Comparing nonlinear regression and markov chain monte carlo methods for assessment of prediction uncertainty in vadose zone modeling

Vadose Zone Journal

Volumn 11, Issue 4, 2012, Pages

  Shi, Xiaoqing ^a,c   Ye, Ming ^a   Finsterle, Stefan ^b   Wu, Jichun ^c  

^a FLORIDA STATE UNIVERSITY   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

^c NANJING UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BAYESIAN METHODS; BAYESIAN PREDICTIONS; CONFIDENCE INTERVAL; CREDIBLE INTERVAL; CROSS VALIDATION; DATA COLLECTION; DIFFERENTIAL EVOLUTION; MARKOV CHAIN MONTE CARLO; MARKOV CHAIN MONTE CARLO METHOD; MCMC METHOD; MODEL PREDICTION; NON-LINEAR REGRESSION; NON-LINEAR REGRESSION METHOD; PARAMETER ESTIMATE; PARAMETER SPACES; PERFORMANCE MEASURE; PREDICTION INTERVAL; PREDICTION UNCERTAINTY; PREDICTIVE CAPABILITIES; PREDICTIVE PERFORMANCE; PREDICTIVE UNCERTAINTY; UNCERTAINTY QUANTIFICATIONS; VADOSE ZONE MODELING;

BAYESIAN NETWORKS; DATA FUSION; EVOLUTIONARY ALGORITHMS; FORECASTING; GROUNDWATER; MONTE CARLO METHODS; PARAMETER ESTIMATION; REGRESSION ANALYSIS;

UNCERTAINTY ANALYSIS;

ALGORITHM; COMPARATIVE STUDY; COMPUTER SIMULATION; MARKOV CHAIN; MEASUREMENT METHOD; MONTE CARLO ANALYSIS; NONLINEARITY; PREDICTION; REGRESSION ANALYSIS; UNCERTAINTY ANALYSIS; VADOSE ZONE;

EID: 84866642544     PISSN: None     EISSN: 15391663     Source Type: Journal    
DOI: 10.2136/vzj2011.0147     Document Type: Article

References (73)

