In many GNSS applications users feel a need for transformation between ellipsoidal height and orthometric height
. The main reason of this is using orthometric heights
in engineering, determined by levelling, and the difficulty of making levelling measurements for each point.
where h is the ellipsoid height is measured from GPS surveying, H is the orthometric height
measured from spirit leveling.
The actual orthometric height
difference [DELTA]H of point B is the length of the plumb line (passing through the point B) in between the reference surface [W.sub.0] and the surface [W.sub.B].
Based on a series of GPS measurements made in 2002 on top of peak Bolivar, the highest Venezuelan mountain, and on seven other nearby sites along the Venezuelan Andes, including three other of the highest peaks of the country; and using a recently derived local geoid for Venezuela, the orthometric height
of Peak Bolivar, 4978.4 [+ o -] 0.4 m, and of other nearby mountains were determined.
In many positioning, mapping, and exploration applications, conventional spirit levelling is being replaced by orthometric height
determination using GPS and the geoid.
where [rho] is the mean topographic mass density, G is the gravitational constant, [[gamma].sub.[iota]], is the normal gravity and H is the orthometric height
where point position is represented by geographical latitude and longitude (B , L), h is ellipsoidal height, H is orthometric height
, [N.sub.G] is geoid height, N is normal radius of curvature, W = a / N, [e.sup.2] = 2f--[f.sup.2] (a = main axis f = flattening of reference ellipsoid GRS80), three translations (u--[u.sub.G], v--[v.sub.G], w--[w.sub.G]), two rotations ([e.sub.x]--[e.sub.x,G], [e.sub.y]--[e.sub.y,G]) in horizontal plane and scale difference ([[DELTA].sub.m], [[DELTA].sub.mG]) are present (Jager 1999).
The topographic relief has a mean orthometric height
of about 1000 m.
The Orthometric Height
: Master of Science thesis, Dept.
A yet further opportunity for injecting error into the whole process can arise from the perceived need to operate in orthometric height