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Absolute Heights and the Elusive 1 cm Geoid Dr. Dru Smith Chief Geodesist, NOAA/NGS
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Transcript of Absolute Heights and the Elusive 1 cm Geoid Dr. Dru Smith Chief Geodesist, NOAA/NGS
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Absolute Heights Absolute Heights and the Elusive and the Elusive
1 cm Geoid1 cm Geoid
Dr. Dru Smith Dr. Dru Smith Chief Geodesist, NOAA/NGSChief Geodesist, NOAA/NGS
NRC - National Academies’ NRC - National Academies’ Mapping Science Committee Mapping Science Committee
MeetingMeeting
Washington, D.C.September 11, 2007
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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?
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Defining “Height”
• Height is…
• Some length• (usually)* • along some path • between two points • in some specified “up”
direction.
?
A
B
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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!– More on this later…
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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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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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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?
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Earth’s Surface
Mean Sea LevelW=WC
Let’s take a closer look at what happens rightat the coastline…
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Earth’s Surface
Q
Q= 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
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Absolute vs. Relative Heights
• Determining heights at the highest accuracy is mostly relative
• Assume some known absolute (=true) height at point A (HA)
• Determine height differences between A and B (HAB = HB-HA)
• Compute height at B:– HB = HA + HAB
• Generally true for accurate Orthometric, Ellipsoidal and Dynamic heights
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Examples of relative heights
• Leveling– Measure geometric changes point to point– Correct for multiple physical effects– Attempts to yield differential geopotential (energy) levels
– Convert from geopotential to dynamic height or orthometric height
– Very time consuming and tedious
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Examples of relative heights• DGPS
– Begin with a known (often permanent) GPS station (pt A)• (Even this is “known” from a global relative
adjustment of stations and orbits)• NGS manages a network of such stations: CORS
– Set up a temporary GPS receiver over point “B”– Take enough measurements (15+ minutes) to drive GPS
inaccuracies out of the equation
• Voila! hAB without any line of sight between A & B
(latitude,longitude,h)
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What does this mean so far?
• Orthometric heights are the most used / most needed for mapping applications
• Determining orthometric heights from leveling is time consuming!
• Determining ellipsoid heights is fast and easy, but they aren’t as useful
• If only there was some way to get “accurate” and “fast and easy”…
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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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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…
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The elusive 1 cm geoid
• Can we know the geoid to 1 cm absolutely?
– Probably
– Basics go back to 1888• With global surface gravity measurements, the
equations exist to approximate the geoid’s location
– Refinements over decades
– “GPS-for-H” drove this from an academic question to a practical one in the last 20 years
– Without consideration of “1 cm” just yet, NGS embarked upon “geoid modeling” in 1990 as a service to the people of the USA
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NGS and the geoid
• 1990 / 1993 – First attempts to get N– Geocentric ellipsoid (shape was “GRS-80”)– Best global MSL fit for geoid
• Problem:– h in USA is h(NAD 83) which is non-geocentric– H in USA is H(NAVD 88) which isn’t fit to MSL
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NGS and the geoid
h
H
N (GEOID93)
The Geoid
A chosen Ellipsoid(Geocentric, GRS-80)
h (NAD 83)
NAVD 88 reference level
(W = constant????)
H (NAVD 88)
The NAD 83 ellipsoidN (GEOID96)
H (NAVD 88) ≈ h (NAD 83) – N (GEOID96)
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NGS and the geoid
• From 1996 on, NGS created “hybrid geoids” to convert from h (NAD 83) to H (NAVD 88)– For 10 year has done its job well:
• “To convert one erroneous datum into another erroneous datum”
– Has never given people “absolute orthometric heights”
• Problems:– NAD 83 is non-geocentric– NAVD 88 has systematic errors (especially in mountains)– Relies on GPS surveys on passive NAVD 88 monuments
• Vulnerable, sparse and moving in time– Requires re-leveling to get updated NAVD 88 heights– Requires re-DGPS to get updated NAD 83 heights
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NGS and the geoid
• The NGS 10 year plan (2007-2017)– Recognizes a better way of doing business
• Remove the non-geocentricity of the ellipsoidal datum
• Define the vertical datum reference surface as being the geoid
• Compute the geoid accurately, and track its changes in time using sparse gravity resurveys– No re-leveling, no re-DGPS– If we know changes to “g” we know changes to “N”
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Can we know the geoid to 1 cm?
• Again, “probably”
• What stands in the way?– Aged and aging gravity data
• 1000’s of surveys, dozens of years
– No existing model for gravity change
– Existing theory has “a few cm” of approximations still built in
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How will NGS achieve a 1 cm geoid?
• Snapshot of gravity– A country-wide airborne survey spanning a few years
and focusing on accuracy and self-consistency
• Temporal gravity tracking– Using both GRACE and episodic absolute gravity
surveys, model g(latitude, longitude, time)
• Improve theory– Chairing an international collaboration of theorists to
drive the last few cm of approximations out of existing computational methods
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Gravity Survey Plan
• Airborne– 10 km spacing over the USA and territories– One time survey– Estimated cost: 5-8 years and $30-50M
• Absolute– Cyclical for episodic checks in fixed locales– Two field meters plus one fixed Superconducting
Gravimeter• Relative
– More frequently attached to “Height Mod” surveys– For field checking aged data against new surveys
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Theoretical Improvements
• New International Association of Geodesy study group devoted to finding this:
– Mathematical equations which, if perfect data were applied, would yield the location of the geoid to sub-cm accuracy
• Estimated time frame: 5-7 years
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Summary
• The use of passive monuments as the method to define and provide access to absolute heights in a dynamic world with access to GPS is no longer appropriate
• A better way, involving a one-time airborne survey followed by low-cost gravity tracking and low-cost GPS-CORS is the best method for delivering accurate absolute orthometric heights quickly
• By 2017, NGS expects to implement these full changes and deliver a new ellipsoidal (“horizontal”) and geopotential (“vertical”) datum– And be able to sustain their absolute accuracy long
into the future
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Questions/Comments?
• Dr. Dru Smith• Chief Geodesist, National Geodetic Survey
• [email protected]• 301-713-3222 x 144