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Stochastic rainfall-runoff model with explicit soil moisture dynamics

Publication ,  Journal Article
Bartlett, MS; Daly, E; McDonnell, JJ; Parolari, AJ; Porporato, A
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
November 8, 2015

Stream runoff is perhaps the most poorly represented process in ecohydrological stochastic soil moisture models. Here we present a rainfall-runoff model with a new stochastic description of runoff linked to soil moisture dynamics. We describe the rainfall-runoff system as the joint probability density function (PDF) of rainfall, soil moisture and runoff forced by random, instantaneous jumps of rainfall. We develop a master equation for the soil moisture PDF that accounts explicitly for a general state-dependent rainfall-runoff transformation. This framework is then used to derive the joint rainfall-runoff and soil moisture-runoff PDFs. Runoff is initiated by a soil moisture threshold and a linear progressive partitioning of rainfall based on the soil moisture status.We explore the dependence of the PDFs on the rainfall occurrence PDF (homogeneous or state-dependent Poisson process) and the rainfall magnitude PDF (exponential or mixed-exponential distribution). We calibrate the model to 63 years of rainfall and runoff data from the Upper Little Tennessee watershed (USA) and show how the new model can reproduce the measured runoff PDF.

Duke Scholars

Published In

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

DOI

EISSN

1471-2946

ISSN

1364-5021

Publication Date

November 8, 2015

Volume

471

Issue

2183

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

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Bartlett, M. S., Daly, E., McDonnell, J. J., Parolari, A. J., & Porporato, A. (2015). Stochastic rainfall-runoff model with explicit soil moisture dynamics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2183). https://doi.org/10.1098/rspa.2015.0389
Bartlett, M. S., E. Daly, J. J. McDonnell, A. J. Parolari, and A. Porporato. “Stochastic rainfall-runoff model with explicit soil moisture dynamics.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2183 (November 8, 2015). https://doi.org/10.1098/rspa.2015.0389.
Bartlett MS, Daly E, McDonnell JJ, Parolari AJ, Porporato A. Stochastic rainfall-runoff model with explicit soil moisture dynamics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2015 Nov 8;471(2183).
Bartlett, M. S., et al. “Stochastic rainfall-runoff model with explicit soil moisture dynamics.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 471, no. 2183, Nov. 2015. Scopus, doi:10.1098/rspa.2015.0389.
Bartlett MS, Daly E, McDonnell JJ, Parolari AJ, Porporato A. Stochastic rainfall-runoff model with explicit soil moisture dynamics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2015 Nov 8;471(2183).
Journal cover image

Published In

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

DOI

EISSN

1471-2946

ISSN

1364-5021

Publication Date

November 8, 2015

Volume

471

Issue

2183

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences