1. Introduction
GNSS (Global Navigation Satellite System) Radio Occultation (RO) technique provides unique measurements of atmospheric density vertical distribution, which is a function of temperature, moisture, and pressure in the neutral atmosphere [
1,
2,
3]. [
4] and [
5] demonstrated that the ROderived temperature profiles in the lower stratosphere and water vapor profiles in the troposphere are instrumental in identifying the calibration biases from the satellite infrared (IR) and microwave (MW) sensors, respectively. The raw RO observation is the time delay owing to the ray path occurring through the atmosphere between the GNSS RO emitters and receivers. The RO receivers are onboard Low Earth Orbit (LEO) satellites. Unlike IR and MW sensors, RO measurements are of a very high vertical resolution (~300 – 600 meters) and are unaffected by clouds and precipitations [
1,
2]. As a result, the RO data products are very suitable for atmospheric studies for all weather conditions [
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19]. In addition, because the clocks on GNSS and LEO satellites are traceable to the International System of Unit (SI) of time (SItraceable), RO data are also very suitable for climate studies [
20,
21,
22,
23,
24,
25,
26,
27,
28]. In the global operational numerical weather prediction (NWP) centers, GNSS RO data were used as inspace references to correct other satellite data [
1,
2,
29].
Many new GNSS RO missions were launched in the past five years, implementing different RO receivers and covering different orbits. The new missions included Taiwan/US Formosat7/Constellation Observing System for Meteorology, Ionosphere, and Climate2 (COSMIC2), the European Space Agency (ESA)/European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT)/US Sentinel6, and commercial RO missions from GeoOptics, Inc. and Spire Global, Inc. [
30]. NOAA has included GNSS RO data as one of the crucial longterm observables for weather and climate applications, just as those from IR and MW measurements [
30,
31]. NOAA National Center for Environmental Prediction (NCEP) has assimilated the RO data from NOAA missions (i.e., COSMIC2 and Sentinel6) and partners’ missions (i.e., Korea MultiPurpose Satellite/Arirang5 (KOMPSAT5), Meteorological Operational SatelliteA, B, and C (MetopA, B, and C)) into their NWP system. Around 10K daily occultation profiles were ingested into the NCEP global NWP system. The RO data demonstrated apparent impacts on the NCEP global NWP, especially in the lower stratosphere [
29]. The International Radio Occultation Working Group (IROWG) from World Meteorology Organization (WMO) recommended the optimal occultation number for NWP and climate applications is at least 20K per day with a uniform spatial and temporal distribution [
30].
To include more GNSS RO data in the NWP system, NOAA initiated the Commercial Weather Data Pilot (CWDP) program to assess commercial GNSS RO data available on the market. After two rounds of pilot studies, the CDWP decided to award the first Indefinite Delivery Indefinite Quantity (IDIQ) contract to GeoOptics and Spire Incs. in 2020. Unlike those nationalsupported RO missions with more expensive receivers and larger antennae (see below), GeoOptics and Spire used CubeSats. Using the miniature 6U CubeSat version onboard the Community Initiative for Cellular Earth Remote Observation (CICERO) satellites, GeoOptics can collect approximately 1000 to 2000 occultation profiles per day. While GeoOptics data are collected from ten CubeSats, Spire GNSS RO data are collected from over thirty CubeSats. Currently, Spire can collect around 20K occultation profiles per day. COSMIC2 used the TriG (Global Positioning System  GPS, GALILEO, and GLObal NAvigation Satellite System  GLONASS) RO Receiver System (TGRS) receiver. The Spire STRATOS RO antennareceiver payload can track GNSS signals from GPS, GLONASS, and GALILEO, and QuasiZenith Satellite System (QZSS).
To use the RO data collected from commercial CubeSats in the neutral atmosphere for climate and weather prediction studies, we must first quantify their observation quality and retrieval data product quality. More specifically, we need to provide detailed quantitative analyses to answer the following questions:
 1)
Does lower SignalNoiseRatio (SNR) commercial CubeSats RO data lead to lower precision and more significant observation errors? The SNR is defined as the magnitude of the RO signals divided by the noise level from that receiver in the voltagetovoltage unit (V/V). The SNR of the RO signal is one of the critical parameters to indicate the quality of RO measurements (i.e., time delay and excess phases) and L2 data products (i.e., bending angle (BA), refractivity, temperature, and moisture profiles). When RO signals are stronger, or the noise level is smaller, the magnitude of the SNR will be larger, which may indicate an improved observation quality. While Formosa Satellite Mission 3–Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC1 hereafter) and COSMIC2 used an antenna of 2 feet, the antenna from CubeSat is only 1 foot.
