Can GPS horizontals provide useful information about surface loading?  Case studies in California and Greenland.

John Wahr (U of Colorado) Abbas Khan (DTU Space), Tonie van Dam (U of Luxembourg), Lin Liu (Stanford U), Michiel van den Broeke (U of Utrecht), Chuck Meertens (UNAVCO)

The main issue addressed in this talk:

Most published GPS-based studies of surface loading use only the GPS verticals.

Can GPS horizontals also provide useful information?

GPS

Add load GPS

Add load GPS

GPS receiver moves downward and towards the load

Displacements caused by adding a load

remove load GPS

GPS receiver moves upward and away from the load

Displacements caused by removing a load

0 50 100 150distance between GPS site and disc center (km)

0

1

2

3

Uplift caused by the removal of a 1-m thick, 20-km radius, disc load.

Uplift sensitivity kernel falls off with distance, but has a long tail.

Vertical displacements can help determine the total nearby mass loss (or gain).

Horizontal displacements can help determine the location of the mass loss

.

For example:

If a load to the north is removed, the site goes up and moves southward.

If a load to the south is removed, the site goes up and moves northward

Sensitivity to the removal of a 20-km disc load.

Vertical displacements are 2.0-2.5 times larger than horizontal displacements

Displacements caused by removing a disc of water

of radius 20 km and thickness 1 meter

0 50 100 150distance between GPS site and disc center (km)

0

1

2

3

upward displacement

horizontal displacement, away from disc

Ratio of vertical to horizontal displacement

0 50 100 150distance between GPS site and disc center (km)

0

1

2

3

4

What happens to the vertical-to-horizontal ratio if there are loads at different azimuths?

One thinning glacier

Two thinning glaciers

2.2 × Horizontal = Up

2.2 × Horizontal < Up

The Up values add.The Horizontal vectors partially cancel. So:

GPS

But, it could also work the other way around:

Thinning glacier

2.2 × Horizontal = Up

2.2 × Horizontal > Up

The Up values cancel (one is positive, the other negative).The Horizontal vectors largely add. So:

GPS

Thinning glacier

Thickening glacier

Rest of talk: apply these ideas to two examples of localized load.

Lake Shasta, a reservoir in northern California

Kulusk, a GPS site in southeast Greenland

Lake Shasta

20 km

P349P341

P338

P060

Lake Shasta

1990 1995 2000 2005 2010

-30

-20

-10

0

10

Direction of horizontal motion, for a lake level decrease

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Crustal uplift for 1 m decrease in lake level

mm

2.3 2.8 3.3 3.8 4.3 4.8 5.3 5.8 6.3

Ratio of vertical to horizontal

P349 Up

2007 2008 2009 2010

-1

0

1

East

2007 2008 2009 2010

-2

-1

0

1

North

2007 2008 2009 2010

-2

-1

0

1

P349 lies just south of the lake, and is the site closest to it.

Daily station positions obtained from UNAVCO’s PBO website. SNARF 1.0 reference frame.

P349

P349 Up

2007 2008 2009 2010

-1

0

1

East

2007 2008 2009 2010

-0.4

-0.2

0.0

0.2

0.4

North

2007 2008 2009 2010

-0.4

-0.2

0.0

0.2

0.4

Data have been detrended. Black line = smoothed values.

The horizontals are dominated by north-south displacements

The lake is due north of this site.

P349 Up

2007 2008 2009 2010 2011

-0.6

-0.4

-0.2

0.0

0.2

0.4

GPS

GLDAS

East

2007 2008 2009 2010 2011

-0.10

-0.05

0.00

0.05

0.10

0.15

North

2007 2008 2009 2010 2011

-0.10

-0.05

0.00

0.05

0.10

0.15

Remove loading signal caused by regional soil moisture variability.

Computed using water storage output from Goddard’s GLDAS/Noah land surface model (Rodell, et al 2004).

P349 GPS-minus-GLDAS. Up

2007 2008 2009 2010 2011

-0.4

-0.2

0.0

0.2

0.4

East

2007 2008 2009 2010 2011

-0.10

-0.05

0.00

0.05

0.10

0.15 North

2007 2008 2009 2010 2011

-0.10

-0.05

0.00

0.05

0.10

0.15

GPS minus GLDAS/Noah soil moisture load

Horizontals are mostly in the north-south direction, which is consistent with lake loading.

