Residual Ionospheric Error Research Articles

Understanding Ionospheric and Geomagnetic Effects on Residual Biases in Radio Occultation Data for Stratospheric Climate Monitoring

AbstractHigher‐order residual ionospheric errors in Global Navigation Satellite System (GNSS) radio occultation (RO) data can induce a systematic residual ionospheric bias (RIB) in RO bending angles, which can impact stratospheric climate monitoring. The main RIB causes are the ray path splitting of dual‐frequency GNSS signals, the electron density distribution along the ray path and at the RO receiver location, and the geomagnetic field. In this study, we investigate the ionospheric and geomagnetic effects on RO‐retrieved stratospheric bending angle and temperature profiles by inspecting the kappa and bi‐local RIB correction methods, the current state‐of‐the‐art methods, using multiple RO satellite mission data in different ionospheric and geomagnetic conditions. We find that, globally, the layer mean/median RIBs of the kappa and bi‐local correction methods exhibit similar behaviors for different RO missions: the estimated bending angle RIBs reach about −0.025/−0.01 and −0.024/−0.008 μrad in the upper (40–45 km) and lower (30–35 km) stratosphere, respectively, while the temperature RIBs reach about −1.0/−0.3 and −0.2/−0.1 K in these layers. However, in the equatorial day time region, the RIB statistics of the mission results diverge. Both the kappa and bi‐local RIBs increase in magnitude with increasing ionization and geomagnetic field strength but show no increase with an increasing degree of ionospheric asymmetry. Overall, the more refined bi‐local method has higher capacity than the comparatively simple kappa method to represent the variability of the ionospheric and geomagnetic conditions that affect RO events. This is important for regional‐scale studies, where the geomagnetic term can be of key relevance.

Performance of the Ionospheric Kappa-Correction of Radio Occultation Profiles Under Diverse Ionization and Solar Activity Conditions.

The kappa‐correction is an easy‐to‐use method to correct for residual ionospheric errors in radio occultation (RO) data. It is a simple empirical model term that only depends on readily available data. While its basic utility was well proven in previous studies, including a recent predecessor study on RO climatologies under solar cycle variations, its performance for individual RO profile correction under diverse and extreme ionization conditions is unclear so far. Here we tackle this gap and focus on investigating (extremely) low and high solar activity and ionization conditions of individual RO events, including inspection of ionospheric symmetry between inbound and outbound raypaths. Using a global multi‐year ensemble of MetOp‐A and GRACE‐A RO events over 2008–2015 as basis, we applied a sampling approach leading to six characteristic condition cases. These cases also relate to day and night time variations and geographic variations from the equatorial to the high latitude region. We inspected the kappa‐correction and its performance relative to the standard bending angle correction for RO‐retrieved stratospheric profiles and found mean deviations in temperature of near −0.3 K in the upper stratosphere (40–45 km) for high ionization conditions, with extreme deviations exceeding −2 K for strong inbound/outbound asymmetry. The kappa‐correction term itself reaches a mean value near 0.05 μrad under these high conditions. Low solar activity and ionization conditions lead to a mean correction smaller than 0.005 μrad and mean temperature deviations smaller than 0.02 K. An intercomparison to other quality datasets, predominantly showed a decrease in mean temperature difference when applying the kappa‐correction.

New Higher-Order Correction of GNSS RO Bending Angles Accounting for Ionospheric Asymmetry: Evaluation of Performance and Added Value

The residual ionospheric error (RIE) from higher-order terms in the refractive index is not negligible when using global navigation satellite system (GNSS) radio occultation (RO) data for climate and meteorology applications in the stratosphere. In this study, a new higher-order bending angle RIE correction named “Bi-local correction approach” has been implemented and evaluated, which accounts for the ray path splitting of the dual-frequency GNSS signals, the altitude of the low Earth orbit (LEO) satellite, the ionospheric inbound (GNSS to tangent point) vs. outbound (tangent point to LEO) asymmetry, and the geomagnetic field. Statistical results based on test-day ensembles of RO events show that, over the upper stratosphere and mesosphere, the order of magnitude of the mean total RIE in the bi-local correction approach is 0.01 μrad. Related to this, the so-called electron-density-squared (Ne2) and geomagnetic (BNe) terms appear to be dominant and comparable in magnitude. The BNe term takes negative or positive values, depending on the angle between the geomagnetic field vector and the direction of RO ray paths, while the Ne2 term is generally negative. We evaluated the new approach against the existing “Kappa approach” and the standard linear dual-frequency correction of bending angles and found it to perform well and in many average conditions similar to the simpler Kappa approach. On top of this, the bi-local approach can provide added value for RO missions with low LEO altitudes and for regional-scale applications, where its capacity to account for the ionospheric inbound-outbound asymmetry as well as for the geomagnetic term plays out.

