Calibration of GRACE on-board accelerometers for thermosphere density derivation

Figures & data

Figure 1. GRACE satellite SBF definition (Doornbos 2012).

Table 1. Processing strategy in aspects of dynamic models and observation models

Dynamic models
Gravity Model	EIGEN_6C, 130 × 130 for static field and periodic terms
Solid Earth tide and pole tide	IERS2003
Ocean tide	FES2004 40 × 40
N-body perturbation	JPL DE405; planets include sun, moon, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto
Atmosphere gravity	GRACE Atmosphere Ocean De-aliasing (AOD) (Release-0005) products 40 × 40
Relativity	IERS 2003
Nongravitational accelerations such as drag and radiations	Represented by accelerometer data
Observation model
Observation	PC, LC
Arc length and interval	24 h, 30 s
GPS ephemeris and clock	JPL repro2 precision orbit and clock products; fixed
Ionosphere delay	First-order delay eliminated by ionosphere-free combination, higher orders are neglected
GPS satellite antenna PCO, PCV	IGS ATX
GRACE satellite receiver antenna PCO/PCV	PCO corrected using VOGPSN product, PCV not considered
Relativistic effect	Bending and Sagnac effect
Estimating Parameters
GRACE initial state	Estimated with a-priori deviation of 1000 m and 1 m/s for positions and velocities, respectively
Accelerometer bias	Estimated as piecewise-constant at specific time interval with a priori deviation of 1 μm/s^2
Phase ambiguity	Estimated as constants per each continuous arc with a priori deviation of 10 m
Receiver clock error	Estimated as random-walk parameters per epoch with a priori deviation and a priori process noise of 9000 m and $900\mathrm{m}/\sqrt{\mathrm{s}}$, respectively

Figure 2. GRACE-A satellite orbit differences with respect to the JPL PSO. Different colors demonstrate different accelerometer bias parameterization.

Table 2. GRACE-A satellite orbit precision with respect to the JPL PSO and SLR OMC statistics with different accelerometer bias parameterization

Bias parameterization	Orbit comparison to JPL PSO (cm)				SLR OMC (cm)
	Along-track	Cross-track	Radial	3D	Mean	STD
acc_45	4.96 (1.82)	1.62 (1.59)	1.12 (1.08)	5.34 (2.65)	−0.26	2.15
acc_60	1.78	1.35	1.00	2.45	−0.37	1.78
acc_90	1.74	2.66	1.02	3.34	−0.35	2.11
acc_180	1.91	2.60	0.99	3.37	−0.39	2.06
acc_360	2.48	2.65	1.21	3.82	−0.41	2.20

The values in the parentheses indicate the RMS statistics with DOY 112 removed.

Figure 3. Estimated Bx, By, Bz parameters during DOY 100–150 in 2006 with different parameterizations.

Table 3. The mean and STD values of estimated Bx, By, Bz parameters during DOY 100–150 in 2006

Bias parameterization	Bx (m/s^2)		By (m/s^2)		Bz (m/s^2)
	Mean	STD	Mean	STD	Mean	STD
acc_45	−1.1700 × 10^−6	4.5200 × 10^−9	2.8855 × 10^−5	1.8979 × 10^−8	−5.4400 × 10^−7	1.6800 × 10^−8
acc_60	−1.1691 × 10^−6	2.0788 × 10^−9	2.8855 × 10^−5	1.8966 × 10^−8	−5.4393 × 10^−7	1.4676 × 10^−8
acc_90	−1.1691 × 10^−6	1.0217 × 10^−9	2.8855 × 10^−5	2.7284 × 10^−8	−5.4357 × 10^−7	1.8280 × 10^−8
acc_180	−1.1691 × 10^−6	6.5104 × 10^−10	2.8854 × 10^−5	2.5583 × 10^−8	−5.4382 × 10^−7	1.7553 × 10^−8
acc_360	−1.1691 × 10^−6	4.9096 × 10^−10	2.8853 × 10^−5	2.3874 × 10^−8	−5.4359 × 10^−7	2.2016 × 10^−8

Figure 4. GRACE-A satellite orbit precision for POD and orbit-fitting schemes in along-track, cross-track, and radial components with respect to JPL PSOs.

Table 4. GRACE-A satellite orbit precision statistics during 2004–2007

Calibration scheme	Orbit comparison to JPL PSOs (cm)				SLR OMC (cm)
	Along-track	Cross-track	Radial	3D	Mean	STD	RMS
Orbit fitting	2.21	1.55	1.27	2.98	−0.53	2.52	2.58
POD	1.36	1.49	1.65	2.61	0.11	1.92	1.92

Figure 5. SLR OMC mean and STD values of GRACE-A satellite during 2004 and 2007.

Figure 6. GRACE-A satellite bias parameter series during 2004–2007.

Figure 7. Bias parameter difference series between the orbit-fitting and POD schemes for GRACE-A satellite.

Table 5. GRACE-A satellite bias parameter differences between the orbit-fitting and POD schemes

Components	Mean (nm/s^2)	STD (nm/s^2)	Relative mean (%)	Relative STD (%)
ΔBx	0.52	2.97	−0.04	0.26
ΔBy	−1.48	31.82	0.00	0.11
ΔBz	42.71	22.63	−7.25	3.85

Figure 8. Density series of the HASDM model, NRLMSISE00 model, POD, orbit fitting, and Density_Direct on DOY 002, 2004.

Table 6. Density ratio statistics of NRLMSISE00, HASDM, and Density_Direct over POD and orbit-fitting-derived densities on DOY 002, 2004

Calibration scheme	Mean			STD
	NRLMSISE00	HASDM	Density_Direct	NRLMSISE00	HASDM	Density_Direct
POD	1.522	1.115	1.047	0.256	0.206	0.047
Orbit fitting	1.474	1.078	1.013	0.273	0.212	0.067

Figure 9. Frequency count of density ratios of orbit fitting over POD densities and its log-normal distribution fit. The bin interval for the frequency count is 0.01.

Table 7. Log-normal distribution fit to density ratios of NRLMSISE00, HASDM, and Density_Direct to POD and orbit-fitting densities (all the density results during 2004 and 2007 are considered)

Calibration scheme	Log-normal distribution fit mean			Log-normal distribution fit STD
	NRLMSISE00	HASDM	Density_Direct	NRLMSISE00	HASDM	Density_Direct
POD	1.337	1.088	1.016	0.262	0.205	0.057
Orbit fitting	1.299	1.059	0.990	0.272	0.210	0.056

Doornbos, E. 2012. Thermospheric Density and Wind Determination from Satellite Dynamics. Berlin, Heidelberg: Springer Science & Business Media.

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Data availability statement

All data included in this research are available upon request by contacting with the corresponding author by [email protected].