Height systems and vertical datums: A review in the Australian context

Long-wavelength SSTop charts show a general north-south trend of about 1 m in the deep oceans around Australia.

“Long-wavelength SSTop charts show that there is a general north-south trend of ~1m in the deep oceans around Australia (cf.Featherstone, 2001).”

• cites Featherstone, 2001Could not verify

  Section 4.2 discusses a local gravity survey across the Darling Fault, and Section 6 discusses orthometric corrections; neither addresses sea-surface topography in the deep oceans around Australia. Searches for SSTop charts and a north–south trend of about 1 m found no supporting passage. Page numbers were unavailable in our copy. (LLM, conf=0.74)

  Experimental — accuracy not yet measured

Since GRS67 is a geocentric reference ellipsoid, geocentric coordinates must be used to compute normal gravity.

“Since GRS67 is a geocentric reference ellipsoid, geocentric coordinates must be used to compute normal gravity (cf.Featherstone, 1995).”

• cites Featherstone, 1995Partly supported

  The Normal Gravity section says geodetic coordinates must refer to the normal ellipsoid used for the gravimetric geoid, and specifies WGS84 coordinates for its calculations. It identifies GRS80—not GRS67—as the geocentric normal ellipsoid it discusses. The general requirement for matching coordinates is supported, but the claim about GRS67 is not established by this paper. (LLM, conf=0.85)

  Experimental — accuracy not yet measured

The epoch of the AHD is effectively 5 May 1971.

“The epoch of the AHD is effectively 5 May 1971 (Roelse et al., 1975), though the date is rarely appended (i.e., AHD71) because this was the only nation-wide adjustment conducted.”

• cites Roelse et al., 1975Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In the AHD, observations collected over preceding years were implicitly assumed to refer to a single epoch.

“In the case of the AHD, no such variations were assumed and the observations collected over the preceding years (see Lines (1992) and Rolese et al. (1975) for the time-evolution of the spirit-levelling coverage) were implicitly assumed to refer to a single epoch.”

• cites Lines (1992)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Rolese et al. (1975)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The aliasing effect is difficult to quantify but is crudely estimated to be as much as 10 cm.

“This aliasing effect is difficult to quantify, but is crudely estimated here to be as much as 10 cm.”

Equipment failure and noise in AHD tide-gauge measurements may cause 10-15 cm offsets from true MSL at each tide-gauge.

“In addition, equipment failure and noise in the tide-gauge measurements used for the AHD may cause 10-15 cm offsets from true MSL at each tide-gauge (Coleman et al., 1979;Mitchell, 1973b).”

• cites Coleman et al., 1979Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Mitchell, 1973bNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Residual distortions persist that the fixed-net adjustment strategy cannot fully account for.

“Additional distortions remain that cannot be completely explained by the fixed-net adjustment strategy.”

The AHD fixed the time-limited MSL height to zero at multiple tide-gauges.

“However, the AHD fixed the time-limited MSL height to zero at multiple tide-gauges.”

Approximately 195,000 km of spirit-levelling observations were used in the AHD.

“Approximately 195,000 km of spirit-levelling observations were used in the AHD (Roelse et al., 1975).”

• cites Roelse et al., 1975Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

GRS67 normal gravity used in the AHD was computed for the horizontal coordinates of benchmarks along the levelling lines.

“The GRS67 normal gravity used in the AHD was computed for the horizontal coordinates of the benchmarks along the levelling lines.”

Fixing tide-gauges to zero height introduces distortions of approximately 1.5 m in the AHD.

“More importantly, fixing the tide-gauges to zero height introduces distortions of approximately 1.5m in the AHD, which was recognised at the time (Roelse et al., 1975).”

• cites Roelse et al., 1975Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Increasing numbers of gravity observations at AHD benchmarks for geophysical surveys allow direct computation of natural/physical heights.

“In addition, increasing numbers of gravity observations have been made at AHD benchmarks for geophysical surveys, which would allow the direct computation of the natural/physical heights.”

Normal gravity from the GRS67 reference ellipsoid was used to compute the truncated normal-orthometric corrections in the AHD.

“Instead, normal gravity from the GRS67 reference ellipsoid (IAG, 1967) -noting that the updated GRS80 ellipsoid (Moritz, 1980) is now the internationally adopted standard -was used to compute the truncated normal-orthometric corrections.”