Estimation of Ionospheric Delay Influence on the Efficiency of Precise Positioning of Multi-GNSS Observations

Currently, Global Navigation Satellite Systems (GNSS) are developing at a fairly rapid pace. Over the last years US GPS and Russian GLONASS were modernizing, whilst new systems like European Galileo and Chinese BDS are launched. The modernizations of the existing and the deployment of new GNSS made a whole range of new signals available to the users, and create a new concept  multi-GNSS. Ionospheric delay is one of the major error sources in multi-GNSS observations. At present, GNSS users usually eliminate the influence of ionospheric delay of the first order items by dual-frequency ionosphere-free combinations. But there is still residual ionospheric delay error of higher orders. In this paper we present four different processing scenarios to exclude the higher orders ionospheric delay effects on multi-GNSS Precise Point Positioning (PPP) performance, including: “only GPS” and “GPS+GLONASS+Galileo+BDS” – without/with eliminating ionospheric delay error of higher orders. Dataset collected from one GNSS station BOR1 (Borowiec, Poland) over almost two years provided by multi-GNSS experiment (MGEX) were used for dual-frequency PPP tests with one- and quadconstellation signals. For the second pair of scenarios were used a IONosphere map EXchange format (IONEX) that supports the exchange of 2- and 3-dimensional TEC maps given in a geographic grid. Numeric experiments show that, the results of different pairs of scenarios differ at the submillimeter level. The results also show that the multi-GNSS processing are better than those based on “only GPS”.

Characterizing Ionospheric Effect on GNSS Radio Occultation Atmospheric Bending Angle

AbstractGlobal Navigation Satellite System (GNSS) atmospheric radio occultation (RO) has been an active remote sensing method to explore the Earth's atmosphere recently. The RO products especially atmospheric bending angles have been widely used for climate study. However, the residual ionospheric error (RIE) still exists to a certain extent after the widely used linear combination in bending angle calculation. In this study, we analyzed both CHAMP and COSMIC data and did full 3‐D ray tracing to characterize RIE. It is found that the order of RIE is around ±0.1 μrad and has an obvious dependency on a variety of factors including altitude, latitude, local time, season, and solar activity level. The amplitude and complexity of RIE generally increase with altitude. It is closely related to the strength of the E layer and the asymmetry between LEO side and GNSS side. Along magnetic latitude direction, the RIE shows a pronounced feature of two peaks and three troughs. From both the simulated and observed RIE, we can identify clearly the ionospheric seasonal variation features, such as the semiannual variation, the equinox asymmetry and the annual anomaly. A spherical asymmetry factor was also defined to quantify the correlation between ionospheric spherical asymmetry degree and RIE. The study provides a comprehensive understanding of RIE, which could contribute to the correction of RIE in the future.

A Cycle Slip Repair Method Against Ionospheric Effects and Observational Noises for BDS Triple-Frequency Undifferenced Phases.

