• Beyerle, G., Schmidt T. , Michalak G. , Heise S. , Wickert J. , and Reigber C. , 2005: GPS radio occultation with GRACE: Atmospheric profiling utilizing the zero difference technique. Geophys. Res. Lett., 32 , L13806. doi:10.1029/2005GL023109.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorbunov, M. E., 2002: Ionospheric correction and statistical optimization of radio occultation data. Radio Sci., 37 , 1084. doi:10.1029/2000RS002370.

    • Search Google Scholar
    • Export Citation
  • Hajj, G. A., Kursinski E. R. , Romans L. J. , Bertiger W. I. , and Leroy S. S. , 2002: A technical description of atmospheric sounding by GPS occultation. J. Atmos. Sol.-Terr. Phys, 64 , 451469.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hardy, K. R., Hajj G. A. , and Kursinski E. R. , 1994: Accuracies of atmospheric profiles obtained from GPS occultations. Int. J. Satell. Commun., 12 , 463473.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuo, Y-H., Wee T-K. , Sokolovskiy S. , Rocken C. , Schreiner W. , Hunt D. , and Anthes R. A. , 2004: Inversion and error estimation of GPS radio occultation data. J. Meteor. Soc. Japan, 82 , 507531.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kursinski, E. R., Hajj G. A. , Schofield J. T. , Linfield R. P. , and Hardy K. R. , 1997: Observing Earth’s atmosphere with radio occultation measurements using the Global Positioning System. J. Geophys. Res., 102 , 2342923465.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ladreiter, H., and Kirchengast G. , 1996: GPS/GLONASS sensing of the neutral atmosphere: Model-independent correction of ionospheric influences. Radio Sci., 31 , 877891.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leandro, R. F., Langley R. B. , Santos M. C. , Sükeová L. , and Thirumurthi T. , 2008: Innovation: The GPS L2C signal: A preliminary analysis of data quality. GPS World, Vol. 19, No. 10, 42–47. [Available online at http://sidt.gpsworld.com/].

    • Search Google Scholar
    • Export Citation
  • Lohmann, M., 2005: Application of dynamical error estimation for statistical optimization of radio occultation bending angles. Radio Sci., 40 , RS3011. doi:10.1029/2004RS003117.

    • Search Google Scholar
    • Export Citation
  • Melbourne, W. G., and Coauthors, 1994: The application of spaceborne GPS to atmospheric limb sounding and global change monitoring. Jet Propulsion Laboratory Rep. 94-18, 147 pp.

    • Search Google Scholar
    • Export Citation
  • Rocken, C., and Coauthors, 1997: Analysis and validation of GPS/MET data in the neutral atmosphere. J. Geophys. Res., 102 , 2984929860.

  • Sokolovskiy, S., and Hunt D. , 1996: Statistical optimization approach for GPS/MET data inversion. Proc. Second Int. URSI GPS/MET Workshop, Tucson, AZ, Union Radio Science International.

    • Search Google Scholar
    • Export Citation
  • Steiner, A. K., Kirchengast G. , and Ladreiter H. P. , 1999: Inversion, error analysis and validation of GPS/MET radio occultation data. Ann. Geophys., 17 , 122138.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Syndergaard, S., 2000: On the ionosphere calibration in GPS radio occultation measurements. Radio Sci., 35 , 865883.

  • Vorob’ev, V. V., and Krasil’nikova T. G. , 1994: Estimation of the accuracy of the atmospheric refractive index recovery from Doppler shift measurements at frequencies used in the NAVSTAR system. Atmos. Ocean. Phys., 29 , 602609.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    L1 and L2 excess Doppler frequency shift profiles for COSMIC occultations A, B, and C on 18 Sep 2006. For visualization, the L1 and L2 Dopplers are shifted by −0.5 and +0.5 m s−1, respectively. The mean vertical ray velocities in the interval 60–80 km are (a) −3.0, (b) −2.1, and (c) 2.0 km s−1.

