1. Introduction
Precise orbit determination (POD) has become indispensable for many space-borne applications that monitor the Earth’s climate system, one of which is Global Navigation Satellite System (GNSS) [
1,
2] radio occultation (RO) [
3,
4,
5]. The RO remote sensing technique is considered highly valuable for atmosphere and climate sciences since it provides high-vertical-resolution measurements over the troposphere and stratosphere with global coverage, high accuracy, long-term stability, and virtually all-weather capability [
6,
7]. During an occultation measurement GNSS signals scan the atmosphere in limb sounding geometry and arrive with a time delay at the receiving RO satellite in low Earth orbit (LEO), which is due to the signal’s refraction in the Earth’s atmosphere. A vertically rising or setting occultation event is observed depending on whether the GNSS transmitter satellite rises or sets behind the Earth’s horizon from the viewpoint of the rapidly moving LEO receiver satellite.
The atmospheric excess phase path, which denotes the difference between the geometric straight-line distance between transmitter and receiver satellite and the signal’s bended propagation path, can be derived from the measured time delays and reliable POD results. This traceability to fundamental time standards ensures long-term stability and no need for calibration [
8,
9,
10]. The short-term stability of an individual RO event of about 1 to 2 min duration is satisfied by highly stable clock oscillators. Finally, essential climate variables (ECVs) [
11], such as temperature, pressure, and tropospheric water vapor, can be derived from the raw measurements utilizing a dedicated RO
retrieval. Resulting, the GNSS RO space-geodetic observing system delivers an abundance of geographically distributed vertical profiles of ECVs all over the globe, which can be averaged and used for climate studies.
Due to the unique properties of occultation soundings introduced above and global availability since 2001, records of basic RO measurements (i.e., atmospheric excess phase or derived Doppler shift) have the potential to serve as
Fundamental Climate Data Record (FCDR): A well-characterized, global, and long-term stable data record for the derivation of accurate and stable ECVs, globally and covering timespans from days to decades [
12,
13]. However, in order to fully exploit this potential and provide climate benchmark data for meteorology, climate research, climate monitoring as well as for calibration and validation, the accuracy of RO data needs to be assessed. That includes quantification of remaining uncertainties throughout the entire retrieval, starting from raw measurement data with the modeling of the observation geometry, to derivation of atmospheric excess phase data, to the final thermodynamic ECVs (
Figure 1).
While the quality and high accuracy of RO in the upper-troposphere and lower-stratosphere regions is well-acknowledged (e.g., [
14,
15,
16]) and high consistency has been assessed between different RO retrievals of leading international processing centers [
10,
17,
18], a rigorous uncertainty estimation and propagation throughout the entire RO retrieval remains an important but incomplete task. In addition, the former occultation processing system at WEGC [
16] lacks this utility since the retrieval starts from external excess phase data and thus does not tie to the raw measurements and the physical unit of time. The new Reference Occultation Processing System (rOPS) [
19,
20] developed at WEGC, on the contrary, aims to establish such a fully traceable processing comprising all retrieval steps [
19,
21,
22]. For this reason, the rOPS features the integration of RO low-level data processing starting from the raw satellite observation data. This low-level processing comprises the RO observation geometry modeling within the daily system modeling (DSM) and the level 1a (L1a) excess phase processing [
23] as part of the occultation data processing (ODP) chain (cf.
Figure 1). The DSM provides an advanced setup for POD of the RO receiver satellites in LEO, including the capability to routinely assess the uncertainties of the computed orbit data for climate-quality processing, which is presented in this paper.
In order to ensure highly consistent and accurate RO-derived ECVs tied to the raw measurements, precise orbit positions, velocities, and clock estimates of the GNSS transmitter satellites and LEO RO receiver satellites need to be determined and their attributed uncertainty assessed. In this study we focus on the assessment of orbit position and velocity, whereas the satellites clock characteristics and stability will be discussed in a separate publication focusing on RO excess phase processing. Numerous past studies have evaluated the relationship between LEO orbit accuracy and atmospheric parameters derived from RO [
3,
24,
25,
26,
27,
28,
29]. Based on the orbit accuracy specifications deduced from these studies, the POD processing presented in this study aims for a daily LEO orbit accuracy within 5 cm in position and 0.05 mm/s in velocity respectively, enabling highest quality RO retrieval results. In order to test these orbit requirements we routinely calculate different orbit solutions for mutual consistency check employing two independent POD software packages Bernese GNSS software v5.2 [
30] (in short “Bernese” hereafter) and NAPEOS v3.3.1 [
31], and use GNSS orbit and clock data from different orbit data archives, the Center for Orbit Determination in Europe (CODE) [
32] and the International GNSS Service (IGS) [
33].
