The DEM Based 5-Node Second-order Finite Difference Model for Slope Computation

Slope is the most basic terrain parameter to construct geo-science models.The accuracy analysis of the computing model is one of the most important issues in the geo-science.A lot of studies focused on error analysis of the computing model over the past few decades.The source of the error and the relationship between the error and the other parameters were studied.However,few studies were aimed to put forward a new model to decrease the error,which is more important for high resolution DEMs.By analyzing the error source of the slope computing model,this paper put forward a new model called 5 Node Second-order Finite Difference(5N-2FD).The characteristic of this model is that it is able to consider the multi-distance neighbor node: firstly it builds two difference models using different grid sizes,and then combines the two models into one with different weights.It is proved that it can improve the accuracy of the results remarkably through mathematical analysis.In this paper,a mathematical surface is selected to verify the accuracy of the new model.In order to study the influence of the resolution to the accuracy of the slope,this paper generated DEMs from the mathematical surface with different resolution,one is 1m,and the other is 5m.The results show that the new model can significantly improve the accuracy of the result compared with the common models.This study enriched the method system of digital terrain analysis,and provided slope data of high accuracy for many geo-science models.In addition,besides slope,there are many terrain parameters which are calculated through finite difference,such as aspect and various kinds of curvature,and the methods of this paper could afford some useful references in improving the accuracy of such terrain parameters.