Estimating epistemic and aleatory uncertainties during hydrologic modeling: An information theoretic approach
dc.contributor.author | Gong, Wei | en_US |
dc.contributor.author | Gupta, Hoshin V. | en_US |
dc.contributor.author | Yang, Dawen | en_US |
dc.contributor.author | Sricharan, Kumar | en_US |
dc.contributor.author | Hero, Alfred O. | en_US |
dc.date.accessioned | 2013-06-18T18:32:40Z | |
dc.date.available | 2014-05-23T15:04:18Z | en_US |
dc.date.issued | 2013-04 | en_US |
dc.identifier.citation | Gong, Wei; Gupta, Hoshin V.; Yang, Dawen; Sricharan, Kumar; Hero, Alfred O. (2013). "Estimating epistemic and aleatory uncertainties during hydrologic modeling: An information theoretic approach." Water Resources Research 49(4): 2253-2273. <http://hdl.handle.net/2027.42/98239> | en_US |
dc.identifier.issn | 0043-1397 | en_US |
dc.identifier.issn | 1944-7973 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/98239 | |
dc.publisher | Princeton University Press | en_US |
dc.publisher | Wiley Periodicals, Inc. | en_US |
dc.subject.other | Uncertainty Analysis | en_US |
dc.subject.other | Entropy | en_US |
dc.subject.other | Model Structure Adequacy | en_US |
dc.subject.other | Information Theory | en_US |
dc.subject.other | Mutual Information | en_US |
dc.title | Estimating epistemic and aleatory uncertainties during hydrologic modeling: An information theoretic approach | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Natural Resources and Environment | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/98239/1/wrcr20161.pdf | |
dc.identifier.doi | 10.1002/wrcr.20161 | en_US |
dc.identifier.source | Water Resources Research | en_US |
dc.identifier.citedreference | Young, P. C., P. Mckenna, and J. Bruun ( 2001 ), Identification of non‐linear stochastic systems by state dependent parameter estimation, Int. J. Contr., 74 ( 18 ), 1837 – 1857, doi: 10.1080/00207170110089824. | en_US |
dc.identifier.citedreference | Reichert, P., and J. Mieleitner ( 2009 ), Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time‐dependent parameters, Water Resour. Res., 45, W10402, doi: 10.1029/2009WR007814. | en_US |
dc.identifier.citedreference | Ruddell, B. L., and P. Kumar ( 2009 ), Ecohydrologic process networks: 1. Identification, Water Resour. Res., 45, W03419, doi: 10.1029/2008WR007279. | en_US |
dc.identifier.citedreference | Scott, D. W. ( 2004 ), Handbook of Computational Statistics—Concepts and Methods, Springer, New York. | en_US |
dc.identifier.citedreference | Seo, D. J., H. D. Herr, and J. C. Schaake ( 2006 ), A statistical post‐processor for accounting of hydrologic uncertainty in short‐range ensemble streamflow prediction, Hydrol. Earth Syst. Sci. Discuss., 3 ( 4 ), 1987 – 2035. | en_US |
dc.identifier.citedreference | Shannon, C. E. ( 1948 ), A mathemetical theory of communication, The Bell System Technical Journal, 27, 379 – 423, 623–656. | en_US |
dc.identifier.citedreference | Sharma, A. ( 2000 ), Seasonal to interannual rainfall probabilistic forecasts for improved water supply management: Part 1—A strategy for system predictor identification, J. Hydrol., 239 ( 1–4 ), 232 – 239, doi: 10.1016/S0022‐1694(00)00346‐2. | en_US |
dc.identifier.citedreference | Singh, V. P. ( 1997 ), The use of entropy in hydrology and water resources, Hydrol. Process., 11 ( 6 ), 587 – 626, doi: 10.1002/(SICI)1099‐1085(199705)11:6<587::AID‐HYP479>3.3.CO;2‐G. | en_US |