The computation of estimated random and systematic orbit uncertainties is based on orbit inter-comparison between the different solutions, the analysis of satellite laser ranging (SLR) residuals, and random error propagation within Bernese. Finally, days exceeding the orbit accuracy target specifications are associated with increased uncertainty estimates and flagged for the subsequent occultation data processing. Building (also) on these POD uncertainty estimates, the uncertainty propagation along the RO level 1 and level 2 data processing chain (ODP in
Figure 1) ultimately delivers thermodynamic ECVs jointly with uncertainty estimates. This processing leads to reference data products enabling added-value for climate monitoring and applications from the co-estimated uncertainties.
Following this introduction,
Section 2 starts with an overview of the processed missions.
Section 3 introduces the data and software used followed by the description of POD and SLR technique, and the uncertainty estimation approach. Results are presented and discussed in
Section 4. In
Section 5 a summary and conclusion is provided.
2. Missions and Spacecraft Payload
The life-time of the RO satellite missions selected for the present study of POD for climate applications span the entire RO era, starting with first continuous long-term RO measurements obtained by CHAllenging Minisatellite Payload (CHAMP) in February 2001. The Gravity And Climate Experiment (GRACE) mission provided RO measurements since 2006, although it has been in space since 2002 and previously activated the RO receiver for testing [
34]. Meteorological operational satellite A (Metop-A), the first of a series of three meteorological satellites developed in cooperation by the European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) and the European Space Agency (ESA), switched on its RO instrument 8 days after its launch on 19 October, 2006, followed by Metop-B on 17 December, 2012, before the series was completed with the launch of Metop-C from Guiana Space Centre, Kourou on 7 November, 2018 [
35].
The CHAMP satellite was launched on July 15, 2000 into a near-polar but non sun-synchronous orbit of 87.3° inclination and a mean initial orbit altitude of 454 km which decreased over time despite intermediate orbit raise maneuvers, to 325 km approaching the decay. The German Research Centre for Geosciences (GFZ) managed mission provided measurements for atmospheric, magnetic and gravity field research before its end-of-lifetime after over 10 years in space [
36]. The onboard
BlackJack Global Positioning System (GPS) receiver [
37], manufactured by the National Aeronautics and Space Administration’s (NASA) Jet Propulsion Laboratory (JPL), is connected to a multi-antenna system including a zenith-looking choke ring antenna for navigation tracking of inter-satellite links at a rate of 0.1 Hz, an anti-velocity facing antenna array for occultation tracking at 50 Hz, and a nadir looking antenna for altimetry measurements.
The receiver front-end and electronics support dual-frequency tracking in 16 × 3 channels for C/A, P1, and P2 code respectively. Out of all channels, 12 are allocated for POD (effectively only a maximum of 10 GPS satellites were tracked simultaneously [
37,
38]) and the remaining 4 channels are reserved for operation in occultation mode for atmospheric sounding [
27,
39] or alternatively for altimetry measurements. The satellite’s orientation relative to the inertial reference frame is recorded in quaternions (1 Hz) by two dual-headed Advanced Star Camera (ASC) assemblies developed by the Technical University of Denmark (DTU) [
40,
41]. Also onboard, a Laser Retroreflector (LRR), consisting of four cube corner prisms designed by GFZ [
42,
43], is mounted on the platform. The LRR passively reflects short laser pulses from an emitting ground station on Earth, thus allowing for the calculation of satellite laser ranges [
44].
The GRACE twin satellite mission was a joint mission between NASA and the German Aerospace Center (DLR) and launched into similar near-circular orbits of 89.5° inclination and about 500 km altitude on 17 March, 2002. The two identical satellites were separated approximately 220 km in nominal orbit for the primary mission goal of measuring climate-relevant variations of the Earth’s gravity field [
45,
46]. As a follow-on mission to CHAMP, GRACE features a similar design and payload, with an identical ASC and LRR mounted on the platform. Supplementary, the K-Band ranging system enables measuring the separation changes between the two satellites to micrometer precision in order to map the Earth’s gravity field [
47]. Equipped with a similar BlackJack GPS receiver as CHAMP [
48], signals received with the zenith antenna are used for POD and the aft-looking antenna provides RO measurements for sensing physical properties of the atmosphere [
34,
49].
