A refined conversion from normal height to orthometric height

The difference between orthometric and normal heights (or the height anomaly and the geoid height) is usually approximated by a term consisting of the Bouguer anomaly times elevation divided by normal gravity. We derive an improved formula, which includes a topographic roughness term (terrain correction) and a term due to the lateral variation of topographic density, for the practical application of this conversion. It is shown that for high mountainous areas with rough topography these two terms are of the same order as the Bouguer anomaly related term. Already for elevations of a few hundred metres they could reach the order of a centimetre. In addition, for the more precise computations in high mountainous areas, a term related with the downward continuation of topographic potential from the surface to sea level could be significant.