Figure 1 depicts the SNR histogram of Spire, COSMIC2, and KOMPSAT5 for the corresponding emitters. The sample numbers are normalized to the maximum number of the SNR bin. With the TGRS receiver, COSMIC2 has a larger mean SNR than Spire and KOMPSAT5. The mean COSMIC2 L1 SNR ranges from 250 to 2500 V/V [
31,
32], and the L1 SNR for Spire ranges from 200 V/V to 1500 V/V, lower than those from COSMIC2 (
Figure 1). The mean L1 SNR for KOMPAST5 is 570 V/V. With higher SNR than other RO missions, COSMIC2 is expected to penetrate deeper into the lower troposphere [
30]. With such a smaller antenna size for the Spire, one might expect the detected SNR to be much smaller than those from a larger antenna, which may lead to higher measurement and retrieval uncertainty. The antenna’s geometry may also influence the SNR distribution (see
Section 2). The RO signals received from different receivers may also introduce extra retrieval uncertainty [
31,
32,
33].
 2)
Does lower SNR Spire RO data lead to less accurate retrieval results? Whether the RO data products derived from lower SNR signals obtained from the commercial CubeSats are as accurate as those from high SNR signals is a significant concern for the RO community and climate and atmospheric scientists. The causes of the retrieval uncertainty may include receiver quality, antenna geometry, the accuracy of Precise Orbit Determination (POD) estimation, L0 to L1a processing, L1aL1b (excess phase) processing, and L1bL2 (bending angle and refractivity profiles) processing [
33]. Because RO data quality and retrieval uncertainty may also be affected by atmospheric conditions, especially in the lower troposphere, assessing RO data accuracy and identifying the accuracy uncertainty from different RO missions is still a significant challenge.
 3)
How to optimize Spire RO data in the NWP system through data assimilation? As mentioned above, because RO bending angle and refractivity uncertainty, especially in the lower troposphere, are highly related to the atmospheric condition, we must carefully examine the observation uncertainty for each RO mission to use RO data optimally in the NWP through data assimilation (DA). An accurate estimate of retrieval uncertainty is also critical for optimizing the RO impacts in the NWP through the data assimilation system [
1,
2].
This study aims to use COSMIC2, ERA5, and highquality radiosonde data to quantify the Spire RO data quality. NOAA Center for Satellite Applications and Research (STAR) has developed capabilities as a GNSS RO science and data center (STAR RO DSC, see
https://www.star.nesdis.noaa.gov/smcd/GNSSRO/RO/index.php, also see [
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41]). STAR RO DSC aims to develop enterprise RO processing algorithms for all RO missions, like other NOAA infrared and microwave satellite missions. STAR has developed the RO inversion package for COSMIC2 [
33,
35]. In addition to the Spire RO data processed by UCAR, STAR also processed Spire data using an independently developed inversion package (see
Appendix A). In this study, we will compare the STARprocessed Spire products with those from UCAR to evaluate the uncertainty due to the differences in the processing algorithm implementation. This study examines the Spire data processed by UCAR (see
http://cdaacwww.cosmic.ucar.edu/cdaac/doc/documents/ Sokolovskiy_newroam.pdf). We will examine the Spire data quality during the CWDP DeliveryOrder 3 (DO3, from September 8, 2021, to March 15, 2022) and DeliveryOrder 4 (DO4, from March 16, 2022, to January 16, 2023). NOAA purchased about 3000 Spire RO profiles daily in DO3 and about ~50006000 in DO4 (not shown). We will conduct the quality assessment of the UCAR Spire neutral atmospheric profiles regarding their stability, precision, and accuracy.
We first describe the Spire data spatial and temporal distribution in
Section 2. We also detail the data used to validate the Spire retrievals in
Section 2. The procedures to obtain the simultaneous limb overpass RO (SRO) were introduced by [
32,
42].
Section 3 presents the SRO method for our studies to collect the SpireSpire pairs, Spireother RO mission pairs, and COSMIC2 – COSMIC2 pairs. Because the Spire satellites are in the Sunsynchronized orbits, which also cover the globe, we can collect many coplanar SpireSpire pairs and SpireCOSMIC2 pair at all latitudes during the performance period. This provides an excellent opportunity to examine the climate quality regarding each RO mission’s precision, stability, and accuracy. We quantify the Spire penetration, precision, and stability in
Section 4.
Section 5 quantified the Spire retrieval accuracy and uncertainties using STAR Spire retrievals, the fifth generation European Centre for MediumRange Weather Forecasts (ECMWF) atmospheric reanalysis (ERA5), and RS41 radiosondes. We compared Spire BA profiles with ERA5 and the Spire temperature and water vapor profiles with those of RS41 in
Section 5.2 and
Section 5.3, respectively. We further estimated the Spire error covariance matrix for NWP data assimilation in
Section 6. We concluded this paper in
Section 7.
6. Estimates of the Error Covariance Matrix for NWP Data Assimilation
The observation error matrix is an important component of any NWP model data assimilation (DA) algorithm because it modulates the relative weighting assigned to individual observations and the background state when generating the analysis solution, regardless of whether the algorithm is variational, ensemble Kalman filter (EnKF), or hybrid flavored. RO profiles from different receiver satellite platforms may have systematic differences in their observation uncertainty, which must be specified in the RO DA system. Based on the calibration and validation results, we can provide the RO data quality information to NWP centers and collaborate to optimize RO data assimilation. We also use NWP diagnostic tools to analyze RO data usage from our forecast experiment datasets and provide feedback to NCEP for assessing RO DA impacts on the current NCEP data assimilation system.
