APPENDIX C — ELEVATION SURVEYS
APPENDIX C — ELEVATION SURVEYS
Vertical Datums.
In 2001, the American Society for Photogrammetry and Remote Sensing
(ASPRS) published a manual entitled: "Digital Elevation Model Technologies and
"Applications: The DEM Users Manual." Chapter 2 of this manual provides an
excellent reference on vertical datums. It explains reasons why the North
American Vertical Datum of 1988 (NAVD 88) has replaced the obsolete National
Geodetic Vertical Datum of 1929 (NGVD 29). NGVD 29 was based on an
erroneous assumption that mean sea level at 26 tidal gauge sites all represented
the same (zero) elevation. Furthermore, NGVD 29 benchmarks throughout the
U.S. suffered from an accumulation of relative errors, exceeding 1.5 meters in
some locations.
NAVD 88 is the only official vertical datum of the U.S., and it is best suited for
GPS surveys that yield network accuracies. However, the NSRS still includes
many NGVD 29 benchmarks that were surveyed with differential leveling and
have never been rigorously surveyed with GPS to establish accurate ellipsoid
heights.
For any point on the Earth being surveyed with GPS, the ellipsoid height is the
height above or below the WGS84 reference ellipsoid, i.e., the distance between
a point on the Earth's surface and the WGS84 ellipsoidal surface, as measured
along the normal (perpendicular) to the ellipsoid at the point and taken positive
upward from the ellipsoid. Defined as "h" in the equation: h = H + N (see Figure
C.1).
The geoid is that equipotential (level) surface of the Earth's gravity field which, on
average, coincides with mean sea level in the open undisturbed ocean. In
practical terms, the geoid is the imaginary surface where the oceans would seek
mean sea level if allowed to continue into all land areas so as to encircle the
Earth. The geoid undulates up and down with local variations in the mass and
density of the Earth. The local direction of gravity is always perpendicular to the
geoid.
What we call the elevation on a FEMA EC is technically its orthometric height.
The orthometric height is the height of a point above the geoid as measured
along the plumbline between the geoid and a point on the Earth's surface, taken
positive upward from the geoid. It is defined as "H" in the equation: H = h - N
(transposed from the above equation).
Evaluation of Alternatives in Obtaining Structural Elevation Data
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APPENDIX C — ELEVATION SURVEYS
“Geoid”
PO
P
Earth’s
Surface
Ocean
Mean
Sea
Level
Ellipsoid
“h = H + N”
N
h
Q
h (Ellipsoid Height) = Distance along ellipsoid normal (Q to P)
H
(Plumb Line)
N (Geoid Height) = Distance along ellipsoid normal (Q to PO)
H (Orthometric Height) = Distance along plumb line (PO to P)
Figure C.1 — Relationships between Ellipsoid, Geoid*, and Orthometric Heights
*
In the U.S., "N" is a negative number because the geoid is below the
ellipsoid, making this formula (h = H + N) correct, although it appears in
the above example to have its algebraic sign reversed. Throughout much
of the Earth elsewhere, the geoid is above the ellipsoid.
Differential Leveling. Differential leveling establishes a horizontal line-of-sight
that is perpendicular to the direction of gravity. Differential leveling follows the
rules of gravity, and all elevations are above the geoid. Differential leveling has
traditionally been the most common way to determine differences in elevation
between points A and B, between points B and C, between points C and D, and
on and on using multiple surveyors with diverse instruments over many decades
of time until the last surveyor arrives at a theoretical final benchmark somewhere
in the U.S. and calculates the elevation as __ ft above mean sea level, assuming
point A was at mean sea level with zero elevation. The accuracy of each
benchmark is relative to the accuracy of each of the preceding benchmarks
surveyed enroute to the theoretical final benchmark. Furthermore, the elevation
at the theoretical final benchmark is dependent upon the route surveyed,
because of variations in the slope of the geoid along different routes; thus
different elevations can be surveyed for the same point when using differential
leveling simply by following different routes to the final destination (the final
benchmark). Although these differences are insignificant for short distances
surveyed, they accumulate and become significant over large distances.
Furthermore, differential leveling does not provide geographic coordinates
(latitude and longitude). When approximate latitude and longitude are required, a
map is usually scaled to estimate these coordinates; when accurate latitude and
longitude are required, GPS procedures are the preferred option.
GPS Surveying. Whereas traditional surveying follows the rules of gravity, GPS
surveys follow the rules of geometry. The GPS surveyor does not establish
elevations (orthometric heights) directly, but indirectly, because GPS yields
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APPENDIX C — ELEVATION SURVEYS
ellipsoid heights which are converted into orthometric heights (elevations) by
applying the latest geoid model from NGS which models the undulation of the
geoid (the Geoid Height "N" in the above formula, i.e., the distance of the geoid
below the ellipsoid in the U.S.) at any given latitude and longitude. NGS' latest
geoid model is Geoid 03, released in January, 2004.
GPS surveys best support network accuracy because they are most easily tied to
CORS stations that are used to define the geodetic datum defined by WGS84.
Furthermore, GPS surveys always yield accurate latitude and longitude values.
National Spatial Reference System (NSRS). NOAA's National Geodetic Survey
(NGS) defines and manages the National Spatial Reference System (NSRS) -- a
consistent coordinate system that defines latitude, longitude, height, scale,
gravity, and orientation throughout the U.S. NSRS comprises a consistent,
accurate and up-to-date network of continuously operating reference stations
(CORS) which support 3-dimensional positioning activities, a network of
permanently marked survey points (monuments and benchmarks), and a set of
accurate models describing dynamic, geophysical processes that affect spatial
measurements.
The accuracy and accessibility of NSRS is dependent on contributions of GPS or
leveling observations by state, local, and private surveyors. Survey data must
meet rigorous "bluebook" standards and achieve minimum accuracies of first-
order horizontal or second-order vertical, with accuracies verified using NGS-
approved software.
NGS Data Sheets are available nationwide from the NSRS at
www.ngs/noaa.gov. These Data Sheets include 6-digit Permanent Identifiers
(PID numbers), name stamped on the monuments, latitude and longitude based
on the NAD 83 horizontal datum, elevations (orthometric heights) based on the
NAVD 88 vertical datum, geoid height, ellipsoid height, horizontal order and
class, vertical order and class, stability, station descriptions (to-reach directions)
and station recovery information.
Because these NSRS monuments and benchmarks are considerably more
accurate and stable than FEMA's elevation reference marks (ERMs), NSRS
monuments are mandatory as GPS base stations from GPS land surveys as well
as airborne GPS surveys for photogrammetry, LIDAR and IFSAR.
National Height Modernization Study. In 1998, NGS contracted with Dewberry to
prepare the "National Height Modernization Study, Report to Congress." This
report documented the advantages of GPS over traditional differential leveling
and provided recommendations for modernizing the National Height System in
the U.S. based on GPS. The recommendations of this study are now being
implemented, and Height Modernization surveys are now in progress nationwide
that will further serve to improve the ability of GPS surveyors to routinely
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APPENDIX C — ELEVATION SURVEYS
establish network accuracies of 5-cm and local accuracies of 2-cm and 5-cm
when specified survey procedures are followed. On behalf of NGS, Dewberry is
currently researching and revising these specifications in NGS-58.
Evaluation of Alternatives in Obtaining Structural Elevation Data
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