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Uncertainty in high and low flows due to model structure and parameter errors

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Abstract

This paper aims to investigate the uncertainty in simulated extreme low and high flows originating from hydrological model structure and parameters. To this end, three different rainfall-runoff models, namely GR4J, HBV and Xinanjiang, are applied to two subbasins of Qiantang River basin, eastern China. The Generalised Likelihood Uncertainty Estimation approach is used for estimating the uncertainty of the three models due to parameter values, henceforth referred as parameter uncertainty. Uncertainty in simulated extreme flows is evaluated by means of the annual maximum discharge and mean annual 7-day minimum discharge. The results show that although the models have good performance for the daily flows, the uncertainty in the extreme flows could not be neglected. The uncertainty originating from parameters is larger than uncertainty due to model structure. The parameter uncertainty of the extreme flows increases with the observed discharge. The parameter uncertainty in both the extreme high flows and the extreme low flows is the largest for the HBV model and the smallest for the Xinanjiang model. It is noted that the extreme low flows are mostly underestimated by all models with optimum parameter sets for both subbasins. The largest underestimation is from Xinanjiang model. Therefore it is not reliable enough to use only one set of the parameters to make the prediction and carrying out the uncertainty study in the extreme discharge simulation could give an overall picture for the planners.

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References

  • Akhtar M, Ahmad N, Booij MJ (2008) The impact of climate change on the water resources of Hindu kush–Karakorum-Himalaya region under different glacier coverage scenarios. J Hydrol 355(1–4):148–163. doi:10.1016/j.jhydrol.2008.03.015

    Article  Google Scholar 

  • Akhtar M, Ahmad N, Booij MJ (2009) Use of regional climate model simulations as input for hydrological models for the Hindukush–Karakorum-Himalaya region. Hydrol Earth Syst Sci 13(7):1075–1089

    Article  Google Scholar 

  • Andersson L, Samuelsson P, Kjellstrom E (2011) Assessment of climate change impact on water resources in the Pungwe river basin. Tellus A 63(1):138–157. doi:10.1111/j.1600-0870.2010.00480.x

    Article  Google Scholar 

  • Aubert D, Loumagne C, Oudin L (2003) Sequential assimilation of soil moisture and streamflow data in a conceptual rainfall–runoff model. J Hydrol 280(1):145–161

    Article  Google Scholar 

  • Bastola S, Murphy C, Sweeney J (2011) The role of hydrological modelling uncertainties in climate change impact assessments of Irish river catchments. Adv Water Resour 34(5):562–576. doi:10.1016/j.advwatres.2011.01.008

  • Bates BC, Campbell EP (2001) A Markov chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall-runoff modeling. Water Resour Res 37(4):937–947

    Article  Google Scholar 

  • Bergström S (1976) Development and application of a conceptual runoff model for Scandinavian catchments. SMHI Report RHO No. 7, Norrköping, Sweden

  • Beven K (1988) Interflow. Paper presented at the in unsaturated flow in hydrologic modelling, theory and practice, Kluwer Academic, Dordrecht

  • Beven K (2006) A manifesto for the equifinality thesis. J Hydrol 320(1–2):18–36. doi:10.1016/j.jhydrol.2005.07.007

    Article  Google Scholar 

  • Beven K, Binley A (1992) The future of distributed models: model calibration and uncertainty prediction. Hydrol Process 6(3):279–298. doi:10.1002/hyp.3360060305

    Article  Google Scholar 

  • Beven KJ, Smith PJ, Freer JE (2008) So just why would a modeller choose to be incoherent? J Hydrol 354(1):15–32

    Article  Google Scholar 

  • Blasone RS, Madsen H, Rosbjerg D (2008) Uncertainty assessment of integrated distributed hydrological models using GLUE with Markov chain Monte Carlo sampling. J Hydrol 353(1):18–32

    Article  Google Scholar 

  • Booij MJ (2005) Impact of climate change on river flooding assessed with different spatial model resolutions. J Hydrol 303(1–4):176–198. doi:10.1016/j.jhydrol.2004.07.013

