Inverse modeling of vadose zone flow processes using squared ε-insensitivity loss function

BROOKS R. H., COREY A. T., 1964: Hydraulic properties of porous media, Colorado State University, Fort Collins.Search in Google Scholar

DIRKSEN C., 1991: Unsaturated hydraulic conductivity. In Smith, K. A., and C. E. Mullins, Soil analysis: physical methods. Marcel Dekker, New York. p. 209-269.Search in Google Scholar

ECHING S. O., HOPMANS J. W., 1993: Optimization of hydraulic functions from transient outflow and soil water pressure data. Soil Science Society of America J., 57, 5, 1167-1175.10.2136/sssaj1993.03615995005700050001xSearch in Google Scholar

FINSTERLE S., NAJITA J., 1998: Robust estimation of hydrologic model parameters. Water Resour. Res., 34, 11, 2939-2947.10.1029/98WR02174Search in Google Scholar

GARDNER W. R., 1958: Some steady state solutions of unsaturated moisture flow equations with applications to evaporation from a water table. Soil Sci. Society of Amer. J., 85, 228-232.10.1097/00010694-195804000-00006Search in Google Scholar

HASTIE T., TIBSHIRANI R., FRIEDMAN J., 2001: The Elements of Statistical Learning: Data Mining, Inference and Prediction. Springer, New York.10.1007/978-0-387-21606-5Search in Google Scholar

HOPMANS J. W., CLAUSNITZER V., KOSUGI K. I., NIELSEN D. R., SOMMA F., 1997: Vadose zone measurement and modeling. Sci. agric. (Piracicaba, Braz.), 54, 22-26, ISSN 0103-9016.10.1590/S0103-90161997000300004Search in Google Scholar

HOPMANS J. W., ŠIMŮNEK J., ROMANO N., DURNER W., 2002: Inverse Modeling of Transient Water Flow, In: Methods of Soil Analysis, Part 1, Physical Methods, Chapter 3.6.2, Eds. J. H. Dane and G. C. Topp, Third edition, SSSA, Madison, WI, 963-1008.Search in Google Scholar

JURY W. A., GARDNER W. R., GARDNER W. H., 1991: Soil physics. 5th ed. John Wiley and Sons, New York.Search in Google Scholar

KECMAN V., 2001: Learning and Soft Computing, SVM, NN, and FLS. The MIT Press, Cambridge, MA. URL: http://support-vector.ws http://support-vector.wsSearch in Google Scholar

KLUTE A., DIRKSEN C., 1986: Conductivities and diffusivities of unsaturated soils. In: A. Klute (ed.). Methods of soil analysis. Part 1. 2nd ed. Agronomy Monograph 9, ASA and SSSA, Madision, WI. p. 687-734.Search in Google Scholar

KOOL J. B., PARKER J. C., 1987: Estimating soil hydraulic functions from transient flow experiments: SFIT User's Guide. Soil and Environmental Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA.Search in Google Scholar

KOOL J. B., PARKER J. C., VAN GENUCHTEN M.TH., 1985: Determining soil hydraulic properties for one-step outflow experiments by parameter estimation. I. Theory and numerical studies. Soil Sci. Society of Amer. J., 49, 1348-1354.10.2136/sssaj1985.03615995004900060004xSearch in Google Scholar

KWOK J. T., TSANG I. W., 2003: Linear Dependency between ε and the Input Noise in ε-Support Vector Regression. IEEE Transactions on Neural Networks, 14, 3, 544-553.10.1109/TNN.2003.81060418238038Search in Google Scholar

LEIJ F. J., RUSSELL W. B., LESCH S. M., 1997: Closed-form expressions for water retention and conductivity data, Groundwater, 35, 848-858.10.1111/j.1745-6584.1997.tb00153.xSearch in Google Scholar

MARQUARDT D. W., 1963: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. Ind. Appl. Math., 11, 431-441.10.1137/0111030Search in Google Scholar

MUALEM Y., 1976: New Model for Predicting Hydraulic Conductivity of Unsaturated Porous-Media. Wat. Resour. Res., 12, 3, 513-522.10.1029/WR012i003p00513Search in Google Scholar

PRUESS K., 2004: The TOUGH codes-A family of simulation tools for multiphase flow and transport processes in permeable media. Vadose Zone J., 3, 738-746.10.2113/3.3.738Search in Google Scholar

