A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments

Franssen, Harrie‐Jan Hendricks; Alcolea, Andrés; Riva, Mònica; Bakr, M.; Wiel, N Van Der; Stauffer, Fritz; Guadagnini, Alberto

doi:10.1016/j.advwatres.2009.02.011

Cited by 170 publications

(90 citation statements)

References 111 publications

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“…This holds, in particular, for all conditional distributions (via Bayesian updating [e.g., Smith and Gelfand, 1992]) of parameters and model predictions that arise when conditioning on hypothetical data from proposed designs, often calling for (geo)statistical inversion tools. For mildly nonlinear cases, we recommend the quasilinear geostatistical approach [Kitanidis, 1995] and its upgrades [e.g., Nowak and Cirpka, 2004], ensemble Kalman filters [Zhang et al, 2005;Nowak, 2009], and biasaware modifications of it [e.g., Drécourt et al, 2006;Kollat et al, 2011], or other conditional Monte Carlo methods based on successive linearization compared in Franssen et al [2009]. In some situations, analytical solutions and linearized approaches are inappropriate.…”

Section: A1 Conditional Simulation and Bayesian Inferencementioning

confidence: 99%

A hypothesis‐driven approach to optimize field campaigns

Nowak¹,

Rubin²,

Barros³

2012

Water Resources Research

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[1] Most field campaigns aim at helping in specified scientific or practical tasks, such as modeling, prediction, optimization, or management. Often these tasks involve binary decisions or seek answers to yes/no questions under uncertainty, e.g., Is a model adequate? Will contamination exceed a critical level? In this context, the information needs of hydro(geo)logical modeling should be satisfied with efficient and rational field campaigns, e.g., because budgets are limited. We propose a new framework to optimize field campaigns that defines the quest for defensible decisions as the ultimate goal. The key steps are to formulate yes/no questions under uncertainty as Bayesian hypothesis tests, and then use the expected failure probability of hypothesis testing as objective function. Our formalism is unique in that it optimizes field campaigns for maximum confidence in decisions on model choice, binary engineering or management decisions, or questions concerning compliance with environmental performance metrics. It is goal oriented, recognizing that different models, questions, or metrics deserve different treatment. We use a formal Bayesian scheme called PreDIA, which is free of linearization, and can handle arbitrary data types, scientific tasks, and sources of uncertainty (e.g., conceptual, physical, (geo)statistical, measurement errors). This reduces the bias due to possibly subjective assumptions prior to data collection and improves the chances of successful field campaigns even under conditions of model uncertainty. We illustrate our approach on two instructive examples from stochastic hydrogeology with increasing complexity.

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Section: A1 Conditional Simulation and Bayesian Inferencementioning

confidence: 99%

A hypothesis‐driven approach to optimize field campaigns

Nowak¹,

Rubin²,

Barros³

2012

Water Resources Research

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“…Constraining it in such a way that the calculated heads are similar to the observed heads is a typical inverse problem amenable to be solved in a stochastic framework. This inverse problem can be solved using different techniques in the framework of multi-Gaussian fields (de Marsily et al, 1999;Carrera et al, 2005;Hendricks Franssen et al, 2009). Here, the regularized pilot-points method (Alcolea et al, 2006) was used to obtain 200 Monte Carlo simulations of the hydraulic conductivity and storativity fields (not displayed here) constrained by all available data.…”

