Dynamic Identifiability Analysis-Based Model Structure Evaluation Considering Rating Curve Uncertainty
Publication: Journal of Hydrologic Engineering
Volume 20, Issue 5
Abstract
When applying hydrological models, different sources of uncertainty are present, and evaluations of model performances should take these into account to assess model outcomes correctly. Furthermore, uncertainty in the discharge observations complicates the model identification, both in terms of model structure and parameterization. In this paper, the authors compare two different lumped model structures (PDM and NAM) considering uncertainty coming from the rating curve. Limits of acceptability for the model simulations were determined based on derived uncertainty bounds of the discharge observations. The authors applied the DYNamic Identifiability Approach (DYNIA) to identify structural failure of both models and to evaluate the configuration of their structures. In general, similar model performances are observed. However, the model structures tend to behave differently in the course of time, as revealed by the DYNIA approach. Based on the analyses performed, the probability based soil storage representation of the PDM model outperforms the NAM structure. The incorporation of the observation error did not prevent the DYNIA analysis to identify potential model structural deficiencies that are limiting the representation of the seasonal variation, primarily indicated by shifting regions of parameter identifiability. As such, the proposed approach is able to indicate where deficiencies are found and model improvement is needed.
Get full access to this article
View all available purchase options and get full access to this article.
References
Abebe, N. A., Ogden, F. L., and Pradhan, N. R. (2010). “Sensitivity and uncertainty analysis of the conceptual HBV rainfallrunoff model: Implications for parameter estimation.” J. Hydrol., 389(3–4), 301–310.
Beck, B., and Young, P. (1976). “Systematic Identification of DO-BOD model structure.” J. Environ. Eng. Div., 102(5), 909–927.
Beven, K. (2006). “A manifesto for the equifinality thesis.” J. Hydrol., 320(1–2), 18–36.
Beven, K. (2008). Environmental modelling: An uncertain future?, Taylor & Francis, London.
Beven, K., and Binley, A. M. (1992). “The future of distributed models: Model calibration and uncertainty prediction.” Hydrol. Processes, 6(3), 279–298.
Beven, K., and Freer, J. (2001). “Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology.” J. Hydrol., 249(1–4), 11–29.
Beven, K., Smith, P., and Freer, J. (2008). “So just why would a modeller choose to be incoherent?” J. Hydrol., 354(1–4), 15–32.
Beven, K., Smith, P. J., and Wood, A. (2011). “On the colour and spin of epistemic error (and what we might do about it).” Hydrol. Earth Syst. Sci., 15(10), 3123–3133.
Beven, K., and Westerberg, I. (2011). “On red herrings and real herrings: Disinformation and information in hydrological inference.” Hydrol. Processes, 25(10), 1676–1680.
Blazkova, S., and Beven, K. (2009). “A limits of acceptability approach to model evaluation and uncertainty estimation in flood frequency estimation by continuous simulation: Skalka catchment, Czech Republic.” Water Resour. Res., 45(12), W00B16.
Boyle, D. P., Gupta, H. V., and Sorooshian, S. (2000). “Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods.” Water Resour., 36(12), 3663–3674.
Brun, R., Reichert, P., and Kfinsch, H. R. (2001). “Practical identifiability analysis of large environmental simulation.” Water Resour. Res., 37(4), 1015–1030.
Cabus, P. (2008). “River flow prediction through rainfall runoff modelling with a probability-distributed model (PDM) in Flanders, Belgium.” Agric. Water Manage., 95(7), 859–868.
Clark, M. P., Kavetski, D., and Fenicia, F. (2011). “Pursuing the method of multiple working hypotheses for hydrological modeling.” Water Resour. Res., 47(9), 1–16.
Cullmann, J., and Wriedt, G. (2008). “Joint application of event-based calibration and dynamic identifiability analysis in rainfall-runoff modelling: Implications for model parameterisation.” J. Hydroinform., 10(4), 301–316.
