scholarly journals Analysis of reflections in GNSS radio occultation measurements using the phase matching amplitude

2018 ◽  
Vol 11 (1) ◽  
pp. 569-580 ◽  
Author(s):  
Thomas Sievert ◽  
Joel Rasch ◽  
Anders Carlström ◽  
Mats Ingemar Pettersson
Keyword(s):  
Radio Occultation ◽  
Complex Function ◽  
Lower Troposphere ◽  
Phase Matching ◽  
Matching Method ◽  
Bending Angle ◽  
Abel Transform ◽  
Lower Region ◽  
Additional Information ◽  
The Impact

Abstract. It is well-known that in the presence of super-refractive layers in the lower-tropospheric inversion of GNSS radio occultation (RO) measurements using the Abel transform yields biased refractivity profiles. As such it is problematic to reconstruct the true refractivity from the RO signal. Additional information about this lower region of the atmosphere might be embedded in reflected parts of the signal. To retrieve the bending angle, the phase matching operator can be used. This operator produces a complex function of the impact parameter, and from its phase we can calculate the bending angle. Instead of looking at the phase, in this paper we focus on the function's amplitude. The results in this paper show that the signatures of surface reflections in GNSS RO measurements can be significantly enhanced when using the phase matching method by processing only an appropriately selected segment of the received signal. This signature enhancement is demonstrated by simulations and confirmed with 10 hand-picked MetOp-A occultations with reflected components. To validate that these events show signs of reflections, radio holographic images are generated. Our results suggest that the phase matching amplitude carries information that can improve the interpretation of radio occultation measurements in the lower troposphere.

scholarly journals Detection of reflections in GNSS radio occultation measurements using phase matching

2017 ◽  
Author(s):  
Thomas Sievert ◽  
Joel Rasch ◽  
Anders Carlström ◽  
Mats I. Pettersson
Keyword(s):  
Radio Occultation ◽  
Complex Function ◽  
Lower Troposphere ◽  
Phase Matching ◽  
Matching Method ◽  
Bending Angle ◽  
Abel Transform ◽  
Lower Region ◽  
Additional Information ◽  
The Impact

Abstract. It is well-known that in the presence of super-refractive (SR) layers in the lower troposphere inversion of GNSS radio occultation (RO) measurements using the Abel transform yields biased refractivity profiles. As such it is problematic to reconstruct the true refractivity from the RO signal. Additional information about this lower region of the atmosphere might be embedded in reflected parts of the signal. To retrieve the bending angle, the phase matching operator can be used. This operator produces a complex function of the impact parameter, and from its phase we can calculate the bending angle. Instead of looking at the phase, in this paper we focus on the function's amplitude. The results in this paper show that the signatures of surface reflections in GNSS RO measurements can be significantly enhanced when using the phase matching method by processing only an appropriately selected segment of the received signal. We can then identify reflection signatures even in cases where they are normally obscured by the direct signal's influence on the phase matching amplitude. This signature enhancement is demonstrated by simulations and confirmed with real MetOp-A data.

scholarly journals Retrieval of temperature and water vapor profiles from radio occultation refractivity and bending angle measurements using an Optimal Estimation approach: a simulation study

2005 ◽  
Vol 5 (6) ◽  
pp. 1665-1677 ◽  
Author(s):  
A. von Engeln ◽  
G. Nedoluha
Keyword(s):  
Water Vapor ◽  
Radio Occultation ◽  
A Priori ◽  
Estimation Method ◽  
Lower Troposphere ◽  
Optimal Estimation ◽  
Pronounced Difference ◽  
Bending Angle ◽  
Advantages And Disadvantages ◽  
The Impact

Abstract. The Optimal Estimation Method is used to retrieve temperature and water vapor profiles from simulated radio occultation measurements in order to assess how different retrieval schemes may affect the assimilation of this data. High resolution ECMWF global fields are used by a state-of-the-art radio occultation simulator to provide quasi-realistic bending angle and refractivity profiles. Both types of profiles are used in the retrieval process to assess their advantages and disadvantages. The impact of the GPS measurement is expressed as an improvement over the a priori knowledge (taken from a 24h old analysis). Large improvements are found for temperature in the upper troposphere and lower stratosphere. Only very small improvements are found in the lower troposphere, where water vapor is present. Water vapor improvements are only significant between about 1 km to 7 km. No pronounced difference is found between retrievals based upon bending angles or refractivity. Results are compared to idealized retrievals, where the atmosphere is spherically symmetric and instrument noise is not included. Comparing idealized to quasi-realistic calculations shows that the main impact of a ray tracing algorithm can be expected for low latitude water vapor, where the horizontal variability is high. We also address the effect of altitude correlations in the temperature and water vapor. Overall, we find that water vapor and temperature retrievals using bending angle profiles are more CPU intensive than refractivity profiles, but that they do not provide significantly better results.