Accurate estimates of RO observation errors and their dependence on the platform, observation location, and meteorological fields are needed for optimal usage of RO data assimilated into an NWP model. In the operational NCEP Global Forecast System (GFS) model’s Gridpoint Statistical Interpolation (GSI) DA system, BA instead of refractivity data are assimilated [
45]. RO observation error sources associated with signal measurement and processing into bending angle profiles can be grouped into measurement and calibration errors [
46]. The measurement errors include SNR performance, openloop tracking error, clock instability, and local multipath propagation; calibration errors include residual ionospheric effects, orbit determination accuracy, and clock error removal. In an NWP framework, “representativeness errors” arising from uncertainties in simulating observations from the background forecast field – i.e., forward operator errors – provide an additional observation error source. The perturbation method can theoretically predict the observation error for the individual error sources and then assemble it to establish an overall accuracy estimate.
The differences (aka apparent or perceived error) between observations and their corresponding values estimated from the background forecast contain contributions from observation and model forecast errors. One method of estimating observation error variance uses observation innovation (i.e., observationminusbackground) and shortterm forecast error statistics, as [
47] described. Under the assumption that the observation errors are uncorrelated with the forecast errors, the apparent error variance (
${{\sigma}_{a}}^{2}$) can be divided into model forecast error variance (
${{\sigma}_{b}}^{2}$) and observation error variance (
${{\sigma}_{o}}^{2})$ components:
Therefore, if the model forecast error could be reasonably well estimated, one can estimate the observation error by subtracting the model forecast error variance from the apparent error variance. Our work calculates the model forecast error using the National Meteorological Center (NMC) method [
48], which approximates
${\sigma}_{b}^{2}$ using the differences between sets of 12h and 24h GFS forecasts verifying simultaneously. The apparent error was calculated using the difference between the RO observations and 6h GFS forecasts.
A recent STAR’s RO DSC study estimated the bending angle observation error for four RO missions: COSMIC2, KOMPSAT5, GeoOptics, and Spire, from December 15, 2022, to January 15, 2023. Note that because the Spire quality does not change at different Delivery Orders, the estimated errors from the DO3 are very similar to those from other Delivery Orders and are not repeated here. A bending angle forward model developed by the STAR RO DSC (see [
33]) was used to calculate a corresponding model background forecast bending angle for each RO observation by (i) interpolating the GFS 6h forecast pressure, temperature, and water vapor fields to a grid column at the RO observation’s latitude/longitude location and time; (ii) computing the forecast BA/refractivity from these fields; and then (iii) integrating the forecast BA/refractivity field’s vertical gradient from the model top down to the observation impact height. The observation errors are estimated from the observationminusbackground sample variance (
${\sigma}_{a}$) and the model error variance estimate (
${\sigma}_{b}$) using Eq. (1).
Figure 18 shows estimates of the four RO missions’ bending angle observation errors (normalized by the mean BA profile, aka the relative BA error (%)) based on one month of observations and the corresponding GFS forecasts from 45
^{o}S to 45
^{o}N over oceans (
Figure 18a), land (
Figure 18b), and both oceans and land (
Figure 18c). The observation errors are less than 4% above 9 km and below 36 km. We also depict the relative BA error over oceans for Midlatitude South Hemisphere (from 20
^{o}S to 45
^{o}S, Figure 20d), the tropical region (from 20oN to 20oS, Figure 18e), and Midlatitude North Hemisphere (from 45oN to 20oN, Figure 20f).
Below 9 km, the observation errors increase with decreasing height and peak at around 2 km. For all four missions, the lower troposphere peak value over the ocean (~15%) is larger than that over land (~12%). These significant errors in the lower troposphere may result from greater RO retrieval uncertainty relative to the middle and upper troposphere due to multipath propagation and a smaller SNR over the midlatitudes for COSMIC2. Larger observation errors also exist in the upper stratosphere above 36 km. This likely results from larger GFS forecast field errors at these altitudes and RO retrieval uncertainty (i.e., residual ionospheric errors). The overland observation errors (
Figure 18b) are generally smaller than those over oceans. Owing to the significantly larger number of RO observations over the oceans than over land, the fullsample observation errors (
Figure 18c) are similar to the overocean observation errors shown in
Figure 18a. We can implement the defined COSMIC2, PAZ, MetopC, KOMPSAT5, and Sentinel6 RO observation errors and updated forward operator (including QC settings) generated based on these results into STAR’s offline RO data assessment system. The NCEP can also use these results for the global NWP through DA. The relative BA error over oceans is larger for the tropical region and midlatitude summer (in the southern hemisphere) than in the midlatitude winter region (in the northern hemisphere) (see
Figure 18d–f).
