We verify the performance ofionospheric phase error cor- rection using this CSs based autofocus, by applying a sim- ulated ionospheric phase error on a real SAR image, fol- lowed by its estimation and comparison with the original one. Firstly, a one-dimensional (azimuth) phase error is applied, being common to the whole range dimension. In a second step, a two-dimensional phase error is applied, for which more difficulties are expected due to the lower num- ber of CSs sharing the same phase error along the range direction. The used SAR image has been acquired at L- band by the E-SAR system of the German Aerospace Cen- ter over the city of Munich in Germany. The ionospheric phase disturbances have been simulated under typical con- ditions.
Received: 24 September 2020; Accepted: 19 October 2020; Published: 21 October 2020 Abstract: This work presents a new method for assessing global ionospheric maps (GIM) using ionosonde data. The method is based on the critical frequency at the F 2 layer directly measured by ionosondes to validate VTEC (vertical total electron content) values from GIMs. The analysis considered four different approaches to using foF 2 . The study was performed over one of the most challenging scenarios, the Brazilian region, considering four ionosondes (combined in six pairs) and thirteen GIM products available at CDDIS (Crustal Dynamics Data Information System). Analysis was conducted using daily, weekly, one year (2015), and four years (2014–2017) of data. Additional information from the ionosphere was estimated to complement the daily analysis, such as slab thickness and shape function peak. Results indicated that slab thickness and shape function peak could be used as alternative indicators of periods and regions where this method could be applied. The weekly analysis indicated the squared frequency ratio with local time correction as the best approach of using foF 2 , between the ones evaluated. The analysis of one-year data (2015) was performed considering thirteen GIMs, where CODG and UQRG were the two GIMs that presented the best performance. The four-year time series (2014–2017) were analyzed considering these two products. Regional and temporal ionospheric influences could be noticed in the results, with expected larger errors during the solar cycle peak in 2014 and at locations with pairs of ionosondes with the larger distance apart. Therefore, we have confirmed the viability of the developed approach as an assessment method to analyze GIMs quality based on ionosonde data.
Precise interferometric SAR measurements as well as characterization and information extraction of individual targets can be performed on natural or artificial point-like scatterers in SAR images. This is due, mainly, to the possibility to estimate their phase information very accurately, widely unaffected by speckle. Up to now, bymeansof two different techniques, two categories of such point-like scatterers have been treated: the Persistent Scatterers (PSs) and the CoherentScatterers (CSs). On one hand, PSs are characterized by long term temporal stability and are detected using long time series of acquisitions. They enabled the development of geophysical applications as millimetric terrain motion monitoring and accurate DEM refinement. On the other hand, CSs can be detected on a single SAR image basis, by exploiting image spectral correlation properties, without any assumption of temporal stability. They are very promising concerning parameters extraction as LOS rotation angle and dielectric constants estimation. Due to the wide spectrum of informations provided by the combination of the two concepts in this paper we investigate the CSs temporal stability and the relationships existing between CSs and PSs based on the analysis of image time series.
processing, which represent a missed opportunity to get more information about the underlying anthropogenic or natural de- formation process. Compared to metropolitan regions with several man-made structures, the prevalence ofcoherent scat- terers in alpine regions is already low, while at the same time layovers are generally more widespread due to the rugged- ness of the topography. Settlements and other infrastructure in the valleys are often partly and sometimes completely in layover cast by the adjoining mountain(s). Moreover, mass movements of interest such as landslides and rockfalls often take place in mountainous regions. Timely deformation mea- surements on slopes close to the villages can potentially assist in preventing untoward incidents. These concerns motivate this investigation on the potential of differential SAR tomog- raphy [3, 4, 5] as a means to resolve the layovers and allow spatio-temporal inversion of individually coherentscatterers interfering in the same resolution cell. The prospects of SAR tomography in alpine regions come across several challenges. Among them, a particularly complex issue is the phase cali- bration of the interferometric stack as a prerequisite for tomo- graphic inversion. The refractivity of the troposphere changes spatially over the scene as well as from one pass to the next, incurring variable phase delays which in general do not cancel out in interferogram formation, leaving behind a phase foot- print, i.e the atmospheric phase. It acts as a disturbance in fo- cusing the scatterers in 3-D [6, 7] and needs to be corrected. In mountainous regions, the local atmospheric conditions and the propagation paths through the troposphere may strongly vary spatially due to the extremely rugged topography which may change by as much as a few kilometers between the val- ley floor and the mountain top. Therefore, the atmospheric correction in such areas is more involved.