scholarly journals A variational regularization of Abel transform for GPS radio occultation

2017 ◽  
Author(s):  
Tae-Kwon Wee
Keyword(s):  
Radio Occultation ◽  
Control Variable ◽  
Bending Angle ◽  
Abel Transform ◽  
True Solution ◽  
Height Determination ◽  
Error Covariance ◽  
The Impact ◽  
Variational Regularization

Abstract. In the Radio Occultation (RO), the refractivity is generally obtained from the inverse Abel transform of measured bending angle, often called Abel inversion (AI). While concise and straightforward to apply, AI is susceptible to the error present in the bending angle. Aiming at reducing the adverse effects of the measurement error, this study proposes a new method for determining the refractivity through a variational regularization (VR). The method approximates the inversion of the forward Abel transform by an optimization problem in which the regularized solution describes the measurement as closely as possible within the measurement’s considered accuracy. The optimal problem is then solved iteratively by means of the adjoint technique. VR incorporates the prior information about measurement characteristics and desired behaviour of the solution into the regularization via error covariance matrices. In contrast to variational data assimilations, VR holds the control variable in the measurement space. This makes VR particularly effective by allowing the method to benefit from the posterior height determination and to deal with model’s error in the impact parameter. The advantages are elaborated using a purposely corrupted synthetic sounding and with known true solution. The competency of VR relative to AI is validated with a large number of actual RO soundings. The comparison with nearby radiosonde observations shows that VR is considerably smaller than AI in both random and systematic errors. It is concluded based on the results presented in this study that VR offers a definite advantage over AI in the quality of refractivity.

scholarly journals Generalized Canonical Transform method for radio occultation sounding with improved retrieval in the presence of horizontal gradients

2020 ◽  
Author(s):  
Michael Gorbunov ◽  
Gottfried Kirchengast ◽  
Kent B. Lauritsen
Keyword(s):  
Linear Combination ◽  
Impact Parameter ◽  
Radio Occultation ◽  
Lower Troposphere ◽  
General Idea ◽  
Fourier Integral Operators ◽  
Full Spectrum ◽  
Bending Angle ◽  
Horizontal Gradients ◽  
The Impact

Abstract. By now, a series of advanced Wave Optical (WO) approaches to the processing of Radio Occultation (RO) observations are widely used. In particular, the Canonical Transform (CT) method and its further developments need to be mentioned. The latter include the Full Spectrum Inversion (FSI) method, the Geometric Optical (GO) Phase Matching (PM) method, and the general approach based on the Fourier Integral Operators (FIOs), also referred to as the CT type 2 (CT2) method. The general idea of these methods is the application of a canonical transform that changes the coordinates in the phase space from time and Doppler frequency to impact parameter and bending angle. For the spherically symmetric atmosphere, the impact parameter, being invariant for each ray, is a unique coordinate of the ray manifold. Therefore, the derivative of the phase of the wave field in the transformed space is directly linked to the bending angle, as a single-valued function of the impact parameter. However, in the presence of horizontal gradients, this approach may not work. Here we introduce a further generalization of the CT methods in order to reduce the errors due to horizontal gradients. We describe, in particular, the modified CT2 method denoted CT2A, which complements the former with one more affine transform: a new coordinate that is a linear combination of the impact parameter and bending angle. The linear combination coefficient is a tunable parameter. We derive the explicit formulas for the CT2A and develop the updated numerical algorithm. For testing the method, we performed statistical analyses based on COSMIC RO retrievals and (collocated) ECMWF analysis profiles. We demonstrate that it is possible to find a reasonably optimal value of the new tunable CT2A parameter that mitigates systematic errors in the lower troposphere and allows the practical realization of the improved capability to cope with horizontal gradients.

scholarly journals Generalized canonical transform method for radio occultation sounding with improved retrieval in the presence of horizontal gradients

2021 ◽  
Vol 14 (2) ◽  
pp. 853-867
Author(s):  
Michael Gorbunov ◽  
Gottfried Kirchengast ◽  
Kent B. Lauritsen
Keyword(s):  
Linear Combination ◽  
Impact Parameter ◽  
Radio Occultation ◽  
Lower Troposphere ◽  
General Idea ◽  
Control Procedure ◽  
Fourier Integral Operators ◽  
Bending Angle ◽  
Horizontal Gradients ◽  
The Impact

