Various spatial phenomena such as population density and sales data of a store are represented as surfaces in GIS as continuous distribution. It often happens that multiple surfaces exist simultaneously in the same region. Including population density, elevation distribution is measured and represented as multiple surfaces in the same region. We recognize the spatial properties of surfaces and evaluate the similarity among surfaces in various aspects through comparison. Comparing multiple surfaces becomes a necessary process of analysis to understand the difference or relationship among them. Existing approaches of surface comparison are useful to explain the relationship of surfaces either in quantitative or qualitative aspects. However, it is difficult to understand spatial differences between surfaces from these approaches. Quantitative measures only indicate the degree of similarity by numbers and the qualitative approach rarely distinguishes spatial differences if their topologies are the same. To overcome such problems, a new method of surface comparison, minimum transformation, is proposed in this study. The method transports an amount of surface volume either in horizontal or vertical direction within its four adjacent cells (the rook's case) where a surface is given in raster form. The model is defined as a combination of these two transformation patterns. The model explains the difference between two surfaces not only by numbers but direction information showing structural difference of surfaces. The method is applied to hypothetical and actual data for its evaluation. The results of the empirical data show that the proposed method could evaluate the effectiveness of current urban facilities with how urban phenomena have changed.