Ground observation is able to obtain highly accurate data with high temporal resolution at observation points, but these observation points are too sparsely to satisfy the application requirements at regional scale. Satellite remote-sensing can frequently supply spatially continuous information on earth surface, which is impossible from ground-based investigations, but remote sensing description is not able to directly obtain process parameters.

In fact, in terms of fundamental theorem of surfaces, a surface is uniquely defined by the first fundamental coefficients, about the details of the surface observed when researchers stay on the surface, and the second fundamental coefficients, the change of the surface observed from outside the surface. A high accuracy and speed method (HASM) for surface modeling has been developed initiatively to find solutions for error problem and slow-speed problem of earth surface modeling since 1986 after fundamental theorem of surfaces.

It is found that when a preconditioned conjugate gradient (PCG) algorithm is used to solve the large sparse linear system, which HASM can be transferred into, HASM performs best in terms of simulation compared with all other algorithms. But its computing speed is not fast enough for all applications.

A multi-grid method is introduced into HASM to try to shorten its computing time. Both numerical and real-world tests demonstrate that there is a range of stop error (SE).

The numerical tests indicated that the multi-grid method of HASM (HASM-MG) greatly increases computing speed when SEs are within this range, compared with the PCG algorithm of HASM (HASM-PCG). HASM-MG is suitable for applications with a need for less accuracy and a shorter computing time. HASM-PCG is appropriate for issues needing higher accuracy. HASM-MG performs better than HASM-PCG in flat areas, while HASM-PCG does better in complex terrainm in terms of accuracy and computing time.

Related results have been published in the journal of Transactions in GIS, (Tian-Xiang Yue, Na Zhao, Hai Yang, Yin-Jun Song, Zheng-Ping Du, Ze-Meng Fan and Dun-Jiang Song, A Multi-Grid Method of High Accuracy Surface Modelingand Its Validation. Transactions in GIS, 2013, 17(6): 943–952).