The cycle slip detection (CSD) and cycle slip repair (CSR) are easily affected by ionospheric delay and observational noise. Aiming at mitigating the above disadvantage, a new BeiDou navigation satellite system (BDS) triple-frequency CSR method (BTCSR) is proposed for the undifferenced phase. BTCSR learns from the classic triple-frequency CSR (CTCSR), with combinations of phases and pseudoranges in correcting ionospheric delay and optimizing observational noise. Different from CTCSR, though, BTCSR has made the following improvements: (1) An optimal model of calculating cycle slip combination is established, which further takes into account the minimization of the effect of residual ionospheric error after the correction. The calculation of cycle slip combination is obtained with the root mean squared errors (0.0646, 0.1261, 0.1069) of cycles, resulting in CSR success rate of 99.9927%, and the wavelengths (4.8842,3.5738,8.1403) of m. (2) A discriminant function is added to guarantee the CSR correctness. This function utilizes epoch-difference value of the ionosphere-free and geometry-free phase to select the correct cycle slip value, which eliminates the interference of large pseudorange errors in determining the final cycle slip. Consequently, the performances of BTCSR and CTCSR have been compared. For the real BDS pseudorange observation with additional 1.5 m errors, which can cover situations of 99.96% pseudorange noise, results of CTCSR show failure, but results of BTCSR keep correct. Moreover, BTCSR has made the following improvements relative to the geometry-free cycle slip detection method (GFCSD) and Melboune–Wubbena cycle slip combination detection method (MWCSD): (1) During a moderate magnetic storm of level 6, CSR testing, with the BDS monitoring station in a low latitude region, showed that some failures occur in GFCSD because of severe ionospheric variation, but BTCSR could correctly identify and fix cycle slips. (2) For the BDS observation data with an additional 1.5 m error on the actual pseudoranges, MWCSD exhibited failures, but the repair results of BTCSR were correct and reliable. (3) For the special slips of (0,59,62) cycles, and equal slips of (1,1,1) cycles on (B1,B2,B3), that are hard to detect by GFCSD and MWCSD, respectively, BTCSR could repair these correctly. Finally, BTCSR obtains reliable repair results under large pseudorange errors and severe ionospheric variations, and the cut-off elevation larger than 10 degrees is the suggested background.

GNSS Radio Occultation Simulation Using Multiple Phase Screen Orbit Sampling

Wave optics propagators (WOPs) are commonly used to describe the propagation of radio signals through earth’s atmosphere. In radio occultation (RO) context, multiple phase screen (MPS) method has been used to model the effects of the atmosphere in Global Navigation Satellite System (GNSS) signals during an occultation event. WOP implementation includes, in addition to MPS, a diffraction integral as the final step to calculate the radio signal measured in the low-earth orbit (LEO) satellite. This approach considers vacuum as the propagation medium at high altitudes, which is not always the case when the ionosphere is taken into account in simulations. An alternative approach is using MPS all the way to LEO in order to sample the GNSS signal in orbit. This approach, named MPS orbit sampling (MPS-OS), is evaluated in this letter. Different scenarios of setting occultation assuming a short segment of the LEO orbit have been simulated using MPS and MPS-OS. Results have been compared to Abel transform references. Furthermore, a long segment scenario has been evaluated as well. A comparison of bending angle (BA) and residual ionospheric error (RIE) shows the equivalence between MPS and MPS-OS results. The main application of MPS-OS should be in occultation events with long segments of orbit and including ionosphere, in which a standard WOP may not be appropriate.

Correlation between Ionospheric Spatial Decorrelation and Space Weather Intensity for Safety-Critical Differential GNSS Systems.

An ionospheric spatial decorrelation is one of the most dominant error factors that affects the availability of safety-critical differential global navigation satellite systems (DGNSS). This is because systems apply significant conservatism on the error source when ensuring navigation safety due to its unpredictable error characteristic. This paper investigates a correlation between GNSS-derived ionospheric spatial decorrelation and space weather intensity. The understanding of the correlation has significant advantages when modeling residual ionospheric errors without being overly pessimistic by exploiting external sources of space weather information. An ionospheric spatial decorrelation is quantified with a parameter of spatial gradient, which is an ionosphere total electron content (TEC) difference per unit distance of ionospheric pierce point (IPP). We used all pairs of stations from dense GNSS networks in the conterminous United States (CONUS) that provide an IPP separation distance of less than 100 km to obtain spatial gradient measurements under both ionospherically quiet and active conditions. Since the correlation results would be applied to safety-critical navigation applications, special attention was paid by taking into consideration all non-Gaussian tails of a spatial gradient distribution when determining spatial gradient statistics. The statistics were compared with space weather indices which are disturbance storm time (Dst) index and interplanetary magnetic field (IMF) Bz index. As a result, the ionospheric spatial decorrelation showed a significant positive correlation with both indices, especially under active ionospheric conditions. Under quiet conditions, it showed positive correlation slightly weaker than those under active conditions, and the IMF Bz showed preceding response to the spatial gradient statistics revealing the potential applicability for predicting the spatial decorrelation conditions.

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

Abstract. 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.

