Recent Research at The National Geodetic Survey Dru Smith Chief Geodesist, NGS

Recent Research at The National Geodetic Survey

Dru SmithChief Geodesist, NGS

University of New HampshireNov 16, 2012 1

Outline

• Overview of NGS and NOAA• Primer on Physical Geodesy• Recent Research

– Geoid Slope Validation Survey of 2011

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President

Department of Commerce

NOAA

National Ocean Service

National Geodetic Survey

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NOAA

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5

NOS Organization

*

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Navigation Services of NOS

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Tides and CurrentsSea Level Datums (MLLW, MSL, MHW, etc)Water Levels (Great Lakes, etc)

National Spatial Reference System Terrestrial Datums Coordinates Shoreline DefinitionImageryGravityGeodesy

Nautical ChartsHydrodynamic Models

NGS Mission StatementTo define, maintain and provide access to the National

Spatial Reference System (NSRS) to meet our nation’s economic, social, and environmental needs.

The NSRS is a consistent coordinate system that defines latitude, longitude, height, scale,

gravity, and orientation throughout the United States.

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Geodesy

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What is Geodesy?• The scientific study of

– the size and shape of the Earth, – its gravity field, – the precise determination of positions on the Earth’s surface

and – the measurement of geodynamic phenomena

• such as the motion of the magnetic poles,• tides and • tectonic plate motion.

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“Physical” Geodesy

• Gravity• Heights• Geoid• Vertical Datum

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Defining “Height”• Isn’t it intuitive? Don’t we already “know” what it

means?

– Generally…yes

– Specifically…no (and it’s important!)

• These statements keep geodesists awake at night:– What is the height of __________?– How accurately can we know a height?– Where will water flow if this region is flooded?– How fast are heights changing?Nov 16, 2012 University of New Hampshire 11

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Defining “Height”• Height is…

• Some length• (usually)* • along some path • between two points • in some specified “up”

direction.

?

* = More on this later

A

B

Dominant Height Systems in use in the USA

• Orthometric– Colloquially, but incorrectly, called “height above mean sea level”– On most topographic maps– Is a >99% successful method to tell which way water will flow

• Ellipsoid– Almost exclusively from GPS– Poor at determining water flow anywhere “non mountainous”

• Dynamic– Directly proportional to potential energy : always tells which way water will

flow– Dynamic heights are not lengths!– Used primarily in describing water levels in the Great Lakes

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Orthometric Height (H)• The distance along the plumb line from the geoid up

to the point of interest

H

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“The Geoid”

Ellipsoid Height (h)• The distance along the ellipsoidal normal from some

ellipsoid up to the point of interest

h

hh

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Some definitions are required…

• “the geoid”

– is the one equipotential surface surrounding the Earth which best fits to global mean sea level in a least squares sense.

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Orthometric Height (H)• The distance along the plumb line from the geoid up

to the point of interest

H

The geoid. Its gravity potential energy (W) is constant at all points on itself. That is W = W0 = Constant. There are an infinitude of such surfaces where W=Constant…

W=W1=Constant

W=W2=Constant

W=W3=Constant

W=W4=Constant

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Figure of the Earth – The geoid

Yes, the ocean surface does “dip” toward the center of the Earth in the Indian Ocean*

…and it “swells” away from the center of the Earth nearNew Guinea*

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* Relative to an ellipsoid. To be formal, the geoid is entirely convex, not “star shaped”

Earth’s Surface

Mean Sea Level

W=WA

W=WE

W=WD

W=WC

W=WB

W=WF

So…which one is the geoid?C…correct! Why?