Concerning the PSs, in  the selection has been obtained bymeansof the Dispersion Index method. In this paper, instead, it has been considered the Signal to Clutter (SCR) method  that is based on the identification of targets having a suitable SNR to be classified as PSs. The main idea is to estimate a mean Rayleigh distribution of the clutter surrounding the PS candidate using the realizations of the neighbourhood pixels during the whole time span . Finally, the pixels which have a value of SCR higher than a given threshold are selected as PSs candidate. This technique results to be less biased and has the advantage to be able to track the evolution of the SCR in time.
One of the prominent objectives of the next generation space remote sensing missions is the accurate and continuous mon- itoring of the terrestrial biomass distribution bymeansof low frequency SAR. Low frequency microwaves are characterized by higher penetration ability through vegetation foliage, as well as higher temporal stability facilitating vegetation moni- toring bymeansof SAR and InSAR. However, the distortion due to the ionosphere is no longer negligible . In this sense the estimation and compensation of the ionospheric impact is critical for the success of such missions.
This paper investigates the detection ofCoherentScatterers (CSs) in ice and glacier terrain bymeansof TerraSAR-X time series data in the test site of the Helheim Glacier in Greenland. CSs are evaluated with respect to detection and potential applications. Applying optimized detection scheme can be useful for retrieving information about the glacier movement using time series data. Finally, some conclusions about the temporal stability of natural CSs are obtained by analyzing the rocky area around the glacier.
Abstract: The estimation of deformation parameters using persistent scatterer interferometry (PSI) is limited to single dominant coherentscatterers. As such, it rejects layovers wherein multiple scatterers are interfering in the same range-azimuth resolution cell. Differential synthetic aperture radar (SAR) tomography can improve deformation sampling as it has the ability to resolve layovers by separating the interfering scatterers. In this way, both PSI and tomography inevitably require a means to detect coherentscatterers, i.e., to perform hypothesis testing to decide whether a given candidate scatterer is coherent. This paper reports the application of a detection strategy in the context of “tomography as an add-on to PSI”. As the performance of a detector is typically linked to the statistical description of the underlying mathematical model, we investigate how the statistics of the phase instabilities in the PSI analysis are carried forward to the subsequent tomographic analysis. While phase instabilities in PSI are generally modeled as an additive noise term in the interferometric phase model, their impact in SAR tomography manifests as a multiplicative disturbance. The detection strategy proposed in this paper allows extending the same quality considerations as used in the prior PSI processing (in terms of the dispersion of the residual phase) to the subsequent tomographic analysis. In particular, the hypothesis testing for the detection ofcoherentscatterers is implemented such that the expected probability of false alarm is consistent between PSI and tomography. The investigation is supported with empirical analyses on an interferometric data stack comprising 50 TerraSAR-X acquisitions in stripmap mode, over the city of Barcelona, Spain, from 2007–2012.
The main problem in the detection of CSs in natural scenes lies in the fact that “natural” CSs are - in gen- eral - less deterministic than the ones detected in ur- ban scenes. In order to be detected one needs to relax the estimation threshold. But this is linked to an in- crease of false alarm rate at the same time. The trade- off between number of detected CSs and at the same time the number of false alarms is in natural scenarios especially critical. In the following we will discuss ways to relax this trade-off.
The potential of using azimuth sublooks to estimate the backscattering radiation pattern of CSs aiming their geomet- rical characterisation was demonstrated. A simple model for the backscattering radiation of canonical CSs was used and the model parameters were inverted. Using dihedral corner reflectors in controlled experiments, the theory and assump- tions were verified and a reasonable agreement was achieved. However, for accurate estimation, a large azimuth bandwidth is essential. For more complex types of CSs, the model of (3) will probably not apply making an extention of the model necessary.
