In terms of the fundamental theorem of surfaces, High Accuracy Surface Modeling (HASM) method, which is based on the differential geometry theory, transforms the surface modeling to a linear system by using the principle of least square method and describes the properties of the surface. Comparing with the classical surface methods in GIS application, such as inverse distance weight (IDW), triangulated irregular network (TIN), KRIGING and SPLINE, HASM has a much higher accuracy and the error problem of the surface modeling is solved in theory by HASM. However, the computational cost of HASM is high. The cost of HASM algorithm is expensive when it applies preconditioned conjugate gradient method (PCG). Using compressed storage formats can effectively save memory. Among these formats, the three-tuple storage format of the sparse matrix is widely used in the past. In this paper, based on the characteristic of HASM-PCG, we modify a large part of the sparse matrix-vector multiplication by using three-tuple technology. The computational efficiency is enhanced though adjusting the calculation order of HASM-PCG and abandoning some nonzero elements that are not need to store. Long term (1998-2008) averaged monthly data were obtained from site measuring temperature (3000 sites). Combining with the digital elevation model of the globe, the data are used to simulate the global mean temperature in May, June, July, and August of the eleven years from 1998 to 2008. Numerical results show that with this three-tuple technique, the computing efficiency of HASM is great improved.