Rate-Independent Hysteresis in Terrestrial Hydrology

Appelbe, Brian; Flynn, D.; McNamara, Hugh; O'Kane, Philip; Pimenov, Alexander; Pokrovskiĭ, A. V.; Рачинский, Дмитрий; Zhezherun, A.

doi:10.1109/mcs.2008.930923

Cited by 37 publications

(36 citation statements)

References 43 publications

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“…The proper step size depends on the value of γ [5,28]. We found that the regularisation substantially improves the efficiency of the calculation, while γ = 0.001 is sufficiently small to ensure good accuracy.…”

Section: Dissipation Of Energy For Sinusoidal Forcingmentioning

confidence: 95%

“…8 satisfies x * (ω −1 t) → b (ω −1 t) as ω → 0+ (further details of theoretical and numerical analysis of the adiabatic limit of Eq. 8 can be found in [5,30]). Hence, x M * → p + |q|, x m * → p − |q| as ω → 0+ and formula (12) implies that the area σ (ω) of one hysteresis loop of x * tends to the limit…”

Section: Limits Of Low and High Frequencies ωmentioning

confidence: 95%

“…We use the approach to modelling spatially homogeneous flows proposed in [3][4][5][6], where the soil-water hysteresis is described by the Preisach operator. The simplest form of both the balance equation ('linear reservoir') and the Preisach operator (homogeneous Preisach measure) is adopted in order to understand qualitative aspects of the relationship between the rainfall pattern and the associated energy dissipation due to soil-water hysteresis.…”

Section: Introductionmentioning

confidence: 99%

“…The simplest form of both the balance equation ('linear reservoir') and the Preisach operator (homogeneous Preisach measure) is adopted in order to understand qualitative aspects of the relationship between the rainfall pattern and the associated energy dissipation due to soil-water hysteresis. The lumped form of the balance equation where the spatial variation is eliminated by a homogenisation procedure is a major simplification in the proposed model and the main factor in restricting its applicability to the conditions described in [3,5].…”

Section: Introductionmentioning

confidence: 99%

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Modelling Energy Dissipation Due to Soil-Moisture Hysteresis

Brokate

MacCarthy

Pimenov

et al. 2011

Environ Model Assess

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Cyclic wetting and drying of soils due to changing weather conditions is characterised by a welldocumented hysteresis in the relationship between the pressure or matric potential and the water content in the soil. Hysteresis manifests itself through a difference in drying and wetting curves. Its presence suggests that there is dissipation of energy associated with intermittent wetting and drying of the soil, which can be released in the form of heat. In this paper, we discuss a model for evaluation of the energy dissipation rate due to soil-moisture hysteresis. The model has three main ingredients: (a) a hysteresis constitutive relationship between soil-water potential and moisture content in the soil, which is modelled by the Preisach operator; (b) a lumped form of Darcy's law assuming that the water flux is proportional to the difference of potentials in the soil and on its surface; (c) a rainfall term governing the evolution of the outer potential, which is modelled by a periodic forcing or a Poisson process. We propose a combination of analytic and numerical methods to evaluate the energy dissipation rate and how it is affected by the variation of rain parameters, such as the frequency of arrivals of rain cells and their shape, intensity and duration.

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Section: Dissipation Of Energy For Sinusoidal Forcingmentioning

confidence: 95%

Section: Limits Of Low and High Frequencies ωmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling Energy Dissipation Due to Soil-Moisture Hysteresis

Brokate

MacCarthy

Pimenov

et al. 2011

Environ Model Assess

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“…The use of models of hysteresis in magnetism, as well as in other natural, engineering, and social sciences, confronts with problems of identification of parameters, which requires to obtain a sufficient number of observations of hysteresis system states [2,8]. The phenomenological nature of the Preisach model, which is based on superposition of multiple elementary hysteresis operators called non-ideal relays (switches), and the representation theorem of Mayergoyz allow to apply the model to various hysteretic systems using a phenomenological argument or the black box approach without complex analysis of such systems based on first principles [3,7,10,11,[15][16][17]20].…”

mentioning

confidence: 99%

Convergence of Direct Recursive Algorithm for Identification of Preisach Hysteresis Model with Stochastic Input

Рачинский¹,

Ruderman

2016

SIAM J. Appl. Math.

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Abstract. We consider a recursive iterative algorithm for identification of parameters of the Preisach model, one of the most commonly used models of hysteretic input-output relationships. The classical identification algorithm due to Mayergoyz defines explicitly a series of test inputs that allow one to find parameters of the Preisach model with any desired precision provided that (a) such input time series can be implemented and applied; and, (b) the corresponding output data can be accurately measured and recorded. Recursive iterative identification schemes suitable for a number of engineering applications have been recently proposed as an alternative to the classical algorithm. These recursive schemes do not use any input design but rather rely on an input-output data stream resulting from random fluctuations of the input variable. Furthermore, only recent values of the input-output data streams are available for the scheme at any time instant. In this work, we prove exponential convergence of such algorithms, estimate explicitly the convergence rate, and explore which properties of the stochastic input and the algorithm affect the guaranteed convergence rate.

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An estimate of energy dissipation due to soil-moisture hysteresis

McNamara

2014

Water Resour. Res.

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[1] Processes of infiltration, transport, and outflow in unsaturated soil necessarily involve the dissipation of energy through various processes. Accounting for these energetic processes can contribute to modeling hydrological and ecological systems. The welldocumented hysteretic relationship between matric potential and moisture content in soil suggests that one such mechanism of energy dissipation is associated with the cycling between wetting and drying processes, but it is challenging to estimate the magnitude of the effect in situ. The Preisach model, a generalization of the Independent Domain model, allows hysteresis effects to be incorporated into dynamical systems of differential equations. Building on earlier work using such systems with field data from the south-west of Ireland, this work estimates the average rate of hysteretic energy dissipation. Through some straightforward assumptions, the magnitude of this rate is found to be of O(10

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Rate-Independent Hysteresis in Terrestrial Hydrology

Cited by 37 publications

References 43 publications

Modelling Energy Dissipation Due to Soil-Moisture Hysteresis

Modelling Energy Dissipation Due to Soil-Moisture Hysteresis

Convergence of Direct Recursive Algorithm for Identification of Preisach Hysteresis Model with Stochastic Input

An estimate of energy dissipation due to soil-moisture hysteresis

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