53965413
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.
128808308
Geodetic leveling and its applications
The inherent precision of spirit leveling has preserved its utility as a geodetic measurement system for over a century. While various instrumental and procedural modifications designed to enhance this precision have been introduced over the years, the basic measurement system has remained virtually unchanged since the mid-nineteenth century. Possible systematic error has dictated the majority of the procedural and instrumental requirements associated with geodetic leveling; the physical source(s) of several of these errors remain poorly understood. Statistically independent random errors, which accumulate according to the square root of the survey distance, are generally controlled through redundancy and procedural randomization; they range from 0.5 mm L1/2 for the highest-order modern leveling to about 6 mm L1/2 for the lowest-order nineteenth-century geodetic surveys, where L is the survey distance in kilometers. Height differences are conceptually distinct from observed or measured elevation differences in the sense that the former are uniquely defined, whereas the latter are path dependent, a distinction that arises from the nonparallelism of the equipotential surfaces of the earth’s gravity field. The number of possible height systems is virtually limitless. They include the systems of geopotential numbers and dynamic heights; although neither of these systems is geometrically informative, each provides perfectly valid height characterizations that may be especially useful in the solution of certain physical problems. The most generally used system of heights is the orthometric height system; the resulting heights are true geometric heights above the geoid. Normal height systems are referred to the quasi-geoid rather than the geoid. Each of the various height systems meets the requirement of uniqueness, and none can be viewed as being conceptually superior. Conversion of the observed elevation differences obtained from leveling into uniquely defined height differences requires the application of a gravity-dependent correction. Because gravity coverage in North America was generally sparse until recently, an approximation for this correction, which provides for the effects of the poleward covergence of the equipotential surfaces, has usually been used on this continent. Heights have been traditionally referred to mean sea level as a datum, a usage that implies coincidence between mean sea level and the geoid (or quasi-geoid). Because the determination of mean sea level is dependent on the length of the observation period, because its definition makes no allowance for vertical crustal displacements or changes in eustatic sea level, and because its definition disregards the demonstrable existence of sea surface topography, local mean sea level generally departs from the geoid. This introduces errors in computed heights that probably equal or exceed those due to leveling. Repeated levelings continue to provide the best basis for determining terrestrial vertical displacements. These displacements are necessarily measured with respect to the time-dependent (instantaneous) geoid. Analysis of changes in the orthometric correction and changes in the geoid as a function of changes in gravity indicates that height determinations are almost insensitive to temporal variations in gravity. The simplest and probably the most accurate procedure for determining vertical displacements is based on direct comparisons between observed elevations derived from repeated levelings along the same line. The estimated errors associated with these displacements are a function of the precision of the utilized levelings and have been shown to be much smaller than those associated with heights. A smoothed representation of the vertical displacement field can be obtained by the fitting of a mathematical surface to the results of segmented relevelings. Surface-fitting techniques usually tend to subdue short-wavelength features, but they are especially useful in depicting artificially induced subsidence and broadly defined tectonic uplift or collapse.
122012607
Geodetic aspects concerning possible subsidence in southeastern England
The various geodetic levellings carried out by the Ordnance Survey are reviewed briefly and the evidence of land movement in Great Britain shown by the results of these levellings is considered. Current lower order levelling in southeast England is compared with levelling carried out before 1949 described by Longfield (1932) and Lloyd (1831). Attention is drawn to the existence of deep bench marks in London. Consideration is given o e a that is needed to ensure that the relative movements of land and sea can be suitably monitored in the future.
129225213
A Combination of Space and Terrestrial Geodetic Techniques to Monitor Land Subsidence: Case Study, the Southeastern Po Plain, Italy
[1] The southeastern Po Plain is affected by high natural and anthropogenic subsidence. The area is well suited to test the application of an observational strategy which combines different techniques to extract information on the spatial and temporal variability of the subsidence. The simultaneous availability, at a few stations, of several geodetic observation techniques such as Global Positioning System (GPS), gravity, and Interferometric Synthetic Aperture Radar (InSAR) allows for validation of the individual time series. The combination takes advantage of the complementary strengths of each technique by overcoming the limitations inherent in each single technique alone. The combination of velocities derived from the GPS and gravity data, further complemented by the results of the InSAR Permanent Scatterers technique, allows us to monitor continuously, in space and time, vertical crustal movements. This high-density information is of major importance for understanding the processes responsible for the observed deformation. Here long-term trends were derived, enabling us to map the behavior of subsidence (even exceeding 20 mm/yr) with high spatial resolution in the southeastern Po Plain. The uplifting behavior of the Apennines chain bordering the Po Plain is identified together with a narrow zone separating the contrasting vertical crustal movements.
