The Wonder & Mystery of

Dynamic Heightsand IGLD 85 Hydraulic Correctors

Michael Dennis, RLS, PEmichael.dennis@noaa.gov

Height Modernization Coordination MeetingJanuary 9, 2014 ● Silver Spring, MDNational Geodetic Survey Headquarters

Heights Matter!Heights Matter!PhysicalPhysical

Heights are not merely fascinating…

NC0371 ***********************************************************************NC0371 DESIGNATION - 906 3020 BUFFALO GAGENC0371 PID - NC0371NC0371 STATE/COUNTY- NY/ERIENC0371 COUNTRY - USNC0371 USGS QUAD - BUFFALO NW (1965)NC0371NC0371 *CURRENT SURVEY CONTROLNC0371 ______________________________________________________________________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 NC0371 ______________________________________________________________________NC0371 GEOID HEIGHT - -35.15 (meters) GEOID12ANC0371 DYNAMIC HEIGHT - 176.264 (meters) 578.29 (feet) COMPNC0371 MODELED GRAVITY - 980,352.2 (mgal) NAVD 88NC0371NC0371.The orthometric height was determined by differential leveling andNC0371.adjusted by the NATIONAL GEODETIC SURVEYNC0371.in June 1991.NC0371NC0371.The dynamic height is computed by dividing the NAVD 88NC0371.geopotential number by the normal gravity value computed on theNC0371.Geodetic Reference System of 1980 (GRS 80) ellipsoid at 45NC0371.degrees latitude (g = 980.6199 gals.).NC0371NC0371.The modeled gravity was interpolated from observed gravity values.

Physical heights: Orthometric and dynamicThe NGS DatasheetThe NGS Datasheet

= HD

= H

Ortho and dynamic heights not equal

H ≠ HD

e.g., 176.311 – 176.264 = 0.047 m

Rod 1

Rod 2

B

Backsight Foresight

F

Δn

SB

S

SF

Setup of Leveling, Δn = B – F and S = SB + SF

Leveling is simple… right?

Leveled Height Differences

AC

B Topography

…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

**

g

CH

"" gravityofvaluesome

energypotentialGravityheightPhysical

• 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

NC0371 ***********************************************************************NC0371 DESIGNATION - 906 3020 BUFFALO GAGENC0371 PID - NC0371NC0371 STATE/COUNTY- NY/ERIENC0371 COUNTRY - USNC0371 USGS QUAD - BUFFALO NW (1965)NC0371NC0371 *CURRENT SURVEY CONTROLNC0371 ______________________________________________________________________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 NC0371 ______________________________________________________________________NC0371 GEOID HEIGHT - -35.15 (meters) GEOID12ANC0371 DYNAMIC HEIGHT - 176.264 (meters) 578.29 (feet) COMPNC0371 MODELED GRAVITY - 980,352.2 (mgal) NAVD 88NC0371NC0371.The orthometric height was determined by differential leveling andNC0371.adjusted by the NATIONAL GEODETIC SURVEYNC0371.in June 1991.NC0371NC0371.The dynamic height is computed by dividing the NAVD 88NC0371.geopotential number by the normal gravity value computed on theNC0371.Geodetic Reference System of 1980 (GRS 80) ellipsoid at 45NC0371.degrees latitude (g = 980.6199 gals.).NC0371NC0371.The modeled gravity was interpolated from observed gravity values.

Geopotential and physical heightsThe NGS DatasheetThe NGS Datasheet

= HD

= g

= H

= γ45

Geopotential numberC = × H = γ45 × HD g

Mean gravity on plumbline: = g + 4.24 × 10-7 s-2 × H0g

Image credit:University of Texas Center

for Space Research and NASA

GRACE Gravity Model 01- Released July 2003

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).

Geoid Geopotentialsurfaces

Gravity vector(aka “plumbline”),

pointing “up”

Ellipsoid surface

The ellipsoid, the geoid, and The ellipsoid, the geoid, and youyou

Earth Earth surfacesurface

Ellipsoid

EllipsoidGeoidGeoid

Orthometric height, Orthometric height, HH

Geoid height, Geoid height, NNGG

Ellipsoid height, Ellipsoid height, hh

Deflection of the verticalDeflection of the vertical

Mean Mean sea levelsea level

h ≈ H + NG

Note: Geoid height is negative everywhere in the coterminous US

h = H + NG

You are hereYou are here

The trouble with leveling…What is the“elevation”

here?

HC

Level surface at geoid(“mean sea level”) HB = 0HA = 0

HC = ? Level surface

Level surface

Level surface

Level surface

Level surface

Leveled height

differences, Δn

ΔnAC ≠ ΔnBC

…and with orthometric heights

Level surface at geoid(“mean sea level”) HB = 0HA = 0

HC Level surface

Level surface

Level surface

Level surface

Level surface

HD

HE

HD ≠ HE

…even though they are on the same

level surface

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 HiteGlen Canyon Dam Hite

HD = 3700.00 ft HD = 3700.00 ftΔHD = 0.00 ft

3700

3705

3695

3685

3690

3675

3680

3710

3670

3665

3660

Water surface

3660

3665

3670

3675

3680

3685

3690

3695

3700

3705

3710

0 20 40 60 80 100Distance upstream from Glen Canyon Dam (miles)

Water surface profile from Glen Canyon Dam to HiteGlen Canyon Dam Hite

HD = 3700.00 ft HD = 3700.00 ft

h = 3626.92 ft h = 3634.41 ft

ΔHD = 0.00 ft

Δh = +7.49 ft

3700

3705

3695

3630

3635

3620

3625

3710

3615

3610

3605

Water surface

Water surface

Water surface profile from Glen Canyon Dam to HiteGlen Canyon Dam Hite

HD = 3700.00 ft HD = 3700.00 ft

H = 3703.88 ft H = 3703.58 ft

h = 3626.92 ft h = 3634.41 ft

ΔH = +2.24 ft(@ 45 miles)

ΔHD = 0.00 ft

ΔH = −0.30 ft

Δh = +7.49 ft

3700

3705

3695

3630

3635

3620

3625

3710

Water surface

Water surface

3615

3610

3605

Water surface

Water surface profile from Glen Canyon Dam to HiteGlen Canyon Dam Hite

HD = 3700.00 ft HD = 3700.00 ft

H = 3703.88 ft H = 3703.58 ft

h = 3626.92 ft h = 3634.41 ft

ΔH = +2.24 ft(@ 45 miles)

ΔHD = 0.00 ft

ΔH = −0.30 ft

Δh = +7.49 ft

ΔNG = +7.79 ft

3700

3705

3695

3630

3635

3620

3625

3710

−70

−75

−80

Water surface

Water surface

Water surface

Geoid surface

No gravity, no No gravity, no height.height.

Know gravity,Know gravity,know height.know height.

LVL_DH (leveled height differences)

NAVD 88 Modeled Surface Gravity

• 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

International Great Lakes Datum of 1985

IGLD 85 Hydraulic Correctors