Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models

Water Resources Research

Volumn 46, Issue 10, 2010, Pages

  Schoups, G ^a   Vrugt, J A ^b,c,d   Fenicia, F ^a,e   Van De Giesen, N C ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b University of California at Irvine   (United States)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

^d UNIVERSITY OF AMSTERDAM   (Netherlands)

^e LUXEMBOURG INSTITUTE OF SCIENCE AND TECHNOLOGY   (Luxembourg)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL INTEGRATION; COMPUTATIONAL SPEED; ESTIMATING PARAMETERS; FINITE DIFFERENCE SCHEME; FINITE DIFFERENCING; FIRST-ORDER; HYDROLOGIC MODELS; IMPLICIT METHODS; INTEGRATION METHOD; MARKOV CHAIN MONTE CARLO METHOD; MARKOV CHAIN MONTE CARLO SIMULATION; NUMERICAL ERRORS; NUMERICAL IMPLEMENTATION; OPERATOR SPLITTING METHOD; OPERATOR-SPLITTING; PARAMETER DISTRIBUTIONS; POOR PERFORMANCE; PREDICTIVE DISTRIBUTIONS; PREDICTIVE UNCERTAINTY; RAINFALL-RUNOFF MODELS; SECOND ORDERS; SIMULATION MODEL; SPLITTING METHOD; TEMPORAL INTEGRATION; WATER BALANCE;

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; MARKOV PROCESSES; MATHEMATICAL OPERATORS; MONTE CARLO METHODS; PARAMETER ESTIMATION; RAIN; RUNOFF; UNCERTAINTY ANALYSIS;

MATHEMATICAL MODELS;

HYDROLOGICAL MODELING; MARKOV CHAIN; MONTE CARLO ANALYSIS; NUMERICAL MODEL; RAINFALL-RUNOFF MODELING; TEMPORAL ANALYSIS; WATER BUDGET;

EID: 78049432883     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2009WR008648     Document Type: Article

References (40)