7. Conclusions, Discussions, and Future Work
Recently, NOAA has included GNSS RO data as one of the crucial longterm observables for weather and climate applications, just as those from IR and MW measurements. To include more GNSS RO data in the NWP system, the NOAA CWDP program started to explore the commercial RO data available on the market. CWDP awarded the first IDIQ contract to GeoOptics and Spire Incs. in 2020. Both GeoOptics and Spire RO data were collected from commercial CubeSats. [
32] examined the GeoOptics data quality. This study examines the specific quality of Spire data products during the DO3 and DO4 periods (from September 8, 2021, to January 16, 2023) for climate and weather applications. We carefully examined the Spire data penetration, precision, stability, and accuracy. We also quantified the Spire BA vertical error uncertainty (the diagonal terms in the error covariance matrix), which is crucial for the RO NWP through DA. We reach the following conclusions.
 1)
The spatial and temporal coverage. Spire has close to 30 satellites at LEO orbits during the DO3 and DO4. Although the complete global Spire RO occultation is around 20K per day during the performance periods, CWDP purchased about 3000 Spire occultation profiles per day during the DO3 and 5500 Spire per day in DO4. While COSMIC2 has an inclination angle of 24^{o}, Spire is at the Sunsynchronized orbits. While Spire data cover the globe and are distributed relatively evenly across all latitudes, COSMIC2 observation can cover all latitudes within [45^{o}S, 45^{o}N]. The Spire has observations peaking local time ranges in 23, 910, 1415, and 2122, while KOMPSAT5 observation peaking local time is located at 6 and 18, and COSMIC2 observations are independent of the local time.
 2)
The effect of SNR on Spire data penetration. The lowest penetration height is an essential indicator of RO data quality. The lowest penetration height of RO tracking is usually related to the data’s SNR and the atmosphere’s dryness. Although with lower SNR in general, the pattern of the lowest penetration height for Spire is similar to those for COSMIC2. The Spire and COSMIC2 penetrate heights are around 0.6 to 0.8 km altitude at the tropical oceans. We also compared the lowest penetration height of 80% of the total data for different RO missions at different latitudinal zones. GeoOptics and Spire have lower penetration heights (for 80% of the total data) than COSMIC2 at latitudinal zones [45^{o}S, 30^{o}S] and [30^{o}N, 45^{o}N]. This may be owing to COSMIC2 SNR being lower at latitudinal zones [45^{o}S, 30^{o}S] and [30^{o}N, 45^{o}N].
 3)
The Spire data precision and stability. We used the SpireSpire SRO pairs to quantify the Spire precision for bending angle, dry temperature, and water vapor mixing ratio. Results showed that the mean differences are very close to zero from the surface to 40 km altitude for all three physical quantities. The standard deviations from the bending angle, dry temperature, and water vapor mixing ratio are similar to those from other RO missions, such as COSMIC2 and COSMIC1. We also compare the fractional mean BA difference for Spire S124 and S120 from surface to 40 km altitudes but separated with GPS, GLONASS, and GALILEO, respectively. Although the SNRs from different emitters ranges are different, the mean difference for GPS, GLONASS, and GALILEO are all close to zero with the STD of 1.81, 1.78, and 1.78, respectively. We also compared the precision of COSMIC1 (SRO pairs collected from 2006) and COSMIC2 (SRO pairs collected from 2021) and compared with those from Spire (SRO pairs collected from 2022). All comparisons are within [45^{o}N45^{o}S]. We found that COSMIC2 STDs over midlatitude are slightly more significant than those from Spire, which may be owing to their lower SNR over the same regions. Although it was not shown in this paper, the receiver quality for different flight modules is very close. Although using slightly different receivers, the precision of Spire STRASP receivers is of the same quality as those of COSMIC2 TGRS receivers.
 4)
The effect of SNR on Spire retrieval accuracy. The UCAR Spire retrievals are consistent with those from STARindependent derived BA retrievals. The independent statistical analysis and validation from ERA5 and direct bending angle profile comparison from these SRO cases above 35 km suggest: i) RO bending angle profiles retrieved from GPS satellites are, in general, better than those from GLONASS satellites; ii) Significant uncertainty exists for RO bending angle profiles from GLONASS, which may indicate potential RO phase issue related to the clock, residual ionospheric effects, receiver noise, and orbit determination errors for GLONASS. We validated Spire temperature and water vapor profiles by comparing them with collocated radiosonde insitu data. Generally, over the height region between 8 km and 16.5 km, the RS41 RAOB matches Spire temperature profiles very well with temperature biases < 0.02 K. Over the height range from 17.8 to 26.4 km, the temperature biases are ~0.034 K with RS41 RAOB being warmer.
 5)
Estimates of the error covariance matrix for NWP. Below 9 km, the RO observation errors increase with decreasing height and peak at around 2 km. For all Spire, COSMIC2, KOMPSAT5, and GeoOptics missions, the lower troposphere peak value over the ocean (~15%) is more significant than that over land (~12%). These significant errors in the lower troposphere may result from greater RO retrieval uncertainty relative to the middle and upper troposphere due to multipath propagation and a smaller SNR over the midlatitudes for COSMIC2. The COSMIC2 retrieval uncertainty is slightly more significant over the oceans at the midlatitudes (45^{o}N30^{o}N and 30 ^{o}S45^{o}S), which may also be owing to COSMIC2 SNR being lower at those latitudinal zones.
