Recovery of orthometric heights from ellipsoidal heights using offsets method over Japan

Patroba Achola Odera,Yoichi Fukuda

doi:10.1186/s40623-015-0306-z

Patroba Achola Odera, Yoichi Fukuda

Open Access

https://doi.org/10.1186/s40623-015-0306-z

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Abstract

One of the most important applications of a geoid model is a recovery of orthometric heights from ellipsoidal heights (normally obtained from GNSS). The application of the geoid model for recovering orthometric heights from ellipsoidal heights is normally achieved by fitting the geoid model to a local vertical datum. The fitting procedure is usually accomplished by least squares collocation (LSC), using planar or spherical covariance functions. This procedure warps the gravimetric geoid model onto the local vertical datum, hence the local geoid model derived by this procedure, though convenient for local applications, it is not an equipotential surface. We propose offsets method for practical orthometric height recovery from a geoid model. The proposed procedure is more realistic because it does not constrain the local geoid to be coincident to the local vertical datum. We compare the performance of plannar fitting and offsets methods over Japan using a cross-validation procedure. Results show that offsets method performs better than the normally used planar fitting in the recovery of orthometric heights from ellipsoidal heights using a geoid model. The standard deviations of the differences between established and converted orthometric heights at randomly selected GPS/levelling test points over Japan are ±4 and ±3 cm for planar fitting and offsets methods, respectively. The offsets method is therefore more appropriate for converting ellipsoidal heights to orthometric heights than the planar fitting in the area of study.

Highlights

One of the challenges to geodesists today is how to determine a consistent and functional vertical component of the geodetic datum
The local vertical datum offsets over Japan are computed by Equation (2) at 816 Global Positioning System (GPS)/levelling points using gravimetric geoid undulations on a 1 × 1.5 arc-minute grid (Odera and Fukuda 2014)
The offsets are interpolated onto the grids (1 by 1.5 arc-minute) using Kriging technique

Summary

Introduction

One of the challenges to geodesists today is how to determine a consistent and functional vertical component of the geodetic datum. The natural height datum is the geoid, which is part of the integrated geodetic datum. The geoid is normally approximated with a rotational reference ellipsoid (with semi-minor axis perpendicular to the equatorial plane) as a conventional reference surface. Satellite positioning is gaining a lot of applications in Earth sciences today. One of the most extensively used satellite positioning in Earth sciences is the Global Positioning System (GPS). It is fast and efficient in determination of positions based on the World Geodetic System of 1984 (WGS84). It measures heights above WGS84 reference ellipsoid.

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