Gravity Recovery And Climate Experiment Orbits Research Articles

A Probabilistic Approach to Characterizing Drought Using Satellite Gravimetry

AbstractIn the recent past, the Gravity Recovery and Climate Experiment (GRACE) satellite mission and its successor GRACE Follow‐On (GRACE‐FO), have become invaluable tools for characterizing drought through measurements of Total Water Storage Anomaly (TWSA). However, the existing approaches have often overlooked the uncertainties in TWSA that stem from GRACE orbit configuration, background models, and intrinsic data errors. Here we introduce a fresh view on this problem which incorporates the uncertainties in the data: the Probabilistic Storage‐based Drought Index (PSDI). Our method leverages Monte Carlo simulations to yield realistic realizations for the stochastic process of the TWSA time series. These realizations depict a range of plausible drought scenarios that later on are used to characterize drought. This approach provides probability for each drought category instead of selecting a single final category at each epoch. We have compared PSDI with the deterministic approach (Storage‐based Drought Index, SDI) over major global basins. Our results show that the deterministic approach often leans toward an overestimation of storage‐based drought severity. Furthermore, we scrutinize the performance of PSDI across diverse hydrologic events, spanning continents from the United States to Europe, the Middle East, Southern Africa, South America, and Australia. In each case, PSDI emerges as a reliable indicator for characterizing drought conditions, providing a more comprehensive perspective than conventional deterministic indices. In contrast to the common deterministic view, our probabilistic approach provides a more realistic characterization of the TWS drought, making it more suited for adaptive strategies and realistic risk management.

Observational Evidence and Formation Mechanism of Low‐Density Cells in the Upper Thermosphere on September 8, 2017

AbstractThe low‐density cell structure in the high‐latitude thermosphere is referred to as the density depletion with respect to the adjacent area. Based on Gravity Recovery and Climate Experiment (GRACE) accelerometer data during the September 2017 geomagnetic storms, the thermospheric mass density at about 350 km are estimated and further investigated especially in the high‐latitude regions. At least two kinds of low‐density cells over the Southern Hemisphere (SH) are observed along the GRACE orbit. To understand the low‐density cell structures over the SH observed by GRACE, we investigate the underlying physical mechanism based on thermosphere‐ionosphere numerical simulations using Thermosphere‐Ionosphere Electrodynamic General Circulation Model and Global Ionosphere Thermosphere Model. According to the simulation results, the formation mechanism of the low‐density cell is attributed to the storm‐time vertical advection and horizontal velocity divergence driven by the auroral ion convection. The critical height of observable low‐density cells is shown to be not less than 350 km. The meridional spatial scale of observed low‐density cells over the SH are approximately or slightly larger than 1,500 km. Three low‐density cells, including two in the dawn sector and one in the night sector were observed about 1 hour after the direction of interplanetary magnetic field BY component reversed. The occurrence of thermospheric low‐density structure is essential to be included in the empirical model during geomagnetic storm time.

A simultaneous calibration and data assimilation (C/DA) to improve NRLMSISE00 using thermospheric neutral density (TND) from space-borne accelerometer measurements

SUMMARY Improving thermospheric neutral density (TND) estimates is important for computing drag forces acting on low-Earth-orbit (LEO) satellites and debris. Empirical thermospheric models are often used to compute TNDs for the precise orbit determination experiments. However, it is known that simulating TNDs are of limited accuracy due to simplification of model structure, coarse sampling of model inputs and dependencies to the calibration period. Here, we apply TND estimates from accelerometer measurements of the Challenging Minisatellite Payload (CHAMP) and the Gravity Recovery and Climate Experiment (GRACE) missions as observations to improve the NRLMSISE-00 model, which belongs to the mass spectrometer and incoherent scatter family of models. For this, a novel simultaneous calibration and data assimilation (C/DA) technique is implemented that uses the ensemble Kalman filter and the ensemble square-root Kalman filter as merger. The application of C/DA is unique because it modifies both model-derived TNDs, as well as the selected model parameters. The calibrated parameters derived from C/DA are then used to predict TNDs in locations that are not covered by CHAMP and GRACE orbits, and forecasting TNDs of the next day. The C/DA is implemented using daily CHAMP- and/or GRACE-TNDs, for which compared to the original model, we find 27 per cent and 62 per cent reduction of misfit between model and observations in terms of root mean square error and Nash coefficient, respectively. These validations are performed using the observations along the orbital track of the other satellite that is not used in the C/DA during 2003 with various solar activity. Comparisons with another empirical model, that is, Jacchia-Bowman, indicate that the C/DA results improve these quality measurements on an average range of 50 per cent and 60 per cent, respectively.

