The apparent British sea slope is caused by systematic errors in the levelling-based vertical datum

The spirit-levelling–based British vertical datum (Ordnance Datum Newlyn) implies a south–north apparent slope in mean sea level of up to 53 mm deg –1 latitude, due to the datum falling on heading northwards. Although this apparent slope has been investigated since the 1960s, explanations of its origin have remained inconclusive. It has also been suggested that, rather than a slope, the British vertical datum includes a step of about 240 mm affecting all sites north of about 53°N. In either case, the British vertical datum may be of limited use for any study requiring accurate heights or changes in heights, such as testing geoid models, groundwater and hydrocarbon extraction, the calibration and validation of satellite-based digital terrain models, and the unification of vertical datums internationally. Within the last decade, however, based on an apparent reduction in the slope to only −12 mm deg –1 latitude with respect to recent geoid models, it has been claimed that the British vertical datum does provide a physically meaningful surface for use in scientific applications. In this paper, we reinvestigate the presence of apparent south–north sea slopes around Britain and reported slopes in the vertical datum, using the EGM2008 global gravitational model, together with mean sea level and GPS data from British tide gauges, GPS ellipsoidal heights of 178 fundamental benchmarks across mainland Britain, and vertical deflection observations at 192 stations. We demonstrate a south–north slope in the British vertical datum of −(20–25) mm deg –1 latitude with respect to both mean sea level (corrected for the ocean's mean dynamic topography and the inverse barometer response to atmospheric pressure loading) and the EGM2008 quasigeoid model, while EGM2008 is shown to exhibit a negligible slope of (2 ± 4) mm deg –1 with respect to mean sea level. It is clear, therefore, that the slope can only arise from systematic errors in the levelling, although we are unable to isolate their exact origin. Using an offset detection method based on a penalized likelihood maximization using the Schwarz Information Criterion, we do not detect a step in the vertical datum affecting all sites north of 53°N, but do identify regional distortions that we attribute to the inhomogeneity in both the levelling data used and the least squares adjustment procedures used to realize the datum. We conclude that the British vertical datum remains unsuitable for scientific purposes.

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title: Slope of sea level along the Pacific coast of the United States
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title: The north‐south tilt in the Australian Height Datum is explained by the ocean's mean dynamic topography
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title: A geodetic investigation of the British sea slope anomaly
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title: Geoid models for Great Britain and the North Sea
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title: The geoid EDIN2000 and mean sea surface topography around the British Isles
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title: Heights, the Geopotential, and Vertical Datums
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title: The effect of EGM2008-based normal, normal-orthometric and Helmert orthometric height systems on the Australian levelling network
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title: FROM MILES TO MILLIMETRES: THE STORY OF GEODESY AT ORDNANCE SURVEY 1791–1991
abstract: Know … That on the summit whither thou art bound A geographic Labourer pitched his tent, With books supplied and instruments of art, To measure height and distance; lonely task, Week after week pursued!Wordsworth, 1813, from ‘Written with a slate pencil on a stone on the side of the Mountain of Black Comb’.

title: A NEW GEODETIC HEIGHTING STRATEGY FOR GREAT BRITAIN
abstract: AbstractDue to unresolved problems between the three different geodetic levellings of Great Britain, OS has been looking at the possibilities of a Fourth Geodetic Levelling for over 20 years. However, scientific requirements have now changed, the Global Positioning System (GPS) can give precise ellipsoid height differences and a centimetric national geoid model has been developed. As a result, the concept of a Fourth Geodetic Levelling has been abandoned. The existing geodetic network is satisfactory for controlling lower orders of levelling, and destroyed marks will be replaced on an as-needed basis, not as a programme of cyclic or ad hoc infill levelling. This new strategy reduces conventional levelling and relies more on high-technology solutions to provide users with the information they require.

title: Using a ‘GPS/MSL Geoid’ to Test Geoid Models in the UK
abstract: GPS has been used to compute the height of mean sea level (MSL) above a reference ellipsoid at a network of 14 tide gauge sites, several hundred kilometres apart in the UK. The resultant ‘GPS/MSL geoid’ heights have then been compared to values taken from a global, an European and a national geoid model. Through these comparisons an assessment of the vertical datum offsets, and of the magnitude of any long wavelength errors in the geoid models, has been carried out.

