Recent Research at The National Geodetic Survey Dru Smith Chief Geodesist, NGS
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Transcript of 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.
?
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?
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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