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Gottfried Kirchengast - One of the best experts on this subject based on the ideXlab platform.
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integrating uncertainty propagation in gnss radio occultation retrieval from excess phase to atmospheric Bending Angle profiles
Atmospheric Measurement Techniques, 2017Co-Authors: Jakob Schwarz, Gottfried Kirchengast, M SchwaerzAbstract:Abstract. Global Navigation Satellite System (GNSS) radio occultation (RO) observations are highly accurate, long-term stable data sets and are globally available as a continuous record from 2001. Essential climate variables for the thermodynamic state of the free atmosphere – such as pressure, temperature, and tropospheric water vapor profiles (involving background information) – can be derived from these records, which therefore have the potential to serve as climate benchmark data. However, to exploit this potential, atmospheric profile retrievals need to be very accurate and the remaining uncertainties quantified and traced throughout the retrieval chain from raw observations to essential climate variables. The new Reference Occultation Processing System (rOPS) at the Wegener Center aims to deliver such an accurate RO retrieval chain with integrated uncertainty propagation. Here we introduce and demonstrate the algorithms implemented in the rOPS for uncertainty propagation from excess phase to atmospheric Bending Angle profiles, for estimated systematic and random uncertainties, including vertical error correlations and resolution estimates. We estimated systematic uncertainty profiles with the same operators as used for the basic state profiles retrieval. The random uncertainty is traced through covariance propagation and validated using Monte Carlo ensemble methods. The algorithm performance is demonstrated using test day ensembles of simulated data as well as real RO event data from the satellite missions CHAllenging Minisatellite Payload (CHAMP); Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC); and Meteorological Operational Satellite A (MetOp). The results of the Monte Carlo validation show that our covariance propagation delivers correct uncertainty quantification from excess phase to Bending Angle profiles. The results from the real RO event ensembles demonstrate that the new uncertainty estimation chain performs robustly. Together with the other parts of the rOPS processing chain this part is thus ready to provide integrated uncertainty propagation through the whole RO retrieval chain for the benefit of climate monitoring and other applications.
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wave optics uncertainty propagation and regression based bias model in gnss radio occultation Bending Angle retrievals
Atmospheric Measurement Techniques, 2017Co-Authors: Michael E Gorbunov, Gottfried KirchengastAbstract:Abstract. A new reference occultation processing system (rOPS) will include a Global Navigation Satellite System (GNSS) radio occultation (RO) retrieval chain with integrated uncertainty propagation. In this paper, we focus on wave-optics Bending Angle (BA) retrieval in the lower troposphere and introduce (1) an empirically estimated boundary layer bias (BLB) model then employed to reduce the systematic uncertainty of excess phases and Bending Angles in about the lowest 2 km of the troposphere and (2) the estimation of (residual) systematic uncertainties and their propagation together with random uncertainties from excess phase to Bending Angle profiles. Our BLB model describes the estimated bias of the excess phase transferred from the estimated bias of the Bending Angle, for which the model is built, informed by analyzing refractivity fluctuation statistics shown to induce such biases. The model is derived from regression analysis using a large ensemble of Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) RO observations and concurrent European Centre for Medium-Range Weather Forecasts (ECMWF) analysis fields. It is formulated in terms of predictors and adaptive functions (powers and cross products of predictors), where we use six main predictors derived from observations: impact altitude, latitude, Bending Angle and its standard deviation, canonical transform (CT) amplitude, and its fluctuation index. Based on an ensemble of test days, independent of the days of data used for the regression analysis to establish the BLB model, we find the model very effective for bias reduction and capable of reducing Bending Angle and corresponding refractivity biases by about a factor of 5. The estimated residual systematic uncertainty, after the BLB profile subtraction, is lower bounded by the uncertainty from the (indirect) use of ECMWF analysis fields but is significantly lower than the systematic uncertainty without BLB correction. The systematic and random uncertainties are propagated from excess phase to Bending Angle profiles, using a perturbation approach and the wave-optical method recently introduced by Gorbunov and Kirchengast (2015), starting with estimated excess phase uncertainties. The results are encouraging and this uncertainty propagation approach combined with BLB correction enables a robust reduction and quantification of the uncertainties of excess phases and Bending Angles in the lower troposphere.