  • View in gallery

    Normalized S2 measure of residual noise [defined by Eq. (4)] computed from the ionosphere-corrected GPS RO signals by applying different smoothing windows w4 for L4 = L1 − L2 phases.

  • View in gallery

    Ionosphere-corrected bending angles obtained with different smoothing windows w4 for L4 = L1 − L2. The solid line shows the optimal smoothing results. (a) Optimal smoothing is achieved for 0.5 s and the dashed line shows the effect of 0.5-s smoothing. (b) Optimal smoothing is achieved for ∼0.7 s and the effects of 0.5- and 2-s smoothings (dashed lines) are shown. (c) Optimal smoothing is for 2 s and the dashed line.

  • View in gallery

    Distribution of the optimal smoothing windows w4opt for 6576 COSMIC occultations from 1 to 5 Sep 2006 sampled in 0.04-s bins.

  • View in gallery

    Standard deviations of COSMIC GPS RO refractivity profiles from the collocated refractivity profiles obtained from ECMWF global analysis for 1–5 Sep 2006. COSMIC inversions were obtained with fixed 0.5 (dashed line) and 2 s (dotted line), and optimal (solid line) L4 smoothing windows.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 252 140 3
PDF Downloads 66 35 1

Optimal Noise Filtering for the Ionospheric Correction of GPS Radio Occultation Signals

View More View Less
  • 1 University Corporation for Atmospheric Research, Boulder, Colorado
Full access

Abstract

GPS radio occultation remote sensing of the neutral atmosphere requires ionospheric correction of L1 and L2 signals. The ionosphere-corrected variables derived from radio occultation signals—such as the phase, Doppler, and bending angle—are affected by small-scale ionospheric effects that are not completely eliminated by the ionospheric correction. They are also affected by noise from mainly the L2 signal. This paper introduces a simple method for optimal filtering of the L4 = L1 − L2 signal used to correct the L1 signal, which minimizes the combined effects of both the small-scale ionospheric residual effects and L2 noise on the ionosphere-corrected variables. Statistical comparisons to high-resolution numerical weather models from the European Centre for Medium-Range Weather Forecasts (ECMWF) validate that this increases the accuracy of radio occultation inversions in the stratosphere.

Corresponding author address: Sergey Sokolovskiy, UCAR, P.O. Box 3000, Boulder, CO, 80307-3000. Email: sergey@ucar.edu

Abstract

GPS radio occultation remote sensing of the neutral atmosphere requires ionospheric correction of L1 and L2 signals. The ionosphere-corrected variables derived from radio occultation signals—such as the phase, Doppler, and bending angle—are affected by small-scale ionospheric effects that are not completely eliminated by the ionospheric correction. They are also affected by noise from mainly the L2 signal. This paper introduces a simple method for optimal filtering of the L4 = L1 − L2 signal used to correct the L1 signal, which minimizes the combined effects of both the small-scale ionospheric residual effects and L2 noise on the ionosphere-corrected variables. Statistical comparisons to high-resolution numerical weather models from the European Centre for Medium-Range Weather Forecasts (ECMWF) validate that this increases the accuracy of radio occultation inversions in the stratosphere.

Corresponding author address: Sergey Sokolovskiy, UCAR, P.O. Box 3000, Boulder, CO, 80307-3000. Email: sergey@ucar.edu

1. Introduction

When probing the neutral atmosphere by global positioning system (GPS) radio occultation (RO) at L-band frequencies f1 = 1.575 42 GHz and f2 = 1.2276 GHz, the L1 and L2 signals must be subjected to ionospheric correction (removal of the effects induced by propagation in the ionosphere; Melbourne et al. 1994; Hardy et al. 1994; Kursinski et al. 1997). Commonly, model-independent ionospheric correction is applied to a GPS RO-derived variable x, such as the excess phase, Doppler frequency, or bending angle (Vorob’ev and Krasil’nikova 1994; Ladreiter and Kirchengast 1996; Syndergaard 2000). The model-independent ionospheric correction implies that the ionospheric contribution is additive and to first order proportional to f−2. The results of this study can be applied to any GPS RO-derived variable x that can be approximately modeled as x = xa + xi + xi + xn, where xa and xi are the neutral atmospheric and the first order ionospheric contributions, respectively; xi represents the higher-order ionospheric effects; and xn is the noise. The ionosphere-corrected variable xc is calculated as the linear combination of the variables at two frequencies:
i1520-0426-26-7-1398-e1
where c1 = f12/( f12f22) and c2 = f22/( f12f22). The residual term Ri = c1xi1c2xi2 depends on higher-order ionospheric effects, including (but not limited to) the separation of ray paths and diffraction at different frequencies. The residual term Rn = c1xn1c2xn2 depends on noise.

