remote sensing Review Digital Elevation Model Quality Assessment Methods: A Critical Review Laurent Polidori 1,* and Mhamad El Hage 2 1 CESBIO, Université de Toulouse, CNES/CNRS/INRAE/IRD/UPS, 18 av. Edouard Belin, bpi 2801, 31401 Toulouse CEDEX 9, France 2 Laboratoire d’Etudes Géospatiales (LEG), Université Libanaise, Tripoli, Lebanon; [email protected] * Correspondence: [email protected] Received: 31 May 2020; Accepted: 23 October 2020; Published: 27 October 2020 Abstract: Digital elevation models (DEMs) are widely used in geoscience. The quality of a DEM is a primary requirement for many applications and is affected during the different processing steps, from the collection of elevations to the interpolation implemented for resampling, and it is locally influenced by the landcover and the terrain slope. The quality must meet the user’s requirements, which only make sense if the nominal terrain and the relevant resolution have been explicitly specified. The aim of this article is to review the main quality assessment methods, which may be separated into two approaches, namely, with or without reference data, called external and internal quality assessment, respectively. The errors and artifacts are described. The methods to detect and quantify them are reviewed and discussed. Different product levels are considered, i.e., from point cloud to grid surface model and to derived topographic features, as well as the case of global DEMs. Finally, the issue of DEM quality is considered from the producer and user perspectives. Keywords: digital elevation model; nominal terrain; quality; accuracy; error; autocorrelation; landforms 1. Introduction Terrestrial relief is essential information to represent on a map. For centuries, it has been displayed symbolically to indicate the presence of landforms like mountains or valleys (Figure1a). By definition, a landform is “any physical, recognizable form or feature on the Earth’s surface having a characteristic shape and produced by natural causes” [1] and is the result of endogenous processes such as tectonic motion and exogenous ones such as climate [2]. During the 19th and the first half of 20th century, when topographic methods became more operational and geodetically more rigorous in terms of cartographic projection and physical altitude definition, a new relief representation appeared on topographic maps with elevation value indications and contour lines (Figure1b). To produce these maps, elevation values must be collected point by point in field surveys, and contour lines are then generated by interpolation. While this type of primitive survey has evolved towards more efficient techniques, it has long been supplemented by photogrammetry. Although terrestrial photogrammetry was first proposed as early as the 1860s by Captain Laussedat [3], this technique began to be seriously implemented at the end of the 19th century, initially in mountainous areas where it brought clear advantages, like in the French Alps by Henri and Joseph Vallot, and in western Canada by Gaston Deville. Although the stereoplotter industry began in the early 20th century, photogrammetry became fully operational after World War I with the development of aerial photography, and it became the standard method for elevation mapping worldwide after World War II. Remote Sens. 2020, 12, 3522; doi:10.3390/rs12213522 www.mdpi.com/journal/remotesensing Remote Sens. 2020, 12, x FOR PEER REVIEW 2 of 36 Remoteaerial Sens.photography,2020, 12, 3522 and it became the standard method for elevation mapping worldwide 2after of 36 World War II. (a) (b) Figure 1.1. Cartographic representation of terrestrial relief in maps in SouthernSouthern France: Cassini map, 18th18th centurycentury ((aa);); IGNIGN map,map, 19571957 ((bb).). Several majormajor innovationsinnovations took took place place during during the the last last quarter quarter of the of 20ththe century:20th century: black black and white and photographywhite photography gave way gave to color, way analytical to color, photogrammetry analytical photogrammetry became the standard became for three-dimensionalthe standard for (3D)three-dimensional mapping, digital (3D) databases mapping, were digital implemented databases were by mapping implemented agencies, by mapping and a growing agencies, variety and of a platforms,growing variety sensors, of and platforms, processing methodssensors, extendedand processing the possibility methods of photogrammetry, extended the whichpossibility became of anphotogrammetry, increasingly powerful which became toolbox an [4]: increasingly powerful toolbox [4]: • New platformsplatforms extended extended the the capabilities capabilities of theof aircraft:the aircraft: satellites satellites covering covering larger larger areas (firstareas TIROS (first • observationTIROS observation satellite satellite in 1960, in 1960, across-track across-track stereoscopy stereoscopy from from different different orbits orbits with with SPOT-1 SPOT-1 in 1986,in 1986, along-track along-track stereoscopy stereoscopy with with SPOT-5 SPOT-5 in in 2002), 2002), UAVs UAVs (fixed-wing (fixed-wing forfor largelarge area surveys, multirotor forfor smallsmall area surveyssurveys requiringrequiring agilityagility and precision), and mobile mapping systems on landland vehicles.vehicles. • New processingprocessing methodsmethods werewere developed,developed, such asas aerotriangulationaerotriangulation and automaticautomatic imageimage • matching thatthat made made it possibleit possible to process to process large quantitieslarge quantities of images of forimages the industrial for the productionindustrial ofproduction orthophoto of mosaicsorthophoto and altimetricmosaics and databases altimetric with databases few ground with control few ground points [ 5control], and the points synergy [5], betweenand the synergy digital photogrammetrybetween digital photogrammetry and computer vision and computer led to very vision powerful led to 3Dvery reconstruction powerful 3D methodsreconstruction such as methods SfM (structure such as fromSfM (structure motion). from motion). • New sensorssensors broadenedbroadened thethe imagingimaging possibilities,possibilities, like spacebornespaceborne and airborne SAR (synthetic • aperture radar)radar) [6[6–8]–8] and and lidar lidar [9 [9,10],,10], i.e., i.e., active active sensors sensors that that made made it possible it possible to acquire to acquire data data day andday night,and night, even even in cloudy in cloudy areas areas and beneathand beneath forests. forests. These innovationsinnovations contributed contributed to theto rapid the developmentrapid development of geographic of geographic information technologiesinformation bytechnologies providing by a vastproviding amount a vast of data, amount among of data, which among the digital which elevation the digital model elevation (DEM) model is one (DEM) of the is mostone of widely the most utilized. widely Both utilized. public and Both private public initiatives and private have led initiatives to an increasing have led availability to an increasing of digital elevationavailability models, of digital either elevation produced models, on demand either or storedproduced in multi-user on demand databases. or stored This hasin stimulatedmulti-user thedatabases. development This has of astimulated wide range the of applicationsdevelopment in of which a wide a quantitative range of descriptionapplications of in the which terrain a geometryquantitative is needed,description such of as the geoscientific terrain geometry studies (floodis needed, or landslide such ashazard geoscientific assessment) studies [11 (flood,12] and or thoselandslide based hazard on spatial assessment) analysis [11,12 (soil] properties,and those based location on spatial of a telecommunication analysis (soil properties, tower or location of a new of company)a telecommunication [13,14], etc., tower as well or as of image a new orthorectification company) [13,14], [15 etc.,,16]. as Some well of as those image applications orthorectification require shape[15,16]. and Some topology of those description applications based require on quantitative shape and terrain topology descriptors description extracted based from on DEMs, quantitative such as slopeterrain maps, descriptors drainage extracted networks, from or watershed DEMs, such delineation, as slope leading maps, todrainage the emergence networks, of a or new watershed scientific disciplinedelineation, called leading “geomorphometry” to the emergence [ 12of ,a17 new–19]. scientific discipline called “geomorphometry” [12,17– 19]. As with any other product, the ability of a DEM to fulfil user requirements is characterized by a number of quality criteria. Once the general characteristics of the DEM have been agreed (resolution, spatial coverage, date etc.), the main requirements relate to the quality of the data themselves, which can Remote Sens. 2020, 12, 3522 3 of 36 be divided into two main types, namely, elevation quality (generally defined in terms of absolute or relative accuracy) and shape and topologic quality (related to the accuracy of DEM derivatives such as slope, aspect, curvature etc. that are quantitative descriptors of the relief [11,20–23]). The quality of these descriptors is decisive for the applications that use them [24]. If we express these two types of quality criteria in natural language, they mean that the model must be as close as possible to the real terrain position, and that it must look as much as possible like the real terrain,