title: Impacts of geodynamic phenomena on systems for height and gravity
abstract: Geodynamic phenomena of permanent or secular characters play a significant role when defining height systems and gravity systems. A treatment is here given of the permanent earth tide, postglacial land uplift, sea level changes and polar drift from this point of view.1.The various gravity and geoid concepts originating from differing ways of handling the permanent tide are treated, and transformations between them are given. Numerical applications are made to height and gravity systems in the Nordic countries, including determination of land uplift. The oceanographic deviation of mean sea level in the Baltic Sea is discussed with respect to the permanent tide. Problems caused by the permanent tide in height determination based onGPS are illustrated.2.The effects of postglacial land uplift and sea level changes are dealt with together. Again, numerical applications are made to height and gravity systems in the Nordic countries. It is discussed how sea level data should be included in the determination of land uplift. An attempt to estimate the remaining land uplift is made.3.A few words are said on the role of polar drift when defining a gravity system.

title: The permanent tide in GPS positioning
abstract: The treatment of the permanent tidal deformation of the Earth in GPS computation has been an almost unmentioned topic in the GPS literature. However, the ever increasing accuracy and the need to combine the GPS based coordinates with other methods requires a consistent way to handle the tides. Our survey shows that both the ITRF-xx coordinates and the GPS based coordinates are nowadays reduced to a “non-tidal” crust, conventionally defined using physically meaningless parameters. We propose to use instead the zero-crust concept which corresponds to concepts already accepted in the resolution of IAG in 1983 for gravimetric works.

title: The Permanent Tide In Height Systems
abstract: We describe the treatment of the permanent tide in various geodetic quantities with an emphasis on systems of gravity-related heights. We review the historical development leading to the present situation, and discuss possible scenarios for the future, especially in view of the adoption of a World Height System

title: Modelling the glacial isostatic adjustment of the UK region
abstract: The glacial isostatic adjustment of the UK region has been considered in a number of recent studies. We have revisited this problem in order to: (i) highlight some key issues with regard to limitations in the ice modelling approach adopted in these studies and (ii) consider the constraints provided from observations of crustal motion available via continuous global positioning system monitoring. With regard to the first aim, we have found that: (i) previous studies have significantly overestimated ice thicknesses in regions where trim line field constraints were adopted and (ii) the duration of the glaciation phase of the UK ice sheet is a critical aspect of the model and that discrepancies in this model component have led to inconsistent inferences of Earth model parameters. With regard to the second aim, we have found that predictions of horizontal velocities (relative to a chosen site) based on a UK ice model calibrated to fit the regional sea-level database capture the geometry of the signal well but only account for 10% of the magnitude (for a range of Earth models).

title: Using continuous GPS and absolute gravity to separate vertical land movements and changes in sea-level at tide-gauges in the UK
abstract: Researchers investigating climate change have used historical tide-gauge measurements from all over the world to investigate the changes in sea-level that have occurred over the last century or so. However, such estimates are a combination of any true sea-level variations and any vertical movements of the land at the specific tide-gauge. For a tide- gauge record to be used to determine the climate related component of changes in sea-level, it is therefore necessary to correct for the vertical land movement component of the observed change in sea-level. In 1990, the Institute of Engineering Surveying and Space Geodesy and Proudman Oceanographic Laboratory started developing techniques based on the Global Positioning System (GPS) for measuring vertical land movements (VLM) at tide-gauges in the UK. This paper provides brief details of these early developments and shows how they led to the establishment of continuous GPS (CGPS) stations at a number of tide-gauges. The paper then goes on to discuss the use of absolute gravity (AG), as an independent technique for measuring VLM at tide-gauges. The most recent results, from CGPS time-series dating back to 1997 and AG time-series dating back to 1995/1996, are then used to demonstrate the complementarity of these two techniques and their potential for providing site-specific estimates of VLM at tide-gauges in the UK.

