# Use of the L2C signal for inversions of GPS radio occultation data in the neutral atmosphere

## Abstract

Results from processing FORMOSAT-3/COSMIC radio occultations (RO) with the new GPS L2C signal acquired both in phase locked loop (PLL) and open loop (OL) modes are presented. Analysis of L2P, L2C, and L1CA signals acquired in PLL mode shows that in the presence of strong ionospheric scintillation not only L2P tracking, but also L1CA tracking often fails, while L2C tracking is most stable. The use of L2C improves current RO processing in the neutral atmosphere mainly by increasing the number of processed occultations (due to significant reduction in the number of L2 tracking failures) and marginally by a reduction in noise in statistics. The latter is due to the combination of reduced L2C noise (compared to L2P) and increased L1CA noise in those occultations where L2P would have failed. This result suggests application of OL tracking for L1CA and L2C signals throughout an entire occultation to optimally acquire RO data. Two methods of concurrent processing of L1CA and L2C RO signals are considered. Based on testing of individual occultations, these methods allow: (1) reduction in uncertainty of bending angles retrieved by wave optics in the lower troposphere and (2) reduction in small-scale residual errors of the ionospheric correction in the stratosphere.

### Keywords

GPS radio occultation Signal tracking Inversion methods## Introduction

To date, GPS radio occultation remote sensing of the neutral atmosphere (Kursinski et al. 1997) has been using two GPS signals: L1CA at 1.57542 GHz and L2P at 1.2276 GHz, where the second signal is used for ionospheric correction. While the L1CA signal is open, the L2P signal is encrypted. In FORMOSAT-3/COSMIC (hereafter referred to as F3/C for brevity), L1CA is tracked in a phase locked loop (PLL) mode between the top of an occultation and a transition point corresponding to about −10 km height of straight line (HSL) between the GPS and low earth orbiting (LEO) satellite (approximately equal to 10 km height of ray tangent point (HTP)). L2P is tracked in a semi-codeless PLL mode (aided by L1CA) (Woo 2000; Meehan et al. 2000) between the top of an occultation and the transition point. Below the transition point, L1CA is tracked in the model-aided open loop (OL) mode (Sokolovskiy 2001; Ao et al. 2009; Sokolovskiy and Rocken 2004), while L2P is not tracked. Semi-codeless PLL tracking of L2P results in low signal-to-noise ratio (SNR) and tracking instability in the presence of the ionospheric scintillation, thus making L2P noisy and unusable in some occultations well above the transition point.

In the RO inversion processing at the F3C Data Analysis and Archive Center (CDAAC), the L1CA-connected phase provided by the RO receiver is not used. The L1CA signal is used as a sequence of complex samples I and Q, which is down-converted with a Doppler model based on positions, velocities, and bending angle climatology. Then, the phase is connected by resolving full cycle ambiguities. Additionally, in PLL mode (and in OL mode when data modulation replica is not available), the connection of the phase includes resolving of half-cycle ambiguities. This pre-processing is discussed in details in Sokolovskiy et al. (2009). Since, in most cases, the tracking errors on L1CA result in Doppler shifts multiple of 25 Hz, the pre-processing corrects the Doppler. The corrected L1CA Doppler is also shown in Fig. 3. It has significant noise due to integration of I and Q with significant frequency shift in RO receiver. The tracking errors of L2P Doppler, in most cases, cannot be corrected (though, at CDAAC, the correction of the full cycle ambiguities is applied). The large errors of L2P Doppler impede normal processing by making the ionospheric correction impossible, which results in the loss of about 15–20 % of all F3C occultations acquired with L2P.

The un-encrypted L2C signal (sharing frequency with L2P), first broadcast by PRN 17 in 2005, is currently being broadcast by PRNs 1, 5, 7, 12, 15, 17, 25, 29, and 31. The Jet Propulsion Laboratory (JPL) has modified the F3C receiver firmware to track L2C in both PLL and OL modes. The first test of L2C tracking on one of the F3C flight modules was performed in 2008 (Meehan et al. 2008). At the beginning of 2012, the updated modified firmware was uploaded to all flight modules. While Meehan et al. (2008) focused mainly on a description of the new L2C signal processing in receiver, the current study is focused more on improvements of RO inversions with L2C.