• cites IAG, 1967Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Many AHD tide-gauges were located in or near estuaries and are subject to systematic MSL offset due to freshwater and reef-constrained outflow.

“Many of the tide-gauges used in the realisation of the AHD were located in or near estuaries and are thus subject to the systematic offset of MSL due to the different equipotential surface occupied by the relatively lighter freshwater, as well as the back-up of this outflow constrained by the many reefs surrounding Australia, notably in Queensland.”

The AHD height system is a modified normal-orthometric system in which a truncated form of Rapp's normal-orthometric correction was applied to spirit-levelling observations.

“The height system used in the AHD is actually a modified version of the normal-orthometric height system (e.g., Holloway, 1988), where a truncated form of Rapp's (1961) normal-orthometric correction was applied to the spirit-levelling observations (Roelse et al., 1975).”

• cites Holloway, 1988Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Rapp's (1961)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Roelse et al., 1975Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The 32 tide-gauges used as zero points in the AHD only observed MSL over a 2-3 year period.

“However, the 32 tide-gauges used as the zero points in the realisation of the AHD (30 on the Australian mainland and two in Tasmania) only observed MSL over a 2-3 year period (Roelse et al., 1975).”

• cites Roelse et al., 1975Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Most original AHD tide-gauges have been removed or moved vertically since the AHD realisation.

“Since the realisation of the AHD, most of the original tide-gauges have either been removed or moved vertically, usually due to equipment upgrades.”

A bias is introduced in the AHD due to the north-south difference of about 150 m between AGD66 and a geocentric horizontal datum.

“As well as using an outdated model for normal gravity, there is a bias introduced due to the northsouth difference of ~150m between the AGD66 and a geocentric horizontal datum.”

• AssumptionThe authors state this as an assumption: The horizontal coordinates of AHD benchmarks refer to the Australian Geodetic Datum 1966 (AGD66).

Over short distances, normal corrections are usually very small and may be neglected depending on the precision of spirit-levelling data.

“Over short distances, the normal corrections are usually very small and may be neglected, depending on the precision of the spirit-levelling data.”

Using spirit-levelling loop closures as a field check is flawed because a pair of equal and opposite gross errors within a loop can still permit closure.

“As well as the use of levelling loop closures being flawed (two equal and opposite gross errors in a loop will still allow that loop to close)”

Because geopotential numbers control how fluids move, they are the sensible foundation for physical height systems.

“geopotential numbers govern fluid flow, thus forming the logical basis for physically meaningful and conceptually sensible heights.”

Because the normal gravity field captures real gravity-vector changes only crudely, normal heights suit the real Earth less well than orthometric heights.

“the spatial variations in the Earth's gravity vector are only modelled very simplistically by the normal gravity field generated by the reference ellipsoid (e.g., Moritz, 1980Moritz, , 1992)).As such, the normal height system is less applicable to the real Earth than, say, the orthometric height.”

• cites Moritz, 1980 sourceNot checked — no full text of the source
• cites Moritz, 1992 sourceNot checked — no full text of the source

In theory, geopotential numbers close to zero no matter which levelling path is used.

“geopotential numbers provide a theoretical zero misclose regardless of what spirit-levelling route has been taken.”

The normal-orthometric height system was introduced as a surrogate because precise gravimeters were lacking before the 1950s and field gravity observations were labour-intensive.

“Due to the lack of precise gravimeters (before the 1950s), as well as the relatively labour-intensive nature of making gravity observations in the field, the normal-orthometric height system was introduced and adopted as a surrogate.”

In practice, most nations claiming orthometric heights rely on Helmert's approximation.

“Most countries that claim to use an orthometric height system actually use Helmert's (1890) approximation, where a number of simplifying hypotheses are made concerning the gravity field inside the topography.”

• cites Helmert (1890)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Computing normal heights requires gravity observations at sufficiently dense spacing along the spirit-levelling traverse.

“Importantly, this also requires that gravity observations be made at a sufficiently dense spacing along the spirit-levelling traverse.”

Some tasks can use ellipsoidal heights alone, for example the vertical part of airborne mapping or GPS-based marine navigation where a vessel must clear seabed depths given as ellipsoidal heights.

“there are cases where the use of ellipsoidal heights alone may suffice, such as the vertical component of an airborne mapping project or marine navigation where the hull/keel of a GPS-navigated ship has to clear seabed depths expressed in ellipsoidal heights.”

Least-squares adjustment is not applicable to height systems with systematic theoretical misclosures because it assumes random errors.

