Parameter uncertainty methods in evaluating a lumped hydrological model

Authors

  • Jairo Diaz-Ramirez Department of Civil and Environmental Engineering, Mississippi State University, USA https://orcid.org/0000-0003-1815-8028
  • Rene Camacho Department of Civil and Environmental Engineering, Mississippi State University, USA
  • William McAnally Department of Civil and Environmental Engineering, Mississippi State University, USA https://orcid.org/0009-0002-3397-0401
  • James Martin Department of Civil and Environmental Engineering, Mississippi State University, USA

DOI:

https://doi.org/10.4067/S0718-28132012000200004

Keywords:

HSPF, parameter uncertainty, Monte Carlo simulation, Harr's point estimation method, uncertainty bounds of streamflow simulations

Abstract

Water resources modelers face the challenge of dealing with numerous uncertainties due to the lack of knowledge of the natural systems, numerical approaches used in modeling (equations, parameters, structures, solutions), and field data collected to set up and evaluate models. Propagation of parameter uncertainty into model results is a relevant topic in environmental hydrology. Uncertainty analyses improve assessment ofhydrological modeling. There is a need in modern hydrology of developing and testing uncertainty analysis methods that support hydrological model evaluation. In this research the propagation of model parameter uncertainty into streamflow model results is evaluated. The Hydrological Simulation Program - FORTRAN (HSPF) supported by the US Environmental Protection Agency was evaluated using hydroenvironmental data from the Luxapallila Creek watershed located in Mississippi and Alabama, USA. The uncertainty bounds ofmodel outputs were computed using the Monte Carlo simulation and Harr 's point estimation methods. Analysis of parameter uncertainty propagation on streamflow simulations from 12 HSPF parameters was accomplished using 5,000 Monte Carlo random samples and 24 Harr selected points for each selected parameter. The comparison showed that Harr's method could be an appropriate initial indicator of parameter uncertainty propagation on streamflow simulations, particularly for hydrology models with several parameters.

References

Al-Abed, N.A. and Whiteley, H.R. (2002). Calibration of the hydrological simulation program fortran (HSPF) model using automatic calibration and geographical information systems. Hydrological Process 16, 3169-3188. https://doi.org/10.1002/hyp.1094

Alarcon V.J., McAnally, W., Diaz-Ramirez, J., Martin, J. and Cartwright, J. (2009). A hydrological model of the Mobile River watershed, Southeastern USA. AIP Conference Proceedings 1148, 641-645. https://doi.org/10.1063/1.3225392

Albek, M., Ogiitveren, Ü.B. and Albek, E. (2004). Hydrological modeling of Seydi Suyu watershed (Turkey) with HSPF. Journal ofHydrology 285, 260-271. https://doi.org/10.1016/j.jhydrol.2003.09.002

Beven, K. and Binley, A. (1992). The future of distributed models: model calibration and uncertainty prediction. Hydrological Processes 6(3), 279-298. https://doi.org/10.1002/hyp.3360060305

Bicknell, B.R., Imnoff, J.C., Jobes, T.H. and Donigian, A.S. (2001). Hydrological Simulation Program - Fortran HSPF version 12, User's Manual. Prepared for AQUA TERRA Consultants Mountain View, California, in co-operation with Water Resources Discipline U.S. Geological Survey Reston, Virginia , and U.S. Environmental Protection Agency Athens, Georgia

Binley, A.M., Beven, K.J., Calver, A. and Watts, L.G. (1991). Changing responses in hydrology: assessing the uncertainty in physically based model predictions. Water Resources Research 27(6), 1253-1261. https://doi.org/10.1029/91WR00130

Butts, M.B., Payne, J.T., Kristensen, M. and Madsen, H. (2004). An evaluation of the impact of model structure on hydrological modelling uncertainty for streamflow simulation. Journal of Hydrology 298, 242-266. https://doi.org/10.1016/j.jhydrol.2004.03.042

Carpenter, T.M. and Georgakakos, K.P. (2004). Impacts of parametric and radar rainfall uncertainty on the ensemble streamflow simulations of a distributed hydrologic model. Journal ofHydrology 298, 202-221. https://doi.org/10.1016/j.jhydrol.2004.03.036

Christian, J.T. and Baecher, G.B. (2002). The point-estimate method with large numbers of variables. International Journal for Numerical and Analytical Methods in Geomechanics 26, 1515-1529. https://doi.org/10.1002/nag.256

Diaz-Ramirez, J.N., Perez-Alegria, L.R. and McAnally. W.H. (2008). Hydrology and sediment modeling using HSPF/BASINS in a tropical island watershed. Transactions of the ASABE 51(5), 1555-1565. https://doi.org/10.13031/2013.25312

