THE NOS PROGRAM FOR TIDAL DATUM FIELD MODELING FOR VDATUM

1. THE NOS PROGRAM FOR TIDAL DATUM FIELD MODELING FOR VDATUM Kurt Hess Office of Coast Survey National Ocean Service, NOAA Tidal datum fields are important for: • Data for the VDatum Software • K-GPS Hydrographic Surveys • Shoreline Definition • Bathymetric Data Base • Bathy/Topo DEMs • Tide Coordination of Aerial Photography

2. DELAWARE BAY K-GPS SURVEY, JUNE 2001 Tide Zones K-GPS vs Zoning VDatum: MSL-to-MLLW from TCARI

3. COMMON VERTICAL DATUMS VERTICAL DATUM = base elevation used as a height reference 1. THREE-DIMENSIONAL DATUMS -Datum defined in Earth-centered X,Y,Z-coordinates used with GPS North American Datum of 1983 [NAD 86(86)] WGS 84 = World Geodetic System of 1984 ITRFxxxx = International Terrestrial Reference Frame for Year xxxx 2. ORTHOMETRIC DATUMS - Datum defined by an equipotential (as defined by gravity) surface NAVD 88 = North American Vertical Datum of 1988 3. TIDAL DATUMS -Datum defined by an average water level, usually at a specific phase of the tide MLLW = Mean Lower Low Water

4. 3-D Datums Orthometric Datums Tidal Datums VERTICAL DATUMS IN TAMPA BAY

5. VDATUM TRANSFORMATION ‘ROADMAP’ Each straight black line is a transformation WGS 84 (G873) ITRF2000 WGS 84 (G1150) MHHW WGS 84 (G730) Under Develop- ment WGS 84 (orig.) ITRF97 MHW NGVD29 ITRF96 ITRF94 MTL ITRF93 NAD 83 (86) NAVD 88 LMSL ITRF92 ITRF91 TSS GEOID99 (USHG2003 USGG2003) DTL ITRF90 ITRF89 MLW ITRF88 SIO/MIT 92 NEOS 90 MLLW PNEOS 90 3-D Datums Orthometric Tidal Datums Datums

6. THE TIDAL DATUM FIELD GENERATION PROCESS Access the Tidal Constant Data Base Run Numerical Model to Get Tides & Datums Run TCARI on Errors Run TCARI for Datums Create ‘Corrected’ Datum Create Datum Difference Fields Create and Populate the VDatum Grid

7. TIDAL CONSTANT DATA BASE • CSDL file of tidal data for appx. 4,000 U.S. locations • From CO-OPS quality-controlled official data • Additional data from non-QC’d data, paper records, non-NOAA sources, etc. • For each station, contains: • 7-digit (NOS) identification number • Latitude, longitude • Station name and state • Occupation and Nat. Tidal Datum Epoch dates • 9 tidal and ortho. datums and their source (if available) • 37 amplitudes, epochs, their source (if available) • Greenwich intervals (if available)

8. PRIMER ON TIDAL DATUMS Higher High Higher High MHHW MHW Lower High Observed Water Level DTL LMSL MTL ? Higher Low MLW Lower Low Higher Low MLLW Lower Low Day 1 Day 2 LMSL = avg. of hourly levels MTL = avg. of MHW and MLW DTL = avg. of MHHW and MLLW LAT = lowest astronomical tide Water level record of 19 years Nat. Tidal Datum Epoch: 1983-2001

9. NUMERICAL TIDE MODELING: REGIONAL STRATEGY ADCIRC Finite-Element Model of J. Westerink, U. of Notre Dame Rick Luettich, U.N.C. Can also use: Quoddy, ELCIRC, FVCOM models

10. HIGH SPATIAL RESOLUTION AT THE LOCAL LEVEL Smallest cell size: 100 m

11. MODEL SIMULATION OF TIME SERIES OF WATER LEVELS At every cell, extract highs and lows, define higher highs and lower lows, then compute averages. 30-day time series of 6-min values

12. MODEL VS DATA: MHHW AND MLLW 38 North Carolina Stations Mean absolute error = 4.4 cm 38 locations + 5 cm

13. COMPUTED TIDAL DATUM FIELD: MSL ABOVE MODEL ZERO Ocean: 0.0 m Pamlico Sound: 0.04 m Core Sound, Back Sound, Bogue Sound: 0.04 to 0.15 m

14. COMPUTED TIDAL DATUM FIELD: MHHW ABOVE MSL Ocean: 0.5 m Pamlico Sound: 0.03 m Core Sound, Back Sound, Bogue Sound: 0.03 to 0.4 m

15. VDATUM MARINE GRID:TIDAL DATUMS AND TSS • Point spacing = 0.24 nmi = 0.004 deg • Red points have tidal and other datums • Other points have null tidal datums, but valid 3-D and orthometric values • ‘Water‘ points overlap land

16. VDATUM CONVERSION SOFTWARE

17. TIDAL DATUM FIELDS BY SPATIAL INTERPOLATION: TCARI (TIDAL CONSTITUENT AND RESIDUAL INTERPOLATION) Interpolation by Laplace’s Equation: 2f = 0 Subject to boundary conditions: f(xi, yi) = fiobs ____ f = datum, amp, cos(phase) Mf/Mn = aMf/Mn a = 0 a = 0.95 a = 1.0

18. | 6 nmi | SPATIAL INTERPOLATION: WHY A NEW METHOD? Because of the presence of intervening land | +9 deg | -57 deg |

19. SPATIAL INTERPOLATION IN A DATA-RICH REGION • Puget Sound, Washington • Datums available at 69 NOS tide stations • 61 were used (solid blue squares) • 8 not used (some up rivers, etc.)

20. TCARI RESULTS: MHHW RELATIVE TO LMSL • Grid generated from coastline • No depths used • Grid size: 0.125 nmi • 37,280 water cells • 1,700 iterations required (SOR) • Range of MLLW values: 1.1 to 1.8 m

21. COMPARISON WITH DATA Average RMS error is 2.5 to 3.0 cm

22. SEA SURFACE TOPOGRAPHY • Result for Puget Sound • Created by NGS • Based on 11 tidal benchmarks • Avg. value of • NAVD 88 - LMSL=-1.3 m • Spatially interpolated

23. TCARI-CORRECTED TIDE MODEL TCARI Corrected TCARI Interpolation Tide Interpolation Of Data Model Of Error

24. VDATUM TODAY • Six existing regions • Three in development Puget Sound New York Bight Delaware Bay Chesapeake Bay Central Coastal Louisiana North Carolina Central California Lake Calcasieu Tampa Bay

25. EXTENSION OF VDATUM TO ENTIRE COASTAL U.S.:LIMITING FACTORS • Human resources • Lack of recent tidal data • Lack of GPS-referenced benchmarks • Old bathymetry • Outdated shoreline • Vertical datum issues in Great Lakes, Alaska, Hawai’i

26. WHAT’S NEXT • Hire UCAR post-doc for tidal datum modeling • Complete VDatum for North Carolina, Lake Calcasieu, and Chesapeake Bay • Extend VDatum to other areas: Long Island Sound, San Juan Islands • Build DEM for coastal Carolina • Transfer TCARI to CO-OPS