Scale problem: Influence of grid spacing of digital elevation model on computed slope and shielded extra-terrestrial solar radiation

Abstract

Solar radiation is the primary energy source that drives many of Earth’s physical and biological processes and determines the patterns of climate and productivity on the surface of the Earth. A fundamental proportion of solar radiation is composed of shielded extra-terrestrial solar radiation (SESR), which can be computed using the slope and aspect derived from a digital elevation model (DEM). The objective of this paper is to determine the influence of the grid spacing of the DEM (the influence of the scale of the DEM) on the errors of slope, aspect and SESR. This paper puts forward the concepts of slope representation error, aspect representation error, and SESR representation error and then studies the relations among these errors and the grid spacing of DEMs. We find that when the grid spacing of a DEM becomes coarser, the average SESR increases; the increase in SESR is dominated by the grid cells of the DEM with a negative slope representation error, whereas SESR generally decreases in the grid cells with a positive slope representation error. Although the grid spacing varies, the distribution of the percentages of positive SESR representation errors on the slope, which is classified into 11 slope intervals, is independent of the grid spacing; this distribution is concentrated across some slope intervals. Moreover, the average absolute value and mean square error of the SESR representation error are closely related to those of the slope representation error and the aspect representation error. The findings in this study may be useful for predicting and reducing the errors in SESR measurements and may help to avoid mistakes in future research and in practical applications in which SESR is the data of interest or plays a vital role in an analysis.

Keywords

scale problem / digital elevation model / grid spacing / slope / shielded extra-terrestrial solar radiation

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 41771423, 41930102, 41601408 and 41471331) and the Industry University Research Cooperation Project for the Social Development of Fujian Province, China (No. 2018Y0054). The author is thankful to the anonymous reviewers for their helpful comments; the author is indebeted to his students, Wenzhen Zhou, Huange LI, Quanjin LI and Tinmin Lin for retouching the figures.

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