Simulation study of a follow-on gravity mission to GRACE

TLDR: In this paper, an interferometric laser ranging system was developed to specifically address the limitations of the K-band microwave ranging system that provides the satellite-to-satellite measurements for the GRACE mission.

Abstract: The gravity recovery and climate experiment (GRACE) has been providing monthly estimates of the Earth's time-variable gravity field since its launch in March 2002. The GRACE gravity estimates are used to study temporal mass variations on global and regional scales, which are largely caused by a redistribution of water mass in the Earth system. The accuracy of the GRACE gravity fields are primarily limited by the satellite-to-satellite range-rate measurement noise, accelerometer errors, attitude errors, orbit errors, and temporal aliasing caused by unmodeled high-frequency variations in the gravity signal. Recent work by Ball Aerospace and Technologies Corp., Boulder, CO has resulted in the successful development of an interferometric laser ranging system to specifically address the limitations of the K-band microwave ranging system that provides the satellite-to-satellite measurements for the GRACE mission. Full numerical simulations are performed for several possible configurations of a GRACE Follow-On (GFO) mission to determine if a future satellite gravity recovery mission equipped with a laser ranging system will provide better estimates of time-variable gravity, thus benefiting many areas of Earth systems research. The laser ranging system improves the range-rate measurement precision to approximately 0.6 nm/s as compared to approx. 0.2 micro-seconds for the GRACE K-band microwave ranging instrument. Four different mission scenarios are simulated to investigate the effect of the better instrument at two different altitudes. The first pair of simulated missions is flown at GRACE altitude (approx. 480 km) assuming on-board accelerometers with the same noise characteristics as those currently used for GRACE. The second pair of missions is flown at an altitude of approx. 250 km which requires a drag-free system to prevent satellite re-entry. In addition to allowing a lower satellite altitude, the drag-free system also reduces the errors associated with the accelerometer. All simulated mission scenarios assume a two satellite co-orbiting pair similar to GRACE in a near-polar, near-circular orbit. A method for local time variable gravity recovery through mass concentration blocks (mascons) is used to form simulated gravity estimates for Greenland and the Amazon region for three GFO configurations and GRACE. Simulation results show that the increased precision of the laser does not improve gravity estimation when flown with on-board accelerometers at the same altitude and spacecraft separation as GRACE, even when time-varying background models are not included. This study also shows that only modest improvement is realized for the best-case scenario (laser, low-altitude, drag-free) as compared to GRACE due to temporal aliasing errors. These errors are caused by high-frequency variations in the hydrology signal and imperfections in the atmospheric, oceanographic, and tidal models which are used to remove unwanted signal. This work concludes that applying the updated technologies alone will not immediately advance the accuracy of the gravity estimates. If the scientific objectives of a GFO mission require more accurate gravity estimates, then future work should focus on improvements in the geophysical models, and ways in which the mission design or data processing could reduce the effects of temporal aliasing.

Figures

Figure 5.32: Errors in trend and amplitude estimates for each Greenland basin for GRACE and GFO Case 3: instrument noise only.

Table 5.8: Best fit trend, annual amplitude, and phase values for Greenland basins: instrument noise only.

Figure 5.57: Mass variations for Greenland basins from temporal aliasing.

Figure 5.15: Greenland basin mass variations time series for different mascon constraint scenarios.

Figure 5.17: South America gravity estimates for GFO Case 1 (480 km altitude / Laser / Accelerometer): instrument noise only.

Figure 5.34: Mass recovered within a given size block for different mission configurations: instrument noise only.

Full text

Simulation Study of a Follow-On Gravity Mission
to GR ACE
by
Bryant Loomis
B.S., Hope College, 2003
M.S., University of Colorado at Boulder, 2005
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Do ctor of Philosophy
Department of Aerospace En gineering Sciences
2009

This thesis entitled:
Simulation Study of a Follow-On Gravity Mission to GRACE
written by Bryant Loomis
has been approved for the Department of Aerospace Engineering Sciences
R. Steven Nerem
George Born
Peter Bender
John Wahr
Scott Luthcke
Date
The final copy of this thesis has been examined by the signatories, and we find that
both the content and the form meet acceptable presentation standards of scholarly
work in the above mentioned discipline.

Loomis, Bryant (Ph.D., Aerospace Engineering Sciences)
Simulation Study of a Follow-On Gravity Mission to GRACE
Thesis directed by Professor R. Steven Nerem
The Gravity Recovery and Climate Experiment (GRACE) has been providing
monthly estimates of th e Earth’s time variable gravity field since its launch in March
2002. The GRACE gravity estimates are used to study temporal mass variations on
global and regional scales, which are largely caused by a redistribution of water mass in
the Earth system. The accuracy of the GRACE gravity fields are primarily limited by
the satellite-to-satellite range-rate measurement noise, accelerometer errors, and tem-
poral aliasing caused by un-modeled high-frequency variations in the gravity signal.
Full numerical simulations are performed for a GRACE Follow-On mission (GFO) to
determine if a future satellite gravity recovery miss ion with improved technologies will
provide better estimates of time-variable gravity, thus benefiting many areas of Earth
systems research.
Several GFO configurations are considered for this study. The first case considered
is a two-satellite collinear pair similar to GRACE. The best-case two-satellite mission
is equipped with an interferometric laser ran ging system and a drag-free system in a
lower altitude orbit. The laser ranging system improves the satellite-to-satellite range-
rate measurement accuracy to ∼1 nm/s as compared to ∼1 micron/s for GRACE K-
band microwave ranging, and the drag-free system more accurately removes the non-
conservative forces acting on the satellites than the GRACE on-board accelerometers.
Two “hyb rid” missions are also con sidered. One hybrid is the GRACE design where th e
K-band ranging is replaced by the laser; and the other is a drag-free, low altitude scenario
iii