1. Abbaspour, K.C., C.A. Johnson, and M.T. van Genuchten. 2004. Estimating un-certain flow and transport parameters using a sequential uncertainty fiting procedure. Vadose Zone J. 3:1340-1352.
2. Abbaspour, K.C., R. Schulin, E. Schlappi, and H. Fluhler. 1996. A Bayesian ap-proach for incorporating uncertainty and data worth in environmental proj-ects. Environ. Model. Assess. 1:151-158. doi:10.1007/BF01874902.
3. Adams, B.M., W.J. Bohnhoff, K.R. Dalbey, J.P. Eddy, M.S. Eldred, D.M. Gay, K. Haskell, P.D. Hough, and L.P. Swiler. 2010. DAKOTA, A multilevel parallel object-oriented framework for design optimization, parameter estima-tion, uncertainty quantification, and sensitivity analysis. Sandia Tech. Rep. SAND2010-2183, December 2009. Sandia Natl. Lab.
4. Albuquerque, NM., Bates, D.M., and D.G. Watis. 1988. Nonlinear regression analysis and its appli-cations. John Wiley and Sons, New York.
5. Box, E.P., and G.C. Tiao. 1992. Bayesian inference in statistical analysis. Wiley, New York.
6. Carrera, J., and S.P. Neuman. 1986. Estimation of aquifer parameters under transient and steady state conditions: 1. Maximum likelihood method incor-porating prior information. Water Resour. Res. 22:199-210. doi:10.1029/WR022i002p00199.
7. Casella, G., and R.L. Berger. 2002. Statistical inference. 2nd ed. Duxbury Press, New York.
8. Chen, M.H., and Q.M. Shao. 1999. Monte Carlo estimation of Bayesian Credible and HPD intervals, J. Comput. Graphical Stat. 8:69-92.
9. Christensen, S., and R.L. Cooley. 1999. Evaluation of confidence intervals for a steady-state leaky aquifer model. Adv. Water Resour. 22:807-817. doi:10.1016/S0309-1708(98)00055-4.
10. Christensen, S., C. Moore, and J. Doherty. 2005. Comparison of stochastic and regression based methods for quantification of predictive uncertainty of model-simulated wellhead protection zones in heterogeneous aquifers. ModelCARE 2005, 5th Int. Conf. on Calibration and Reliability in Groundwa-ter Modelling-From Uncertainty to Decision Making, the Hague (Scheve-ningen), the Netherlands, 6-9 June 2005. p. 440-447.
11. Christensen, S., C. Moore, and J. Doherty. 2006. Comparison of stochastic and regression based methods for quantification of predictive uncertainty of model-simulated wellhead protection zones in heterogeneous aquifers. In: Calibration and reliability in groundwater modelling: From uncertainty to decision making. IAHS Publ. 304:202-208.
12. Cooley, R.L. 2004. A theory for modeling ground-water flow in heterogeneous media. Prof. Pap. 1679. U.S. Geol. Surv., Reston, VA.
13. Cooley, R.L., and R.L. Naff. 1990. Regression modeling of ground-water flow. In: USGS Techniques in Water-Resources Investigations, Book 3, Chapter B4, USGS, Reston, VA.
14. Cooley, R.L., and A.V. Vecchia. 1987. Calculation of nonlinear confidence and prediction intervals for groundwater flow models. Water Resour. Bull. 23:581-599. doi:10.1111/j.1752-1688.1987.tb00834.x.
15. Deng, H., M. Ye, M.G. Schaap, and R. Khaleel. 2009. Quantification of uncertainty in pedotransfer function-based parameter estimation for unsaturated flow modeling. Water Resour. Res. 45:W04409. doi:10.1029/2008WR007477.
16. Doherty, J. 2005. PEST: Software for model-independent parameter estimation, Watermark Numerical Computing, Australia.
17. Draper, N.R., and H. Smith. 1981. Applied regression analysis. 2nd ed. John Wi-ley and Sons, New York.
18. USEPA. 2002. Supplemental guidance for developing soil screening levels for superfund sites. Office of Emergency and Remedial Response, Washington, DC.