title: Crustal motions in Great Britain: evidence from continuous GPS, absolute gravity and Holocene sea level data
abstract: Two independent continuous global positioning system (CGPS) processing strategies, based on a double-difference regional network and a globally transformed precise point positioning solution, provide horizontal and vertical crustal motion estimates for Great Britain. Absolute gravity and geological information from late Holocene sea level data further constrain the vertical motion estimates. For 40 CGPS stations we estimate station velocities and associated uncertainties using maximum likelihood estimation, assuming the presence of white and coloured noise. Horizontal station velocity estimates agree to <1 mm yr(-1) between the two CGPS processing strategies and closely follow predicted plate motions. Residual velocities, generally < 1 mm yr(-1), follow no regular pattern, that is, there is no discernible internal deformation, nor any dependence on station monumentation or time-series length. Vertical station velocity estimates for the two CGPS processing strategies agree to similar to 1 mm yr(-1), but show an offset of similar to 1 mm yr(-1) with respect to the absolute gravity (AG) estimates. We attribute this offset to a bias related to known issues in current CGPS results and correct for it by AG-alignment of our CGPS estimates of vertical station velocity. Both CGPS estimates and AG-aligned CGPS estimates of present-day vertical crustal motions confirm the pattern of subsidence and uplift in Great Britain derived from Holocene sea level data for the last few thousand years: ongoing subsidence on Shetland, uplift in most areas of Scotland, and subsidence in large areas of England and Wales.

title: Using sea-level and land motion data to develop an improved glacial isostatic adjustment model for the British Isles
abstract: The Glacial Isostatic Adjustment (GIA) of the British Isles is of interest due to the constraints that can be provided on key model parameters such as regional ice sheet history, viscoelastic earth structure and the global meltwater (eustatic) signal. Many past studies have used as their primary observable the high quality relative sea level (RSL) data from this region. However, as indicated in these studies, the data are notoriously difficult to fit due to the highly complex non-monotonic nature of the observed sea level change. In addition, the model predictions show a strong sensitivity to both regional ice and earth model parameters as well as the global meltwater history, resulting in a high degree of non-uniqueness when seeking an optimum model solution. 
 
The principle aim of this thesis is to address this inherent non-uniqueness in the British Isles GIA problem and reduce the viable solution parameter space by considering additional datasets that display distinct sensitivities to local and global components of the GIA signal. This was achieved in a number of stages, using a combination of relative sea level data from both near and far-field sites, Continuous GPS data and the most recent geomorphological field constraints. 
 
GPS observations of present day vertical crustal motion at sites across Great Britain are employed to provide an independent constraint on the choice of regional earth model parameters (viscoelastic earth structure). It was shown that the data are relatively insensitive to plausible variations in both the regional and global ice model history and as such, the data are used to identify an optimum range of earth model parameters for the region. 
 
Using a set of previously un-modelled far-field sea level data from China and Malay-Thailand, a revised model of eustatic sea level change over the Holocene was developed. Constraining the eustatic component of sea level change is useful since it provides a direct measure of continental ice volume that can be compared to results from oxygen isotope methods. Additionally, inference of the eustatic signal over the mid-late Holocene, which was the primary focus of one aspect of this thesis can provide information on both: (i) the rate and timing of major ice melting at the end of the last deglaciation and (ii) the magnitude of melting during the late Holocene, which is an important baseline that can be compared to estimates of global sea-level rise in the 20th century. This new global ice model is characterised by an initial slowdown in the rate of eustatic sea level rise at 7 kyr BP, followed by a continuing rise, until 2 kyr BP, driven by continued melting from the Antarctic Ice sheet. 
 
A new British-Irish Ice sheet model over the most recent glacial cycle was produced. This model was constrained to fit to most recent geomorphological field constraints and includes an extensive two-stage glaciation across the North Sea basin, with a greatly thickened and extended ice sheet within the Irish Sea, out along the NE Atlantic margin and across Ireland. During deglaciation, the Irish ice sheet now undergoes a very rapid thinning and retreat. 
 
These results have been combined to produce a final new GIA model for the region, which has been constrained, for the first time, using an extended RSL database which includes observations from both Great Britain and Ireland. This new model captures reasonably well the regional trends in the observed sea level, with previous unresolved misfits relating to the timing and height of the Holocene highstand now largely removed.

title: Annual and interannual variability of sea level in the northern North Atlantic Ocean
abstract: The combined TOPEX/Poseidon + ERS-1/2 sea level anomaly (SLA) data from the northern North Atlantic Ocean for the time period 22 October 1992 to 29 December 2000 (300 cycles) were processed. The annual and interannual signals were examined, and their contribution to the total variance is estimated. Both signals appeared to be responsible for a greatest portion of variability outside the North Atlantic Current (NAC) and its branches. The annual signal manifested consistency with seasonal changes in the heat storage, possibly enhanced by seasonal variations of advection. A considerable interannual change was monitored in the vast areas of the northern North Atlantic Ocean as well as along the NAC. The interannual change in SLA was found to be consistent with the North Atlantic Oscillation (NAO) index when it changed from its positive to its negative phase in 1996. The significant negative correlation coefficient between the annually averaged SLA and NAO index time series was estimated in all dynamically calm areas outside the NAC. Hydrographic data obtained during several cruises for the time interval studied were also investigated and coupled with the variations of SLA and NAO index. The analysis showed a good agreement between the altimeter-derived SLA and dynamic height anomalies suggesting that the sea level changes in the northern North Atlantic have a baroclinic nature.