dc.identifier.citedreference | Singh, V. P. ( 2000 ), The entropy theory as a tool for modelling and decision‐making in environmental and water resources, Water SA, 26 ( 1 ), 1 – 11. | en_US |
dc.identifier.citedreference | Sivapalan, M., et al. ( 2003 ), IAHS decade on predictions in ungauged basins (Pub), 2003–2012: Shaping an exciting future for the hydrological sciences, Hydrol. Sci. J., 48 ( 6 ), 857 – 880, doi: 10.1623/hysj.48.6.857.51421. | en_US |
dc.identifier.citedreference | Sorooshian, S., and J. A. Dracup ( 1980 ), Stochastic parameter‐estimation procedures for hydrologic rainfall‐runoff models—Correlated and heteroscedastic error cases, Water Resour. Res., 16 ( 2 ), 430 – 442, doi: 10.1029/WR016i002p00430. | en_US |
dc.identifier.citedreference | Sorooshian, S., Q. Y. Duan, and V. K. Gupta ( 1993 ), Calibration of rainfall‐runoff models—Application of global optimization to the Sacramento soil‐moisture accounting model, Water Resour. Res., 29 ( 4 ), 1185 – 1194, doi: 10.1029/92WR02617. | en_US |
dc.identifier.citedreference | Thiemann, M., M. Trosset, H. Gupta, and S. Sorooshian ( 2001 ), Bayesian recursive parameter estimation for hydrologic models, Water Resour. Res., 37 ( 10 ), 2521 – 2535, doi: 10.1029/2000WR900405. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Vrugt, J. A., C. Diks, H. V. Gupta, W. Bouten, and J. M. Verstraten ( 2005 ), Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation, Water Resour. Res., 41, W01017, doi: 10.1029/2004WR003059. | en_US |
dc.identifier.citedreference | Vrugt, J. A., C. 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. | en_US |
dc.identifier.citedreference | Wagener, T., D. P. Boyle, M. J. Lees, H. S. Wheater, H. V. Gupta, and S. Sorooshian ( 2001 ), A framework for development and application of hydrological models, Hydrol. Earth Syst. Sci., 5 ( 1 ), 13 – 26. | en_US |
dc.identifier.citedreference | Wagener, T., N. Mcintyre, M. J. Lees, H. S. Wheater, and H. V. Gupta ( 2003 ), Towards reduced uncertainty in conceptual rainfall‐runoff modelling: Dynamic identifiability analysis, Hydrol. Process., 17 ( 2 ), 455 – 476, doi: 10.1002/hyp.1135. | en_US |
dc.identifier.citedreference | Weijs, S. V., and N. van de Giesen ( 2011 ), Accounting for observational uncertainty in forecast verification: An information‐theoretical view on forecasts, observations, and truth B‐5010‐2008, Mon. Weather Rev., 139 ( 7 ), 2156 – 2162, doi: 10.1175/2011MWR3573.1. | en_US |
dc.identifier.citedreference | Weijs, S. V., G. Schoups, and N. van de Giesen ( 2010a ), Why hydrological predictions should be evaluated using information theory, Hydrol. Earth Syst. Sci., 14 ( 12 ), 2545 – 2558, doi: 10.5194/hess‐14–2545‐2010. | en_US |
dc.identifier.citedreference | Weijs, S. V., R. van Nooijen, and N. van de Giesen ( 2010b ), Kullback‐Leibler divergence as a forecast skill score with classic reliability‐resolution‐uncertainty decomposition, Mon. Weather Rev, 138 ( 9 ), 3387 – 3399, doi: 10.1175/2010MWR3229.1. | en_US |
dc.identifier.citedreference | Xu, L., D. Yuan, and Z. Ye ( 2010 ), Parameter sensitivity analysis and multi‐objective optimization on Hymod model, Water Resour. Power, 28 ( 11 ), 15 – 17. | en_US |
dc.identifier.citedreference | Young, P. C., and M. Ratto ( 2009 ), A unified approach to environmental systems modeling, Stochastic Environ. Res. Risk Assess., 23 ( 7SI ), 1037 – 1057, doi: 10.1007/s00477‐008‐0271‐1. | en_US |
