Stochastic rainfall-runoff model with explicit soil moisture dynamics

M. S. Bartlett; E. Daly; J. J. McDonnell; A. J. Parolari; A. Porporato

doi:10.1098/rspa.2015.0389

Stochastic rainfall-runoff model with explicit soil moisture dynamics

M. S. Bartlett, E. Daly, J. J. McDonnell, A. J. Parolari, A. Porporato^*

^*Corresponding author for this work

Geography & Environment

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18 Citations (Scopus)

Abstract

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.

Original language	English
Article number	20150389
Pages (from-to)	1-26
Number of pages	26
Journal	Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences
Volume	471
Issue number	2183
Early online date	28 Oct 2015
DOIs	https://doi.org/10.1098/rspa.2015.0389
Publication status	Published - 8 Nov 2015

Bibliographical note

Funding
This work was supported by the Agriculture and Food Research Initiative of the USDA National Institute of Food and Agriculture (2011-67003-30222); National Science Foundation (grants CBET-1033467, EAR-1331846, FESD-1338694 and EAR-1316258); and by the US Department of Energy (DOE) Office of Biological and Environmental Research (BER) Terrestrial Carbon Processes Program (DE-SC0006967).

Acknowledgements
We thank Gaby Katul and Larry Band for early discussions. Thanks to Duke University and UNC Chapel Hill for the Keohane Professorship support of J.J.M. during the preparation of this manuscript. Data sets were provided by the Climate and Hydrology Database Projects, a partnership between the Long-Term Ecological Research program and the US Forest Service Pacific Northwest Research Station, Corvallis, Oregon. Significant funding for these data was provided by the National Science Foundation Long-Term Ecological Research program and the USDA Forest Service.

Keywords

stochastic models in hydrology
watershed rainfall-runoff model
nonlinear thresholds
antecedent soil moisture
marked Poisson
state-dependent Poisson process
WATER-CONTROLLED ECOSYSTEMS
STORM SURFACE RUNOFF
HYDROLOGIC PROCESSES
HEADWATER CATCHMENT
ACTIVE-ROLE
GENERATION
VEGETATION
CLIMATE
BALANCE
INFILTRATION

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Cite this

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title = "Stochastic rainfall-runoff model with explicit soil moisture dynamics",

abstract = "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.",

keywords = "stochastic models in hydrology, watershed rainfall-runoff model, nonlinear thresholds, antecedent soil moisture, marked Poisson, state-dependent Poisson process, WATER-CONTROLLED ECOSYSTEMS, STORM SURFACE RUNOFF, HYDROLOGIC PROCESSES, HEADWATER CATCHMENT, ACTIVE-ROLE, GENERATION, VEGETATION, CLIMATE, BALANCE, INFILTRATION",

author = "Bartlett, {M. S.} and E. Daly and McDonnell, {J. J.} and Parolari, {A. J.} and A. Porporato",

note = "Funding This work was supported by the Agriculture and Food Research Initiative of the USDA National Institute of Food and Agriculture (2011-67003-30222); National Science Foundation (grants CBET-1033467, EAR-1331846, FESD-1338694 and EAR-1316258); and by the US Department of Energy (DOE) Office of Biological and Environmental Research (BER) Terrestrial Carbon Processes Program (DE-SC0006967). Acknowledgements We thank Gaby Katul and Larry Band for early discussions. Thanks to Duke University and UNC Chapel Hill for the Keohane Professorship support of J.J.M. during the preparation of this manuscript. Data sets were provided by the Climate and Hydrology Database Projects, a partnership between the Long-Term Ecological Research program and the US Forest Service Pacific Northwest Research Station, Corvallis, Oregon. Significant funding for these data was provided by the National Science Foundation Long-Term Ecological Research program and the USDA Forest Service.",

year = "2015",

month = nov,

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doi = "10.1098/rspa.2015.0389",

language = "English",

volume = "471",

pages = "1--26",

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

issn = "1364-5021",

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T1 - Stochastic rainfall-runoff model with explicit soil moisture dynamics

AU - Bartlett, M. S.

AU - Daly, E.

AU - McDonnell, J. J.

AU - Parolari, A. J.

AU - Porporato, A.

N1 - Funding This work was supported by the Agriculture and Food Research Initiative of the USDA National Institute of Food and Agriculture (2011-67003-30222); National Science Foundation (grants CBET-1033467, EAR-1331846, FESD-1338694 and EAR-1316258); and by the US Department of Energy (DOE) Office of Biological and Environmental Research (BER) Terrestrial Carbon Processes Program (DE-SC0006967). Acknowledgements We thank Gaby Katul and Larry Band for early discussions. Thanks to Duke University and UNC Chapel Hill for the Keohane Professorship support of J.J.M. during the preparation of this manuscript. Data sets were provided by the Climate and Hydrology Database Projects, a partnership between the Long-Term Ecological Research program and the US Forest Service Pacific Northwest Research Station, Corvallis, Oregon. Significant funding for these data was provided by the National Science Foundation Long-Term Ecological Research program and the USDA Forest Service.

PY - 2015/11/8

Y1 - 2015/11/8

N2 - 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.

AB - 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.

KW - stochastic models in hydrology

KW - watershed rainfall-runoff model

KW - nonlinear thresholds

KW - antecedent soil moisture

KW - marked Poisson

KW - state-dependent Poisson process

KW - WATER-CONTROLLED ECOSYSTEMS

KW - STORM SURFACE RUNOFF

KW - HYDROLOGIC PROCESSES

KW - HEADWATER CATCHMENT

KW - ACTIVE-ROLE

KW - GENERATION

KW - VEGETATION

KW - CLIMATE

KW - BALANCE

KW - INFILTRATION

U2 - 10.1098/rspa.2015.0389

DO - 10.1098/rspa.2015.0389

M3 - Article

SN - 1364-5021

VL - 471

SP - 1

EP - 26

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

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

IS - 2183

M1 - 20150389

ER -

Stochastic rainfall-runoff model with explicit soil moisture dynamics

Abstract

Bibliographical note

Keywords

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