In this paragraph we assume
f(t, x) : R × E → E continuous. (4)
Suppose v, w :[t 0 , t 1 ] → E and F : ]t 0 , t 1 ] → [t 0 , t 1 ] are such that the hypothe- ses of (Q) are fulﬁlled. Passing to the limit t ↓ t 0 in the functional inequality leads to
or situation. “How X” expects an answer that provides a manner in which X might be accom- plished, or a way to perform/achieve (X), where X is again a proposition containing a state of events. “What X” questions are less specific and X is often a phrase which is usually the subject of a transitive verb, so that the answer provides the direct object. Of course these sketches of question-answering are very rough, and there is far more extensive work on the subject. The point here is that if we adopt Graesser’s taxonomy of inquiries discussed earlier in the section on answers, we get much more specific requirements for answerhood, and also, a clearer set of question-types. In any case, our goal is to see how this information can in- form a more specific characterisation of the types of corrections that are coherent given the preced- ing question’s context. Given such specific in- formation about what a question addresses and what sort of answer it expects, it becomes less difficult to see how the questions in Table 1 can be corrected. One way that correcting questions is different from answers is that the former in- volves pointing out how the question itself is in- valid/incorrect/irrelevant (i.e., by providing an ex- planation for this incorrectness), rather than by disagreeing with and providing an alternative an- swer. Here are some example corrections respond- ing to the first few categories in Table 1:
Like in the doch examples above, nicht in (16B) evokes an alternative proposition, here p, and indi- cates that it should be replaced in the CG by what is asserted, namely ¬p. The use of the modal par- ticle also in (16B) is a further indication of this interpretation. The particle also refers to a con- sequence (explanation, constatation, confirmation, summary or result) from a preceding utterance or a deliberation of the speaker or the hearer (K¨onig et al., 1990). Without also, and with the proper intonation, the utterance may also be understood as a clarification question motivated by some con- flicting expectation. That there is a conflicting ex- pectation is indicated by the accent on nicht:
Abstract – Space weather can strongly affect trans-ionospheric radio signals depending on the used frequency. In order to assess the strength of a space weather event from its origin at the sun towards its impact on the ionosphere a number of physical quantities need to be derived from scientiﬁc measurements. These are for example the Wolf number sunspot index, the solar ﬂux density F10.7, measurements of the interplanetary magnetic ﬁeld, the proton density, the solar wind speed, the dynamical pressure, the geomagnetic indices Auroral Electrojet, Kp, Ap and Dst as well as the Total Electron Content (TEC), the Rate of TEC, the scintillation indices S4 and s(’) and the Along-Arc TEC Rate index index. All these quantities provide in combination with an additional classiﬁcation an orientation in a physical complex environment. Hence, they are used for brief communication of a simpliﬁed but appropriate space situation awareness. However, space weather driven ionospheric phenomena can affect many customers in the communication and navigation domain, which are still served inadequately by the existing indices. We present a new robust index, that is able to properly characterize temporal and spatial ionospheric variations of small to medium scales. The proposed ionospheric disturbance index can overcome several drawbacks of other ionospheric measures and might be suitable as potential driver for an ionospheric space weather scale.
