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References

  • Andričević, R. (1998), Effects of local dispersion and sampling volume on the evolution of concentration fluctuations in aquifers, Water Resour. Res., 34(5), 11151129.
  • Attinger, S., M. Dentz, and W. Kinzelbach (2004), Exact transverse macro dispersion coefficients for transport in heterogeneous porous media, Stochastic Environ. Res. Risk Assess., 18(1), 915.
  • Bakr, A. A., L. W. Gelhar, A. L. Gutjahr, and J. R. MacMillan (1978), Stochastic analysis of spatial variability in subsurface flows: 1. Comparison of one-dimensional and three-dimensional flows, Water Resour. Res., 14(2), 263271.
  • Beckie, R. (1996), Measurement scale, network sampling scale, and groundwater model parameters, Water Resour. Res., 32(1), 6576.
  • Bellin, A., and D. Tonina (2007), Probability density function of non-reactive solute concentration in heterogeneous porous formations, J. Contam. Hydrol., 94(1–2), 109125, doi:10.1016/j.jconhyd.2007.05.005.
  • Brooks, A. N., and T. J. R. Hughes (1982), Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Eng., 32(1–3), 199259.
  • Caroni, E., and V. Fiorotto (2005), Analysis of concentration as sampled in natural aquifers, Transp. Porous Media, 59(1), 1945.
  • Cirpka, O. A., and P. K. Kitanidis (2000), Characterization of mixing and dilution in heterogeneous aquifers by means of local temporal moments, Water Resour. Res., 36(5), 12211236.
  • Cirpka, O. A., and A. J. Valocchi (2007), Two-dimensional concentration distribution for mixing-controlled bioreactive transport in steady state, Adv. Water Resour., 30(6–7), 16681679.
  • Cirpka, O. A., R. L. Schwede, J. Luo, and M. Dentz (2008), Concentration statistics for mixing-controlled reactive transport in random heterogeneous media, J. Contam. Hydrol., 98(1–2), 6174.
  • Dagan, G. (1984), Solute transport in heterogeneous porous formations, J. Fluid Mech., 145, 151177.
  • Dagan, G. (1989), Flow and Transport in Porous Formations, Springer, Berlin.
  • Dentz, M., H. Kinzelbach, S. Attinger, and W. Kinzelbach (2000a), Temporal behavior of a solute cloud in a heterogeneous porous medium 1. Point-like injection, Water Resour. Res., 36(12), 35913604.
  • Dentz, M., H. Kinzelbach, S. Attinger, and W. Kinzelbach (2000b), Temporal behavior of a solute cloud in a heterogeneous porous medium: 2. Spatially extended injection, Water Resour. Res., 36(12), 36053614.
  • Dentz, M., H. Kinzelbach, S. Attinger, and W. Kinzelbach (2002), Temporal behavior of a solute cloud in a heterogeneous porous medium 3. Numerical simulations, Water Resour. Res., 38(7), 1118, doi:10.1029/2001WR000436.
  • De Simoni, M., X. Sanchez-Vila, J. Carrera, and M. W. Saaltink (2007), A mixing ratios-based formulation for multicomponent reactive transport, Water Resour. Res., 43, W07419, doi:10.1029/2006WR005256.
  • Dietrich, C. R., and G. N. Newsam (1993), A fast and exact method for multidimensional gaussian stochastic simulations, Water Resour. Res., 29(8), 28612869.
  • Eberhard, J. (2004), Approximations for transport parameters and self-averaging properties for point-like injections in heterogeneous media, J. Phys. A Math. Gen., 37(7), 25492571, doi:10.1088/0305-4470/37/7/003.
  • Englert, A., J. Vanderborght, and H. Vereecken (2006), Prediction of velocity statistics in three-dimensional multi-Gaussian hydraulic conductivity fields, Water Resour. Res., 42, W03418, doi:10.1029/2005WR004014.
  • Fiori, A., and G. Dagan (2000), Concentration fluctuations in aquifer transport: A rigorous first-order solution and applications, J. Contam. Hydrol., 45(1–2), 139163.
  • Fiori, A., S. Berglund, V. Cvetkovic, and G. Dagan (2002), A first-order analysis of solute flux statistics in aquifers: The combined effect of pore-scale dispersion, sampling, and linear sorption kinetics, Water Resour. Res., 38(8), 1137, doi:10.1029/2001WR000678.
  • Fiorotto, V., and E. Caroni (2002), Solute concentration statistics in heterogeneous aquifers for finite Peclet values, Transport Porous Media, 48, 331351, (Erratum, Transp. Porous Media, 50(3), 373, 2003.).
  • Gelhar, L. W., and C. L. Axness (1983), Three-dimensional stochastic-analysis of macrodispersion in aquifers, Water Resour. Res., 19(1), 161180.
