## 1. Introduction

[2] Selection of an appropriate quantitative model and associated parameter calibration are key issues in the interpretation of transport experiments in natural and reconstructed porous media. The assessment of model sensitivity to parameter uncertainty, and comparison among different models on the basis of model selection criteria, are at the core of an appropriate methodology to address this problem [e.g., *Barth and Hill*, 2005a, 2005b]. Key sources of uncertainty associated with modeling of processes governing conservative transport in porous media at different scales of observations include hydraulic and transport parameters (e.g., hydraulic conductivity, porosity, and dispersivity) and boundary conditions (e.g., the concentration at the source location or the fluid flow rate). Sensitivity of model response to these parameters typically varies in space and time. An important step in a parameter estimation procedure is to identify locations in the system where the model is most sensitive to its parameters [e.g., *Tiedeman et al*., 2003, 2004]. This, in turn, constitutes the basis for model-based experiment design and interpretation [e.g., *Fajraoui et al*., 2011, and references therein].

[3] A useful approach for the design, analysis, and interpretation of conservative transport experiments in porous media is based on Global Sensitivity Analysis (GSA). GSA provides a convenient and powerful way to (a) analyze the influence of the uncertainty associated with model parameter values on the variability of model response and (b) identify space-time locations where a model is most sensitive to its unknown parameters. GSA is applied in several fields of engineering [*Saltelli et al*., 2000; *Sudret*, 2008] and has recently been employed for risk analysis of environmental contamination scenarios [*Volkova et al*., 2008; *Oladyshkin et al*., 2012; *Ciriello et al*., 2013]. It has also been used to illustrate how to improve the design of laboratory-scale experiments and parameter calibration based on the classical Advection-Dispersion Equation (ADE) model [*Fajraoui et al*., 2011]. Such analyses are typically based on the Sobol indices [*Sobol*, 1993; *Archer et al*., 1997]; these are variance-based sensitivity measures and do not require assumptions on linearity or monotonic behavior of the specific model. Their computation is generally performed within a Monte Carlo (MC) framework [*Sobol*, 2001], thus potentially leading to heavy computational cost for complex models and large parameter number [*Sudret*, 2008].

[4] Among different alternatives, the Sobol indices can be computed through the Polynomial Chaos Expansion (PCE) technique [*Wiener*, 1938]. This methodology was introduced in the engineering context through the stochastic spectral finite element analysis by *Ghanem and Spanos* [1991]. It is a useful tool for high-performance and accurate GSA analysis, relying on the definition of a surrogate model to calculate the sensitivity indices analytically via a simple postprocessing operation and requiring negligible computational time [*Sudret*, 2008; *Ciriello and Di Federico*, 2013; *Ciriello et al*., 2013 and references therein]. A PCE-based GSA has been presented in the literature for the ADE model in diverse settings [e.g., *Volkova et al*., 2008; *Zhang et al*., 2010; *Shi et al*., 2010; *Fajraoui et al*., 2011, 2012; *Ciriello et al*., 2013 and references therein].

[5] To the best of our knowledge, a detailed study of parameter sensitivity for the design and interpretation of laboratory scale, conservative transport experiments, based on a set of alternative process-based models, has not been undertaken. Most notably, quantification and comparative analysis of the sensitivity of widely used transport formulations such as (a) a dual-porosity (DP) model with mass transfer between mobile and immobile regions [*Huang et al*., 2003; *Liu et al*., 2010], and (b) the Continuous Time Random Walk (CTRW) [*Berkowitz et al*., 2006 and references therein] to their parameters has not been reported in the literature.

[6] Here we focus on the conservative, one-dimensional transport experiment presented by *Gramling et al*. [2002], performed within a laboratory chamber filled with a uniform, reconstructed porous medium. As candidate one-dimensional interpretive models, we select (a) the classical ADE, (b) a dual-porosity (DP) scheme with mass transfer between mobile and immobile regions, and (c) the Continuous Time Random Walk (CTRW) formulation. The space-time distribution of solute concentration along the chamber is considered as the system state against which we (a) perform a PCE-based GSA, (b) analyze the sensitivity of each model to its parameters, (c) explore the feasibility of estimating key model parameters based on a limited set of data, measured at locations determined by the results of the GSA, (d) apply model discrimination criteria to quantify (in a relative sense) the ability of these alternative models to interpret experimental observations, and estimate the relative degree of likelihood of the models through a posterior probability measure for the specific case study [*Ye et al*., 2008; *Bianchi Janetti et al*., 2012, and references therein], and (e) assess the predictive ability of the selected models.

[7] Our methodology allows quantification of (a) the relative importance of the parameters associated with each model, and (b) the space-time locations where the system state is most sensitive to model parameters. This information is relevant for model-based experiment design and robust parameter calibration at affordable computational cost. In our application, parameter calibration is performed within a Maximum Likelihood (ML) context [e.g., *Carrera and Neuman*, 1986].