Abstract. Uncoupling between the flow field and the stress field in pumped aquifers is the basis of the classical groundwater hydrology. Recently, some authors have disputed the assumption of uncoupling with regard to both fluid dynamics and porous medium deformation. The issue is very important as it could undermine the traditional approach to simulate subsurface flow, analyze pumping tests, and predict land subsidence caused by fluid withdrawal. The present paper addresses the problem of coupling versus uncoupling in the Po river plain, a normally consolidated and normally pressurized basin which has experienced in the last 50 years a pronounced pore pressure drawdown because of water and gas removal and where a large hydromechanical database is available from the ground surface down to 4000 m depth. A numerical study is performed which shows that the matrix which relates flow to stress is very similar to the capacity matrix of the uncoupled flow equation. A comparison of results obtained with the finite element integration of the coupled and uncoupled models indicates that pore pressure is rather insensitive to coupling anywhere within the pumped formation while in the adjacent aquitard-aquifer units, coupling induces a slight overpressure which quickly dissipates in time with a small initial influence on medium deformation, and specifically on land subsidence. As a major consequence the uncoupled solutions to the fluid dynamic and the structural problems appear to be fully warranted on any timescale of practical interest in a typical normally consolidated and pressurized basin. IntroductionWhen an aquifer, an oil/gas reservoir, or a confining bed experiences a change of the internal flow and stress fields (typically due to fluid withdrawal), the incremental effective stresses and the fluid dynamic gradients that develop within the porous medium are intimately connected. This complex interrelation was first mathematically described by Biot [1941]. A model of flow and stress based on the Biot equations is said to be a coupled model.Groundwater hydrologists and petroleum engineers who are mostly concerned with the fluid dynamic aspects of the coupled process have developed the uncoupled flow theory, whose most widespread and used equation, the so-called diffusion equation, was originally derived by Theis [1935] more than 60 years ago. This equation incorporates the rock structural behavior into a lumped mechanical parameter (the elastic storage coefficient) and is solved separately and independently for the pore pressure p. Once p is obtained, it may be used as an external source of strength in a poroelastic model of the porous system to provide the medium deformation, typically, land subsidence, i.e., the vertical displacement at the surface boundary. This is the uncoupled, or two-step, approach followed by many authors to simulate and predict land settlement due to

[1] Numerical groundwater models, frequently used to enhance understanding of the hydrologic and chemical processes in local or regional aquifers, are often hindered by an incomplete representation of the parameters which characterize these processes. In this study, we present the use of a data assimilation algorithm that incorporates all past model results and data measurements, an ensemble smoother (ES) to provide enhanced estimates of aquifer hydraulic conductivity (K) through assimilation of hydraulic head (H) and groundwater return flow volume (RFV) measurements into groundwater model simulation results. On the basis of the Kalman filter methodology, residuals between forecasted model results and measurements, together with covariances between model results at measurement locations and nonmeasurement locations, are used to correct model results. Parameter estimation is achieved by incorporating model parameters into the algorithm, thus allowing the correlation between H, RFV, and K to correct the K fields. The applicability of the ES is demonstrated using a synthetic two-dimensional transient groundwater modeling simulation. Sensitivity analyses are carried out to show the performance of the ES in regard to measurement error, number of measurements, number of assimilation times, correlation length of the K fields, and the number of stream gage locations. Results show that the departure of the K fields from a reference K field is greatly reduced through data assimilation and demonstrate that the ES scheme is a promising alternative to other inverse modeling techniques because of low computational burden and the ability to run the algorithm entirely independent of the groundwater model simulation.Citation: Bailey, R., and D. Baù (2010), Ensemble smoother assimilation of hydraulic head and return flow data to estimate hydraulic conductivity distribution, Water Resour. Res., 46, W12543,

Abstract. Estimating the spatial variability of hydraulic conductivity K in natural aquifers is important for predicting the transport of dissolved compounds. Especially in the nonreactive case, the plume evolution is mainly controlled by the heterogeneity of K. At the local scale, the spatial distribution of K can be inferred by combining the Lagrangian formulation of the transport with a Kalman-filter-based technique and assimilating a sequence of time-lapse concentration C measurements, which, for example, can be evaluated on site through the application of a geophysical method. The objective of this work is to compare the ensemble Kalman filter (EnKF) and the ensemble smoother (ES) capabilities to retrieve the hydraulic conductivity spatial distribution in a groundwater flow and transport modeling framework. The application refers to a two-dimensional synthetic aquifer in which a tracer test is simulated. Moreover, since Kalmanfilter-based methods are optimal only if each of the involved variables fit to a Gaussian probability density function (pdf) and since this condition may not be met by some of the flow and transport state variables, issues related to the nonGaussianity of the variables are analyzed and different transformation of the pdfs are considered in order to evaluate their influence on the performance of the methods. The results show that the EnKF reproduces with good accuracy the hydraulic conductivity field, outperforming the ES regardless of the pdf of the concentrations.

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