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Amir, Orna; Neuman, Shlomo P.

doi:10.1023/a:1010706223350

Cited by 21 publications

(1 citation statement)

References 14 publications

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“…One important reason for this is the lack of a robust hydrological theory at the macroscale, and in fact most ''physically based'' models of hydrologic systems are based on an implicit upscaling premise, that the behavior at the system/model scale can be described by governing equations inferred from small-scale physics, field studies and observations (with spatial averaging of the state variables and use of ''effective'' parameters) [e.g., Arain et al, 1996Arain et al, , 1997Beven and Binley, 1992;Freer et al, 1996;Thiemann et al, 2001;Wagener et al, 2003]. Given the strong nonlinearities and heterogeneities in a hydrological system, the upscaling assumption is clearly questionable and we might therefore expect the large-scale ''effective'' governing equations for the system to be different in form (not just different in parameters) from the equations inferred at the small scale [Amir and Neuman, 2001;Tartakovsky et al, 2003;Ye et al, 2004].…”

Section: Introductionmentioning

confidence: 99%

Estimating the uncertain mathematical structure of a water balance model via Bayesian data assimilation

Bulygina

Gupta

2009

Water Resources Research

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[1] When constructing a hydrological model at the macroscale (e.g., watershed scale), the structure of this model will inherently be uncertain because of many factors, including the lack of a robust hydrological theory at that scale. In this work, we assume that a suitable conceptual model structure for the hydrologic system has already been determined; that is, the system boundaries have been specified, the important state variables and input and output fluxes to be included have been selected, the major hydrological processes and geometries of their interconnections have been identified, and the continuity equation (mass balance) has been assumed to hold. The remaining structural identification problem that remains, then, is to select the mathematical form of the dependence of the output on the inputs and state variables, so that a computational model can be constructed for making simulations and/or predictions of the system input-state-output behavior. The conventional approach to this problem is to preassume some fixed (and possibly erroneous) mathematical forms for the model output equations. We show instead how Bayesian data assimilation can be used to directly estimate (construct) the form of these mathematical relationships such that they are statistically consistent with macroscale measurements of the system inputs, outputs, and (if available) state variables. The resulting model has a stochastic rather than deterministic form and thereby properly represents both what we know (our certainty) and what we do not know (our uncertainty) about the underlying structure and behavior of the system. Further, the Bayesian approach enables us to merge prior beliefs in the form of preassumed model equations with information derived from the data to construct a posterior model. As a consequence, in regions of the model space for which observational data are available, the errors in preassumed mathematical form of the model can be corrected, improving model performance. For regions where no such data are available the ''prior'' theoretical assumptions about the model structure and behavior will dominate. The approach, entitled Bayesian estimation of structure, is used to estimate water balance models for the Leaf River Basin, Mississippi, at annual, monthly, and weekly time scales, conditioned on the assumption of a simple single-state-variable conceptual model structure. Inputs to the system are uncertain observed precipitation and potential evapotranspiration, and outputs are estimated probability distributions of actual evapotranspiration and streamflow discharge. Results show that the models estimated for the annual and monthly time scales perform quite well. However, model performance deteriorates for the weekly time scale, suggesting limitations in the assumed form of the conceptual model.

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Section: Introductionmentioning

confidence: 99%

Estimating the uncertain mathematical structure of a water balance model via Bayesian data assimilation

Bulygina

Gupta

2009

Water Resources Research

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Stochastic analysis of unsaturated seepage through randomly heterogeneous earth embankments

Gallipoli

Sánchez

et al. 2011

Num Anal Meth Geomechanics

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Spatial variability of material properties is inherent in both natural soil deposits and earth structures, yet it is often ignored during geotechnical design. With the objective of developing novel methods for assessing the effects of soil variability on groundwater flow, this study presents a stochastic finite element model of seepage through a flood defense embankment with randomly heterogeneous material properties. Stochastic modeling is undertaken by means of a Monte Carlo simulation which involves a large number of finite element analyses, each with randomly varied porosity at element level, which leads to a corresponding random variation of both permeability and water retention properties across the embankment domain. This provides a statistical distribution of responses, such as total flow rate and time to reach steady state, instead of a single deterministic result as in conventional studies of seepage through unsaturated heterogeneous soils. As the degree of heterogeneity increases, water tends to flow along the most permeable paths inside the soil mass, resulting in an irregular shape of the predicted wetting fronts and pore pressure contours. The mean and standard deviation of the computed quantities strongly depend on the statistics of the input porosity field. Simulations are also conducted to compare the statistical variation of flow rate with and without dependency of the water retention curve on porosity. With recent growth in computer speed, stochastic finite element models based on the Monte Carlo approach can become a powerful design tool, especially if a quantitative assessment of geotechnical risks is required.where s o and ϕ o are the reference suction and reference porosity, respectively. HETEROGENEOUS UNSATURATED SEEPAGE

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Modeling of filtration through multiple layers of dual scale fibrous porous media

et al. 2006

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Cited by 21 publications

References 14 publications

Estimating the uncertain mathematical structure of a water balance model via Bayesian data assimilation

Estimating the uncertain mathematical structure of a water balance model via Bayesian data assimilation

Stochastic analysis of unsaturated seepage through randomly heterogeneous earth embankments

Modeling of filtration through multiple layers of dual scale fibrous porous media

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