geodesy noaa gov Leveling After 2022 Dan Gillins

geodesy. noaa. gov Leveling After 2022 Dan Gillins, Ph. D. , P. L. S. April 25, 2017 Geospatial Summit 2017

Differential Leveling Rod 1 Setup of Leveling, Δn = B – F Rod 2 Foresight Backsight F B Δn SB 2 S SF

Differential Leveling Advantages: • Leveling is used to determine differences in heights between marks – Highly accurate (i. e. , mm to sub-mm) height differences can be obtained in less than one km Challenges: • A tedious process – Line-of-sight technology, restricted to 50 -100 m sight lengths; prone to blunders • Requires starting from a mark with a “known” height (i. e. , vertical control point or bench mark) 3

Heights on Bench Marks • NGS publishes orthometric heights on bench marks referenced to NAVD 88 • NAVD 88: – Realized by over 700, 000 km of leveling lines – Over 500, 000 monumented bench marks – Minimally Constrained adjustment, holding fixed the Father Point/Rimouski tide station in Canada 4

NAVD 88 Courtesy Brian Shaw

Challenges with NAVD 88 6 • Bench marks may not be in convenient locations or near a project area • Must assume the bench marks have not moved, and their published heights are without error • Bench marks are often destroyed and rarely replaced • Sparse number of bench marks outside of CONUS • Heights for the bench marks were derived from a single point, allowing error to build up across the country

Bias and Tilt of NAVD 88 7

NAPGD 2022 • The North American-Pacific Geopotential Datum of 2022 (NAPGD 2022) will replace NAVD 88 – Will not be realized by leveling between passive marks – Accessed by GNSS observations (referenced to NATRF 2022) and a high-accuracy gravimetric geoid model (GEOID 2022) 8

GNSS-Derived Orthometric Heights H≈h-N HNAPGD 2022 = h. NATRF 2022 – NGEOID 2022 h d i o s p i l l E n a e c O 9 Geoid N H

Advantages of NAPGD 2022 • Easily accessed by making GNSS observations – Establish vertical control in convenient locations – Level from this control to other stations in your survey – Possible to derive orthometric heights on marks at the time of your survey 10 • Enables monitoring orthometric heights on marks

Estimated Accuracy of GNSSDerived Height Differences h 2 h 1 d i o s p i l l E n a e c O 11 N 1 Geoid N 2

Accuracy of Leveling 12

Principles of Least Squares Two Components of a least squares adjustment: 1. Mathematical Model 2. Stochastic Model – How to weight your observations and constraints – Weights inversely proportional to variances 13

Case Study: GSVS 11 Austin • 325 km line from Austin to Rockport, TX • Static GPS collected on 218 stations (48 -h sessions) • First-order Class 2 geodetic leveling • Surface gravimetry Rockport 14

Preliminary Adjustments of Austin GSVS 11 • Free adjustment of leveling observations: – ΔH = 158. 454 m – σH, end = ± 0. 014 m • Simply differencing GNSSderived orthometric heights at each end of line: – ΔH = 158. 398 m – σH, ends ≈ ± 0. 04 m Rockport 15

GNSS+Leveling Adjustments ΔH H 2 ΔH H 1 16 Geoid

GNSS+Leveling Adjustments ΔH H 2 ΔH H 1 17 Geoid

GNSS+Leveling Adjustments ΔHadj H 2, adj ΔHadj H 1, adj 18 Ha Hb Hc Geoid Hd He Hf

Test Adjustment Results BM Input H (m) 2003 3006 159. 828 1. 430 Output H (m) Input Sigma (cm) 159. 851 ± 3. 5 1. 401 ± 4. 0 ΔHGNSS+L 158. 450 ΔHleveling 158. 454 Difference -0. 004 19 Output Sigma (cm) ± 2. 7 ± 2. 8 Hin Hout (cm) -2. 3 +2. 9

Test Adjustment Results 20

Additional Tests

Conclusions • GNSS and a high-accuracy geoid model connects network to NAPGD 2022 – (network accuracy) • Leveling improves accuracy of height differences between marks – (local accuracy) • Addition of leveling with GNSS increases overall redundancy in a survey network

Ongoing Research and Development • Develop models to combine and adjust GNSS -derived heights and/or observations with leveling • More tests with other GNSS+leveling projects • Add a new section to the NOS NGS Manual 3 on “Geodetic Leveling” • Provide guidance for the necessary spacing of vertical control from GNSS • Update FGCS specifications for leveling 23

OPUS-Projects for GNSS & Leveling 24 24

OPUS-Projects for GNSS & Leveling 25 25

Questions? 26 Dan Gillins Daniel. Gillins@noaa. gov