Since the first analysis of GPS/Meteorology (MET) RO data, it has been known (Rocken et al. 1997) that the effect of small-scale ionospheric irregularities (with the scales of order of 1 km) is eliminated by model-independent ionospheric correction to a lesser extent than that of the large-scale structures. Thus, small-scale fluctuations dominate Ri. The magnitude of these fluctuations can be very different depending on the strength and location of the ionospheric irregularities.

The magnitude of the residual noise depends on the receiver antenna gain, the power of transmitted GPS signals, and the method of their demodulation in the receiver. Also, the elimination of receiver clock errors by differencing occulted and reference link data results in propagation of the phase noise from the reference link to the occulted link. In most cases, the main contribution to the residual noise Rn comes from the less powerful and encrypted L2 signal, especially, when codeless or semicodeless tracking is employed. To reduce the effect of noise, both L1 and L2 phases (Dopplers) are commonly subjected to smoothing (low-pass filtering).

The ratio of magnitudes of the residual ionospheric modulation Ri and the noise Rn can be different. During the limited periods of the GPS/MET RO mission when the L2 encryption was disabled by the U.S. Department of Defense, L2 noise was small compared to residual ionospheric modulation in most occultations. The same will happen for the new GPS unencrypted L2C signals (Leandro et al. 2008) in the future. Codeless (GPS/MET) or semicodeless [Challenging Minisatellite Payload (CHAMP), Satelite de Aplicaciones Cientificas-C (SAC-C), Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC), and other missions] tracking of the encrypted L2 signal has the effect that L2 noise overshadows the residual ionospheric modulation in many occultations.

To reduce the effect of L2 noise on the ionosphere-corrected GPS RO variables, Rocken et al. (1997) suggested application of the ionospheric correction (1) in the form of
i1520-0426-26-7-1398-e2
with different smoothing for x1 and x4 = x1x2. Application of standard smoothing for x1 and larger smoothing for x4 suppresses the effect of L2 noise by not degrading xa, which is canceled in x4. Although this comes at the expense of an increase of uncorrected small-scale ionospheric residual effect in Ri, the overall noise reduction may be significant. This approach was applied for processing of the GPS/MET data obtained with codeless tracking of L2. The smoothing windows for x1 and x4 were fixed ad hoc to 0.5 and 2 s. Later, similar approaches, aimed at damping L2 noise by applying smoothing with different fixed windows for x1 and x4, were used for the ionospheric correction of GPS RO data on both occulted and reference links by other researchers (Steiner et al. 1999; Gorbunov 2002; Hajj et al. 2002; Beyerle et al. 2005).

It is clear that the ratio of magnitudes of the ionospheric residual Ri and noise Rn is different not only for different GPS RO missions but also for different occultations. In this study we generalize the approach originally introduced by Rocken et al. (1997) by finding an optimal smoothing window for x4, for each occultation individually. We then test it by processing COSMIC RO signals.

