面栅格表达方式引起的DEM地形表达误差

Representation Error of Terrain Caused by GRID DEM

通过对规则格网DEM对地面表达方式的分析,指出基于面栅格理解的DEM的表达方式会产生DEM对实际地形的表达误差,该误差与格网尺寸密切相关。在一个DEM格网内,地形表达误差分为正负两个部分,在上坡方向,误差为负值,下坡方向则为正值;格网尺寸越大,误差的其空间分布越复杂;在地面坡度较大时,距离格网中心点越远,误差越大。通过基于全数字摄影测量得到的黄土高原区陕西省绥德县多种格网尺寸DEM数据系列的比较验证,结果表明,在格网内部的误差分布随格网尺寸密切相关,特别是在地形复杂的地区,误差的绝对值较大,且空间分布越加复杂。根据对该误差的统计特征及中误差与DEM格网尺寸关系分析,可利用格网尺寸估计误差的统计特征及中误差。随着格网尺寸增大,中误差和误差最大值都在增大,均值基本不变;且无论基准DEM格网尺寸大小,在增大格网尺寸的情况下,均有此规律。在实际DEM生产及应用过程中,需要注意区分上述地形表达误差与我国测绘标准中定义的中误差的区别,避免在DEM的实际应用中出现偏差。

After analysis of terrain representation introduced by regular grid DEM, this research found that grid DEM could lead to representative errors in actual terrain and the deviation must be related closely to the size of grid. Within a GRID, errors generally consisted of two opposite parts. In the direction of upslope, the error was negative whereas positive in the downslope direction. With gradual increase in the size of GRID, a more complicat- ed distribution of errors would be. In case of steeper slope, errors would grow along with increased distance from the center of the grid to any point inside the grid. The comparison between the data from DEMs with various grid si- zes in Suide county generated by the full digital photogrammetry shows that the distribution of the errors within one GRID is closely related to the grid size. Especially in the area with complicated terrain, the more complicated the terrain, the bigger the absolute value of the errors is. So by analyzing the statistical characteristics of the error and the relationship between RMSE of the representation error and the grid size, the statistical characteristics of the er- ror and RMSE of the errors could be estimated from the grid size. With the increasing of the grid size, the maxi- mum value of the RMSE of the representation error and the error both rises and the mean value keeps constant. And whatever the base grid size is, RMSE of the errors could be calculated under the condition of the increase of the grid size. In summary, in the practical production and application of DEM, it is strongly advised that the attention should be focused on the distinguishing of the above mentioned representation errors of terrain and the RMSE of the DEMs defined by Chinese surveying and mapping standards hence to avoid making mistakes in the application of DEM.