Natural springs protection and probabilistic risk assessment under uncertain conditions

The study introduces a comprehensive framework for natural springs' protection and probabilistic risk assessment in the presence of uncertainty associated with the characterization of the groundwater system. The methodology is applied to a regional-scale hydrogeological setting, located in Northern Italy and characterized by the presence of high-quality natural springs forming a unique system whose preservation is of critical importance for the region. Diverse risk pathways are presented to constitute a fault tree model enabling identification of all basic events, each associated with uncertainty and contributing to an undesired system failure. The latter is quantified in terms of hydraulic head falling below a given threshold value for at least one amongst all active springs. The workflow explicitly includes the impact of model parameter uncertainty on the evaluation of the overall probability of system failure due to alternative groundwater extraction strategies. To cope with conceptual model uncertainty, two models based on different reconstructions of the aquifer geological structure are considered. In each conceptual model, hydraulic conductivities related to the geomaterials composing the aquifer are affected by uncertainty. It is found that (a) the type of conceptual model employed to characterize the aquifer structure strongly affects the probability of system failure and (b) uncertainties associated with the ensuing conductivity fields, even as constrained through model calibration, lead to different impacts on the variability of hydraulic head levels at the springs depending on the conceptual model adopted. The results of the study demonstrate that the proposed approach enables one to (i) quantify the risk associated with springs depletion due to alternative strategies of aquifer exploitation; (ii) quantify the way diverse sources of uncertainty (i.e., model and parameter uncertainty) affect the probability of system failure; (iii) determine the optimal exploitation strategy ensuring system functioning; and (iv) identify the most vulnerable springs, where depletion first occurs

Analytical expressions for upscaled relative permeabilities in three-phase flow

We present analytical solutions for the relative permeabilities governing a Darcy scale description of threephase flow of immiscible fluids. We consider flow taking place within a capillary tube with circular crosssection for two settings corresponding to (a) a water wet and (b) an oil wet configuration. Momentum transfer between the moving phases, which leads to the phenomenon of viscous coupling, is explicitly accounted by imposing continuity of velocity and shear stress at the fluid-fluid interfaces. The macroscopic model describing the system at the Darcy scale includes three-phase effective relative permeabilities, Kij, r, accounting for the flow rate of the ith-phase due to the presence of the jth-phase. These effective coefficients are function of phases saturation, fluids viscosity and wettability of the medium. Our results show that (i) the relative permeability Kii, r of the wetting phase is only a function of its own saturation while Kii, r of the non-wetting phases depend on the saturations of all the fluids; (ii) viscous coupling effects (elucidated by Kij, r with i ≠, j) can be relevant in water wet and oil wet systems

Stochastic characterization of the Montalto Uffugo reasearch site (Italy) by geostatistical inversion of moment equations of groundwater flow.

We assess the applicability and performance of a methodology of inverting stochastic mean groundwater flow equations to characterize the spatial variability of (natural) log-transmissivity (Y) of a heterogeneous aquifer. The methodology, originally proposed by Hernandez et al. (2003, 2006), relies on a nonlinear geostatistical inverse algorithm for recursive approximations of steady-state (ensemble) mean groundwater flow that allows estimating jointly the spatial variability of Y, the underlying variogram parameters, and the variance-covariance of the estimates. Estimates of prediction errors of hydraulic heads and fluxes are then calculated a posteriori, upon solving equations satisfied by the corresponding co-variances. Here, we extend the methodology to quasi-steady state flow conditions and present its first field application by using information collected during a pumping test performed at the Montalto Uffugo research site (Italy). Log-transmissivity is parameterized geostatistically on the basis of an available measured value and a set of unknown values at discrete pilot points. Best estimates of Y at the measurement location and at the pilot points are obtained by a maximum likelihood fit of computed and measured heads. These posterior estimates are then projected onto the computational grid by kriging. Information on head drawdowns is provided through self-potential signals recorded by 47 surface electrodes during the test. The maximum likelihood-based objective function includes a regularization term reflecting prior information about Y. The relative weight assigned to this term is evaluated separately from other model parameters to avoid bias and instability. We explore the effectiveness of both a zero- and a second-order closure of the mean flow equation at providing a proper geostatistical characterization of the log-transmissivity field. The parameters of the variogram of Y are estimated a posteriori using formal model selection criteria. The adoption of a second-order mean flow model renders the sharpest definition of the regularization term and of the Y variogram parameters

Global sensitivity analyses of multiple conceptual models with uncertain parameters driving groundwater flow in a regional-scale sedimentary aquifer

