Calibration of a distributed flood forecasting model with input uncertainty using a Bayesian framework

Water Resources Research

Volumn 48, Issue 8, 2012, Pages

  Li, Mingliang ^a   Yang, Dawen ^a   Chen, Jinsong ^b   Hubbard, Susan S ^b  

^a TSINGHUA UNIVERSITY   (China)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AUTO REGRESSIVE MODELS; BAYESIAN FRAMEWORKS; BAYESIAN MODEL; COMPLEX FIELDS; COMPLEX MODEL; CONTINUOUS RANKED PROBABILITY SCORES; DISTRIBUTED HYDROLOGICAL MODEL; DISTRIBUTED MODELS; FIELD DATA SETS; FIRST-ORDER; FLOOD FORECASTING MODELS; GIBBS SAMPLING; HYDROLOGICAL MODELS; HYDROLOGICAL PROCESS; INPUT UNCERTAINTY; MARKOV CHAIN MONTE CARLO METHOD; OBSERVED DATA; PHYSICALLY BASED; PREDICTIVE DISTRIBUTIONS; RELATIVE ERRORS; TEMPORAL DEPENDENCE;

BAYESIAN NETWORKS; CALIBRATION; ERRORS; ESTIMATION; FLOOD CONTROL; HYDROLOGY; MONTE CARLO METHODS; PROBABILITY DISTRIBUTIONS; SOIL STRUCTURE INTERACTIONS; UNCERTAINTY ANALYSIS;

PARAMETER ESTIMATION;

BAYESIAN ANALYSIS; CALIBRATION; DATA SET; DISCHARGE; ERROR ANALYSIS; FLOOD FORECASTING; FLOW MODELING; MARKOV CHAIN; MONTE CARLO ANALYSIS; NUMERICAL MODEL; RAINFALL-RUNOFF MODELING; SAMPLING; SPATIAL DISTRIBUTION; UNCERTAINTY ANALYSIS;

EID: 84865464020     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2010WR010062     Document Type: Article

References (52)