De Pauw, D., Steppe, K., and De Baets, B. (2008). “Identifiability analysis and improvement of a tree water flow and storage model.” Math. Biosci., 211(2), 314–332.
de Vos, N. J., Rientjes, T. H. M., and Gupta, H. V. (2010). “Diagnostic evaluation of conceptual rainfall-runoff models using temporal clustering.” Hydrol. Processes, 24(20), 2840–2850.
DHI. (2008). MIKE 11, a modelling system for rivers and channels, reference manual, Horsholm, Denmark.
Fenicia, F., McDonnell, J. J., and Savenije, H. H. G. (2008). “Learning from model improvement: On the contribution of complementary data to process understanding.” Water Resour. Res., 44(6), 1–13.
Gupta, H. V., Sorooshian, S., and Yapo, P. O. (1998). “Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information.” Water Resour. Res., 34(4), 751–763.
Hengl, S., Kreutz, C., Timmer, J., and Maiwald, T. (2007). “Data-based identifiability analysis of non-linear dynamical models.” Bioinformatics, 23(19), 2612–2618.
Hornberger, G., and Spear, R. (1981). “An approach to the preliminary analysis of environmental systems.” J. Environ. Manage., 12, 7–18.
Kavetski, D., Kuczera, G., and Franks, S. W. (2006a). “Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory.” Water Resour. Res., 42(3), 1–9.
Kavetski, D., Kuczera, G., and Franks, S. W. (2006b). “Bayesian analysis of input uncertainty in hydrological modeling: 2. Application.” Water Resour. Res., 42(3), 1–10.
Krueger, T., et al. (2010). “Ensemble evaluation of hydrological model hypotheses.” Water Resour. Res., 46(7), 1–17.
Kuczera, G., Kavetski, D., Franks, S., and Thyer, M. (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.
Lee, H., Mcintyre, N., Wheater, H., Young, A., and Wagener, T. (2004). “Assessment of rainfall-runoff model structures for regionalisation purposes.” Hydrology: Science and Practice for the 21st Century, Volume 1. Proc., British Hydrological Society Int. Conf., B. Webb, N. Arnell, C. Onof, N. MacIntyre, R. Gurney, and C. Kirby, eds., Imperial College, London, 302–308.
Lin, Z., and Beck, M. B. (2007). “On the identification of model structure in hydrological and environmental systems.” Water Resour. Res., 43(2), 1–19.
Liu, Y., Freer, J., Beven, K., and Matgen, P. (2009). “Towards a limit of acceptability approach to the calibration of hydrological models: Extending observation error.” J. Hydrol., 367(1–2), 93–103.
McMillan, H., Clark, M. P., Bowden, W. B., Duncan, M., and Woods, R. A. (2011). “Hydrological field data from a modeller’s perspective: Part 1. Diagnostic tests for model structure.” Hydrol. Processes, 25(4), 511–522.
McMillan, H., Freer, J., Pappenberger, F., Krueger, T., and Clark, M. P. (2010). “Impacts of uncertain river flow data on rainfall-runoff model calibration and discharge predictions.” Hydrol. Processes, 24(10), 1270–1284.
Moore, R. J. (2007). “The PDM rainfall-runoff model.” Hydrol. Earth Syst. Sci., 11(1), 483–499.
Muleta, M. K. (2012). “Improving model performance using season-based evaluation.” J.Hydrol. Eng., 191–200.
Nielsen, S. A., and Hansen, E. (1973). “Numerical simulation of the rainfall-runoff process on a daily basis.” Nordic Hydrol., 4(3), 171–190.
Pappenberger, F., Matgen, P., Beven, K. J., Henry, J., Pfister, L., and De Fraipont, P. (2006). “Influence of uncertain boundary conditions and model structure on flood inundation predictions.” Adv. Water Resour., 29(10), 1430–1449.
Peters, N. E., Freer, J., and Beven, K. (2003). “Modelling hydrologic responses in a small forested catchment (Panola Mountain, Georgia, USA): A comparison of the original and a new dynamic TOPMODEL.” Hydrol. Processes, 17(2), 345–362.
Reichert, P., and Mieleitner, J. (2009). “Analyzing input and structural uncertainty of nonlinear dynamic models with stochastic, time-dependent parameters.” Water Resour. Res., 45(10), 1–19.