Using quantum optical sensors for determining the Earth\u2019s gravity field from space

Quantum optical technology provides an opportunity to develop new kinds of gravity sensors and to enable novel measurement concepts for gravimetry. Two candidates are considered in this study: the cold atom interferometry (CAI) gradiometer and optical clocks. Both sensors show a high sensitivity and long-term stability. They are assumed on board of a low-orbit satellite like gravity field and steady-state ocean circulation explorer (GOCE) and gravity recovery and climate experiment (GRACE) to determine the Earth’s gravity field. Their individual contributions were assessed through closed-loop simulations which rigorously mapped the sensors’ sensitivities to the gravity field coefficients. Clocks, which can directly obtain the gravity potential (differences) through frequency comparison, show a high sensitivity to the very long-wavelength gravity field. In the GRACE orbit, clocks with an uncertainty level of 1.0times 10^{-18} are capable to retrieve temporal gravity signals below degree 12, while 1.0times 10^{-17} clocks are useful for detecting the signals of degree 2 only. However, it poses challenges for clocks to achieve such uncertainties in a short time. In space, the CAI gradiometer is expected to have its ultimate sensitivity and a remarkable stability over a long time (measurements are precise down to very low frequencies). The three diagonal gravity gradients can properly be measured by CAI gradiometry with a same noise level of 5.0 {mathrm{mE}/sqrt{mathrm{Hz}}}. They can potentially lead to a 2–5 times better solution of the static gravity field than that of GOCE above degree and order 50, where the GOCE solution is mainly dominated by the gradient measurements. In the lower degree part, benefits from CAI gradiometry are still visible, but there, solutions from GRACE-like missions are superior.

Improving the GRACE Kinematic Precise Orbit Determination Through Modified Clock Estimating.

Utilizing global positioning system (GPS) to determine the precise kinematic orbits for the twin satellites of the Gravity Recovery and Climate Experiment (GRACE) plays a very important role in the earth’s gravitational and other scientific fields. However, the orbit quality is highly depended on the geometry of observed GPS satellites. In this study, we propose a kinematic orbit determination method for improving the GRACE orbit quality especially when the geometry of observed GPS satellites is weak, where an appropriate random walk clock constraint between adjacent epochs is recommended according to the stability of on-board GPS receiver clocks. GRACE data over one month were adopted in the experimental validation. Results show that the proposed method could improve the root mean square (RMS) by 20–40% in radial component and 5–20% in along and cross components. For those epochs with position dilution of precision (PDOP) larger than 4, the orbits were improved by 50–70% in radial component and 17–50% in along and cross components. Meanwhile, the Allan deviation of clock estimates in the proposed method was much closer to the reported Allan deviation of GRACE on-board oscillator. All the results confirmed the improvement of the proposed method.

Assessment of Earth Gravity Field Models in the Medium to High Frequency Spectrum Based on GRACE and GOCE Dynamic Orbit Analysis

An analysis of current static and time-variable gravity field models is presented focusing on the medium to high frequencies of the geopotential as expressed by the spherical harmonic coefficients. A validation scheme of the gravity field models is implemented based on dynamic orbit determination that is applied in a degree-wise cumulative sense of the individual spherical harmonics. The approach is applied to real data of the Gravity Field and Steady-State Ocean Circulation (GOCE) and Gravity Recovery and Climate Experiment (GRACE) satellite missions, as well as to GRACE inter-satellite K-band ranging (KBR) data. Since the proposed scheme aims at capturing gravitational discrepancies, we consider a few deterministic empirical parameters in order to avoid absorbing part of the gravity signal that may be included in the monitored orbit residuals. The present contribution aims at a band-limited analysis for identifying characteristic degree ranges and thresholds of the various GRACE- and GOCE-based gravity field models. The degree range 100–180 is investigated based on the degree-wise cumulative approach. The identified degree thresholds have values of 130 and 160 based on the GRACE KBR data and the GOCE orbit analysis, respectively.

