Bayesian estimation of the hydraulic and solute transport properties of a small-scale unsaturated soil column

Open access

Abstract

In this study the hydraulic and solute transport properties of an unsaturated soil were estimated simultaneously from a relatively simple small-scale laboratory column infiltration/outflow experiment. As governing equations we used the Richards equation for variably saturated flow and a physical non-equilibrium dual-porosity type formulation for solute transport. A Bayesian parameter estimation approach was used in which the unknown parameters were estimated with the Markov Chain Monte Carlo (MCMC) method through implementation of the Metropolis-Hastings algorithm. Sensitivity coefficients were examined in order to determine the most meaningful measurements for identifying the unknown hydraulic and transport parameters. Results obtained using the measured pressure head and solute concentration data collected during the unsaturated soil column experiment revealed the robustness of the proposed approach.

Abbaspour, K., Schulin, R., van Genuchten, M.Th., 2001. Estimating unsaturated soil hydraulic parameters using ant colony optimization. Adv Water Resour., 24, 827–841.

Abbaspour, K., Johnson, C., van Genuchten, M.Th., 2004. Estimating uncertain flow and transport parameters using a sequential uncertainty fitting procedure. Vadose Zone J., 3, 1340–1352.

Beck, J., Arnold, K., 1997. Parameter Estimation in Engineering and Science. Wiley Interscience, New York.

Carducci, C.E., de Oliviera, G.C., da Costa, S., Zeviani, W.M., 2011. Modeling the water retention curve in Oxisols using the double van Genuchten equation. R. Bras. Ci. Solo., 35, 77–86. (In Portuguese.)

Dane, J.H., Topp, G.C., 2002. Methods of Soil Analysis, part 4, Physical Methods. Soil Sci. Soc. Am., Madison, WI.

De Smedt, F., Wierenga, P.J., 1984. Solute transfer through columns of glass beads. Water Resour. Res., 20, 225–232.

Diamantopoulos, E., Iden, S.C., Durner, W., 2012. Inverse modeling of dynamic nonequilibrium in water flow with an effective approach. Water Resour. Res., 48, W03503, doi: 10.1029/2011WR010717.

Franssen, H.J.H., Gómez-Hernández, J.J., Sahuquillo, A., 2003a. Coupled inverse modeling of groundwater flow and mass transport and the worth of concentration data. J. Hydrol., 281, 281–295.

Franssen, H.J.H., Stauffer, F., Kinzelbach, W., 2003b. Joint estimation of transmissivity and recharges-application: Stochastic characterization of well capture zones. J. Hydrol., 294, 1–3, 87–102.

Fu, J., Gómez-Hernández, J.J., 2009. Uncertainty assessment and data worth in groundwater flow and mass transport modeling using a blocking Markov chain Monte Carlo method. J. Hydrol., 364, 3–4, 328–341.

Geweke, J., 1992. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In: Bernardo, J., Berger, J., Dawid, A., Smith, A. (Eds): Bayesian Statistics. Oxford University Press, London.

Goldberg, S., Kabengi, N.J., 2010. Bromide adsorption by reference minerals and soils. Vadose Zone J., 9, 780–786.

Hastings, W. K., 1970. Monte Carlo Sampling Methods Using Markov Chains and Their Applications, Biometrika, 57, 97–109.

Hosseini, A.H., Deutsch, C.V., Mendoza, C.A., Biggar, K.W., 2011. Inverse modeling for characterization of uncertainty in transport parameters under uncertainty of source geometry in heterogeneous aquifers. J Hydrol., 405, 3–4, 402–416.

Kaipio, J., Somersalo, E., 2004. Statistical and Computational Inverse Problems. Applied Mathematical Sciences 160, Springer-Verlag.

Kaipio, J., Somersalo, E., 2007. Statistical inverse problems: discretization, model reduction and inverse crimes. J. Comp. Appl. Math, 198, 493–504.