The stability of L2C PLL tracking in the presence of scintillation is better than that of L2P and even better than that of L1CA (see next section). This allows application of the ionospheric correction for almost all L2C occultations thus increasing the number of processed occultations. Furthermore, concurrent wave optics processing of L1CA and L2C signals allows: (1) reduction in the uncertainty of the retrieved bending angles in the lower troposphere; (2) reduction in the small-scale residual errors of the ionospheric correction in the stratosphere, in some occultations. We present initial results obtained with concurrent wave optical processing of L1CA and L2C, while implementation of these approaches into operational processing requires more effort and will be addressed in the future.

## L2C tracking

A better approach to remove the L2C data modulation would be to first provide *I* and *Q* for L2CL and L2CM separately on output from the receiver and post-process them with a replica of the L2CM data modulation. This approach, however, would increase the data volume and require L2CM data modulation replica, but may be considered for future data processing architecture.

## Improvement of current RO inversions in the neutral atmosphere with L2C

Improvement of the current CDAAC RO processing in the neutral atmosphere with the use of L2C comes mainly from the increase in the number of RO soundings that pass the L2 signal quality control (QC) check. At CDAAC, the following criterion is used to evaluate the quality of L2 signal: the difference between raw and 1-s-smoothed L2 Doppler values exceeds 6 Hz or the difference between 1-s-smoothed L2 and L1 (scaled by the ratio of L2–L1 frequencies) Doppler values exceeds 1 Hz. This semi-empirical criterion was found to satisfactorily detect L2 tracking errors similar to those shown in Fig. 1 and, all the more, in Figs. 2 and 3. The maximal height above the transition point and below 40 km where this criterion is satisfied is called the L2 drop height. Below this height, the standard ionospheric correction of the bending angles is replaced with a correction of L1 bending angle by the difference of L1 and L2 bending angles extrapolated from above (Kuo et al. 2004). If the L2 drop height is found to be larger than 20 km, the occultation is discarded (because of large errors of the extrapolated ionospheric correction).

## Use of L1CA and L2C for wave optics inversions of bending angles in the lower troposphere

It is known that the bending angle retrieved from an RO signal by wave optics (WO) methods (which transform RO signal from time/coordinate to impact parameter representation (Gorbunov 2002; Jensen et al. 2003, 2004; Gorbunov and Lauritsen 2004)) has significant uncertainty in the moist troposphere (Sokolovskiy et al. 2010). One of the reasons is the effect of non-spherically symmetric irregularities of refractivity. For a spherically symmetric refractivity, even under severe multipath in the time/coordinate representation, the signal is quasi-monochromatic in the impact parameter representation. In this case, the bending angle calculated by differentiation of the phase has very small uncertainty. In the presence of non-spherically symmetric irregularities, the signal transformed to the impact parameter representation has multitone structure. This results in fluctuations of the amplitude and phase, where the strongest fluctuations of the frequency (contributing to the bending angle uncertainty) correspond to the regions with minimum amplitude.

*h*at L1 and L2 frequencies. This can be explained by the difference of the diffraction effects at the L1 and L2 frequencies, which manifests itself mainly in the small-scale variations (larger-scale variations are more correlated). This permits the following approach for the calculation of neutral atmospheric bending angle from L1 and L2 bending angles \(\alpha_{1} (h)\) and \(\alpha_{2} (h)\) by utilizing the WO-transformed amplitudes \(B_{1} (h)\) and \(B_{2} (h)\):

## Reduction in ionospheric correction errors by back propagation of L1CA and L2C signals

Dual frequency model-independent ionospheric correction of bending angles applied in GPS RO has both large- and small-scale residual errors that represent a dominant error source of RO in the middle and upper stratosphere (above about 30 km). The large-scale errors mainly arise from the separation of rays at L1 and L2 frequencies and from the higher order terms of the dependence of refractivity on frequency (Hardy et al. 1993; Syndergaard 2000). Mitigation of the large-scale errors is outside the scope of this study. The small-scale errors (with scales of order of 1 km or less) have much larger magnitude and mainly arise from diffraction effects that are different at L1 and L2 frequencies, and from the ray separation as well. Below, we consider mitigation of the diffraction effects.

Since the diffraction effects increase with propagation distance, they may be reduced by propagation of the complex electromagnetic field from the observational trajectory back to the location of the ionospheric irregularities. Such back propagation (BP) of the 50-Hz sampled L1CA signal has been applied previously for localization of the ionospheric irregularities (Gorbunov et al. 2002; Sokolovskiy et al. 2002).