[
31] has demonstrated that the accuracy and uncertainty of retrieved water vapor and refractivity profiles for COSMIC2 from higher SNR (> 2000 V/V) signals are similar to those from the lower SNR (less than 1000 V/V) signals. [
51] demonstrated that even with smaller SNR the retrievals uncertainty from COSMIC (SNR ~1200V/V) is almost identical to that of COSMIC2. However, the SNR may not be the only factor that affects the RO retrieval uncertainty. For example, the horizontal water vapor irregularity and turbulence may also affect the RO retrieval uncertainty (JPL, personal communication), especially in the lower troposphere. A simulation study showed that the retrieval biases and uncertainty are identical for all SNR groups while we increase the turbulence effect.
In this study, we also notice that the antenna’s viewing geometry affects the SNRs’ latitudinal distribution, affecting the observation error distribution. As discussed in
Section 3, the factors that affect the SNR include i) the GNSS emitter’s signal power, ii) the receiver intermediate frequency bandwidth, iii) RO antenna design, iv) the antenna gain pattern related to the viewing geometry, and v) the azimuth angle, where the antenna viewing geometry directly affects the SNR latitudinal distribution. With the highgain sidemounted antenna for both L1 and L2 frequencies, the Spire SNR for GPS, GLONASS, and GALILEO are uniformly distributed at all latitudes. Unlike Spire, the COSMIC2 RO antenna points to the nadir, and the positiontracking antenna points to the sideway. As a result, the COSMIC2 SNR is smaller in the midlatitude. Generally, COSMIC2 SNR has a broader distribution (from 200 V/V to 2000 V/V) from 30
^{o}N30
^{o}S. The COSMIC2 event distribution as a function of the antenna view angle was also shown by Chen et al. (2021). The geolocation distribution of COSMIC2 SNR may affect the COSMIC2 penetration depth at different latitudes. We demonstrated that owing to the viewing geometry, the COSMIC2 SNR is lowest (~1000 V/V) in midlatitudes (45
^{o}N30
^{o}N and 30
^{o}S45
^{o}S). As a result, the COSMIC2 retrieval uncertainty at the midlatitudes is higher than those from Spire and other RO missions.
The GNSS landscape has been rapidly evolving. Besides GeoOptics and Spire, more commercial RO data are available on the market (i.e., PlanetiQ and others). More than 100 GNSS RO sensors are currently in orbit to track more signals (i.e., GPS, GLONASS, QZSS, IRNSS, GALILEO, Beidou, and GPS III). To use all the above different tracking and receiver system for climate and NWP applications, we need to carefully examine the quality of each receiver and the interconsistency of the retrieved data products. NOAA STAR has become a GNSS RO DSC (see
https://www.star.nesdis.noaa.gov/smcd/GNSSRO/RO/index.php and [
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41]. We will continue developing the RO processing packages for PlanetiQ and other RO missions and use our validation system (see [
37]) to provide independent validation results. That will be for future work.
Figure 1.
The distribution of the normalized SNR frequency sample numbers (defined as the sample numbers for each SNR bin normalized to the maximum number of the SNR bin) for GPS (in red line), GLONASS (in orange line), and GALILEO (in blue line) signals on a) Spire, b) COSMIC2, and c) KOMPSAT5 over the CWDP DeliveryOrder 3 (DO3, from September 8, 2021 to March 15, 2022). The total number of observations from each GNSS satellite is listed in the Figures.
Figure 1.
The distribution of the normalized SNR frequency sample numbers (defined as the sample numbers for each SNR bin normalized to the maximum number of the SNR bin) for GPS (in red line), GLONASS (in orange line), and GALILEO (in blue line) signals on a) Spire, b) COSMIC2, and c) KOMPSAT5 over the CWDP DeliveryOrder 3 (DO3, from September 8, 2021 to March 15, 2022). The total number of observations from each GNSS satellite is listed in the Figures.
Figure 2.
Spatial distribution of the RO sample numbers for each 5^{o}×5^{o} grid for a) Spire, b) COSMIC2, and c) KOMPSAT5 for the whole DO3 period.
Figure 2.
Spatial distribution of the RO sample numbers for each 5^{o}×5^{o} grid for a) Spire, b) COSMIC2, and c) KOMPSAT5 for the whole DO3 period.
Figure 3.
Same as
Figure 2, but for the hourly local time distribution binned at 5
^{o} latitude bin for a) Spire, b) COSMIC2, and c) KOMPSAT5 for the DO3 period. The observation numbers at each box are indicated by the color bar.
Figure 3.
Same as
Figure 2, but for the hourly local time distribution binned at 5
^{o} latitude bin for a) Spire, b) COSMIC2, and c) KOMPSAT5 for the DO3 period. The observation numbers at each box are indicated by the color bar.
