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The Wonder & Mystery of Dynamic Heights 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. Heights are not merely fascinating…. Physical.

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The Wonder & Mystery of Dynamic Heights and IGLD 85 Hydraulic Correctors

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  1. 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

  2. Heights are not merely fascinating… Physical Heights Matter!

  3. 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 ______________________________________________________________________ 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 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. Ortho and dynamic heights not equal H ≠ HD e.g., 176.311 – 176.264 = 0.047 m = H = HD

  4. Leveling is simple… right? Rod 1 Setup of Leveling, Δn = B – F and S = SB + SF Rod 2 Foresight Backsight F B Δn SB SF S

  5. Leveled Height Differences B Topography A C

  6. …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

  7. 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

  8. 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 ______________________________________________________________________ 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 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. Geopotential number C = × H = γ45 × HD = H = HD = g Mean gravity on plumbline: = g + 4.24 × 10-7 s-2 × H0 = γ45

  9. GRACE Gravity Model 01 - Released July 2003 Image credit:University of Texas Centerfor Space Research and NASA

  10. Ellipsoid surface Geopotential surfaces Geoid 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).

  11. 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

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

  13. …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

  14. Imagine Lake Powell as an equipotential surface(i.e., it has zero hydraulic slope, so water will not flow)

  15. ΔHD = 0.00 ft Water surface profile from Glen Canyon Dam to Hite Hite Glen Canyon Dam HD = 3700.00 ft HD = 3700.00 ft 3710 3705 Water surface 3700 3695 3690 3685 3680 3675 3670 3665 3660

  16. Water surface profile from Glen Canyon Dam to Hite Hite Glen Canyon Dam HD = 3700.00 ft HD = 3700.00 ft ΔHD = 0.00 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

  17. Water surface profile from Glen Canyon Dam to Hite Hite Glen Canyon Dam H = 3703.88 ft ΔH = −0.30 ft H = 3703.58 ft HD = 3700.00 ft HD = 3700.00 ft ΔHD = 0.00 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

  18. Water surface profile from Glen Canyon Dam to Hite Hite Glen Canyon Dam H = 3703.88 ft ΔH = −0.30 ft H = 3703.58 ft HD = 3700.00 ft HD = 3700.00 ft ΔHD = 0.00 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

  19. No gravity, no height. Know gravity, know height.

  20. LVL_DH (leveled height differences)

  21. NAVD 88 Modeled Surface Gravity

  22. 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

  23. IGLD 85 Hydraulic Correctors

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