  • Graham, W., G. Destouni, G. Demmy, and X. Foussereau (1998), Prediction of local concentration statistics in variably saturated soils: Influence of observation scale and comparison with field data, J. Contam. Hydrol., 32(1–2), 177199.
  • Gutjahr, A. L., L. W. Gelhar, A. A. Bakr, and J. R. MacMillan (1978), Stochastic analysis of spatial variability in subsurface flows: 2. Evaluation and application, Water Resour. Res., 14(5), 953959.
  • Kapoor, V., and L. W. Gelhar (1994), Transport in three-dimensionally heterogeneous aquifers: 1. Dynamics of concentration fluctuations, Water Resour. Res., 30(6), 17751788.
  • Kitanidis, P. K. (1988), Prediction by the method of moments of transport in a heterogeneous formation, J. Hydrol., 102(1–4), 453473.
  • Kitanidis, P. K. (1995), Quasi-linear geostatistical theory for inversing, Water Resour. Res., 31(10), 24112419.
  • Li, S. G., and D. McLaughlin (1991), A nonstationary spectral method for solving stochastic groundwater problems: Unconditional analysis, Water Resour. Res., 27(7), 15891605.
  • Li, S. G., and D. McLaughlin (1995), Using the nonstationary spectral method to analyze flow-through heterogeneous trending media, Water Resour. Res., 31(3), 541551.
  • Liu, G. S., Z. M. Lu, and D. X. Zhang (2007), Stochastic uncertainty analysis for solute transport in randomly heterogeneous media using a Karhunen-Loeve-based moment equation approach, Water Resour. Res., 43(7), W07427, doi:10.1029/2006WR005193.
  • Lu, Z. M., and D. X. Zhang (2004), Comparative study on uncertainty quantification for flow in randomly heterogeneous media using Monte Carlo simulations and conventional and KL-based moment-equation approaches, SIAM J. Sci. Comput., 26(2), 558577.
  • Michalak, A. M., and P. K. Kitanidis (2003), A method for enforcing parameter nonnegativity in Bayesian inverse problems with an application to contaminant source identification, Water Resour. Res., 39(2), 1033, doi:10.1029/2002WR001480.
  • Neuman, S. P. (1993), Eulerian-langrangian theory of transport in space-time nonstationary velocity fields: Exact nonlocal formalism by conditional moments and weak approximation, Water Resour. Res., 29(3), 633645.
  • Neuman, S. P., and S. Orr (1993), Prediction of steady-state flow in nonuniform geologic media by conditional moments: Exact nonlocal formalism, effective conductivities, and weak approximation, Water Resour. Res., 29(2), 341364.
  • Neuman, S. P., C. L. Winter, and C. M. Newman (1987), Stochastic-theory of field-scale fickian dispersion in anisotropic porous-media, Water Resour. Res., 23(3), 453466.
  • Neupauer, R. M., and J. L. Wilson (1999), Adjoint method for obtaining backward-in-time location and travel time probabilities of a conservative groundwater contaminant, Water Resour. Res., 35(11), 33893398.
  • Nowak, W., R. L. Schwede, O. A. Cirpka, and I. Neuweiler (2008), Probability density functions of hydraulic head and velocity in three-dimensional heterogeneous porous media, Water Resour. Res., 44, W08452, doi:10.1029/2007WR006383.
  • Pope, S. B. (1985), Pdf methods for turbulent reactive flows, Prog. Energy Combust. Sci., 11(2), 119192.
  • Rubin, Y. (2003), Applied Stochastic Hydrogeology, Oxford Univ. Press, Oxford, U.K.
  • Rubin, Y., A. Sun, R. Maxwell, and A. Bellin (1999), The concept of block-effective macrodispersivity and a unified approach for grid-scale- and plume-scale-dependent transport, J. Fluid Mech., 395, 161180.
  • Stüben, K. (2001), A review of algebraic multigrid, J. Comput. Appl. Math., 128(1–2), 281309.
  • Sun, N., and W. Yeh (1990), Coupled inverse problems in groundwater modeling: 1. Sensitivity analysis and parameter identification, Water Resour. Res., 26(10), 25072525.
  • Werth, C. J., O. A. Cirpka, and P. Grathwohl (2006), Enhanced mixing and reaction through flow focusing in heterogeneous porous media, Water Resour. Res., 42, W12414, doi:10.1029/2005WR004511.
  • Zhang, D. X. (1998), Numerical solutions to statistical moment equations of groundwater flow in nonstationary, bounded, heterogeneous media, Water Resour. Res., 34(3), 529538.
  • Zhang, D. X., and Z. M. Lu (2004), An efficient, high-order perturbation approach for flow in random porous media via Karhunen-Loeve and polynomial expansions, J. Comput. Phys., 194(2), 773794.