The Geometrical Distortion of Discrete Global Grid in Multi-resolution Expression

Multi-resolution expression is the import characteristic of discrete global grid. The geometrical distortion in multi-resolution expression can decide the ability of multi-scale transformation of discrete global grid. It is also the influencing factor of stability of discrete global grid. The source of geometrical distortion in multi-resolution expression was analyzed in this article. The method of expressing low-resolution partition by high-resolution partition in different parting depth was researched. The difference of error between expression by partition in steady depth and expression by direct calculation was analysed. Four representative discrete global grids were selected as objects of study. They were QTM, Synder, SQT and STQIE. To every kind of discrete global grid, the quantity of area distortion and side distortion of parting triangle between actual partition and ideal partition was calculated. Based on the data of area and side and their error of each grid, the statistical indicators such as mean value standard deviation, relative range, Relative error of mean were analyzed. Finally the rules of area distortion in multi-resolution expression of different kind of discrete global grid were gotton. And it was also concluded that the influence of side distortion was few in multi-resolution expression.