1. Bates, B. C., and E. P. Campbell (2001), A Markov chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfallrunoff modeling, Water Resour. Res., 37(4), 937-947.
2. Butcher, J. C. (2008), Numerical Methods for Ordinary Differential Equations, John Wiley, Chichester, U. K.
3. Clark, M. P., and D. Kavetski (2010), The ancient numerical daemons of conceptual hydrological modeling: Fidelity and efficiency of time stepping schemes, Water Resour. Res., W10510, doi:10.1029/2009WR008894.
4. Cowles, M. K., and B. P. Carlin (1996), Markov chain Monte Carlo convergence diagnostics: A comparative review, J. Am. Stat. Assoc., 91(434), 883-904.
5. Cox, B. A., and P. G. Whitehead (2005), Parameter sensitivity and predictive uncertainty in a new water quality model Q2, J. Environ. Eng., 131(1), 147-157.
6. Csomos, P., and I. Farago (2008), Error analysis of the numerical solution of split differential equations, Math. Comput. Modell, 48, 1090-1106.
7. Csomos, P., I. Farago, and A. Havasi (2005), Weighted Sequential Splittings and Their Analysis, Comput. Math. Appl, 50, 1017-1031.
8. Duan, Q., V. K. Gupta, and S. Sorooshian (1993), Shuffled complex evolution approach for effective and efficient global minimization, J. Optim. Theory Appl, 76(3), 501-521.
9. Duan, Q., et al. (2006), Model Parameter Estimation Experiment (MOPEX): An overview of science strategy and major results from the second and third workshops, J. Hydrol., 320 (1-2), 3-17.
10. Engeland, K., C. Y. Xu, and L. Gottschalk (2005), Assessing uncertainties in a conceptual water balance model using Bayesian methodology, Hydrol. Sci. J., 50(1), 45-63.
11. Fenicia, F., H. H. G. Savenije, P. Matgen, and L. Pfister (2007), A comparison of alternative multiobjective calibration strategies for hydrological modeling, Water Resour. Res., 43, W03434, doi:10.1029/2006WR005098. (Pubitemid 46682804)
12. Gelman, A., and D. B. Rubin (1992), Inference from iterative simulation using multiple sequences, Stat. Sci., 7, 457-472.
13. Hastings, W. K. (1970), Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 97-109.
14. Kavetski, D., and M. P. Clark (2010), The ancient numerical daemons of conceptual hydrological modeling: 2. Impact of time stepping schemes on model analysis and prediction, Water Resour. Res., W10511, doi:10.1029/2009WR008896.
15. Kavetski, D., and G. Kuczera (2007), Model smoothing strategies to remove microscale discontinuities and spurious secondary optima in objective functions in hydrological calibration, Water Resour. Res., 43, W03411, doi:10.1029/2006WR005195. (Pubitemid 46682781)
16. Kavetski, D., P. Binning, and S. W. Sloan (2001), Adaptive time stepping and error control in a mass conservative numerical solution of the mixed form of Richards equation, Adv. Water Resour, 24(6), 595-605.
17. Kavetski, D., G. Kuczera, and S. W. Franks (2003), Semidistributed hydrological modeling: A "saturation path" perspective on TOPMODEL and VIC, Water Resour. Res., 39(9), 1246, doi:10.1029/2003WR002122.
18. Kavetski, D., G. Kuczera, and S. W. Franks (2006a), Calibration of conceptual hydrological models revisited: 1. Overcoming numerical artefacts, J. Hydrol, 320 (1-2), 173-186.
19. Kavetski, D., G. Kuczera, and S. W. Franks (2006b), Calibration of conceptual hydrological models revisited: 2. Improving optimization and analysis, J. Hydrol, 320 (1-2), 187-201.
20. Kuczera, G. (1983), Improved parameter inference in catchment models: 1. Evaluating parameter uncertainty, Water Resour. Res., 19(5), 1151-1162.
21. Kuczera, G., and E. Parent (1998), Monte Carlo assessment of parameter uncertainty in conceptual catchment models: The Metropolis algorithm, J. Hydrol, 211 (1-4), 69-85.
22. Kuczera, G., D. Kavetski, B. Renard, and M. Thyer (2010), A limitedmemory acceleration strategy for MCMC sampling in hierarchical Bayesian calibration of hydrological models, Water Resour. Res., 46, W07602, doi:10.1029/2009WR008985.
23. McLachlan, R. I., and G. R. W. Quispel (2002), Splitting methods, Acta Numer., 11, 341-434, doi:10.1017/S0962492902000053.
24. Parkhurst, D. L., and C. A. J. Appelo (1999), User's guide to PHREEQC-A computer program for speciation, reaction-path, 1D-transport, and inverse geochemical calculations, U. S. Geol. Surv. Water Resour. Invest. Rep., 99-4259, 312 pp.
25. Perrin, C., C. Michel, and V. Andreassian (2003), Improvement of aparsimonious model for streamflow simulation, J. Hydrol, 279 (1-4), 275-289.
26. Press, W. H., B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling (1990), Numerical Recipes, Cambridge Univ. Press, New York.
27. Qu, Y., and C. J. Duffy (2007), A semi-discrete finite volume formulation for multiprocess watershed simulation, Water Resour. Res., 43, W08419, doi:10.1029/2006WR005752. (Pubitemid 47509801)
28. Robert, C. P., and G. Casella (2004), Monte Carlo Statistical Methods, 2nd ed., 536 pp., Springer, New York.
29. Singh, V. P., and D. A. Woolhiser (2002), Mathematical modeling of watershed hydrology, J. Hydrol. Eng., 7(4), 270-292.
30. Smith, T. J., and L. A. Marshall (2008), Bayesian methods in hydrologic modeling: A study of recent advancements in Markov chain Monte Carlo techniques, Water Resour. Res., 44, W00B05, doi:10.1029/2007WR006705.
31. Steefel, C. I., and K. T. B. MacQuarrie (1996), Approaches to modeling of reactive transport in porous media, Rev. Mineral, 34, 83-129.
32. Strang, G. (1968), On the construction and comparison of difference schemes, SIAM J. Numer. Anal, 5(3), 506-517.
33. ter Braak, C. J. F., and J. A. Vrugt (2008), Differential evolution Markov chain with snooker updater and fewer chains, Stat. Comput., 18(4), 435-446.
34. Vrugt, J. A., H. V. Gupta, W. Bouten, and S. Sorooshian (2003), A shuffled complex evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters, Water Resour. Res., 39(8), 1201, doi:10.1029/2002WR001642.
35. Vrugt, J. A., H. V. Gupta, S. C. Dekker, S. Sorooshian, T. Wagener, and W. Bouten (2006), Application of stochastic parameter optimization to the Sacramento soil moisture accounting model, J. Hydrol, 325 (1-4), 288-307.
36. Vrugt, J. A., C. J. F. ter Braak, M. P. Clark, J. M. Hyman, and B. A. Robinson (2008), 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.
37. 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. Numer. Simul., 10(3), 273-290.
38. Wagener, T., M. Sivapalan, P. Troch, and R. Woods (2007), Catchment classification and hydrologic similarity, Geogr. Compass, 1(4), 901-931.
39. Wood, E. F., D. P. Lettenmaier, and V. G. Zartarian (1992), A land-surface hydrology parameterization with subgrid variability for general circulation models, J. Geophys. Res., 97 (D3), 2717-2728.
40. Woodward, D. B. (2007), Detecting poor convergence of posterior samplers due to multimodality, Discuss. Pap. 2008-05, Dept. of Stat. Sci. Duke Univ., Durham, N. C.