title: The NCEP/NCAR 40-Year Reanalysis Project
abstract: The NCEP and NCAR are cooperating in a project (denoted “reanalysis”) to produce a 40-year record of global analyses of atmospheric fields in support of the needs of the research and climate monitoring communities. This effort involves the recovery of land surface, ship, rawinsonde, pibal, aircraft, satellite, and other data; quality controlling and assimilating these data with a data assimilation system that is kept unchanged over the reanalysis period 1957–96. This eliminates perceived climate jumps associated with changes in the data assimilation system. The NCEP/NCAR 40-yr reanalysis uses a frozen state-of-the-art global data assimilation system and a database as complete as possible. The data assimilation and the model used are identical to the global system implemented operationally at the NCEP on 11 January 1995, except that the horizontal resolution is T62 (about 210 km). The database has been enhanced with many sources of observations not available in real time for operations, provided by differe...

title: SINGLE RECEIVER HEIGHTING USING THE ACTIVE STATIONS OF THE NATIONAL GPS NETWORK OF GREAT BRITAIN
abstract: Precise height determination using a single GPS receiver is now possible, following the establishment of GPS networks that include active stations with typical separations of about 100km. A method is described to determine precise heights when using a single GPS receiver and active stations of the National GPS Network of Great Britain. From the computation of the heights of 188 GPS stations distributed across the British mainland, a precision of 1.5cm was attained. This was achieved using only 4 hours of dual frequency static GPS data, but with scientific GPS processing soflware to mitigate systematic error effects.

title: Non‐tidal ocean loading effects on geodetic GPS heights
abstract: GPS observations used in geophysical studies are not usually corrected for non-tidal ocean loading (NTOL) displacement. Here we investigate NTOL effects on 3–4 year GPS height time series from 17 sites around the southern North Sea, and compute the NTOL displacement according to two ocean models; the global ECCO model and a high resolution regional model, POLSSM, which covers the northwest European continental shelf. To assess the susceptibility of GPS height estimates to NTOL, reprocessed GIPSY PPP daily solutions are corrected for the resulting displacement, together with atmospheric pressure loading (ATML). We find that the displacements due to NTOL are comparable in size to ATML and the combined correction reduces the variance by 12–22 mm2 (20–30% reduction in RMS). We find that POLSSM outperforms ECCO, with around an 11% greater variance reduction, and hence high resolution models are recommended to correct GPS heights for NTOL.

title: ITRF2008: an improved solution of the international terrestrial reference frame
abstract: ITRF2008 is a refined version of the International Terrestrial Reference Frame based on reprocessed solutions of the four space geodetic techniques: VLBI, SLR, GPS and DORIS, spanning 29, 26, 12.5 and 16 years of observations, respectively. The input data used in its elaboration are time series (weekly from satellite techniques and 24-h session-wise from VLBI) of station positions and daily Earth Orientation Parameters (EOPs). The ITRF2008 origin is defined in such a way that it has zero translations and translation rates with respect to the mean Earth center of mass, averaged by the SLR time series. Its scale is defined by nullifying the scale factor and its rate with respect to the mean of VLBI and SLR long-term solutions as obtained by stacking their respective time series. The scale agreement between these two technique solutions is estimated to be 1.05 ± 0.13 ppb at epoch 2005.0 and 0.049 ± 0.010 ppb/yr. The ITRF2008 orientation (at epoch 2005.0) and its rate are aligned to the ITRF2005 using 179 stations of high geodetic quality. An estimate of the origin components from ITRF2008 to ITRF2005 (both origins are defined by SLR) indicates differences at epoch 2005.0, namely: −0.5, −0.9 and −4.7 mm along X, Y and Z-axis, respectively. The translation rate differences between the two frames are zero for Y and Z, while we observe an X-translation rate of 0.3 mm/yr. The estimated formal errors of these parameters are 0.2 mm and 0.2 mm/yr, respectively. The high level of origin agreement between ITRF2008 and ITRF2005 is an indication of an imprecise ITRF2000 origin that exhibits a Z-translation drift of 1.8 mm/yr with respect to ITRF2005. An evaluation of the ITRF2008 origin accuracy based on the level of its agreement with ITRF2005 is believed to be at the level of 1 cm over the time-span of the SLR observations. Considering the level of scale consistency between VLBI and SLR, the ITRF2008 scale accuracy is evaluated to be at the level of 1.2 ppb (8 mm at the equator) over the common time-span of the observations of both techniques. Although the performance of the ITRF2008 is demonstrated to be higher than ITRF2005, future ITRF improvement resides in improving the consistency between local ties in co-location sites and space geodesy estimates.