P349 GPS-minus-GLDAS. Up

2007 2008 2009 2010 2011-0.6

-0.4

-0.2

0.0

0.2

0.4

scaled horizontal

scale factor = 4.1

Toward Lake

2007 2008 2009 2010 2011

-0.10

-0.05

0.00

0.05

0.10

0.15 Perpendicular to Lake

2007 2008 2009 2010 2011

-0.10

-0.05

0.00

0.05

0.10

0.15

Rotate the horizontals through the angle expected from lake loading.

For lake loading, the expected ratio of vertical to horizontal at P349 is 4.1

Direction of horizontal motion, for a lake level decrease

2.3 2.8 3.3 3.8 4.3 4.8 5.3 5.8 6.3

Ratio of vertical to horizontal

P341 GPS-minus-GLDAS. Up

2007 2008 2009 2010 2011

-0.2

-0.1

0.0

0.1

0.2

scaled horizontal

scale factor = 2.3

Toward Lake

2007 2008 2009 2010 2011

-0.05

0.00

0.05

Perpendicular to Lake

2007 2008 2009 2010 2011

-0.05

0.00

0.05

P349 GPS-minus-GLDAS. Up

2007 2008 2009 2010 2011-0.6

-0.4

-0.2

0.0

0.2

0.4

scaled horizontal

scale factor = 4.1

Toward Lake

2007 2008 2009 2010 2011

-0.10

-0.05

0.00

0.05

0.10

0.15 Perpendicular to Lake

2007 2008 2009 2010 2011

-0.10

-0.05

0.00

0.05

0.10

0.15

P060 GPS-minus-GLDAS. Up

2007 2008 2009 2010 2011

-0.2

-0.1

0.0

0.1

scaled horizontal

scale factor = 2.4

Toward Lake

2007 2008 2009 2010 2011

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

Perpendicular to Lake

2007 2008 2009 2010 2011

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

P338 GPS-minus-GLDAS. Up

2007 2008 2009 2010 2011

-0.2

-0.1

0.0

0.1

0.2

scaled horizontal

scale factor = 2.4

Toward Lake

2007 2008 2009 2010 2011

-0.05

0.00

0.05

Perpendicular to Lake

2007 2008 2009 2010 2011

-0.05

0.00

0.05

Vertical Displacement

2007 2008 2009 2010 2011

-0.4

-0.2

0.0

0.2

0.4

P349

P341

P060

P338

inferred lake level (m)

2007 2008 2009 2010 2011

-30

-20

-10

0

10

20

30

P349

P341

P060

P338

from tide gauges

Each site’s vertical displacements have been scaled by the expected (lake level)-to-(vertical) ratio for that site.

Generally good agreement with the observed lake level from tide gauges. The agreement is best for P349, which is closest to the lake.

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Crustal uplift for 1 m decrease in lake level

mm

Greenland

GNET permanent GPS stations (from Mike Bevis, Ohio State)

Kulusuk (KULU), 1996

GPS receiver at Kulusuk, on bedrock along the southeast Greenland coast

All GPS analyses, below, were done by Abbas Khan, using GIPSY.

Helheim Glacier

Catchment

Kangerdlugssuaq glacier

Other glaciers

KULU

Helheim+Kangerdlugssuaq Glaciers

2003 2004 2005 2006 2007 2008 2009 2010 2011

-60

-40

-20

0

20

40

GRACE time series of surface mass, averaged over a disc of radius 250 km.

Helheim+Kangerdlugssuaq Glaciers

2003 2004 2005 2006 2007 2008 2009 2010 2011

-60

-40

-20

0

20

40

GRACE time series of surface mass, averaged over a disc of radius 250 km.

Mass loss began accelerating in 2003/04.

Helheim+Kangerdlugssuaq Glaciers

2003 2004 2005 2006 2007 2008 2009 2010 2011

-60

-40

-20

0

20

40

GRACE time series of surface mass, averaged over a disc of radius 250 km.

Mass loss began accelerating in 2003/04.

Deceleration in 2007/08.

KULU GPS data. IGS05 reference frame.

Trends have not been removed.

KULU GPS. Up

1998 2000 2002 2004 2006 2008 2010

-40

-20

0

20

40

60

KULU GPS. North

1998 2000 2002 2004 2006 2008 2010

-100

-50

0

50

100

KULU GPS. East

1998 2000 2002 2004 2006 2008 2010

-100

-50

0

50

100

KULU up

1998 2000 2002 2004 2006 2008 2010

-15

-10

-5

0

5

10

15

KULU east

1998 2000 2002 2004 2006 2008 2010

-4

-3

-2

-1

0

1

2

KULU north

1998 2000 2002 2004 2006 2008 2010

-4

-3

-2

-1

0

1

2

Trends have been fit and removed over the entire time span. There’s a clear change in slope in late 2003/early 2004.

