Michael Filmer

Comparison and validation of 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.

Detecting spirit-levelling errors in the AHD: recent findings and issues for any new Australian height datum*

The Australian Height Datum (AHD) forms the vertical geodetic datum for Australia and is thus the framework for all heights, including those used to establish digital elevation models (DEMs). The AHD was established over quite a short time frame, due to the urgent requirement for height control for topographic mapping. This necessitated the use of lower quality spirit-levelling observations over long distances and approximate data reductions. Geoscience Australia has kindly supplied us with height differences for all sections of the basic and supplementary spirit-levelling used to establish the AHD, allowing us to analyse loop closures to detect spirit-levelling (or data entry/transcription) errors in this dataset. In the case-studies presented here, we show that GPS and a precise gravimetric quasigeoid model can be used to identify the sections in a levelling loop that cause misclosure, reflecting the relative quality of modern quasigeoid models over the spirit-levelling originally used to establish the AHD. We also consider and discuss some of the other issues that would have to be considered if Australia is to implement a new vertical geodetic datum from these data to support, for example, improved DEMs in the future.

A Re-Evaluation of the Offset in the Australian Height Datum Between Mainland Australia and Tasmania

The adoption of local mean sea level (MSL) at multiple tide-gauges as a zero reference level for the Australian Height Datum (AHD) has resulted in a spatially variable offset between the geoid and the AHD. This is caused primarily by sea surface topography (SSTop), which has also resulted in the AHD on the mainland being offset vertically from the AHD on the island of Tasmania. Errors in MSL observations at the 32 tide-gauges used in the AHD and the temporal bias caused by MSL observations over different time epochs also contribute to the offset, which previous studies estimate to be between ∼+100 mm and ∼+400 mm (AHD on the mainland above the AHD on Tasmania). This study uses five SSTop models (SSTMs), as well as GNSS and two gravimetric quasigeoid models, at tide-gauges/tide-gauge benchmarks to re-estimate the AHD offset, with the re-evaluated offset between −61 mm and +48 mm. Adopting the more reliable CARS2006 oceanographic-only SSTM, the offset is −12 ± 11 mm, an order of magnitude less than three previous studies that used geodetic data alone. This suggests that oceanographically derived SSTMs should be considered as a viable alternative to geodetic-only techniques when attempting to unify local vertical datums.

Using Models of the Ocean's Mean Dynamic Topography to Identify Errors in Coastal Geodetic Levelling

Identifying errors (blunders and systematic errors) in coastal geodetic levelling networks has often been problematic, primarily for two reasons. First, mean sea level (MSL) at tide gauges cannot be directly compared to height differences from levelling because the geoid/quasigeoid and MSL are not parallel, being separated by the oceans mean dynamic topography (MDT). Second, there is a the lack of redundancy at the edge of the levelling network. This article sets out a methodology to independently identify blunders and/or systematic errors (over long distances) in geodetic levelling using MDT models to account for the separation between the geoid/quasigeoid and MSL at tide gauges. This method is then tested in a case study using an oceanographic MDT model, MSL observations, GNSS data, and a quasigeoid model. The results are significant because the errors found could not be detected by standard levelling misclosure checks alone, with supplementary data from an MDT model, with cross-validation from GNSS-quasigeoid allowing their detection. In addition, it appears that an oceanographic-only MDT is as effective as GNSS and a quasigeoid model for detecting levelling errors, which could be particularly useful for countries with coastal levelling errors in their levelling networks that cannot be identified by conventional levelling closure checks.

Variance component estimation uncertainty for unbalanced data: application to a continent-wide vertical datum

Variance component estimation (VCE) is used to update the stochastic model in least-squares adjustments, but the uncertainty associated with the VCE-derived weights is rarely considered. Unbalanced data is where there is an unequal number of observations in each heterogeneous data set comprising the variance component groups. As a case study using highly unbalanced data, we redefine a continent-wide vertical datum from a combined least-squares adjustment using iterative VCE and its uncertainties to update weights for each data set. These are: (1) a continent-wide levelling network, (2) a model of the ocean’s mean dynamic topography and mean sea level observations, and (3) GPS-derived ellipsoidal heights minus a gravimetric quasigeoid model. VCE uncertainty differs for each observation group in the highly unbalanced data, being dependent on the number of observations in each group. It also changes within each group after each VCE iteration, depending on the magnitude of change for each observation group’s variances. It is recommended that VCE uncertainty is computed for VCE updates to the weight matrix for unbalanced data so that the quality of the updates for each group can be properly assessed. This is particularly important if some groups contain relatively small numbers of observations. VCE uncertainty can also be used as a threshold for ceasing iterations, as it is shown—for this data set at least—that it is not necessary to continue time-consuming iterations to fully converge to unity.