Diaz-Ramirez, J.N., McAnally, W.H. and Martin, J.L. (2011). Analysis of hydrological processes applying the HSPF model in selected watersheds in Alabama, Mississippi, and Puerto Rico. Applied Engineering in Agriculture 27(6), 937-954. https://doi.org/10.13031/2013.40627

Dilks, D.W., Canale, R.P. and Meier, P.G. (1992). Development of Bayesian Monte Carlo techniques for water quality model uncertainty. Ecological Modelling 62, 149-162

Donigian, A.S., Bicknell, B.R. and Imhoff, J.C. (1995). Hydrological Simulation Program - FORTRAN (HSPF). In: Computer Models of Watershed Hydrology. Chapter 12, V.P. Sigh (editor). Water Resources Publications

Duan, Z., Diaz, J.N., Martin, J.L. and McAnally, W.H. (2008). Effects of land-use changes on Saint Louis Bay watershed modeling. Journal of Coastal Research, Special Issue 52, 117-124. https://doi.org/10.2112/1551-5036-52.sp1.117

Georgakakos, K.P., Seo, D.J. Gupta, H., Schaake, J. and Butts, M.B. (2004). Towards the characterization of streamflow simulation uncertainty through multimodel ensembles. Journal ofHydrology 298, 222-241. https://doi.org/10.1016/j.jhydrol.2004.03.037

Gupta, H.V., Beven, K.J. and Wagener, T. (2005).Model Calibration and Uncertainty Estimation. In: Encyclopedia of Hydrological Sciences, M. Anderson (editor). John Wiley & Sons Ltd.

Haan, C.T. (2002). Statistical Methods in Hydrology. 2nd ed., Iowa State Press

Harr, M.E. (1989). Probabilistic estimates for multivariate analysis. Applied Mathematical Modelling 13, 313-318. https://doi.org/10.1016/0307-904X(89)90075-9

Hayashi, S., Murakami, S., Watanabe, M. and Bao-Hua, X. (2004). HSPF simulation of runoff and sediment loads in the upper Changjiang River Basin, China. Journal ofEnvironmental Engineering 130(7), 801-815. https://doi.org/10.1061/(ASCE)0733-9372(2004)130:7(801)

Hummel, P., Kittle, J. and Gray, M. (2001). WDMUtil User's Manual Version 2.0: A Tool for Managing Watershed Modeling Time-Series Data. U.S. Environmental Protection Agency, Office of Science and Technology and Office of Water, Washington, D.C.

Jia, Y. (2004). Robust Optimization for Total Maximum Daily LoadAllocations. Ph.D. dissertation, University of Virginia

Laroche, A., Gallichand, J., Lagacé, R. and Pesant, A. (1996). Simulating atrazine transport with HSPF in an agricultural watershed. Journal ofEnvironmental Engineering 122(7), 622-630. https://doi.org/10.1061/(ASCE)0733-9372(1996)122:7(622)

McAnally, W.H., Martin, J.L., Diaz, J.N., Duan, Z., Mancilla, C.A., Tagert, M.L., O'Hara, C. and Ballweber, J.A. (2006). Assimilating Remotely Sensed Data into Hydrologic Decision Support Systems: BASINS Evaluation. Department of Civil Engineering and GeoResources Institute, Mississippi State University, MS

McIntyre, N., Wheater, H. and Lees, M. (2002). Estimation and propagation of parametric uncertainty in environmental models. Journal ofHydroinformatics 4(3), 177-197. https://doi.org/10.2166/hydro.2002.0018

Melching, C.S. (1992). An improved first-order reliability approach for assessing uncertainties in hydrologic modeling. Journal ofHydrology 132, 157-177. https://doi.org/10.1016/0022-1694(92)90177-W

Melching, C.S. (1995). Reliability Estimation. In: Computer Models of Watershed Hydrology, Chapter 3, V.P. Sigh (editor). Water Resources Publications, Littleton, CO

Metropolis, N. and Ulam, S. (1949). The Monte Carlo method. Journal of the American Statistical Association 44(247), 335-341

Moore, L.W., Matheny, H., Tyree, T., Sabatini, D. and Klaine, S.J. (1988). Agricultural runoff modeling in a small west Tennessee watershed. Research Journal of the Water Pollution Control Federation 60(2), 242-249

Morgan, M.G. and Henrion, M. (1990). Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis. Cambridge University Press

Nasr, A., Bruen, M., Jordan, P., Moles, R., Kiely, G. and Byrne. P. (2007). A comparison of SWAT, HSPF and SHETRAN/GOPC for modelling phosphorus export from three catchments in Ireland. Water Research 41(5), 1065-1073. https://doi.org/10.1016/j.watres.2006.11.026