To make use of BP, the irregularities must satisfy the following conditions: they must occupy a volume much smaller than the propagation distance and they must be anisotropic (elongated) with known orientation. The latter condition is necessary because RO signal is measured on a 1D trajectory and thus only 2D (not 3D) propagation can be applied. The BP plane must be normal to projections of the irregularities on the plane normal to propagation direction. The receiver trajectory is projected on the BP plane by assuming stationary transmitter. Then, the location of the minimum of the amplitude fluctuation of the BP field corresponds to the location of the irregularities. Ionospheric correction of the bending angles calculated from BP field at the location of irregularities must have minimal residual errors related to diffraction effects on L1 and L2 frequencies. When the orientation of the irregularities is not known, then the location of the minimum of the amplitude fluctuation is different from the true location of the irregularities, but the ionospheric correction at the location of the minimum of amplitude fluctuation still results in the minimal errors related to diffraction effects. This was confirmed by modeling the 2D wave propagation at two frequencies (not shown).

While BP of L1CA is feasible, BP of L2P, encrypted by Y-code and tracked in semi-codeless mode, is not feasible in most cases affected by scintillation due to large tracking errors. In Gorbunov et al. 2002, the BP of L2P was applied for the data obtained in GPS/MET mission during limited periods (prime times) when L2P encryption was temporary turned off. Transmission of L2C allows application of BP for both L1 and L2 for the purpose of reduction in the diffraction-induced errors of the ionospheric correction.

Technical details of BP, including calculation of the virtual positions of GPS and LEO (to make transmitter stationary) and projection of the virtual LEO trajectory on the BP plane with arbitrary orientation, were discussed in Sokolovskiy et al. (2002). As mentioned above, for the purpose of the ionospheric correction, there is no need to account for the orientation of irregularities, and in this study, we project the virtual LEO trajectory on a vertical BP plane (thus assuming that the irregularities are aligned horizontally).

Our testing shows that application of WO methods (Gorbunov 2002; Jensen et al. 2003, 2004; Gorbunov and Lauritsen 2004) for calculation of bending angles yields similar reduction in the ionospheric correction errors as BP + GO when fluctuation of BP amplitude has minimum at a distance close to zero (i.e., at the limb). If the minimum is far away from the limb, the error of the ionospheric correction of WO-calculated bending angles is larger than of those calculated by BP + GO. This is related to uncertainty of the bending angles calculated by WO methods for non-spherically symmetric refractivity. For large-scale irregularities, this uncertainty has been demonstrated in Gorbunov et al. (2010).

## Conclusions

Current RO processing is substantially affected by PLL tracking errors on L2P (to a lesser extent on L1CA) signals caused by ionospheric scintillation and low SNR. At CDAAC, due to the inability to apply an ionospheric correction because of corrupted L2P signal, about 15–20 % of the occultations with L2P are discarded.

The new L2C signal has PLL tracking stability in the presence of scintillation that is better than L2P and even better than L1CA. Also, L2C allows OL tracking for the whole occultation. F3C receivers were modified to track L2C signals from beginning January 1, 2012. Currently, both L1CA and L2C are tracked in OL mode in the troposphere (below about 10 km) and in PLL mode above. This results in processing of about 100 % of occultations from the PRNs with available L2C (compared to about 80–85 % with L2P), thus increasing the total number of processed occultations. The quality of the refractivity profiles retrieved with L2C is not substantially improved in statistical sense. This is explained by extra noise on L1CA Doppler due to ionospheric scintillation and low SNR for those occultations that would not pass QC due to tracking errors if processed with L2P.

In the future, improvement of the quality of refractivity profiles retrieved with the use of L2C is possible in two ways: in the receiver and in the inversions. In the receiver, increasing the antenna gain and/or applying OL tracking for L1CA and L2C for the whole occultation will eliminate tracking errors. In the inversion process: (1) combining L1CA and L2C in wave optics inversions in the troposphere reduces the uncertainty of the retrieved bending angle; and (2) reduction in the diffractional effects on L1CA and L2C signals by BP reduces the small-scale residual errors of the ionospheric correction for the occultations affected by ionospheric scintillation. Both approaches, which are introduced and tested by individual occultations in this study, will be applied and tested in routine RO processing in the future.

## Notes

### Acknowledgments

Research performed at the University Corporation for Atmospheric Research was supported by the National Science Foundation under the Cooperative Agreement AGS-1033112. Portions of this research were carried out at the Jet Propulsion Laboratory of the California Institute of technology, under a contract with the National Aeronautics and Space Administration.

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