Multiresponse multilayer vadose zone model calibration using Markov chain Monte Carlo simulation and field water retention data

Water Resources Research

Volumn 47, Issue 4, 2011, Pages

  Wöhling, Thomas ^a,b   Vrugt, Jasper A ^c,d,e  

^a RUAKURA RESEARCH CENTRE   (New Zealand)

^b UNIVERSITY OF TÜBINGEN   (Germany)

^c University of California at Irvine   (United States)

^d UNIVERSITY OF AMSTERDAM   (Netherlands)

^e LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOREGRESSIVE ERROR MODEL; BAYESIAN FRAMEWORKS; DATA TYPE; DIFFERENTIAL EVOLUTION; EVOLUTIONARY SEARCH ALGORITHMS; HOMOGENEOUS MEDIUM; HYDRAULIC PARAMETERS; HYDRUS-1D; IN-SITU MEASUREMENT; INVERSE MODELING; LIKELIHOOD FUNCTIONS; MARKOV CHAIN MONTE CARLO; MARKOV CHAIN MONTE CARLO SIMULATION; MULTILAYER MODELS; MULTIPLE DATA TYPES; MULTIPLE OBJECTIVES; MULTIRESPONSE; NEW ZEALAND; PARAMETER ESTIMATION ALGORITHM; POSTERIOR PROBABILITY; PREDICTION UNCERTAINTY; PREDICTIVE UNCERTAINTY; PRESSURE HEADS; SOIL HYDRAULIC PARAMETERS; SOIL HYDRAULICS; SPATIAL SCALE; SPATIAL VARIABILITY; STATISTICAL PROPERTIES; VADOSE ZONE; VOLUMETRIC WATER CONTENT; WATER RETENTION;

CALIBRATION; COMPUTER SIMULATION; ERROR STATISTICS; EVOLUTIONARY ALGORITHMS; GROUNDWATER; HYDRAULIC CONDUCTIVITY; INVERSE PROBLEMS; MARKOV PROCESSES; MONTE CARLO METHODS; MULTILAYERS; PROBABILITY; PROBABILITY DENSITY FUNCTION; WATER CONTENT;

PARAMETER ESTIMATION;

BAYESIAN ANALYSIS; DECADAL VARIATION; HYDRAULIC CONDUCTIVITY; MARKOV CHAIN; MODEL VALIDATION; MONTE CARLO ANALYSIS; RETENTION; RICHARDS EQUATION; SPATIAL VARIATION; VADOSE ZONE; WATER CONTENT;

NEW ZEALAND;

EID: 79952028458     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2010WR009265     Document Type: Article

References (78)

