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.