From Local to Global: Systematic Valley Floor Extraction for Characterizing Valley Width-Area Scaling in Mountainous Landscapes

Mountainous landscapes often contain sediment-filled valleys that control ecosystem diversity, flood hazards, and the distribution of human populations. Valley-floor geometry has been shown to correlate with climate proxies such as discharge or drainage area and is also influenced by lithology and tectonic uplift. However, the relative importance of these controls remains poorly constrained, and no global dataset of valley geometry currently exists.Here, we focus on the automatic mapping of valley floors at the scale of entire mountain ranges. We compare two methods for extracting valley floors from digital elevation models, based on different conceptual definitions. The first is a geometric approach following Clubb et al. (2017, 2022), which defines valleys as low slope areas with a low relative elevation to the nearest river. The second is a new method that identifies valleys as floodplains using a simplified hydraulic model that locally distributes water across flat surfaces adjacent to channels. We evaluate and calibrate both methods by comparison with maps of alluvial cover in four catchments spanning a wide range of tectonic and climatic settings: the European Alps, Scottish Highlands, Pyrenees, and Taiwan. Both methods achieve comparable agreement with alluvial data, although the geometric method is more sensitive to calibration parameters. We compute valley width along the stream network by identifying valley centers and measuring the distance to valley margins, allowing us to quantify the scaling between valley width and drainage area.  The scaling relationships of width with drainage area shows exponents ranging from 0.3 to 0.5, consistent with values reported in the literature, with an inter-catchment variability. We show that large-scale valley extraction also allows a more precise characterization of valley networks by identifying local deviations from width–area scaling by using a wideness index similar to the steepness index for channel gradient, and by extracting additional valley attributes such as slope and elevation. This study paves the way for a global analysis of valley morphology to better constraints its dependency to climate, tectonic and geological conditions the controls acting on it.