Objectives  The accurate and fast multi-scale representation of digital elevation model (DEM) is the key basis for its multi-scale application. We aim to propose an automated and high-quality multi-scale representation method for DEM.

  Methods  We construct a model of DEM data for multi-scale representation, according to the corresponding relationship of "low-frequency - high-energy - large scale" in energy spectral density, and relate topographic semantic features in simplification.

  Results  The result shows that this model can dynamically derive DEM data at different scales. The figure of contour lines derived from this model can meet the basic principle of "retaining main topographic features and abandoning secondary topographic features"in topographic expression, spatial cognition and cartographic generalization. Quantificationally compared with traditional DEM simplification methods in elevation and slope shape, this method shows similar or better effect in statistical and structural significance.

  Conclusions  The model based on the Fourier energy spectrum can effectively express DEM data with different scale requirements.