Getting AHD heights from GNSS: some “insider information”

1. Getting AHD heights from GNSS: some “insider information” Will Featherstone Western Australian Centre for Geodesy, Curtin University

2. Outline • The basics and not so basics of heights • North-south tilt and distortions in the AHD • Geoid comps 101 (without maths, I promise) • Vertical errors in GNSS, AHD and geoid • What’s new in AUSGeoid09? • Weaknesses of AUSGeoid09 • Check, check and check again • Q&A

3. The basics: AHD from GNSS • Absolute (AUSPOS or PPP) • H (AHD) ~= h (from GNSS) – N (from AUSGeoid) • Suffers from biases [covered later] • Relative (GNSS baselines) • ΔH (AHD) ~= Δh (from GPS/GNSS) – ΔN (from AUSGeoid) • Constant biases cancel over shorter baselines • Remember that it’s algebraic • Important over most of WA as N can be negative • E.g., h=0m, N=-30m, thus H~=+30m

4. The not-so basics • Geoid vs quasigeoid - subtly different surfaces • AHD fixed to MSL @ 32 TGs • MDT+IBR+voffsets AHDfrom geoid • AHD is normalorthometric H* • Need AHD-ellipsoid separation HAHD AHD

5. North-south tilt in the AHD • Slope of 48mm/deg explained near-fully by MDT+IBR+v • Distortions (>10cm)

6. Geoid comps 101 • Because the AHD is normal-orthometric, we must model the quasigeoid • Long-wavelengths from an Earth gravity model • satellite orbit analyses, land, airborne and altimeter gravity (EGM2008) • Add gravity and terrain data via Stokes’s integral • Integral must be modifiedto filter out errors • Our modifier works OK

7. H errors: levelling/vertical datum • Datum point(s) offset from geoid (0-2m) • Type/realisation of height system (~5-20cm) • Temporal variations, e.g. GIA (~0-10cm) • Instrumentation & methodology (? 2-50cm) • Refraction, # setups, tedious method, etc. • Tidal system (1-2cm) • Distortion in the vertical datum (10-50cm) • Confusion over height system

8. h errors: GNSS ellipsoidal heights • Vintage of data (2-10cm) • e.g. pre-IGS, old equipment/methods/models, etc. • Datum (1-5cm) • e.g., variants of ITRF, observed vs transformed, etc. • Antenna height measurement (2mm-1.8m) • And… to which point: ARP, slope, true vertical, top, bottom, etc. • Intrinsic GNSS errors(? 2-20cm) • VDOP, orbits, atmospherics, multipath, RF interference, etc. • Algorithmic/theoretical errors • Occupation time (longer needed for h)

9. N errors: quasigeoid model • Earth gravity model (EGM) (~5-20cm) • Data treatment errors (? 10-20cm) • Local gravity and terrain data (? ~20cm) • Algorithmic/theoretical errors (? 1-20cm) • Zero- and first-degree terms (~1-10cm) • Temporal geoid variations (? ~2-10cm) • Tidal system (1-2cm) • Mountains and coasts – quasigeoid poorer

10. What’s new in AUSGeoid09? • Lots of new data • >0.5M extra gravity obs, new TCs, new EGM • Improved processing • Higher resolution (1’x1’) • Better interpolation • Perth has v steep gradient • LSC-fitted to AHD using ~6,000 GPS-levelling points • RMSE 3-5cm

11. Weaknesses of AUSGeoid09 • Poorer in the coasts and hills • Lack of data • AHD not defined offshore, but LSC-fitting has extrapolated • Model of MSL (loosely) • LSC correlation length • Some large residuals &randomly scattered • Sources still unknown • Checks always needed mm

12. Check, check and check again • A blanket statement of the precision of AHD heights from GNSS is indefensible • AUSGeoid09 is a weak link, though errors in GNSS and AHD cannot be dismissed • e.g., GNSS and/or AHD used in fitting may be wrong • Just as the good surveyor validates his/her levelling, the same applies to GNSS-AHD • Do your own validation for each and every project • Always remain sceptical

13. Check, check and check again • Just because AUSGeoid09 may have performed well on previous projects does not mean that it will elsewhere! • GNSS heighting is spatially and temporally variable • [Bad] anecdote • “Oh, it’s been OK, sowe don’t bother checking any more”

14. References (all in PDF on my website) Featherstone WE (1998) Do we need a gravimetric geoid or a model of the base of the AHD to transform GPS heights? Australian Surveyor 43(4):273-280 Featherstone WE, Kuhn M (2006) Height systems and vertical datums: a review in the Australian context, J Spatial Sci 51(1):21-42, Featherstone WE, Kirby JF, Hirt C, Filmer MS, Claessens SJ, Brown NJ, Hu G, Johnston GM (2011) The AUSGeoid09 model of the AHD, J Geodesy 85(3):133-150 Brown NJ, Featherstone WE, Hu G, Johnston GM (2011) AUSGeoid09: a more direct and more accurate model for converting ellipsoidal heights to AHD heights, J Spatial Sci 56(1):27-37 Featherstone WE, Filmer MS (2012) The north-south tilt in the AHD is explained by the ocean’s MDT, J Geophys Res 117, C08035, doi: 10.1029/2012JC007974

15. Acknowledgements • Australian Research Council for endorsement and funding for nearly two decades • My numerous collaborators on geoid and height determination • The many providers of data, particularly Geoscience Australia Q&A

16. Australian surveyors already well know that GPS-measured ellipsoidal heights have to be transformed to AHD heights by application of AUSGeoid; it’s a simple [algebraic] subtraction (i.e., AHD=GPSh--AUSGeoid).  However, knowing how reliable, precise and accurate this seemingly simple coordinate conversion is rather murky, and varies widely depending on location.  • As the chief investigator on the production of the AUSGeoid98 and AUSGeoid09 national standards, which are promulgated by Geoscience Australia, I will attempt to demystify really how well we might be able to measure reliable heights on the AHD with GPS and AUSGeoid.   • Some of the considerations to be covered are practical and simple (e.g., remembering to measure the antenna height and to which point); some are rather more esoteric (e.g., the effect of gravity on heights and the north-south slope in the AHD with respect to the geoid).  • In conclusion, the veracity of GPS-AUSGeoid-derived AHD heights has to be treated sceptically by the practicing surveyor before supplying so-derived AHD heights to clients.