Hydraulic conductivity fields: Gaussian or not?

Meerschaert, Mark M.; Doğan, Mine; Dam, Remke L. Van; Hyndman, D. W.; Benson, David A.

doi:10.1002/wrcr.20376

Cited by 30 publications

(22 citation statements)

References 57 publications

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“…In applications, a fractional difference is applied to a time series data set, and the order α of the fractional difference is chosen to remove long range correlations from the data. See [50] for a recent application to ground water hydrology.…”

Section: Artfima Modelmentioning

confidence: 99%

Tempered fractional calculus

Sabzikar

Meerschaert

Chen

2015

Journal of Computational Physics

Self Cite

287

168

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Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution. The limiting tempered stable probability densities exhibit semi-heavy tails, which are commonly observed in finance. Tempered power law waiting times lead to tempered fractional time derivatives, which have proven useful in geophysics. The tempered fractional derivative or integral of a Brownian motion, called a tempered fractional Brownian motion, can exhibit semi-long range dependence. The increments of this process, called tempered fractional Gaussian noise, provide a useful new stochastic model for wind speed data. A tempered difference forms the basis for numerical methods to solve tempered fractional diffusion equations, and it also provides a useful new correlation model in time series.

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Section: Artfima Modelmentioning

confidence: 99%

Tempered fractional calculus

Sabzikar

Meerschaert

Chen

2015

Journal of Computational Physics

Self Cite

287

168

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“…Investigation of when functions will satisfy self similarity relationships, which gives insight into the applicable extent of scaling transformations and the regimes in which multi-scale models must be developed for a particular problem. Particularly for hydrological phenomena, investigations have concluded that certain medium and fluid parameters, such as the hydraulic conductivity, undergo fundamental changes in their distribution as the scale increases from the pore scale to the watershed scale (and above) (Kavvas, 1999;Meerschaert et al, 2013).…”

Section: Discussionmentioning

confidence: 99%

A comparison of the modern Lie scaling method to classical scaling techniques

Polsinelli¹,

Kavvas²

2016

Hydrol. Earth Syst. Sci.

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Abstract. In the past 2 decades a new modern scaling technique has emerged from the highly developed theory on the Lie group of transformations. This new method has been applied by engineers to several problems in hydrology and hydraulics, including but not limited to overland flow, groundwater dynamics, sediment transport, and open channel hydraulics. This study attempts to clarify the relationship this new technology has with the classical scaling method based on dimensional analysis, non-dimensionalization, and the Vaschy-Buckingham-theorem. Key points of the Lie group theory, and the application of the Lie scaling transformation, are outlined and a comparison is made with two classical scaling models through two examples: unconfined groundwater flow and contaminant transport. The Lie scaling method produces an invariant scaling transformation of the prototype variables, which ensures the dynamics between the model and prototype systems will be preserved. Lie scaling can also be used to determine the conditions under which a complete model is dynamically, kinematically, and geometrically similar to the prototype phenomenon. Similarities between the Lie and classical scaling methods are explained, and the relative strengths and weaknesses of the techniques are discussed.

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“…In this domain as well, however, increased computer power has led to the use of finer resolution models but mostly in hypothetical virtual reality simulations to explore the impacts of subsurface heterogeneities on flow and transport processes. This type of study also has a long history, from the early random field experiments of Freeze (1975Freeze ( , 1980, Smith and Schwarz (1980) and Smith and Hebbert (1979) to the recent multimillion element simulations of, for example, Zinn et al (2003), Feyen et al (2006), Michael et al (2010), Guilleminot et al (2012), and Meerschaert et al (2013).…”

Section: Hyperresolution Informationmentioning

confidence: 97%

Hyperresolution information and hyperresolution ignorance in modelling the hydrology of the land surface

Beven

Cloke

Pappenberger

et al. 2014

Sci. China Earth Sci.

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There is a strong drive towards hyperresolution earth system models in order to resolve finer scales of motion in the atmosphere. The problem of obtaining more realistic representation of terrestrial fluxes of heat and water, however, is not just a problem of moving to hyperresolution grid scales. It is much more a question of a lack of knowledge about the parameterisation of processes at whatever grid scale is being used for a wider modelling problem. Hyperresolution grid scales cannot alone solve the problem of this hyperresolution ignorance. This paper discusses these issues in more detail with specific reference to land surface parameterisations and flood inundation models. The importance of making local hyperresolution model predictions available for evaluation by local stakeholders is stressed. It is expected that this will be a major driving force for improving model performance in the future. hyperresolution models, epistemic uncertainties, models of everywhere, communicating uncertainty, flood risk Citation: Beven K, Cloke H, Pappenberger F, et al. 2014. Hyperresolution information and hyperresolution ignorance in modelling the hydrology of the land surface. Science China: Earth Sciences,It is a general expectation in earth system science modelling that we will continue to move to higher and higher resolution coupled models, with so called hyperresolution models (on the order of 1km or less) becoming computationally feasible for operational forecasts within the foreseeable future (e.g. Wood et al., 2011). Many of the forecasting centres that produce global Numerical Weather Predictions (NWP) are already running tests with models at such scales or have plans to move to scales of the order of 1-10 km in the near future. Many Limited Area Models are already run at hyperresolution. It is also likely that global climate models will follow in due course, again with some regional climate models already running at such scales. The principle driver behind these developments is to resolve finer scales of motion in the atmosphere and oceans, with an expectation that the accuracy and precision of forecasts and projections will be improved. Past experience suggests that this will be the case. There have been improvements in both forecast performance and lead times as more powerful computers have become available and grid scales have reduced and as the

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Hydraulic conductivity fields: Gaussian or not?

Cited by 30 publications

References 57 publications

Tempered fractional calculus

Tempered fractional calculus

A comparison of the modern Lie scaling method to classical scaling techniques

Hyperresolution information and hyperresolution ignorance in modelling the hydrology of the land surface

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