title: The AUSGeoid09 model of the Australian Height Datum
abstract: AUSGeoid09 is the new Australia-wide gravimetric quasigeoid model that has been a posteriori fitted to the Australian Height Datum (AHD) so as to provide a product that is practically useful for the more direct determination of AHD heights from Global Navigation Satellite Systems (GNSS). This approach is necessary because the AHD is predominantly a third-order vertical datum that contains a ~1 m north-south tilt and ~0.5 m regional distortions with respect to the quasigeoid, meaning that GNSS-gravimetric-quasigeoid and AHD heights are inconsistent. Because the AHD remains the official vertical datum in Australia, it is necessary to provide GNSS users with effective means of recovering AHD heights. The gravimetric component of the quasigeoid model was computed using a hybrid of the remove-compute-restore technique with a degree-40 deterministically modified kernel over a one-degree spherical cap, which is superior to the remove-compute-restore technique alone in Australia (with or without a cap). This is because the modified kernel and cap combine to filter long-wavelength errors from the terrestrial gravity anomalies. The zero-tide EGM2008 global gravitational model to degree 2,190 was used as the reference field. Other input data are ~1.4 million land gravity anomalies from Geoscience Australia, 1′ × 1′ DNSC2008GRA altimeter-derived gravity anomalies offshore, the 9′′ × 9′′ GEODATA-DEM9S Australian digital elevation model, and a readjustment of Australian National Levelling Network (ANLN) constrained to the CARS2006 mean dynamic ocean topography model. To determine the numerical integration parameters for the modified kernel, the gravimetric component of AUSGeoid09 was compared with 911 GNSS-observed ellipsoidal heights at benchmarks. The standard deviation of fit to the GNSS-AHD heights is ±222 mm, which dropped to ±134 mm for the readjusted GNSS-ANLN heights showing that careful consideration now needs to be given to the quality of the levelling data used to assess gravimetric quasigeoid models. The publicly released version of AUSGeoid09 also includes a geometric component that models the difference between the gravimetric quasigeoid and the zero surface of the AHD at 6,794 benchmarks. This a posteriori fitting used least-squares collocation (LSC) in cross-validation mode to determine a correlation length of 75 km for the analytical covariance function, whereas the noise was taken from the estimated standard deviation of the GNSS ellipsoidal heights. After this LSC surface fitting, the standard deviation of fit reduced to ±30 mm, one-third of which is attributable to the uncertainty in the GNSS ellipsoidal heights.

title: The US Gravimetric Geoid of 2009 (USGG2009): model development and evaluation
abstract: A new gravimetric geoid model, USGG2009 (see Abbreviations), has been developed for the United States and its territories including the Conterminous US (CONUS), Alaska, Hawaii, Guam, the Commonwealth of the Northern Mariana Islands, American Samoa, Puerto Rico and the US Virgin Islands. USGG2009 is based on a 1′ × 1′ gravity grid derived from the NGS surface gravity data and the DNSC08 altimetry-derived anomalies, the SRTM-DTED1 3′′ DEM for its topographic reductions, and the global geopotential model EGM08 as a reference model. USGG2009 geoid heights are compared with control values determined at 18,398 Bench Marks over CONUS, where both the ellipsoidal height above NAD 83 and the Helmert orthometric height above NAVD 88 are known. Correcting for the ellipsoidal datum difference, this permits a comparison of the geoid heights to independent data. The standard deviation of the differences is 6.3 cm in contrast to 8.4 cm for its immediate predecessor— USGG2003. To minimize the effect of long-wavelength errors that are known to exist in NAVD88, these comparisons were made on a state-by-state basis. The standard deviations of the differences range from 3–5 cm in eastern states to about 6–9 cm in the more mountainous western states. If the GPS/Bench Marks-derived geoid heights are corrected by removing a GRACE-derived estimate of the long-wavelength NAVD88 errors before the comparison, the standard deviation of their differences from USGG2009 drops to 4.3 cm nationally and 2–4 cm in eastern states and 4–8 in states with a maximum error of 26.4 cm in California and minimum of −32.1 cm in Washington. USGG2009 is also compared with geoid heights derived from 40 tide-gauges and a physical dynamic ocean topography model in the Gulf of Mexico; the mean of the differences is 3.3 cm and their standard deviation is 5.0 cm. When USGG2009-derived deflections of the vertical are compared with 3,415 observed surface astro-geodetic deflections, the standard deviation of the differences in the N–S and E–W components are 0.87′′ and 0.94′′, respectively.

