Granularity of Digital Elevation Model and Optimal Level of Detail in Small-Scale Cartographic Relief Presentation

Abstract

One of the key applications of digital elevation models (DEMs) is cartographic relief presentation. DEMs are widely used in mapping, most commonly in the form of contours, hypsometric tints, and hill shading. Recent advancements in the coverage, quality, and resolution of global DEMs facilitate the overall improvement of the detail and reliability of terrain-related research. At the same time, geographic problem solving is conducted in a wide variety of scales, and the data used for mapping should have the corresponding level of detail. Specifically, at small scales, intensive generalization is needed, which is also true for elevation data. With the widespread accessibility of detailed DEMs, this principle is often violated, and the data are used for mapping at scales far smaller than what is appropriate. Small-scale relief shading obtained from fine-resolution DEMs is excessively detailed and brings an unclear representation of the Earth’s surface instead of emphasizing what is important at the scale of visualization. Existing coarse-resolution global DEMs do not resolve the issue, since they accumulate the maximum possible information in every pixel, and therefore also require reduction in detail to obtain a high-quality cartographic image. It is clear that guidelines and effective principles for DEM generalization at small scales are needed. Numerous algorithms have been developed for the generalization of elevation data represented either in gridded, contoured, or pointwise form. However, the answer to the most important question—When should we stop surface simplification?—remains unclear. Primitive error-based measures such as vertical distance are not effective for cartography, since they do not account for the landform structure of the surface perceived by the map reader. The current paper approached the problem by elaborating the granularity—a newly developed property of DEMs, which characterizes the typical size of a landform represented on the DEM surface. A methodology of estimating the granularity through a landform width measure was conceptualized and implemented as software. Using the developed program tools, the optimal granularity was statistically learned from DEMs reconstructed for multiple fragments of manually drawn 1:200,000, 1:500,000, and 1:1,000,000 topographic maps covering different relief types. It was shown that the relative granularity should be 5–6 mm at the mapping scale to achieve the clearness of relief presentation typical for manually drawn maps. We then demonstrate how the granularity measure can be used effectively as a constraint during DEM generalization. Experimental results on a combination of contours, hypsometric tints, and hill shading indicated clearly that the optimal level of detail in small-scale cartographic relief presentation can be achieved by DEM generalization constrained by granularity in combination with fine DEM resolution, which facilitates high-quality rendering.