Reusser, D. E., and Zehe, E. (2011). “Inferring model structural deficits by analyzing temporal dynamics of model performance and parameter sensitivity.” Water Resour. Res., 47(7), 1–15.
Rouhani, H., Willems, P., Wyseure, G., and Feyen, J. (2007). “Parameter estimation in semi-distributed hydrological catchment modelling using a multi-criteria objective function.” Hydrol. Processes, 21(22), 2998–3008.
Rubarenzya, M. H., Willems, P., and Berlamont, J. (2007). “Identification of uncertainty sources in distributed hydrological modelling: Case study of the Grote Nete catchment in Belgium.” Water SA, 33(5), 633–642.
Shrestha, R. R., and Simonovic, S. P. (2009). “Fuzzy nonlinear regression approach to stage-discharge analyses: Case study.” J. Hydrol. Eng., 15(1), 49–56.
Sobol, I. M. (1967). “On the distribution of points in a cube and the approximate evaluation of integrals.” USSR Comput. Math. Math. Phys., 7(4), 86–112.
Sobol, I. M. (1976). “Uniformly distributed sequences with an additional uniform property.” USSR Comput. Math. Math. Phys., 16(5), 236–242.
Tomassini, L., Reichert, P., Künsch, H. R., Buser, C., Knutti, R., and Borsuk, M. E. (2009). “A smoothing algorithm for estimating stochastic, continuous time model parameters and its application to a simple climate model.” J. R. Stat. Soc. Ser. C, 58(5), 679–704.
Tripp, D. R., and Niemann, J. D. (2008). “Evaluating the parameter identifiability and structural validity of a probability-distributed model for soil moisture.” J. Hydrol., 353(1–2), 93–108.
Vansteenkiste, T., Pereira, F., Willems, P., and Mostaert, F. (2011). “Effect of climate change on the hydrological regime of navigable water courses in Belgium: Subreport 2—Climate change impact analysis by conceptual models. Versie 1_0., 706_18.” Waterbouwkundig Laboratorium & K.U. Leuven, Antwerpen, België.
Vrugt, J. A., Bouten, W., Gupta, H. V., and Sorooshian, S. (2002). “Toward improved identifiability of hydrologic model parameters: The information content of experimental data.” Water Resour. Res., 38(12), 48-1–48-13.
Vrugt, J. A., and Robinson, B. A. (2007). “Treatment of uncertainty using ensemble methods: Comparison of sequential data assimilation and Bayesian model averaging.” Water Resour. Res., 43(1), 1–15.
Vrugt, J. A., ter Braak, C. J. F., Clark, M. P., Hyman, J. M., and Robinson, B. A. (2008). “Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation.” Water Resour. Res., 44(12), 1–15.
Wagener, T., Boyle, D. P., Lees, M. J., Wheater, H. S., Gupta, H. V., and Sorooshian, S. (2001). “A framework for development and application of hydrological models.” Hydrol. Earth Syst. Sci., 5(1), 13–26.
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.” Hydrol. Processes, 17(2), 455–476.
Westerberg, I., et al. (2011). “Calibration of hydrological models using flow-duration curves.” Hydrol. Earth Syst. Sci., 15(7), 2205–2227.
Winsemius, H. C., Schaefli, B., Montanari, A., and Savenije, H. H. G. (2009). “On the calibration of hydrological models in ungauged basins: A framework for integrating hard and soft hydrological information.” Water Resour. Res., 45(12), 1–15.
Wriedt, G., and Rode, M. (2006). “Investigation of parameter uncertainty and identifiability of the hydrological model WaSiM-ETH.” Adv. Geosci., 9, 145–150.
Young, P., Mckenna, P., and Bruun, J. (2001). “Identification of non-linear stochastic systems by state dependent parameter estimation.” Int. J. Control, 74(18), 1837–1857.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 20 • Issue 5 • May 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 6, 2013
Accepted: Mar 4, 2014
Published online: Mar 6, 2014
Discussion open until: Feb 26, 2015
Published in print: May 1, 2015
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.