GRACE time-varying gravity field solutions based on PANDA software

The conventional dynamic approach for gravity filed modelling has been implemented in the PANDA (Position and Navigation Data Analyst) software. A variant of the so-called ‘two-step’ method for gravity field modelling is adopted for this purpose, where the GRACE (Gravity Recovery and Climate Experiment) orbits are derived from the GPS (Global Positioning System) data in a first step followed by a simultaneous determination of dynamic orbit and gravity filed from the GPS-derived orbits and K-band range-rate measurements in a second step. In this way, the monthly gravity field solutions complete to degree and order 96 are produced for the period Jan. 2005 to Dec. 2010. Their performance is assessed by comparing them with the official solutions, i.e., CSR RL05, GFZ RL05a and JPL RL05. A comparison in the spectral domain in terms of geoid heights reveals that the obtained solutions present the smallest degree amplitudes at degree 30–75. A further analysis of mass changes in the spatial domain demonstrates that the main signals observed from the obtained solutions are in great agreement with those from the official solutions. Remarkably, the correlation coefficients of mass changes in large river basins from the official solutions with respect to those from the obtained solutions are all above 0.97. These results demonstrate that the obtained solutions are comparable to the official solutions.

Comparison of precise orbit determination methods of zero-difference kinematic, dynamic and reduced-dynamic of GRACE-A satellite using SHORDE software

Abstract Zero-difference kinematic, dynamic and reduced-dynamic precise orbit determination (POD) are three methods to obtain the precise orbits of Low Earth Orbit satellites (LEOs) by using the on-board GPS observations. Comparing the differences between those methods have great significance to establish the mathematical model and is usefull for us to select a suitable method to determine the orbit of the satellite. Based on the zero-difference GPS carrier-phase measurements, Shanghai Astronomical Observatory (SHAO) has improved the early version of SHORDE and then developed it as an integrated software system, which can perform the POD of LEOs by using the above three methods. In order to introduce the function of the software, we take the Gravity Recovery And Climate Experiment (GRACE) on-board GPS observations in January 2008 as example, then we compute the corresponding orbits of GRACE by using the SHORDE software. In order to evaluate the accuracy, we compare the orbits with the precise orbits provided by Jet Propulsion Laboratory (JPL). The results show that: (1) If we use the dynamic POD method, and the force models are used to represent the non-conservative forces, the average accuracy of the GRACE orbit is 2.40cm, 3.91cm, 2.34cm and 5.17cm in radial (R), along-track (T), cross-track (N) and 3D directions respectively; If we use the accelerometer observation instead of non-conservative perturbation model, the average accuracy of the orbit is 1.82cm, 2.51cm, 3.48cm and 4.68cm in R, T, N and 3D directions respectively. The result shows that if we use accelerometer observation instead of the non-conservative perturbation model, the accuracy of orbit is better. (2) When we use the reduced-dynamic POD method to get the orbits, the average accuracy of the orbit is 0.80cm, 1.36cm, 2.38cm and 2.87cm in R, T, N and 3D directions respectively. This method is carried out by setting up the pseudo-stochastic pulses to absorb the errors of atmospheric drag and other perturbations. (3) If we use the kinematic POD method, the accuracy of the GRACE orbit is 2.92cm, 2.48cm, 2.76cm and 4.75cm in R, T, N and 3D directions respectively. In conclusion, it can be seen that the POD of GRACE satellite is practicable by using different strategies and methods. The orbit solution is well and stable, they all can obtain the GRACE orbits with centimeter-level precision.

