1) As in simulated data, true values of coefficient are known, improvements of the estimated coefficient can be seen by comparing results from conventional linear model and LMMRTA method. (2) We also analysed sensitivity of the minimization step to demonstrate the robustness of the algorithm. In situations where other phase components (linear deformation pattern and turbulent APS) are mixed with stratified APS, while the minimum for conventional method is not evident, we can get a manifest minimum from LMMRTA algorithm, which is closer to true coefficient additionally. (3) We compare LMMRTA modelled stratified delay with phase delay derived from NWP. Delay-elevation ratios obtained from LMMRTA show good agreement with corresponding ratios predicted from NWP method.

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Linear motion rates with millimeter per year precision can be estimated from a deep stack of InSAR images; it is more challenging to quantify the onset, expanse, and severity of new motion because this information is often captured in a single image. However, this non-linear component of the motion is far more interesting because it enables ongoing risk management for a host of geophysical applications. The presence of atmospheric water vapour delay in interferograms poses a major difficulty to the task of extracting non-linear motion time-series from InSAR data [1]. External models and information can be used to simulate the expected delay--Numerical Weather Prediction (NWP) [1]--but its limited availability makes it impractical to use on a large scale.
In order to address the difficulty of separating the atmospheric and non-linear motion signal contributions we devise a decomposition technique similar to sparse coding[2][3], albeit with augmented priors. The decomposition attempts to solve for an interferometric (spatially varying) atmospheric constant as well as temporal basis vectors that
(1) Along with the atmospheric constant reconstruct the observed data with high accuracy.
(2) Are uncorrelated with the time series of atmospheric constants.
(3) Have minimal acceleration (penalized under either the L1 or L2 norm).
The resulting model requires specifying an expected spatial correlation length of the atmosphere and a tunable penalty on the norm of the acceleration of each component. The algorithm outputs a decomposition between the estimated non-linear motion and atmospheric delay constant as well as an estimated error. Intuitively, this algorithm learns a basis of the interferometric time series that is low in acceleration, explains the data well, and is uncorrelated with a simultaneously decomposed time series of atmospheric constants. In this sense it is comparable to other factorization techniques such as ICA, PCA and sparse coding, to name a few.
The optimization of this model is implemented by applying the techniques of [4] and [5]. We show excellent decompositions of atmosphere and non-linear motion over several InSAR stacks, for varying applications with varying severity in atmospheric delays.
Future work includes investigating alternative criteria to the three points described above, comparison of this technique to the methodology of [1] and extension of the model to handle very widespread non-linear displacement.
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Sporadic E (Es) is known to generate unusual propagation of VHF waves over long distances, and is caused by a layer of ionization that irregularly appears within the E region of the ionosphere. However, the generation mechanism of Es remains unclear, because the conventional ionosonde observation of Es has limited spatial resolution. Maeda et al. (2016, GRL) first succeeded in detecting mid-latitude Es signal over Japan as a two-dimensional image, using InSAR, and demonstrated the detailed spatial structure of Es.  The first objective of this study is to detect mid-latitude Es by InSAR, in order to add more dection examples to better understand the mechanisms of Es. Secondly, with the use of split-band InSAR (SBI) technique, we examine the dispersive and non-dispersive components during Es episodes.

First, we chose the dates whose critical frequencies of Es (foEs) were more than 15MHz at ionosonde in Kokubunji, Wakkanai and Yamagawa in the morning and noon in 2016 from May to June; Es is known to be frequent in the local daytime of summer season. Secondly, we chose the ALOS-2/PALSAR-2 data sets whose observation area, dates and time matches the data above as closely as possible. Thirdly, we generated Global Navigation Satellite System – Total Electron Content (GNSS-TEC) map whose areas, dates and time become the same as the above and if Es appeared in GNSS-TEC map, we generate interferogram. We could detect interesting phase changes in the pair of February 17, 2016 (Master) and May 25, 2016 (Slave) along a track from Tottori to Okayama. The location of the phase shift is close to the Es on the GNSS-TEC image. Therefore, we can consider the phase shift as the edge of Es.

Secondly, we separated the Es signal into dispersive and non-dispersive signals, using SBI technique. Our results indicate that the spatial patterns are largely similar to those observed in the original interferogram. However, besides the dispersive signals due to the changes in TEC, there also appeared such phase changes in the non-dispersive signals whose spatial pattern and scale were quite similar to those detected in the dispersive signals. We speculate that the latter non-dispersive signals could indicate the presence of positivelcharged ions, which has never been reported before. We will discuss the possible mechanisms of Es, based on these observations.

Synthetic aperture radar (SAR) and interferometric SAR (InSAR) measurements are disturbed by the propagation velocity changes of microwaves that are caused by the high density of free electrons in the ionosphere. Most affected are low-frequency (L- or P-band) radars although higher frequency (C- or X-band) systems, as the recently launched Sentinel-1, are not immune. Since the ionosphere is an obstacle to increasing the precision of SAR systems needed to remotely measure the Earth’s dynamic processes, as ground deformation, it is necessary to estimate and compensate ionospheric propagation delays in SAR signals. In this work we work discuss about the influence of the ionosphere on interferograms and the possible correction methods.

The ionospheric error, when measuring ground motion with C-band InSAR systems, is often considered small enough to be ignored. In this work we assess the average ionospheric error level occurring in non-compensated interferograms by using global ionospheric measurements, to show that the correction of ionospheric effects can sensibly increase the measurement accuracy. A statistical analysis of IGS global ionospheric TEC maps is used to calculate the standard deviation of the LOS and along-track error caused by ionospheric effects. IGS global TEC maps are generated assimilating a network of GPS-based TEC measurements with ionospheric models. The resolution and accuracy of these maps are too low to allow the correction of interferograms. Nevertheless, we use them for the statistical analysis to obtain a reasonable assessment of the possible ionospheric error when no correction is applied to interferograms. Firstly, we produce a histogram of the differential ionospheric TEC level considering all possible 12-days interferograms of one year (2015). In fact, a different absolute ionospheric level during the two acquisitions generates a linear phase term in the interferogram range direction due to the incidence angle change. This additional phase term introduces a measurement error. A global map of the expected LOS error can then be produced; an example is reported in Figure 1. Such a map can be used to predict the ionospheric error to ground deformation measurements. Solar cycle, diurnal, seasonal, and geographical variations of the ionosphere influence the error level for different satellites with different orbits, acquisition times, and for different geographical regions. For example, the result shows how the standard deviation of the LOS deformation error for a single Sentinel-1 interferogram in ascending geometry is, in low latitude regions, about 4 cm every 100 ground range km. The latter considers only the effect due to the incidence angle change; a similar analysis has been also realized for the ionospheric gradients in the range and azimuth directions.

The analysis indicates that the ionosphere can sensibly reduce the accuracy of ground deformation measurements. To increase such accuracy, the split-spectrum method can be used to estimate and remove the ionospheric phase screen from interferograms. In the second part of the work, the processing workflow of the split-spectrum method, applied to the special case of TOPS images, will be presented. Practical examples of successful correction of ionospheric disturbances, as well as possible issues, will also be presented. Figure 2 shows a disturbed interferogram and its compensated version. The phase screens estimated with the split-spectrum method will then be compared to the ones derived from the global TEC maps, to verify the quality of the statistical analysis. ­Finally, other ionospheric effects on Sentinel-1 interferograms, such as ionosphere-induced azimuth shifts will also be discussed with some examples, and possible correction strategies proposed.