“Otherwise, the least squares adjustment will not be applicable because it is based on the assumption of random errors, whereas the theoretical misclosures of an imperfect height system are systematic, thus violating the principles upon which a leastsquares adjustment is based.”

• cites Sansò and Vaníček, 2005Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Both orthometric and normal height systems require actual gravity observations along the levelling traverse to derive geopotential numbers or corrections.

“Both orthometric and normal height systems require actual gravity observations to be taken along the levelling traverse in order to derive the geopotential numbers (or the orthometric or normal corrections).”

The normal-orthometric height system uses only the normal gravity field as an approximation to derive all necessary gravity-field-related quantities.

“This height system uses only the normal gravity field as an approximation of the Earth's gravity field to derive all necessary gravity-field-related quantities.”

Dynamic, orthometric and normal heights use the geopotential number.

“Note that dynamic, orthometric and normal heights use the geopotential number.”

Dynamic, orthometric and normal heights theoretically have zero misclosure irrespective of levelling path if rigorous gravity corrections are used.

“Therefore, from the theoretical point of view, these heights will have a zero misclosure irrespective of the levelling path taken, provided that rigorous gravity corrections are used.”

The Australian Height Datum was created by adjusting roughly 195,000 km of spirit-levelling observations tied to short-term mean sea level records from several tide gauges.

“The AHD was realised by the adjustment of ~195,000 km of spirit-levelling observations fixed to limited-term observations of mean sea level at multiple tide-gauges.”

• cites Roelse et al., 1975Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Dennis and Featherstone's simulation of an Everest-sized mountain with known gravity showed Mader and Niethammer heights outperform Helmert orthometric heights.

“Using a simulated Everest-sized mountain of constant mass-density, where the gravity field was completely known, Dennis and Featherstone (2003) show that the Mader and Neithammar heights are superior to Helmert orthometric heights”

• cites Dennis and Featherstone (2003)Not checked — no full text of the source

Normal heights are computed from spirit-levelled height differences using the normal correction.

“In practice, like orthometric heights, normal heights are computed from spirit-levelled height differences using the normal correction (e.g., Heiskanen and Moritz, 1967, Chapter 4;Torge, 2001).”

• cites Heiskanen and Moritz, 1967 sourceNot checked — no full text of the source
• cites Torge, 2001 sourceNot checked — no full text of the source

The normal gravity field cannot accurately represent Earth's real gravity field, with discrepancies reaching a few hundred milliGal.

“It cannot accurately model the real gravity field of the Earth, with differences amounting to a few hundred milliGal.”

If ellipsoidal heights are used without care, datasets may become incompatible, as non-specialists could mix them with other height types.

“the uncontrolled use of ellipsoidal heights raises the issue of compatibility of datasets, where lay users may incorrectly integrate them with other types of height.”

Only the dynamic height system is physical-geodetically rigorous because it accurately describes fluid flow in Earth's gravity field.

“Of them, only the dynamic height system is physical-geodetically rigorous because it accurately describes fluid flow in the Earth's gravity field.”

For most uses, heights must be tied correctly to Earth's gravity field to be natural and physically meaningful.

“only heights properly related to the Earth's gravity field are natural and physically meaningful for most (but not all) applications.”

If gravity is handled correctly, height systems founded on geopotential numbers should close exactly in theory, assuming no measurement error.

“height systems based on them and with the proper treatment of gravity will also theoretically close (with error-free measurements); see Sansò and Vaníček (2005) for a theoretical discussion on this point.”

• cites Sansò and Vaníček (2005)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• AssumptionThe authors state this as an assumption: The theoretical loop-closure analysis assumes there are no measurement errors.

The theoretical loop closure obtained from spirit-levelling data depends on the levelling route taken.

“the theoretical loop closure using spirit-levelling data depends on the route taken (e.g., Heiskanen and Moritz, 1967, Chapter 4).”

• cites Heiskanen and Moritz, 1967 sourceNot checked — no full text of the source

Perfect orthometric heights are difficult in practice, needing the plumbline's exact route through terrain and gravity values all along it.

“The orthometric height system is hard to realise perfectly in practice, because we need to know the exact path of the plumbline within the topography and the Earth's gravity acceleration at all points along the plumbline.”

To obtain geopotential numbers, levelling must be combined with gravity readings taken along the levelling lines.

“spirit-levelling measurements have to be supplemented by gravity observations along the traverses to determine the gravity potential differences, and hence the geopotential numbers.”