1. Abbasi, F., D. Jacques, J.Šimůnek, J. Feyen, and M. T. van Genuchten (2003a), Inverse estimation of soil hydraulic and solute transport parameters from transient field experiments: Heterogeneous soil, Trans. ASAE, 46, 1097-1111. (Pubitemid 37358468)
2. Abbasi, F., J.Šimůnek, J. Feyen, P. J. Shouse, and M. T. van Genuchten (2003b), Simultaneous inverse estimation of soil hydraulic and transport parameters from transient field experiments: homogeneous soil, Trans. ASAE, 46, 1085-1093.
3. Abbaspour, K., R. Kasteel, and R. Schulin (2000), Inverse parameter estimation in a layered unsaturated field soil, Soil Sci., 165, 109-123. (Pubitemid 30149744)
4. Allen, R. G., L. S. Pereira, D. Raes, and M. Smith (1998), Crop evapotranspiration, FAO Irr. Drainage Pap. 56, Food and Agric. Org., Rome, Italy.
5. American Society of Civil Engineering (1993), Task committee on definition of watershed models of the watershed management committee, Irrigation and drainage division: Criteria for evaluation of watershed models, J. Irrig. Drain.Eng., 119, 429-442.
6. Beven, K. J., and J. Freer (2001), Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology, J. Hydrol., 249, 11-29. (Pubitemid 32664993)
7. Bitterlich, S., W. Durner, S. C. Iden, and P. Knabner (2004), Inverse estimation of the unsaturated soil hydraulic properties from column outflow experiments using free-form parameterizations, Vadose Zone J., 3, 971-981.
8. Botros, F. E., T. Harter, Y. S. Onsoy, A. Tuli, and J. W. Hopmans (2009), Spatial variability of hydraulic properties and sediment characteristics in a deep alluvial unsaturated zone, Vadose Zone J., 8, 276-289.
9. Box, G. E. P., and G. C. Tiao (1992), Bayesian Inference in Statistical Analysis, 908 pp., John Wiley, New York.
10. Celia, M. A., E. T. Bouloutas, and R. L. Zarba (1990), A general mass-conservative numerical solution for the unsaturated flow equation, Water Resour. Res., 26, 1483-1496, doi:10.1029/WR026i007p01483.
11. Coppola, A. (2000), Unimodal and bimodal descriptions of hydraulic properties for aggregated soils, Soil Sci. Soc. Am. J., 64, 1252-1262.
12. Dane, J. H., and J. W. Hopmans (2002), Water retention and storage- Laboratory methods, in Methods of Soil Analysis, Part 4, Physical Methods, edited by J. H. Dane and G. C. Topp, pp. 675- 720, Soil Sci. Soc. of Am., Madison, Wis.
13. Dane, J. H., and S. Hruska (1983), In-situ determination of soil hydraulic properties during drainage, Soil Sci. Soc. Am. J., 47, 619-624.
14. Deb, K. (2001), Multi-objective optimization using evolutionary algorithms, 518 pp., John Wiley, Chicester, UK.
15. Doherty, J. (2009), PEST, model-independent parameter estimation, in Watermark Numerical Computing, 5th ed., 336 pp., Brisbane, Australia.
16. Durner, W. (1994), Hydraulic conductivity estimation for soils with heterogeneous pore structure, Water Resour. Res., 30, 211-223, doi:10.1029/ 93WR02676.
17. Eching, S. O., and J. W. Hopmans (1993), Optimization of hydraulic functions from transient outflow and soil water pressure data, Soil Sci. Soc. Am. J., 57, 1167-1175. (Pubitemid 24403398)
18. El Adlouni, S., A.-C. Favre, and B. Bobée (2006), Comparison of methodologies to assess the convergence of Markov chain Monte Carlo methods, Comput. Stat. Data Anal., 50, 2685-2701. (Pubitemid 44389653)
19. Feddes, R. A., P. Kowalik, and H. Zaradny (1978), Simulation of Field Water Use and Crop Yield, 310 pp., PUDOC, Wageningen, Netherlands.
20. Figueras, J., and M. M. Gribb (2009), Design of a user-friendly automated multistep outflow apparatus, Vadose Zone J., 8, 523-529.
21. Gallagher, M., and J. Doherty (2007), Parameter estimation and uncertainty analysis for a watershed model, Environ. Model. Software, 22, 1000-1020. (Pubitemid 46209835)
22. Gelman, A., and D. B. Rubin (1992), Inference from iterative simulation using multiple sequences, Stat. Sci., 7, 457-472.