Kohne, J., Mohanty, B., Simunek, J., 2006. Inverse dual-permeability modeling of preferential water flow in a soil column and implications for field-scale solute transport. Vadose Zone J., 5, 59–76.

Kool, J.B., Parker J.C., van Genuchten, M.T., 1985. Determining soil hydraulic properties from one-step outflow experiments by parameter estimation, I. Theory and numerical studies. Soil Sci. Soc. Am. J., 49, 1348–1354.

Laloy, E., Weynants, M., Bielders, C.L., Vanclooster, M., Javaux, M., 2010. How efficient are one-dimensional models to reproduce the hydrodynamic behavior of structured soils subjected to multi-step outflow experiments. J. Hydrol., 393, 1–2, 37–52, doi: 10.1016/j.jhydrol.2010.02.017.

Lee, P., 2004. Bayesian Statistics. Oxford University Press, London.

Leij, F.J., Russell, W.B., Lesch, S.M., 1997. Closed-form expressions for water retention and conductivity data. Groundwater, 35, 5, 848–858.

Li, L., Zhou, H., Gómez-Hernández, J.J., Franssen, H.J.H., 2012. Jointly mapping hydraulic conductivity and porosity by assimilating concentration data via ensemble Kalman filter. J. Hydrol., 428–429, 152–169.

Maraqa, M.A., Wallace, R.B., Voice, T.C., 1997. Effect of degree of saturation on dispersivity and immobile water in sandy columns. J. Contam. Hydrol., 25, 199–218.

Melamed, R., Jurinak, J.J., Dudley, L.M., 1994. Anion exclusion – pore water velocity interaction affecting transport of bromine through an Oxisol. Soil Sci. Soc. Am. J., 58, 1405–1410.

Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A., Teller, E., 1953. Equation of state calculation by fast computing machines. J. Chemical Phys., 21, 1087–1092.

Miller, C.T., Dawson, C.N., Farthing, M.W., Hou, T.Y., Huang, J., Kees, C.E., Kelley, C.T., Langtangen, H.P., 2013. Numerical simulation of water resources problems: Models, methods, and trends. Adv. Water Resour., 51, 405–437.

Nkedi-Kizza, P., Biggar, J.W., Selim, H.M., van Genuchten, M.Th., Wierenga, P.J., Davidson, J.M., Nielsen, D.R., 1984. On the equivalence of two conceptual models for describing ion exchange during transport through an aggregated oxisol. Water Resour. Res., 20, 8, 1123–1130.

Orlande, H.R.B., van Genuchten, M.Th., Cotta, R.M., Moreira, P.H., 2009. Bayesian estimation of hydraulic and solute transport parameters from laboratory soil column experiments. In: Proc. Int. Symp. Convective heat and mass transfer in sustainable energy, Hammamet, Tunisia, 20 p.

Özisik, M.N., Orlande, H.R.B., 2000. Inverse Heat Transfer: Fundamentals and Applications. Taylor and Francis, New York.

Parker, J.C., Kool, J.B., van Genuchten, M.Th., 1985. Determining soil hydraulic properties from one-step outflow experiments by parameter estimation. II. Experimental studies. Soil Sci Soc. Am. J., 49, 1354–1359.

Raithby, G.D., Torrance, K.E., 1974. Upstream-weighted differencing scheme and their application to elliptic problems involving fluid flow. Computers & Fluids, 2, 191–206.

Schaap, M.G., Leij, F.J., van Genuchten, M.Th., 2001. Rosetta: A computer program for estimating hydraulic parameters with hierarchical pedotransfer functions. J Hydrol., 251, 163–176.

Si, B.C., Kachanoski, R.G., 2000. Estimating soil hydraulic properties during constant flux infiltration: Inverse procedures. Soil Sci. Soc. Am. J., 64, 2, 439–449.

Šimůnek, J., Jarvis, N., van Genuchten, M.Th., Gardenas, A., 2003. Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone. J. Hydrol., 272, 14–35.