Three viable options for a new Australian vertical datum

While the Intergovernmental Committee on Surveying and Mapping (ICSM) has stated that the Australian Height Datum (AHD) will remain Australia’s official vertical datum for the short to medium term, the AHD contains deficiencies that make it unsuitable in the longer term. We present and discuss three different options for defining a new Australian vertical datum (AVD), with a view to encouraging discussion into the development of a medium- to long-term replacement for the AHD. These options are a (1) levelling-only, (2) combined, and (3) geoid-only vertical datum. All have advantages and disadvantages, but are dependent on availability of and improvements to the different data sets required. A levelling-only vertical datum is the traditional method, although we recommend the use of a sea surface topography (SSTop) model to allow the vertical datum to be constrained at multiple tide-gauges as an improvement over the AHD. This concept is extended in a combined vertical datum, where heights derived from GNSS ellipsoidal heights and a gravimetric quasi/geoid model (GNSS-geoid) at discrete points are also used to constrain the vertical datum over the continent, in addition to mean sea level and SSTop constraints at tide-gauges. However, both options are ultimately restricted by the requirement to upgrade the Australian National Levelling Network (ANLN). It is also desirable that the ANLN be kept in reasonable shape for the validation or testing of height products. On the other hand, a geoid-only vertical datum, where GNSS-geoid is used to continuously define the vertical datum, has advantages primarily because it avoids the requirement to level long distances to upgrade the levelling network. However, it is not routinely possible to realise a geoid of the desired 1–2 cm accuracy necessary to develop a geoid-only vertical datum, especially to a local precision that can match levelling, such that a geoid-only vertical datum is considered a long-term proposition. In the meantime, a combined vertical datum is a more suitable option for any new AVD in the next decade or so, although a geoid-based vertical datum which retains only the higher-quality parts of the ANLN in Australias densely settled areas, but connected by a geoid model rather than continent-wide levelling, may also have merit.

Error propagation for three common height-system corrections to differential levelling

This paper investigates the propagation of input data errors through the application of Helmert orthometric, normal and normal-orthometric height corrections to differential levelling observations, these being the three principal height systems in practical use around the world. Height corrections are required to remove the systematic error resulting from the geometric non-parallelism of the Earths equipotential surfaces, but different height systems propagate errors differently. These systematic errors are thus present within levelling networks and subsequently in local vertical datums. Here, we show that the Helmert orthometric correction is sensitive to errors in the mean value of gravity along the plumbline, particularly for heights above 1000 m. The normal correction is much less sensitive due to the use of normal gravity along the normal plumbline. The normal-orthometric correction of Rapp (1961) is largely insensitive to such errors, but it does not properly correct for the non-parallelism of the Earths equipotential surfaces. Information showing the circumstances under which survey practitioners should apply height corrections to levelling lines is provided, demonstrating that normal-orthometric corrections only need be applied to class LC levelling lines that are to be used for large levelling networks extending in the north-south direction, particularly at high elevations.

Erratum to: The effect of EGM2008-based normal, normal-orthometric and Helmert orthometric height systems on the Australian levelling network (J Geod, (2010), 84, (501-513), 10.1007/s00190-010-0388-0)

An error appears in Eq. (36), where the second term in the free-air gravity correction is added, but should be subtracted. This is a typographical error contained in the paper’s original submission, which unfortunately was not detected during the review and revision process. However, it does not affect the scientific results presented, because the correct Eq. (36), as shown below, was used in all computations. Equation (36) to compute the second-order free-air gravity correction (δgF2) should read

Regional geoid-model-based vertical datums – some Australian perspectives

Abstract This article summarises some considerations surrounding a geoid-model-based vertical datum that have to be thought through before its implementation and adoption. Our examples are based on many Australian and some South-East Asian experiences, but these probably also apply elsewhere. The key considerations comprise data quality and availability, politics, and difficulties that users may encounter when adopting quite a different approach to height determination. We advocate some form of new vertical datum to replace the Australian Height Datum, but the exact type (whether using levelling or geoid, or some combination of both) still needs to be decided. We are not specifically opposed to the adoption of a geoid model as the vertical datum, but it is possibly more challenging than appears initially, and may even deter some users that are already well served by levelling-based vertical datums.