A variance and covariance equation for area estimates with a geographic information system

Abstract

Geographic Information Systems automatically calculate the area of a polygon from the coordinate values of the vertices that describe its boundary. Uncertainty in these coordinate values results in uncertainty in area estimates. Earlier articles showed how area uncertainty of individual polygons could be calculated. In this article we propose a covariance equation to quantify the impact of uncertainty in the position of a vertex on uncertainty in the area of all polygons sharing this vertex. The approach is based on the assumption of absence of spatial correlation in positional errors, but includes variation in the positional accuracy. The equations were implemented and applied to a case study area, described by a set of 97 adjacent polygons with different per unit area utility values (€/ha). We were then able to calculate how uncertainty in the coordinate values propagated into uncertainty in the utility value of the complete set of polygons. Copyright © 2005 by the Society of American Foresters.