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Accurate estimation of clocks, for example for the Gravity Recovery And Climate Experiment (GRACE) twin-satellites, is a critical part of precise orbit determination (POD) that ensures temporal gravity inversion. Characterizing the periodic variations of the receiver clocks is critical for precise clock modeling and prediction. In this study, the receiver clock is estimated using two different POD procedure: kinematic and reduced-dynamic approaches. Choices and the number of orbital parameters estimated in POD process affect the clock estimates, e.g., there are 8895 and 34,560 total parameters in the reduced-dynamic and kinematic approaches, respectively. In the both cases, the periodic variations of GRACE receiver clock are mainly dominated by the GPS orbit period, as well as once- (1-pr) and twice-per-revolution (2-pr) effects. Here the 1-pr effect is coupled with the relativistic effect, resulting in a difficulty to separate both signals. The clock amplitudes caused by the GPS orbit period, 1-pr and 2-pr are about 0.1, 0.03 and 0.01 ns, respectively. The GPS orbit period is almost one order magnitude larger than the 1- and 2-pr effect. The 0.1-ns amplitude of the 12-h periodic variation is equivalent to a 3-cm error in range. Such a systematic error should be considered in the receiver clock modeling for both the improvement of positioning accuracy and the reduction of number of unknown parameters, if the precise point positioning (PPP) technique is used for the orbit determination of the GRACE. Keywords: GPS, GRACE, Precision orbit determination, Clock modeling

Satellite altimetry has been proven as an effective technology to accurately measure water level, ice elevation, and flat land surface changes since the 1990s. To overcome limitations of pulse-limi...

Global sea level rise due to an increasingly warmer climate has begun to induce hazards, adversely affecting the lives and properties of people residing in low-lying coastal regions and islands. Therefore, it is important to monitor and understand variations in coastal sea level covering offshore regions. Signal-to-noise ratio (SNR) data of Global Navigation Satellite System (GNSS) have been successfully used to robustly derive sea level heights (SLHs). In Taiwan, there are a number of continuously operating GNSS stations, not originally installed for sea level monitoring. They were established in harbors or near coastal regions for monitoring land motion. This study utilizes existing SNR data from three GNSS stations (Kaohsiung, Suao, and TaiCOAST) in Taiwan to compute SLHs with two methods, namely, Lomb–Scargle Periodogram (LSP)-only, and LSP aided with tidal harmonic analysis developed in this study. The results of both methods are compared with co-located or nearby tide gauge records. Due to the poor quality of SNR data, the worst accuracy of SLHs derived from traditional LSP-only method exceeds 1 m at the TaiCOAST station. With our procedure, the standard deviations (STDs) of difference between GNSS-derived SLHs and tide gauge records in Kaohsiung and Suao stations decreased to 10 cm and the results show excellent agreement with tide gauge derived relative sea level records, with STD of differences of 7 cm and correlation coefficient of 0.96. In addition, the absolute GNSS-R sea level trend in Kaohsiung during 2006–2011 agrees well with that derived from satellite altimetry. We conclude that the coastal GNSS stations in Taiwan have the potential of monitoring absolute coastal sea level change accurately when our proposed methodology is used.

Rapid sea level rise, a severe consequence of global warming, could significantly damage the lives and properties of numerous human beings living in low-lying coastal areas. Therefore, realizing and monitoring coastal sea level variations are of great importance for human society. Conventionally, sea level heights are measured by using tide gauges; however, the records are contaminated by vertical land motions which are difficult to be separated. Recently, Global Navigation Satellite System Reflectometry (GNSS-R) technology has been proved to effectively monitor the coastal sea level changes from GNSS signal-to-noise ratio (SNR) data. However, the generation of detrended SNR ( SNR) depending on different satellite elevation angle intervals via a quadratic fitting, considerably influences the accuracy of sea level retrievals. Moreover, the quadratic fitting cannot perfectly describe the trend of SNR data. Therefore, we proposed a method combining ensemble empirical mode decomposition (EEMD) and ocean tide model to compute SLHs. EEMD can decompose the original SNR data into several intrinsic mode functions (IMFs) corresponding to specific frequencies. Then, Lomb-Scargle Periodogram (LSP) is applied to calculate the dominant frequency of the IMF with maximum spectral power. EEMD is not only suitable for dealing with nonlinear and nonstationary data but also eliminates the mode mixing problem of empirical mode decomposition (EMD) by adding white noises. In addition, we set an empirical SLH interval from ocean tide model as a quality control. In this study, the existing GNSS stations at the coasts of Taiwan are used to examine the proposed approach and then compare the results with those from the traditional quadratic fitting. Finally, the measurements from co-located or nearby traditional tide gauges are served as ground truth to evaluate the accuracy and stability of the mentioned methods.