2. Optimal L4 smoothing window

We consider the following ionospheric correction of a variable x:
i1520-0426-26-7-1398-e3
where 〈〉w means smoothing (low-pass filtering) with window w. Estimation of the window w1 is not directly related to the ionospheric correction, may be subject to different criteria, and is not considered in this study related to the choice of the optimal window w4 for a given w1. For example, w1 may be correlated with the size of the first Fresnel zone at the ray tangent point. Then, it must be proportional to the ascent/descent rate v; however, establishing an optimal coefficient in that relation needs separate justification. We apply Fourier filtering with a Gaussian response function of half-width w (Kuo et al. 2004). We set the window w1, responsible for smoothing of the neutral atmospheric component xa, to 0.5 s for all occultations (the corresponding smoothing window in height is approximately equal to the size of the first Fresnel zone for v ∼ 3 km s−1). Then, for each occultation we find the window w4, which minimizes the magnitude of residual fluctuations of xc and dxc/dt by using the following criterion:
i1520-0426-26-7-1398-e4
We found that the results do not significantly depend on the criterion once it reasonably quantifies the magnitude of fluctuations. The interval (t1, t2) must correspond to observations at a sufficiently high altitude, so that the fluctuations of xc related to the neutral atmosphere xa are small. On the other hand, the interval must be below the E-layer, so that the residual ionospheric fluctuations in this interval are representative of the fluctuations at lower heights. We use the interval (60 km, 80 km).

Figure 1 shows L1 and L2 excess Dopplers dx1/dt and dx2/dt for three COSMIC occultations (A, B, and C) with different ratios of L2 noise and small-scale ionospheric fluctuations. We note that these ratios also depend on the vertical velocities v that are different in different occultations (as indicated in the figure caption). The L2 noise is about the same for occultations A and B, but the small-scale ionospheric effect (visible in L1 and L2 Dopplers) is larger for A. Especially large ionospheric effect (as it follows from the ratio of magnitudes of L1 and L2 Dopplers) is seen at height ∼55 km (although the ionospheric perturbation itself is at a greater height). Occultation C shows large L2 noise. We search for the optimal value w4opt, which minimizes S2(w4), in the smoothing interval (0.5, 2 s). Figure 2 shows S2(w4) normalized by the minimal value of S2 in this interval. For occultations A and C w4opt is close to the ends of the interval, 0.5 s and 2 s, respectively. For occultation B w4opt is inside the interval.

Since, for small fluctuations, the bending angle is proportional to v−1dx/dt, the optimal window w4 that minimizes fluctuations in dxc/dt also minimizes them in the bending angle. Figure 3 shows the ionosphere-corrected bending angles as functions of impact height (solid lines correspond to w4, which minimize the residual fluctuation). For occultations A and C, the residual fluctuations of the bending angle are smaller for w4 = 0.5 s and for w4 = 2 s, respectively. For the low-noise occultation A, w4 = 0.5 s results in significantly smaller residual error of the ionospheric correction at ∼55 km, where the bending angle is affected by strong ionospheric perturbation, than w4 = 2 s. For occultation B the residual fluctuations of the bending angle are smaller for w4 = w4opt than for both w4 = 0.5 s and w4 = 2 s. The smaller magnitude of residual noise in the ionosphere-corrected bending angle results in smaller refractivity retrieval errors because of both the lower noise and the lower weight of the background bending angle profile used for optimization of the Abel inversion [in our processing, we use statistical optimization of bending angles described by Sokolovskiy and Hunt (1996) and modified by Lohmann (2005)].

Figure 4 shows the distribution of w4opt (sampled in 0.04-s time bins) for all COSMIC occultations from 1 to 5 September 2006. For most of the occultations, w4opt is different from both 0.5 and 2 s; however, the maximum is close to 0.5 s, indicating a statistically low L2 noise level in COSMIC data. We found that accounting for the tail of the distribution at w4opt > 2 s does not significantly affect the refractivity inversion errors in a statistical sense. Figure 5 shows the standard deviations of COSMIC refractivity profiles from the corresponding (i.e., interpolated in space and time to RO) refractivity profiles obtained from European Centre for Medium-Range Weather Forecasts (ECMWF) global analysis, for the same date range as for Fig. 4 (COSMIC data were not yet assimilated into the ECMWF model). Different lines indicate processing with w4 = 0.5 s, w4 = 2 s, and w4 = w4opt. Differences between different processing modes become noticeable above 30 km. The smallest standard deviation between COSMIC and ECMWF corresponds to processing with w4 = w4opt, although the difference between w4 = 0.5 s and w4 = w4opt is not as significant as between both and w4 = 2 s by confirming statistically low noise level in COSMIC L2 data. We note that GPS RO inversion errors are smaller, and their fractional differences for different w4 are larger than those directly deduced from Fig. 5 because of the ECMWF analysis errors.