In what follows we shall show that for every r-dimensional lattice Λ in R r and for every , δ ∈ R, 0 < ≤ 1, 0 < δ ≤ 1 there exists a basis of Λ that is (, δ)-constructable. The proof of this claim shall be constructive and lead to an algorithm for computing such a basis. We start with the following observations: Let a 1 , . . . , a k be linearly independent vectors in R r . Then for any orthog-
Finally, certain parameters that enter the model cannot be observed and hence need to be estimated with econometric techniques. These include the so called “trade elasticity“ which measures the sen- sitivity of sectoral trade flows towards changes in the costs of conducting trade in these sectors —- e.g., through tariffs, NTBs or sanctions. We calculate the required parameters with the well known gravity model of international trade (see e.g. Head and Mayer, 2014). The KITE model belongs to a wider class of models that give rise to exactly such a gravity equation. Data on defense spending is drawn from official NATO statistics on defense spending 6 and the Stockholm International Peace
As discussed in section 3.1, the lift coefficient can be varied by altering the gap size g s . This is utilized by the TIM control to lower the lift fluctuation by a sinusoidal variation of the slat trailing edge position and hence an approximately sinusoidal variation of the gap size. The measurements are repeated for 10 different phase shifts, ψ, between slat gap size variations and inflow angle fluctuations. The visual inspection of the C L time series of the static slat at aerodynamic reference gap size in comparison with the TIM controlled slat with phase shift ψ = 36 ° shows a reduction in the C L fluctuations, on the other hand for ψ = 216 ° the C L fluctuations are increased (figure 7(a)). The standard deviation of the lift for TIM controlled slat with different ψ is compared with the static slat reference case (figure 7(b)). A reduction of the standard deviation of approximately 20.1 % can be achieved for a phase shift of ψ = 36 °. For ψ = 161 ° to ψ = 324° an amplification of the standard deviation of up to 8.4 % by the dynamic slat gap size variation is recognized. However, no significant influence of the phase shift on the drag coefficient is found. Based on the phase shift the standard deviation of the lift coefficient can be reduced by a coupled actuation of active slat and active grid. This control strategy does not take into account the detailed dependency of the lift coefficient on the slat position and mainly relies on the fact that superposition of two sinusoidal wave forms with the correct phase shift reduces the amplitude of the resultant wave form. An improved mitigation of the lift coefficients may be achieved by a tailored control strategy considering the dependency of the lift coefficient on gap size and angle of attack.
The optical appearance and shape of a drop is influenced by different factors like the collision with the cooling surface, diameter, density, viscosity, surface tension, temper- ature and contact angle [Ber99]. The surface tension and gravity are the main factors that influence the shape of a liquid drop. Gravity is forcing the liquid to spread on the surface and the surface tension is counteracting and is keeping the drop in shape. Low viscous drops will spread more than high viscous drops. Bigger drops with a larger diameter will spread more because the higher mass is easier affected by gravity. Looking at the capsules, the solidification process of the drop has a major impact on the capsule’s shape. When the supersaturated drop hits the cooled surface and gets in contact with the seed crystals, the crystallization is initiated and a thin crystalline shell will be formed. If the crystallization of the shell is faster than the deformation of the liquid drop due to gravity, the capsule will have a more hemispheric shape. If the crystallization is too slow, the drop will spread on the surface before the first crystal layer could grow.
Since synthetic aperture radar is sensitive to surface roughness on various scales, it is a useful instrument for mapping sea ice deformation. Sea ice covers huge ocean areas, which means that the monitoring devices need a large field of view in order to enable a suffi- cient coverage in space and time, favouring wide- swath imaging modes of satellite SARs such as ENVISAT ASAR and ALOS PALSAR. A problem of these modes, however, is the loss of details about ice surface characteristics due to the coarse spatial image resolution. In this paper, we discuss our activities re- lated to sea ice deformation and thickness mapping bymeansof airborne and spaceborne SAR and related field campaigns during which complementary meas- urement devices are employed. Besides spatial resolu- tion, effects of SAR frequency, polarization, and inci- dence angle are considered in a number of finished and ongoing studies.
This paper presents a new method of wake-vortex characterization by using the 2- m coherent Doppler lidar in airborne con ﬁguration. After modiﬁcation of the scanning and data acquisition tools, the lidar system has been integrated in the DLR research aircraft Falcon 20. For wake-vortex generation a second DLR aircraft, the Advanced Technologies Testing Aircraft System equipped with a smoke generator on the portside wing, was used. Different scanning modes and ﬂight strategies have been investigated and tested during three tryout ﬂights. Results of vortex trajectories and circulation strengths, measured in the upper part of and above the atmospheric boundary layer, are presented. Based on the results of the tryout ﬂights, the potential of this method for characterization of wake vortices from large transport aircraft equipped with smoke generators is estimated.