We assess the impact of orbit modeling on the origin offsets between GRACE kinematic and reduced-dynamic orbits. The origin of the kinematic orbit is the center of IGS network (CN), whereas the origin of the reduced-dynamic orbit is assumed to be the center of mass of the Earth (CM). Theoretically, the origin offset between these two orbits is associated with the geocenter motion. However, the dynamic property of the reduced-dynamic orbit is highly related to orbit parameterizations. The assessment of the F10.7 impact on the geocenter motion is implemented by using different orbit parameterization setups in the reduced-dynamic method. We generate two types of reduced-dynamic orbits using 15 and 240 empirical parameters per day from 2005 to 2012. The empirical parameter used in Bernese GNSS Software is called piece-wise constant empirical acceleration (PCA) and is mainly to absorb the non-gravitational forces mostly related to the atmospheric drag and solar radiation pressure. The differences between kinematic and dynamic orbits can serve as a measurement for geocenter. The RMS value of the geocenter measurement in the 15-PCA case is approximately 3.5 cm and approximately 2 cm in the 240-PCA case. The correlation between the orbit difference and F10.7 is about 0.90 in the 15-PCA case and −0.10 to 0 in the 240-PCA case. This implies that the reduced-dynamic orbit modeled with 240 PCAs absorbs the F10.7 variation, which aliases to the 15-PCA orbit solution. The annual amplitudes of the geocenter motion are 3.1, 3.1 and 2.5 mm in the 15-PCA case, compared to 0.9, 2.0 and 1.3 mm in the 240-PCA case in the X, Y and Z components, respectively. The 15-PCA solution is thus closer to the geocenter motions derived from other space-geodetic techniques. The proposed method is limited to the parameterizations in the reduced-dynamic approach.

In this study, we determine the near real-time (NRT) clocks of the Global Positioning System (GPS) and Globalnaya Navigatsionnaya Sputnikovaya Sistema (GLONASS) satellites in the Taiwan RO Process System (TROPS), which is mainly designed for the data processing in both the FORMOSAT-3/COSMIC (F3C) and FORMOSAT-7/COSMIC-2 (F7C2) satellite missions. The accuracy of GNSS clocks defines the quality of the atmospheric excess phase, which is used for the retrieval of bending angle profiles in GNSS radio occultation (RO) observations. The accuracy of the NRT GNSS clocks is assessed by comparing the clock rate, clock stability and clock-induced positioning error on receivers with the final solutions given by the European Space Agency (ESA). Overall, the standard deviations of the clock rates from TROPS agree with those from ESA within 0.05 mm/s over 2304 clock solutions. Additionally, we find that the clock stability of the GPS Block IIF type (3 × 10−13) is an order of magnitude better than that of IIR Block types (3 × 10−12) over a time interval of 30 s. In comparison, the stabilities of GLONASS clocks are approximately 3 × 10−12. We quantify the NRT clock error on the receiver positioning by using the precise point positioning technique obtained from the Bernese GNSS software. The 3-dimensional clock-induced positioning error is approximately 3.3, 3.2 and 0.9 cm for station AUCK and 6.9, 6.3 and 3.1 cm for station NRC1 for the GPS-only, GLONASS-only and GPS + GLONASS cases, respectively. For GNSS-RO applications, the bending angle profiles derived using TROPS GPS clocks agree with the COSMIC Data Analysis and Archive Center products to within 0.01–1.00 μrad. However, this is not the case for the GLONASS clock, because the GLONASS clock-induced errors on the RO profile are 10–100 times greater than those induced by the GPS clock. This suggests that different weightings should be used for RO applications, such as data assimilation, when different satellite clocks are involved in GNSS-RO retrievals. This study serves as a reference for assessing the impact of GNSS clocks on both GNSS-POD (precise orbit determination) and GNSS-RO in preparation for the F7C2 satellite mission.

GPS Radio Occultation (RO) is a space-based technique for sounding the Earth's atmosphere. This technique has demonstrated great potential for improving numerical weather prediction and climate monitoring. This investigation utilises FORMOSAT-3/COSMIC RO data to identify the differences between the results obtained using two different data processing packages – the Radio Occultation Processing Package (ROPP) and the COSMIC Data Analysis and Archive Center (CDAAC) software package. The introduced RO measurements for two software packages are all obtained from CDAAC dataset. This study analyses 20,210 events located in the Australian region in the year 2010. The results of this study show a negative bias between the two software packages in the bending angle at heights below approximately 5 km. The refractivity also shows a negative bias, which is consistent with previous results from the Global Navigation Satellite System Receiver for Atmospheric Sounding Satellite Application Facilities (GRAS SAF) report....