title: The European Gravimetric Quasigeoid EGG97 - An IAG Supported Continental Enterprise -
abstract: In 1990, the Institut fur Erdmessung (IfE), University of Hannover, started with the calculation of a gravimetric (quasi)geoid for Europe and the surrounding marine areas, operating as the computing center of the International Association of Geodesy (IAG) Geoid Commission. The requirements for accuracy and resolution were derived from the potential of GPS heighting and satellite altimetry, and defined at the “cm” to “dm” level over distances from a few km to some 1000 km, which requires a spatial resolution of a few km.

title: Yet more evidence for a North‐South slope in the Australian Height Datum
abstract: The results here add to the body of evidence for a systematic north‐south error in the Australian Height Datum (AHD). Previous studies based solely on Global Positioning System (GPS) and a gravimetric geoid model have suffered from the ‘inseparability problem’, where it is not possible to discriminate between errors in the AHD and geoid. Instead, this study compares horizontal gradients of the AUSGeoid98 regional gravimetric geoid model with totally independent astrogeodetically observed vertical deflections at 741 Laplace stations across Australia. These comparisons do not show any significant latitude‐dependent residuals, thus significantly reducing the likelihood of a north‐south slope in AUSGeoid98. Subsequently using GPS and AUSGeoid98, now that the inseparability problem has been addressed, there is very compelling evidence for a real north‐south slope of ∼1.5m in the AHD.

title: SPACE-DERIVED GEOID MAPS OF GREAT BRITAIN
abstract: Maps of the geoid of Great Britain have been determined by three independent space techniques: from Global Positioning System observations; by the astrogeodetic method; and by means of a geopotential model OSU91A, all referred to Geodetic Reference System 1980 (GRS80). Maps referred to the Airy ellipsoid are also given for the first two methods.

title: An analysis of vertical deflections derived from high-degree spherical harmonic models
abstract: The theoretical differences between the Helmert deflection of the vertical and that computed from a truncated spherical harmonic series of the gravity field, aside from the limited spectral content in the latter, include the curvature of the normal plumb line, the permanent tidal effect, and datum origin and orientation offsets. A numerical comparison between deflections derived from spherical harmonic model EGM96 and astronomic deflections in the conterminous United States (CONUS) shows that correcting these systematic effects reduces the mean differences in some areas. Overall, the mean difference in CONUS is reduced from −0.219 arcsec to −0.058 arcsec for the south–north deflection, and from +0.016 arcsec to +0.004 arcsec for the west–east deflection. Further analysis of the root-mean-square differences indicates that the high-degree spectrum of the EGM96 model has significantly less power than implied by the deflection data.

title: A new GPS-based evaluation of distortions in the Australian Height Datum in Western Australia
abstract: Previous work on assessing the errors in the Australian Height Datum (AHD) across Western Australia used fewer and older global positioning system (GPS) data and a global quasigeoid model. A larger and improved State-wide set of 243 GPS-derived ellipsoidal heights and a regional gravimetric quasigeoid model are now available. Therefore, it is possible to re-evaluate the northsouth tilt in the AHD and look for regional systematic distortions with some more confidence in Western Australia. This new analysis shows an apparent north-south tilt of ~0.27 mm/km in the existing AHD over the whole of the State, but which increases to ~0.6 mm/km over smaller regions, showing regional systematic distortions. When mean sea-level constraints are removed from the AHD by a minimally constrained least-squares adjustment of the spirit-levelling observations that is less prone to the effect of sea-surface topography, the north-south tilt reduces to ~0.18 mm/km, but the regional distortions remain, showing that errors are present in the spirit-levelling observations.