Comparative study of numerical methods for normal transformation of geographical coordinate projection at regional scale

Rapid transformation from WGS 1984 (World Geodetic System-1984 Coordinate System) geographic coordinate system to Lambert projection coordinate system helps to realize timely merging, inversion and analysis of some of high frequency partitioned raster data．In this study, three numerical methods (linear rule approximation method, hyperbolic transformation method and conformal transformation method) were used to transform coordinates of sample points in three regions from WGS 1984 coordinate system to WGS 1984-Lambert projection coordinates．For each area, coordinate transformation error and calculation efficiency of each numerical method when using segmentation scheme of rectangular grid with different sizes and shapes were compared．Influence of grid aspect ratio on coordinate transformation error of conformal transformation method was studied．Spatial distribution pattern of sampling point error based on conformal transformation method was analyzed．Conformal transformation method was found to show better balance of error and efficiency than other numerical methods．The error was controlled within 0.75 m to perform coordinate transformation on grid point data, conversion time of the 3 numerical methods was similarly less than 30% of the transformation time of the analytical method．Error of conformal transformation method was less affected by change of grid size; when the grid size reached 10°×10°, maximum error was < 0.22 m．When grid area was fixed, grid in square shape had the least error．Within the same grid, both error distribution dispersion and maximum error of sample points decreased with their minimum distance to grid edge: the closer to the center of the grid, the smaller the error．