The COSMIC-2 mission is a follow-on mission of the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) with an upgraded payload for improved radio occultation (RO) applications. The objective of this paper is to develop a near-real-time (NRT) orbit determination system, called NRT National Chiao Tung University (NCTU) system, to support COSMIC-2 in atmospheric applications and verify the orbit product of COSMIC. The system is capable of automatic determinations of the NRT GPS clocks and LEO orbit and clock. To assess the NRT (NCTU) system, we use eight days of COSMIC data (March 24-31, 2011), which contain a total of 331 GPS observation sessions and 12 393 RO observable files. The parallel scheduling for independent GPS and LEO estimations and automatic time matching improves the computational efficiency by 64% compared to the sequential scheduling. Orbit difference analyses suggest a 10-cm accuracy for the COSMIC orbits from the NRT (NCTU) system, and it is consistent as the NRT University Corporation for Atmospheric Research (URCA) system. The mean velocity accuracy from the NRT orbits of COSMIC is 0.168 mm/s, corresponding to an error of about 0.051 μrad in the bending angle. The rms differences in the NRT COSMIC clock and in GPS clocks between the NRT (NCTU) and the postprocessing products are 3.742 and 1.427 ns. The GPS clocks determined from a partial ground GPS network [from NRT (NCTU)] and a full one [from NRT (UCAR)] result in mean rms frequency stabilities of 6.1E-12 and 2.7E-12, respectively, corresponding to range fluctuations of 5.5 and 2.4 cm and bending angle errors of 3.75 and 1.66 μrad .

We provide suggestions for the approved COSMIC-2 satellite mission regarding the field of view (FOV) and the clock stability of its future GNSS receiver based on numerical analyses using COSMIC GPS data. While the GRACE GPS receiver is mounted on the zenith direction, the precise orbit determination (POD) antennas of COSMIC are not. The COSMIC antenna design results in a narrow FOV and a reduction in the number of GPS observations. To strengthen the GPS geometry, GPS data from two POD antennas of COSMIC are used to estimate its orbits. The phase residuals of COSMIC are at the centimeter level, compared to the millimeter level of GRACE. The receiver clock corrections of COSMIC and GRACE are at the microsecond and nanosecond levels, respectively. The clock spectra of COSMIC at the frequencies of 0---0.005 Hz contain significant powers, indicating potential systematic errors in its clock corrections. The clock stability, expressed by the Allan deviation, of COSMIC ranges from 10?9 to 10?11 over 1 to 104 s, compared to 10?12 to 10?14 for GRACE. Compared to USO-based clock of GRACE, the clock of COSMIC is degraded in its stability and is linked to the reduction of GPS data quality. Lessons for improvement of COSMIC-2 over COSMIC in FOV and receiver clock stability are given.

An attitude determination and control system (ADCS) is critical to satellite attitude maneuvers and to the coordinate transformation from the inertial frame to the spacecraft frame. This paper shows specific sensors in the ADCS of the satellite mission FORMOSAT-3/COSMIC (F3/C) and the impact of the ADCS quality on orbit accuracy. The selection of main POD antenna depends on the beta angles of the different F3/C satellites (for FM2 and FM4) during the inflight phase. In particular, under the eclipse, alternative attitude sensors are activated to replace the Sun sensors, and such a sensor change leads to anomalous GPS phase residuals and a degraded orbit accuracy. Since the nominal attitude serves as a reference for ADCS, the 3-dimensional attitude-induced errors in reduced dynamic orbits over selected days in 2010 show 9.35, 10.78, 4.97, 5.48, 7.18, and 6.89 cm for FM1–FM6. Besides, the 3-dimensional velocity errors induced by the attitude effect are 0.10, 0.10, 0.07, 0.08, 0.09, and 0.10 for FM1–FM6. We analyze the quality of the observed attitude transformation matrix of F3/C and its impact on kinematic orbit determination. With 249 days of GPS in 2008, the analysis leads to the following averaged 3-dimensional attitude-induced orbit errors: 2.72, 2.62, 2.37, 1.90, 1.70, and 1.99 cm for satellites FM1–FM6. Critical suggestions of geodetic payloads for the follow-on mission of F3/C are presented based on the current result.

The precise orbit determination antennas of F3/C and GRACE-A satellites are from the same manufacturer, but are installed in different configurations. The current orbit accuracy of F3/C is 3 cm at arcs with good GPS data, compared to 1 cm of GRACE, which has a larger ratio of usable GPS data. This paper compares the qualities of GPS observables from F3/C and GRACE. Using selected satellites and time spans, the following average values for the satellite F3/C and satellite A of GRACE are obtained: multipath effect on the pseudorange P1, 0.78 and 0.38 m; multipath effect on the pseudorange P2, 1.03 and 0.69 m; occurrence frequency of cycle slip, 1/29 and 1/84; standard error of unit weight, 4 and 1 cm; dynamic–kinematic orbit difference, 10 and 2 cm. For gravity determination using F3/C GPS data, a careful selection of GPS data is critical. With six satellites in orbit, F3/C’s large amount of GPS data will make up the deficiency in data quality.

