The scale-mosaic hypothesis: A framework for heterogeneous scale selection in geomorphometry and DEM-based terrain analysis

Abstract. Scale is among the most consequential issues in geomorphometry and terrain analysis. Land-surface parameters (LSP) derived from digital elevation models (DEMs) are scale dependent because they are either defined over a neighbourhood or affected by the topographic detail retained in a DEM. The dominant multiscale workflow generates dense stacks of homogeneously scaled LSP predictors and then applies feature-selection or dimensionality-reduction procedures to retain a subset of scales. Although this approach has proven useful, it assumes that selected scales can be imposed uniformly across space. That assumption is difficult to justify in heterogeneous terrain, where landforms are nested, process domains overlap, and characteristic scales vary locally.

This paper formalizes the scale-mosaic hypothesis: land-surface parameter scale mosaics based on locally optimized scale-selection criteria can provide terrain representations and model predictors with greater scale-space information density, improved correspondence with spatially heterogeneous process scales, and consequently equal or improved modelling performance relative to homogeneous multiscale alternatives.

The paper defines the principal concepts underlying the hypothesis, including scale signatures, characteristic scales, key-scale rasters, scale-space partitions, and scale mosaics. It distinguishes heterogeneous scale selection from conventional homogeneous multiscale feature selection, clarifies the relationship with scale-space theory and automatic scale selection, and identifies why a scale mosaic is not merely a visualization of a multiscale stack but a different way of collapsing scale-space. Scale mosaicking is therefore not simply another scale-selection method, but a distinct mode of scale-space reduction in which scale itself becomes a mapped property of the terrain representation.

The hypothesis is developed as a set of linked and falsifiable claims concerning information density, process-scale representation, and predictive performance. Existing evidence is reviewed according to these claims. This evidence includes scale-signature analysis, DEV_max and key-scale mapping, scale-optimized roughness and anisotropy, Gaussian scale-space optimization of derivative-based land-surface parameters, digital soil mapping, wetland prediction, information-density analysis, and emerging terrain-classification applications. Together, these studies indicate that characteristic scales are spatially structured, that heterogeneous scale representation is applicable across multiple parameter families, that scale mosaics can preserve information from more of the sampled scale domain than any sparse homogeneous subset, and that terrain-driven local scale optimization can match or exceed model-optimized homogeneous scale selection. The framework therefore repositions scale from a fixed analytical parameter to a spatially distributed property of terrain representation.