Consistency of Earth Rotation, Gravity,
and Shape Measurements
Richard S. Gross*, David Lavallée‡, Geoffrey Blewitt†‡, Peter Clarke‡
*Jet
Propulsion Laboratory, California Institute of Technology, Pasadena, USA
†University of Nevada, Reno, USA
‡University of Newcastle, Newcastle upon Tyne, UK
GRACE Science Team Meeting
October 15–17, 2007
Potsdam, Germany
Overview
• Changes in the surface density field of the Earth
•
Change the Earth’s shape
• Measured by GPS
•
Change the Earth’s rotation
• Measured by variousspace-geodetic techniques
•
Change the Earth’s gravitational field
• Measured by SLR and GRACE
• Study the degree-2 harmonics of changing surface mass loads
•
Measurements
• GRACE (UTCSR RL01 & RL04)
• GPS
• Earth rotation (SPACE2005)
•
Models
• Atmospheric surface pressure (NCEP/NCAR Reanalysis)
• Ocean bottom pressure (ECCO/JPL data assimilating model kf049f)
• Land hydrology (LaDWorld-Euphrates)
• Global surficial fluid mass conservation
• Assess consistency of measurements and models
•
Increases confidence in both measurements and models if they agree
GRACE Mass Load Measurements
• GRACE
• Monthly valuessince April 2002
• UTCSR RL01 and UTCSR RL04
• 34 values spanning April 2002 to
May 2005 (end of GPS data)
• Pre-processing
• Add back monthly averaged
AOD1B product
• Remove effects of ocean pole
tide from RL01 (but not RL04)
• Convert degree-2 Stokes
coefficients to coefficients of
surface mass density
• Remove mean and trend
SLR Mass Load Measurements
• UT Center for Space Research
• GRACE replacement series
• Provided to replace UTCSR RL01
C20 coefficient
• C20 from GRACE Technical Note 05
• C21, S21, C22, and S22 from Cheng
(personal communication, 2007)
• Monthly valuessince April 2002
• 34 values spanning April 2002 to
May 2005 (end of GPS data)
• Pre-processing
• Add back monthly averaged
AOD1B product
• Remove effects of ocean pole tide
• SLR series consistent with UTCSR
RL01 which included ocean pole tide
• Convert degree-2 Stokes
coefficients to coefficients of
surface mass density
• Remove mean and trend
GPS Mass Load Measurements
• GPS station distribution
• Land-rich, ocean-poor
• Surface mass load
• Strong over land, weak over oceans
• Designer basis functions
(Clarke et al., 2007)
• Expand load over just the land
• Ocean load includedby conserving
mass
• Land-ocean mass transfer
• Equilibrium responseof oceans to load
• Transform coefficients of new basis
functions back to SH coefficients
• GPS mass load series
• From SIO reanalysis GPS data
• Spans 1996.0 – 2005.4
at fortnightly intervals
• Pre-processing
• Form monthly averages
• Linearly interpolate to epochs
of GRACE data
• Remove mean and trend
Earth Rotation Mass Load Measurements
• Combined EOP Series
• SPACE2005
• Kalman filter-based combination
of LLR, SLR, VLBI, and GPS Earth
orientation measurements
• Kalman filter self-consistently
estimates polar motion rate & hence
polar motion excitation functions
• Spans 1976 – 2005 at daily intervals
• Pre-processing
• Remove long-period tidal effects
• High pass filter with 4-year cutoff
period to remove signals longer
than span of GRACE data
• Remove NCEP Reanalysis
winds and ECCO/JPL data
assimilative (kf049f) currents
• Convert residual to degree-2
harmonics of surface mass density
• Form monthly averages to be
