Standardization of figures and assessment procedures for DTM vertical accuracy

Digital Terrain Models (DTMs) are widely used in many sectors. They play a key role in hydrological risk prevention, risk mitigation and numeric simulations. This paper deals with two questions: (i) when it is stated that a DTM has a given vertical accuracy, is this assertion univocal? (ii) when DTM vertical accuracy is assessed by means of checkpoints, does their location influence results? First, the paper illustrates that two vertical accuracy definitions are conceivable: Vertical Accuracy at the Nodes (VAN, the average vertical distance between the model and the terrain, evaluated at the DTM's nodes) and Vertical Accuracy at the interpolated Points (VAP, in which the vertical distance is evaluated at the generic points). These two quantities are not coincident and, when they are calculated for the same DTM, different numeric values are reached. Unfortunately, the two quantities are often interchanged, but this is misleading. Second, the paper shows a simulated example of a DTM vertical accuracy assessment, highlighting that the checkpoints’ location plays a key role: when checkpoints coincide with the DTM nodes, VAN is estimated; when checkpoints are randomly located, VAP is estimated, instead. Third, an in-depth, theoretical characterization of the two considered quantities is performed, based on symbolic computation, and suitable standardization coefficients are proposed. Finally, our discussion has a well-defined frame: it doesn't deal with all the items of the DTM vertical accuracy budget, which would require a much longer essay, but only with one, usually called fundamental vertical accuracy.