Local variance for multi-scale analysis in geomorphometry

Increasing availability of high resolution Digital Elevation Models (DEMs) is leading to a paradigm shift regarding scale issues in geomorphometry, prompting new solutions to cope with multi-scale analysis and detection of characteristic scales. We tested the suitability of the local variance (LV) method, originally developed for image analysis, for multi-scale analysis in geomorphometry. The method consists of: 1) up-scaling land-surface parameters derived from a DEM; 2) calculating LV as the average standard deviation (SD) within a 3 × 3 moving window for each scale level; 3) calculating the rate of change of LV (ROC-LV) from one level to another, and 4) plotting values so obtained against scale levels. We interpreted peaks in the ROC-LV graphs as markers of scale levels where cells or segments match types of pattern elements characterized by (relatively) equal degrees of homogeneity. The proposed method has been applied to LiDAR DEMs in two test areas different in terms of roughness: low relief and mountainous, respectively. For each test area, scale levels for slope gradient, plan, and profile curvatures were produced at constant increments with either resampling (cell-based) or image segmentation (object-based). Visual assessment revealed homogeneous areas that convincingly associate into patterns of land-surface parameters well differentiated across scales. We found that the LV method performed better on scale levels generated through segmentation as compared to up-scaling through resampling. The results indicate that coupling multi-scale pattern analysis with delineation of morphometric primitives is possible. This approach could be further used for developing hierarchical classifications of landform elements.