## 1 Introduction  
Digital Elevation Models (DEMs) are widely used to represent terrain topography (Digital Terrain Models (DTMs)) and other surfaces (Digital Surface Models (DSMs)), including those features related to the biosphere, anthroposphere, etc. [1]. From a geometric point of view, DEMs represent height values using raster and vector models. Raster DEMs are based on grids, composed of a regular array of cells, including heights, as an attribute (this model is commonly referred to as 2.5D data because it only supports a single z-value for each plaimimetric location in a specific column and row), while vector DEMs are based on 3D surfaces composed of meshes derived from a set of 3D points. The raster model considered in this study can be managed using images that represent height as digital levels of pixels determined by a given bit-depth capacity (e.g., ArcGIS Pro uses 32-bit depth in grids [2]. These values can be obtained from a single sample point or the average measurements representing the height values of a given area (e.g., the area covered by the pixel). In any case, the values of adjacent cells are highly correlated because these surfaces represent elements with a physical continuity (e.g., terrain), where drastic changes are not common (except in cases of steep slopes, such as gorges, cliffs, etc.). Therefore, we must consider a low variance in this data, at least in a close environment. This aspect is very important when we are detecting points (e.g., using point detection algorithms) in grid DEMs because the location of a specific point can be influenced by its surroundings. The height values contained in DEMs are derived from measurements that are characterized by a certain level of accuracy that is influenced by acquisition and processing errors. The ISO 19157 standard [3;4] defines five elements of data quality, including positional accuracy, which is related to the location of features. In this context, positional accuracy has three sub-elements: absolute or external accuracy, relative or internal accuracy, and gridded data position accuracy. These are related to the closeness of the reported coordinate values, relative positions, and gridded data positions to values accepted as true, respectively [3]. This aspect implies that the assessment of the positional accuracy of any cartographic product must include a comparison of data (absolute or relative positions), with respect to other independent datasets that are considered true values. The accuracy of these reference datasets should be at least three times higher than that of the product to be assessed [5]. In the case of DEMs, positional accuracy has been widely analyzed in the literature [6], considering error causes and consequences and the methodologies developed to assess them [7;8], by considering several aspects (data model, data acquisition, accuracy measures, etc.). In addition, some standards [9; 10; 11; 12], published during the last decade by several institutions, have described the procedures to carry out this assessment. These studies have traditionally considered vertical accuracy without considering the effect of horizontal accuracy. It is unusual to include a report about horizontal accuracy [6;7], although there are some studies that have analyzed the impact of horizontal errors on the accuracy of DEMs, proposing an improvement in the final vertical accuracy after correcting them [13]. Although there are recent initiatives proposing the use of surfaces to check DEMs [14], most of the studies developed until now are based on a comparison of a set of checkpoints, whose coordinates are obtained from a more accurate independent source, and using some measures (e.g., Root Mean Squared Error (RMSE)) to describe the deviations with respect to the value that is considered true. These checkpoints are usually well-defined points that are selected and measured manually.