Abstract. By now, a series of advanced wave optical approaches to the processing of radio occultation (RO) observations are widely used. In particular, the canonical transform (CT) method and its further developments need to be mentioned. The latter include the full spectrum inversion (FSI) method, the geometric optical phase matching (PM) method, and the general approach based on the Fourier integral operators (FIOs), also referred to as the CT type 2 (CT2) method. The general idea of these methods is the application of a canonical transform that changes the coordinates in the phase space from time and Doppler frequency to impact parameter and bending angle. For the spherically symmetric atmosphere, the impact parameter, being invariant for each ray, is a unique coordinate of the ray manifold. Therefore, the derivative of the phase of the wave field in the transformed space is directly linked to the bending angle as a single-valued function of the impact parameter. However, in the presence of horizontal gradients, this approach may not work. Here we introduce a further generalization of the CT methods in order to reduce the errors due to horizontal gradients. We describe, in particular, the modified CT2 method, denoted CT2A, which complements the former with one more affine transform: a new coordinate that is a linear combination of the impact parameter and bending angle. The linear combination coefficient is a tunable parameter. We derive the explicit formulas for the CT2A and develop the updated numerical algorithm. For testing the method, we performed statistical analyses based on RO retrievals from data acquired by the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) and collocated analysis profiles of the European Centre for Medium-Range Weather Forecasts (ECMWF). We demonstrate that it is possible to find a reasonably optimal value of the new tunable CT2A parameter that minimizes the root mean square difference between the RO retrieved and the ECMWF refractivity in the lower troposphere and allows the practical realization of the improved capability to cope with horizontal gradients and serve as the basis of a new quality control procedure.

scholarly journals Retrieval of temperature and water vapor profiles from radio occultation refractivity and bending angle measurements using an optimal estimation approach: a simulation study

2005 ◽  
Vol 5 (2) ◽  
pp. 1585-1617 ◽  
Author(s):  
A. von Engeln ◽  
G. Nedoluha
Keyword(s):  
Water Vapor ◽  
Radio Occultation ◽  
A Priori ◽  
Estimation Method ◽  
Lower Troposphere ◽  
Optimal Estimation ◽  
Pronounced Difference ◽  
Bending Angle ◽  
Advantages And Disadvantages ◽  
The Impact

Abstract. The Optimal Estimation Method is used to retrieve temperature and water vapor profiles from simulated radio occultation measurements in order to assess possible assimilation impacts of this data. High resolution ECMWF global fields are used by 5 a state-of-the-art radio occultation simulator to provide quasi-realistic bending angle and refractivity profiles. Both types of profiles are used in the retrieval process to assess their advantages and disadvantages. The impact of the GPS measurement is expressed as an improvement over the a priori knowledge (taken from a 24 h old analysis). Large improvements are found for temperature in the upper troposphere and 10 lower stratosphere. Only very small improvements are found in the lower troposphere, where water vapor is present. Water vapor improvements are only significant between about 1 km to 7 km. No pronounced difference is found between retrievals based upon bending angles or refractivity. Results are compared to idealized retrievals, where the atmosphere is spherically symmetric and instrument noise is not included. Comparing 15 idealized to quasi-realistic calculations shows that the main impact of a ray tracing algorithm can be expected for low latitude water vapor, where the horizontal variability is high. We also address the effect of altitude correlations in the temperature and water vapor. Overall, we find that water vapor and temperature retrievals using bending angle profiles are significantly more CPU intensive than refractivity profiles, but that they do 20 not provide significantly better results.

scholarly journals Using A Sliding Window Phase Matching Method for Imaging of GNSS Radio Occultation Signals

2021 ◽  
Vol 13 (5) ◽  
pp. 970
Author(s):  
Thomas Sievert ◽  
Joel Rasch ◽  
Anders Carlström ◽  
Vinícius Ludwig Barbosa ◽  
Mats I. Pettersson ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Radio Occultation ◽  
Time Window ◽  
Lower Troposphere ◽  
Sliding Window ◽  
Spectral Amplitude ◽  
Phase Matching ◽  
Two Dimensional ◽  
Bending Angle ◽  
Time Frequency

Global Navigation Satellite System Radio Occultation (GNSS-RO) is a technique used to sound the atmosphere and derive vertical profiles of refractivity. Signals from GNSS satellites are received in a low-Earth orbit, and they are then processed to produce bending angle profiles, from which meteorological parameters can be retrieved. Generating two-dimensional images in the form of spectrograms from GNSS-RO signals is commonly done to, for instance, investigate reflections or estimate signal quality in the lower troposphere. This is typically implemented using, e.g., the Short-Time Fourier Transform (STFT) to produce a time-frequency representation that is subsequently transformed to bending angle (BA) and impact height (IH) coordinates by non-linear mapping. In this paper, we propose an alternative method based on a straightforward extension of the Phase Matching (PM) operator to produce two-dimensional spectral images in the BA-IH domain by applying a sliding window. This Sliding Window Phase Matching (SWPM) method generates the spectral amplitude on an arbitrary grid in BA and IH, e.g., along the coordinate axes. To illustrate, we show both SWPM and STFT methods applied to operational MetOp-A data. For SWPM we use a constant window in the BA-dimension, whereas for STFT we use a conventional constant time window. We show that the SWPM method produces the same result as STFT when the same window length is used for both methods. The sample points in impact parameter and bending angle are those generated by and the main advantage is that SWPM offers the user a convenient way to freely sample the BA-IH space. The cost for this is processing time that is somewhat longer than implementations based on the Fast Fourier Transform, such as the STFT method.

