Digital elevation models (DEMs) provide fundamental depictions of the three-dimensional shape of the Earth’s surface and are useful to a wide range of disciplines. Ideally, DEMs record the interface between the atmosphere and the lithosphere using a discrete two-dimensional grid, with complexities introduced by the intervening hydrosphere, cryosphere, biosphere, and anthroposphere. The treatment of DEM surfaces, affected by these intervening spheres, depends on their intended use, and the characteristics of the sensors that were used to create them. DEM is a general term, and more specific terms such as digital surface model (DSM) or digital terrain model (DTM) record the treatment of the intermediate surfaces. Several global DEMs generated with optical (visible and near-infrared) sensors and synthetic aperture radar (SAR), as well as single/multi-beam sonars and products of satellite altimetry, share the common characteristic of a georectified, gridded storage structure. Nevertheless, not all DEMs share the same vertical datum, not all use the same convention for the area on the ground represented by each pixel in the DEM, and some of them have variable data spacings depending on the latitude. This paper highlights the importance of knowing, understanding and reflecting on the sensor and DEM characteristics and consolidates terminology and definitions of key concepts to facilitate a common understanding among the growing community of DEM users, who do not necessarily share the same background.

The Friedman's test is used for assessing the independence of repeated experiments resulting in ranks, summarized as a table of integer entries ranging from 1 to k, with k columns and N rows. For its practical use, the hypothesis testing can be derived either from published tables with exact values for small k and N, or using an asymptotic analytical approximation valid for large N or large k. The quality of the approximation, measured as the relative difference of the true critical values with respect those arising from the asymptotic approximation is simply not known. The literature review shows cases where the wrong conclusion could have been drawn using it, although it may not be the only cause of opposite decisions. By Monte Carlo simulation we conclude that published tables do not cover a large enough set of (k, N) values to assure adequate accuracy. Our proposal is to systematically extend existing tables for k and N values, so that using the analytical approximation for values outside it will have less than a prescribed relative error. For illustration purposes some of the tables have been included in the paper, but the complete set is presented as a source code valid for Octave/Matlab/Scilab etc., and amenable to be ported to other programming languages.

Gathering data accounts for more than 80% of the cost of any GIS project. Fast Internet connections and digital datasets threaten the investments of data producers through data piracy. Outside the GIS community this problem has been known for a long time, and possible solutions exist for digital imagery, formatted text, 3D meshes and so on, showing possible links to typical spatial data. This is largely achieved through embedding hidden information in a dataset without producing perceptible changes in the data, a process known as watermarking. The producer can recover the embedded information on request in order to produce evidence of ownership in a court, so the overall strategy relies on a legal basis rather than technical ones. This paper analyses the state-of-the-art for watermarking protection in digital geographical datasets. Digital imagery is demonstrably a more mature area than geographical information, even with multiple commercial vendors offering watermarking protection. 2D vector and point datasets have received less attention from the research community; however, 3D meshes have been considered by the CAD community and a handful of techniques are available for that case, and they are reviewed here.

This paper focuses on a topic barely considered in the literature: how to improve the accuracy of a given Digital Elevation Model (DEM) irrespective of its lineage by identifying its most suspicious values (also denoted here as outliers). Methods tailored to a specific procedure and source (contour maps, remote sensing image, etc.) exist but they are not valid for other cases. This is a problem for both the producer and end user. The results of a comparison of two methods using six DEMs intended to be representative of different landscapes are reported here. Both methods have been applied to each DEM, producing a number of height candidates to be analysed. Assuming that all candidates are wrong, their elevations have been blindly replaced by interpolated heights, simulating the behaviour of the inexperienced user. The improved (or degraded) DEMs are then compared against the ground truth, and updated accuracy figures are calculated. The RMSE can diminish by 2 to 8% of the original value by changing less than 1% of the elevations in the dataset.