Application of the optimal L4 filtering is also possible on the reference link. The reference link is used for elimination of receiver clock errors by differencing the L1 and L2 phases from the occulted link with the ionosphere-corrected phase from the reference link. However, the spectrum of clock errors may be different in differet receivers. For example, the CHAMP receiver data contain 1-s spikes (Beyerle et al. 2005). In such cases independent smoothing of the ionosphere-corrected signal on the reference link will introduce significant errors after differencing and must be done in one loop with smoothing on the occulted link. This can make processing overly complicated.

3. Conclusions

The main sources of noise in the ionosphere-corrected GPS RO signals, affecting the accuracy of GPS RO in the stratosphere, are uncorrected small-scale ionospheric residuals and noise on the L2 signal. The ratio of these effects is different for different occultations. An increase of the smoothing time window for L4 = L1 − L2 reduces the effect of L2 noise but increases the ionospheric residual effect after correction (and vice versa). The introduced simple method determines an optimal filter bandwidth for L4 for each occultation by minimizing the combined effect of the L2 noise and the ionospheric residuals. This improves the accuracy of GPS RO in the stratosphere as evidenced by statistical comparison of GPS RO to ECMWF global analysis. The introduced method is important for weak and/or encrypted L2 signals, and especially for climate applications. It may be less important in the future when stronger and unencrypted L2C signals become available on newly launched GPS satellites.

Acknowledgments

This work was supported by the National Science Foundation as part of the development of the COSMIC Data Analysis and Archiving Center (CDAAC) at UCAR under the Cooperative Agreement ATM-9732665. The authors are grateful to anonymous referees whose comments helped to improve this paper.

REFERENCES

  • Beyerle, G., Schmidt T. , Michalak G. , Heise S. , Wickert J. , and Reigber C. , 2005: GPS radio occultation with GRACE: Atmospheric profiling utilizing the zero difference technique. Geophys. Res. Lett., 32 , L13806. doi:10.1029/2005GL023109.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gorbunov, M. E., 2002: Ionospheric correction and statistical optimization of radio occultation data. Radio Sci., 37 , 1084. doi:10.1029/2000RS002370.

    • Search Google Scholar
    • Export Citation
  • Hajj, G. A., Kursinski E. R. , Romans L. J. , Bertiger W. I. , and Leroy S. S. , 2002: A technical description of atmospheric sounding by GPS occultation. J. Atmos. Sol.-Terr. Phys, 64 , 451469.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hardy, K. R., Hajj G. A. , and Kursinski E. R. , 1994: Accuracies of atmospheric profiles obtained from GPS occultations. Int. J. Satell. Commun., 12 , 463473.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kuo, Y-H., Wee T-K. , Sokolovskiy S. , Rocken C. , Schreiner W. , Hunt D. , and Anthes R. A. , 2004: Inversion and error estimation of GPS radio occultation data. J. Meteor. Soc. Japan, 82 , 507531.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kursinski, E. R., Hajj G. A. , Schofield J. T. , Linfield R. P. , and Hardy K. R. , 1997: Observing Earth’s atmosphere with radio occultation measurements using the Global Positioning System. J. Geophys. Res., 102 , 2342923465.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ladreiter, H., and Kirchengast G. , 1996: GPS/GLONASS sensing of the neutral atmosphere: Model-independent correction of ionospheric influences. Radio Sci., 31 , 877891.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leandro, R. F., Langley R. B. , Santos M. C. , Sükeová L. , and Thirumurthi T. , 2008: Innovation: The GPS L2C signal: A preliminary analysis of data quality. GPS World, Vol. 19, No. 10, 42–47. [Available online at http://sidt.gpsworld.com/].