As secondary mission goal RO instrumentation was tested on both GRACE satellites for shorter periods before continuous activation of RO measurements on 22 May, 2006 on GRACE-A [
27]. The majority of measurements were obtained by GRACE-A intermitted by shorter periods of occultations by GRACE-B (Jul-Dec 2014, Jun-Oct 2015, Apr-Sep 2016) when swapping maneuvers took place, making GRACE-B the trailing satellite [
16]. Therefore, we limit the evaluations in this paper to the quality assessment of GRACE-A, seen as representative for both flight models. After decommissioning and atmospheric reentry of GRACE on 24 December, 2017 (GRACE-B) and 10 March, 2018 (GRACE-A) the success of the mission was continued with the launch of GRACE follow-on in May 2018 [
50,
51]. However, as of early 2020, RO data from this follow-on mission are not yet available to the community.
As part of the EUMETSAT Polar System the Meteorological Operational (Metop) satellite series consists of three flight models Metop-A/B/C, which were placed sequentially in time (see above) in a sun-synchronous polar orbit of about 98.7° inclination and an altitude between 796 and 884 km [
52]. The centerpiece for GPS inter-satellite tracking is the onboard GNSS Receiver for Atmospheric Sounding (GRAS) developed by Saab Ericsson Space [
53,
54]. The GRAS unit provides dual-frequency navigation and occultation tracking at 12 × 3 channels for L1 C/A and L1/L2 P(Y). A zenith-looking antenna observes GPS satellite signals at 8 channels with a sampling rate of 1 Hz for POD [
28,
29]. Furthermore, 4 channels are shared by two high-gain beam forming antennas looking in flight velocity and anti-velocity direction for rising and setting occultations respectively, supporting closed loop (50 Hz) and open loop (1 kHz) measurements [
55].
For orientation of the satellite a nominal alignment is applied for the POD. In contrast to CHAMP and GRACE, the Metop satellites are not equipped with an LRR for orbit verification from the terrestrial laser tracking network. Up to this day, the Metop satellite series serves with an almost constant number of occultations per day and thereby underscores its importance as a reliable long-term backbone mission for numerical weather prediction and climate research [
56].
4. Results and Discussion
Three different orbit solutions are calculated routinely within WEGC’s POD processing (listed in
Table 2). In order to assess the quality of the orbit solution designated for further RO processing (WEGC-BC), different analyses are performed. The WEGC-BC primary solution is compared to internal control runs (WEGC-BI, WEGC-NC) and orbit solutions from external processing centers (
Section 4.1). Satellite laser ranging residuals are analyzed (
Section 4.2), and measures for the orbit uncertainties are derived (
Section 4.3). The results cover the analysis for CHAMP and GRACE-A in July to September 2008 and the same time period in 2013 for Metop-A/B.
4.1. Orbit Comparison
As outlined in
Section 3.5, the inter-comparison of the different precise orbit products allows for a realistic assessment of the accuracy and might reveal possible systematic errors.
Figure 4 shows daily 3D-RMS differences in position between the WEGC-BC solution and externally provided orbits. The corresponding position and velocity differences in radial, along-track, and cross-track directions are summarized in
Table 3. When comparing the different orbit solutions overall best agreement is found for the comparison of WEGC-BC and WEGC-BI. This can be expected from the fact that in this case the differences are simply governed by the impact of different GNSS orbit, clock, and associated EOP data while using the same POD software with consistent processing settings. For all missions the RMS of the daily 3D-RMS series does not exceed 1.4 cm. However, a single day for GRACE-A of about 4 cm difference can be found. The WEGC-NC solution generally compares at a similar level to WEGC-BC as the external solutions, with the exception of decreased differences found between WEGC-BC and AIUB for CHAMP.
CHAMP. For the CHAMP mission best agreement is found with AIUB with an RMS of about 1.8 cm (note: 3 days from AIUB are missing in the provided data). Solutions from WEGC-NC, EUMETSAT, and UCAR compare at a similar level, where the comparison to UCAR features a slightly better comparison with an RMS of about 4.0 cm. Individual days still exhibit differences above the 5 cm threshold.
GRACE. Differences from orbit comparison for GRACE-A presented are higher than results from space-geodetic applications, such as gravity field recovery [
46]. However, results from those applications are based on screened observation files (available from JPL) where the clock error was detrended and altered substantially, compared to the raw observation files available at CDAAC. As already outlined in
Section 3.1, dealing with such large clock trends poses challenges in handling the data by the POD software packages. This leads to comparison results indicating a slightly degraded quality but still within the conservative bounds for RO. Note that while the WEGC-NC and AIUB solutions are based on these screened L1B products, all other solutions are based on the raw L1A observation data.