consistent with GRACE and
land hydrology data
• Linearly interpolate to epochs
of GRACE data
• Remove mean and trend
Atmospheric Surface Pressure Model
• NCEP/NCAR Reanalysis
• 6-hour values
• Spans 1948 to present
• Inverted barometer
approximation
• Obtained from IERS Special
Bureau for the Atmosphere
• Pre-processing
• Determine degree-2 harmonics
of surface mass density
• Form monthly averages to be
consistent with GRACE and
land hydrology data
• Linearly interpolateto epochs
of GRACE data
• Remove mean and trend
Ocean Bottom Pressure Model
• ECCO/JPL data assimilative
• Spans 1993 – 2006.2 at 12-hour
intervals
• Near global spatial domain
• 72.5°S to 72.5°N latitude with a variable
resolution of 1/3° at equator to 1° at
poles and a longitudinal resolution of 1°
• 46 vertical levels with thickness ranging
from 10 m at surface to 400 m at depth
• Forced with NCEP/NCAR reanalysis
surface fluxes
• Twice daily wind stress
• Daily heat flux and evaporationprecipitation fields (freshening only)
• Atmospheric surface pressure not used
• Assimilated altimetry and XBT data
• Series designator: kf049f
• Pre-processing
• Correct for Boussinesq effects
• Determine degree-2 harmonics
of surface mass density
• Form monthly averages
• Linearly interpolate toepochs
of GRACE data
• Remove mean and trend
Land Hydrology Model
• LaDWorld (Euphrates)
• Land Dynamics(LaD) model of
Milly and Shmakin (2002)
• Global spatial domain
• 89.5°S to 89.5°N latitude with a
1°x1° horizontal resolution
• Forced by
• Climate Prediction Center Merged
Analysis of Precipitation (CMAP)
• Near-surface air temperature,
humidity, and wind speed
• Radiation
• Spans 1980–2005.4 at monthly
intervals
• Pre-processing
• Determine degree-2 harmonics
of surface mass density
• Sum contributions of snow,
root-zone soil water, and
groundwater
• Linearly interpolateto epochs
of GRACE data
• Remove mean and trend
Global Mass Conservation
• Impose global mass
conservation
• Total mass of atmosphere,
oceans, and land water should
be constant
• Mass of an individual component,
such as the atmosphere, will change
as water in its various phases cycles
through it
• Models of atmosphere and land
hydrology include mass changes
• Ocean model does not
• Applied forcing mechanisms do not
change mass of ocean model
• Add layer of water to surface of
oceans of just the right time
varying thickness to make total
mass of atmosphere, oceans,
and land water a constant
• Pre-processing
• Determine degree-2 harmonics
of surface mass density of this
global mass conserving layer
• Remove mean and trend
Mass Load Measurements
Correlation
(95% significance level = 0.51)
(2,0) cosine
RL01 RL04
RL01
1.0
RL04
0.83
1.0
(2,1) cosine
(2,1) sine
RL01 RL04
RL01
1.0
RL04
RL01 RL04
0.40
RL01
1.0
RL04
1.0
1.0
(2,2) cosine
(2,2) sine
RL01 RL04
RL01
RL04
1.0
0.81
RL01 RL04
0.55
RL01
1.0
RL04
1.0
0.95
1.0
Mass Load Measurements
Correlation
(95% significance level = 0.51)
(2,0) cosine
RL01 RL04
RL01
1.0
RL04
SLR
0.83
0.65
1.0
0.73
SLR
1.0
(2,1) cosine
RL01 RL04
RL01
1.0
RL04
(2,1) sine
SLR
RL01 RL04
0.40
0.52
RL01
1.0
0.03
RL04
1.0
SLR
SLR
1.0
RL01
RL04
SLR
1.0
0.56
1.0
0.53
1.0
(2,2) cosine
RL01 RL04
SLR
0.81
(2,2) sine
SLR
RL01 RL04
0.55
0.34
RL01
1.0
0.45
RL04
1.0
SLR
1.0
SLR
0.95
0.83
1.0
0.85
1.0
Mass Load Measurements
