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

Abstract

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.