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Runoff on rooted trees

Jones, Owen 2019. Runoff on rooted trees. Journal of Applied Probability 56 , -.
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Abstract

We introduce an idealised model for overland flow generated by rain falling on a hill-slope. Our prime motivation is to show how the coalescence of runoff streams promotes the total generation of runoff. We show that, for our model, as the rate of rainfall increases in relation to the soil infiltration rate, there is a distinct phase-change. For low rainfall (the subcritical case) only the bottom of the hill-slope contributes to the total overland runoff, while for high rainfall (the supercritical case) the whole slope contributes and the total runoff increases dramatically. We identify the critical point at which the phase-change occurs, and show how it depends on the degree of coalescence. When there is no stream coalescence the critical point occurs when the rainfall rate equals the average infiltration rate, but when we allow coalescence the critical point occurs when the rainfall rate is less than the average infiltration rate, and increasing the amount of coalescence increases the total expected runoff.

Item Type: Article
Status: In Press
Schools: Mathematics
Publisher: Applied Probability Trust
ISSN: 0021-9002
Date of First Compliant Deposit: 16 July 2019
Date of Acceptance: 28 June 2019
Last Modified: 17 Jul 2019 10:45
URI: http://orca.cf.ac.uk/id/eprint/124258

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