A Variance and Covariance Equation for Area Estimates with a Geographic Information System
Authors: van Oort, P. A. J.1; Stein, A.2; Bregt, A. K.3; de Bruin, S.4; Kuipers, J.5
Source: Forest Science, Volume 51, Number 4, August 2005 , pp. 347-356(10)
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. FOR. SCI. 51(4):347–356.
Keywords: GIS; area; polygons; error; covariance; environmental management; forest; forest management; forest resources; forestry; forestry research; forestry science; natural resources; natural resource management
Document Type: Regular article
Affiliations: 1: Centre for Geo-Information Wageningen University and Research Centre PO Box 47 Wageningen AA The Netherlands 6700 Phone: 031-317-474403;, Fax: 031-317-419000, Email: pepijn.vanoort@wur.nl 2: Biometrics Wageningen University and Research Centre PO Box 100 Wageningen AC The Netherlands 6700, Email: alfred.stein@wur.nl 3: Centre for Geo-Information Wageningen University and Research Centre PO Box 47 Wageningen AA The Netherlands 6700, Email: arnold.bregt@wur.nl 4: Centre for Geo-Information Wageningen University and Research Centre PO Box 47 Wageningen AA The Netherlands 6700, Email: sytze.debruin@wur.nl 5: Staatsbosbeheer National Forest Service of the Netherlands PO Box 1300 Driebergen BH The Netherlands 3970, Email: j.kuipers@sbb.agro.nl
