j. huang and j. halpenny geodetic survey division, ess 615 booth st., ottawa, on

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.