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Entropy 2017, 19(6), 249; doi:10.3390/e19060249

Horton Ratios Link Self-Similarity with Maximum Entropy of Eco-Geomorphological Properties in Stream Networks

1
Department of Biology, 1 University of New Mexico, MSC03-2020, Albuquerque, NM 87131, USA
2
Department of Civil, Environmental and Architectural Engineering and Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, CO 80309, USA
*
Author to whom correspondence should be addressed.
Academic Editor: Samuel A. Cushman
Received: 17 March 2017 / Revised: 25 May 2017 / Accepted: 27 May 2017 / Published: 30 May 2017
(This article belongs to the Special Issue Entropy in Landscape Ecology)
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Abstract

Stream networks are branched structures wherein water and energy move between land and atmosphere, modulated by evapotranspiration and its interaction with the gravitational dissipation of potential energy as runoff. These actions vary among climates characterized by Budyko theory, yet have not been integrated with Horton scaling, the ubiquitous pattern of eco-hydrological variation among Strahler streams that populate river basins. From Budyko theory, we reveal optimum entropy coincident with high biodiversity. Basins on either side of optimum respond in opposite ways to precipitation, which we evaluated for the classic Hubbard Brook experiment in New Hampshire and for the Whitewater River basin in Kansas. We demonstrate that Horton ratios are equivalent to Lagrange multipliers used in the extremum function leading to Shannon information entropy being maximal, subject to constraints. Properties of stream networks vary with constraints and inter-annual variation in water balance that challenge vegetation to match expected resource supply throughout the network. The entropy-Horton framework informs questions of biodiversity, resilience to perturbations in water supply, changes in potential evapotranspiration, and land use changes that move ecosystems away from optimal entropy with concomitant loss of productivity and biodiversity. View Full-Text
Keywords: Budyko; coupled eco-hydrology; Horton law; networks; scaling; Strahler streams; vegetation Budyko; coupled eco-hydrology; Horton law; networks; scaling; Strahler streams; vegetation
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Milne, B.T.; Gupta, V.K. Horton Ratios Link Self-Similarity with Maximum Entropy of Eco-Geomorphological Properties in Stream Networks. Entropy 2017, 19, 249.

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