Identifying “The geoid”

Earth’s Surface

Mean Sea LevelW=WC

Let’s take a closer look at what happens rightat the coastline…

Earth’s Surface

hQ

hQ = Distance above Local Mean Sea Level (LMSL)

Q

Q = Reference point for a tide gage

HQ = Orthometric Height

HQ

Mean Sea Level

The Geoid

eQ

eQ = Error in assuming MSL = geoid at this tide gage

Geoid Undulation (N)• The distance along the ellipsoidal normal from some

ellipsoid up to the geoid

h H

N

The Geoid

A chosen Ellipsoid

H ≈ h-N

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Stokes Integral

• Just because a really complicated equation had to be in here somewhere

• In English: if we measure gravity all over the Earth, we can know the geoid undulation at any location on Earth

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ddSgN cos),,,(,),( 00

90

90

360

000

Geoid

Ellipsoid

Earth’sSurface

Coast

From GPS

How “high above‘sea level’ ” am I?(FEMA, USACE,Surveying and Mapping)

From Gravity

OceanSurface

From Satellite Altimetry

How large are near-shorehydrodynamic processes?(Coast Survey, CSC,CZM)

Gravity measurements help answer two big questions…

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GRAV-D• In FY12 airborne surveys have been conducted

in the Great Lakes and Texas• 16.23% of the country is completed• Subsequent FY12 surveys will focus on the

Great Lakes, Maine, and Alaska

Pre-FY 2010FY 2010

FY 2011

Planned FY 2012

• All Gulf of Mexico data released publicly, more coming soon

• Data and metadata at: http://www.ngs.noaa.gov/GRAV-D/data_products.shtml

Data Released

FY 2012

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H ≈ h-N

• Good to sub-mm over most of the world

• Good to < 1 cm anywhere in the USA

• If determining N were fast (it is) and accurate (well…) then H can be determined from GPS!

• That brings us to…Nov 16, 2012 University of New Hampshire 26

The Geoid Slope Validation Survey of 2011

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Goal of the survey

• Observe geoid shape (slope) using multiple independent terrestrial survey methods– GPS + Leveling– Deflections of the Vertical

• Compare observed slopes (from terrestrial surveys) to modeled slopes (from gravimetry or satellites)– With / Without new GRAV-D airborne gravity

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The Chosen Line

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325 km218 points1.5 km spacing

South TexasJuly-October, 2011hot…Hot…HOT!

Surveys Performed

• GPS: 20 identical. units, 10/day leapfrog, 40 hrs ea.

• Leveling: 1st order, class II, digital barcode leveling

• Gravity: FG-5 and A-10 anchors, 4 L/R in 2 teams

• DoV: ETH Zurich DIADEM GPS & camera system

• LIDAR: Riegl Q680i-D, 2 pt/m2 spacing, 0.5 km width

• Imagery: Applanix 439 RGB DualCam, 5000’ AGL

• Other:– RTN, short-session GPS, extra gravity marks around Austin, gravity

gradients

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GPSDoV

Leveling

Gravity

LIDAR/Imagery

LIDAR

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Blended LIDAR with NED

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Empirical Error Estimates

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• sh (OPUS-S) : 2 - 6 cm – GPSCOM combination: ~ 4 mm – (no significant baseline dependency)

• => 16 mm RMS over GSVS11

• sx , sh : 0.06 arcseconds – ~ 0.43 mm / 1.5 km => 6.6 mm RMS over GSVS11

Existing Geoids vs GSVS11

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Austin (North end)

Rockport (South end)

0.4 - 15

15 - 30

30 - 46

46 - 63

63 - 81

81 - 101

101 - 122

122 - 145

145 - 172

172 - 204

204 - 247

247 - 325

0

0.5

1

1.5

2

2.5

3

3.5

Combined RMS errors of GPS, Leveling and Gravimetric Geoid models

USGG2009

Distances between points (km)

RMS

Erro

rs (c

m)

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0.4 - 15

15 - 30

30 - 46

46 - 63

63 - 81

81 - 101

101 - 122

122 - 145

145 - 172

172 - 204

204 - 247

247 - 325

0

0.5

1

1.5

2

2.5

3

3.5

Combined RMS errors of GPS, Leveling and Gravimetric Geoid models

USGG2009EGM2008

Distances between points (km)

RMS

Erro

rs (c

m)

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EGM2008 is better here

USGG2009 is

better h

ere

0.4 - 15

15 - 30

30 - 46

46 - 63

63 - 81

81 - 101

101 - 122

122 - 145

145 - 172

172 - 204

204 - 247

247 - 325

0

0.5

1

1.5

2

2.5

3

3.5

Combined RMS errors of GPS, Leveling and Gravimetric Geoid models

USGG2009EGM2008xEGM-G

Distances between points (km)