An Idealized Method of Simulating Residual Ionospheric Errors in Radio Occultation

An idealized model is used to simulate radio occultation bending angles and residual ionospheric errors. The test results of the proposed simulation method agree with those of previous studies that use end-to-end simulation tools. Also, a new residual ionospheric error model proposed by Healy and Culverwell (2015) is verified in this letter by characterizing the key parameter, κ. A simple model, κ(a) = A − B × (a − 20)/60, is used to estimate the values of κ, where A and B are constants that indicate the magnitude and variation of the values of κ, respectively, and a represents the impact height. When the modelled values of κ are applied in performing ionospheric corrections, the residual ionospheric errors decrease from approximately 5 × 10−8 rad to 1 × 10−9 rad at a latitude of 40°N during the daytime and at a solar activity level of F10.7 = 210. Though the proposed model does not assess other error terms, such as those associated with asymmetry and noise, it will likely prove to be an effective tool for describing idealized residual ionospheric errors in radio occultation, and the features of the κ values identified in this study may be helpful in improving ionospheric correction methods.

Instantaneous BDS + GPS undifferenced NRTK positioning with dynamic atmospheric constraints

As the Chinese BeiDou Navigation Satellite System (BDS) has become operational in the Asia-Pacific region, it is important to better understand and demonstrate the benefits of combining triple-frequency BDS with dual-frequency GPS observations for network-based real-time kinematic (NRTK) services. Undifferenced NRTK is a new NRTK service mode, it extends the concept of NRTK by not requiring reference station and specified reference satellite at the rover processing. In order to realize the undifferenced NRTK service, a strategy for real-time modeling the undifferenced (UD) augmentation information is given, in which the fixed double-differenced ambiguities are transformed into UD ones with the help of datum settings. Since this strategy is insensitive to existing ephemeris products, it is applicable to the services of current BDS regional reference networks. Furthermore, a processing scheme for ambiguity resolution (AR) with arbitrary-frequency observations is also presented in detail. An instantaneous and reliable BDS + GPS positioning service can be provided to the rovers in undifferenced NRTK processing mode. With the data collected at 31 stations from a continuously operating reference station network in Guangdong Province (GDCORS) of China, the efficiency of the proposed approaches using combined BDS and GPS observations is confirmed. For three rover stations during days 327–329, a total of 12,960 1-min tests were performed separately to demonstrate the performance of AR. Thanks to the dynamically refined priori information of residual tropospheric and ionospheric error, and the availability of more satellites and observations, the AR fixing rates of combined BDS and GPS systems improve by 13 to 65%, compared with those of the GPS-only system using the traditional WL-L1-IF scheme. The positioning accuracy has also significantly improved.

On the residual ionospheric error in radio occultation measurements

AbstractThe residual ionospheric error (RIE) in radio occultation (RO) measurement analysis is investigated through both analytic and numerical ray tracing. The study has shown that the difference between the propagation paths at different frequencies is an extremely important factor in determining the level of the RIE. Further, that horizontal ionospheric structure, such as the equatorial anomaly, can have a substantial impact. The results confirm the conclusion of previous studies that asymmetry in the ionosphere between the upward and downward legs of the propagation is a significant factor. The study has also considered the effect of traveling ionospheric disturbances upon the RIE. It has been shown that there can be dramatic changes in RIE through the full period of a traveling ionospheric disturbance (TID). Consequently, because of their frequency and unpredictability, TIDs have the potential to set a limit on the achievable accuracy of RO measurement analysis.

Influence of higher-order ionospheric delay correction on GPS precise orbit determination and precise positioning

At present, Global Navigation Satellite Systems (GNSS) users usually eliminate the influence of ionospheric delay of the first order items by dual-frequency ionosphere-free combination. But there is still residual ionospheric delay error of higher order term. The influence of the higher-order ionospheric corrections on both GPS precision orbit determination and static Precise Point Positioning (PPP) are studied in this paper. The influence of higher-order corrections on GPS precision orbit determination, GPS observations and static PPP are analyzed by neglecting or considering the higher-order ionospheric corrections by using a globally distributed network which is composed of International GNSS Service (IGS) tracking stations. Numerical experimental results show that, the root mean square (RMS) in three dimensions of satellite orbit is 36.6 mm–35.5 mm. The maximal second-order ionospheric correction is 9 cm, and the maximal third-order ionospheric correction is 1 cm. Higher-order corrections are influenced by latitude and station distribution. PPP is within 3 mm in the directions of east and up. Furthermore, the impact is mainly visible in the direction of north, showing a southward migration trend, especially at the lower latitudes where the influence value is likely to be bigger than 3 mm.