19. Feyen, L., and S.M. Gorelick. 2005. Framework to evaluate the worth of hy-draulic conductivity data for optimal groundwater resources manage-ment in ecologically sensitive areas. Water Resour. Res. 41:W03019. doi:10.1029/2003WR002901.
20. Finsterle, S. 1999. iTOUGH2 sample problems. Rep. LBNL-40042. Lawrence Berkeley National Laboratory, Berkeley, CA.
21. Finsterle, S. 2004. Multiphase inverse modeling: Review and iTOUGH2 applica-tions. Vadose Zone J. 3:747-762.
22. Finsterle, S. 2007. iTOUGH2 command reference, Rep. LBNL-40041. Lawrence Berkeley National Laboratory, Berkeley, CA.
23. Finsterle, S., and K. Pruess. 1995. Solving the estimation-identification problem in two-phase flow modeling. Water Resour. Res. 31:913-924. doi:10.1029/94WR03038.
24. Finsterle, S., and Y. Zhang. 2011. Solving iTOUGH2 simulation and optimiza-tion problems using the PEST protocol. Environ. Model. Softw. 26:959-968. doi:10.1016/j.envsoti.2011.02.008.
25. Gallagher, M., and J. Doherty. 2007. Parameter estimation and uncertainty analysis for a watershed model. Environ. Model. Softw. 22:1000-1020. doi:10.1016/j.envsoti.2006.06.007.
26. Gelman, A., and D.B. Rubin. 1992. Inference from iterative simulation using Multiple sequences. Stat. Sci. 7:457-511. doi:10.1214/ss/1177011136.
27. Gimmi, T., M. Schneebeli, H. Fluhler, H. Wydler, and T. Baer. 1997. Field-scale water transport in unsaturated crystalline rock. Water Resour. Res. 33:589-598. doi:10.1029/96WR03974.
28. Good, I.J. 1952. Rattonal decisions. J. R. Stat. Soc., B 14:107-114.
29. Hill, M.C., and C.R. Tiedeman. 2007. Effective calibration of ground water mod-els, with analysis of data, sensitivities, predictions, and uncertainty. John Wiley and Sons, New York.
30. Hou, Z., and Y. Rubin. 2005. On minimum relative entropy concepts and prior compatibility issues in vadose zone inverse and forward modeling. Water Resour. Res. 41:W12425. doi:10.1029/2005WR004082.
31. Huisman, J.A., J. Rings, J.A. Vrugt, J. Sorg, and H. Vereecken. 2010. Hydrau-lic properties of a model dike from coupled Bayesian and multicriteria hydrogeophysical inversion. J. Hydrol. 380:62-73. doi:10.1016/j.jhy-drol.2009.10.023.
32. Keating, E.H., J. Doherty, J.A. Vrugt, and Q. Kang. 2010. Optimization and uncertainty assessment of strongly nonlinear groundwater models with high parameter dimensionality. Water Resour. Res. 46:W10517. doi:10.1029/2009WR008584.
33. Laloy, E., D. Fasbender, and C.L. Bielders. 2010b. Parameter optimization and uncertainty analysis for plot-scale continuous modeling of runoffusing a formal Bayesian approach. J. Hydrol. 380(1-2):82-93. doi:10.1016/j.jhy-drol.2009.10.025.
34. Laloy, E., and J.A. Vrugt. 2012. High-dimensional posterior exploration of hydro-logic models using Multiple-try DREAM(ZS) and high-performance comput-ing. Water Resour. Res. 48:W01526. doi:10.1029/2011WR010608.
35. Laloy, E., M. Weynants, C.L. Bielders, M. Vanclooster, and M. Javaux. 2010a. How efficient are one-dimensional models to reproduce the hydrodynamic behavior of structured soils subjected to multi-step outflow experimentsti J. Hydrol. 393:37-52. doi:10.1016/j.jhydrol.2010.02.017.
36. Liu, S.Y., and T.-C.J. Yeh. 2004. An integrative approach for monitoring water movement in the vadose zone. Vadose Zone J. 3:681-692.
37. Lu, D., M. Ye, and M.C. Hill. 2012. Analysis of regression confidence intervals and Bayesian credible intervals for uncertainty quantification. Water Re-sour. Res., doi:10.1029/2011WR011289 (in press).
38. Lu, D., M. Ye, and S.P. Neuman. 2012. Dependence of Bayesian model selec-tion criteria and Fisher information matrix on sample size. Math. Geosci. 43(8):971-993. doi:10.1007/s11004-011-9359-0.
