Two-Quark Correlations in the Hard Electromagnetic Nucleon Form Factors

The, so called, "hard-scattering approach" represents a suitable framework for the perturbative treatment of exclusive hadronic processes at large energies and (transverse) momentum transfers. In this context, diquarks can serve as a useful phenomenological concept to model non-perturbative effects which are still observable in the kinematic range accessible by present-day experiments. We outline how a description of baryons as quark-diquark systems can be understood as an effective theory in the sense that the pure quark hard-scattering approach is recovered in the limit of asymptotically large momentum transfers. Our arguments are based on a reformulation of the hard-scattering formalism in terms of quark-diquark degrees of freedom. This reformulation provides the exact form of photon- and gluon-diquark vertices and corresponding vertex functions (diquark form factors) in the limit of asymptotically large momentum transfers -- and thus also asymptotic constraints which should be fulfilled by phenomenological quark-diquark models for hard scattering. As an application of this reformulation we present an analysis of the hard electromagnetic nucleon form factors with respect to their quark-diquark content.Comment: 4 pages, uses aipproc.cl

Integrating uncertainty propagation in GNSS radio occultation retrieval: from excess phase to atmospheric bending angle profiles

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

Dynamic statistical optimization of GNSS radio occultation bending angles: an advanced algorithm and its performance analysis

We introduce a new dynamic statistical optimization algorithm to initialize ionosphere-corrected bending angles of Global Navigation Satellite System (GNSS) based radio occultation (RO) measurements. The new algorithm estimates background and observation error covariance matrices with geographically-varying uncertainty profiles and realistic global-mean correlation matrices. The error covariance matrices estimated by the new approach are more accurate and realistic than in simplified existing approaches and can therefore be used in statistical optimization to provide optimal bending angle profiles for high-altitude initialization of the subsequent Abel transform retrieval of refractivity. The new algorithm is evaluated against the existing Wegener Center Occultation Processing System version 5.6 (OPSv5.6) algorithm, using simulated data on two test days from January and July 2008 and real observed CHAMP and COSMIC measurements from the complete months of January and July 2008. The following is achieved for the new method's performance compared to OPSv5.6: (1) significant reduction in random errors (standard deviations) of optimized bending angles down to about two-thirds of their size or more; (2) reduction of the systematic differences in optimized bending angles for simulated MetOp data; (3) improved retrieval of refractivity and temperature profiles; (4) produces realistically estimated global-mean correlation matrices and realistic uncertainty fields for the background and observations. Overall the results indicate high suitability for employing the new dynamic approach in the processing of long-term RO data into a reference climate record, leading to well characterized and high-quality atmospheric profiles over the entire stratosphere

Analysis of ionospheric structure influences on residual ionospheric errors in GNSS radio occultation bending angles based on ray tracing simulations

The Global Navigation Satellite System (GNSS) radio occultation (RO) technique is widely used to observe the atmosphere for applications such as numerical weather prediction and global climate monitoring. The ionosphere is a major error source to RO at upper stratospheric altitudes, and a linear dual-frequency bending angle correction is commonly used to remove the first-order ionospheric effect. However, the higher-order residual ionospheric error (RIE) can still be significant, so it needs to be further mitigated for high-accuracy applications, especially from 35 km altitude upward, where the RIE is most relevant compared to the decreasing magnitude of the atmospheric bending angle. In a previous study we quantified RIEs using an ensemble of about 700 quasi-realistic end-to-end simulated RO events, finding typical RIEs at the 0.1 to 0.5 µrad noise level, but were left with 26 exceptional events with anomalous RIEs at the 1 to 10 µrad level that remained unexplained. In this study, we focused on investigating the causes of the high RIE of these exceptional events, employing detailed along-ray-path analyses of atmospheric and ionospheric refractivities, impact parameter changes, and bending angles and RIEs under asymmetric and symmetric ionospheric structures. We found that the main causes of the high RIEs are a combination of physics-based effects – where asymmetric ionospheric conditions play the primary role, more than the ionization level driven by solar activity – and technical ray tracer effects due to occasions of imperfect smoothness in ionospheric refractivity model derivatives. We also found that along-ray impact parameter variations of more than 10 to 20 m are possible due to ionospheric asymmetries and, depending on prevailing horizontal refractivity gradients, are positive or negative relative to the initial impact parameter at the GNSS transmitter. Furthermore, mesospheric RIEs are found generally higher than upper-stratospheric ones, likely due to being closer in tangent point heights to the ionospheric E layer peaking near 105 km, which increases RIE vulnerability. In the future we will further improve the along-ray modeling system to fully isolate technical from physics-based effects and to use it beyond this work for additional GNSS RO signal propagation studies