RICHARDS L. A., 1931: Capillary conduction of liquids through porous media. Physics, 1, 318-333.10.1063/1.1745010Search in Google Scholar

ROTH K., SCHULIN R., FLÜHLER H., ATTINGER W., 1990: Calibration of Time Domain Reflectometry for Water Content Measurement Using a Composite Dielectric Approach. Water Resources Research, 26, 10, 2267-2273.10.1029/WR026i010p02267Search in Google Scholar

ŠIMŮNEK J., VAN GENUCHTEN M.TH., 1996: Estimating unsaturated soil hydraulic properties from tension disc infiltrometer data by numerical inversion. Wat. Resour. Res., 32, 9, 2683-2696.10.1029/96WR01525Search in Google Scholar

ŠIMŮNEK J., HOPMANS J. W., 2002: Parameter Optimization and Nonlinear Fitting. In: Methods of Soil Analysis, Part 1, Physical Methods, Chapter 1.7, Eds. J. H. Dane and G. C. Topp, Third edition, SSSA, Madison, WI, 139-157.10.2136/sssabookser5.4.c7Search in Google Scholar

ŠIMŮNEK J., VAN GENUCHTEN M.TH., ŠEJNA M., 2005: The HYDRUS-1D Software Package for Simulating the Movement of Water, Heat, and Multiple Solutes in Variably Saturated Media, Version 3.0, Department of Environmental Sciences, University of California Riverside, Riverside, CA, pp. 270.Search in Google Scholar

ŠIMŮNEK J., VAN GENUCHTEN M.TH., ŠEJNA M., 2008: Development and applications of the HYDRUS and STANMOD software packages, and related codes, Vadose Zone Journal, doi: 10.2136/VZJ2007.0077, Special Issue "Vadose Zone Modeling", 7, 2, 587-600.Search in Google Scholar

SMOLA A. J., MURATA N., SCHOLKOPF B., MULLER K. R., 1998: Asymptotically optimal choice of - loss for support vector machines. In Proceedings, Intl. Conf. on Artificial Neural Networks (ICANN'98), 1, 105-110.10.1007/978-1-4471-1599-1_11Search in Google Scholar

VACHAUD G., 1968: Contribution to the study of flow problems in unsaturated porous media. Theses presented at the Scholl in Physical Sciences of the Univ. of Grenoble, Grenoble, France, Catalog Number: A. O.2655, pp. 259.Search in Google Scholar

VAN DAM J. C., STRICKER J. N. M., DROOGERS P., 1994: Inverse method for determining soil hydraulic functions from multi-step outflow experiments. Soil Sci. Soc. Amer. J., 58, 647-652.10.2136/sssaj1994.03615995005800030002xSearch in Google Scholar

VAN GENUCHTEN M.TH., 1980: A Closed-Form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Sci. Society of Amer. J., 44, 5, 892-898.10.2136/sssaj1980.03615995004400050002xSearch in Google Scholar

VAPNIK V. N., 1995: The Nature of Statistical Learning Theory, Springer Verlag, New York.10.1007/978-1-4757-2440-0Search in Google Scholar

VOGEL T., HUANG K., ZHANG R., VAN GENUCHTEN M.TH., 1996: The HYDRUS code for simulating one-dimensional water flow, solute transport, and heat movement in variably-saturated media, Version 5.0, Research Report No. 140, U. S. Salinity laboratory, USDA, ARS, Riverside, CA.Search in Google Scholar

VRUGT J. A., DIKS C. G. H., GUPTA H. V., BOUTEN W., VERSTRATEN J. M., 2005: Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation. Wat. Resour. Res., 41, W01017, doi: 10.1029/2004WR003059.10.1029/2004WR003059Search in Google Scholar

VRUGT J. A., STAUFFER P. H., WÖHLING T., ROBINSON B. A. VESSELINOV V. V., 2008: Inverse modeling of sub-surface flow and transport properties: A review with new developments. Vadose Zone J., doi:10.2136/VZJ2007.0078, Special Issue "Vadose Zone Modeling", 7, 2, 843-864.Search in Google Scholar

YEH W. G., 1986: Review of parameter identification procedures in groundwater hydrology: The inverse problem. Wat. Resour. Res., 22, 2, 95-108.10.1029/WR022i002p00095Search in Google Scholar