In
Figure 4b increased values of comparison in September 2008 and missing days end of August for UCAR can be seen for GRACE-A, which is in accordance with periods when the satellite clock error is peaking before it is reset. Also, increased along-track differences (
Table 3) compared to solutions based on pre-screened RINEX suggest a shift in time. In particular for the comparison of the primary solution, and the one by AIUB, the use of different low-level input data leads to increased differences for GRACE-A (4.3 cm) compared to the same comparison conducted for CHAMP (1.8 cm). With respect to the AIUB solution as reference, which can be considered a particularly reliable reference due to its K-band validation [
69], WEGC orbits compare better than UCAR (WEGC-NC 1.5 cm, WEGC-BC 4.3 cm, WEGC-BI 4.7 cm; UCAR 6.5 cm).
Metop. In principle, a similar characteristics of the comparison results is found for both Metop satellites. Apart from the WEGC-BI solution, best agreement is found against WEGC-NC with an RMS of about 4.0 cm and 4.2 cm for Metop-A and Metop-B, respectively. Individual days of the comparison are slightly exceeding the 5 cm threshold, and furthermore days with increased differences against UCAR can be observed in August and September leading to an overall RMS close to and slightly exceeding 5 cm for Metop-A and Metop-B, respectively. These findings are consistent with earlier results from orbit inter-comparison for Metop [
28]. Note that both Metop satellites undergo a maneuver in the considered period. Additionally, two days with missing attitude from CDAAC remain currently unprocessed.
Finally we note that in general all orbit solutions for the presented missions (including those from UCAR, EUMETSAT, and AIUB) satisfy the introduced RO-application-oriented target specification of 5 cm in position and 0.05 mm/s in velocity.
4.2. Satellite Laser Ranging Validation
Limited to the CHAMP and GRACE-A missions, which are equipped with an LRR,
Table 4 summarizes the laser ranging residuals statistics for the two missions using normal point data available from (1) all stations and (2) a high-quality subset of 12 stations. The station selection was applied in order to discriminate between different performance levels among the stations of the ILRS network [
44]. The results comprise the internal and external POD solutions derived from GPS measurements.
Figure 5 illustrates SLR residuals that were calculated based on observations from the selected high-quality stations only and the WEGC-BC primary orbit.
In general, the mean and standard deviation for the validated orbit solutions (
Table 4) decreases with the limitation to high-quality (HQ) stations. For GRACE-A, however, the WEGC-BC, WEGC-BI, and UCAR solutions, which are all solutions based on unscreened L1A GPS navigation tracking data, show a larger mean for the HQ station selection than for all stations. Furthermore, regardless of the station selection, those solutions exhibit standard deviations more than two times larger than the WEGC-NC and AIUB solutions, which are based on the screened L1B GPS navigation tracking data (see
Section 3.1).
Overall, the SLR intercomparison results do not exhibit notable systematic variations within the time periods considered. With a similar number of observations (CHAMP: 8271, GRACE-A: 8533) both data series show a small mean. However, the larger scattering which is observed for GRACE-A (
Figure 5b) manifests in an increased standard deviation of about 1 cm compared to CHAMP. Furthermore, it was found that using screened L1B RINEX data for the GRACE-A POD reduces the standard deviation (comparable to CHAMP), although this is not applicable in the case of RO (
Section 3.1).
4.3. Uncertainty Estimation
The results of the uncertainty estimation as introduced in
Section 3.5 are illustrated in
Figure 6, and summarized in
Table 5 (3-month mean and standard deviation range), for the RO LEO satellites under investigation and two representative GPS transmitter satellites possibly involved in an occultation event (one GPS delivering good estimates and one slightly degraded). The component estimates in
Table 5 use plausible fractional weighting of the 3D variance (
) [
69,
89]. In case of a typical day, when the geometry modeling system (
Figure 1) delivers results within highest-quality demands for RO processing, the 3D-RMS uncertainties are generally obtained near the conservative bound of 5 cm in position and 0.05 mm/s in velocity for the LEO satellite.
LEO satellites. The estimated random uncertainties for all missions (
Figure 6, panels (a) to (d)) show consistent behavior over time, with lowest values found for GRACE. On days where the uncertainty calculation failed due to missing input (i.e., the POD of one of the control orbit runs was not successful) the estimated random uncertainty is set to a conservative estimate of 2 cm, which leads to a slightly increased combined uncertainty estimation on those days for GRACE. For the majority of days, the raw-estimated systematic uncertainty component stays within the conservative bound. In particular this applies to most days for GRACE and the Metop satellites. For CHAMP some more days are found that moderately exceed the conservative-bound threshold.