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integrating uncertainty propagation in gnss radio occultation retrieval from Bending Angle to dry air atmospheric profiles
Earth and Space Science, 2017Co-Authors: Jakob Schwarz, Gottfried Kirchengast, M SchwaerzAbstract:Global Navigation Satellite Systems (GNSS) Radio Occultation (RO) observations, globally available as a continuous record since 2001, are highly accurate and long-term stable data records. Essential climate variables for the thermodynamic state of the free atmosphere, such as temperature and tropospheric water vapor profiles (involving background information), can be derived from these records, which consequentially have the potential to serve as climate benchmark data. In order to exploit this potential, atmospheric profile retrievals need to be very accurate and the remaining uncertainties need to be quantified and traced throughout the retrieval chain. The new Reference Occultation Processing System at the Wegener Center aims to deliver such an accurate retrieval chain with integrated uncertainty propagation. Here we introduce and demonstrate the algorithms implemented for uncertainty propagation from RO Bending Angle profiles to dry-air variables (pressure and temperature), for estimated random and systematic uncertainties, and for coestimates of observation-to-background weighting ratio profiles. We estimated systematic uncertainty profiles with the same operators as used for the basic profiles retrieval. The random uncertainty propagation was integrated by a covariance propagation approach and validated using Monte-Carlo ensemble methods. We present the results of the validation and demonstrate how the algorithm performs for individual simulated RO events and for ensembles of real RO events. We also compare the new results from the integrated uncertainty propagation to previous ones from empirical error analyses for RO-retrieved atmospheric profiles. We find that the new uncertainty estimation chain shows robust performance and is in good agreement with previous comparable results.
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uncertainty propagation through wave optics retrieval of Bending Angles from gps radio occultation theory and simulation results
Radio Science, 2015Co-Authors: Michael E Gorbunov, Gottfried KirchengastAbstract:The wave optical technique for Bending Angle retrieval in processing radio occultation observations is nowadays widely used by different data processing and assimilation groups and centers. This technique uses Fourier Integral Operators that map the observed records of the amplitude and phase into the impact parameter representation, which allows for the retrieval of Bending Angle as a function of impact parameter. We investigate the propagation of uncertainty in the observed amplitude and excess phase to the retrieved Bending Angle. We construct a simple linear approximation, where the excess phase uncertainty is mapped into the Bending Angle uncertainty. This results in a simple analytical expression for the final uncertainty. To verify our approximation, we perform numerical Monte Carlo simulations for three example occultation events (tropical, middle, and polar latitude profiles from an atmospheric analysis). We demonstrate that our approximation basically gives good results in all cases over the entire troposphere. Exception is the narrow area near the top of the sharp boundary layer, especially in tropics, where, due to nonlinear effects, a significant systematic error arises accompanied by increased uncertainty.
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quantifying residual ionospheric errors in gnss radio occultation Bending Angles based on ensembles of profiles from end to end simulations
Atmospheric Measurement Techniques, 2015Co-Authors: Gottfried Kirchengast, Congliang Liu, Kefei Zhang, Robert J Norman, S C ZhangAbstract:Abstract. The radio occultation (RO) technique using signals from the Global Navigation Satellite System (GNSS), in particular from the Global Positioning System (GPS) so far, is currently widely used to observe the atmosphere for applications such as numerical weather prediction and global climate monitoring. The ionosphere is a major error source in RO measurements at stratospheric altitudes, and a linear ionospheric correction of dual-frequency RO Bending Angles is commonly used to remove the first-order ionospheric effect. However, the residual ionospheric error (RIE) can still be significant so that it needs to be further mitigated for high-accuracy applications, especially above about 30 km altitude where the RIE is most relevant compared to the magnitude of the neutral atmospheric Bending Angle. Quantification and careful analyses for better understanding of the RIE is therefore important for enabling benchmark-quality stratospheric RO retrievals. Here we present such an analysis of Bending Angle RIEs covering the stratosphere and mesosphere, using quasi-realistic end-to-end simulations for a full-day ensemble of RO events. Based on the ensemble simulations we assessed the variation of Bending Angle RIEs, both biases and standard deviations, with solar activity, latitudinal region and with or without the assumption of ionospheric spherical symmetry and co-existing observing system errors. We find that the Bending Angle RIE biases in the upper stratosphere and mesosphere, and in all latitudinal zones from low to high latitudes, have a clear negative tendency and a magnitude increasing with solar activity, which is in line with recent empirical studies based on real RO data although we find smaller bias magnitudes, deserving further study in the future. The maximum RIE biases are found at low latitudes during daytime, where they amount to within −0.03 to −0.05 μrad, the smallest at high latitudes (0 to −0.01 μrad; quiet space weather and winter conditions). Ionospheric spherical symmetry or asymmetries about the RO event location have only a minor influence on RIE biases. The RIE standard deviations are markedly increased both by ionospheric asymmetries and increasing solar activity and amount to about 0.3 to 0.7 μrad in the upper stratosphere and mesosphere. Taking also into account the realistic observation errors of a modern RO receiving system, amounting globally to about 0.4 μrad (unbiased; standard deviation), shows that the random RIEs are typically comparable to the total observing system error. The results help to inform future RIE mitigation schemes that will improve upon the use of the linear ionospheric correction of Bending Angles and also provide explicit uncertainty estimates.