Figure 4.
Latitudinal distribution for Spire L1 SNR from February 15 to March 15, 2022 for a) GPS, b) GLONASS, and c) GALILEO.
Figure 4.
Latitudinal distribution for Spire L1 SNR from February 15 to March 15, 2022 for a) GPS, b) GLONASS, and c) GALILEO.
Figure 5.
Latitudinal distribution for COSMIC2 L1 SNR from February 15 to March 15, 2022, for a) GPS and b) GLONASS. .
Figure 5.
Latitudinal distribution for COSMIC2 L1 SNR from February 15 to March 15, 2022, for a) GPS and b) GLONASS. .
Figure 6.
The global mean of the lowest penetration height in June 2022 binned into 5º$\times $
Figure 6.
The global mean of the lowest penetration height in June 2022 binned into 5º$\times $
Figure 7.
a) the RO penetration percentage (defined as the observation number at each penetration depth relative to the observation number at 8 km) over oceans within [45^{o}N, 45^{o}S] during the DO3 period and b) the corresponding numbers of observations from surface to 14 km altitude for COSMIC2, Spire, KOMPSAT5, and PAZ.
Figure 7.
a) the RO penetration percentage (defined as the observation number at each penetration depth relative to the observation number at 8 km) over oceans within [45^{o}N, 45^{o}S] during the DO3 period and b) the corresponding numbers of observations from surface to 14 km altitude for COSMIC2, Spire, KOMPSAT5, and PAZ.
Figure 8.
The mean difference (in red line) and standard deviation (in green line) for a) fractional bending angle, b) dry temperature, and c) water vapor mixing ratio comparison for the Spire S128 and S119 DO3 SRO pairs. .
Figure 8.
The mean difference (in red line) and standard deviation (in green line) for a) fractional bending angle, b) dry temperature, and c) water vapor mixing ratio comparison for the Spire S128 and S119 DO3 SRO pairs. .
Figure 9.
The DO3 SRO fractional BA comparison for Spire S120 and S124 receivers for GPS (in red line), GLONASS (in orange line), and GALILEO (in blue line) for a) the fractional mean difference, b) the standard deviation, and c) the observation numbers from surface to 40 km altitude.
Figure 9.
The DO3 SRO fractional BA comparison for Spire S120 and S124 receivers for GPS (in red line), GLONASS (in orange line), and GALILEO (in blue line) for a) the fractional mean difference, b) the standard deviation, and c) the observation numbers from surface to 40 km altitude.
Figure 10.
The fractional BA difference, the corresponding standard deviation, and the sample number at each vertical level from surface to 40 km altitude for Spire (in red line), COSMIC2 (in green line), and COSMIC1 (in blue line) for a) midlatitude for the southern hemisphere (20°S45°S), b) tropical region (20°N20°S), and c) midlatitude northern hemisphere (45°N20°N). We also compute the standard error of the mean (SEM) in a vertical line superimposed on the mean. .
Figure 10.
The fractional BA difference, the corresponding standard deviation, and the sample number at each vertical level from surface to 40 km altitude for Spire (in red line), COSMIC2 (in green line), and COSMIC1 (in blue line) for a) midlatitude for the southern hemisphere (20°S45°S), b) tropical region (20°N20°S), and c) midlatitude northern hemisphere (45°N20°N). We also compute the standard error of the mean (SEM) in a vertical line superimposed on the mean. .
Figure 11.
The fractional BA SpireRO comparison for a) mean differences, b) the standard deviations, and c) observation numbers for the SpirePAZ, SpireKOMPSAT5, SpireMetopB, SpireMetopC, and SpireTerraSARX SRO pairs during the D04 period.
Figure 11.
The fractional BA SpireRO comparison for a) mean differences, b) the standard deviations, and c) observation numbers for the SpirePAZ, SpireKOMPSAT5, SpireMetopB, SpireMetopC, and SpireTerraSARX SRO pairs during the D04 period.
Figure 12.
Bending angle profile comparison between COSMIC2 and Spire for a) fractional BA profile differences, b) the standard deviations, and c) vertical observation numbers for five COSMIC2 SNR groups (i.e., 0–500 V/V, 500–1000 V/V, 1000–1500 V/V, 1500–2000 V/V, >2000 V/V).
Figure 12.
Bending angle profile comparison between COSMIC2 and Spire for a) fractional BA profile differences, b) the standard deviations, and c) vertical observation numbers for five COSMIC2 SNR groups (i.e., 0–500 V/V, 500–1000 V/V, 1000–1500 V/V, 1500–2000 V/V, >2000 V/V).
Figure 13.
Bending angle profile comparison between STAR and UCAR Spire for GPS (in red line), GLONASS (in orange line), and GALILEO (in blue line) for a) the fractional mean difference, b) the standard deviation, and c) the observation numbers from surface to 40 km altitude. .
Figure 13.