Paul, S. (2003). Bacterial Total Maximum Daily Load (TMDL): Development and Evaluation of a New Classification Scheme for Impaired Waterbodies of Texas. Ph.D. dissertation, Texas A & M University

Refsgaard, J.C., and Henriksen, H.J. (2004). Modelling guidelines-terminology and guiding principles. Advances in Water Resources 27(1):71-82. https://doi.org/10.1016/j.advwatres.2003.08.006

Refsgaard, J.C., van der Sluijs, J.P., Hojberg, A.L. and Vanrolleghem, P.A. (2007). Uncertainty in the environmental modelling process - a framework and guidance. Environmental Modelling and Software 22, 1543-1556. https://doi.org/10.1016/j.envsoft.2007.02.004

Rogers, C.C.M., Beven, K.J., Morris, E.M. and Anderson, M.G. (1985). Sensitivity analysis, calibration and predictive uncertainty of the institute of hydrology distributed model. Journal of Hydrology 81, 179-191. https://doi.org/10.1016/0022-1694(85)90175-1

Ronen, Y. (1988). The Role of Uncertainties. In: Uncertainty Analysis, Y. Ronen (ed.). CRC Press

Rosenblueth, E. (1975). Point estimates for probability moments. Proceedings of the National Academy of Sciences of the United States of America 72(10), 3812-3814. https://doi.org/10.1073/pnas.72.10.3812

Singh, V.P. (1995). Computer Models of Watershed Hydrology. Water Resources Publications

Singh, V.P. and Woolhiser, D.A. (2002). Mathematical modeling of watershed hydrology. Journal of Hydrology Engineering 7(4), 270-292. https://doi.org/10.1061/(ASCE)1084-0699(2002)7:4(270)

Singh, V.P. and Frevert, D.K. (2002). Mathematical Models of Large Watershed Hydrology. Water Resources Publications

Sobol', I.M. (1994). A Primer for the Monte Carlo Method. CRC Press

Souid, M.A. (1999). Reliability of Rainfall-Runoff Models. Ph.D. dissertation, State University of New York

Thiemann, M., Trosset, M., Gupta, H. and Sorooshian, S. (2001). Bayesian recursive parameter estimation for hydrologic models. Water Resources Research 37(10), 2521-2535. https://doi.org/10.1029/2000WR900405

Tung, Y.K. (1996). Uncertainty and Reliability Analysis. In: Water Resources Handbook, L.W. Mays (editor). McGraw-Hill

Tung, Y.K. and Yen, B.C. (2005). Hydrosystems Engineering Uncertainty Analysis. McGraw-Hill

USEPA US Environmental Protection Agency (2000). BASINS technical note 6: estimating hydrology and hydraulic parameters for HSPF. Available at: http://www.epa.gov/waterscience/basins/docs/tecnote6.pdf. Accessed in November 2008

USEPA US Environmental Protection Agency (2006). HSPFParm version 1.3 beta July 2002. Available at: http://www.epa.gov/OST/ftp/basins/HSPFParm/. Accessed in April 7, 2006

USEPA US Environmental Protection Agency (2011). Better assessment science integrating point and nonpoint sources (BASINS) web site. Available at http://water.epa.gov/scitech/datait/models/basins/index.cfm. Accessed in November 2011

USEPA US Environmental Protection Agency (2012). Flow calibration tutorial: calibration scenarios. Available at: http://water.epa.gov/scitech/datait/models/basins/scenario.cfm. Accessed in June 13, 2012

Wagener, T., McIntyre, N., Lees, M.J., Wheater, H.S. and Gupta, H.V. (2003). Towards reduced uncertainty in conceptual rainfall-runoff modelling: dynamic identifiability analysis. Hydrological Processes 17(2), 455-476. https://doi.org/10.1002/hyp.1135

Wu, J. (2004). Water-Quality-Based BMP Design Approach and Uncertainty Analysis for Integrated Watershed Management. Ph.D. dissertation, University of Virginia

Zhang, H.X. and Yu, S.L. (2004). Applying the first-order error analysis in determining the margin of safety for total maximum daily load computations. Journal of Environmental Engineering 130(6), 664-673. https://doi.org/10.1061/(ASCE)0733-9372(2004)130:6(664)

Yu, P.S., Yang, T.C. and Chen, S.J. (2001). Comparison of uncertainty analysis methods for a distributed rainfall-runoff model. Journal of Hydrology 244, 43-59. https://doi.org/10.1016/S0022-1694(01)00328-6

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2012-12-01

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How to Cite

Parameter uncertainty methods in evaluating a lumped hydrological model. (2012). Obras Y Proyectos, 12, 42-56. https://doi.org/10.4067/S0718-28132012000200004