In theory, spirit levelling should not be expected to close to zero unless gravity effects are correctly included.

“a zero misclose is never expected in theory unless the Earth's gravity field is properly taken into account.”

Ellipsoidal-only height systems cannot serve applications where fluids flow.

“Clearly, these are unsuitable for any application that involves fluid flow in any way, among other reasons (e.g., Vaníček, 1998).”

• cites Vaníček, 1998Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Normal height determination is iterative because it depends on the normal height itself, since the telluroid point is initially unknown.

“However, due to the dependency on the normal height itself (the point on the telluroid is initially unknown) the determination becomes iterative (e.g., Heiskanen and Moritz 1967, Chapter 4).”

• cites Heiskanen and Moritz 1967 sourceNot checked — no full text of the source

Because the normal gravity field is well defined, the integral-mean normal gravity along the normal plumbline can be found from the point's latitude alone.

“On the other hand, as the normal gravity field is well defined, the integral-mean value of normal gravity along the normal plumbline can be determined knowing the position (notably only the latitude) of the point of interest.”

Australian spirit-levelling work has mostly followed class LC tolerances, allowing loop misclose of 12√k mm for k kilometres levelled.

“most spirit-levelling observations have been or are conducted to Australian class LC tolerances (ICSM, 2002), which permit a loop misclose of 12 k mm, where k is the distance levelled in kilometres.”

• cites ICSM, 2002Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In mountains, refined orthometric heights may differ from Helmert orthometric heights by over 10 cm.

“the differences between refined and Helmert orthometric heights can amount to more than 10 cm in mountainous regions (Kingdon et al., 2005).”

• cites Kingdon et al., 2005Not checked — no full text of the source

Approximations of dynamic, orthometric and normal heights, and normal-orthometric heights using spheropotential numbers, do not have zero misclosure.

“This, however, does not hold for any approximations of these heights (e.g., Helmert orthometric heights), nor does it hold for the normal-orthometric heights that use the spheropotential number instead of the actual geopotential number.”

Normal-orthometric corrections are usually negligible for spirit-levelling data over short distances.

“Once again, the normal-orthometric corrections are usually negligible for spirit-levelling data over short distances.”

This length of observation is rarely practical for a vertical datum.

“However, this length of observation is rarely practical in relation to the demand for a vertical datum (e.g., Lines, 1992;Roelse et al., 1971).”

• cites Lines, 1992Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Roelse et al., 1971Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The ~1.7-km uncertainty in AHD benchmark locations will cause interpolation errors, especially where horizontal gravity gradients are steep.

“The ~1.7-km (one mile) uncertainty in the benchmark locations will cause interpolation errors, especially in areas of steep horizontal gravity gradients.”

Several effects cause tide-gauge estimates of local MSL, held fixed to zero height in the 1971 AHD, to be offset from one another and from true MSL.

“Suffice it to say, there are several effects that cause the tide-gauge estimates of local MSL, which were held fixed to zero height in the 1971 realisation of the AHD, to be offset from one another and from true MSL.”

The infrastructure is being developed to allow upgrade to a more rigorous natural/physical height system in the AHD.

“As such, the infrastructure is (perhaps inadvertently) being developed to allow the upgrade to a more rigorous natural/physical height system in the AHD.”

Current uncertainty in the horizontal position of AHD benchmarks will also affect computation of new orthometric corrections from surrounding gravity, density and elevation models.

“Of course, the current uncertainty in the horizontal position of the benchmarks will also affect this approach.”

Observed MSL departs from the classical W0 geoid due to sea surface topography.

“Even if the full tidal cycle were to have been observed, a more problematic effect is the departure of the observed MSL from the classical W 0 geoid (e.g., Ekman and Mäkkinen, 1991;Ekman, 1994).”

• cites Ekman and Mäkkinen, 1991Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Ekman, 1994 sourceNot checked — no full text of the source

Many countries or continents have adopted a single tide-gauge as the zero point for their local vertical datum.

“Acknowledging these problems, many countries -or even continents -have adopted a single tide-gauge as the zero point for the realisation of their local vertical datum.”

In some national vertical datums, including the AHD, using more than one tide-gauge causes distortions because the tide-gauge datum points refer to different levels due to tidal aliasing and SSTop-induced offsets.

