Using GRACE Satellite

Acceleration Data to Recover Arctic

Ocean TidesBryan Killett 1, John Wahr 1, Shailen D.

Desai 2, Dah-Ning Yuan 2, Mike Watkins 2,

1 University of Colorado and CIRES,

Boulder, CO, USA2 Jet Propulsion Laboratory, Pasadena, CA,

USA

Quick Overview Motivation: FES 2004 is primarily based on

TOPEX/Poseidon data, which does not extend north of 66° N. Thus, Arctic ocean tides are not well constrained by satellite altimetry.

Relative acceleration values between the two GRACE satellites are used to solve for “mass concentrations” (mascons) on Earth’s surface. The solution method allows each mascon’s mass to oscillate at tidal and seasonal frequencies, as well as changing linearly.

FES 2004 effects have been subtracted from the acceleration values, so the amplitudes at tidal periods represent errors in FES 2004. The mass amplitudes are converted to equivalent “cm of water” amplitudes.

B A

MASCON

GRACE relative accel. due to a mascon directly

below satellitesRelative acceleration > 0

MASCON

GRACE relative accel. due to a mascon directly

below satellites

B A

MASCON

GRACE relative accel. due to a mascon directly

below satellites

B A

Relative acceleration < 0

MASCON

GRACE relative accel. due to a mascon directly

below satellites

B A

MASCON

GRACE relative accel. due to a mascon directly

below satellites

B A

Relative acceleration > 0

GRACE relative accel. due to a mascon not

below satellites

Inversion Details Smoothed residual acceleration values

were averaged at 5 second intervals when satellites are north of 50° N latitude.

6 million accelerations total over 5 years. A constant offset, secular trend and

amplitude/phase at seasonal and tidal periods are simultaneously solved for at each mascon.

Mascons are ~230km apart; 1200 mascons cover the area north of 50° N latitude.

Mascons are modeled as point masses for speed.

Simulations

To test the inversion program, arbitrary mascon amplitudes were created on Earth’s surface. These mascons have constant values, linear trends and amplitudes at M2 and K1 periods.

Next, the accelerations that GRACE would record due to these mascons were calculated using the actual times and positions of the GRACE satellites.

Finally, these simulated accelerations were inverted to solve for surface mascon amplitudes using the same algorithm used for real data.

Simulation – Constant Term

Simulation – Secular Trend

Simulation – M2 (Sine)

Simulation – M2 (Cosine)

Simulation – K1 (Sine)

Simulation – K1 (Cosine)

Inversion of Real GRACE Data

Real Data – Secular Trend

Real Data – Annual Amplitude

FES 2004 – M2 Amplitude

Residual M2 Amplitude

FES 2004 – K1 Amplitude

Residual K1 Amplitude

FES 2004 – O1 Amplitude

Residual O1 Amplitude

Conclusion

Existing tide models such as FES 2004 have room for improvement.

GRACE is a useful tool for recovering tidal signals even at semidiurnal frequencies.

Errors in FES2004 aren’t significantly larger north of 66°N compared to south of 66°N (the TOPEX/Poseidon turning point).

Simulations suggest that the large K1 amplitudes at the north pole are not real.

http://bryankillett.com

Main grid pointsare white, and spaced 230 kmapart.

Supporting grid points arecolored differentlyaccording to which main grid point they’reassociated with.

Each main gridpoint has 8 supporting points.

The red area contains points at which a solution is desired for region #1.

In order to properly account for gravity due to mascons in the green area, stack accelerations are loaded from both red and green regions.

Mascons in the red AND green regions are then solved for, but only mascons in the red region are saved.

Notice that the red areas do not overlap, while the green areas do overlap.

The green “overlap” areas represent computational waste, but they help reduce edge effects.

This region can be larger than the 1st polar region because GRACE’s ground track density is higher at the poles, making polar region computations lengthy.