Geodetic World Height System Unification

Abstract

Elevations are one of the positional attributes embedded in all geospatial data. They are essential for a wide range of engineering and scientific activities. Some of the activities requiring precise elevations are activities of high societal impacts, such as sea level rise, storm surges and coastal inundation, floods and evacuation route planning, and crustal motion, subsidence, and other surface deformations due to seismic, mining, or other events. In order to successfully monitor and manage such events regionally (e.g., floods) or globally (e.g., sea level rise), the elevation information needs to not only be accurate but to also refer to the same zero-height reference surface (vertical datum). Accurate elevations can be obtained using spirit leveling, or by combining Global Navigation Satellite Systems (GNSS) positioning methods with a model of the geoid (the equipotential surface of the Earth's gravity field approximating the idealized mean sea surface). So although the high accuracy requirements can in general be met, the need for a common reference surface often cannot. This is because there are currently over 100 different vertical datums around the world. Their unification is therefore a scientific problem of high practical significance.Height system unification is the process of determining the offsets between existing vertical datums, each of which is defined with a fundamental zero-elevation point and the equipotential (level) surface of the Earth's gravity field that passes through that point. These offsets can be estimated if the geodetic (from GNSS), physical (from spirit leveling), and geoid (from gravity information) heights are known for the fundamental and/or other points in each datum. GNSSsurveyed leveling benchmarks on land, GNSS-surveyed tide gauge stations at the coasts, and a mean dynamic topography model at sea can be used as data, together with a geoid model. The need to estimate geoid undulations implies the solution of a geodetic boundary value problem (GBVP); see, e.g., Colombo (1980), Rummel and Teunissen (1988), Rapp and Balasubramania (1992), Venuti (2002), andMoritz (2013). Although normal heights and height anomalies from the solution of Molodensky's GBVP can and have been used for datum unification, here we work with orthometric heights and geoid undulations from the solution of the classical (Stokes) GBVP. We first review briefly the key concepts of leveling and vertical datum definition and realization, and then discuss, in spherical approximation, the single (global) vertical datum GBVP and the multiple vertical datum GBVP following primarily the developments of Rummel and Teunissen (1988). We also introduce the functional and stochastic models used for the least-squares estimation of datum offsets and their accuracies. Using an example from North America with tide gauges, we address a few important practical aspects, such as the magnitude of the so-called indirect bias term resulting from the use of biased local gravity data, and the commission and omission geoid un...

Height Systems, Vertical Datums and Their Unification

“…70, this term is below 1 cm. Numerical results for both the omission error and the indirect bias term can be found in Sideris and Fotopoulos (2012), Sideris (2014), and Sánchez and Sideris (2017).…”

“…Vertical datum unification by use of the MSL is in fact possible by the ocean method (or ocean levelling method), which relies on the connection of the MSL at various tide gauges by the mean dynamic topography (MDT), i.e., the height of the average sea surface above the geoid (see, e.g., Rummel and Ilk 1995;Woodworth et al 2012). Here, we will concentrate on the geodetic method that uses as observables gravity measurements, orthometric heights from levelling, and ellipsoidal heights from GNSS, and determines the geoid by solving the Stokes geodetic BVP; see also Heck and Rummel (1990) and Sideris (2014).…”

“…where, for simplicity, we assume the same reference ellipsoid for all datums, we see that with respect to the corresponding values for the reference datum, in datum j not only the geoid undulations N j and the orthometric heights H j will be biased but so will the gravity anomalies, as well (Sideris 2014). Specifically, Dg j are biased with respect to those on the reference datum by the second term in the right hand side of Eq.…”

Activities and plans of the GGOS Focus Area Unified Height System

“…It presents discrepancies of about -2.6 m 2 s -2 (corresponding to a level difference of around +27 cm) with respect to newest computations based on the latest Earth's surface and gravity field models (e.g. Čunderlík et al, 2009;2014;Dayoub et al, 2012;Sánchez, 2008). In this context, the first activities faced by this working group concentrated on -Making an inventory about the published W0 computations to identify methodologies, conventions, standards, and models presently applied (cf.…”

“…Sánchez and Sideris (2017) rigorously derive the observation equations for the vertical datum unification in terms of potential quantities based on the geodetic boundary value problem (GBVP) approach (cf. Rummel and Teunissen, 1988;Heck and Rummel, 1990;Lehmann, 2000;Sideris, 2014;Rummel et al, 2014). Those observation equations are then empirically evaluated for the vertical datum unification of the North American and South American height systems.…”