Sensitivity studies of a high accuracy surface modeling method

Abstract

The sensitivities of the initial value and the sampling information to the accuracy of a high accuracy surface modeling (HASM) are investigated and the implementations of this new modeling method are modified and enhanced. Based on the fundamental theorem of surface theory, HASM is developed to correct the error produced in geographical information system and ecological modeling process. However, the earlier version of HASM is theoretically incomplete and its initial value must be produced by other surface modeling methods, such as spline, which limit its promotion. In other words, we must use other interpolators to drive HASM. According to the fundamental theorem of surface theory, we modify HASM, namely HASM.MOD, by adding another important nonlinear equation to make it independent of other methods and, at the same time, have a complete and solid theory foundation. Two mathematic surfaces and monthly mean temperature of 1951-2010 are used to validate the effectiveness of the new method. Experiments show that the modified version of HASM is insensitive to the selection of initial value which is particular important for HASM. We analyze the sensitivities of sampling error and sampling ratio to the simulation accuracy of HASM.MOD. It is found that sampling information plays an important role in the simulation accuracy of HASM.MOD. Another feature of the modified version of HASM is that it is theoretically perfect as it considers the third equation of the surface theory which reflects the local warping of the surface. The modified HASM may be useful with a wide range of spatial interpolation as it would no longer rely on other interpolation methods.