grace science team meeting october 15-17, 2007 potsdam germany alternative gravity field...

GRACE Science Team Meeting October 15-17, 2007 Potsdam Germany

Alternative Gravity Field Representations: Solutions, Characteristics, and Issues

Michael M. Watkins, Dah-Ning Yuan, Gerhard Kruizinga

Jet Propulsion LaboratoryCalifornia Institute of Technology


Overview

• GRACE gravity validation solutions

• Mascon modeling for surface mass variations• Characterisics• Issues

• Mascon solution from GRACE KBRR data

• Mascon solution from “filtered” GRACE KBRR residual

• Summary


JPL GRACE Gravity Validation Solution

• KBR1B, GPS1B, ACC1B, and SCA1B from GRACE L1B– AOD RL04– FLINN GPS ephemeris and clock solution

• Release 4 harmonic solutions from April 2002 to July 2007– Stochastic GPS transmitter clock & GPS phase biases– Daily ACC biases, KBRR empirical biases every orbital revolution– Global 120x120 harmonic partials from KBRR data– Global 90x90 harmonic partials from GPS data


Mascon Modeling for Surface Mass Variation

• Mascon models in MIRAGE software– Point mass, flat disk, spherical cap and spherical ring– Equal area or variable area (with latitude)– Compute direct gravity acceleration from mascons, no truncation from any conversion to harmonics

• Same dynamic models, local parameterization, and reference orbit for GRACE as our harmonic solution.

• Simultaneous solution for all mascon regions – Use both GPS and KBR data for solution


Advantages of Mascon Basis vs. Spherical Harmonic Basis Functions

• The mass concentration solution is localized in both time and space.

• Weakens correlations between regional solutions– Less “leakage” and propagation of long period errors

• The application of spatial constraints are easier to implement than with spherical harmonics

• Potentially higher temporal and spatial resolution than harmonic solution


Distribution of 4 Equal Area Spherical Caps

Monthly Smoothed Surface Mass Variation Mapfrom KBRR Mascon Solution


Gravity Solution from Filtered KBRA Residual

RR-Resid.RR-Obs. MIRAGE

GravitySolution

FilterRA-Resid.

Monthly Stacked Residual Map vsSmoothed Surface Mass Variation Map from Mascon Solution

Using CRN filtered KBRA Residual


Issues on the Estimate of Mascon

• Loading effect not included in the computation of perturbing force on a spacecraft

• Optimal time and spatial correlation between the mascons

• Apriori constraint for the mascons


Summary - I

• JPL RL04 harmonic solutions are available from Apr. 2002 through Jul. 2007 (except Jun/03, Jul-Oct/04).

• Mascon solutions computed for entire globe of Earth with KBRR are availabe from Jan. 2003 through Dec. 2007.

• Surface mass variation map from mascons generally consistent with harmonics for large features but appear able to resolve and localize smaller features more cleanly.


Summary - II

• Stacked CRN filtered KBRA residual map provides the most detail RA anomaly in a geographical map. Thanks to the near realistic nominal mean gravity model.

• Mascon solution using CRN filtered KBRA residual provides the cleanest surface mass variation map compared to KBRR solutions.


Background Material


Harmonic Solution

• FLINN GPS ephemeris and clock solution

• Parameterization for GRACE orbit determination– Daily ACC biases– KBR empirical biases every orbital revolution– Stochastic GPS transmitter clock & GPS phase biases

• Estimated gravity harmonics– 120x120 harmonic partials from KBRR data– 90x90 harmonic partials from GPS data.


Background Model Improvement

• Nominal gravity model - GIF22A to degree 180

• IERS 2003– J2-dot, J3-dot, J4-dot, C21/S21-dot– solid earth tide– solid earth pole tide

• Ocean tide using convolution formalism with weights derived from FES04 model to degree 90 (Desai)

• Ocean pole tide SCEQ (Desai) model to 30x30


• Estimated globally distributed 4 equal-area spherical cap mascons

• Optionally apply a spatial correlation of the form:

dij is the angular distance between mascon i and j; D is the correlation distance

Mascon Solution

(dij D)e


• Gaussian spectral smoothing with a spherical cap applied to harmonic solutions (Swenson and Wahr, 2002).

• Gaussian discrete smoothing with a spherical cap applied to mascon solutions (Jekeli, 1981).

Post-processing of Harmonic and Mascon Solutions in Surface Water Variations

msinSmcosC

)(sinWK

aH

mm

mmwater

earthe),(water

0 01

12

3

2


Post-processing of Harmonic Solution in Surface Water Variations

= Gaussian smoothing factor W

= Load Love number K

= Normalized Legendre Function m

= Mean density of Earth earth

= Density of water water

meanmSmonthlymSmS meanmCmonthlymCmC

(Swenson and Wahr, 2002)

msinSmcosC

)(sinWK

aH

mm

mmwater

earthe),(water

0 01

12

3

2

Monthly Surface Mass Variation Mapfrom KBRR Harmonics Solution


Gravity Solution from Filtered KBRA Residual

• KBRR residual

• CRN filter

• KBRA residual

– Monthly stacked residual map

• Gravity solution (harmonics and mascon)

– Monthly smoothed surface mass variation map


Future Works

• Comparisons with hydrology models & in-situ data will be used for selection of solution strategy in general.

• Mascon solution strategies• Submonthly intervals• Correlation between regional mascon solutions• Sensitivity to the modeling errors

Monthly Surface Mass Variation Map from L1B KBRA Mascon Solution

Monthly Surface Mass Variation Map from CRN filtered KBRA-only Mascon Solution

grace science team meeting october 15-17, 2007 potsdam germany alternative gravity field...

Documents

grace kbrr datamascon

potsdam germanydistribution

mascon solutions

simultaneous solution

potsdam germanymascon

kbrr empirical biases

kbra residual map

mascon regions