Establishment of a Unified Country-Wide Plane Coordinate System For Zambia

Abstract

Planet Earth is approximately spherical in shape, and is three dimensional. To map the Earth on a flat piece of paper, in two dimensions, a map projection must be carried out. A map projection is a mathematical technique of how to represent the Earth’s curved surface on a flat surface. In Zambia, the map projection used for national mapping is the Universal Transverse Mercator (UTM) in 6 degree zones. Globally UTM zones run from zone 1 to zone 60 with Zambia falling onto zones 34, 35 and 36, and with central meridians at 21⁰ E, 27⁰ E and 33⁰ E, respectively. The central meridians and the equator form three separate plane coordinate systems, with origins at the intersection of the equator and the particular central meridian. Map projections come with distortions since there is “stretching” or “shrinking” of the curved surface of the reference ellipsoid or spheroid. In order to compute distortions, a scale factor is introduced to determine scale errors from the central meridian. For UTM projection the scale factor at the central meridian is 0.9996. To avoid negative coordinates for the southern hemisphere and the western part of the central meridian, a false easting and northing of 500,000m and 10,000,000m are introduced, respectively. The problem with the UTM projection system is that data from different zones cannot easily be combined to create integrated, seamless maps of geographic features across zone boundaries. Therefore, in this study, the UTM projection and grid system was modified to cover the whole country Zambia in a single zone. To achieve this, a computer program was written to determine the scale factor at central meridian suitable for country-wide mapping. The central meridian was set to 28⁰ E, and the scale factor at the central meridian was reduced to 0.9984 to minimise the mean scale error of mapping. A False-Easting of 800,000m was applied to eliminate negative coordinates, while a False-Northing of 10,000,000m was maintained. The new plane coordinate system is intended to be used for country-wide, seamless landcover/use mapping projects such as Task 151 of the Southern African Science Service Centre for Climate Change and Adaptive Land Management (SASSCAL) project.