scholarly journals Uncertainty propagation through wave optics retrieval of bending angles from GPS radio occultation: Theory and simulation results

Radio Science ◽  
2015 ◽  
Vol 50 (10) ◽  
pp. 1086-1096 ◽  
Author(s):  
Michael E. Gorbunov ◽  
Gottfried Kirchengast
Keyword(s):  
Radio Occultation ◽  
Uncertainty Propagation ◽  
Wave Optics ◽  
Gps Radio Occultation ◽  
Simulation Results ◽  
Bending Angles

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

2015 ◽  
Vol 8 (8) ◽  
pp. 3385-3393 ◽  
Author(s):  
S. B. Healy ◽  
I. D. Culverwell
Keyword(s):  
Impact Parameter ◽  
Radio Occultation ◽  
Order Term ◽  
Weather Prediction ◽  
Implicit Assumption ◽  
Ionospheric Correction ◽  
Gps Radio Occultation ◽  
Uncertainty Estimates ◽  
The Impact ◽  
Bending Angles

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.

scholarly journals Wave-optics uncertainty propagation and regression-based bias model in GNSS radio occultation bending angle retrievals

2017 ◽  
Author(s):  
Michael Gorbunov ◽  
Gottfried Kirchengast
Keyword(s):  
Regression Analysis ◽  
Systematic Uncertainty ◽  
Radio Occultation ◽  
Uncertainty Propagation ◽  
Lower Troposphere ◽  
Wave Optics ◽  
Bending Angle ◽  
Excess Phase ◽  
Excess Phases ◽  
Random Uncertainties

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 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 the lowest about two kilometers 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 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 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, capable of reducing bending angle and corresponding refractivity biases by about a factor of five. The estimated residual systematic uncertainty, after the BLB profile subtraction, is lower-bounded by the uncertainty from (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 that 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.

scholarly journals Ionospheric correction of GPS radio occultation data in the troposphere

2016 ◽  
Vol 9 (2) ◽  
pp. 335-346 ◽  
Author(s):  
Z. Zeng ◽  
S. Sokolovskiy ◽  
W. Schreiner ◽  
D. Hunt ◽  
J. Lin ◽  
...  
Keyword(s):  
Radio Occultation ◽  
Neutral Atmosphere ◽  
Ionospheric Correction ◽  
Bending Angle ◽  
Gps Radio Occultation ◽  
Strong Inversion ◽  
Occultation Data ◽  
Horizontal Inhomogeneity ◽  
L1 And L2 ◽  
Bending Angles

Abstract. For inversions of the GPS radio occultation (RO) data in the neutral atmosphere, this study investigates an optimal transition height for replacing the standard ionospheric correction using the linear combination of the L1 and L2 bending angles with the correction of the L1 bending angle by the L1–L2 bending angle extrapolated from above. The optimal transition height depends on the RO mission (i.e., the receiver and firmware) and is different between rising and setting occultations and between L2P and L2C GPS signals. This height is within the range of approximately 10–20 km. One fixed transition height, which can be used for the processing of currently available GPS RO data, can be set to 20 km. Analysis of the L1CA and the L2C bending angles shows that in some occultations the errors of standard ionospheric correction substantially increase around the strong inversion layers (such as the top of the boundary layer). This error increase is modeled and explained by the horizontal inhomogeneity of the ionosphere.

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

2015 ◽  
Vol 8 (1) ◽  
pp. 1177-1201 ◽  
Author(s):  
S. B. Healy ◽  
I. D. Culverwell
Keyword(s):  
Impact Parameter ◽  
Radio Occultation ◽  
Order Term ◽  
Weather Prediction ◽  
Implicit Assumption ◽  
Ionospheric Correction ◽  
Gps Radio Occultation ◽  
Uncertainty Estimates ◽  
The Impact ◽  
Bending Angles

Abstract. A modification to the standard bending angle correction used in GPS radio occultation 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)-αL1(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 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 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.

scholarly journals Wave-optics uncertainty propagation and regression-based bias model in GNSS radio occultation bending angle retrievals

2018 ◽  
Vol 11 (1) ◽  
pp. 111-125 ◽  
Author(s):  
Michael E. Gorbunov ◽  
Gottfried Kirchengast
Keyword(s):  
Regression Analysis ◽  
Systematic Uncertainty ◽  
Radio Occultation ◽  
Uncertainty Propagation ◽  
Lower Troposphere ◽  
Wave Optics ◽  
Bending Angle ◽  
Excess Phase ◽  
Excess Phases ◽  
Random Uncertainties

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.

scholarly journals Analysis of GPS radio occultation data from the FORMOSAT-3/COSMIC and Metop/GRAS missions at CDAAC

2011 ◽  
Vol 4 (10) ◽  
pp. 2255-2272 ◽  
Author(s):  
W. Schreiner ◽  
S. Sokolovskiy ◽  
D. Hunt ◽  
C. Rocken ◽  
Y.-H. Kuo
Keyword(s):  
Noise Level ◽  
Radio Occultation ◽  
Signal To Noise Ratio ◽  
Lower Troposphere ◽  
Mean Difference ◽  
Bending Angle ◽  
Tropical Regions ◽  
Gps Radio Occultation ◽  
Single Difference ◽  
Bending Angles

