The Research of the Accuracy of Area Determination on Plans and Maps

Abstract

Determining land areas on the plans and maps is one of the most common surveying and land management problems in the preparation of cadastral plans of agricultural land, forest inventory, ecology and geology. Although there are various methods of datamining land area, the need to provide acuracy of determining still exists. Thus, the study aims at determining the accuracy of land areas on the basis of geostatistics theory. The authors suggest executing the estimation of accuracy of areas determination on the basis of the theory of geostatistics of J. Materon. One of the basic concepts of the theory is a spatial variable that is considered as the realisation of random function. The mathematical apparatus of the theory of spatial variables was formed arising from the theory of random functions. The authors have obtained the following results. Firstly, a formula for the estimation of accuracy of closed curvilinear contour areas determination by the method of numerical integration on rectangular grid is offered. Secondly, the experimental calculations of precision of areas determination on rectangular grid are executed. The dependence of a relative mean quadratic error on the amount of points, that get in a curvilinear contour, is defined. Finally, it is recommended to use a geostatistical formula for the previous calculation of accuracy, depending on the number of rectangular grid. Thus the conclusions are as follows. The executed researches allow us to recommend the method of integration on a square grid (method of point reticulations) for determination of areas of curvilinear contours on plans and maps. For the previous calculation of accuracy with the aim of determination of density of the square grid, depending on necessary accuracy of areas determination, it is suggested using formula (1) obtained on the basis of the theory of geostatistics.