    Article  Google Scholar 

  • Booij MJ, Krol MS (2010) Balance between calibration objectives in a conceptual hydrological model. Hydrol Sci J 55(6):1017–1032. doi:10.1080/02626667.2010.505892

    Article  Google Scholar 

  • Brazier RE, Beven KJ, Anthony SG, Rowan JS (2001) Implications of model uncertainty for the mapping of hillslope-scale soil erosion predictions. Earth Surf Processes 26(12):1333–1352. doi:10.1002/esp.266

    Article  Google Scholar 

  • Cameron D (2007) Flow, frequency, and uncertainty estimation for an extreme historical flood event in the Highlands of Scotland, UK. Hydrol Process 21(11):1460–1470. doi:10.1002/Hyp.6321

    Article  Google Scholar 

  • Cheng C-T, Wu X-Y, Chau KW (2005) Multiple criteria rainfall–runoff model calibration using a parallel genetic algorithm in a cluster of computers/Calage multi-critères en modélisation pluie–débit par un algorithme génétique parallèle mis en œuvre par une grappe d’ordinateurs. Hydrol Sci J 50(6):1069–1088. doi:10.1623/hysj.2005.50.6.1069

    Google Scholar 

  • Christensen S (2004) A synthetic groundwater modelling study of the accuracy of GLUE uncertainty intervals. Nord Hydrol 35(1):45–59

    Google Scholar 

  • Edijatno, Nascimento NDEO, Yang X, Makhlouf Z, Michel C (1999) GR3J: a daily watershed model with three free parameters. Hydrol Sci J 44(2):263–277

    Article  Google Scholar 

  • Engeland K, Hisdal H (2009) A comparison of low flow estimates in ungauged catchments using regional regression and the HBV-model. Water Resour Manag 23(12):2567–2586

    Article  Google Scholar 

  • Feyen L, Beven KJ, De Smedt F, Freer J (2001) Stochastic capture zone delineation within the generalized likelihood uncertainty estimation methodology: conditioning on head observations. Water Resour Res 37(3):625–638

    Article  Google Scholar 

  • Filliben JJ (1975) The probability plot correlation coefficient test for normality. Technometrics 17:111–117

    Article  Google Scholar 

  • Harlin J, Kung CS (1992) Parameter uncertainty and simulation of design floods in Sweden. J Hydrol 137(1–4):209–230

    Article  Google Scholar 

  • Hindley DR (1973) The definition of dry-weather flow in river flow measurement. J Inst Water Eng Sci 27:438–440

    Google Scholar 

  • IPCC (2002) Workshop on changes in extreme weather and climate events. Beijing, China

  • IPCC (2007) Climate change 2007: synthesis report, Contribution of working groups I, II and III to the fourth assessment report of the intergovernmental panel on climate change. Geneva, Switzerland

  • Jin X, Xu CY, Zhang Q, Singh V (2010) Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model. J Hydrol 383(3–4):147–155

    Article  Google Scholar 

  • Kobold M, Brilly M (2006) The use of HBV model for flash flood forecasting. Nat Hazard Earth Sys 6(3):407–417

    Article  Google Scholar 

  • Kuczera G, Parent E (1998) Monte Carlo assessment of parameter uncertainty in conceptual catchment models: the Metropolis algorithm. J Hydrol 211(1):69–85

    Article  Google Scholar 

  • Le Moine N, Andréassian V, Mathevet T (2008) Confronting surface-and groundwater balances on the La Rochefoucauld-Touvre karstic system (Charente, France). Water Resour Res 44(3):W03403. doi:10.1029/2007WR005984

  • Lindström G, Harlin J (1992) Spillway design floods in Sweden: II. Applications and sensitivity analysis. Hydrol Sci J 37(5):521–539

    Article  Google Scholar 

  • Lindström G, Johansson B, Persson M, Gardelin M, Bergström S (1997) Development and test of the distributed HBV-96 hydrological model. J Hydrol 201(1–4):272–288

    Article  Google Scholar 

  • Madigan D, Raftery AE, Volinsky C, Hoeting J (1996) Bayesian model averaging. AAAI Press, Menlo Park, pp 77–83