Bending angle profile comparison between STAR and UCAR Spire for GPS (in red line), GLONASS (in orange line), and GALILEO (in blue line) for a) the fractional mean difference, b) the standard deviation, and c) the observation numbers from surface to 40 km altitude. .
Figure 14.
SpireERA5 mean BA fractional difference and corresponding standard deviations for a) 45°N to 45°S, b) 45°N to 30°N, c) 30°N to 30°S, and d) 30°S to 45°S. Similar to a)d), we also compared the COSMIC2 and ERA5 BA fractional difference and corresponding standard deviations in e) 45°N to 45°S, f) 45°N to 30°N, g) 30°N to 30°S, and h) 30°S to 45°S.
Figure 14.
SpireERA5 mean BA fractional difference and corresponding standard deviations for a) 45°N to 45°S, b) 45°N to 30°N, c) 30°N to 30°S, and d) 30°S to 45°S. Similar to a)d), we also compared the COSMIC2 and ERA5 BA fractional difference and corresponding standard deviations in e) 45°N to 45°S, f) 45°N to 30°N, g) 30°N to 30°S, and h) 30°S to 45°S.
Figure 15.
a) Differences (dash lines) and uncertainties (dot lines) of Spire temperature profiles retrieved by UCAR wetPf2 compared to RS41 RAOB data. c) Differences (dash lines) and uncertainties (dot lines) of Spirespecific humidity profiles retrieved by UCAR wetPf2 compared to RS41 RAOB data. b) shows the number of collocated SpireRAOB temperature profiles, and d) is the number of SpireRAOB water vapor profiles. .
Figure 15.
a) Differences (dash lines) and uncertainties (dot lines) of Spire temperature profiles retrieved by UCAR wetPf2 compared to RS41 RAOB data. c) Differences (dash lines) and uncertainties (dot lines) of Spirespecific humidity profiles retrieved by UCAR wetPf2 compared to RS41 RAOB data. b) shows the number of collocated SpireRAOB temperature profiles, and d) is the number of SpireRAOB water vapor profiles. .
Figure 16.
a) heightdependent mean temperature differences (K) of UCAR wetPf2 versus RS41 RAOB in the zones of daytime (SZA < 80^{o}), nighttime (SZA > 100^{o}), and dusk/dawn (80^{o} < SZA <100^{o}) in the upper troposphere and lower stratosphere. b) the heightdependent profile numbers for the analysis.
Figure 16.
a) heightdependent mean temperature differences (K) of UCAR wetPf2 versus RS41 RAOB in the zones of daytime (SZA < 80^{o}), nighttime (SZA > 100^{o}), and dusk/dawn (80^{o} < SZA <100^{o}) in the upper troposphere and lower stratosphere. b) the heightdependent profile numbers for the analysis.
Figure 17.
a) the heightdependent mean humidity differences (g/kg) of UCAR wetPf2 versus RS41 RAOB for daytime (SZA < 80^{o}), nighttime (SZA > 100^{o}), and dusk/dawn (80^{o} < SZA <100^{o}). Corresponding profile numbers are shown in b).
Figure 17.
a) the heightdependent mean humidity differences (g/kg) of UCAR wetPf2 versus RS41 RAOB for daytime (SZA < 80^{o}), nighttime (SZA > 100^{o}), and dusk/dawn (80^{o} < SZA <100^{o}). Corresponding profile numbers are shown in b).
Figure 18.
Fractional BA observation errors (in %) estimated for the region within [45^{o}S, 45^{o}N] for a) over oceans, b) over land, and c) over oceans and land, d) over ocean [45^{o}S, 20^{o}S], e) over ocean [20^{o}S, 20^{o}N], f) over ocean [20^{o}N, 45^{o}N]. One month (from December 15, 2020, to January 15, 2021) of COSMIC2, KOMPSAT5, GeoOptics, and Spire bending angle observations were used for generating these figures.
Figure 18.
Fractional BA observation errors (in %) estimated for the region within [45^{o}S, 45^{o}N] for a) over oceans, b) over land, and c) over oceans and land, d) over ocean [45^{o}S, 20^{o}S], e) over ocean [20^{o}S, 20^{o}N], f) over ocean [20^{o}N, 45^{o}N]. One month (from December 15, 2020, to January 15, 2021) of COSMIC2, KOMPSAT5, GeoOptics, and Spire bending angle observations were used for generating these figures.
Table 1.
The lowest penetration height of 80% of the total data for different RO missions at different latitudinal zones.
Table 1.
The lowest penetration height of 80% of the total data for different RO missions at different latitudinal zones.

10^{o}N10^{o}S 
30^{o}N10^{o}N 
10^{o}S30^{o}S 
45^{o}N30^{o}N 
30^{o}S45^{o}S 
60^{o}N45^{o}N 
45^{o}N60^{o}S 
90^{o}N60^{o}N 
60^{o}S90^{o}S 
COSMIC2 
0.85 
0.90 
0.75 
1.35 
1.10 




Spire 
0.90 
0.90 
0.75 
0.80 
0.55 
0.45 
0.25 
0.45 
0.20 
KOMPSAT5 
1.85 
1.50 
1.15 
0.40 
0.95 
0.35 
0.40 
0.25 
0.20 
PAZ 
2.65 
1.85 
2.05 
0.90 
1.30 
0.45 
0.45 
0.35 
0.35 
Table 2.