RMS

Erro

rs (c

m)

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Adding GOCO2s makes th

ings worse

hereAdding GOCO2s makes

things better here

0.4 - 15

15 - 30

30 - 46

46 - 63

63 - 81

81 - 101

101 - 122

122 - 145

145 - 172

172 - 204

204 - 247

247 - 325

0

0.5

1

1.5

2

2.5

3

3.5

Combined RMS errors of GPS, Leveling and Gravimetric Geoid models

USGG2009EGM2008xEGM-GxEGM-GA

Distances between points (km)

RMS

Erro

rs (c

m)

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Airborne Gravity Improves the Geoid across ALL DISTANCES

0.4 - 15

15 - 30

30 - 46

46 - 63

63 - 81

81 - 101

101 - 122

122 - 145

145 - 172

172 - 204

204 - 247

247 - 325

0

0.5

1

1.5

2

2.5

3

3.5

Combined RMS errors of GPS, Leveling and Gravimetric Geoid models

USGG2009EGM2008xEGM-GxEGM-GAxUSGG-GA-R-K480

Distances between points (km)

RMS

Erro

rs (c

m)

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New software makes

things worse here

New software

Makes things

better here

0.4 - 15

15 - 30

30 - 46

46 - 63

63 - 81

81 - 101

101 - 122

122 - 145

145 - 172

172 - 204

204 - 247

247 - 325

0

0.5

1

1.5

2

2.5

3

3.5

Combined RMS errors of GPS, Leveling and Gravimetric Geoid models

USGG2009EGM2008xEGM-GxEGM-GAxUSGG-GA-R-K480GPS/Leveling Errors

Distances between points (km)

RMS

Erro

rs (c

m)

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Let’s remove thisfrom all of the other bars to leave geoid-only RMSE

0.4 - 15

15 - 30

30 - 46

46 - 63

63 - 81

81 - 101

101 - 122

122 - 145

145 - 172

172 - 204

204 - 247

247 - 325

0

0.5

1

1.5

2

2.5

3

3.5

Predicted Errors of various geoid models over GSVS11 after removal of GPS/Leveling error budget

USGG2009EGM2008xEGM-GxEGM-GAxUSGG-GA-R-K480

Distances between points (km)

RMS

Erro

rs (c

m)

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The “1 cm geoid”

Old minus new leveling

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North (Austin)

South(Rockport)

Conclusions• For GSVS11, adding airborne gravity data

improves geoid slope accuracy at nearly all distances <325 km

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Conclusions• A “1 cm” geoid is achievable in coastal areas

– With good GPS, this means “2 cm” differential orthometric heights for all distances between 0 and 300 km (at least)

– An acceptable replacement for leveling over “long” (> 150 km) lines

– Leveling remains the most precise local differential height tool

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Future Work

• Dozens of studies, comparing all of the terrestrial positioning techniques of GSVS11

• GSVS13: IOWA!!!– Higher elevation, more complicated geoid,

additional measurements (borehole gravimetry?)

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Questions/Comments?

Dru.Smith@noaa.gov

http://www.ngs.noaa.gov/GEOID/GSVS11/index.shtml

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Extra Slides

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Ortho = 500 mDynam = 498 m

Ortho = 501 mDynam = 498 m

Ortho = 503 mDynam = 498 m

Ortho = 502 mDynam = 498 m

The Geoid(W = constant = W0)

Some Equipotential Surface(W = constant = W1)

Orthometric Height = Physical Length along Plumb Line from Geoid to SurfaceDynamic Height = (W0-W1) / g45 : Has no geometrical meaning

Plumb Lines

Orthometric versus Dynamic Heights

Equipotential : Having constant gravity potential energy (W) [Not the same as “constant gravity (g)”]

g45 = A constant arbitrary gravity value

• At the Geoid: Ortho. = Dynamic = 0• As ortho Height increases, so does the potential discrepancy between orthometric and dynamic height

Dynamic Heights are directly related to water levels!!

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