The unexpected signal in GRACE estimates of $$C_{20}$$

For science applications of the gravity recovery and climate experiment (GRACE) monthly solutions, the GRACE estimates of \(C_{20}\) (or \(J_{2}\)) are typically replaced by the value determined from satellite laser ranging (SLR) due to an unexpectedly strong, clearly non-geophysical, variation at a period of \(\sim \)160 days. This signal has sometimes been referred to as a tide-like variation since the period is close to the perturbation period on the GRACE orbits due to the spherical harmonic coefficient pair \(C_{22}/S_{22}\) of S2 ocean tide. Errors in the S2 tide model used in GRACE data processing could produce a significant perturbation to the GRACE orbits, but it cannot contribute to the \(\sim \)160-day signal appearing in \(C_{20}\). Since the dominant contribution to the GRACE estimate of \(C_{20}\) is from the global positioning system tracking data, a time series of 138 monthly solutions up to degree and order 10 (\(10\times 10\)) were derived along with estimates of ocean tide parameters up to degree 6 for eight major tides. The results show that the \(\sim \)160-day signal remains in the \(C_{20}\) time series. Consequently, the anomalous signal in GRACE \(C_{20}\) cannot be attributed to aliasing from the errors in the S2 tide. A preliminary analysis of the cross-track forces acting on GRACE and the cross-track component of the accelerometer data suggests that a temperature-dependent systematic error in the accelerometer data could be a cause. Because a wide variety of science applications relies on the replacement values for \(C_{20}\), it is essential that the SLR estimates are as reliable as possible. An ongoing concern has been the influence of higher degree even zonal terms on the SLR estimates of \(C_{20}\), since only \(C_{20}\) and \(C_{40}\) are currently estimated. To investigate whether a better separation between \(C_{20}\) and the higher-degree terms could be achieved, several combinations of additional SLR satellites were investigated. In addition, a series of monthly gravity field solutions (\(60\times 60\)) were estimated from a combination of GRACE and SLR data. The results indicate that the combination of GRACE and SLR data might benefit the resonant orders in the GRACE-derived gravity fields, but it appears to degrade the recovery of the \(C_{20}\) variations. In fact, the results suggest that the poorer recovery of \(C_{40}\) by GRACE, where the annual variation is significantly underestimated, may be affecting the estimates of \(C_{20}\). Consequently, it appears appropriate to continue using the SLR-based estimates of \(C_{20}\), and possibly also \(C_{40}\), to augment the existing GRACE mission.

Monthly gravity field recovery from GRACE orbits and K-band measurements using variational equations approach

The Gravity Recovery and Climate Experiment (GRACE) mission can significantly improve our knowledge of the temporal variability of the Earth's gravity field. We obtained monthly gravity field solutions based on variational equations approach from GPS-derived positions of GRACE satellites and K-band range-rate measurements. The impact of different fixed data weighting ratios in temporal gravity field recovery while combining the two types of data was investigated for the purpose of deriving the best combined solution. The monthly gravity field solution obtained through above procedures was named as the Institute of Geodesy and Geophysics (IGG) temporal gravity field models. IGG temporal gravity field models were compared with GRACE Release05 (RL05) products in following aspects: (i) the trend of the mass anomaly in China and its nearby regions within 2005–2010; (ii) the root mean squares of the global mass anomaly during 2005–2010; (iii) time-series changes in the mean water storage in the region of the Amazon Basin and the Sahara Desert between 2005 and 2010. The results showed that IGG solutions were almost consistent with GRACE RL05 products in above aspects (i)–(iii). Changes in the annual amplitude of mean water storage in the Amazon Basin were 14.7 ± 1.2 cm for IGG, 17.1 ± 1.3 cm for the Centre for Space Research (CSR), 16.4 ± 0.9 cm for the GeoForschungsZentrum (GFZ) and 16.9 ± 1.2 cm for the Jet Propulsion Laboratory (JPL) in terms of equivalent water height (EWH), respectively. The root mean squares of the mean mass anomaly in Sahara were 1.2 cm, 0.9 cm, 0.9 cm and 1.2 cm for temporal gravity field models of IGG, CSR, GFZ and JPL, respectively. Comparison suggested that IGG temporal gravity field solutions were at the same accuracy level with the latest temporal gravity field solutions published by CSR, GFZ and JPL.

Dynamic orbit parameterization and assessment in the frame of current GOCE gravity models

The role of gravity models is fundamental in satellite orbit determination representing the dynamical contribution of the observed gravity field in the equation of motion. We examine the validation of gravity models by implementing numerically an adapted dynamic orbit determination algorithm. We focus on GOCE (Gravity field and steady-state Ocean Circulation Explorer) and GRACE (Gravity Recovery And Climate Experiment) orbit analysis based on real orbital data and current GOCE gravity models. The contribution of the gravity models is implemented in a degree-wise cumulative sense, thus quantifying the band-limited performance of the individual models at satellite altitude. Furthermore, the proposed orbit analysis scheme leads to a validation of the different gravity models, providing an insight to the effect of the gravitational counterpart to the geometry of the orbit by expressing explicitly all computations to orbit perturbations defined along the three components of the orbital frame.