Correlation
(95% significance level = 0.51)
(2,0) cosine
RL01 RL04
RL01
1.0
RL04
SLR
GPS
0.83
0.65
0.61
1.0
0.73
0.71
1.0
0.87
SLR
GPS
1.0
(2,1) cosine
RL01 RL04
RL01
1.0
RL04
(2,1) sine
SLR
GPS
0.40
0.52
0.49
RL01
RL01 RL04
1.0
0.03
0.19
SLR
1.0 −0.03
RL04
GPS
1.0
GPS
1.0
RL01
RL04
1.0
GPS
0.56
0.71
1.0
0.53
0.61
1.0
0.53
SLR
1.0
(2,2) cosine
RL01 RL04
SLR
0.81
(2,2) sine
SLR
GPS
RL01 RL04
0.55
0.34
0.18
RL01
1.0
0.45
0.43
SLR
1.0 −0.09
RL04
GPS
1.0
GPS
SLR
1.0
SLR
GPS
0.95
0.83
0.61
1.0
0.85
0.64
1.0
0.63
1.0
Mass Load Measurements
Correlation
(95% significance level = 0.51)
(2,0) cosine
RL01 RL04
RL01
1.0
RL04
SLR
GPS EOP
0.83
0.65
0.61 0.47
1.0
0.73
0.71 0.53
1.0
0.87 0.68
SLR
GPS
1.0 0.60
EOP
1.0
(2,1) cosine
RL01 RL04
RL01
1.0
RL04
(2,1) sine
SLR
GPS EOP
0.40
0.52
0.49 0.37
RL01
RL01 RL04
1.0
0.03
0.19 0.59
SLR
1.0 −0.03 0.07
RL04
GPS
1.0 0.40
GPS
EOP
1.0
EOP
1.0
RL01
1.0
EOP
0.71
0.83
1.0
0.53
0.61
0.81
1.0
0.53
0.60
1.0
0.56
1.0
(2,2) sine
SLR
GPS
RL01 RL04
0.55
0.34
0.18
RL01
1.0
0.45
0.43
SLR
1.0 −0.09
RL04
GPS
1.0
GPS
RL04
GPS
0.56
SLR
(2,2) cosine
RL01 RL04
SLR
0.81
SLR
1.0
SLR
GPS
0.95
0.83
0.61
1.0
0.85
0.64
1.0
0.63
1.0
Mass Load Measurements & Models
Mass Load Measurements & Models
(95% significance level of correlation = 0.51)
(2,0) cosine
Models
RL01
RL04
SLR
GPS
EOP
Models RL01
1.0
0.62
(37.9)
1.0
(48.5)
(88.3)
(6.1)
(25.7)
RL04
0.70
0.83
1.0
SLR
0.94
0.65
0.73
1.0
GPS
0.88
0.61
0.71
0.87
1.0
EOP
0.57
0.47
0.53
0.68
0.60
1.0
(2,1) cosine
Models
RL01
RL04
SLR
GPS
EOP
Models RL01
0.70
1.0
(44.4)
1.0
(−14.4)
(−5.9)
(38.1)
(−14.9)
RL04
0.26
0.40
1.0
SLR
0.33
0.52
0.03
1.0
greatest correlation between independent measurements
greatest correlation with models
(variance of measurement explained by models in percent)
(greatest variance explained)
(2,1) sine
GPS
0.65
0.49
0.19
−0.03
1.0
EOP
0.46
0.37
0.59
0.07
0.40
1.0
Models RL01
Models
1.0
0.76
RL01 (55.9)
1.0
RL04 (58.9)
SLR
(42.4)
GPS (30.2)
EOP
(61.0)
(2,2) cosine
Models
RL01
RL04
SLR
GPS
Models RL01
1.0
0.40
(16.2)
1.0
(51.4)
(5.0)
(15.2)
RL04
0.74
0.55
1.0
SLR
0.26
0.34
0.45
1.0
RL04
0.78
0.81
1.0
SLR
0.67
0.56
0.53
1.0
GPS
0.56
0.71
0.61
0.53
1.0
(2,2) sine
GPS
0.59
0.18
0.43
−0.09
1.0
Models RL01
Models
1.0
0.93
RL01 (69.2)
1.0
RL04 (75.9)
SLR
(61.9)
GPS (29.1)
RL04
0.92
0.95
1.0
SLR
0.82
0.83
0.85
1.0
GPS
0.60
0.61
0.64
0.63
1.0
EOP
0.78
0.83
0.81
0.60
0.56
1.0
Summary
• Studied degree-2 harmonics of the Earth’s surface mass load
•
•
•
Gravity (GRACE & SLR), displacement (GPS), and rotation measurements
Atmosphere, ocean, and land hydrology models including global mass conservation
During April 2002 (start of GRACE) through April 2005 (end of GPS)
• GRACE measurements
•
•
•
RL04 & RL01 agree best with models of surface mass load for (2,2) sine coefficient
RL04 agrees best with models of surface mass load for (2,2) cosine coefficient
RL01 agrees best with models of surface mass load for (2,1) cosine coefficient
• GPS measurements
•
Agree nearly as well with models of surface mass load as RL01 for (2,1) cosine
• SLR measurements
•
Agree best with models of surface mass load for (2,0) cosine coefficient
• Earth rotation measurements
•
Agree best with models of surface mass load for (2,1) sine coefficient
• Each technique contributes tounderstanding surface mass load