129455144
Geodetic evidence for subsidence due to groundwater withdrawal in many parts of the United States of America
Abstract Analysis of repeated levelings conducted by the National Geodetic Survey indicates many locations of relative subsidence in the U.S.A. Specific criteria are used to identify those subsidence features which most likely result from sediment compaction due to lowering of water levels in underground aquifer systems. Previously reported areas of such subsidence that seem to be confirmed by this study include: south-central Arizona; Savannah, Georgia; Pecos and Houston-Galveston, Texas; Denver, Colorado; San Joaquin Valley, Santa Clara Valley, Saugus Basin, Los Angeles Basin and Bunker Hill-San Timoteo, California; Milford, Utah; Raft River Valley, Idaho; Baton Rouge and New Orleans, Louisiana; and Las Vegas, Nevada. In addition, our analysis indicates that such subsidence is more widespread than previously reported occurring in a number of locations within the Atlantic and Gulf of Mexico coastal plains and along the Mississippi Valley as well as in many other unconsolidated sedimentary basins from which groundwater has been extracted and for which repeated leveling measurements are available. More than 30 new locations of subsidence possibly due to water withdrawal have been identified. The best documented of these include: Ventura, Ontario and San Pedro-Santa Monica, California; Monroe and Alexandria, Louisiana, and Jackson, Mississippi. Subsidence in newly identified locations ranges from several tens of millimeters to a few hundred millimeters over distances of ∼ 10–60 km and times of 2–48 yr. Subsidence may also have occurred in other groundwater basins where water levels have been drawn down, and remained undetected because of a lack of repeated levelings. It is important to be aware of and to continue to monitor such effects because of increasing rates of utilization of groundwater resources and the potential for significant engineering problems due to surface movements. In addition, identifying cases of subsidence due to water withdrawal is essential in order to use effectively releveling observations for investigating tectonic deformation. Along these lines, our analysis suggests that some of the releveling observations used to define a region of tectonic uplift in southern California more likely reflect subsidence due to water-level declines within sedimentary basins around the periphery of the presumed zone of uplift.
128822207
Analysis of satellite and in situ ground deformation data integrated by the SISTEM approach: The April 3, 2010 earthquake along the Pernicana fault (Mt. Etna - Italy) case study
Abstract Etna is known worldwide as one of the most studied and monitored active volcanoes. Flank instability along the eastern and southern portions of Mt. Etna has been observed and measured thanks to geodetic networks and InSAR data analysis. The spreading area is bordered to the north by the east–west Pernicana Fault System (PFS) whose dynamics is often linked with the eruptive activity, as recently observed during the 2002–2003 eruption. A seismic sequence occurred from April 2–3, 2010, along the PFS with very shallow (a few hundred meters) mainshocks of magnitude 4.3 and 3.6. Explosions and ash emissions at the summit craters followed this swarm culminating a few days later (April 7–8). Despite their small magnitude, the earthquakes caused damage and significant surface fracturing along the PFS. In order to investigate and measure the deformations in the near field of the earthquakes, the SISTEM integration approach has been exploited. The SISTEM enabled integrating geodetic in situ ground deformation measurements (GPS and leveling) with satellite interferometric measurements (ENVISAT and ALOS), in order to obtain high resolution 3D displacement maps, allowing to overcome the limitations of each technique and take advantage of the particular features of each of them. The integrated ground deformation field evidenced that the medium behave elastically. We inverted the SISTEM results using an optimization algorithm based on the Genetic Algorithm (GA) in order to model the kinematics of the PFS associated to seismic swarm; the results are in good agreement with the field evidence and improved the knowledge on the kinematics of the PFS and Mt. Etna's unstable flank.
129592464
Determination of post-glacial land uplift from the three precise levellings in Finland
Abstract. We have calculated vertical velocities and their change in time from three precise levellings in Finland, with central epochs 1902, 1946, and 1986. Models with and without simultaneous determination of heights give the same results for velocities. Evidence for velocity change in time appears at first sight strong but on closer examination turns out to be inconclusive. We offer an alternative explanation in terms of levelling errors and estimate them. A new uplift map closely reproduces main features of earlier maps from partial data, but does not support some details in them.
