and IGLD 85 Hydraulic Correctors 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 michael.dennis@noaa.gov

Physical Heights Matter! Heights are not merely fascinating… An example of the need for height modernization. Several states, along with North Carolina, have launched major efforts to update vertical positions with height modernization. On September 15, 1999, Hurricane Floyd dropped 21 inches of rain on North Carolina, damaging more than 67,000 homes and destroying nearly 8,000. Many of the homeowners did not have flood insurance, because their residences were built on land that had not been designated as flood prone on the Federal Emergency Management Agency’s (FEMA) Flood Insurance Rate Maps (FIRMs). Physical Heights Matter!

Physical heights: Orthometric and dynamic The NGS Datasheet NC0371 *********************************************************************** NC0371 DESIGNATION - 906 3020 BUFFALO GAGE NC0371 PID - NC0371 NC0371 STATE/COUNTY- NY/ERIE NC0371 COUNTRY - US 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 NC0371 GEOID HEIGHT - -35.15 (meters) GEOID12A NC0371 DYNAMIC HEIGHT - 176.264 (meters) 578.29 (feet) COMP NC0371 MODELED GRAVITY - 980,352.2 (mgal) NAVD 88 NC0371.The orthometric height was determined by differential leveling and NC0371.adjusted by the NATIONAL GEODETIC SURVEY NC0371.in June 1991. 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.The modeled gravity was interpolated from observed gravity values. Ortho and dynamic heights not equal H ≠ HD e.g., 176.311 – 176.264 = 0.047 m = H = HD

Setup of Leveling, Δn = B – F and S = SB + SF Leveling is simple… right? Rod 1 Setup of Leveling, Δn = B – F and S = SB + SF Rod 2 Backsight Foresight F B Leveling; a very simple form of surveying. Transferring elevation through the use of an observing instrument and calibrated rods with a backsight and a foresight measurement. Δn SB SF S

Leveled Height Differences B Topography A C Leveling is a very “simple” survey practice - determining elevation differences through use of conventional leveling procedures – through backsight minus foresight measurements between points A to B and B to C. Differential leveling surveys, being a “piecewise” metric measurement technique, accumulate local height differences (dh). But, being a piecewise metric measurement system, we must also be aware and account for factors affecting our understanding and use of height interpretations. Traditionally, orthometric heights can be considered as a distance (elevation difference) above a reference surface or datum.

…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 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 NC0371 COUNTRY - US 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 NC0371 GEOID HEIGHT - -35.15 (meters) GEOID12A NC0371 DYNAMIC HEIGHT - 176.264 (meters) 578.29 (feet) COMP NC0371 MODELED GRAVITY - 980,352.2 (mgal) NAVD 88 NC0371.The orthometric height was determined by differential leveling and NC0371.adjusted by the NATIONAL GEODETIC SURVEY NC0371.in June 1991. 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.The modeled gravity was interpolated from observed gravity values. Geopotential number C = × H = γ45 × HD = H = HD = g Mean gravity on plumbline: = g + 4.24 × 10-7 s-2 × H0 = γ45

Image credit: University of Texas Center for Space Research and NASA GRACE Gravity Model 01 - Released July 2003 To fully appreciate the reasoning for many of strict requirements for geodetic leveling we must begin with understanding what are orthometric heights. A realistic “view” of our very irregular shaped Earth as depicted in this gravity model determined from space borne gravity measurements by GRACE, gravity recovery and climate experiment. Every time we set up and plumb our level equipment we are then determining our horizon through the optics of the instrument perpendicular to the attraction of gravity at that point. Now, envision about 26 setups per mile and hundreds and thousands of setups over distances covering a County, each perpendicular to the attraction at that point on our irregular shaped, curved Earth and you can begin to get the feeling that leveling must be much more than a “simple” routine of backsights minus foresights. Image credit: University of Texas Center for Space Research and NASA

Gravity vector (aka “plumbline”), pointing “up” Geoid Geopotential surfaces Ellipsoid surface Looking at a side view of the irregular shaped Earth and the relationships between surfaces of equal potential (equipotential or geopotential surfaces), perpendicular to the attraction of gravity at that point. Note these geopotential surfaces are not geometrically parallel due to the variations in the earth’s irregular gravity field. Also, the geopotential surfaces converge (become closer together) at the poles due in large part to Earth’s rotation. As you run levels across theses surfaces the equipment is plumbed per the attraction of gravity at that point. Our assumption is that our horizontal field of view can be corrected for a nice consistent Earth curvature when in fact a correction for conditions affecting us at a particular point must be accounted for. Running levels north and south require more correction for the convergence of the geopotential surfaces than when running levels east and west. The red oval illustrates the reference ellipsoid for our space based coordinate system and, though a close approximation of the size and shape of the Earth, is an entire, unrelated reference surface when determining GPS-derived ellipsoid heights. 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, h Orthometric height, H Mean sea level Geoid height, NG Ellipsoid Geoid h ≈ H + NG h = H + NG Note: Geoid height is negative everywhere in the coterminous US

The trouble with leveling… What is the “elevation” here? HC = ? Level surface ΔnAC ≠ ΔnBC Level surface Leveled height differences, Δn Level surface HC Level surface Level surface Level surface at geoid (“mean sea level”) HA = 0 HB = 0

…and with orthometric heights HD ≠ HE HC Level surface …even though they are on the same level surface Level surface Level surface HE HD Level surface Level surface Level surface at geoid (“mean sea level”) HA = 0 HB = 0

Imagine Lake Powell as an equipotential surface (i. e 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 HD = 3700.00 ft ΔHD = 0.00 ft HD = 3700.00 ft 3710 3705 Water surface 3700 3695 3690 3685 3680 3675 3670 3665 3660

Water surface profile from Glen Canyon Dam to Hite HD = 3700.00 ft ΔHD = 0.00 ft HD = 3700.00 ft h = 3626.92 ft Δh = +7.49 ft h = 3634.41 ft 3710 3705 Water surface 3700 3695 3635 Water surface 3630 3625 3620 3615 3610 3605

Water surface profile from Glen Canyon Dam to Hite H = 3703.88 ft ΔH = −0.30 ft H = 3703.58 ft HD = 3700.00 ft ΔHD = 0.00 ft HD = 3700.00 ft h = 3626.92 ft Δh = +7.49 ft h = 3634.41 ft 3710 Water surface 3705 Water surface 3700 ΔH = +2.24 ft (@ 45 miles) 3695 3635 Water surface 3630 3625 3620 3615 3610 3605

Water surface profile from Glen Canyon Dam to Hite H = 3703.88 ft ΔH = −0.30 ft H = 3703.58 ft HD = 3700.00 ft ΔHD = 0.00 ft HD = 3700.00 ft h = 3626.92 ft Δh = +7.49 ft h = 3634.41 ft 3710 Water surface 3705 Water surface 3700 ΔH = +2.24 ft (@ 45 miles) 3695 3635 Water surface 3630 3625 3620 Geoid surface −70 ΔNG = +7.79 ft −75 −80

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