scholarly journals Global 3D Features of Error Variances of GPS Radio Occultation and Radiosonde Observations

2020 ◽  
Vol 13 (1) ◽  
pp. 1
Author(s):  
Xu Xu ◽  
Xiaolei Zou
Keyword(s):  
Radio Occultation ◽  
Weather Prediction ◽  
Lower Troposphere ◽  
Error Variance ◽  
Specific Humidity ◽  
Temperature Error ◽  
Observation Error ◽  
Bending Angle ◽  
Gps Radio Occultation ◽  
Low Latitudes

Global Positioning System (GPS) radio occultation (RO) and radiosonde (RS) observations are two major types of observations assimilated in numerical weather prediction (NWP) systems. Observation error variances are required input that determines the weightings given to observations in data assimilation. This study estimates the error variances of global GPS RO refractivity and bending angle and RS temperature and humidity observations at 521 selected RS stations using the three-cornered hat method with additional ERA-Interim reanalysis and Global Forecast System forecast data available from 1 January 2016 to 31 August 2019. The global distributions, of both RO and RS observation error variances, are analyzed in terms of vertical and latitudinal variations. Error variances of RO refractivity and bending angle and RS specific humidity in the lower troposphere, such as at 850 hPa (3.5 km impact height for the bending angle), all increase with decreasing latitude. The error variances of RO refractivity and bending angle and RS specific humidity can reach about 30 N-unit2, 3 × 10−6 rad2, and 2 (g kg−1)2, respectively. There is also a good symmetry of the error variances of both RO refractivity and bending angle with respect to the equator between the Northern and Southern Hemispheres at all vertical levels. In this study, we provide the mean error variances of refractivity and bending angle in every 5°-latitude band between the equator and 60°N, as well as every interval of 10 hPa pressure or 0.2 km impact height. The RS temperature error variance distribution differs from those of refractivity, bending angle, and humidity, which, at low latitudes, are smaller (less than 1 K2) than those in the midlatitudes (more than 3 K2). In the midlatitudes, the RS temperature error variances in North America are larger than those in East Asia and Europe, which may arise from different radiosonde types among the above three regions.

Evaluating the Impact of the COSMIC RO Bending Angle Data on Predicting the Heavy Precipitation Episode on 16 June 2008 during SoWMEX-IOP8

2014 ◽  
Vol 142 (11) ◽  
pp. 4139-4163 ◽  
Author(s):  
Shu-Chih Yang ◽  
Shu-Hua Chen ◽  
Shu-Ya Chen ◽  
Ching-Yuang Huang ◽  
Ching-Sen Chen
Keyword(s):  
Lower Troposphere ◽  
Heavy Precipitation ◽  
Southwest Monsoon ◽  
Weather Research And Forecasting ◽  
Heavy Rainfall Event ◽  
Bending Angle ◽  
Angle Data ◽  
Ensemble Transform Kalman Filter ◽  
The Impact ◽  
Better Than

Abstract Global positioning system (GPS) radio occultation (RO) data have been broadly used in global and regional numerical weather predictions. Assimilation with the bending angle often performs better than refractivity, which is inverted from the bending angle under spherical assumption and is sometimes associated with negative biases at the lower troposphere; however, the bending angle operator also requires a higher model top as used in global models. This study furnishes the feasibility of bending-angle assimilation in the prediction of heavy precipitation systems with a regional model. The local RO operators for simulating bending angle and refractivity are implemented in the Weather Research and Forecasting (WRF)–local ensemble transform Kalman filter (LETKF) framework. The impacts of assimilating RO data from the Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC) using both operators are evaluated on the prediction of a heavy precipitation episode during Southwest Monsoon Experiment intensive observing period 8 (SoWMEX-IOP8) in 2008. Results show that both the refractivity and bending angle provide a favorable condition for generating this heavy rainfall event. In comparison with the refractivity data, the advantage of assimilating the bending angle is identified in the midtroposphere for deepening of the moist layer that leads to a rainfall forecast closer to the observations.

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