Reconstructing contours through a DEM is one of the methods of the DEM accuracy assessment. It can be used to detect terrain levels of fidelity. However

these methods show all a relative fidelity accuracy.Therefore

we present a membership function of the matching between drainage and terrain in this paper

we use the matching difference between drainage and terrain to quantitatively assess the DEM precision and to detect terrain levels of fidelity. First

we establish the matching offset membership function in accordance with the linear element displacement criterion

the scale criterion

the average slope criterion

the maximum matching offset criterion

and the visual effect criterion. Second

we use a 1:50 000 topographic map data of the four regions as the source data. Then the experiment of quantitative descriptive model of the matching precision explained how to use it in scaling transform of DEM. Finally

the experimental results show that the quantitative descriptive model of the matching precision not only can be used for the quantitative assessment of the extent of DEM terrain fidelity

but also can be used to determine the conversion of DEM scale appropriate range.