Section: A Practical Illustration In Omanmentioning

confidence: 99%

Stochastic versus Deterministic Approaches

Renard¹,

Alcolea

Ginsbourger³

2013

Environmental Modelling

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In broad sense, modelling refers to the process of generating a simplified representation of a real system. A suitable model must be able to explain past observations, integrate present data and predict with reasonable accuracy the response of the system to planned stresses (Carrera et al., 1987). Models have evolved together with science and nowadays modelling is an essential and inseparable part of scientific activity. In environmental sciences, models are used to guarantee suitable conditions for sustainable development and are a pillar for the design of social and industrial policies.Model types include analogue models, scale models and mathematical models. Analogue models represent the target system by another, more understandable or analysable system. These models rely on Feynman's principle (Feynman et al., 1989, sec. 12-1): 'The same equations have the same solutions.' For example, the electric/hydraulic analogy (Figure 8.1a) establishes the parallelism between voltage and water-pressure difference or between electric current and flow rate of water. Scale models are representations of a system that is larger or smaller (most often) than the actual size of the system being modelled. Scale models (Figure 8.1b) are often built to analyse physical processes in the laboratory or to test the likely performance of a particular design at an early stage of development without incurring the full expense of a full-sized prototype. Notwithstanding the use of these types of models in other branches of science and engineering, the most popular models in environmental sciences are mathematical. A mathematical model describes a system by a set of state variables and a set of equations that establish relationships between those variables and the governing parameters. Mathematical models can be analytical or numerical. Analytical models often require many simplifications to render the equations amenable to solution. Instead, numerical models are more versatile and make use of computers to solve the equations.Mathematical models (either analytical or numerical) can be deterministic or stochastic (from the Greek τóχoς for 'aim' or 'guess'). A deterministic model is one in which state variables are uniquely determined by parameters in the model and by sets of previous states of these variables. Therefore, deterministic models perform the same way for a given set of parameters and initial conditions and their solution is unique. Nevertheless, deterministic models are sometimes unstable -i.e., small perturbations (often below the detection limits) of the initial conditions or the parameters governing the problem lead to large variations of the final solution (Lorenz, 1963). Thus, despite the fact that the solution is unique, one can obtain solutions that are dramatically different by perturbing slightly a single governing parameter or the initial condition at a single point of the domain.

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“…High-parameter dimensionality poses considerable challenges for the inversion of groundwater flow and transport data [e.g., Kitanidis, 1995;Hendricks-Franssen et al, 2009;Laloy et al, 2013;Zhou et al, 2014, and references therein]. What is more, conceptual and structural inadequacies of the subsurface model and measurement errors of the model input (boundary conditions) and output (calibration) data introduce uncertainty in the estimated parameters and model simulations.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic inference of multi‐Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction

Laloy

Linde

Jacques

et al. 2015

Water Resources Research

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We present a Bayesian inversion method for the joint inference of high-dimensional multiGaussian hydraulic conductivity fields and associated geostatistical parameters from indirect hydrological data. We combine Gaussian process generation via circulant embedding to decouple the variogram from grid cell specific values, with dimensionality reduction by interpolation to enable Markov chain Monte Carlo (MCMC) simulation. Using the Matern variogram model, this formulation allows inferring the conductivity values simultaneously with the field smoothness (also called Matern shape parameter) and other geostatistical parameters such as the mean, sill, integral scales and anisotropy direction(s) and ratio(s). The proposed dimensionality reduction method systematically honors the underlying variogram and is demonstrated to achieve better performance than the Karhunen-Loè ve expansion. We illustrate our inversion approach using synthetic (error corrupted) data from a tracer experiment in a fairly heterogeneous 10,000-dimensional 2-D conductivity field. A 40-times reduction of the size of the parameter space did not prevent the posterior simulations to appropriately fit the measurement data and the posterior parameter distributions to include the true geostatistical parameter values. Overall, the posterior field realizations covered a wide range of geostatistical models, questioning the common practice of assuming a fixed variogram prior to inference of the hydraulic conductivity values. Our method is shown to be more efficient than sequential Gibbs sampling (SGS) for the considered case study, particularly when implemented on a distributed computing cluster. It is also found to outperform the method of anchored distributions (MAD) for the same computational budget.

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A comparison of seven methods for the inverse modelling of groundwater flow. Application to the characterisation of well catchments

Cited by 170 publications

References 111 publications

A hypothesis‐driven approach to optimize field campaigns

A hypothesis‐driven approach to optimize field campaigns

Stochastic versus Deterministic Approaches

Probabilistic inference of multi‐Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction

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