Hydrology without dimensions

Abstract. By rigorously accounting for dimensional homogeneity in physical laws, the ? theorem and related self-similarity hypotheses allow us to achieve a dimensionless reformulation of scientific lower-dimensional context. This paper presents applications these concepts partitioning water soil on terrestrial landscapes. For such processes, their complexity lack first principle formulation make analysis an excellent tool formulate theories that are amenable empirical testing analytical developments. The resulting scaling laws help reveal dominant environmental controls partitionings. In particular, we discuss how dryness index storage affect long-term rainfall partitioning, key nonlinear control global datasets weathering rates, existence new macroscopic relations among average variables landscape evolution statistics. sediments, elevation profile, spectral self-similar topographies also unveil tantalizing analogies with turbulent flows.