23. Gupta, H. V., S. Sorooshian, and P. O. Yapo (1998), Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information, Water Resour. Res., 34, 751-764, doi:10.1029/ 97WR03495.
24. Hall, J. M. (2001), How well does your model fit the data?, J. Hydroinf., 3, 49-55.
25. Hopmans, J. W., J.Šimůnek, N. Romano, and W. Durner (2002), Simultaneous determination of water transmission and retention properties: Inverse methods, in Methods of Soil Analysis, Part 4, Physical Methods, edited by J. H. Dane and G. C. Topp, pp. 963-1008, Soil Sci. Soc. of Am., Madison, Wis.
26. Huisman, J. A., J. Rings, J. A. Vrugt, J. Sorg, and H. Vereecken (2010), Hydraulic properties of a model dike from coupled Bayesian and multi-criteria hydrogeophysical inversion, J. Hydrol., 380, 62-73.
27. Iman, R. L. (1999), Latin hypercube sampling, in Encyclopedia of Statistical Sciences, vol. 3, pp. 408- 411, John Wiley, New York.
28. Inoue, M., J.Šimů nek, J. W. Hopmans, and V. Clausnitzer (1998), In situ estimation of soil hydraulic functions using a multistep soil-water extraction technique, Water Resour. Res., 34, 1035-1050, doi:10.1029/ 98WR00295.
29. Jacques, D., J.Šimůnek, A. Timmerman, and J. Feyen (2002), Calibration of Richards' and convection-dispersion equations to field-scale water flow and solute transport under rainfall conditions, J. Hydrol., 259, 15-31. (Pubitemid 34175763)
30. Kelleners, T. J., R. W. O. Soppe, J. E. Ayars, J.Šimůnek, and T. H. Skaggs (2005), Inverse analysis of upward water flow in a groundwater table lysimeter, Vadose Zone J., 4, 558-572.
31. Kendall, M., and J. K. Ord (1990), Time series analysis, 3rd ed., 320 pp., Edward Arnold, London, U.K.
32. Köhne, J. M., S. Köhne, and H. H. Gerke (2002), Estimating the hydraulic functions of dual-permeability models from bulk soil data, Water Resour. Res., 38(7), 1121, doi:10.1029/2001WR000492.
33. Köhne, J. M., B. P. Mohanty, and J.Šimůnek (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. (Pubitemid 47254009)
34. Mertens, J., R. Stenger, and G. F. Barkle (2006), Multiobjective inverse modeling for soil parameter estimation and model verification, Vadose Zone J., 5, 917-933. (Pubitemid 47253973)
35. Mirus, B. B., K. S. Perkins, J. R. Nimmo, and K. Singha (2009), Hydrologic characterization of desert soils with varying degrees of pedogenesis: 2. Inverse modeling for effective properties, Vadose Zone J., 8, 496-509.
36. Mualem, Y. (1976), A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 12, 513-522, doi:10.1029/WR012i003p00513.
37. Mualem, Y. (1978), Hydraulic conductivity of unsaturated porous media: Generalized macroscopic approach, Water Resour. Res., 14, 325-334, doi:10.1029/WR014i002p00325. (Pubitemid 8602494)
38. Musters, P. A. D., and W. Bouten (1999), Assessing rooting depths of an Austrian pine stand by inverse modeling soil water content maps, Water Resour. Res., 35, 3041-3048, doi:10.1029/1999WR900173. (Pubitemid 29461968)
39. Musters, P. A. D., and W. Bouten (2000), A method for identifying optimum strategies of measuring soil water contents for calibrating a root water uptake model, J. Hydrol., 227, 273-286. (Pubitemid 30104932)
40. Peters, A., and W. Durner (2006), Improved estimation of soil water retention characteristics from hydrostatic column experiments, Water Resour. Res., 42, W11401, doi:10.1029/2006WR004952. (Pubitemid 46134873)
41. Puhlmann, H., K. von Wilpert, M. Lukes, and W. Dröge (2009), Multistep outflow experiments to derive a soil hydraulic database for forest soils, Eur. J. Soil Sci., 60, 792-806.
42. Raftery, A. E., and S. Lewis (1992), Bayesian Statistics 4, How many Iterations in the Gibbs Sampler?, Oxford Univ. Press, Oxford, U.K.
43. Richards, L. A. (1931), Capillary conduction of liquids through porous media, Physics, 1, 318-333.