dc.identifier.citedreference | Abebe, A. J., and R. K. Price ( 2003 ), Managing uncertainty in hydrological models using complementary models, Hydrol. Sci. J., 48 ( 5 ), 679 – 692, doi: 10.1623/hysj.48.5.679.51450. | en_US |
dc.identifier.citedreference | Ajami, N. K., Q. Y. Duan, X. G. Gao, and S. Sorooshian ( 2006 ), Multimodel combination techniques for analysis of hydrological simulations: application to distributed model intercomparison project results, J Hydrometeorol, 7 ( 4 ), 755 – 768, doi: 10.1175/JHM519.1. | en_US |
dc.identifier.citedreference | Ajami, N. K., Q. Y. Duan, and S. Sorooshian ( 2007 ), An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction, Water Resour. Res., 43, W01403, doi: 10.1029/2005WR004745. | en_US |
dc.identifier.citedreference | Amorocho, J., and B. Espildor ( 1973 ), Entropy in assessment of uncertainty in hydrologic systems and models, Water Resour. Res., 9 ( 6 ), 1511 – 1522, doi: 10.1029/WR009i006p01511. | en_US |
dc.identifier.citedreference | 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. | en_US |
dc.identifier.citedreference | Bellman, R. E., and R. Corporation ( 1957 ), Dynamic Programming, Princeton University Press, Princeton NJ. | en_US |
dc.identifier.citedreference | Beven, K. ( 1989 ), Changing ideas in hydrology—The case of physically‐based models, J. Hydrol., 105 ( 1–2 ), 157 – 172, doi: 10.1016/0022‐1694(89)90101‐7. | en_US |
dc.identifier.citedreference | Beven, K., and A. Binley ( 1992 ), The future of distributed models—Model calibration and uncertainty prediction, Hydrol. Process., 6 ( 3 ), 279 – 298, doi: 10.1002/hyp.3360060305. | en_US |
dc.identifier.citedreference | Beven, K., P. J. Smith, and A. Wood ( 2011 ), On the colour and spin of epistemic error (and what we might do about it), Hydrol. Earth Syst. Sci. Discuss., 8, 5355 – 5386, doi: 10.5194/hessd‐8–5355‐2011. | en_US |
dc.identifier.citedreference | Box, G. E. P., and G. M. Jenkins ( 1976 ), Time Series Analysis: Forecasting and Control, revised ed., Holden‐Day, San Francisco, Calif. | en_US |
dc.identifier.citedreference | Boyle, D. P. ( 2000 ), Multicriteria calibration of hydrological models, Ph.D. thesis, Dep. of Hydrology and Water Resources, Univ. of Arizona, Tucson, Ariz. | en_US |
dc.identifier.citedreference | Brazil, L. E. ( 1988 ), Multilevel calibration strategy for complex hydrologic simulation models, Ph.D. thesis, 217 pp., Colorado State Univ., Fort Collins, Colo. | en_US |
dc.identifier.citedreference | Bulygina, N., and H. Gupta ( 2009 ), Estimating the uncertain mathematical structure of a water balance model via Bayesian data assimilation, Water Resour. Res., 45, W00B13, doi: 10.1029/2007WR006749. | en_US |
dc.identifier.citedreference | Bulygina, N., and H. Gupta ( 2010 ), How Bayesian data assimilation can be used to estimate the mathematical structure of a model, Stochastic Environ Res. Risk Assess., 24 ( 6SI ), 925 – 937, doi: 10.1007/s00477‐010‐0387‐y. | en_US |
dc.identifier.citedreference | Bulygina, N., and H. Gupta ( 2011 ), Correcting the mathematical structure of a hydrological model via Bayesian data assimilation, Water Resour. Res., 47, W05514, doi: 10.1029/2010WR009614. | en_US |
dc.identifier.citedreference | Burnash, R. J. E., R. L. Ferral, and R. A. Mcguire ( 1973 ), A Generalized Streamflow Simulation System, 204 pp., Joint Fed.‐State River Forecast Center, Sacramento, Calif. | en_US |
dc.identifier.citedreference | Butts, M. B., J. T. Payne, M. Kristensen, and H. Madsen ( 2004 ), An evaluation of the impact of model structure on hydrological modelling uncertainty for streamflow simulation, J. Hydrol., 298 ( 1–4 ), 242 – 266, doi: 10.1016/j.hydrol.2004.03.042. | en_US |
dc.identifier.citedreference | Chapman, T. G. ( 1986 ), Entropy as a measure of hydrologic data uncertainty and model performance, J. Hydrol., 85 ( 1–2 ), 111 – 126, doi: 10.1016/0022–1694(86)90079‐X. | en_US |
dc.identifier.citedreference | Clark, M. P., A. G. Slater, D. E. Rupp, R. A. Woods, J. A. Vrugt, H. V. Gupta, T. Wagener, and L. E. Hay ( 2008 ), Framework for understanding structural errors (fuse): A modular framework to diagnose differences between hydrological models, Water Resour. Res., 44, W00B02, doi: 10.1029/2007WR006735. | en_US |
dc.identifier.citedreference | Cover, T. M., and J. A. Thomas ( 2006 ), Elements of Information Theory, John Wiley, Hoboken, N. J. | en_US |
dc.identifier.citedreference | Duan, Q., and J. Schaake ( 2002 ), Results from the 2nd International Workshop On Model Parameter Estimation Experiment (MOPEX), NWS, NOAA, Md. | en_US |
dc.identifier.citedreference | Duan, Q. Y., N. K. Ajami, X. G. Gao, and S. Sorooshian ( 2007 ), Multi‐model ensemble hydrologic prediction using Bayesian model averaging, Adv. Water Resour., 30 ( 5 ), 1371 – 1386, doi: 10.1016/j.advwatres.2006.11.014. | en_US |
dc.identifier.citedreference | Ewen, J., G. O'Donnell, A. Burton, and E. O'Connell ( 2006 ), Errors and uncertainty in physically‐based rainfall‐runoff modelling of catchment change effects, J. Hydrol., 330 ( 3–4 ), 641 – 650, doi: 10.1016/j.jhydrot.2006.04.024. | en_US |
dc.identifier.citedreference | Fenicia, F., H. Savenije, P. Matgen, and L. Pfister ( 2008 ), Understanding catchment behavior through stepwise model concept improvement, Water Resour. Res., 44, W01402, doi: 10.1029/2006WR005563. | en_US |
dc.identifier.citedreference | Neuman, S. P. ( 2003a ), Maximum likelihood Bayesian averaging of uncertain model predictions, Stochastic Environ Res. Risk Assess., 17 ( 5 ), 291 – 305, doi: 10.1007/s00477‐003‐0151‐7. | en_US |
dc.identifier.citedreference | Zhang, X. S., F. M. Liang, R. Srinivasan, and M. Van Liew ( 2009 ), Estimating uncertainty of streamflow simulation using Bayesian neural networks, Water Resour. Res., 45, W02403, doi: 10.1029/2008WR007030. | en_US |
dc.identifier.citedreference | Zhao, R. J., Y. L. Zhuang, L. R. Fang, X. R. Liu, and Q. S. Zhang ( 1980 ), The Xinanjiang model, paper presented at Hydrological Forecasting of the Oxford Symposium, IAHS AISH Publ. | en_US |
dc.identifier.citedreference | Moore, R. J. ( 1985 ), The probability‐distributed principle and runoff production at point and basin scales, Hydrolog Sci. J., 30 ( 2 ), 273 – 297, doi: 10.1080/02626668509490989. | en_US |
dc.identifier.citedreference | Nadarajah, S. ( 2005 ), A generalized normal distribution, J. Appl. Stat., 32 ( 7 ), 685 – 694, doi: 10.1080/02664760500079464. | en_US |
dc.identifier.citedreference | Nearing, G. S., H. V. Gupta, W. T. Crow, and W. Gong ( 2013 ), An Approach to Quantifying the Efficiency of a Bayesian Filter, Water Resour. Res., doi: 10.1002/wrcr.20177. | en_US |
