Application of the Preisach Model to Soil-Moisture Hysteresis

Flynn, D.; McNamara, Hugh; O'Kane, Philip; PokrovskÜ, Alexei

doi:10.1016/b978-012480874-4/50025-7

Cited by 44 publications

(38 citation statements)

References 28 publications

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“…The central assumptions of rate-independence and non-local memory are overlooked, not just in these papers, but throughout the soil physics literature (Flynn and OKane, 2004,;Flynn, 2004;. Figure 8 also shows a discrete two-dimensional representation of what is called in this paper, the Preisach density.…”

Section: Reduction Of the Independent Domain Model To The Preisach Modelmentioning

confidence: 99%

“…It has nonlocal memory. The reader is recommended to explore these ideas using the following java applets (Rasskazov, 2002) and (Flynn, 2003).…”

Section: Fig 3 Weighted Parallel Connection Of a Finite Number Of Hmentioning

confidence: 99%

“…To achieve a reduction in the number of parameters it is necessary to use the Preisach model (Preisach, 1935;OKane et al, 2003a,b). Using this model as a basis, the fitting of experimental data was performed in Flynn (2004) and . In that paper, three models were defined, called the Zero, Beak and Wedge Models, which can be seen in Figs.…”

Section: Application Of the Preisach Model To The Soil-moisture Charamentioning

confidence: 99%

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Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory

O’Kane¹,

Flynn²

2007

Hydrol. Earth Syst. Sci.

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Hysteresis is a rate-independent non-linearity that is expressed through thresholds, switches, and branches. Exceedance of a threshold, or the occurrence of a turning point in the input, switches the output onto a particular output branch. Rate-independent branching on a very large set of switches with non-local memory is the central concept in the new definition of hysteresis. Hysteretic loops are a special case. A selfconsistent mathematical description of hydrological systems with hysteresis demands a new non-linear systems theory of adequate generality. The goal of this paper is to establish this and to show how this may be done. Two results are presented: a conceptual model for the hysteretic soil-moisture characteristic at the pedon scale and a hysteretic linear reservoir at the catchment scale. Both are based on the Preisach model. A result of particular significance is the demonstration that the independent domain model of the soil moisture characteristic due to Childs, Poulavassilis, Mualem and others, is equivalent to the Preisach hysteresis model of non-linear systems theory, a result reminiscent of the reduction of the theory of the unit hydrograph to linear systems theory in the 1950s. A significant reduction in the number of model parameters is also achieved. The new theory implies a change in modelling paradigm.

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Section: Reduction Of the Independent Domain Model To The Preisach Modelmentioning

confidence: 99%

“…It has nonlocal memory. The reader is recommended to explore these ideas using the following java applets (Rasskazov, 2002) and (Flynn, 2003).…”

Section: Fig 3 Weighted Parallel Connection Of a Finite Number Of Hmentioning

confidence: 99%

Section: Application Of the Preisach Model To The Soil-moisture Charamentioning

confidence: 99%

See 1 more Smart Citation

Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory

O’Kane¹,

Flynn²

2007

Hydrol. Earth Syst. Sci.

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“…In applying the the Darcy-Richards equation it was found that the soil moisture characteristic curves that link soil moisture content, soil water potential and hydraulic conductivity, were not single valued but were rather different for wetting and drying (see the review of concepts and models by Jaynes, 1990). Thus, the soil moisture characteristics must be considered to be hysteretic, even though this is very often forgotten in applying the Darcy-Richards equation because there is little information available on the nature of the hysteresis for different soils (what there is has been collected in the GRIZZLY database of Haverkamp et al, 2002), multiple physical hypotheses about the causes of hysteresis, and no consensus about how it should be parameterised (see the recent discussions of O'Kane, 2004;Flynn et al, 2005).…”

Section: So If We Have Been Searching In the Wrong Places How Can Wementioning

confidence: 99%

Searching for the Holy Grail of scientific hydrology: Qt=(S, R, Δt)A as closure

Beven

2006

Hydrol. Earth Syst. Sci.

209

179

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Abstract. Representative Elementary Watershed concepts provide a useful scale-independent framework for the representation of hydrological processes. The balance equations that underlie the concepts, however, require the definition of boundary flux closures that should be expected to be scale dependent. The relationship between internal state variables of an REW element and the boundary fluxes will be nonlinear, hysteretic and scale-dependent and may depend on the extremes of the heterogeneities within the REW. Because of the nonlinearities involved, simple averaging of local scale flux relationships are unlikely to produce an adequate decription of the closure problem at the REW scale. Hysteresis in the dynamic response is demonstrated for some small experimental catchments and it is suggested that at least some of this hysteresis can be represented by the use of simple transfer functions. The search for appropriate closure schemes is the second most important problem in hydrology of the 21st Century (the most important is providing the techniques to measure integrated fluxes and storages at useful scales). The closure problem is a scientific Holy Grail: worth searching for even if a general solution might ultimate prove impossible to find.

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“…A lot of works have been devoted to this phenomenon, see, e. g., [1,2,3,4,10,11,13]. Mathematical analysis of various mechanical porous media models with capillary hysteresis and without temperature effects has been carried out in [6,7,22,23].…”

Section: Introductionmentioning

confidence: 99%

Solvability of an Unsaturated Porous Media Flow Problem with Thermomechanical Interaction

Detmann¹,

Krejčı́²,

Rocca³

2016

SIAM J. Math. Anal.

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A PDE system consisting of the momentum balance, mass balance, and energy balance equations for displacement, capillary pressure, and temperature as a model for unsaturated fluid flow in a porous viscoelastoplastic solid is shown to admit a solution under appropriate assumptions on the constitutive behavior. The problem involves two hysteresis operators accounting for plastic and capillary hysteresis.

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Application of the Preisach Model to Soil-Moisture Hysteresis

Cited by 44 publications

References 28 publications

Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory

Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory

Searching for the Holy Grail of scientific hydrology: <i>Q<sub>t</sub></i>=(<i>S, R, Δt</i>)<i>A</i> as closure

Solvability of an Unsaturated Porous Media Flow Problem with Thermomechanical Interaction

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Application of the Preisach Model to Soil-Moisture Hysteresis

Cited by 44 publications

References 28 publications

Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory

Thresholds, switches and hysteresis in hydrology from the pedon to the catchment scale: a non-linear systems theory

Searching for the Holy Grail of scientific hydrology: &lt;i&gt;Q&lt;sub&gt;t&lt;/sub&gt;&lt;/i&gt;=(&lt;i&gt;S, R, Δt&lt;/i&gt;)&lt;i&gt;A&lt;/i&gt; as closure

Solvability of an Unsaturated Porous Media Flow Problem with Thermomechanical Interaction

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Product

Resources

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Searching for the Holy Grail of scientific hydrology: <i>Q<sub>t</sub></i>=(<i>S, R, Δt</i>)<i>A</i> as closure