Abstract
In this paper, the way topographic spatial information changes with resolution was investigated using semi-variograms and an Independent Structures Model (ISM) to identify the mechanisms involved in changes of topographic parameters as resolution becomes coarser or finer. A typical Loess Hilly area in the Loess Plateau of China was taken as the study area. DEMs with resolutions of 2.5 m and 25 m were derived from topographic maps with map scales of 1:10,000 using ANUDEM software. The ISM, in which the semi-variogram was modeled as the sum of component semi-variograms, was used to model the measured semi-variogram of the elevation surface. Components were modeled using an analytic ISM model and corresponding landscape components identified using Kriging and filter bank analyses. The change in the spatial components as resolution became coarser was investigated by modeling upscaling as a low pass linear filter and applying a general result to obtain an analytic model for the scaling process in terms of semi-variance. This investigation demonstrated how topographic structures could be effectively characterised over varying scales using the ISM model for the semi-variogram. The loss of information in the short range components with resolution is a major driver for the observed change in derived topographic parameters such as slope. This paper has helped to quantify how information is distributed among scale components and how it is lost in natural terrain surfaces as resolution becomes coarser. It is a basis for further applications in the field of geomorphometry.
Highlights
Terrain variables such as slopes, curvatures and catchment structures are primary parameters for applications in hydrology, soil erosion, soil water and carbon budgets [1,2,3,4,5]
It has been widely reported that terrain variables are sensitive to the resolution of the Digital Elevation Models (DEMs) used [6,7] and the effect of resolution on terrain variables can be significant for these applications
As the resolution of available DEMs increases, the issue of matching DEM and processing scale has not become less important as DEM scale is a matter of grid cell resolution and the information content of the DEM down to the finest scales is provided by the resolution
Summary
Terrain variables such as slopes, curvatures and catchment structures are primary parameters for applications in hydrology, soil erosion, soil water and carbon budgets [1,2,3,4,5]. Semi-variograms are used to explore the topographic structures represented by DEMs at different scales and to help characterize landscapes in terms of the topographic structures found in the data. The paper outlines the form of geostatistical model most useful for this task It develops new analytic methods and a general result that allows the effects of scaling to be quantified. Tools from geostatistics can, be successfully generalized to handle these types of data [21]
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