Numerical troubles in conceptual hydrology: Approximations, absurdities and impact on hypothesis testing

Hydrological Processes

Volumn 25, Issue 4, 2011, Pages 661-670

  Kavetski, Dmitri ^a   Clark, Martyn P ^b  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b NATIONAL CENTER FOR ATMOSPHERIC RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

HYDROLOGICAL MODELING; HYPOTHESIS TESTING; NUMERICAL MODEL;

EID: 79551474924     PISSN: 08856087     EISSN: 10991085     Source Type: Journal    
DOI: 10.1002/hyp.7899     Document Type: Article

References (52)

1. Andreassian V, Lerat J, Loumagne C, Mathevet T, Michel C, Oudin L, Perrin C. 2007. What is really undermining hydrologic science today? Hydrological Processes 21: 2819-2822.
2. Beven K. 1997. TOPMODEL: a critique. Hydrological Processes 11(9): 1069-1085.
3. Beven K. 2008. On doing better hydrological science. Hydrological Processes 22: 3549-3553.
4. Beven KJ, Binley AM. 1992. The future of distributed hydrological models: model calibration and uncertainty prediction. Hydrological Processes 6: 279-298.
5. Beven KJ, Smith PJ, Freer JE. 2008. So just why would a modeller choose to be incoherent? Journal of Hydrology 354(1-4): 15-32.
6. Binning PJ, Celia MA. 2008. Pseudokinetics arising from the upscaling of geochemical equilibrium. Water Resources Research 44: W07410. DOI: 07410.01029/02007WR006147.
7. Butcher J. 2008. Numerical Methods for Ordinary Differential Equations, 2nd edn. Wiley: Chichester.
8. Buytaert W, Reusser D, Krause S, Renaud J-P. 2008. Why can't we do better than Topmodel? Hydrological Processes 22: 4175-4179.
9. Cherkauer KA, Bowling LC, Lettenmaier DP. 2003. Variable infiltration capacity cold land process model updates. Global and Planetary Change 38(1-2): 151-159.
10. Clark MP, Kavetski D. 2010. Ancient numerical daemons of conceptual hydrological modeling. Part 1: Fidelity and efficiency of time stepping schemes. Water Resources Research 46: W10510, DOI: 10.1029/2009WR008894.
11. Clark MP, Slater AG, Rupp DE, Woods RA, Vrugt JA, Gupta HV, Wagener T, Hay LE. 2008. Framework for Understanding Structural Errors (FUSE): A modular framework to diagnose differences between hydrological models. Water Resources Research 44: W00B02. DOI: 10.1029/2007WR006735.
12. Doherty J, Welter D. 2010. A short exploration of structural noise. Water Resources Research 46: W05525. DOI: 05510.01029/02009WR008377.
13. Duan Q, Schaake J, Andreassian V, Franks SW, Goteti G, Gupta HV, Gusev YM, Habets F, Hall A, Hay L, Hogue T, Huang M, Leavesley G, Liang X, Nasonova ON, Noilhan J, Oudin L, Sorooshian S, Wagener T, Wood EF. 2006. Model parameter estimation experiment (MOPEX): an overview of science strategy and major results from the second and third workshops. Journal of Hydrology 320(1-2): 3-17.
14. Duan QY, Sorooshian S, Gupta V. 1992. Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resources Research 28(4): 1015-1031.
15. Dunne T, Black RD. 1970. Partial area contributions to storm runoff in a small New England watershed. Water Resources Research 6: 1296-1311.
16. Euler L. 1768-1770. Institutiones Calculi Integrals Volumen Primum (MCMXIII)., [11 September ], published by Lipsiae et Berolini.
17. Gill PE, Murray W, Wright MH. 1981. Practical Optimization. Academic Press: London.
18. Harbaugh AW. 2005. MODFLOW-2005, the U.S. Geological Survey modular ground-water model-the Ground-Water Flow Process, U.S. Geological Survey Techniques and Methods 6-A16.
19. Hendrickson JD, Sorooshian S, Brazil LE. 1988. Comparison of Newton-type and direct search algorithms for calibration of conceptual rainfall-runoff models. Water Resources Research 24(5): 691-700.
20. Hughes DA, Sami K. 1994. A semi-distributed, variable time interval model of catchment hydrology-structure and parameter estimation procedures. Journal of Hydrology 155: 265-291.
21. Ivanov VY, Vivoni ER, Bras RL, Entekhabi D. 2004. Catchment hydrologic response with a fully distributed triangulated irregular network model. Water Resources Research 40(11): W11102. DOI: 11110.11029/12004WR003218.
22. Kahaner D, Moler C, Nash S. 1989. Numerical Methods and Software. Prentice-Hall: Englewood Cliffs, NJ.
23. Kavetski D. 2005. Analysis of input data uncertainty and numerical robustness in conceptual rainfall-runoff modelling. PhD thesis, Faculty of Engineering, University of Newcastle, Australia.
24. Kavetski D, Binning P, Sloan SW. 2002. Adaptive backward Euler time stepping with truncation error control for numerical modelling of unsaturated fluid flow. International Journal for Numerical Methods in Engineering 53(6): 1301-1322.
25. Kavetski D, Clark MP. 2010. Ancient numerical daemons of conceptual hydrological modeling. Part 2: Impact of time stepping schemes on model analysis and prediction. Water Resources Research 46: W10511, DOI: 10.1029/2009WR008896.
26. Kavetski D, Kuczera G, Franks SW. 2003. Semidistributed hydrological modeling: a "saturation path" perspective on TOPMODEL and VIC. Water Resources Research 39(9): 1246. DOI: 1210.1029/2003WR002122.
