A method for comparing numerical variables defined in a region

This paper develops a new method for comparing numerical variables defined in a region. This method covers numerical variables defined over a two-dimensional space, such as temperature and humidity distributions, as well as those defined on a discrete space such as the height of trees and the age of buildings. To evaluate the difference between two variables, this method considers three types of transformations that convert one variable so that it fits the other as well as possible. The result gives a basis for the separate evaluation of spatial and aspatial differences between the variables. The transformations also permit us to describe the spatial difference in more detail. To test the validity of the method, this paper applies it to an analysis of three spatial datasets of different sizes. The result shows that the proposed method is effective for evaluating and visualizing the difference between numerical variables.