128912442
Determination of Postglacial Land Uplift in Fennoscandia from Leveling, Tide-gauges and Continuous GPS Stations using Least Squares Collocation
Precise leveling, tide-gauge recordings and time series from continuous GPS stations are all sources of information about the ongoing postglacial land uplift in Fennoscandia. This article describes how to gather these three sources of data together in a least-squares collocation adjustment in order to calculate uplift rates, as well as new heights for the benchmarks in the leveling network. The estimated reliability of the resulting uplift model is in general better than 0.4 mm/year, decreasing in areas of fewer data.
140651372
Comparison and validation of the recent freely available ASTER-GDEM ver1, SRTM ver4.1 and GEODATA DEM-9S ver3 digital elevation models over Australia
This study investigates the quality (in terms of elevation accuracy and systematic errors) of three recent publicly available elevation model datasets over Australia: (i) the 9 arc second national GEODATA DEM-9S ver3 from Geoscience Australia and the Australian National University; (ii) the 3 arc second SRTM ver4.1 from CGIAR-CSI; and (iii) the 1 arc second ASTER-GDEM ver1 from NASA/METI. The main features of these datasets are reported from a geodetic point of view. Comparison at about 1 billion locations identifies artefacts (e.g. residual cloud patterns and stripe effects) in ASTER. For DEM-9S, the comparisons against the space-collected SRTM and ASTER models demonstrate that signal omission (due to the ∼270 m spacing) may cause errors of the order of 100–200 m in some rugged areas of Australia. Based on a set of geodetic ground control points over Western Australia, the vertical accuracy of DEM-9S is ∼9 m, SRTM ∼6 m and ASTER ∼15 m. However, these values vary as a function of the terrain type and shape. Thus, CGIAR-CSI SRTM ver4.1 may represent a viable alternative to DEM-9S for some applications. While ASTER GDEM has an unprecedented horizontal resolution of ∼30 m, systematic errors present in this research-grade version of the ASTER GDEM ver1 will impede its immediate use for some applications.
129361850
Convergence of the UK OSGM05 GRACE-based geoid and the UK fundamental benchmark network
[1] The results of this study suggest that a traditional height network based on fundamental benchmarks can be used meaningfully to assess the quality of a satellite-derived geoid model. We compare the pre- Gravity Recovery and Climate Experiment (GRACE) OSGM02 and the recent OSGM05 geoid models with the datum surface inferred by the UK fundamental benchmark network combined with network monument ellipsoidal heights derived from GPS data. OSGM05 incorporates long-wavelength gravity field data from GRACE to degree/order 90. Switching from OSGM02 to OSGM05, the mean difference between the leveling datum and the geoid model reduces from −0.129 m to −0.004 m, and RMS differences reduce from 0.110 m to 0.048 m. The mean tilt between the height datum and the geoid model in the north-south direction reduces from 34 mm to 12 mm per degree of latitude. Hence we demonstrate a systematic convergence between the geoid models and the leveling datum surface in terms of mean offset, RMS scatter and tilt without any fitting of one surface to the other. The implication is that the leveling datum surface represented a more accurate model of the geoidal geometry compared to OSGM02 in terms of form (in both short- and long-wavelength features) and surprisingly also in terms of its offset from the GRS80 ellipsoid. While the latter point can be no more than a coincidence, the former indicates that the UK leveling network, based on its fundamental benchmark network, can be used to test the accuracy of geoid model improvements derived from missions such as GRACE, with implications for the forthcoming Gravity Field and Steady State Ocean Circulation Explorer (GOCE) mission.
129152995
Slope of sea level along the Pacific coast of the United States
The long-term mean slope of sea level along the Pacific coast of the United States is estimated for comparison with the rise from south to north reported by precise leveling. Oceanographic evidence does not support the leveling results. Steric levels at the coast relative to 1000 db strongly suggest that the slope reported by leveling is nonexistent. Careful examination of the 1000-db surface shows it to be a sufficiently level reference surface along the coast. Mean sea level at Neah Bay, Washington, is found to stand 9 cm lower than at San Diego, California, rather than 46 cm higher as suggested by leveling. A leveling error that could cause a slope of the observed sign and amount is discussed. The 9-cm difference found in the present study is consistent with the effect of changing latitude as the California Current flows south.
