Local Terrain Morphological Error Measurement Model Of Digital Elevation Model(DEM)

As an indispensable part of spatial data infrastructure,Digital Elevation Model(DEM)has become the direct supporting data for geoscience research,engineering planning,disaster prevention and mitigation,and military strategic decision-making.DEM error model is the precondition and reliability assurance for the technique assessment,analysis and application of DEM.But at present,a single DEM numerical precision model can hardly meet the rapid development of DEM analysis and application.Therefore,This study focuses on the consistency measurement of the DEM topography with different resolutions,so as to carry out the study of DEM local topographic features,and construct the quantitative model of local terrain morphological errors,which possess a very important theoretical significance and practical value for DEM error theory and method system,and improving the service quality and reliability of DEM application in various fields.The China's Loess Plateau is the research area in this paper.Firstly,the terrain shape descriptor is designed to describe the morphological characteristics of terrain surface.Then,a statistical measurement model of local terrain morphological error is constructed and to be expressed by sampling statistics.On this basis,carry out the difference analysis of DEM local topography morphological errors in the loess landform through multiple experiments.The main research contents and results are as follows:(1)Design of local terrain shape detection function.According to the characteristics of terrain surface,and combined with theoretical knowledge of geography and differential geometry,sort out the shape detection function that suitable for describing terrain surface features.There are seven shape descriptors which can reflect the spatial position,local direction,concavity or curvature of the surface:Geodesic distance,Normal vector angle,Average curvature,Gaussian curvature,Shape index,Curvature index and Volume integral invariant.(2)Construction of statistical measurement model of local terrain morphological error.Firstly,determine the layout strategy of random sampling points in the local area.Then,the probabilistic distribution matrix is used to quantitatively describe the terrain shape detection function and the terrain morphological error is expressed by the matrix similarity results.The results show that it is reasonable and effective to construct the statistical measurement model of local terrain morphological error to describe the terrain morphological feature information based on probability statistics.The combination of Geodesic distance and Volume integral invariant is the best descriptor to characterize the terrain feature,which can reflect the position attribute and concaveconvex property of random points on the surface simultaneously.(3)Difference analysis of local terrain morphological error.Firstly,select the typical landform types of the Loess Plateau,and discuss the relationship between local regional and terrain morphological errors based on watershed confluence threshold for achieving quantitative expression of morphological errors and differences of geomorphic types.Secondly,according to the topography complexity and the area of the study area,determine the optimal sampling number of random points in different geomorphic types.Then,the functional relationship between the morphological errors of each geomorphic type and the DEM resolution was fitted by the similarity results.The results show that the spatial difference of local terrain morphological error is consistent with the terrain characteristics of loess landform region.With the increase of DEM grid resolution,the local morphological similarity decreases.But there is local fluctuation due to the influence of grid resolution and the initial location of resampling.Finally,it is proved that the statistical measurement model of local terrain morphological error has good applicability under certain elevation intermediate error through the study of the correlation between morphological error and elevation numerical error.