Evaluation of GRACE filter tools from a hydrological perspective

Approximately seven years of time-variable gravity data from the satellite mission Gravity Recovery and Climate Experiment (GRACE) are available to quantify present-day mass variations on and near the Earth's surface. Mass variations caused by the continental water cycle are the dominant signal component after subtracting contributions from atmosphere and oceans. This makes hydrology a primary area of application of GRACE data. To derive water storage variations at the scale of large river basins, appropriate filter techniques have to be applied to GRACE gravity fields given in a global spherical harmonic representation. A desirable filter technique minimises both GRACE data error and signal leakage across the border of the region of interest. This study evaluates the performance of six widely used filter methods (isotropic filters, anisotropic filters and decorrelation methods) and their parameter values to derive regionally averaged water mass variations from GRACE data. To this end, filtered time series from GRACE for 22 of the world's largest river basins were compared to continental water mass variations from a multimodel mean of three global hydrological models (WGHM, GLDAS and LaD). Filter-induced biases for seasonal amplitudes and phases of water storage variations, as well as satellite and leakage error budgets, were quantified for each river basin and explained in terms of storage variations in and around the basin. The optimum filter types and filter parameters were identified for each basin. The best results were provided by a decorrelation method that uses GRACE orbits for the filter design. Our ranking between all filter types and parameters depended on the geographical location, shape and signal characteristics of the specific river basin. Based on a multicriterial evaluation of satellite and leakage error, as well as an error assessment of the hydrological data, the filter selection and parameter optimisation results were shown to be reliable for 17 river basins. The results serve as a guideline for the optimal filtering of GRACE global spherical harmonic coefficients for hydrological applications.

Gravity Recovery and Climate Experiment (GRACE) alias error from ocean tides

Gravity Recovery and Climate Experiment (GRACE) is able to observe interannual and longer‐period mass redistribution driven by climate changes. However, alias errors due to inaccurate ocean tide models may contaminate these signals. To quantify this problem, we estimate alias contamination due to expected errors in eight tidal constituents (Q1, O1, P1, K1, N2, M2, S2, and K2) for the period August 2002 to February 2006. Differences between GOT00.2 and TPXO6.2 tide models are used as estimates of tide model errors. The alias estimate is based on an approximate method employing least squares fits of spherical harmonics to potential differences between the two GRACE satellites. Results from this method are similar to previous estimates, confirming this is a useful and efficient way to study the alias problem. New findings are (1) the period of the M2 tide alias is about 140 d, much longer than the predicted period (13.5 d) because of monthly sampling of the 13.5‐d period; (2) there are two alias periods for K1 (one about 90 d and one longer than 7 years); and (3) the slow decay in the GRACE orbit causes tide component aliases to differ from pure frequencies as the orbit evolves. We also find that aliases can contaminate in both space and time and thus may affect estimates of mass changes over land. Finally, we compare the simulated S2 alias with the estimated S2 alias in GRACE data. They are similar, but our approximate method appears to overestimate alias error over high‐latitude oceans and along certain coastlines while underestimating error over low‐latitude oceans.

Accuracy assessment of the monthly GRACE geoids based upon a simulation

The purpose of this paper is to demonstrate the effect of geophysical background model errors that affects temporal gravity solutions provided by the Gravity Recovery And Climate Experiment (GRACE). Initial performance estimates by Dickey et al. (1997) suggested a formal geoid RMS error better than 0.1 mm up to spherical harmonic degree 5. Now that the GRACE gravity models and data are available, it is evident that these original expectations were too optimistic. Our hypothesis is that this is partially explained by errors in geophysical background models that need to be applied in the GRACE data reduction, and that this effect was not considered by Dickey et al. (1997). We discuss the results of a closed-loop simulation, where satellite trajectory prediction software is used for the generation of GRACE range-rate data and GRACE orbit solutions with the help of the Global Positioning System (GPS). During the recovery step in our closed-loop simulation, we show that simulated nuisance signals (based on tide and air pressure model differences) map to a 0.7 mm geoid effect for periods longer than 3 months and to less than 0.4 mm for periods shorter than 3 months. The long-period geoid hydrology signal is at a level of 4.5 mm, while the short-period hydrology is at 0.25 mm. The long-period ocean bottom pressure (OBP) signal maps at 0.8 mm and for short periods it is 0.4 mm. We conclude that short-period effects are difficult to observe by GRACE and that long-period effects, like hydrology, are easier to recover than OBP variations.

Precise orbit determination for the GRACE mission using only GPS data

The GRACE (gravity recovery and climate experiment) satellites, launched in March 2002, are each equipped with a BlackJack GPS onboard receiver for precise orbit determination and gravity field recovery. Since launch, there have been significant improvements in the background force models used for satellite orbit determination, most notably the model for the geopotential. This has resulted in significant improvements to orbit accuracy for very low altitude satellites. The purpose of this paper is to investigate how well the orbits of the GRACE satellites (about 470 km in altitude) can currently be determined using only GPS data and based on the current models and methods. The orbit accuracy is assessed using a number of tests, which include analysis of orbit fits, orbit overlaps, orbit connecting points, satellite Laser ranging residuals and K-band ranging (KBR) residuals. We show that 1-cm radial orbit accuracy for the GRACE satellites has probably been achieved. These precise GRACE orbits can be used for such purposes as improving gravity recovery from the GRACE KBR data and for atmospheric profiling, and they demonstrate the quality of the background force models being used.