44. Ritter, A., F. Hupet, R. Muoz-Carpena, S. Lambot, and M. Vanclooster (2003), Using inverse methods for estimating soil hydraulic properties from field data as an alternative to direct methods, Agric. Water Manage., 59, 77-96. (Pubitemid 36325878)
45. Romano, N., and A. Santini (1999), Determining soil hydraulic functions from evaporation experiments by a parameter estimation approach: Experimental verifications and numerical studies, Water Resour. Res., 35, 3343-3359, doi:10.1029/1999WR900155. (Pubitemid 29514608)
46. Schaap, M. G., and F. J. Leij (2000), Improved prediction of unsaturated hydraulic conductivity wth the Mualem-van Genuchten model, Soil Sci. Soc. Am. J., 64, 843-851. (Pubitemid 30416599)
47. Schoups, G., and J. A. Vrugt (2010), A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic and non-Gaussian errors, Water Resour. Res., 46, W10531, doi:10.1029/2009WR008933.
48. Schoups, G., J. A. Vrugt, F. Fenicia, and N. C. van de Giesen (2010), Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models, Water Resour. Res., 46, W10530, doi:10.1029/2009WR008648.
49. Scott, R. L., W. J. Shuttleworth, T. O. Keefer, and A. W. Warrick (2000), Modeling multiyear observations of soil moisture recharge in the semiarid American Southwest, Water Resour. Res., 36, 2233-2248, doi:10.1029/2000WR900116.
50. Šimůnek, J., M.Šejna, and M. T. van Genuchten (1996), HYDRUS-2D, Simulating water flow and solute transport in two-dimensional variably saturated media, version 1.0, User manual, IGWMC-TPS 53 International Ground Water Modeling Center, Colo. School of Mines, Boulder, Colo.
51. Šimůnek, J., O. Wendroth, and M. T. van Genuchten (1998), Parameter estimation analysis of the evaporation method for determining soil hydraulic properties, Soil Sci. Soc. Am. J., 62, 894-905. (Pubitemid 28403919)
52. Šimůnek, J., N. J. Jarvis, M. T. van Genuchten, and A. Gärdenäs (2003), Review and comparison of models for describing non-equilibrium and preferential flow and transport in the vadose zone, J. Hydrol., 272, 14-35. (Pubitemid 36224735)
53. Šimůnek, J., M. T. van Genuchten, and M.Šejna (2005), The HYDRUS-1D software package for simulating the one-dimensional movement of water, heat, and multiple solutes in variably-saturated media, Version 3.0, Dep. of Environ. Sci., Univ. of Calif., Riverside, Calif.
54. Stenger, R., T. Wöhling, G. F. Barkle, and A. Wall (2007), Relationship between dielectric permittivity and water content for vadose zone materials of volcanic origin, Aust. J. Soil Res., 45, 299-309. (Pubitemid 47014219)
55. Tang, Y., P. Reed, and T. Wagener (2006), How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration?, Hydrol. Earth Syst. Sci., 10, 289-307. (Pubitemid 44877445)
56. ter Braak, C. J. F. (2006), A Markov chain Monte Carlo version of the genetic algorithm differential evolution: Easy Bayesian computing for real parameter spaces, Statist. Comput., 16, 239-249. (Pubitemid 43992692)
57. ter Braak, C. J. F. and J. A. Vrugt (2008), Differential evolutionMarkov chain with snooker updater and fewer chains, Statist. Comput., 18, 435-446.
58. Tonkin, M., and J. Doherty (2009), Calibration-constrained Monte Carlo analysis of highly parameterized models using subspace techniques, Water Resour. Res., 45, W00B10, doi:10.1029/2007WR006678.
59. van Genuchten, M. T. (1980), A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892-898.
60. van Genuchten, M. T., and F. J. Leij (1989), Indirect methods for estimating the hydraulic properties of unaturated soils, in Proceedings of the International Workshop on Indirect Methods for Estimating the Hydraulic Properties of Unsaturated Soils, Riverside, Calif., October 11-13.
