A model is a representation of an investigated object for purposes of description, explanation, simulation, or forecast. Spatial models are complicated by the fact that they include information about position, possible topological connections, and attributes of the recorded objects. Spatial modeling of ecological phenomena has always been an important issue in ecology. The mutual influence ofpatterns and processes of ecosystems is manifested in the spatial distribution of ecosystems at different scales, which has long been the main component of spatial models. A spatial model is a mechanism for assembling spatial knowledge from a range of sources and presenting conclusion based on that knowledge in readily used form. Spatial modeling is the process of constructing the spatial model, which can be identified into areal interpolation and surface modeling.

Areal interpolation is the transformation of data between different sets of areal units. The set of zones, for which data are available, are termed source zones. The second set of zones, for which estimates need to be derived, are termed target zones. The third set of zones, for which auxiliary information can be incorporated in the interpolation process, are termed control zones. The methods of areal interpolation based on alternative hypotheses include radially symmetric kernel functions, maximally smooth estimation, piecewise approximation, uniform target-zone densities, and uniform control-zone densities.

Surface modeling is the process of numerically representing a planetary surface (Earth or other planets) by grids with known coordinates in an arbitrary coordinate system. Surface modeling is aimed at formulating an ecological object in a grid system, in which each grid cell contains an estimate of the ecological object that is representative for that particular location. Representing data in grid form has at least three advantages: (1) regular grid can be easily reaggregated to any areal arrangement required; (2) producing ecological data in grid form is one way of ensuring compatibility between heterogeneous data sets; (3) data in grid form make multiresolution and multisource information fusion easier; and (4) converting data into grid form can provide a way of avoiding some of the problems imposed by artificial political boundaries.

Spatial modeling occurred in the 1960s with general availability of computers, but the tools offered by current geographical information systems (GIS) have appeared to be of little interest for spatial modeling because GIS has been restricted to producing cartographic products rather than spatial modeling. Therefore, we introduce a novel method, YUE-HASM, which is based on the fundamental theorem of surfaces and multigrid method. YUE-HASM would be developed into a general platform that would have much stronger capacity of spatial modeling and makes better use of existing data.

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