Characterization of drainage basin hypsometry: A generalized approach

The elevation-area relationship within drainage basins has a strong bearing on manifold biophysical processes. The understanding of erosional and hydrodynamical processes also benefits from quantitative characterization of elevation distribution or basin hypsometry. This study presents a comprehensive review of quantitative approaches to hypsometric analysis, ranging from simple indices to functional formulations (for example, Strahler). Detailed analyses of the goodness-of-fit reveal that the current suite of metrics is deficient when tested over a large number drainage basins (in this study, Congo, Narmada, and Yukon River basins), especially in the head and the toe sections of the hypsometric curve. A new three-parameter formulation is introduced in this study and tested over a large set of drainages (n = 419). We find that this form adapts well to diverse elevational profiles. Application areas, such as large-scale analyses of drainage basin similarity and snowmelt modeling, use hypsometric parameterization and stand to benefit from the new functional characterization discussed here. Efficient estimation of hypsometric curves based on the new formulation also paves the way towards computational research at whole-earth scales utilizing large datasets involving millions of drainages.