The mean BA fractional difference and the corresponding standard deviations, and the sample number at 10 km altitude for the SpirePAZ, SpireKOMPSAT5, SpireMetopB, SpireMetopC, and SpireTerraSARX SRO pairs from surface to 40 km altitude.
Table 2.
The mean BA fractional difference and the corresponding standard deviations, and the sample number at 10 km altitude for the SpirePAZ, SpireKOMPSAT5, SpireMetopB, SpireMetopC, and SpireTerraSARX SRO pairs from surface to 40 km altitude.

Mean Difference 
standard deviation 
Sample Number at 10 km altitude 
Spire PAZ 
0.01% 
3.25% 
113 
Spire KOMSAT5 
0.18% 
3.20% 
54 
Spire MetopA GRAS 
0.12% 
1.94% 
816 
Spire  MetopB GRAS 
0.06% 
2.89% 
792 
Spire TerraSARX 
0.13% 
3.35% 
42 
Table 3.
The mean fractional BA difference, standard deviation of the mean difference, and sample number at 10 km altitude for SpireCOSMIC2 SRO pairs for different COSMIC2 SNR groups (i.e., 0–500 V/V, 500–1000 V/V, 1000–1500 V/V, 1500–2000 V/V, >2000 V/V).
Table 3.
The mean fractional BA difference, standard deviation of the mean difference, and sample number at 10 km altitude for SpireCOSMIC2 SRO pairs for different COSMIC2 SNR groups (i.e., 0–500 V/V, 500–1000 V/V, 1000–1500 V/V, 1500–2000 V/V, >2000 V/V).

Mean 
standard deviation 
Sample Number at 10 km altitude 
0–500 V/V 
0.12% 
4.15% 
364 
500–1000 V/V 
0.10% 
4.14% 
1727 
1000–1500 V/V 
0.24% 
3.97% 
2559 
1500–2000 V/V 
0.16% 
3.87% 
2325 
> 2000 V/V 
0.19% 
4.07% 
332 
Table 4.
The mean and standard deviation for the fractional refractivity difference between STAR and UCAR Spire for GPS, GLONASS, and GALILEO.
Table 4.
The mean and standard deviation for the fractional refractivity difference between STAR and UCAR Spire for GPS, GLONASS, and GALILEO.

Mean 
standard deviation 
GPS 
0.06% 
0.73% 
GLONASS 
0.06% 
0.78% 
GALILEO 
0.06% 
0.69% 
Table 5.
Mean temperature biases (uncertainties) (K) and mean humidity biases (uncertainties) (g/kg) between Spire RO retrievals and RS41 RAOB observations over different height regions.
Table 5.
Mean temperature biases (uncertainties) (K) and mean humidity biases (uncertainties) (g/kg) between Spire RO retrievals and RS41 RAOB observations over different height regions.
Spire Retrieval 
µ(ΔT) (σ(ΔT))(K) (811 km) 
µ(ΔT) (σ(ΔT)) (K) (12.516.5 km) 
µ(ΔT) (σ(ΔT)) (K) (17.826.4 km) 
µ(ΔH) (σ(ΔH)) (g/kg) (below 4.2 km) 
µ(ΔH) (σ(ΔH)) (g/kg) (4.88.4 km) 
UCAR wetPf2 
0.02(1.13) 
0.00(1.22) 
0.01(1.40) 
0.19(1.02) 
0.04(0.45) 
Table 6.
The mean temperature bias (uncertainty) (K) of UCAR Spire wetPf2 versus RS41 RAOB comparisons in three SZA zones over three height regions in the upper and lower stratosphere.
Table 6.
The mean temperature bias (uncertainty) (K) of UCAR Spire wetPf2 versus RS41 RAOB comparisons in three SZA zones over three height regions in the upper and lower stratosphere.
Height Range 
Day 
Night 
Dusk/Dawn 
811 km 
0.06(1.10) 
0.04(1.15) 
0.01(1.21) 
12.516.5 km 
0.01(1.20) 
0.02(1.25) 
0.02(1.25) 
17.826.4 km 
0.02(1.38) 
0.05(1.46) 
0.06(1.35) 
Table 7.
Mean humidity differences (uncertainties) (g/kg) between RO retrievals and RS41 RAOB observations over two height regions and three SZA zones.
Table 7.
Mean humidity differences (uncertainties) (g/kg) between RO retrievals and RS41 RAOB observations over two height regions and three SZA zones.
Height Range 
Day 
Night 
Dusk/Dawn 
Below 4.2 km 
0.17(1.03) 
0.23(1.07) 
0.15(0.89) 
4.88.4 km 
0.04(0.45) 
0.06(0.49) 
0.02(0.39) 