Jan Victor - One of the best experts on this subject based on the ideXlab platform.
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peak stresses shift from femoral tunnel aperture to tibial tunnel aperture in lateral tibial tunnel acl reconstructions a 3d graft Bending Angle measurement and finite element analysis
Knee Surgery Sports Traumatology Arthroscopy, 2017Co-Authors: Hans Van Der Bracht, Thomas Tampere, Pieter Beekman, Alexander Schepens, Wouter Devriendt, Peter Verdonk, Jan VictorAbstract:To investigate the effect of tibial tunnel orientation on graft-Bending Angle and stress distribution in the ACL graft. Eight cadaveric knees were scanned in extension, 45°, 90°, and full flexion. 3D reconstructions with anatomically placed anterior cruciate ligament (ACL) grafts were constructed with Mimics 14.12®. 3D graft-Bending Angles were measured for classic medial tibial tunnels (MTT) and lateral tibial tunnels (LTT) with different drill-guide Angles (DGA) (45°, 55°, 65°, and 75°). A pivot shift was performed on 1 knee in a finite-element analysis. The peak stresses in the graft were calculated for eight different tibial tunnel orientations. In a classic anatomical ACL repair, the largest graft-Bending Angle and peak stresses are seen at the femoral tunnel aperture. The use of a different DGA at the tibial side does not change the graft-Bending Angle at the femoral side or magnitude of peak stresses significantly. When using LTT, the largest graft-Bending Angles and peak stresses are seen at the tibial tunnel aperture. In a classic anatomical ACL repair, peak stresses in the ACL graft are found at the femoral tunnel aperture. When an LTT is used, peak stresses are similar compared to classic ACL repairs, but the location of the peak stress will shift from the femoral tunnel aperture towards the tibial tunnel aperture. Clinical relevance: the risk of graft rupture is similar for both MTTs and LTTs, but the location of graft rupture changes from the femoral tunnel aperture towards the tibial tunnel aperture, respectively. I.
Hideki Asada - One of the best experts on this subject based on the ideXlab platform.
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gravitomagnetic Bending Angle of light with finite distance corrections in stationary axisymmetric spacetimes
Physical Review D, 2017Co-Authors: Toshiaki Ono, Asahi Ishihara, Hideki AsadaAbstract:By using the Gauss-Bonnet theorem, the Bending Angle of light in a static, spherically symmetric and asymptotically flat spacetime has been recently discussed, especially by taking account of the finite distance from a lens object to a light source and a receiver [Ishihara, Suzuki, Ono, Asada, Phys. Rev. D 95, 044017 (2017)]. We discuss a possible extension of the method of calculating the Bending Angle of light to stationary, axisymmetric and asymptotically flat spacetimes. For this purpose, we consider the light rays on the equatorial plane in the axisymmetric spacetime. We introduce a spatial metric to define the Bending Angle of light in the finite-distance situation. We show that the proposed Bending Angle of light is coordinate-invariant by using the Gauss-Bonnet theorem. The nonvanishing geodesic curvature of the photon orbit with the spatial metric is caused in gravitomagnetism, even though the light ray in the four-dimensional spacetime follows the null geodesic. Finally, we consider Kerr spacetime as an example in order to examine how the Bending Angle of light is computed by the present method. The finite-distance correction to the gravitomagnetic deflection Angle due to the Sun's spin is around a pico-arcsecond level. The finite-distance corrections for Sgr ${\mathrm{A}}^{*}$ also are estimated to be very small. Therefore, the gravitomagnetic finite-distance corrections for these objects are unlikely to be observed with present technology.