Degradation of Geopotential Recovery from Short Repeat-Cycle Orbits: Application to GRACE Monthly Fields

Throughout 2004 the GRACE (Gravity Recovery And Climate Experiment) orbit contracted slowly to yield a sparse repeat track of 61 revolutions every 4 days on 19 September 2004. As a result, we show from linear perturbation theory that geopotential information previously available to fully resolve a gravity field every month of 120× 120 (degree by order) in spherical harmonics was compressed then into about one-fourth of the necessary observation space. We estimate from this theory that the ideal gravity field resolution in September 2004 was only about 30 × 30. More generally, we show that any repeat-cycle mission for geopotential recovery with full resolution L × L requires the number of orbit-revolutions-to-repeat to be greater than 2L.

Precise orbit determination for GRACE using accelerometer data

Since the launch of the gravity recovery and climate experiment (GRACE) satellites in March 2002, data quality has been improved significantly. For the star camera and accelerometer data, the calibration parameters have been well determined and used in data generating and processing. The purpose of this paper is to investigate how well the GRACE satellite orbits can be determined using improved accelerometer data and to assess the differences between the use of accelerometer data and the use of a priori models for the surface forces. As is known, the orbit accuracy depends on the force models used in the dynamic orbit determination, but the models for the surface forces acting on low-Earth satellites are uncertain. To alleviate this problem, the GRACE concept uses a three-axis accelerometer to measure the non-gravitational accelerations. To reduce the effects of force model error on precise orbit determination, one can estimate a set of empirical parameters. In the case of highly variable forces acting on satellites (such as high solar activity), the accelerometer provides high quality measurements of the phenomena. For this investigation, we have analyzed the data during high solar activity. The orbit accuracy is assessed using a number of tests, which include analysis of orbit fits, Satellite Laser Ranging (SLR) residuals, K-Band Ranging (KBR) residuals and external orbit comparison. The results show that an accuracy of about 2 cm in each component is achieved for the GRACE orbits and better orbits can be determined using accelerometer data during high solar activity. In addition, the GRACE orbits generated with the accelerometer data are generally better in the high frequency range.

Sumatra tsunami affects observations by GRACE satellites

Changes in the Earth's gravity field are caused by the redistribution of mass within the Earth and on or above its surface. While previous studies [Tapley, 2004; Wahr, 2004] showed that the Gravity Recovery and Climate Experiment (GRACE) satellite mission, executed by NASA, had successfully determined oceanic mass redistribution, the relative motions between two GRACE satellites caused by the 2004 Sumatra tsunami is still uncertain.This present study combines a numerical model of the tsunami and GRACE orbit data to estimate the realistic effect of oceanic mass redistribution on the inter‐satellite range‐rate change between two GRACE satellites. The GRACE mission is designed to map out the Earth's gravity field to high accuracy. Instead of measuring the Earth gravity field or mass variations directly GRACE estimates a set of spherical harmonic coefficients denoting the Earth gravity field each month by measuring range changes between two spacecrafts [Chambers et al., 2004].

Precise orbit determination for GRACE

The twin, co-orbiting GRACE (Gravity Recovery and Climate Experiment) satellites were launched in March 2002. The primary objective of the GRACE mission is to determine the Earth's gravity field and its temporal variations with unprecedented accuracy. To satisfy this objective as well as other applications (e.g. atmospheric profiling by radio occultation), accurate orbits for GRACE are required. This paper describes several results related to the use of the data collected by the GRACE GPS receiver, high precision accelerometer observations and precise attitude data from star trackers in the application of the GRACE Precise Orbit Determination (POD). The orbit accuracy is assessed using a number of tests, which include analysis of GPS tracking observation residuals, Satellite Laser Ranging (SLR) residuals, K-Band Ranging (KBR) residuals and external orbit comparisons. The results show that an accuracy of better than 5 cm in each direction for GRACE orbits can be obtained. The relative accuracy of the two GRACE satellites is about 1 cm in position and 10 micrometers per second in velocity.