GRACE and other results also suggest a 2004 acceleration in nearby mass loss.

Helheim+Kangerdlugssuaq Glaciers

2003 2004 2005 2006 2007 2008 2009 2010 2011

-60

-40

-20

0

20

40

Use only the pre-2004 data to determine the trend.

KULU up

1998 2000 2002 2004 2006 2008 2010

0

10

20

30

40

50

KULU east

1998 2000 2002 2004 2006 2008 2010

-15

-10

-5

0

5

KULU north

1998 2000 2002 2004 2006 2008 2010

-15

-10

-5

0

5

Remove the loading effects of snow accumulation (precip-minus–evap-minus-melt).

Use RACMO surface mass balance (SMB) model (van den Broeke et al, 2011).

KULU up

1998 2000 2002 2004 2006 2008 2010

0

10

20

30

40

50

GPS

SMB

KULU east

1998 2000 2002 2004 2006 2008 2010

-15

-10

-5

0

5

GPS

SMB

KULU north

1998 2000 2002 2004 2006 2008 2010

-15

-10

-5

0

5

GPS

SMB

KULU up

1998 2000 2002 2004 2006 2008 2010

0

10

20

30

40

KULU east

1998 2000 2002 2004 2006 2008 2010

-10

-5

0

KULU north

1998 2000 2002 2004 2006 2008 2010

-10

-5

0

GPS minus SMB The direction of the horizontal motion is south-southeast.

Which suggests the post-2004 mass loss was located north-northwest of the site.

KULU. GPS minus SMB. Up

1998 2000 2002 2004 2006 2008 2010

0

10

20

30

40 UP

Away x 2.2

Away from Load

1998 2000 2002 2004 2006 2008 2010

-2

0

2

4

6

8

10

12

Perpendicular to Load

1998 2000 2002 2004 2006 2008 2010

-2

0

2

4

6

8

10

12

The mean horizontal direction is southward along this green line.

Displacements along mean direction

Displacements perpendicular to mean direction.

Horizontal Angle (degrees)

2004 2006 2008 2010date

-120

-115

-110

-105

-100

-95

-90

The direction away from Helheim

Time series of the horizontal direction

These angles are away from points lying east of Helheim

The direction changed in 2007.

So did the GRACE mass loss rate.

Helheim+Kangerdlugssuaq Glaciers

2003 2004 2005 2006 2007 2008 2009 2010 2011

-60

-40

-20

0

20

40

Helheim Glacier

Kangerdlugssuaq glacier

glaciersKULU

This is consistent with the following sequence of events:

(1)Helheim, and glaciers east of Helheim, underwent an acceleration in mass loss rate around 2004.(2)The Helheim rate decreased around 2007, but the rates of the other glaciers did not.

Assume mass loss occurs in two places. One is Helheim Glacier. The other lies somewhere along the green line.

Use the GPS verticals and horizontals to determine a time series for the horizontal loading signal for Helheim and for the second glacier.

Helheim

KULU

Helheim flattens out between mid-2006 and mid-2008, but then starts to lose mass again. The second glaciers(s) keeps losing mass at a reasonably steady rate.

The second glacier is unlikely to be Kangerdlugssuaq, because it’s so far from KULU. Its mass loss rate would have to be 4-5 times the Helheim mass loss rate to explain these numbers.

Amplitudes of horizontal signals

2004 2006 2008 2010date

2

4

6

8

10from Helheim

from second glacierKangerdlugssuaq

Helheim

Implications of the KULU results

1.Mass loss from Helheim Glacier accelerated around 2004, and then decelerated around 2007.

2.Mass loss rates from glaciers east of Helheim, remained relatively constant from 2004 onwards.

1.The actual locations of the other thinning glaciers (both their azimuth and distance from KULU) cannot be unambiguously determined using data from a single GPS site.

2.Multiple GPS sites would allow triangulation, to help uniquely determine which glaciers are losing mass, and by how much.

3.GNET will help.

GENERAL SUMMARY

1) Vertical displacements help determine the total nearby mass loss. Horizontal displacements help determine the location of the mass loss.

The horizontal displacement caused by the removal of a localized load is away from the load.

2) The vertical displacement is 2.0-2.5 times the horizontal displacement. But the ratio is likely to be larger than this if the loading is spread over a range of azimuths. (Though it could also be smaller than this, if the load is positive on one side of the site and negative on the other.)

The End