dc.identifier.citedreference | Fernando, T., H. R. Maier, and G. C. Dandy ( 2009 ), Selection of input variables for data driven models: An average shifted histogram partial mutual information estimator approach, J. Hydrol., 367 ( 3–4 ), 165 – 176, doi: 10.1016/j.jhydrol.2008.10.019. | en_US |
dc.identifier.citedreference | Freer, J., K. Beven, and B. Ambroise ( 1996 ), Bayesian estimation of uncertainty in runoff prediction and the value of data: An application of the GLUE approach, Water Resour. Res., 32 ( 7 ), 2161 – 2173, doi: 10.1029/95WR03723. | en_US |
dc.identifier.citedreference | Georgakakos, K. P., D. J. Seo, H. Gupta, J. Schaake, and M. B. Butts ( 2004 ), Towards the characterization of streamflow simulation uncertainty through multimodel ensembles, J. Hydrol., 298 ( 1–4 ), 222 – 241, doi: 10.1016/j.jhydrol.2004.03.037. | en_US |
dc.identifier.citedreference | Gong, W. ( 2012 ), Watershed model uncertainty analysis based on information entropy and mutual information, Ph.D. thesis, Dep. of Hydraulic Engineering, Tsinghua Univ., Beijing, China. | en_US |
dc.identifier.citedreference | Granger, C. W. J., and J. Lin ( 1994 ), Using the mutual information coefficient to identify lags in non‐linear models, J. Time Ser. Anal., 15, 371 – 384. | en_US |
dc.identifier.citedreference | Gupta, H. V., and H. Kling ( 2011 ), On typical range, sensitivity, and normalization of mean squared error and Nash‐Sutcliffe efficiency type metrics, Water Resour. Res., 47, W10601, doi: 10.1029/2011WR010962. | en_US |
dc.identifier.citedreference | Gupta, H. V., S. Sorooshian, and P. O. Yapo ( 1998 ), Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information, Water Resour. Res., 34 ( 4 ), 751 – 763, doi: 10.1029/97WR03495. | en_US |
dc.identifier.citedreference | Gupta, H. V., H. Kling, K. K. Yilmaz, and G. F. Martinez ( 2009 ), Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling, J. Hydrol., 377 ( 1–2 ), 80 – 91, doi: 10.1016/j.jhydrol.2009.08.003. | en_US |
dc.identifier.citedreference | Gupta, H. V., M. P. Clark, J. A. Vrugt, G. Abramowitz, and M. Ye ( 2012 ), Towards a comprehensive assessment of model structural adequacy, Water Resour. Res., 48, W08301, doi: 10.1029/2011WR011044. | en_US |
dc.identifier.citedreference | Hero, A. O., B. Ma, O. Michel, and J. Gorman ( 2002 ), Applications of entropic spanning graphs, IEEE Signal Process. Mag., 19 ( 5 ), 85 – 95, doi: 10.1109/MSP.2002.1028355. | en_US |
dc.identifier.citedreference | Hoeting, J. A., D. Madigan, A. E. Raftery, and C. T. Volinsky ( 1999 ), Bayesian model averaging: A tutorial, Stat. Sci., 14 ( 4 ), 382 – 401. | en_US |
dc.identifier.citedreference | Hsu, K. L., H. V. Gupta, X. G. Gao, S. Sorooshian, and B. Imam ( 2002 ), Self‐organizing linear output map (Solo): An artificial neural network suitable for hydrologic modeling and analysis, Water Resour. Res., 38 ( 12 ), 1302, doi: 10.1029/2001WR000795. | en_US |
dc.identifier.citedreference | Hyvarinen, A., and E. Oja ( 1997 ), A fast fixed‐point algorithm for independent component analysis, Neural Comput., 9 ( 7 ), 1483, doi: 10.1162/neco.1997.9.7.1483. | en_US |
dc.identifier.citedreference | Hyvarinen, A., and E. Oja ( 2000 ), Independent component analysis: Algorithms and applications, Neural Netw., 13 ( 4–5 ), 411 – 430, doi: 10.1016/S0893‐6080(00)00026‐5. | en_US |
dc.identifier.citedreference | Hyvarinen, A., J. Karhunen, and E. Oja ( 2001 ), Independent Component Analysis, John Wiley, New York. | en_US |