    Google Scholar 

  • Mannina G (2011) Uncertainty assessment of a water-quality model for ephemeral rivers using GLUE analysis. J Environ Eng 137(3):177–186

    Google Scholar 

  • Mannina G, Viviani G (2010) An urban drainage stormwater quality model: model development and uncertainty quantification. J Hydrol 381(3–4):248–265

    Article  CAS  Google Scholar 

  • Mantovan P, Todini E (2006) Hydrological forecasting uncertainty assessment: incoherence of the GLUE methodology. J Hydrol 330(1):368–381

    Article  Google Scholar 

  • Marin S, Ramirez JA (2006) The response of precipitation and surface hydrology to tropical macro-climate forcing in Colombia. Hydrol Process 20(17):3759–3789

    Article  Google Scholar 

  • Menzel L, Thieken AH, Schwandt D, Bürger G (2006) Impact of climate change on the regional hydrology–Scenario-based modelling studies in the German Rhine catchment. Nat Hazards 38(1):45–61

    Article  Google Scholar 

  • Mishra AK, Singh VP (2010) A review of drought concepts. J Hydrol 391(1–2):202–216

    Article  Google Scholar 

  • Montanari A (2005) Large sample behaviors of the generalized likelihood uncertainty estimation (GLUE) in assessing the uncertainty of rainfall-runoff simulations. Water Resour Res 41(8):W08406

    Google Scholar 

  • Monteith J (1965) Evaporation and environment. Symp Soc Exp Biol 19:205–232

    Google Scholar 

  • Nash JE, Sutcliffe J (1970) River flow forecasting through conceptual models part I—a discussion of principles. J Hydrol 10(3):282–290

    Article  Google Scholar 

  • Oudin L, Andréassian V, Perrin C, Michel C, Le Moine N (2008) Spatial proximity, physical similarity, regression and ungaged catchments: a comparison of regionalization approaches based on 913 French catchments. Water Resour Res 44(3):3413. doi:10.1029/2007WR006240

    Google Scholar 

  • Perrin C, Michel C, Andreassian V (2003) Improvement of a parsimonious model for streamflow simulation. J Hydrol 279(1–4):275–289

    Article  Google Scholar 

  • Raftery AE, Gneiting T, Balabdaoui F, Polakowski M (2005) Using Bayesian model averaging to calibrate forecast ensembles. Mon Weather Rev 133(5):1155–1174

    Article  Google Scholar 

  • Refsgaard JC, Van der Sluijs JP, Brown J, Van der Keur P (2006) A framework for dealing with uncertainty due to model structure error. Adv Water Resour 29(11):1586–1597

    Article  Google Scholar 

  • Refsgaard JC, Van Der Sluijs JP, Højberg AL, Vanrolleghem PA (2007) Uncertainty in the environmental modelling process–A framework and guidance. Environ Model Softw 22(11):1543–1556

    Article  Google Scholar 

  • Renard B, Kavetski D, Kuczera G, Thyer M, Franks SW (2010) Understanding predictive uncertainty in hydrologic modeling: the challenge of identifying input and structural errors. Water Resour Res 46(5):W05521

    Google Scholar 

  • Seibert J (1997) Estimation of parameter uncertainty in the HBV model. Nord Hydrol 28(4):247–262

    Google Scholar 

  • Shrestha DL, Kayastha N, Solomatine DP (2009) A novel approach to parameter uncertainty analysis of hydrological models using neural networks. Hydrol Earth Syst Sci Discuss 6(2):1677–1706. doi:10.5194/hessd-6-1677-2009

    Article  Google Scholar 

  • Smakhtin V (2001) Low flow hydrology: a review. J Hydrol 240(3):147–186

    Article  Google Scholar 

  • Smith TJ, Marshall LA (2008) Bayesian methods in hydrologic modeling: a study of recent advancements in Markov chain Monte Carlo techniques. Water Resour Res 44(12):W00B05. doi:10.1029/2007WR006705

  • Tang B (1993) Orthogonal array-based Latin hypercubes. J Am Stat Assoc 88(424):1392–1397

