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 extraterrestrial 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.

中文翻译：

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比例尺问题：数字高程模型的网格间距对计算坡度和屏蔽的地面太阳辐射的影响

太阳辐射是驱动地球许多物理和生物过程并确定地球表面气候和生产力模式的主要能源。太阳辐射的基本比例由屏蔽的地球外太阳辐射（SESR）组成，可以使用从数字高程模型（DEM）得出的坡度和坡度来计算。本文的目的是确定DEM的网格间距（DEM的比例的影响）对坡度，纵横比和SESR误差的影响。提出了坡度表示误差，坡向表示误差和SESR表示误差的概念，然后研究了这些误差与DEM网格间距之间的关系。我们发现，当DEM的网格间距变粗时，SESR平均增加；SESR的增加主要由具有负斜率表示误差的DEM网格单元主导，而SESR通常在具有正斜率表示误差的网格单元中减小。尽管网格间距变化，但正斜率SESR表示误差在斜坡上的百分比分布（分为11个斜率间隔）与网格间距无关。这种分布集中在一些斜坡区间上。此外，SESR表示误差的平均绝对值和均方误差与斜率表示误差和纵横比表示误差密切相关。