130438578
Sea level slope along continental boundaries
The variation of sea level along continental boundaries is studied from a variety of data. Along the western boundaries of the Atlantic and Pacific oceans, sea level falls approximately 80 cm between the equator and 40°N or S. Along the eastern boundaries the change in level is about one-third this amount. This meridional slope is shown to be the correct amount required by the change with latitude of surface slope across the boundary currents. The meridional slope along the inshore edge of the Gulf Stream has the correct sign and magnitude to be balanced by the gradient of the Reynolds stresses. In the east-west direction, sea level along the Pacific coast of the United States stands about 70 cm higher than that along the Atlantic coast; two-thirds of this difference is concluded to be caused by density differences between the two oceans. The remaining third results because the east coast of the United States is inside the strong slope across a western boundary current, whereas the west coast is next to an eastern boundary current.
207737558
The sea slope problem revisited
Discrepancies in sea surface topography based on comparisons between the results of steric leveling and repeated geodetic levelings have identified what is known as the ‘sea slope problem.’ This problem is actually twofold: (1) the sea surface relief based on steric leveling differs significantly from that based on geodetic leveling along several generally north-south coasts, and (2) successively propagated levelings between several widely separated tide stations indicate that the stationary sea slope seemingly has been changing with time, whereas differenced sea level means between these stations indicate that the sea surface relief has remained virtually invariant during the same intervals. Reexamination of the three reported discrepancies between geodetically and sterically determined sea slopes indicates that the Australian example is based on leveling of a quality inappropriate to the comparison. The discrepancy developed along the Atlantic coast of the United States is limited to the reach between Portsmouth–Hampton Roads, Virginia, and Key West, Florida, where the accuracy of steric leveling may be especially vulnerable owing to the dynamic effects of the Gulf Stream. Reconsideration of the example along the Pacific coast of the United States indicates that the various discrepancies are due chiefly to intrasurvey movement and resultant distortion of geodetically defined height differences between tide stations. Agreement between the results of steric and geodetic leveling along tectonically inactive north-south coasts devoid of strong boundary currents is generally good. This observation supports the conclusions (1) that any directionally dependent systematic error in geodetic leveling is measurably insignificant and (2) that where allowance is made for the possible effects of major boundary currents or intrasurvey movement during levelings between tide stations, the sea slope problem tends to vanish.
54531868
The north‐south tilt in the Australian Height Datum is explained by the ocean's mean dynamic topography
[1] Using geodetic and oceanographic data, we show that the apparent north-south slope between the Australian Height Datum (AHD) and the geoid is caused almost completely by the ocean's time-mean dynamic topography (MDT). This is because the AHD was constrained to zero height at local mean sea level at multiple tide gauges around the Australian continent. Using MDT models and corrected leveling data, almost all of the apparent north-south slope can be removed from the AHD. An auxiliary observation is that a satellite-only MDT model based on only around one year of GOCE data generates results commensurate with geodetic, oceanographic and combined MDT models.
130559183
A geodetic investigation of the British sea slope anomaly
Abstract A project was initiated in 1986 to investigate an apparent significant discrepancy between geodetic and oceanographic leveling determinations of mean sea level around the coast of Great Britain. In oceanographic terms this discrepancy is equivalent to a sea slope in a North‐South direction. The project, which lasted for 3 years, has been carried out in conjunction with research groups at the University of Edinburgh, the Proudman Oceanographic Laboratory, and the Ordnance Survey of Great Britain. It has involved combining Global Positioning System (GPS)‐derived ellipsoidal height differences with a high‐precision geoid, leading to an independent determination of the orthometric heights of tide gauges along the east coast of Great Britain. A major GPS campaign was observed in May 1988. Measurements were made at time gauges between Leith and Lowestoft while simultaneously making measurements at fiducial sites. The results of the 1988 and subsequent campaigns are presented and discussed, and details ...
131815948
Geoid models for Great Britain and the North Sea
This paper describes the new model geoid for Great Britain called EDIN91, as well as its recent predecessors, EDIN89 and EDIN891, also noting the objectives for the next geoid EDIN95, now in preparation. EDIN91 appears to identity a north-south trend of 0.28 mm km -1 in the global gravity model OSU91A over an 800 km baseline in Britain. Accepting this trend and allowing for the 697.7 mm difference in ellipsoidal radius to adjust OSU91A to ITRF90 gives an absolute correction of 3.3 ± 10.3 mm for the Newlyn Datum, based on six GPS/MSL tide gauge geoid heights given by Dodson et al (1995). This result may yet prove spurious because there are known small adjustment errors in the gravity data set. A definitive assessment of the quality of the new geoid awaits the outcome of a re-evaluation of the gravity and topographic data now taking place in preparation for EDIN95 and the availability of better distributed GPS control in northern Britain.
