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A Variance and Covariance Equation for Area Estimates with a Geographic Information System

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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; covariance; environmental management; error; forest; forest management; forest resources; forestry; forestry research; forestry science; natural resource management; natural resources; polygons

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

Publication date: 2005-08-01

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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