A new dynamic approach for statistical optimization of GNSS radio occultation bending angles for optimal climate monitoring utility

Global Navigation Satellite Systems (GNSS) based radio occultation (RO) is a satellite remote sensing technique providing accurate profiles of the Earth's atmosphere for weather and climate applications. Above about 30 km altitude, however, statistical optimization is a critical process for initializing the RO bending angles in order to optimize the climate monitoring utility of the retrieved atmospheric profiles. Here we introduce an advanced dynamic statistical optimization algorithm, which uses bending angles from multiple days of European Centre for Medium-range Weather Forecasts (ECMWF) short-term forecast and analysis fields, together with averaged-observed bending angles, to obtain background profiles and associated error covariance matrices with geographically varying background uncertainty estimates on a daily-updated basis. The new algorithm is evaluated against the existing Wegener Center Occultation Processing System version 5.4 (OPSv5.4) algorithm, using several days of simulated MetOp and observed CHAMP and COSMIC data, for January and July conditions. We find the following for the new method's performance compared to OPSv5.4: 1. it significantly reduces random errors (standard deviations), down to about half their size, and leaves less or about equal residual systematic errors (biases) in the optimized bending angles; 2. the dynamic (daily) estimate of the background error correlation matrix alone already improves the optimized bending angles; 3. the subsequently retrieved refractivity profiles and atmospheric (temperature) profiles benefit by improved error characteristics, especially above about 30 km. Based on these encouraging results we work to employ similar dynamic error covariance estimation also for the observed bending angles and to apply the method to full months and subsequently to entire climate data records

Dynamic statistical optimization of GNSS radio occultation bending angles: advanced algorithm and performance analysis

We introduce a new dynamic statistical optimization algorithm to initialize ionosphere-corrected bending angles of Global Navigation Satellite System (GNSS)-based radio occultation (RO) measurements. The new algorithm estimates background and observation error covariance matrices with geographically varying uncertainty profiles and realistic global-mean correlation matrices. The error covariance matrices estimated by the new approach are more accurate and realistic than in simplified existing approaches and can therefore be used in statistical optimization to provide optimal bending angle profiles for high-altitude initialization of the subsequent Abel transform retrieval of refractivity. The new algorithm is evaluated against the existing Wegener Center Occultation Processing System version 5.6 (OPSv5.6) algorithm, using simulated data on two test days from January and July 2008 and real observed CHAllenging Minisatellite Payload (CHAMP) and Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) measurements from the complete months of January and July 2008. The following is achieved for the new method's performance compared to OPSv5.6: (1) significant reduction of random errors (standard deviations) of optimized bending angles down to about half of their size or more; (2) reduction of the systematic differences in optimized bending angles for simulated MetOp data; (3) improved retrieval of refractivity and temperature profiles; and (4) realistically estimated global-mean correlation matrices and realistic uncertainty fields for the background and observations. Overall the results indicate high suitability for employing the new dynamic approach in the processing of long-term RO data into a reference climate record, leading to well-characterized and high-quality atmospheric profiles over the entire stratosphere

Quantifying residual ionospheric errors in GNSS radio occultation bending angles based on ensembles of profiles from end-to-end simulations

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

Characterisation of residual ionospheric errors in bending angles using GNSS RO end-to-end simulations

Global Navigation Satellite System (GNSS) radio occultation (RO) is an innovative meteorological remote sensing technique for measuring atmospheric parameters such as refractivity, temperature, water vapour and pressure for the improvement of numerical weather prediction (NWP) and global climate monitoring (GCM). GNSS RO has many unique characteristics including global coverage, long-term stability of observations, as well as high accuracy and high vertical resolution of the derived atmospheric profiles. One of the main error sources in GNSS RO observations that significantly affect the accuracy of the derived atmospheric parameters in the stratosphere is the ionospheric error. In order to mitigate the effect of this error, the linear ionospheric correction approach for dual-frequency GNSS RO observations is commonly used. However, the residual ionospheric errors (RIEs) can be still significant, especially when large ionospheric disturbances occur and prevail such as during the periods of active space weather. In this study, the RIEs were investigated under different local time, propagation direction and solar activity conditions and their effects on RO bending angles are characterised using end-to-end simulations. A three-step simulation study was designed to investigate the characteristics of the RIEs through comparing the bending angles with and without the effects of the RIEs. This research forms an important step forward in improving the accuracy of the atmospheric profiles derived from the GNSS RO technique