The precise GPS high-low tracking data from the joint Taiwan-USA mission FORMOSAT-3/COSMIC (COSMIC) can be used for gravity recovery. The current orbital accuracy of COSMIC kinematic orbit is 2 cm and is better than 1 cm for 60-s normal points. We model the perturbing forces acting on the COSMIC spacecraft based on standard models of orbit dynamics. The major tool for the numerical work of force modeling is NASA Goddard's GEODYN II software. Considering that COSMIC spacecraft are not equipped with accelerometers, the accelerations due to atmospheric drag, solar radiation pressure, and other minor surface forces are modeled by estimating relevant parameters over one orbital period from COSMIC's kinematic and reduced dynamic orbits. We carry out experimental solutions of time-varying geopotential coefficients using one month of COSMIC kinematic orbits (August 2006). With the nongravity origin forces properly modeled by GEODYN II, residual orbital perturbations (difference between kinematic and reference orbits) are assumed to be linear functions of time-varying geopotential coefficients and are used as observations to estimate the latter. Both COSMIC and combined COSMIC and GRACE gravity solutions are computed. The COSMIC solution shows some well-known temporal gravity signatures but contains artifacts. The combined COSMIC and GRACE solution enhances some local temporal gravity signatures in the GRACE solution.

The joint Taiwan–US mission FORMOSAT-3/ COSMIC (COSMIC) was launched on April 17, 2006. Each of the six satellites is equipped with two POD antennas. The orbits of the six satellites are determined from GPS data using zero-difference carrier-phase measurements by the reduced dynamic and kinematic methods. The effects of satellite center of mass (COM) variation, satellite attitude, GPS antenna phase center variation (PCV), and cable delay difference on the COSMIC orbit determination are studied. Nominal attitudes estimated from satellite state vectors deliver a better orbit accuracy when compared to observed attitude. Numerical tests show that the COSMIC COM must be precisely calibrated in order not to corrupt orbit determination. Based on the analyses of the 5 and 6-h orbit overlaps of two 30-h arcs, orbit accuracies from the reduced dynamic and kinematic solutions are nearly identical and are at the 2–3 cm level. The mean RMS difference between the orbits from this paper and those from UCAR (near real-time) and WHU (post-processed) is about 10 cm, which is largely due to different uses of GPS ephemerides, high-rate GPS clocks and force models. The kinematic orbits of COSMIC are expected to be used for recovery of temporal variations in the gravity field.

Spherical harmonics (SH) and mascon solutions are the two most common types of solutions for Gravity Recovery and Climate Experiment (GRACE) mass flux observations. However, SH signals are degraded by measurement and leakage errors. Mascon solutions (the Jet Propulsion Laboratory (JPL) release, herein) exhibit weakened signals at submascon resolutions. Both solutions require a scale factor examined by the CLM4.0 model to obtain the actual water storage signal. The Slepian localization method can avoid the SH leakage errors when applied to the basin scale. In this study, we estimate SH errors and scale factors for African hydrological regimes. Then, terrestrial water storage (TWS) in Africa is determined based on Slepian localization and compared with JPL-mascon and SH solutions. The three TWS estimates show good agreement for the TWS of large-sized and humid regimes but present discrepancies for the TWS of medium and small-sized regimes. Slepian localization is an effective method for deriving the TWS of arid zones. The TWS behavior in African regimes and its spatiotemporal variations are then examined. The negative TWS trends in the lower Nile and Sahara at −1.08 and −6.92 Gt/year, respectively, are higher than those previously reported.

This paper demonstrates estimation of time-varying gravity harmonic coefficients from GPS data of COSMIC and GRACE satellite missions. The kinematic orbits of COSMIC and GRACE are determined to the cm-level accuracy. The NASA Goddard's GEODYN II software is used to model the orbit dynamics of COSMIC and GRACE, including the effect of a static gravity field. The surface forces are estimated per one orbital period. Residual orbits generated from kinematic and reference orbits serve as observables to determine the harmonic coefficients in the weighted-constraint least-squares. The monthly COSMIC and GRACE GPS data from September 2006 to December 2007 (16 months) are processed to estimate harmonic coefficients to degree 5. The geoid variations from the GPS and CSR RL04 (GRACE) solutions show consistent patterns over space and time, especially in regions of active hydrological changes. The monthly GPS-derived second zonal coefficient closely resembles the SLR-derived and CSR RL04 values, and third and fourth zonal coefficients resemble the CSR RL04 values.