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finite distance corrections to the gravitational Bending Angle of light in the strong deflection limit
Physical Review D, 2017Co-Authors: Asahi Ishihara, Yusuke Suzuki, Toshiaki Ono, Hideki AsadaAbstract:Continuing work initiated in an earlier publication [A. Ishihara, Y. Suzuki, T. Ono, T. Kitamura, and H. Asada, Phys. Rev. D 94, 084015 (2016).], we discuss a method of calculating the Bending Angle of light in a static, spherically symmetric, and asymptotically flat spacetime, especially by taking into account the finite distance from a lens object to a light source and a receiver. For this purpose, we use the Gauss-Bonnet theorem to define the Bending Angle of light, such that the definition can be valid also in the strong deflection limit. Finally, this method is applied to Schwarzschild spacetime in order to discuss also possible observational implications. The proposed corrections for Sgr ${\mathrm{A}}^{*}$ for instance are able to amount to $\ensuremath{\sim}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{arcseconds}$ for some parameter range, which may be within the capability of near-future astronomy, while also the correction for the Sun in the weak-field limit is $\ensuremath{\sim}{10}^{\ensuremath{-}5}\text{ }\text{ }\mathrm{arcseconds}$.
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gravitational Bending Angle of light for finite distance and the gauss bonnet theorem
Physical Review D, 2016Co-Authors: Asahi Ishihara, Yusuke Suzuki, Toshiaki Ono, Takao Kitamura, Hideki AsadaAbstract:We discuss a possible extension of calculations of the Bending Angle of light in a static, spherically symmetric and asymptotically flat spacetime to a nonasymptotically flat case. We examine a relation between the Bending Angle of light and the Gauss-Bonnet theorem by using the optical metric. A correspondence between the deflection Angle of light and the surface integral of the Gaussian curvature may allow us to take account of the finite distance from a lens object to a light source and a receiver. Using this relation, we propose a method for calculating the Bending Angle of light for such cases. Finally, this method is applied to two examples of the nonasymptotically flat spacetimes to suggest finite-distance corrections: the Kottler (Schwarzschild\char21{}de Sitter) solution to the Einstein equation and an exact solution in Weyl conformal gravity.
S B Healy - One of the best experts on this subject based on the ideXlab platform.
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Improved model for correcting the ionospheric impact on Bending Angle in radio occultation measurements
Copernicus Publications, 2018Co-Authors: M. J. Angling, S. Elvidge, S B HealyAbstract:The standard approach to remove the effects of the ionosphere from neutral atmosphere GPS radio occultation measurements is to estimate a corrected Bending Angle from a combination of the L1 and L2 Bending Angles. This approach is known to result in systematic errors and an extension has been proposed to the standard ionospheric correction that is dependent on the squared L1 ∕ L2 Bending Angle difference and a scaling term (κ). The variation of κ with height, time, season, location and solar activity (i.e. the F10.7 flux) has been investigated by applying a 1-D Bending Angle operator to electron density profiles provided by a monthly median ionospheric climatology model. As expected, the residual Bending Angle is well correlated (negatively) with the vertical total electron content (TEC). κ is more strongly dependent on the solar zenith Angle, indicating that the TEC-dependent component of the residual error is effectively modelled by the squared L1 ∕ L2 Bending Angle difference term in the correction. The residual error from the ionospheric correction is likely to be a major contributor to the overall error budget of neutral atmosphere retrievals between 40 and 80 km. Over this height range κ is approximately linear with height. A simple κ model has also been developed. It is independent of ionospheric measurements, but incorporates geophysical dependencies (i.e. solar zenith Angle, solar flux, altitude). The global mean error (i.e. bias) and the standard deviation of the residual errors are reduced from −1.3×10−8 and 2.2×10−8 for the uncorrected case to −2.2×10−10 rad and 2.0×10−9 rad, respectively, for the corrections using the κ model. Although a fixed scalar κ also reduces bias for the global average, the selected value of κ (14 rad−1) is only appropriate for a small band of locations around the solar terminator. In the daytime, the scalar κ is consistently too high and this results in an overcorrection of the Bending Angles and a positive Bending Angle bias. Similarly, in the nighttime, the scalar κ is too low. However, in this case, the Bending Angles are already small and the impact of the choice of κ is less pronounced
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a simplified approach for generating gnss radio occultation refractivity climatologies
Atmospheric Measurement Techniques, 2013Co-Authors: Hans Gleisner, S B HealyAbstract:Abstract. The possibility of simplifying the retrieval scheme required to produce GNSS radio occultation refractivity climatologies is investigated. In a new, simplified retrieval approach, the main statistical analysis is performed in Bending Angle space and an estimate of the average Bending Angle profile is then propagated through an Abel transform. The average is composed of means and medians of ionospheric corrected Bending Angles up to 80 km. Above that, the observed profile is exponentially extrapolated to infinity using a fixed a priori scale height. The new approach circumvents the need to introduce a "statistical optimisation" processing step in which individual Bending Angle profiles are merged with a priori data, often taken from a climatology. This processing step can be complex, difficult to interpret, and is generally recognised as a potential source of structural uncertainty. The new scheme is compared with the more conventional approach of averaging individual refractivity profiles, produced with the implementation of statistical optimisation used in the EUMETSAT Radio Occultation Meteorology Satellite Application Facility (ROM SAF) operational processing. It is shown that the two GNSS radio occultation climatologies agree to within 0.1% from 5 km up to 35–40 km, for the three months January, February, and March 2011. During this time period, the new approach also produces slightly better agreement with ECMWF analyses between 40–50 km, which is encouraging. The possible limitations of the new approach caused by mean residual ionospheric errors and low observation numbers are discussed briefly, and areas for future work are suggested.
