In order to solve the error problem in the spatial surface simulation

the high accuracy surface modeling (HASM) method

which is based on the fundamental theorem of the surface theory

has been developed during the past decades. Numerical tests have already shown that HASM is much more accurate than the classical methods such as Kring

inverse weighting (IDW) method

and splines. In addition

surface modeling of digital elevation model and spatial simulation of soil properties also indicate that the HASM indeed increases interpolation accuracy. However

the huge time consumption of the HASM limits its application at large scales. Numerical analysis have found that the main reason that lead to large time consumption is that the out-iteration process consume too much time

so an effective way to improve the simulation efficiency is speed up the out-iteration process. Therefore we propose a new method to construct the difference equations of the HASM in this paper. The new difference equation employs five grids to compute the first difference

while the original method only uses three grids. First

we prove that the modified difference equation could really improve the simulation accuracy by formula derivation. Then we design several numerical tests to verify the simulation accuracy of the new method. Sampling rate and the spatial position of the sample points are considered in the numerical tests. Three kinds of sampling rate are designed (0.5%

1%

and 2%) to analysis the new method's advantage for different sampling rates. One of the numerical tests removes key points of the study area (valley bottom of the simulation surface) to analysis the influence of the missing of key sampling points to the origin and new methods. numerical test results show that HASM that adopted the new difference equation can improve the single iteration accuracy significantly. At the same time

the contrast experiments indicate that the modified HASM could decreases the influence of the key missing sample points

which is very important in the practical application because it is often impossible to identify all the key sample points. It should be pointed that the modified HASM does not require increasing memory to obtain these advantages. Furthermore the study reveals that the out-iteration process that employed the modified difference equations and the origin difference equations in turn could speed up the increasing of the simulation accuracy. This trait is of great help to arrive at the specified simulation accuracy quickly in practical application. Compared to the classical interpolation methods

HASM possess significant advantages on simulation accuracy. However the huge time consumption limits its wide application. Aiming to perfect HASM's simulation efficiency

we propose the modified HASM algorithm by building new difference equations. Compared to the origin one

the modified HASM has three advantages: First

the modified HASM could improve the single iteration accuracy significantly. Second

the modified HASM could get better simulation results when some key sample points are missing. Third we could accelerate the error decreasing in the out-iteration process when using the modified and origin HASM.