Preprints
https://doi.org/10.5194/hess-2021-442
https://doi.org/10.5194/hess-2021-442

  27 Aug 2021

27 Aug 2021

Review status: this preprint is currently under review for the journal HESS.

Hydrology without dimensions

Amilcare Porporato Amilcare Porporato
  • Princeton University, Princeton, USA

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

Amilcare Porporato

Status: open (until 22 Oct 2021)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on hess-2021-442', Anonymous Referee #1, 14 Sep 2021 reply

Amilcare Porporato

Amilcare Porporato

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Short summary
Applying dimensional analysis to the partitioning of water and soil on terrestrial landscapes reveals their dominant environmental controls. We discuss how the dryness index and the storage index affect the long term rainfall partitioning, the key nonlinear control of the dryness index in global datasets of weathering rates, and the existence of new macroscopic relations among average variables in landscape evolution statistics with tantalizing analogies with turbulent fluctuations.