Getting AHD heights from GNSS: some “insider information”

Will FeatherstoneWestern Australian Centre for Geodesy, Curtin University

OutlineThe basics and not so basics of heightsNorth-south tilt and distortions in the AHDGeoid comps 101 (without maths, I promise)Vertical errors in GNSS, AHD and geoidWhat’s new in AUSGeoid09?Weaknesses of AUSGeoid09Check, check and check againQ&A

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 algebraicImportant over most of WA as N can be negativeE.g., h=0m, N=-30m, thus H ~=+30m

The not-so basicsGeoid vs quasigeoid - subtly different surfacesAHD fixed to MSL @ 32 TGsMDT+IBR+voffsets AHDfrom geoidAHD is normalorthometric H*Need AHD-ellipsoid separation

AHD

HAHD

North-south tilt in the AHD

Slope of 48mm/deg explained near-fully by MDT+IBR+vDistortions (>10cm)

Geoid comps 101Because the AHD is normal-orthometric, we must model the quasigeoidLong-wavelengths from an Earth gravity model

satellite orbit analyses, land, airborne and altimeter gravity (EGM2008)

Add gravity and terrain data via Stokes’s integralIntegral must be modifiedto filter out errors

Our modifier works OK

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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

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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 errorsOccupation time (longer needed for h)

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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

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 interpolationPerth has v steep gradient

LSC-fitted to AHD using ~6,000 GPS-levelling points

RMSE 3-5cm

40.0

32.0

34.532.931.1

29.5

31.7

42.2

63.2

25

30

35

40

45

50

55

60

65

70

0 100 200 300 400 500

Correlation length (km)

RMS (mm)

Weaknesses of AUSGeoid09

Poorer in the coasts and hillsLack 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

Check, check and check again

A blanket statement of the precision of AHD heights from GNSS is indefensibleAUSGeoid09 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 projectAlways remain sceptical

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”

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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

AcknowledgementsAustralian Research Council for endorsement and funding for nearly two decadesMy numerous collaborators on geoid and height determinationThe many providers of data, particularly Geoscience Australia

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Q&A

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.