27. Kavetski D, Kuczera G, Franks SW. 2006. Calibration of conceptual hydrological models revisited: 2. improving optimisation and analysis. Journal of Hydrology 320(1-2): 187-201.
28. Kirchner JW. 2006. Getting the right answers for the right reasons: linking measurements, analyses, and models to advance the science of hydrology. Water Resources Research 42(3): W03S04. DOI: 10.1029/2005WR004362.
29. Kling H, Gupta H. 2009. On the development of regionalization relationships for lumped watershed models: The impact of ignoring sub-basin scale variability. Journal of Hydrology 373: 337-351.
30. Maniak U. 1997. Hydrologie und Wasserwirtschaft: Eine Einführung für Ingenieure, 4th edn. Springer: Heidelberg, Germany.
31. Marks D, Domingo J, Susong D, Link T, Garen D. 1999. A spatially distributed energy balance snowmelt model for application in mountain basins. Hydrological Processes 13: 1935-1959.
32. Michel C, Andreassian V, Perrin C. 2005. Soil conservation service curve number method: how to mend a wrong soil moisture accounting procedure. Water Resources Research 41: W02011. DOI: 02010.01029/02004WR003191.
33. Michel C, Perrin C, Andreassian V. 2003. The exponential store: a correct formulation for rainfall-runoff modelling. Hydrological Sciences Journal-Journal Des Sciences Hydrologiques 48(1): 109-124.
34. Moore RJ, Clarke RT. 1981. A distribution function approach to rainfall runoff modeling. Water Resources Research 17(5): 1367-1382.
35. Perrin C, Michel C, Andreassian V. 2003. Improvement of a parsimonious model for streamflow simulation. Journal of Hydrology 279(1-4): 275-289.
36. Press WH, Flannery BP, Teukolsky SA, Vetterling WT. 1992. Numerical Recipes in Fortran-77: The Art of Scientific Computing. University of Cambridge: Cambridge; 820.
37. Reggiani P, Rientjes THM. 2005. Flux parameterization in the representative elementary watershed approach: Application to a natural basin. Water Resources Research 41: W04013. DOI: 04010.01029/02004WR003693.
38. Renard B, Kavetski D, Thyer M, Kuczera G, Franks SW. 2010. Understanding predictive uncertainty in hydrologic modeling: Le challenge of identifying input and structural errors. Water Resources Research 46: W05521. DOI: 05510.01029/02009WR008328.
39. Schoups G, Vrugt JA, Fenicia F, van de Giesen NC. 2010. Corruption of accuracy and efficiency of Markov chain Monte Carlo simulation by inaccurate numerical implementation of conceptual hydrologic models. Water Resources Research 46: W10530, DOI: 10.1029/2009WR008933.
40. Seibert J, McDonnell JJ. 2002. On the dialog between experimentalist and modeler in catchment hydrology: Use of soft data for multicriteria model calibration. Water Resources Research 38(11): 1241. DOI: 1210.1029/2001WR000978.
41. Shampine LF, Reichelt MW. 1997. The MATLAB ODE suite. SIAM Journal on Scientific Computing 18(1): 1-22.
42. Singh VP, Frevert DK. 2002a. Mathematical Models of Large Watershed Hydrology. Water Resources Publications: Highlands Ranch, Colorado.
43. Singh VP, Frevert DK. 2002b. Mathematical Models of Small Watershed Hydrology and Applications. Water Resources Publications: Highlands Ranch, Colorado.
44. Sivapalan M. 2009. The secret to "doing better hydrological science": change the question!. Hydrological Processes 23: 1391-1396.
45. Sivapalan M, Beven K, Wood EF. 1987. On hydrologic similarity: 2. a scaled model of storm runoff production. Water Resources Research 23: 2266-2278.
46. Sivapalan M, Takeuchi K, Franks SW, Gupta VK, Karambiri H, Lakshmi V, Liang X, McDonnell JJ, Mendiondo EM, O'Connell PE, Oki T, Pomeroy JW, Schertzer D, Uhlenbrook S, Zehe E. 2003. IAHS decade on Predictions in Ungauged Basins (PUB). Hydrological Sciences Journal-Journal Des Sciences Hydrologiques 48(6): 857-880.
47. Tromp-van Meerveld HJ, McDonnell JJ. 2006. Threshold relations in subsurface stormflow: 2. the fill and spill hypothesis. Water Resources Research 42: W02411. DOI: 02410.01029/02004WR003800.
48. Vache KB, McDonnell JJ. 2006. A process-based rejectionist framework for evaluating catchment runoff model structure. Water Resources Research 42: W02409. DOI: 02410.01029/02005WR004247.
49. Vrugt JA, Gupta HV, Bouten W, Sorooshian S. 2003. A shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters. Water Resources Research 39(8): 1201. DOI: 1210.1029/2002WR001642.
50. Vrugt JA, ter Braak CJF, Diks CGH, Robinson BA, Hyman JM, Higdon D. 2009. Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling. International Journal of Nonlinear Sciences and Numerical Simulation 10(3): 273-290.
51. Wagener T, Sivapalan M, Troch PA, McGlynn BL, Harman CJ, Gupta HV, Kumar P, Rao PSC, Basu NB, Wilson JS. 2010. The future of hydrology: An evolving science for a changing world. Water Resources Research 46: W05301. DOI: 05310.01029/02009WR008906.
52. Western AW, Zhou SL, Grayson RB, McMahon TA, Bloschl G, Wilson DJ. 2004. Spatial correlation of soil moisture in small catchments and its relationship to dominant spatial hydrological processes. Journal of Hydrology 286: 113-134.