    Article  Google Scholar 

  • Van der Sluijs J, Risbey J, Kloprogge P, Ravetz J, Funtowicz S, Corral Quintana S, Guimaraes Pereira A, De Marchi B, Petersen A, Janssen P (2003) RIVM/MNP guidance for uncertainty assessment and communication: detailed guidance. Copernicus Institute for Sustainable Development, Universität Utrecht und RIVM-MNP, Utrecht

    Google Scholar 

  • Vigiak O, Sterk G, Romanowicz RJ, Beven KJ (2006) A semi-empirical model to assess uncertainty of spatial patterns of erosion. Catena 66(3):198–210

    Article  Google Scholar 

  • Viola F, Noto L, Cannarozzo M, La Loggia G (2009) Daily streamflow prediction with uncertainty in ephemeral catchments using the GLUE methodology. Phys Chem Earth 34(10):701–706

    Article  Google Scholar 

  • Walker WE, Harremoes P, Rotmans J, Van der Sluijs J, Van Asselt M, Janssen P, Von Krauss MPK (2003) Defining uncertainty: a conceptual basis for uncertainty management in model-based decision support. Integr Assess 4(1):5–17

    Article  Google Scholar 

  • Warmink JJ, Janssen JAEB, Booij MJ, Krol MS (2010) Identification and classification of uncertainties in the application of environmental models. Environ Model Softw 25(12):1518–1527. doi:10.1016/j.envsoft.2010.04.011

    Article  Google Scholar 

  • Wilby RL, Harris I (2006) A framework for assessing uncertainties in climate change impacts: low-flow scenarios for the River Thames. UK Water Resour Res 42(2):W02419. doi:10.1029/2005WR004065

  • Wu W, Clark JS, Vose JM (2010) Assimilating multi-source uncertainties of a parsimonious conceptual hydrological model using hierarchical Bayesian modeling. J Hydrol 394(3–4):436–446. doi:10.1016/j.jhydrol.2010.09.017

    Article  Google Scholar 

  • Xu Y-P, Booij MJ, Mynett AE (2007) An appropriateness framework for the Dutch Meuse decision support system. Environ Model Softw 22(11):1667–1678

    Article  Google Scholar 

  • Xu YP, Booij MJ, Tong YB (2010) Uncertainty analysis in statistical modeling of extreme hydrological events. Stoch Environ Res Risk A 24(5):567–578

    Article  Google Scholar 

  • Yang J, Reichert P, Abbaspour K, Xia J, Yang H (2008) Comparing uncertainty analysis techniques for a SWAT application to the Chaohe Basin in China. J Hydrol 358(1):1–23

    Article  Google Scholar 

  • Zhang Q, Liu C, Xu C, Xu Y, Jiang T (2006) Observed trends of annual maximum water level and streamflow during past 130 years in the Yangtze River basin. China J Hydrol 324(1):255–265

    Article  Google Scholar 

  • Zhao R-J (1992) The Xinanjiang model applied in China. J Hydrol 135(1–4):371–381

    Google Scholar 

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Acknowledgments

This research was financially supported by the International Science and Technology Cooperation Program of China (Project No. 2010DFA24320) and the Nature Science Foundation of China (Project No. 50809058). The authors also would like to thank the National Climate Center of China Meteorological Administration and Bureau of Hydrology, Zhejiang Province for providing data for this study.

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Authors and Affiliations

  1. Department of Civil Engineering, Institute of Hydrology and Water Resources, Zhejiang University, Hangzhou, 310058, Zhejiang, China

    Ye Tian & Yue-Ping Xu

  2. Department of Water Engineering and Management, Faculty of Engineering Technology, University of Twente, Enschede, The Netherlands

    Martijn J. Booij

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  1. Ye Tian
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Correspondence to Yue-Ping Xu.

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Tian, Y., Booij, M.J. & Xu, YP. Uncertainty in high and low flows due to model structure and parameter errors. Stoch Environ Res Risk Assess 28, 319–332 (2014). https://doi.org/10.1007/s00477-013-0751-9

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