“In a few cases of national vertical datums (including the AHD), more than one tide-gauge is used, which causes distortions because the tide-gauge datum points refer to different levels due to the tidal aliasing and SSTop-induced offsets.”

Theoretically, AHD loops would never close because of the high approximation in the truncated normal-orthometric correction.

“Theoretically, these loops would never close because of the high level of approximation inherent in the truncated normal-orthometric correction.”

Tide-gauge observations of MSL do not coincide with the classical W0 geoid at that point because of time-limited tidal observation, SSTop and other factors.

“The combination of time-limited observation of the full tidal signature, SSTop and other related factors mean that tide-gauge observations of MSL do not coincide with the classical equipotential W 0 geoid at that point.”

These tide-gauges are aliased by spatially varying tidal effects.

“As such, they are aliased by the spatially varying tidal effects.”

Using a single tide-gauge per datum gives rise to offsets among various vertical datums globally.

“This gives rise to offsets among various vertical datums on a global scale (e.g., Rapp, 1994;Burša et al., 2004).”

• cites Rapp, 1994 sourceNot checked — no full text of the source
• cites Burša et al., 2004 sourceNot checked — no full text of the source

Realising the datum surface for natural/physical height systems requires practical determination of the geoid or quasigeoid.

“A key problem in realising the datum (zero height) surface for the natural/physical height systems is the practical determination of the geoid or quasigeoid.”

Imprecision in the horizontal coordinates of AHD benchmarks will cause problems for future implementation of a more rigorous physical/natural height system based on observed gravity in a revised AHD.

“The imprecision of the horizontal coordinates of the AHD benchmarks will also cause problems for the future implementation of a more rigorous physical/natural height system based on observed gravity in a revised AHD.”

Correct determination of MSL at a coastal tide-gauge requires regular and uninterrupted observation of the full tidal signature.

“To correctly determine MSL at a coastal tide-gauge needs regular and uninterrupted observation of the full tidal signature.”

Even error-free natural/physical heights would not agree with the tide-gauge observations.

“Therefore, even in the case of error-free natural/physical heights, they would not agree with the tide-gauge observations.”

This disagreement is exacerbated when normal-orthometrically corrected spirit-levelling is used.

“This is exacerbated when the observed normal-orthometrically corrected spirit-levelling is used.”

Because most original tide-gauges are missing, it will not be possible to apply this directly to the 1971 AHD realisation.

“However, as most of the original tide-gauges are missing, it will not be possible to apply this directly to the 1971 realisation of the AHD.”

Accurate determination of SSTop is particularly problematic in coastal areas.

“Moreover, accurate determination of the SSTop becomes particularly problematic in coastal areas (e.g., Merry and Vaníček 1983;Hipkin, 2000), where, for instance, the outflow of freshwater from estuaries causes further departure from the classical geoid.”

• cites Merry and Vaníček 1983 sourceNot checked — no full text of the source
• cites Hipkin, 2000 sourceNot checked — no full text of the source

The luni-solar tide has a full period of 18.6 years.

“While the combination [superposition] of the relative motion of the Sun and Moon with respect to the Earth cause noticeable tides at the coast, the [smaller] effects of the precession and nutation of the Earth-Sun-Moon system cause the socalled luni-solar tide, which has a full period of 18.6 years (e.g., Melchior, 1981).”

• cites Melchior, 1981Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Determining MSL correctly requires regular tide-gauge observations over at least the entire 18.6-year luni-solar cycle.

“As such, it is necessary to make regular (e.g., hourly) tide-gauge observations of sea level over at least the entire 18.6-year period of this luni-solar tidal cycle.”

The luni-solar tidal effect may reach several centimetres depending on the averaging period and position.

“Depending on the time period over which the tide-gauge observations were averaged, this luni-solar tidal effect may reach several centimetres, also depending on position because tides are not everywhere equal in phase and amplitude.”

SSTop causes the mean sea surface to depart from the classical geoid by as much as 2 m in the open oceans.

“SSTop causes the mean sea surface to depart from the classical geoid by as much as 2m in the open oceans (e.g., Rapp, 1983;1994;1995;Mitchell, 1973c).”

• cites Rapp, 1983Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites Mitchell, 1973cNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

It is probably impossible to use these tide-gauges to determine a full 18.6-year MSL estimate.

“As such, it is probably impossible to use these tide-gauges to determine a full 18.6-year MSL estimate.”

Tide-gauges do not directly sense the classical geoid because spatially varying SSTop and other biases offset observed MSL.

