Arctic Ocean Tides from GRACE Satellite Accelerations Bryan Killett University of Colorado and CIRES, Boulder, CO, USA TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

The Tidal Potential V T

Tides for order m = 2 ~12 hr periods. Semi-diurnal. Largest tides. Adapted from Dr. Sylvain Paris

Tides for order m = 1 ~24 hr periods. Diurnal. Medium tides. Adapted from Dr. Sylvain Paris

Tides for order m = 0 Adapted from Dr. Sylvain Paris

Diurnal Tidal Spectrum Adapted from Desai (1996)

GRACE NASA/courtesy of nasaimages.org.

B A MASCON GRACE relative accel. due to a mascon directly below satellites 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

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

Motivation FES2004 is primarily based on TOPEX/Poseidon data, which doesnt extend north of 66°N. Thus, Arctic ocean tides arent well constrained by satellite altimetry. The GRACE orbit goes up to 89°N. Relative acceleration values between the two GRACE satellites are used to solve for mass concentrations (mascons) on Earths surface. The solution method allows each mascons mass to oscillate at tidal and seasonal frequencies, as well as changing linearly. FES2004 effects have been subtracted from the acceleration values, so the amplitudes at tidal periods represent errors in FES The mass amplitudes are converted to equivalent cm of water amplitudes.

Inversion Details Smoothed residual acceleration values are averaged at 5 second intervals when satellites are north of 50° N latitude. 7 million accelerations total over 7 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.

Tides are NOT Point Masses

Simulation Input – M2 Sine Coef.

Simulation Output – M2 Sine Coef.

Simulation Error – M2 Cos. Coef.

Simulation Input – K1 Sine Coef.

Simulation Output – K1 Sine Coef.

Simulation Error – K1 Cos. Coef.

Resolution Test

Inversion of Real GRACE Data

Non-tidal parameters

FES 2004 – M2 Amplitude

Residual M2 Amplitude

M2 – Diff. of Two 3.5yr Solutions

FES2004 M2 Deg90 Trunc. Error

Change in FES2004 M2 Amp.

FES 2004 – K1 Amplitude

Residual K1 Amplitude – 5 yrs

Residual K1 Amplitude – 7 yrs

K1 – Diff. of Two 3.5yr Solutions

FES2004 K1 Deg90 Trunc. Error

Change in FES2004 K1 Amp.

Original GRACE Power Spectrum

Noise Reduction for Accelerations Used in the Inversion

Original GRACE Power Spectrum

Noise Reduction for Accelerations NOT Used in the Inversion

Original FES2004 Power Spectrum

Conclusions GRACE-derived corrections are: large where FES2004 is large, not generally larger north of 66°N, and much larger than truncation errors.

Conclusions GRACE-derived corrections are: large where FES2004 is large, not generally larger north of 66°N, and much larger than truncation errors. GRACE-derived corrections to FES2004 reduce the variance of accelerations not used in the inversion, so they can improve GRACE processing but cant currently improve tide gauge predictions, probably due to short-scale effects that GRACE cant resolve.

Conclusions GRACE-derived corrections are: large where FES2004 is large, not generally larger north of 66°N, and much larger than truncation errors. GRACE-derived corrections to FES2004 reduce the variance of accelerations not used in the inversion, so they can improve GRACE processing but cant currently improve tide gauge predictions, probably due to short-scale effects that GRACE cant resolve. Two independent estimates agree on a ~1cm noise floor for the GRACE-derived corrections.

Conclusions GRACE-derived corrections are: large where FES2004 is large, not generally larger north of 66°N, and much larger than truncation errors. GRACE-derived corrections to FES2004 reduce the variance of accelerations not used in the inversion, so they can improve GRACE processing but cant currently improve tide gauge predictions, probably due to short-scale effects that GRACE cant resolve. Two independent estimates agree on a ~1cm noise floor for the GRACE-derived corrections. FES2004 amplitudes are too large in the oceans north of 50°N for the tides M 2, K 1, O 1, P 1.