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The Wonder & Mystery of
Dynamic Heights
and IGLD 85 Hydraulic Correctors
Height Modernization Coordination Meeting
January 9, 2014 ● Silver Spring, MD
National Geodetic Survey Headquarters
Michael Dennis, RLS, PE
[email protected]
Heights are not merely fascinating…
Physical Heights Matter!
Physical heights: Orthometric and dynamic
The NGS Datasheet
NC0371 ***********************************************************************
NC0371 DESIGNATION - 906 3020 BUFFALO GAGE
NC0371 PID
- NC0371
Ortho and dynamic heights not equal
NC0371 STATE/COUNTY- NY/ERIE
D
NC0371 COUNTRY
- US
NC0371 USGS QUAD
- BUFFALO NW (1965)
e.g., 176.311 – 176.264 = 0.047 m
NC0371
NC0371
*CURRENT SURVEY CONTROL
NC0371 ______________________________________________________________________
NC0371* NAD 83(1986) POSITION- 42 52 37.
(N) 078 53 20.
(W)
SCALED
NC0371* NAVD 88 ORTHO HEIGHT 176.311 (meters)
578.45 (feet) ADJUSTED = H
NC0371 ______________________________________________________________________
NC0371 GEOID HEIGHT
-35.15 (meters)
GEOID12A
NC0371 DYNAMIC HEIGHT 176.264 (meters)
578.29 (feet) COMP
= HD
NC0371 MODELED GRAVITY 980,352.2
(mgal)
NAVD 88
NC0371
NC0371.The orthometric height was determined by differential leveling and
NC0371.adjusted by the NATIONAL GEODETIC SURVEY
NC0371.in June 1991.
NC0371
NC0371.The dynamic height is computed by dividing the NAVD 88
NC0371.geopotential number by the normal gravity value computed on the
NC0371.Geodetic Reference System of 1980 (GRS 80) ellipsoid at 45
NC0371.degrees latitude (g = 980.6199 gals.).
NC0371
NC0371.The modeled gravity was interpolated from observed gravity values.
H ≠ H
Leveling is simple… right?
Rod 1
Setup of Leveling, Δn = B – F and S = SB + SF
Rod 2
Foresight
Backsight
F
B
Δn
SB
S
SF
Leveled Height Differences
B
A
Topography
C
…but heights are complicated
• Heights to suit your every need (and mood)!
• Physical heights
– Orthometric heights
• Helmert (NAVD 88), Niethammer, Mader, New Brunswick, etc.
–
–
–
–
Dynamic heights
Normal heights
Normal orthometric heights (e.g., NGVD 29)
Leveled heights
• Geoid heights
– Gravimetric? “Hybrid”? Quasi-geoid?
• Ellipsoid heights
– Referenced to different datums and datum realizations
Physical heights related to gravity
Gravity potential energy
Physical height 
some value of " gravity "
C
H  *
g
*
• C is the geopotential number [m2/s2]
– Gravity potential energy relative to a reference potential
– Reference gravity potential is usually the geoid
• H* is some type of physical height [m]
– Type depends on type of gravity value used for g* [m/s2]
• Why?
– To get unique and meaningful heights
Geopotential and physical heights
The NGS Datasheet
NC0371 ***********************************************************************
NC0371 DESIGNATION - 906 3020 BUFFALO GAGE
NC0371 PID
- NC0371
NC0371 STATE/COUNTY- NY/ERIE
D
NC0371 COUNTRY
- US
45
NC0371 USGS QUAD
- BUFFALO NW (1965)
NC0371
NC0371
*CURRENT SURVEY CONTROL
NC0371 ______________________________________________________________________
NC0371* NAD 83(1986) POSITION- 42 52 37.
(N) 078 53 20.
(W)
SCALED
NC0371* NAVD 88 ORTHO HEIGHT 176.311 (meters)
578.45 (feet) ADJUSTED = H
NC0371 ______________________________________________________________________
NC0371 GEOID HEIGHT
-35.15 (meters)
GEOID12A
NC0371 DYNAMIC HEIGHT 176.264 (meters)
578.29 (feet) COMP
= HD
NC0371 MODELED GRAVITY 980,352.2
(mgal)
NAVD 88
=g
NC0371
NC0371.The orthometric height was determined by differential leveling and
NC0371.adjusted by the NATIONAL GEODETIC SURVEY
Mean gravity on plumbline:
NC0371.in June 1991.
g= g + 4.24 × 10-7 s-2 × H0
NC0371
NC0371.The dynamic height is computed by dividing the NAVD 88
NC0371.geopotential number by the normal gravity value computed on the
NC0371.Geodetic Reference System of 1980 (GRS 80) ellipsoid at 45
NC0371.degrees latitude (g = 980.6199 gals.).
