Volumes determination in terms of various data density and surface diversity

Purpose
The aim of this paper is to assess the impact of input data density and diversity on surfaces obtained using the terrestrial laser scanning (TLS) method for creating digital elevation model (DEM). For this we can use several approaches, while we have chosen an intermediary parameter – volume calculation, which is in practice the most frequently requested requirement from surveyors.
Methods
Precise terrestrial measurement and terrestrial laser scanning were used to ensure that detailed knowledge about the surface and volumes of two piles of earth and a stone pit in comparison with theoretical defined surfaces was obtained.
Results
Mathematically defined surfaces generally have smooth shapes, and thus the effect of different density on the input data is less apparent in the final comparison of volumes. In our case the results for most of the different interpolation methods and the different density of the input data was less than 0.5%. From the experimental measurements of the two earth bodies and the quarry, which have an irregular shape with unsmooth surfaces, we can only test the relative precision of the calculated volumes to the data with the highest density.
Experimental measurements in the area of the quarry, where the scanned surface was uneven and considerably different in height, confirmed the assumption that a vastly irregular surface should exhibit more significant variations than a smooth surface, but for the nearest neighbour method relative errors under 1% were achieved.
Practical implications
According to the results from the analysis above, the lower density of input data we have, the lower the precision of calcula¬ting volumes we can assume, but it is interesting that we did not achieved significantly worse results with strongly irregular surfaces compared to a less irregular surface.
Originality/ value
The input values for the analysis of theoretically defined surfaces were obtained by the calculation of integral calculus and earth-moving bodies and quarry from an experimental measurement terrestrial laser scanning method and were used in Slovakia for the first time.