Improved ambiguity resolution for URTK with dynamic atmosphere constraints

Raw observation processing method with prior knowledge of ionospheric delay could strengthen the ambiguity resolution (AR), but it does not make full use of the relatively longer wavelength of wide-lane (WL) observation. Furthermore, the accuracy of calculated atmospheric delays from the regional augmentation information has quite different in quality, while the atmospheric constraint used in the current methods is usually set to an empirical value. A proper constraint, which matches the accuracy of calculated atmospheric delays, can most effectively compensate the residual systematic biases caused by large inter-station distances. Therefore, the standard deviation of the residual atmospheric parameters should be fine-tuned. This paper presents an atmosphere-constrained AR method for undifferenced network RTK (URTK) rover, whose ambiguities are sequentially fixed according to their wavelengths. Furthermore, this research systematically analyzes the residual atmospheric error and finds that it mainly varies along the positional relationship between the rover and the chosen reference stations. More importantly, its ionospheric part of certain location will also be cyclically influenced every day. Therefore, the standard deviation of residual ionospheric error can be modeled by a daily repeated cosine or other functions with the help of data one day before, and applied by rovers as pseudo-observation. With the data collected at 29 stations from a continuously operating reference station network in Guangdong Province (GDCORS) in China, the efficiency of the proposed approach is confirmed by improving the success and error rates of AR for 10-20 % compared to that of the WL-L1-IF one, as well as making much better positioning accuracy.

Estimation of overbound on ionospheric spatial decorrelation over low‐latitude region for ground‐based augmentation systems

In ground-based augmentation systems (GBAS), such as local area augmentation system (LAAS) of USA, variation of ionospheric delay between LAAS ground facility and the user leads to residual ionospheric error. Hence, the users need to compute the bounds on residual ionospheric error with the help of a parameter, σvertical_ionospheric_gradient (σvig). As σvig is a function of geographic region, the estimated value of σvig for mid-latitude regions (4 mm/km) is not appropriate for low-latitude regions where ionosphere is highly varying and is characterised by large spatial gradients. In this study, gradients are computed with processed total electron content data from 16 stations of global positioning system aided geo augmented navigation network and using the time-step method. The distribution of gradients is compared with one-sigma Gaussian distribution to obtain ‘inflation factor’. σvig overbound is computed for several days data comprising of quiet, moderate and storm conditions of ionosphere using the corresponding inflation factors. It is found that overbound values of 4.5 and 14.4 mm/km are required to bind the gradients under quiet and active conditions. These findings are useful for designing a safe and reliable GBAS for low-latitude stations.

A simulation study with a new residual ionospheric error model for GPS radio occultation climatologies

Abstract. In this study, a new model was explored which corrects for higher order ionospheric residuals in Global Positioning System (GPS) radio occultation (RO) data. Recently, the theoretical basis of this new "residual ionospheric error model" has been outlined (Healy and Culverwell, 2015). The method was tested in simulations with a one-dimensional model ionosphere. The proposed new model for computing the residual ionospheric error is the product of two factors, one of which expresses its variation from profile to profile and from time to time in terms of measurable quantities (the L1 and L2 bending angles), while the other describes the weak variation with altitude. A simple integral expression for the residual error (Vorob’ev and Krasil’nikova, 1994) has been shown to be in excellent numerical agreement with the exact value, for a simple Chapman layer ionosphere. In this case, the "altitudinal" element of the residual error varies (decreases) by no more than about 25 % between ~10 and ~100 km for physically reasonable Chapman layer parameters. For other simple model ionospheres the integral can be evaluated exactly, and results are in reasonable agreement with those of an equivalent Chapman layer. In this follow-up study the overall objective was to explore the validity of the new residual ionospheric error model for more detailed simulations, based on modeling through a complex three-dimensional ionosphere. The simulation study was set up, simulating day and night GPS RO profiles for the period of a solar cycle with and without an ionosphere. The residual ionospheric error was studied, the new error model was tested, and temporal and spatial variations of the model were investigated. The model performed well in the simulation study, capturing the temporal variability of the ionospheric residual. Although it was not possible, due to high noise of the simulated bending-angle profiles at mid- to high latitudes, to perform a thorough latitudinal investigation of the performance of the model, first positive and encouraging results were found at low latitudes. Furthermore, first application tests of the model on the data showed a reduction in temperature level of the ionospheric residual at 40 km from about −2.2 to −0.2 K.

