Estimating variation of groundwater storage within the
Great Lakes Water Basin from GRACE, soil moisture
and lake levels
Joint International GSTM and DFG SPP Symposium,
October 15-17, 2007 at GFZ Potsdam, Germany
J. Huang and J. Halpenny
Geodetic Survey Division, ESS
615 Booth St., Ottawa, ON
Canada’s Natural Resources – Now and for the Future 2
Outline
1. Introduction
2. Method
3. Analysis of monthly GRACE models
4. Estimation of groundwater variation
5. Conclusions
3
1. Introduction
Quebec
L. Superior:82,000 km2
L. Michigan:57,800 km2
L. Huron:59,600 km2
L. Ontario:18,960 km2
L. Erie:25,700 km2
Area of the Great Lakes Water Basin: 766,000 km2
4
2. Method (1/2)
Cnm(ti), Snm(ti)
Least-Squares Fitting
TrendSeasonalSignals
Residuals
GaussianFilter
HarmonicSynthesis
GW VariationEstimation
GL StorageVariation
Snow,Ice, SM
GWVariation
Processing flowchart:
GL: Great Lakes
GW: Groundwater
SM: Soil Moisture
Spherical Harmonic Coefficients
5
2. Method (2/2)
n
m
nminminm
L
n
n
eei PmtSmtC
r
a
r
GMtN
0
*
20
)(sinsin)(cos)()(
Time-Variable (TV) geoid from GRACE:
nirttBttA
ttatttvtCtC
Cnm
CSi
Cnm
CAi
Cnm
iCnmi
Cnmnminm
,...2,14cos2cos
)(2
1))(()()(
00
20000
The model for Least-squares fitting of harmonic time-variable coefficients:
)()()( 00 ttatvtv iCnm
Cnmi
Cnm
Velocity at epoch ti: Signal-to-Noise Ratio (SNR):
Cnm
Cnm
Cnm
Cnm
x
BAavxx
SNR ,,,,ˆ
6
3. Analysis of monthly GRACE models (1/5)
S8,1
Spherical harmonic coefficient time series (red dots) and their LS fitting (blue dot line):
S8,5
S12,1
S12,7
S16,1
S16,9 S20,11
S20,1
7
3. Analysis of monthly GRACE models (2/5)
n
n
m
mCnm
Snm
n
n
m
mCnm
Snm
n
n
m
mCnm
Snm
n
n
m
mCnm
Snm
Linear: Quadratic:
Annual: Semi-annual:
8
3. Analysis of monthly GRACE models (3/5)
Linear: Quadratic:
Annual: Semi-annual:
RMS signal per degree vs. a posteriori standard deviation:
n=14
9
3. Analysis of monthly GRACE models (4/5)Trend (RMS = 15 mm/a): Annual (RMS = 37 mm):
Semi-annual (RMS = 5 mm): Residual (RMS = 27 mm):
10
3. Analysis of monthly GRACE models (5/5)
Method Min Max Mean StdDev RMS
A: Gaussian - 185 262 - 4 46 46
B: Least-Squares + Gaussian - 204 325 - 4 51 51
B - A - 88 103 1 24 24
A: Gaussian Filtering B: Least-Squares Fitting + Gaussian Filtering
Unit: mm
11
4. Estimation of groundwater variation (1/4)
w(,) =
)()()()()( iriannsemiiannitrendiGLB tHtHtHtHtH
dtHwA
tH ixix )(),(1
)(
The mean water-thickness-equivalent over the GLB by:
Each component by:
Simulation:
Global WTE Gridof 15' by 15'
SphericalHarmonic Model
WTE over theGLB
12
CSRRL04:(60 months)
4. Estimation of groundwater variation (2/4)
GFZRL04:(53 months)
13
4. Estimation of groundwater variation (3/4)
Lake Levels:
GLDAS SM&SW:
14
4. Estimation of groundwater variation (4/4)
GroundwaterEstimation fromCSRRL04:
GroundwaterEstimation fromGFZRL04:
15
5. Conclusions
1. The combination of the least-squares fitting and Gaussian filtering enhances the extracted GRACE signal by about 10% over the Gaussian filtering alone.
2. The total water storage variation (RMS=3.5 cm) from GRACE demonstrates close agreement (magnitude and phase) to the soil moisture and snow variation (RMS=3.7 cm) from GLDAS over the Great Lakes Water Basin.
3. The mean lake level variation (RMS=4.1 cm) over the basin demonstrates a comparable magnitude to the GRACE estimate but a phase lag of about 3 months.
4. The estimated groundwater variation (RMS=4.1 cm) implies that groundwater plays a key role in replenishing the Great Lakes.