61. Verbist, K., W. M. Cornelis, D. Gabriels, K. Alaerts, and G. Soto (2009), Using an inverse modelling approach to evaluate the water retention in a simple water harvesting technique, Hydrol. Earth Syst. Sci., 13, 1979-1992.
62. Vereecken, H., J. A. Huisman, H. Bogena, J. Vanderborght, J. A. Vrugt, and J. W. Hopmans (2008), On the value of soil moisture measurements in vadose zone hydrology: A review, Water Resour. Res., 44, W00D06, doi:10.1029/ 2008WR006829.
63. Vogel, H. J., A. Samouelian, and O. Ippisch (2008), Multi-step and twostep experiments in heterogeneous porous media to evaluate the relevance of dynamic effects, Adv. Water Resour., 31, 181-188. (Pubitemid 350103066)
64. Vrugt, J. A., and B. A. Robinson (2007), Improved evolutionary optimization from genetically adaptive multimethod search, Proc. Natl. Acad. Sci. U. S. A., 104, 708-711. (Pubitemid 46154674)
65. Vrugt, J. A., W. Bouten, and A. H. Weerts (2001), Information content of data for identifying soil hydraulic parameters from outflow experiments, Soil Sci. Soc. Am. J., 65, 19-27. (Pubitemid 32169766)
66. Vrugt, J. A., B. O. Nuallain, B. A. Robinson, W. Bouten, S. C. Decker, and P. M. A. Sloot (2006), Application of parallel computing to stochastic parameter estimation in environmental models, Comput. Geosci., 32, 1139-1155. (Pubitemid 44111825)
67. Vrugt, J. A., P. H. Stauffer, Th. Wöhling, B. A. Robinson, and V. V. Vesselinov (2008a), Inverse modeling of subsurface flow and transport properties: A review with new developments, Vadose Zone J., 7, 843-864.
68. Vrugt, J. A., C. J. F. ter Braak, M. P. Clark, J. M. Hyman, and B. A. Robinson (2008b), Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation, Water Resour. Res., 44, W00B09, doi:10.1029/2007WR006720.
69. Vrugt, J. A., C. J. F. ter Braak, C. G. H. Diks, B. A. Robinson, J. M. Hyman, and D. Higdon (2009), Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling, Int. J. Nonlinear Sci. Num. Sim., 10, 271-288.
70. Wesseling, J. G., J. A. Elbers, P. Kabat, and B. J. van den Broek (1991), SWATRE: Instructions for input, Technical report, Winand Staring Centre, Wageningen, Netherlands.
71. Wöhling, T. (2009), Does vadose zone forecasting depend on the type of calibration data?, in 18th World IMACS Congress and MODSIM09 International Congress on Modelling and Simulation, edited by R. S. Anderssen, R. D. Braddock, and L. T. H. Newham, pp. 2377- 2383, Model. and Simul. Soc. of Australia and N. Z. and Int. Assoc. for Math. and Comp. in Simul., Cairns, Australia.
72. Wöhling, T. and J. A. Vrugt (2008), Combining multiobjective optimization and Bayesian model averaging to calibrate forecast ensembles of soil hydraulic models, Water Resour. Res., 44, W12432, doi:10.1029/ 2008WR007154.
73. Wöhling, T., J. A. Vrugt, and G. F. Barkle (2008), Comparison of three multiobjective algorithms for inverse modeling of vadose zone hydraulic properties, Soil Sci. Soc. Am. J., 72, 305-319. (Pubitemid 351399322)
74. Wöhling, T., N. Schütze, B. Heinrich, J.Šimůnek, and G. B. Barkle (2009), Three-dimensional modeling of multiple Automated Equilibrium Tension Lysimeters to measure vadose zone fluxes, Vadose Zone J., 8, 1051-1063.
75. Wollschläger, U., T. Pfaff, and K. Roth (2009), Field-scale apparent hydraulic parameterisation obtained from TDR time series and inverse modelling, Hydrol. Earth Syst. Sci., 13, 1953-1966.
76. Zhang, X., R. Srinivasan, K. Zhao, and M. V. Liew (2009), Evaluation of global optimization algorithms for parameter calibration of a computationally intensive hydrologic model, Hydrol. Processes, 23, 430-441.
77. Zhang, Z. F., A. L. Ward, and G. W. Gee (2003), Estimating soil hydraulic parameters of a field drainage experiment using inverse techniques, Vadose Zone J., 2, 201-211.
78. Zurmühl, T., and W. Durner (1998), Determination of parameters for bimodal hydraulic functions by inverse modeling, Soil Sci. Soc. Am. J., 62, 847-880.