The Lesotho geodetic control network.

Abstract

The Geodetic network of Lesotho as established by the Directorate of Overseas

Surveys in the 1950's, has been known to have distortions of several meters in some

areas. This network is still very much in use today. Several altcmpts were made to

strengthen the DOS network. but these attempts were not used for a complete

readjustment.

The South African Control net, which completely surrounds Lesotho, has recently

been readjusted so as to bring it into sympathy with the WGS reference system used

by GPS. It has become urgent to similarly update the Lesotho control system, to

enable economical use of GPS surveying methods. This thesis addresses the problems

of updating the Lesotho control system and also of bringing existing data onto the

updated systcm.

This thesis first reviews the historical background of Lcsotho and that of its geodetic

net work.

Different sets of data were collected and common points in the compared sets selected

for the analysis. The South African readjustment was chosen as the standard, because

it is the most recent, derived with the support of the new zero-order South African

control net. The data sets were fitted to the reference system using conformal transformations

from first up to fourth order. These comparisons were used to detect outliers. They

revealed systematic distortions in the older data. which could be largely eliminated in

the fourth-order transformation. The opportunity to update control point co-ordinates

also gave an opportunity to revisit the existing choice of using two map panels of the

Gauss Conform projection. The distortions involved in using a single Gauss Conform

panel and also the UTM projection were investigated.

A companson or all the methods and the recommendations concludes the section.

Software was developed for transforming existing survey data onto the recommended

updated reference system.

The height system used in Lesotho is also reviewed because it forms part of the

control net. The focus is on heights in relation to gravity. because that bears on the

relation of published orthometric heights. with GPS-derived ellipsoidal heights. This

section is mostly a literature review, starting with the theory of heights and gravity,

proceeding onto the applied corrections and then showing what relations have been

found.