39. Luckner, L., M.Th. van Genuchten, and D. Nielsen. 1989. A consistent set of para-metric models for the two-phase flow of immiscible fluids in the subsurface. Water Resour. Res. 25:2187-2193. doi:10.1029/WR025i010p02187.
40. Marshall, L., D. Nott, and A. Sharma. 2004. A comparative study of Markov Chain Monte Carlo methods for conceptual rainfall-runoffmodeling. Water Resour. Res. 40:W02501. doi:10.1029/2003WR002378.
41. McClave, J.T., and T. Sincich. 2000. Statistics. 8th ed. Prentice Hall, Englewood Cliffs, NJ.
42. Meyer, P.D., M.L. Rockhold, and G.W. Gee. 1997. Uncertainty analysis of infiltra-tion and subsurface flow and transport for SDMP sites. NUREG/CR-6565, PNNL-11705. U.S. Nucl. Regul. Commiss., Office of Nucl. Regul. Res., Wash-ington, D.C.
43. Minasny, B., and D.J. Field. 2005. Estimating soil hydraulic properties and their uncertainty: The use of stochastic simulation in the inverse modeling of the evaporation method. Geoderma 126:277-290. doi:10.1016/j.geoder-ma.2004.09.015.
44. Morris, M.D. 1991. Factorial sampling plans for preliminary computational ex-periments. Technometrics 21:239-245.
45. Neuman, S.P., L. Xue, M. Ye, and D. Lu. 2011. Bayesian analysis of data-worth considering model and parameter uncertainty. Adv. Water Resour. 36:75-85. doi:10.1016/j.advwatres.2011.02.007.
46. Nowak, W., F.P.J. de Barros, and Y. Rubin. 2010. Bayesian geostatistical design: Task-driven optimal site investigation when the geostatistical model is un-certain. Water Resour. Res. 46:W03535. doi:10.1029/2009WR008312.
47. Pan, F., M. Ye, J.T. Zhu, Y.S. Wu, B.X. Hu, and Z.B. Yu. 2009a. Numerical evalua-tion of uncertainty in water retention parameters and effect on predictive uncertainty. Vadose Zone J. 8:158-166. doi:10.2136/vzj2008.0092.
48. Pan, F., M. Ye, J. Zhu, Y.S. Wu, B. Hu, and Z. Yu. 2009b. Incorporating layer-and local-scale heterogeneities in numerical simulation of unsaturated flow and tracer transport. J. Contam. Hydrol. 103(3-4):194-205. doi:10.1016/j.jconhyd.2008.10.012.
49. Pan, F., J.T. Zhu, M. Ye, Y.A. Pachepsky, and Y.S. Wu. 2011. Sensitivity analysis of unsaturated flow and contaminant transport with correlated parameters. J. Hydrol. 397:238-249. doi:10.1016/j.jhydrol.2010.11.045.
50. Poeter, E., M. Hill, E. Banta, S. Mehl, and S. Christensen. 2005. UCODE2005 and six other computer codes for universal sensitivity analysis, calibration, and uncertainty evaluation. U.S. Geological Survey, Reston, VA.
51. Pruess, K., C. Oldenburg, and G. Moridis. 1999. TOUGH2 user's guide, version 2.0, Rep. LBNL-43134, Lawrence Berkeley Natl. Lab., Berkeley, CA.
52. Schaap, M.G., F.J. Leij, and M.Th. van Genuchten. 2001. Rosetia: A comput-er program for estimating soil hydraulic parameters with hierarchical pedotransfer functions. J. Hydrol. 251:163-176. doi:10.1016/S0022-1694(01)00466-8.
53. Schoups, G., and J.A. Vrugt. 2010. A formal Likelihood function for param-eter and predictive inference of hydrologic models with correlated, het-eroscedastic and non-Gaussian errors. Water Resour. Res. 46:W10531. doi:10.1029/2009WR008933.
54. Seber, G.A.G., and C.J. Wild. 2003. Nonlinear regression. John Wiley and Sons, New York.
55. Shi, X., M. Ye, G. Curtis, et al. 2012. Assessment of parametric uncertainty for surface complexation models of uranium reactive transport modeling. Wa-ter Resour. Res.
56. ter Braak, C.J.F. 2006. A Markov Chain Monte Carlo version of the genetic al-gorithm differential evolution: Easy Bayesian computing for real parameter spaces. Stat Comput. 16:239-249.
