Absolute Heights and the Elusive 1 cm Geoid Dr' Dru Smith Chief Geodesist, NOAANGS

1
Absolute Heights and the Elusive 1 cm Geoid
Dr. Dru Smith Chief Geodesist, NOAA/NGS

• NRC - National Academies
• Mapping Science Committee Meeting
• Washington, D.C.
• September 11, 2007

2
Defining Height

• Isnt it intuitive? Dont we already know what
  it means?
• Generallyyes
• Specificallyno (and its 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?

3
Defining Height

• Height is
• Some length
• (usually)
• along some path
• between two points
• in some specified up direction.

?
B
A
More on this later
4
Dominant Height Systems in use in the USA

• Orthometric
• Colloquially, but incorrectly, called height
  above mean sea level
• On most topographic maps
• Is a gt99 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

5
Orthometric Height (H)

• The distance along the plumb line from the geoid
  up to the point of interest

H
6
Ellipsoid Height (h)

• The distance along the ellipsoidal normal from
  some ellipsoid up to the point of interest

h
h
h
7
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.

8
Orthometric Height (H)

• The distance along the plumb line from the geoid
  up to the point of interest

WW3Constant
H
WW2Constant
WW1Constant
WW4Constant
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 WConstant
9
Sowhich one is the geoid?
Earths Surface
Ccorrect! Why?
WWA
WWB
Mean Sea Level
WWC
WWD
WWE
WWF
10
Earths Surface
Lets take a closer look at what happens right at
the coastline
Mean Sea Level
WWC
11
Q Reference point for a tide gage
Earths Surface
hQ Distance above Local Mean Sea Level (LMSL)
HQ Orthometric Height
Q
HQ
hQ
The Geoid
eQ
Mean Sea Level
eQ Error in assuming MSL geoid at this tide
gage
12
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
  (DHAB HB-HA)
• Compute height at B
• HB HA DHAB
• Generally true for accurate Orthometric,
  Ellipsoidal and Dynamic heights

13
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

14
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! DhAB without any line of sight between A
  B

(Dlatitude, Dlongitude, Dh)
15
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 arent as useful
• If only there was some way to get accurate and
  fast and easy

16
Geoid Undulation (N)

• The distance along the ellipsoidal normal from
  some ellipsoid up to the geoid

h
H h-N
H
The Geoid
N
A chosen Ellipsoid
17
H h-N

• Good to sub-mm over most of the world
• Good to lt 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

18
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 geoids
  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

19
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 isnt fit to MSL

20
NGS and the geoid
H (NAVD 88)
h (NAD 83)
H
NAVD 88 reference level (W constant????)
h
The NAD 83 ellipsoid
The Geoid
N (GEOID96)
N (GEOID93)
A chosen Ellipsoid (Geocentric, GRS-80)
H (NAVD 88) h (NAD 83) N (GEOID96)
21
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

22
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

23
Can we know the geoid to 1 cm?

• Again, probably
• What stands in the way?
• Aged and aging gravity data
• 1000s of surveys, dozens of years
• No existing model for gravity change
• Existing theory has a few cm of approximations
  still built in

24
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

25
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

26
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

27
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

28
Questions/Comments?

• Dr. Dru Smith
• Chief Geodesist, National Geodetic Survey
• Dru.Smith_at_noaa.gov
• 301-713-3222 x 144