= 45
NC0371
NC0371.The modeled gravity was interpolated from observed gravity values.
Geopotential number
C = g× H = γ × H
γ
GRACE Gravity Model 01
- Released July 2003
Image credit:
University of Texas Center
for Space Research and NASA
Geoid
Geopotential
surfaces
Ellipsoid
surface
Gravity vector
(aka “plumbline”),
pointing “up”
The relationships between the ellipsoid surface (solid red), various geopotential
surfaces (dashed blue), and the geoid (solid blue). The geoid exists approximately at
mean sea level (MSL).
The ellipsoid, the geoid, and you
Deflection of the vertical
You are here
Earth
surface
Ellipsoid height,
Mean
sea level
Geoid height,
h
Orthometric height,
H
NG
= H + NG
h≈
Note: Geoid height is negative everywhere in the coterminous US
The trouble with leveling…
ΔnAC ≠
What is the
“elevation”
HC = ?
here?
ΔnBC
Leveled height
differences, Δn
HA = 0
HC
HB = 0
…and with orthometric heights
HD ≠ HE
…even though they
are on the same
level surface
HD
HA = 0
HC
HE
HB = 0
Imagine Lake Powell as an
equipotential surface
(i.e., it has zero hydraulic slope,
so water will not flow)
Water surface profile from Glen Canyon Dam to Hite
Hite
Glen Canyon Dam
HD = 3700.00 ft
ΔHD = 0.00 ft
HD = 3700.00 ft
3710
3710
3705
3705
Water surface
3700
3700
Height (ift)
3695
3695
3690
3690
3685
3685
3680
3680
3675
3675
3670
3670
3665
3665
3660
3660
0
20
40
60
80
Distance upstream from Glen Canyon Dam (miles)
100
Water surface profile from Glen Canyon Dam to Hite
Hite
Glen Canyon Dam
HD = 3700.00 ft
h = 3626.92 ft
ΔHD = 0.00 ft
Δh = +7.49 ft
HD = 3700.00 ft
h = 3634.41 ft
3710
3710
3705
3705
Water surface
3700
3700
Height (ift)
3695
3695
3690
3635
3685
3630
3680
3625
3675
3620
3670
3615
3665
3610
3660
3605
0
20
40
60
80
Distance upstream from Glen Canyon Dam (miles)
100
Water surface profile from Glen Canyon Dam to Hite
Hite
Glen Canyon Dam
ΔH = −0.30 ft
ΔHD = 0.00 ft
Δh = +7.49 ft
H = 3703.88 ft
HD = 3700.00 ft
h = 3626.92 ft
H = 3703.58 ft
HD = 3700.00 ft
h = 3634.41 ft
3710
3710
3705
3705
Water surface
3700
3700
ΔH = +2.24 ft
(@ 45 miles)
3695
Height (ift)
3695
3690
3635
3685
3630
3680
3625
3675
3620
3670
3615
3665
3610
3660
3605
0
20
40
60
80
Distance upstream from Glen Canyon Dam (miles)
100
Water surface profile from Glen Canyon Dam to Hite
Hite
Glen Canyon Dam
ΔH = −0.30 ft
ΔHD = 0.00 ft
Δh = +7.49 ft
H = 3703.88 ft
HD = 3700.00 ft
h = 3626.92 ft
H = 3703.58 ft
HD = 3700.00 ft
h = 3634.41 ft
3710
3710
3705
3705
Water surface
3700
3700
ΔH = +2.24 ft
(@ 45 miles)
3695
Height (ift)
3695
3690
3635
3685
3630
3680
3625
3675
3620
3670
−70
ΔNG = +7.79 ft
−75
3665
3660
−80
0
20
40
60
80
Distance upstream from Glen Canyon Dam (miles)
100
No gravity, no height.
Know gravity,
know height.
LVL_DH (leveled height differences)
NAVD 88 Modeled Surface Gravity
International Great Lakes Datum of 1985
• IGLD 85 uses dynamic heights
– Because these heights give true hydraulic head
– Important that heights be related to actual water levels
• Problem:
– NAVD 88 dynamic heights don’t match lake water levels
– But NAVD 88 dynamic heights on NGS datasheets
• Solution: Hydraulic Correctors (HCs)
– Difference between NAVD 88 and water level at gauges
– Subtract from NAVD 88 dynamic to get IGLD 85 heights
– Each lake has its own “set” of HCs
• By definition is zero at primary gauge for each lake
– Only applied on and adjacent to Great Lakes
• Away from lakes NAVD 88 = IGLD 85 dynamic heights
• Challenge: Determining dynamic heights with GNSS
– Requires knowing mean gravity on the plumbline
IGLD 85 Hydraulic Correctors