“As well as incorrect MSL determination, tide-gauges do not directly sense the classical geoid because spatially varying SSTop and other biases act to offset the observed MSL from the classical geoid.”

A limited observation period cannot determine true MSL at each tide-gauge because tidal range and frequency content differ between gauges.

“That is, the tidal range and tidal frequency content is different at each tide-gauge, thus a limited observation period cannot determine the true MSL at each.”

This offset varies with position.

“Moreover, this offset varies as a function of position.”

Tide-gauge observations of MSL are problematic due to tides, temporal sea-level changes, SSTop and related biases, especially in the coastal zone.

“However, this introduces two further issues: 1) the determination of MSL in the presence of tides and other temporal changes in sea level, and 2) the effect of sea surface topography (SSTop) and related biases; all are particularly problematic in the coastal zone (e.g., Merry and Vaníček, 1983;Hipkin, 2000).”

• cites Merry and Vaníček, 1983 sourceNot checked — no full text of the source
• cites Hipkin, 2000 sourceNot checked — no full text of the source

Soltanpour et al. (2005) produced one using second-generation wavelets.

“Featherstone and Sproule (2005) have completed this for AUSGeoid98 using least squares collocation (LSC) prediction, as have Soltanpour et al. (2005) using second-generation wavelets.”

• cites Soltanpour et al. (2005)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

A surface for directly transforming GPS heights to the AHD has become necessary.

“Since the ICSM has decided to retain the AHD for the”

• cites Featherstone, 1998Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• AssumptionRests on an assumption: The ICSM has decided to retain the AHD for the foreseeable future.

AUSGeoid98 is theoretically more compatible with the AHD, since a quasigeoid should be paired with normal-orthometric heights.

“This makes it theoretically more compatible with the AHD, because a quasigeoid should be used in conjunction with normal-orthometric heights (described earlier).”

Featherstone and Sproule (2005) produced such a surface for AUSGeoid98 using least squares collocation prediction.

“Featherstone and Sproule (2005) have completed this for AUSGeoid98 using least squares collocation (LSC) prediction, as have Soltanpour et al. (2005) using second-generation wavelets.”

• cites Featherstone and Sproule (2005)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

As geoid determination theories and source data improve, especially with GRACE and GOCE, the AHD's problems will become more evident.

“As geoid determination theories and source data continue to improve, notably with the GRACE (Gravity Recovery And Climate Experiment) and GOCE (Gravity field and steadystate Ocean Circulation Explorer) dedicated satellite gravimetry missions, the problems in the AHD will become more apparent.”

• cites Rummel et al. (2002) sourceNot checked — no full text of the source

Evidence is increasing that the systematic differences are mostly due to the AHD rather than AUSGeoid98.

“Due to the separability problem of not being able to determine whether the cause is solely in the AHD or AUSGeoid98 (cf.Featherstone, 2004), this remains an open question, but there is now increasing evidence of the problem lying mostly in the AHD (Baran et al., 2005).”

• cites Baran et al., 2005Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

GPS surveys are incompatible with the AHD.

“The distortions in the AHD are causing problems in that improved gravimetric quasigeoid models are now revealing the fundamental inconsistencies between these two vertical reference surfaces, to the point at which GPS surveys are incompatible with the AHD.”

Molodenskian theories were incorporated, though not fully, into the computation of AUSGeoid98.

“This is because Molodenskian theories were embedded (albeit not completely) in its computation, and no topographic mass-density information was used.”

Surface fitting only hides the AHD's errors.

“Instead, the surface fitting only serves to mask the errors in the AHD.”

No topographic mass-density information was used in computing AUSGeoid98.

“This is because Molodenskian theories were embedded (albeit not completely) in its computation, and no topographic mass-density information was used.”

GPS surveyors must routinely occupy nearby AHD benchmarks and apply a further transformation surface to handle local differences.

“This requires that GPS surveyors have to routinely occupy surrounding AHD benchmarks so as to apply an additional transformation surface to account for these differences in their work area (cf.Featherstone et al., 1998).”

• cites Featherstone et al., 1998Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The AHD's distortions are causing problems because improved gravimetric quasigeoid models now reveal fundamental mismatches between the two vertical reference surfaces.

“The distortions in the AHD are causing problems in that improved gravimetric quasigeoid models are now revealing the fundamental inconsistencies between these two vertical reference surfaces, to the point at which GPS surveys are incompatible with the AHD.”