Slope metrics are usually based on DEM data and are extracted directly using a fixed algorithm. Slope errors mainly are attributed to algorithm model errors and data errors,with little regard for the differences in slopes generated by changes in the directions of a spatial references when building DEM. In this paper,based on the mathematical Gaussian surface and by changing the direction of a reference frame X and Y,the derived slope gradients from DEM data were analyzed by the third-order reverse distance squared weight differential slope algorithm under different reference frames. Results showed that： 1. the influence of the change in the direction of spatial reference systems on slope difference was related to the curvature of a surface profile. In the terrain areas where the slope changes are more obvious,such as the top of a mountain,valley bottom,and saddle,they were positively related to each other. There was also a correlation with the rates of changes in aspect. 2. The difference between slope and slope direction was periodic with the change of the direction of a spatial reference system. The period was 90°,which shifted approximately according to the sine（y = a·sin（1/2 kπ ＋φ） φ∈[0,π/2]″） law,reaching the peak at 45°. Around 0° and 90°,the average variation in the 6° range was relatively flat,but it deviated greatly from the sinusoid,and as the spatial resolution decreased,the slope and slope direction caused by the reference system direction increased. The experiment suggested that the principle of average slope direction should be complied with in the establishment of independent reference system in a study area,so as to reduce the influence of reference system on slope and slope direction.
Journal of Mountain Research
spatial reference system