130217574
The geoid EDIN2000 and mean sea surface topography around the British Isles
SUMMARY This paper describes a new rationale for computing a gravimetric geoid and reports that the resulting geoid model, EDIN2000, is now good enough to resolve previously contradictory estimates for mean sea surface topography (MSST) around Great Britain. For at least 30 yr, it has been known that MSST derived from tide gauges, levelling and oceanography were mutually inconsistent and differed by an order of magnitude. When combined with an altimetric mean sea surface, EDIN2000 is also able to map realistic MSST over the northwest European shelf, and identify and quantify mean currents flowing in the deep ocean parallel to the shelf edge. When compared with 11 GPS referenced tide gauges on the British mainland our estimate of MSST has a standard deviation of only 0.03 m and its variation with latitude is not significantly different from zero. For these sites, long distance levelling errors are larger than geoid errors. We identify a systematic jump (by 0.24 ± 0.05 m) in the levelled transfer of Ordnance Datum Newlyn, affecting all sites in Great Britain to the north of latitude 53 ◦ N. Even after this correction, the variability of levelling remains larger than that of the geoid and GPS, implying a more complex structure to the levelling error than a simple step. Away from coasts we find that the best way to validate marine gravity data is their ability to predict MSST with low local variability when combined with altimetric mean sea level. There is a large reduction in MSST variability when marine gravity data are subjected to an anti-aliased adjustment of the mismatch where ship tracks cross. We also report two MSST model comparisons from a shelf seas and a deep ocean model, both of high resolution. There is quantitative and qualitative agreement between our geoid-derived MSST and the model predictions, indicating significant improvements compared with earlier geoid models. We also show that with the improved accuracy of geoid-based MSST, it will become necessary to validate models and observations at matching epochs.
128825565
A new gravimetric determination of the geoid of the British Isles
AbstractA new gravimetric determination of the geoid of the British Isles has been made, using a modified version of Stokes integral in combination with a global geopotential model and a digital terrain model.
129690397
EUVN_DA: Realization of the European Continental GPS/leveling Network
EUREF, the Sub-commission for the Euro-pean Reference Frame within IAG Commission 1, in cooperation with the European Geoid and Gravity Project (EGGP), is developing a homogeneous continental GPS/leveling database. EUVN_DA, the Densification Action of the EUVN (European Unified Vertical Reference Network) project is designed to support the development of the new European geoid solutions and to contribute to the realization of an accurate continental height reference surface. The cm-accuracy GPS/leveling database could also be used for the realization of the European Vertical Reference System (EVRS) and for the analysis of the national height networks.
128472715
OSGM02: A NEW MODEL FOR CONVERTING GPS-DERIVED HEIGHTS TO LOCAL HEIGHT DATUMS IN GREAT BRITAIN AND IRELAND
Abstract The background to the recent computation of a new vertical datum model for the British Isles (OSGM02) is described After giving a brief description of the computational techniques and the data sets used for the derivation of the gravimetric geoid, the paper focuses on the fitting of this surface to the GPS and levelling networks in the various regions of the British Isles in such a way that it can be used in conjunction with GPS to form a replacement for the existing system of bench marks. The error sources induced in this procedure are discussed, and the theoretical basis given for the fitting procedure. Results for each major region (Great Britain, Ireland, and Northern Ireland) as well as the various independent island datums are described The problems to be expected when working between datums are discussed.
126709300
Heights, the Geopotential, and Vertical Datums
Technical Report. Ohio Sea Grant Development Program, NOAA. Grant No. NA86RG0053 (R/CE-7-PD). "Modern Vertical Datums and Lake Level".
122088142
Use of potential coefficient models for geoid undulation determinations using a spherical harmonic representation of the height anomaly/geoid undulation difference
Abstract This paper suggests that potential coefficient models of the Earth's gravitational potential be used to calculate height anomalies which are then reduced to geoid undulations where such quantities are needed for orthometric height determination and vertical datum definition through a potential coefficient realization of the geoid. The process of the conversion of the height anomaly into a geoid undulation is represented by a height anomaly gradient term and the usual N–ζ term that is dependent on elevation and the Bouguer anomaly. Using a degree 360 expansion of 30′ elevations and the OSU91A potential coefficient model, a degree 360 representation of the correction terms was computed. The magnitude of N–ζ reached –3.4 m in the Himalaya Mountains with smaller, but still significant, magnitudes in other mountainous regions.