dc.identifier.citedreference | Kaheil, Y. H., M. K. Gill, M. Mckee, and L. Bastidas ( 2006 ), A new Bayesian recursive technique for parameter estimation, Water Resour. Res., 42, W08423, doi: 10.1029/2005WR004529. | en_US |
dc.identifier.citedreference | Kavetski, D., G. Kuczera, and S. W. Franks ( 2006a ), Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory, Water Resour. Res., 42, W03407, doi: 10.1029/2005WR004368. | en_US |
dc.identifier.citedreference | Kavetski, D., G. Kuczera, and S. W. Franks ( 2006b ), Bayesian analysis of input uncertainty in hydrological modeling: 2. Application, Water Resour. Res., 42, W03408, doi: 10.1029/2005WR004376. | en_US |
dc.identifier.citedreference | Khan, S., S. Bandyopadhyay, A. R. Ganguly, S. Saigal, D. J. I. Erickson, V. Protopopescu, and G. Ostrouchov ( 2007 ), Relative performance of mutual information estimation methods for quantifying the dependence among short and noisy data, Phys. Rev. E., 76 (2), 26209. | en_US |
dc.identifier.citedreference | Kuczera, G. ( 1982 ), On the relationship between the reliability of parameter estimates and hydrologic time‐series data used in calibration, Water Resour. Res., 18 ( 1 ), 146 – 154, doi: 10.1029/WR018i001p00146. | en_US |
dc.identifier.citedreference | Leiva‐Murillo, J. M., and A. Artes‐Rodriguez ( 2007 ), Maximization of mutual information for supervised linear feature extraction, IEEE Trans. Neural Netw., 18 ( 5 ), 1433 – 1441, doi: 10.1109/TNN.2007.891630. | en_US |
dc.identifier.citedreference | Leonenko, N., L. Pronzat, and V. Savani ( 2008 ), A class of Renyi information estimators for multidimensional densities, Ann. Stat., 36 ( 5 ), 2153 – 2182, doi: 10.1214/07‐AOS539. | en_US |
dc.identifier.citedreference | Li, M., D. Yang, J. Chen, and S. S. Hubbard ( 2012 ), Calibration of a distributed flood forecasting model with input uncertainty using a Bayesian framework, Water Resour. Res., 48 ( 8 ), W08510, doi: 10.1029/2010WR010062. | en_US |
dc.identifier.citedreference | Lin, Z., and M. B. Beck ( 2007 ), On the identification of model structure in hydrological and environmental systems, Water Resour. Res., 43, W02402, doi: 10.1029/2005WR004796. | en_US |
dc.identifier.citedreference | Marshall, L., D. Nott, and A. Sharma ( 2007 ), Towards dynamic catchment modelling: A Bayesian hierarchical mixtures of experts framework, Hydrol. Process., 21 ( 7 ), 847 – 861, doi: 10.1002/hyp.6294. | en_US |
dc.identifier.citedreference | Misirli, F., H. V. Gupta, S. Sorooshian, and M. Thiemann ( 2003 ), Bayesian recursive estimation of parameter and output uncertainty for watershed models, in Calibration of Watershed Models, Water Sci.Appl. Ser., vol. 6, edited by Q. Duan, pp. 113 – 124, AGU, Washington, D. C. | en_US |
dc.identifier.citedreference | Neuman, S. P. ( 2003b ), Accounting for conceptual model uncertainty via maximum likelihood Bayesian model averaging, in Calibration and Reliability in Groundwater Modelling: A Few Steps Closer to Reality, edited by K. Kovar and Z. Hrkal, pp. 303 – 313, Int. Assoc. Hydrol. Sci., Wallingford, Conn. | en_US |
dc.identifier.citedreference | Pokhrel, P., and H. V. Gupta ( 2010 ), On the use of spatial regularization strategies to improve calibration of distributed watershed models, Water Resour. Res., 46, W01505, doi: 10.1029/2009WR008066. | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.