    • Search Google Scholar
    • Export Citation
  • Lohmann, M., 2005: Application of dynamical error estimation for statistical optimization of radio occultation bending angles. Radio Sci., 40 , RS3011. doi:10.1029/2004RS003117.

    • Search Google Scholar
    • Export Citation
  • Melbourne, W. G., and Coauthors, 1994: The application of spaceborne GPS to atmospheric limb sounding and global change monitoring. Jet Propulsion Laboratory Rep. 94-18, 147 pp.

    • Search Google Scholar
    • Export Citation
  • Rocken, C., and Coauthors, 1997: Analysis and validation of GPS/MET data in the neutral atmosphere. J. Geophys. Res., 102 , 2984929860.

  • Sokolovskiy, S., and Hunt D. , 1996: Statistical optimization approach for GPS/MET data inversion. Proc. Second Int. URSI GPS/MET Workshop, Tucson, AZ, Union Radio Science International.

    • Search Google Scholar
    • Export Citation
  • Steiner, A. K., Kirchengast G. , and Ladreiter H. P. , 1999: Inversion, error analysis and validation of GPS/MET radio occultation data. Ann. Geophys., 17 , 122138.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Syndergaard, S., 2000: On the ionosphere calibration in GPS radio occultation measurements. Radio Sci., 35 , 865883.

  • Vorob’ev, V. V., and Krasil’nikova T. G. , 1994: Estimation of the accuracy of the atmospheric refractive index recovery from Doppler shift measurements at frequencies used in the NAVSTAR system. Atmos. Ocean. Phys., 29 , 602609.

    • Search Google Scholar
    • Export Citation

Fig. 1.
Fig. 1.

L1 and L2 excess Doppler frequency shift profiles for COSMIC occultations A, B, and C on 18 Sep 2006. For visualization, the L1 and L2 Dopplers are shifted by −0.5 and +0.5 m s−1, respectively. The mean vertical ray velocities in the interval 60–80 km are (a) −3.0, (b) −2.1, and (c) 2.0 km s−1.

Citation: Journal of Atmospheric and Oceanic Technology 26, 7; 10.1175/2009JTECHA1192.1

Fig. 2.
Fig. 2.

Normalized S2 measure of residual noise [defined by Eq. (4)] computed from the ionosphere-corrected GPS RO signals by applying different smoothing windows w4 for L4 = L1 − L2 phases.

Citation: Journal of Atmospheric and Oceanic Technology 26, 7; 10.1175/2009JTECHA1192.1

Fig. 3.
Fig. 3.

Ionosphere-corrected bending angles obtained with different smoothing windows w4 for L4 = L1 − L2. The solid line shows the optimal smoothing results. (a) Optimal smoothing is achieved for 0.5 s and the dashed line shows the effect of 0.5-s smoothing. (b) Optimal smoothing is achieved for ∼0.7 s and the effects of 0.5- and 2-s smoothings (dashed lines) are shown. (c) Optimal smoothing is for 2 s and the dashed line.

Citation: Journal of Atmospheric and Oceanic Technology 26, 7; 10.1175/2009JTECHA1192.1

Fig. 4.
Fig. 4.

Distribution of the optimal smoothing windows w4opt for 6576 COSMIC occultations from 1 to 5 Sep 2006 sampled in 0.04-s bins.

Citation: Journal of Atmospheric and Oceanic Technology 26, 7; 10.1175/2009JTECHA1192.1

Fig. 5.
Fig. 5.

Standard deviations of COSMIC GPS RO refractivity profiles from the collocated refractivity profiles obtained from ECMWF global analysis for 1–5 Sep 2006. COSMIC inversions were obtained with fixed 0.5 (dashed line) and 2 s (dotted line), and optimal (solid line) L4 smoothing windows.

Citation: Journal of Atmospheric and Oceanic Technology 26, 7; 10.1175/2009JTECHA1192.1

Save