122562239
On the geoid–quasigeoid separation in mountain areas
The separation between the reference surfaces for orthometric heights and normal heights—the geoid and the quasigeoid—is typically in the order of a few decimeters but can reach nearly 3 m in extreme cases. The knowledge of the geoid–quasigeoid separation with centimeter accuracy or better, is essential for the realization of national and international height reference frames, and for precision height determination in geodetic engineering. The largest contribution to the geoid–quasigeoid separation is due to the distribution of topographic masses. We develop a compact formulation for the rigorous treatment of topographic masses and apply it to determine the geoid–quasigeoid separation for two test areas in the Alps with very rough topography, using a very fine grid resolution of 100 m. The magnitude of the geoid–quasigeoid separation and its accuracy, its slopes, roughness, and correlation with height are analyzed. Results show that rigorous treatment of topographic masses leads to a rather small geoid–quasigeoid separation—only 30 cm at the highest summit—while results based on approximations are often larger by several decimeters. The accuracy of the topographic contribution to the geoid–quasigeoid separation is estimated to be 2–3 cm for areas with extreme topography. Analysis of roughness of the geoid–quasigeoid separation shows that a resolution of the modeling grid of 200 m or less is required to achieve these accuracies. Gravity and the vertical gravity gradient inside of topographic masses and the mean gravity along the plumbline are modeled which are important intermediate quantities for the determination of the geoid–quasigeoid separation. We conclude that a consistent determination of the geoid and quasigeoid height reference surfaces within an accuracy of few centimeters is feasible even for areas with extreme topography, and that the concepts of orthometric height and normal height can be consistently realized and used within this level of accuracy.
120831575
The effect of EGM2008-based normal, normal-orthometric and Helmert orthometric height systems on the Australian levelling network
This paper investigates the normal-orthometric correction used in the definition of the Australian Height Datum, and also computes and evaluates normal and Helmert orthometric corrections for the Australian National Levelling Network (ANLN). Testing these corrections in Australia is important to establish which height system is most appropriate for any new Australian vertical datum. An approximate approach to assigning gravity values to ANLN benchmarks (BMs) is used, where the EGM2008-modelled gravity field is used to ‘re-construct’ observed gravity at the BMs. Network loop closures (for first- and second-order levelling) indicate reduced misclosures for all height corrections considered, particularly in the mountainous regions of south eastern Australia. Differences between Helmert orthometric and normal-orthometric heights reach 44 cm in the Australian Alps, and differences between Helmert orthometric and normal heights are about 26 cm in the same region. Normal-orthometric heights differ from normal heights by up to 18 cm in mountainous regions >2,000 m. This indicates that the quasigeoid is not compatible with normal-orthometric heights in Australia.
128615073
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’.
129369378
A NEW GEODETIC HEIGHTING STRATEGY FOR GREAT BRITAIN
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.
127629190
Using a ‘GPS/MSL Geoid’ to Test Geoid Models in the UK
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.
129173078
Impacts of geodynamic phenomena on systems for height and gravity
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.
122198813
The permanent tide in GPS positioning
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.
127024453
The Permanent Tide In Height Systems
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
17379239
Modelling the glacial isostatic adjustment of the UK region
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).
15396931
Using continuous GPS and absolute gravity to separate vertical land movements and changes in sea-level at tide-gauges in the UK
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.
73719021
Crustal motions in Great Britain: evidence from continuous GPS, absolute gravity and Holocene sea level data
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.
127177519
Using sea-level and land motion data to develop an improved glacial isostatic adjustment model for the British Isles
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.
128604114
Annual and interannual variability of sea level in the northern North Atlantic Ocean
[1] 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.
124135431
The NCEP/NCAR 40-Year Reanalysis Project
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...
129458753
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.
128962464
Non‐tidal ocean loading effects on geodetic GPS heights
[1] 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.
55843408
ITRF2008: an improved solution of the international terrestrial reference frame
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.
3818132
The AUSGeoid09 model of the Australian Height Datum
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.
123629598
The US Gravimetric Geoid of 2009 (USGG2009): model development and evaluation
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.
109612758
The European Gravimetric Quasigeoid EGG97 - An IAG Supported Continental Enterprise -
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.
53571234
Yet more evidence for a North‐South slope in the Australian Height Datum
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.
129256106
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.
122213035
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.
54965010
A new GPS-based evaluation of distortions in the Australian Height Datum in Western Australia
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.