A modification to the standard ionospheric correction method used in GPS radio occultation

Abstract. A modification to the standard bending-angle correction used in GPS radio occultation (GPS-RO) is proposed. The modified approach should reduce systematic residual ionospheric errors in GPS radio occultation climatologies. A new second-order term is introduced in order to account for a known source of systematic error, which is generally neglected. The new term has the form κ(a) × (αL1(a)-αL2(a))2, where a is the impact parameter and (αL1, αL2) are the L1 and L2 bending angles, respectively. The variable κ is a weak function of the impact parameter, a, but it does depend on a priori ionospheric information. The theoretical basis of the new term is examined. The sensitivity of κ to the assumed ionospheric parameters is investigated in one-dimensional simulations, and it is shown that κ ≃ 10–20 rad−1. We note that the current implicit assumption is κ=0, and this is probably adequate for numerical weather prediction applications. However, the uncertainty in κ should be included in the uncertainty estimates for the geophysical climatologies produced from GPS-RO measurements. The limitations of the new ionospheric correction when applied to CHAMP (Challenging Minisatellite Payload) measurements are noted. These arise because of the assumption that the refractive index is unity at the satellite, made when deriving bending angles from the Doppler shift values.

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

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.

Characteristics of second-order residual ionospheric error in GNSS radio occultation and its impact on inversion of neutral atmospheric parameters

In Global Navigation Satellite Systems (GNSS) radio occultation (RO), one of the most significant error sources is the ionospheric error, which is largely eliminated by dual-frequency linear combination. However, second-order residual ionospheric error (RIE) in excess phase still remains and affects the retrievals of neutral atmospheric parameters in RO. Second-order RIE varies with RO azimuth in a sinusoidal pattern for a set of simulated RO events occurring in the same location at different azimuths. The amplitude of the sinusoidal curve below 60km is at the order of sub-centimeter under moderate solar activity level. The retrieval biases of the neutral atmospheric parameters induced by second-order RIE also have sinusoidal features with RO azimuth, but have opposite variation trends to that of the second-order RIE. The RO azimuths of the maximum positive and negative retrieval biases correspond approximately to the azimuths of maximum negative and positive second-order RIEs, respectively. The order of the maximum bending angle bias induced by the second-order RIE is about 10−8rad under moderate solar activity level. However, the retrieval errors at low latitude are larger than those at high and middle latitudes, and the maximum temperature bias at low latitude could be 0.35K at 40km. Based on the sinusoidal variation of second-order RIE, it is shown that even at the same RO point and under the same solar activity level, the second-order RIEs at different RO azimuths still have different effects on the retrieval precision of atmospheric parameters. This should be considered carefully when many RO profiles are averaged for climate trend detection, especially at low latitude.

Influence of Ionospheric Irregularities on GNSS Remote Sensing

We have used numerical simulation to study the effects of ionospheric irregularities on accuracy of global navigation satellite system (GNSS) measurements, using ionosphere-free (in atmospheric research) and geometry-free (in ionospheric research) dual-frequency phase combinations. It is known that elimination of these effects from multifrequency GNSS measurements is handi-capped by diffraction effects during signal propagation through turbulent ionospheric plasma with the inner scale being smaller than the Fresnel radius. We demonstrated the possibility of reducing the residual ionospheric error in dual-frequency GNSS remote sensing in ionosphere-free combination by Fresnel inversion. The inversion parameter, the distance to the virtual screen, may be selected from the minimum of amplitude fluctuations. This suggests the possibility of improving the accuracy of GNSS remote sensing in meteorology. In the study of ionospheric disturbances with the aid of geometry-free combination, the Fresnel inversion eliminates only the third-order error. To eliminate the random TEC component which, like the measured average TEC, is the first-order correction, we should use temporal filtering (averaging).