with K-band r anging. A comparison of simulated gravity estimates is an important
design tool in selecting the most important technologies to be considered for a future
mission. A method for local time variable gravity r ecovery through mass concentration
blocks (mascons) is used to form simulated gravity estimates f or Greenland and the
Amazon region for three GFO configurations and GRACE.
Simulation results show that only modest improvement is realized for even the
best-case two-satellite mission due to temporal aliasing errors. These errors are caused
by high-frequency variations in the hydrology s ignal and imperfections in the atmo-
spheric, oceanograp hic, and tidal models which are u sed to remove unwanted signal.
The various sour ces of aliasing errors are investigated separately through a series of
numerical simulations, showing that the leading cause of the errors is dependent on the
considered region.
This work concludes that applying the updated technologies alone, will not im-
mediately advance the accuracy of the gravity estimates. If the scientific objectives
of a GFO require more accurate gravity estimates, then future work should focus on
improvements in the geophysical models, and ways in which the mission design or data
processing could reduce the effects of temporal aliasing.
iv

Acknowledgements
This work was su pported by NASA Headquarters under the Earth Sys tem Science
Fellowship Grant NGT5 and the NASA Instrument Incubator Program (IIP) through
ESTO at NASA/GSFC.
I would like to thank my academic advisor, Dr. R. Steven Nerem, for provid-
ing the direction and supervision of my research. I also thank Dr. George Born, Dr.
Peter Bender, Dr. John Wahr, and Scott L uthcke for serving as members of the PhD
committee. Additionally, I thank Scott Luthcke and Dave Rowlands for providing the
GEODYN and SOLVE software packages and spending a great deal of their time as-
sisting me with a variety of problems.
Lastly, I would like to th ank my amazing wife who has been very supportive
throughout this entire process.
v

Frequently asked questions

Q1. What are the contributions in this paper?

The Gravity Recovery and Climate Experiment ( GRACE ) satellite mission determined the shape of Earth 's gravity field by accurately measuring these perturbations this paper. 

Q2. What are the future works in this paper?

This chapter summarizes the results presented in the previous chapter and makes recommendations for future gravity satellite missions and further research which would benefit the design of such a mission. It is recommended here, that future research in regards to a GFO should focus on ways in which the effects of temporal aliasing can be reduced. 

Q3. How many range-rate and position observations are generated for each one-day arc?

Simulated range-rate and position observations are generated every five seconds for each one-day arc, for a total of 17,280 range-rate and position observations per arc. 

Q4. What is the main reason for the variability in the accuracy of regional gravity estimates?

Due to the spatial variability of the errors in the AOD and tidal models, and the variations of the hydrological signal, the accuracy of regional gravity estimates can vary significantly based on location. 

Q5. What are other techniques of measuring ice mass variations in Greenland and Antarctica?

Other techniques of measuring ice mass variations in Greenland and Antarctica include airborne laser altimetry measurements and satellite radar interferometry [Ramillien et al., 2006]. 

Q6. What is the reason for the aliasing errors in the South America gravity estimates?

Temporal aliasing errors will still be present in the South America gravity estimates due to the high frequency variations in the hydrology signal that is estimated at monthly intervals. 

Q7. What is the way to estimate ocean heat content?

Estimates of SSL, when combined with salinity data, can be used to form accurate estimates of ocean heat content [Jayne et al., 2003]. 

Q8. What are the reasons for the errors in the GRACE gravity estimates?

Modeling errors are caused by imperfections in the geophysical models used to remove unwanted signal from the GRACE gravity estimates. 

Q9. How is the spectral density of the satellite-to-satellite tracking error?

In order to include the satellite-to-satellite tracking error into the numerical simu-lations the spectral density is converted into a time series of range-rate errors by taking the inverse Fourier transform of the range-rate spectral density as given by Eq. (B.4). 

Q10. How many times are the transverse terms assigned a correlation time?

The transverse terms are assigned a correlation time of three hours (approximately two satellite revolutions), and the radial and normal terms are assigned a correlation time of twenty-four hours. 

Q11. Why did the researchers not measure the variations of the gravity field over shorter time intervals?

Due to insufficient data, the temporal variations of the gravity field, which take place over shorter time intervals, could not be measured. 

Q12. What is the spectral density of the satellite-to-satellite ranging?

For more detail on spectral densities refer to Appendix C.4.2.1 GRACEThe spectral density of the satellite-to-satellite ranging measurement noise is givenby 1.8 µm/ √ Hz [Bettadpur , 2007]. 

Q13. How did Luthcke and his team estimate the mass changes in the Alaskan gulf?

Using a local mascon technique Luthcke et al. [2008] estimate mass changes in theGulf of Alaska from April 2003 to September 2007 with a 10-day sampling. 

Q14. What is the possibility that the GOCE satellite mission will provide the static portion of the gravity?

it is also a possibility that the GOCE satellite mission will provide the static portion of the gravity field with unprecedented accuracy prior to the launch of a GFO, thus minimizing this source of error. 

Q15. What is the weighting coefficient for a Gaussian smoothed averaging kernel?

For a Gaussian smoothed averaging kernel the weighting coefficients in Eq. (2.28) are defined by: W CnmW Snm = 2πWn ϑCnmϑSnm , (2.30)whereWn = 1√2n + 1∫ π0 W (γ)P̃n0(cos γ) sin γdγ, (2.31)andW (γ) = b2π exp[−b(1 − cos γ)]