GPS satellites. With regard to the GPS transmitter satellites (
Figure 6, panels (e) and (f)), the estimated random uncertainties are fixed to the predefined conservative value of 1 cm (cf.
Figure 3). The estimated systematic uncertainty, as derived from the accuracy codes, reveals some days of decreased orbit accuracy. Since the estimated uncertainties are empirically mapped with a conversion factor of 1/3000 from position to velocity (
Section 4.3), it is well visible that the contribution of GPS velocity uncertainties is quite minor compared to the velocity uncertainties derived for the LEO satellites.
5. Conclusions
Climate benchmark data derived from GNSS RO require accurate and robust POD of the GNSS transmitter and LEO receiver satellites taking part in an occultation measurement. In this paper we presented a novel setup for routine quality assessment and uncertainty estimation of the daily LEO receiver satellite orbits independent from external validation sources. The GNSS orbit uncertainty estimates were complemented by building on existing error estimates from the GNSS community. As part of WEGC’s rOPS we provide estimates of systematic and random uncertainties associated with the orbit determination, deduced from different LEO POD runs, SLR measurements, and formal uncertainty analysis. We focused on the validation of the WEGC primary orbit solution, which is chosen to deliver the receiver orbit positions, velocities, and clock estimates for subsequent RO processing and the derivation of atmospheric profiles of ECVs.
For the performance assessment of the extended POD setup we investigated 3 representative months of data from July to September in 2008 (CHAMP and GRACE-A) and 2013 (Metop-A/B). The comparison of the WEGC primary solution with orbit solutions from internal control runs showed reliable agreement within 5 cm in position and 0.05 mm/s in velocity, which is the target threshold specification set for high-quality orbit products for RO climate applications. This threshold is also satisfied for most days in an inter-comparison with orbits from the external providers UCAR, EUMETSAT, and AIUB. SLR residuals using selected high-quality ground stations, available and used for CHAMP and GRACE-A, exhibited a mean and standard deviation of cm and cm, respectively, well within the target ranges. Interchange of the GNSS orbit data used with one POD software, without altering the processing setup, shows relatively small differences in the orbit inter-comparison. This suggests that different POD software implementations and configuration settings are more relevant to the uncertainty estimation than potential quality differences in the GNSS orbit data products.
Overall, the uncertainty estimates are found to be within the specified target thresholds for 92% of the days considered. The remaining 8% of days exhibit higher uncertainties of order 5 to 15 cm. This is still adequate for RO processing and at the same time results in somewhat increased uncertainty estimates of the derived ECVs, after propagation through the rOPS retrieval chain. These results suggest a high processing standard and robustness, shared among all processing centers, and indicate rOPS POD system readiness for long-term climate reprocessing of RO data records from CHAMP, GRACE, and the Metop satellite series.
Further modifications of the observation geometry system of rOPS may be applied in future with the inclusion of other RO missions and enhancements of the basic uncertainty estimation. As another important RO mission, we currently integrate POD processing of FORMOSAT-3/COSMIC (Formosa Satellite mission-3/Constellation Observing System for Meteorology, Ionosphere, and Climate) [
103]. This will show the retrieval performance implications of the rOPS POD setup for the case of overall degraded POD quality (about 15–25 cm position uncertainties [
90]), due to less favorable attitude behavior of the rather small COSMIC spacecraft and restrictions in processing observations from two POD antennas.
For the time being, the further RO processing of FORMOSAT-3/COSMIC data, as well as of the RO data from the more recent FengYun-3 operational satellite series [
104] and the commercial CubeSat constellation of Spire [
105], is prepared with using the LEO orbits from these data providers together with fixed adopted values of position and velocity uncertainty estimates based on their orbit quality assessments. As part of the future multi-satellites portfolio, we will also process the very recent FORMOSAT-7/COSMIC-2 RO data [
106]. Another aspect is that the processing of orbit arcs is currently limited to 24 h arcs, restricting calculation of orbit overlap statistics or long-arc analysis, which in future might serve as an additional measure in the uncertainty estimation process.
As a next step, the upcoming RO reprocessing at WEGC will provide a thorough long-term performance check of the current implementation of this new POD subsystem and may motivate additional modifications and improvements. Based on the encouraging results of this study we expect to obtain high-quality ECV data records for climate monitoring and research.