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radio occultation Bending Angle and impact parameter errors caused by horizontal refractive index gradients in the troposphere a simulation study
Journal of Geophysical Research, 2001Co-Authors: S B HealyAbstract:Radio occultation (RO) Bending Angle and impact parameter values are derived from a Doppler shift measurement, assuming spherical symmetry. The purpose of this work is to illustrate the errors that arise when this assumption is not valid. Doppler shift values have been simulated for ray paths through a three-dimensional refractive index field derived from a mesoscale model forecast, which has a horizontal grid of 12 km by 12 km, and includes water vapor. These have then been inverted, making the spherical symmetry assumption. It is demonstrated that refractive index gradients perpendicular to the ray path can cause errors in both the Bending Angle and impact parameter values, but the latter is the more significant. It is shown that the impact parameter value at the tangent point can differ by around ∼ 100 m from the derived value. This can cause an effective Bending Angle error exceeding ∼ 10% near the surface. A statistical analysis of the errors caused by horizontal gradients for simulations through 54 mesoscale forecasts, using fixed spacecraft trajectories and tangent point locations, is presented. In general, the Bending Angle errors are found to be ∼ 3% near the surface. A new set of analytical expressions for errors has been derived. These are based on integrating the horizontal gradients along the ray path and are found to be in good agreement with the simulation results. The implications of this work for the assimilation of RO data into numerical weather prediction models are discussed and areas of future work are outlined.
Hans Van Der Bracht - One of the best experts on this subject based on the ideXlab platform.
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peak stresses shift from femoral tunnel aperture to tibial tunnel aperture in lateral tibial tunnel acl reconstructions a 3d graft Bending Angle measurement and finite element analysis
Knee Surgery Sports Traumatology Arthroscopy, 2017Co-Authors: Hans Van Der Bracht, Thomas Tampere, Pieter Beekman, Alexander Schepens, Wouter Devriendt, Peter Verdonk, Jan VictorAbstract:To investigate the effect of tibial tunnel orientation on graft-Bending Angle and stress distribution in the ACL graft. Eight cadaveric knees were scanned in extension, 45°, 90°, and full flexion. 3D reconstructions with anatomically placed anterior cruciate ligament (ACL) grafts were constructed with Mimics 14.12®. 3D graft-Bending Angles were measured for classic medial tibial tunnels (MTT) and lateral tibial tunnels (LTT) with different drill-guide Angles (DGA) (45°, 55°, 65°, and 75°). A pivot shift was performed on 1 knee in a finite-element analysis. The peak stresses in the graft were calculated for eight different tibial tunnel orientations. In a classic anatomical ACL repair, the largest graft-Bending Angle and peak stresses are seen at the femoral tunnel aperture. The use of a different DGA at the tibial side does not change the graft-Bending Angle at the femoral side or magnitude of peak stresses significantly. When using LTT, the largest graft-Bending Angles and peak stresses are seen at the tibial tunnel aperture. In a classic anatomical ACL repair, peak stresses in the ACL graft are found at the femoral tunnel aperture. When an LTT is used, peak stresses are similar compared to classic ACL repairs, but the location of the peak stress will shift from the femoral tunnel aperture towards the tibial tunnel aperture. Clinical relevance: the risk of graft rupture is similar for both MTTs and LTTs, but the location of graft rupture changes from the femoral tunnel aperture towards the tibial tunnel aperture, respectively. I.