Šimůnek J., Bradford S.A., 2008. Vadose zone modeling: Introduction and importance. Vadose Zone J., 7, 2, 581–586.

Šimůnek, J., Šejna, M., Saito, H., Sakai, M., van Genuchten, M. Th., 2013. The HYDRUS-1D Software Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media, Version 4.16, HYDRUS Software Series 3, Department of Environmental Sciences, University of California Riverside, Riverside, California, USA, 340 p. (http://www.pc-progress.com/Downloads/Pgm_hydrus1D/HYDRUS1D-4.16.pdf).

Shackelford, C.D., 1991. Laboratory diffusion testing for waste disposal – A review. J. Contam. Hydrol., 7, 177–217.

Sommer, R., Fölster, H., Vielhauer, K., Maklouf, E.J., Vlek, P.J.G., 2003. Deep soil water dynamics and depletion by secondary vegetation in the Eastern Amazon. Soil Sci. Soc. Am. J., 67, 1672–1686.

Spohrer, K., Herrmann, L., Ingwersen, J., Stahr, K., 2006. Applicability of uni- and bimodal retention functions for water flow modeling in a tropical Acrisol. Vadose Zone J., 5, 48–58.

Tan, S., Fox, C., Nicholls, G., 2006. Inverse Problems. Course Notes for Physics 707. University of Auckland, Auckland.

van Genuchten, M.Th., Wierenga, P.J., 1976. Mass transfer studies in sorbing porous media, I. Analytical solutions. Soil Sci. Soc. Am. J., 40, 4, 473–480.

van Genuchten, M.Th., 1978. Calculating the unsaturated hydraulic conductivity with a new closed-form analytical model. Hydrology Document Number 412. Department of Civil Engeneering, Princeton University, Princeton, New Jersey, USA.

van Genuchten, M.Th., 1980. A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J., 44, 5, 892–898.

van Genuchten, M.Th., Nielsen, D.R., 1985. On describing and predicting the hydraulic properties of unsaturated soils. Annales Geophysicae, 3, 5, 615-628.

Vrugt, J.A., Gupta, H.V., Dekker, S.C., Sorooshian, S., Wagener, T., Bouten, W., 2006. Application of stochastic parameter optimization to the Sacramento soil moisture accounting model. J. Hydrol., 325, 288–307.

Vrugt, J.A., ter Braak, C.J.F., Diks, C.D.H., Schoups, G., 2013. Hydraulic data assimilation using particle Markov chain Monte Carlo simulation: Theory, concepts and applications. Adv. Water Res., 51, 457–478.

Xu, T., Gómez-Hernández, J.J., Zhou, H., Li, L., 2013. The power of transient piezometric head data in inverse modeling: An application of the localized normal-score EnKF with covariance inflation in a heterogenous bimodal hydraulic conductivity field. Adv. Water Res., 53, 100–118.

Yates, S.R., van Genuchten, M.Th., Warrick, A.W., Leij, F.J., 1992. Analysis of measured, predicted, and estimated hydraulic conductivity using the RETC computer program. Soil Sci. Soc. Am. J., 56, 2, 347–354.

Zhou, H., Gómez-Hernández, J.J., Franssen, H.J.H., Li, L., 2011. An approach to handling non-Gaussianity of parameters and state variables in ensemble Kalman filtering. Adv. Water Res., 34, 7, 844–864.

Journal of Hydrology and Hydromechanics

The Journal of Institute of Hydrology SAS Bratislava and Institute of Hydrodynamics CAS Prague

Journal Information


IMPACT FACTOR 2017: 1.714
5-year IMPACT FACTOR: 1.639



CiteScore 2017: 1.91

SCImago Journal Rank (SJR) 2017: 0.599
Source Normalized Impact per Paper (SNIP) 2017: 1.084

Cited By

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 213 213 39
PDF Downloads 90 90 18