This paper discusses a current issue for several experimental science disciplines, which is the Big Data Problem (BDP). This research study focused on light intensity and ranging (LiDAR) datasets, which are collected for modelling spatial features found on the surface of the earth. Currently, LiDAR datasets are known to be extremely redundant for many applications. Using a formula that allows for calculating the variance of the target-induced error (so-called <i>T-error</i>) caused by the discretisation and quantisation of a 3D surface as a criterion for the quantitative assessment of the fidelity of a model, the use of a Q-tree-based split of the surface is proposed for cells of various sizes depending on the fidelity requirements. A LiDAR dataset representing a 1 km x 1 km terrain surface tile using approximately 12 x 10<sup>6</sup> points was used during the experiments. The initial LiDAR dataset was used to produce a digital terrain model (DTM) at a 0.5 m x 0.5 m resolution, which was used as a reference model. Subsequently, the initial LiDAR dataset was decimated at various rates, and the resulting DTMs were compared with the reference model. The Q-tree based data structure was utilised to illustrate that the Q-tree approach allows for the production of DTMs at a ‘controlled’ fidelity with a considerable reduction in data volume.