57. van Genuchten, M.Th. 1980. A closed form equation for predicting the hy-draulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892-898. doi:10.2136/sssaj1980.03615995004400050002x.
58. Vecchia, A.V., and R.L. Cooley. 1987. Simultaneous confidence and predic-tion intervals for nonlinear-regression models with application to a groundwater-flow model. Water Resour. Res. 23:1237-1250. doi:10.1029/WR023i007p01237.
59. Volinsky, C.T., D. Madigan, A.E. Ratiery, and R.A. Kronmal. 1997. Bayesian model averaging in proportional hazard models: Assessing the risk of a stroke. J. R. Stat. Soc. Ser. C 46:433-448. doi:10.1111/1467-9876.00082
60. Vrugt, J.A., and W. Bouten. 2002. Validity of first-order approximations to de-scribe parameter uncertainty in soil hydrologic models. Soil Sci. Soc. Am. J. 66:1740-1751. doi:10.2136/sssaj2002.1740
61. Vrugt, J.A., B.A. Robinson, and J.M. Hyman. 2009b. Self-adaptive multimethod search for global optimization in real parameter spaces. IEEE Trans. Evol. Comput. 13:243-259. doi:10.1109/TEVC.2008.924428.
62. Vrugt, J.A., P.H. Stauffer, T. Wohling, B.A. Robinson, and V.V. Vesselinov. 2008. In-verse modeling of subsurface flow and transport properties: A review with new developments. Vadose Zone J. 7:843-864. doi:10.2136/vzj2007.0078.
63. Vrugt, J.A., C.J.F. ter Braak, C.G.H. Diks, B.A. Robinson, J.M. Hyman, and D. Hig-don. 2009c. Accelerating Markov chain Monte Carlo simulation by differen-tial evolution with self-adaptive randomized subspace sampling. Int. J. Non-linear Sci. Numer. Simul. 10:273-290. doi:10.1515/IJNSNS.2009.10.3.273.
64. Vrugt, J.A., C.J.F. ter Braak, H.V. Gupta, and B.A. Robinson. 2009a. Equifinal-ity of formal (DREAM) and informal (GLUE) Bayesian approaches in hy-drologic modelingtiStochastic Environ. Res. Risk Assess. 23(7):1011-1026. doi:10.1007/s00477-008-0274-y.
65. Wang, W., S.P. Neuman, T.M. Yao, and P.J. Wierenga. 2003. Simulation of large-scale field infiltration experiments using a hierarchy of models based on public, generic, and site data. Vadose Zone J. 2:297-312.
66. Wohling, T., and J.A. Vrugt. 2011. Multiresponse multilayer vadose zone model calibration using Markov chain Monte Carlo simulation and field water re-tention data. Water Resour. Res. 47:W04510. doi:10.1029/2010WR009265.
67. Yang, J., P. Reichert, K.C. Abbaspour, J. Xia, and H. Yang. 2008. Comparing un-certainty analysis techniques for a SWAT application to the Chaohe Basin in China. J. Hydrol. 358:1-23.
68. Ye, M., and R. Khaleel. 2008. A Markov chain model for characterizing me-dium heterogeneity and sediment layering structure. Water Resour. Res. 44:W09427. doi:10.1029/2008WR006924.
69. Ye, M., R. Khaleel, M.G. Schaap, and J. Zhu. 2007b. Simulation of field injec-tion experiments in heterogeneous unsaturated media using cokrig-ing and artificial neural network. Water Resour. Res. 43:W07413, doi:10.1029/2006WR005030.
70. Ye, M., P.D. Meyer, and S.P. Neuman. 2008. On model selection cri-teria in multimodel analysis. Water Resour. Res. 44:W03428. doi:10.1029/2008WR006803.
71. Ye, M., S.P. Neuman, P.D. Meyer. 2004. Maximum likelihood Bayesian averag-ing of spatial variability models in unsaturated fractured tuff. Water Resour. Res. 40:W05113. doi:10.1029/2003WR002557.
72. Ye, M., F. Pan, Y.S. Wu, B. Hu, C. Shirley, and Z. Yu. 2007a. Assessment of radio-nuclide transport uncertainty in the unsaturated zone at Yucca Mountain. Adv. Water Resour. 30:118-134.
73. Yeh, T.C.J., and J. Simunek. 2002. Stochastic fusion of information for character-izing and monitoring the vadose zone. Vadose Zone J. 1:207-221.