Abstract. This study investigates the noise level and mission-to-mission stability of Global Positioning System (GPS) radio occultation (RO) neutral atmospheric bending angle data at the UCAR COSMIC Data Analysis and Archive Center (CDAAC). Data are used from two independently developed RO instruments currently flying in orbit on the FORMOSAT-3/COSMIC (F3C) and Metop/GRAS (GNSS Receiver for Atmospheric Sounding) missions. The F3C 50 Hz RO data are post-processed with a single-difference excess atmospheric phase algorithm, and the Metop/GRAS 50 Hz closed loop and raw sampling (down-sampled from 1000 Hz to 50 Hz) data are processed with a zero-difference algorithm. The standard deviations of the F3C and Metop/GRAS bending angles from climatology between 60 and 80 km altitude from June–December 2009 are approximately 1.78 and 1.13 μrad, respectively. The F3C standard deviation reduces significantly to 1.44 μrad when single-difference processing uses GPS satellites on the same side of the spacecraft. The higher noise level for F3C bending angles can be explained by additional noise from the reference link phase data that are required with single-difference processing. The F3C and Metop/GRAS mean bending angles differences relative to climatology during the same six month period are statistically significant and have values of −0.05 and −0.02 μrad, respectively. A comparison of ~13 500 collocated F3C and Metop/GRAS bending angle profiles over this six month period shows a similar mean difference of ~0.02 ± 0.02 μrad between 30 and 60 km impact heights that is marginally significant. The observed mean difference between the F3C and Metop/GRAS bending angles of ~0.02–0.03 μrad is quite small and illustrates the high degree of re-produceability and mission independence of the GPS RO data at high altitudes. Collocated bending angles between two F3C satellites from early in the mission differ on average by up to 0.5% near the surface due to systematically lower signal-to-noise ratio for one of the satellites. Results from F3C and Metop/GRAS differences in the lower troposphere suggest the Metop/GRAS bending angles are negatively biased compared to F3C with a maximum of several percents near the surface in tropical regions. This bias is related to different tracking depths (deeper in F3C) and data gaps in Metop/GRAS which make it impossible to process the data from both missions in exactly the same way.

scholarly journals Analysis of GPS radio occultation data from the FORMOSAT-3/COSMIC and Metop/GRAS missions at CDAAC

2011 ◽  
Vol 4 (2) ◽  
pp. 2433-2489
Author(s):  
W. Schreiner ◽  
S. Sokolovskiy ◽  
D. Hunt ◽  
C. Rocken ◽  
Y.-H. Kuo
Keyword(s):  
Noise Level ◽  
Radio Occultation ◽  
Signal To Noise Ratio ◽  
Lower Troposphere ◽  
Mean Difference ◽  
Bending Angle ◽  
Tropical Regions ◽  
Gps Radio Occultation ◽  
Single Difference ◽  
Bending Angles

Abstract. This study investigates the noise level and mission-to-mission stability of Global Positioning System (GPS) radio occultation (RO) neutral atmospheric bending angle data at the UCAR COSMIC Data Analysis and Archive Center (CDAAC). Data are used from two independently developed RO instruments currently flying in orbit on the FORMOSAT-3/COSMIC (F3C) and Metop/GRAS (GNSS Receiver for Atmospheric Sounding) missions. The F3C 50 Hz RO data are post-processed with a single-difference excess atmospheric phase algorithm, and the Metop/GRAS 50 Hz closed loop and raw sampling (down-sampled from 1000 Hz to 50 Hz) data are processed with a zero-difference algorithm. The standard deviations of the F3C and Metop/GRAS bending angles from climatology between 60 and 80 km altitude from June–December 2009 are approximately 1.78 and 1.13 μrad, respectively. The F3C standard deviation reduces significantly to 1.44 μrad when single-difference processing uses GPS satellites on the same side of the spacecraft. The higher noise level for F3C bending angles can be explained by additional noise from the reference link phase data that are required with single-difference processing. The F3C and Metop/GRAS mean bending angles differences relative to climatology during the same six month period are statistically significant and have values of −0.05 and −0.02 μrad, respectively. A comparison of ~13 500 collocated F3C and Metop/GRAS bending angle profiles over this six month period shows a similar mean difference of ~0.02 ± 0.02 μrad between 30 and 60 km impact heights that is marginally significant. The observed mean difference between the F3C and Metop/GRAS bending angles of ~0.02–0.03 μrad is quite small and illustrates the high degree of re-produceability and mission independence of the GPS RO data at high altitudes. Collocated bending angles between two F3C satellites from early in the mission differ on average by up to 0.5% near the surface due to systematically lower signal-to-noise ratio for one of the satellites. Results from F3C and Metop/GRAS differences in the lower troposphere suggest the Metop/GRAS bending angles are negatively biased compared to F3C with a maximum of several percents near the surface in tropical regions. This bias is related to different tracking depths (deeper in F3C) and data gaps in Metop/GRAS which make it impossible to process the data from both missions in exactly the same way.

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