1. Abbott, M. B., J. C. Bathurst, J. A. Cunge, P. E. O'Connell, and J. Rasmussen (1986), An introduction to the European Hydrological System-Systeme Hydrologique Europeen, "SHE", 1: History and philosophy of a physically based, distributed modelling system, J. Hydrol., 87(1-2), 45-59, doi:10.1016/0022-1694(86)90114-9.
2. Ajami, N. K., Q. Y. Duan, and S. Sorooshian (2007), An integrated hydro-logic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction, Water Resour. Res., 43, W01403, doi:10.1029/2005WR004745. (Pubitemid 46364281)
3. Ajami, N. K., Q. Duan, and S. Sorooshian (2009), Reply to Comment by B. Renard et al. on "An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction,", Water Resour. Res., 45, W03604, doi:10.1029/2008WR007215.
4. Bates, B. C, and E. P. Campbell (2001), A Markov chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall-runoff modeling, Water Resour. Res., 37(4), 937-947, doi:10.1029/2000WR900363. (Pubitemid 32516048)
5. Beven, K. (2006), A manifesto for the equifinality thesis, J. Hydrol., 320(1-2), 18-36, doi:10.1016/j.jhydrol.2005.07.007.
6. Chen, J. S., G. M. Hoversten, D. Vasco, Y. Rubin, and Z. S. Hou (2007), A Bayesian model for gas saturation estimation using marine seismic AVA and CSEM data, Geophysics, 72(2), WA85-WA95, doi:10.1190/1.2435082. (Pubitemid 46403904)
7. Chen, J. S., A. Kemna, and S. S. Hubbard (2008), A comparison between Gauss-Newton and Markov-chain Monte Carlo-based methods for inverting spectral induced-polarization data for Cole-Cole parameters, Geophysics, 73(6), F247-F259, doi:10.1190/1.2976115.
8. Chow, V. T., R. M. David, and W. M. Larry (1988), Applied Hydrology, McGraw-Hill, New York.
9. Clark, M. P., and A. G. Slater (2006), Probabilistic quantitative precipitation estimation in complex terrain, J. Hydrometeorol, 7(1), 3-22, doi:10.1175/JHM474.1.
10. Cong, Z. T., D. W. Yang, B. Gao, H. B. Yang, and H. P. Hu (2009), Hydrological trend analysis in the Yellow River basin using a distributed hydrological model, Water Resour. Res., 45, W00A13, doi:10.1029/2008WR006852.
11. Gelfand, A. E., and A. F. M. Smith (1990), Sampling-based approaches to calculating marginal densities, J. Am. Stat. Assoc, 85(410), 398-409, doi:10.2307/2289776.
12. Gelman, A., and D. Rubin (1992), Inference from iterative simulation using multiple sequences, Stat. Sci., 7(4), 457-472, doi:10.1214/ss/1177011136.
13. Geman, S., and D. Geman (1984), Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell, 6(6), 721-741, doi:10.1109/TPAMI.1984.4767596. (Pubitemid 15453722)
14. Gilks, W. R., S. Richardson, and D. J. Spiegelhalter (1996), Markov Chain Monte Carlo in Practice, Chapman and Hall, Boca Raton, Fla.
15. Gneiting, T., A. Westveld, A. Raferty, and T. Goldman (2004), Calibrated probabilistic forecasting using ensemble model output statistics and minimum CRPS estimation, Tech. Rep. 449, Dept. of Statistics, Univ. of Washington, Seattle, Washington.
16. Green, P., and A. Mira (2001), Delayed rejection in reversible jump metropolis-hastings, Biometrika, 88, 1035-1053. (Pubitemid 33771550)
17. Gupta, H., K. Beven, and T. Wagener (2005), Model calibration and uncertainty estimation, in Encyclopedia of Hydrological Sciences, edited by M. G. Anderson, pp. 1-17, John Wiley and Sons, New York.
18. Haario, H., E. Saksman, and J. Tamminen (2001), An adaptive Metropolis algorithm, Bernoulli, 7(2), 223-242, doi:10.2307/3318737. (Pubitemid 33793059)
19. Haario, H., M. Laine, A. Mira, and E. Saksman (2006), DRAM: Efficient adaptive MCMC, Stat. Comput, 16(4), 339-354, doi:10.1007/s11222-006-9438-0. (Pubitemid 44581755)
20. Hastings, W. K. (1970), Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57(1), 97-109, doi:10.1093/biomet/57.1.97.
21. Huard, D., and A. Mailhot (2008), Calibration of hydrological model GR2M using Bayesian uncertainty analysis, Water Resour. Res., 44, W02424, doi:10.1029/2007WR005949. (Pubitemid 351442502)
22. Immerzeel, W. W., and P. Droogers (2008), Calibration of a distributed hydrological model based on satellite evapotranspiration, J. Hydrol, 349(3-4), 411-424, doi:10.1016/j.jhydrol.2007.11.017.
23. Kavetski, D., S. W. Franks, and G. Kuczera (2003), Confronting input uncertainty in environmental modelling, in Calibration of Watershed Models, Water Sci. Appl, vol. 6, edited by Q. Duan et al., pp. 49-68, AGU, Washington, D. C, doi:10.1029/WS006p0049.
24. Kavetski, D., G. Kuczera, and S. W. Franks (2006), Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory, Water Resour. Res., 42, W03407, doi:10.1029/2005WR004368.
25. Khu, S. T., H. Madsen, and F. di Pierro (2008), Incorporating multiple observations for distributed hydrologic model calibration: An approach using a multi-objective evolutionary algorithm and clustering, Adv. Water Resour., 31(10), 1387-1398, doi:10.1016/j.advwatres.2008.07.011.
26. 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, doi:10.1016/S0022-1694(98)00198-X. (Pubitemid 29014557)
27. Kuczera, G., D. Kavetski, S. Franks, and M. Thyer (2006), Towards a Bayesian total error analysis of conceptual rainfall-runoff models: Characterising model error using storm-dependent parameters, J. Hydrol, 331(1-2), 161-177, doi:10.1016/j.jhydrol.2006.05.010. (Pubitemid 44646456)