We rely on various Global Sensitivity Analysis (GSA) approaches to detect the way uncertain parameters linked to diverse conceptual geological models influence spatial distributions of hydraulic heads in a three-dimensional complex groundwater system. We showcase our analyses by considering a highly heterogeneous, large scale aquifer system located in Northern Italy. Groundwater flow is simulated considering alternative conceptual models employed to reconstruct the spatial arrangement of the geomaterials forming the internal makeup of the domain and characterizing the distribution of hydraulic conductivities. For each conceptual model, uncertain factors include the values of hydraulic conductivity associated with the geomaterials composing the aquifer as well as the system boundary conditions. We explore the relative influence of parametric uncertainties to steady-state hydraulic head distributions across the set of conceptual models considered by way of three GSA methodologies, i.e., (a) a derivative-based approach, which rests on the Morris indices; (b) the classical variance-based approach, grounded on the evaluation of the Sobol’ indices; and (c) a moment-based GSA, which takes into account the influence of uncertain parameters on multiple (statistical) moments of a given model output. Due to computational costs, Sobol’ and moment-based indices are obtained numerically through the use of a model-order reduction technique based on the polynomial chaos expansion approach. We find that the sensitivity measures considered convey different yet complementary information. The choice of the conceptual model employed to characterize the lithological reconstruction of the aquifer affects the degree of influence that uncertain parameters can have on modeling results

Geostatistical characterization of a regional-scale sedimentary aquifer

We analyze the impact of the uncertainty associated with (a) the spatial distribution of hydraulic parameters, e.g., hydraulic conductivity, and (b) the conceptual model adopted to describe the system on the characterization of a regional-scale aquifer in the context of inverse modeling of the groundwater flow system. The study aquifer lies within the provinces of Bergamo and Cremona (Italy) and covers a planar extent of approximately 785 km2. Analysis of available sedimentological information allows identifying a set of main geo-materials (facies / phases) which constitute the geological makeup of the system. Hydraulic conductivity (K) distributions are modeled on the basis of the following conceptual schemes: (1) Composite Medium approach, implemented by zonation of the system, and, (2) Overlapping Continua model. The local volumetric fraction of each facies can also be interpreted as the probability of occurrence of that facies in the point (volume) considered and can be assessed by means of indicator-based methodologies. For each of the adopted conceptual models the groundwater flow is simulated with the numerical code MODFLOW-2000. Best estimates of hydraulic conductivities are obtained by a Maximum Likelihood fit of computed versus measured hydraulic heads. Information on hydraulic heads is provided in a set of piezometric level measurements recorded in monitoring wells. The results are examined using formal model quality criteria

Effect of evaporation cooling on drying capillary active building materials

The relevance of evaporation cooling on drying capillary active building materials is investigated through numerical simulation and non-destructive measurements. The drying rate results to be strongly related to the so-called wet bulb temperature, i.e. the temperature reached inside the sample during the early drying phase. It is shown that the faster the process occurs, the lower is the wet bulb temperature. The experiments are carried out inside a climatic chamber under controlled atmospheric conditions (temperature and relative humidity), using calcium silicate samples. The drying rates are determined by weighting the samples during time, while the surface temperature is measured via infrared thermography. A mathematical model describing transient heat and moisture transfer is implemented with the software COMSOL for 3D-simulation, and afterward validated by comparison with the measured data. The numerical solution presents a satisfactory agreement with the experimental results. A sensitivity analysis is also performed for different input parameters including convective heat transfer coefficient and uncertainties in material properties. The validated model is then used for simulation of a set of drying cases by varying the sample thickness and boundary conditions. Hence, the water content distribution inside the samples is investigated by determining boundary conditions and sample dimensions, in which nearly uniform water content can be obtained. In fact, uniform distribution is a prerequisite for an experimental method, recently studied by the authors, that aims at determining the water retention curve of capillary active materials by means of drying tests

Estimation of single-metal and competitive sorption isotherm through Maximum likelihood and model quality criteria

Metal sorption of single and binary (competitive) systems for several soils is analyzed to assess the ability of alternative isotherm models to interpret experimental observations. The analysis is performed within a Maximum Likelihood framework and on the basis of model identifi cation (sometimes termed “quality” or “information”) criteria. These methodologies allow the assessment of the measurement error variance in the parameter estimation process and the uncertainty arising from the use of alternative (conceptual-mathematical) models. We first analyze Cu and Zn sorption in two Israeli soils, Bet Dagan and Yatir, which are slightly alkaline but with substantially different sorption capacities and perform an extensive set of batch experiments in single and binary systems. We then analyze the data set published by Liao and Selim (2009) where Ni and Cd sorption was studied in three different (one neutral and two acidic) soils. Single component data from both sets of experiments are interpreted on the basis of the Langmuir, Freundlich, and Redlich–Peterson (RP) models. The family of binary systems results is analyzed in light of the Sheindorf–Rebhun–Sheintuch (SRS) model, the modified RP model, and the modified and extended Langmuir models. All of the considered models are expressed in terms of initial and equilibrium concentrations, two variables that are measured independently. Maximum Likelihood and model identification criteria (such as Bayesian criteria BIC and KIC, and information theoretic criteria AIC, AICc, and HIC) are employed to (a) estimate model parameters, (b) rank alternative models, and (c) estimate the relative degree of likelihood of each model by means of a weight, or posterior probability. We show that modeling observation error variance either as a constant or as a function of concentration does not significantly affect parameter estimates for a given model. These different representations of measurement error variance impact the ranking of alternative models based on posterior probability weights. The weights associated with different models can be very similar when a uniform measurement error variance is considered, so that it is difficult to clearly identify a single best model