Dynamics of drainage under stochastic rainfall in river networks

Jorge M. Ramirez; Corina Constantinescu

doi:10.1142/S0219493720500422

Dynamics of drainage under stochastic rainfall in river networks

Jorge M. Ramirez
, Corina Constantinescu

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We consider a linearized dynamical system modeling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model describes the evolution, at daily time scales, of an interconnected network of linear reservoirs and takes into account the differences in flow celerity between hillslopes and streams as well as their spatial variation. The resulting stochastic process is a piece-wise deterministic Markov process of the Orstein-Uhlembeck type. We provide an explicit formula for the Laplace transform of the invariant density of streamflow in terms of the geophysical parameters of the river network and the statistical properties of the precipitation field. As an application, we include novel formulas for the invariant moments of the streamflow at the watershed's outlet, as well as the asymptotic behavior of extreme discharge events, and conditions for the statistical scaling of streamflow with respect to Horton order.

Original language	English
Article number	2050042
Journal	Stochastics and Dynamics
Volume	20
Issue number	3
DOIs	https://doi.org/10.1142/S0219493720500422
State	Published - Jun 1 2020
Externally published	Yes

Funding

All relevant numerical calculations and examples included in this paper were performed in MathematicaTM and an interactive notebook is available upon request to the corresponding author. This research was funded by The British Council, through a Researchers Link grant to The University of Liverpool and Universidad Nacional de Colombia. The project also benefited from funding from the European Union’s Seventh Framework Programme for research, technological development and demonstration under Grant Agreement Number 318984-RARE. The authors would also like to thank several people whose comments and suggestions made this work possible. Including Professors Oscar Mesa, Germán Poveda and Carlos Hoyos (Universidad Nacional de Colombia), Alfred Muller (Siegen University), Junyi Guo (Nankai University), Tomasz Kozubowski (University of Nevada), Manuel Correa (Integral S.A., Colombia), Vijay Gupta (University of Colorado, Boulder), Edward Waymire (Oregon State University) and Jesus Gómez (New Mexico Tech).

Keywords

Ornstein-Uhlenbeck type
Rainfall runoff process
invariant distribution of discharge

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10.1142/S0219493720500422

Cite this

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title = "Dynamics of drainage under stochastic rainfall in river networks",

abstract = "We consider a linearized dynamical system modeling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model describes the evolution, at daily time scales, of an interconnected network of linear reservoirs and takes into account the differences in flow celerity between hillslopes and streams as well as their spatial variation. The resulting stochastic process is a piece-wise deterministic Markov process of the Orstein-Uhlembeck type. We provide an explicit formula for the Laplace transform of the invariant density of streamflow in terms of the geophysical parameters of the river network and the statistical properties of the precipitation field. As an application, we include novel formulas for the invariant moments of the streamflow at the watershed's outlet, as well as the asymptotic behavior of extreme discharge events, and conditions for the statistical scaling of streamflow with respect to Horton order.",

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N2 - We consider a linearized dynamical system modeling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model describes the evolution, at daily time scales, of an interconnected network of linear reservoirs and takes into account the differences in flow celerity between hillslopes and streams as well as their spatial variation. The resulting stochastic process is a piece-wise deterministic Markov process of the Orstein-Uhlembeck type. We provide an explicit formula for the Laplace transform of the invariant density of streamflow in terms of the geophysical parameters of the river network and the statistical properties of the precipitation field. As an application, we include novel formulas for the invariant moments of the streamflow at the watershed's outlet, as well as the asymptotic behavior of extreme discharge events, and conditions for the statistical scaling of streamflow with respect to Horton order.

AB - We consider a linearized dynamical system modeling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model describes the evolution, at daily time scales, of an interconnected network of linear reservoirs and takes into account the differences in flow celerity between hillslopes and streams as well as their spatial variation. The resulting stochastic process is a piece-wise deterministic Markov process of the Orstein-Uhlembeck type. We provide an explicit formula for the Laplace transform of the invariant density of streamflow in terms of the geophysical parameters of the river network and the statistical properties of the precipitation field. As an application, we include novel formulas for the invariant moments of the streamflow at the watershed's outlet, as well as the asymptotic behavior of extreme discharge events, and conditions for the statistical scaling of streamflow with respect to Horton order.

KW - Ornstein-Uhlenbeck type

KW - Rainfall runoff process

KW - invariant distribution of discharge

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DO - 10.1142/S0219493720500422

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JO - Stochastics and Dynamics

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ER -

Dynamics of drainage under stochastic rainfall in river networks

Abstract

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Keywords

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