28. Liu, Y. Q., and H. V. Gupta (2007), Uncertainty in hydrologic modeling: Toward an integrated data assimilation framework, Water Resour. Res., 43, W07401, doi:10.1029/2006WR005756. (Pubitemid 350194456)
29. Marcé, R., C. E. Ruiz, and J. Armengol (2008), Using spatially distributed parameters and multi-response objective functions to solve parameterization of complex applications of semi-distributed hydrological models, Water Resour. Res., 44, W02436, doi:10.1029/2006WR005785. (Pubitemid 351442512)
30. Marshall, L., D. Nott, and A. Sharma (2004), A comparative study of Markov chain Monte Carlo methods for conceptual rainfall-runoff modeling, Water Resour. Res., 40, W02501, doi:10.1029/2003WR002378.
31. Metropolis, N., A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller (1953), Equation of state calculations by fast computing machines, J. Chem. Phys., 21(6), 1087-1092, doi:10.1063/1.1699114.
32. Naidu, P. S. (1996), Modern Spectrum Analysis of Time Series, CRC Press, Boca Raton, Fla.
33. Nash, J. E., and J. V. Sutcliffe (1970), River flow forecasting through conceptual models, part I, A discussion of principles, J. Hydrol, 10, 398-409, doi:10.1016/0022-1694(70)90255-6.
34. New, M., M. Hulme, and P. Jones (2000), Representing twentieth-century space-time climate variability. Part II: Development of 1901-96 monthly grids of terrestrial surface climate, J. Clim., 13(13), 2217-2238, doi:10.1175/1520- 0442(2000)0132.0.CO;2.
35. Renard, B., D. Kavetski, and G. Kuczera (2009), Comment on "An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydro-logic prediction" by Newsha K. Ajami et al, Water Resour. Res., 45, W03603, doi:10.1029/2007WR006538.
36. Renard, B., D. Kavetski, G. Kuczera, M. Thyer, and S. W. Franks (2010), Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors, Water Resour. Res., 46, W05521, doi:10.1029/2009WR008328.
37. Renard, B., D. Kavetski, E. Leblois, M. Thyer, G. Kuczera, and S. W. Franks (2011), Toward a reliable decomposition of predictive uncertainty in hydrological modeling: Characterizing rainfall errors using conditional simulation, Water Resour. Res., 47(11), W11516, doi:10.1029/2011WR010643.
38. Robinson, J. S., and M. Sivapalan (1996), Instantaneous response functions of overland flow and subsurface stormflow for catchment models, Hydrol. Processes, 10(6), 845-862, doi:10.1002/(SICI)1099-1085(199606)10:63.0. CO;2-7.
39. Salamon, P., and L. Feyen (2010), Disentangling uncertainties in distributed hydrological modeling using multiplicative error models and sequential data assimilation, Water Resour. Res., 46, W12501, doi:10.1029/2009WR009022.
40. Schaefli, B., D. B. Talamba, and A. Musy (2007), Quantifying hydrological modeling errors through a mixture of normal distributions, J. Hydrol, 332(3-4), 303-315, doi:10.1016/j.jhydrol.2006.07.005. (Pubitemid 44969651)
41. 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.
42. Shrestha, R. R., and M. Rode (2008), Multi-objective calibration and fuzzy preference selection of a distributed hydrological model, Environ. Model. Softw., 23(12), 1384-1395, doi:10.1016/j.envsoft.2008.04.001.
43. Singh, V. P., and D. A. Woolhiser (2002), Mathematical modeling of watershed hydrology, J. Hydrol. Eng., 7(4), 270-292, doi:10.1061/(ASCE) 1084-0699(2002)7:4(270). (Pubitemid 34793868)
44. Sorooshian, S., and J. A. Dracup (1980), Stochastic parameter estimation procedures for hydrologie rainfall-runoff models: Correlated and heteroscedastic error cases, Water Resour. Res., 16, 2, doi:10.1029/WR016i002p00430.
45. Thyer, M., G. Kuczera, and Q. J. Wang (2002), Quantifying parameter uncertainty in stochastic models using the Box-Cox transformation, J. Hydrol, 265(1-4), 246-257, doi:10.1016/S0022-1694(02)00113-0. (Pubitemid 35028776)
46. Thyer, M., B. Renard, D. Kavetski, G. Kuczera, S. W. Franks, and S. Srikanthan (2009), Critical evaluation of parameter consistency and predictive uncertainty in hydrological modeling: A case study using Bayesian total error analysis, Water Resour. Res., 45, W00B14, doi:10.1029/2008WR006825.
47. 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.
48. Yang, D. W. (1998), Distributed hydrological model using hillslope discretization based on catchment area function: Development and applications, PhD dissertation, 179 pp., Univ. of Tokyo, Tokyo.
49. Yang, D. W., and K. Musiake (2003), A continental scale hydrological model using the distributed approach and its application to Asia, Hydrol. Processes, 17, 2855-2869, doi:10.1002/hyp.1438. (Pubitemid 37325925)
50. Yang, D. W., S. Herath, and K. Musiake (2002), A hillslope-based hydro-logical model using catchment area and width functions, Hydrol. Sci. J., 47(1), 49-65, doi:10.1080/02626660209492907. (Pubitemid 34172139)
51. Yang, D. W., T. Koike, and H. Tanizawa (2004), Application of a distributed hydrological model and weather radar observations for flood management in the upper Tone River of Japan, Hydrol. Processes, 18, 3119-3132, doi:10.1002/hyp.5752. (Pubitemid 39621793)
52. Yang, J., P. Reichert, K. C. Abbaspour, and H. Yang (2007), Hydrological modelling of the chaohe basin in china: Statistical model formulation and Bayesian inference, J. Hydrol., 340(3-4), 167-182, doi:10.1016/j.jhydrol.2007. 04.006. (Pubitemid 46935784)