The efficiency of nonparametric methods based on residual analizes and parametric method to estimate hydrological model uncertainty

Document Type : Research Paper


University of Gonbad Kavoos


Despite modern scientific knowledge and computational power in hydrology, the key to properly addressing hydrologic uncertainty remains a critical and challenging one. Here, we applied lumped HBV hydrological model to describe the uncertainty in runoff prediction in Chehl-Chay watershed in Golestan province. We applied a new framework for uncertainty analysis that is rooted on ideas from predicting model residual uncertainty. The uncertainty calculated by local Errors and Clustering (EEC) is compared with estimates from two non parametric methods (quantile regression (QR) and random forest (RF)) and a parametric method (GLUE). Firstly, the model parameters were optimized by Shuffled Complex Evolution approach and model residuals of test data were computed. Fuzzy clustering in EEC is carried out by the fuzzy c-means method and employs four clusters, predictive discharges, observed discharges, rainfall values and residuals in study basin. The results of this case study show that the uncertainty estimates obtained by EES which is trained by SVM gives wider uncertainty band and RF gives narrower uncertainty band. The best overall uncertainty estimates according to the PICP, MPI and ARIL indices were obtained with QR and then EEC. In comparison with non-parametric, with respct to all indices nonparametric methods had better performance than GLUE method.


Main Subjects

AghaKouchak, A. and Habib, E. (2010). Application of a conceptual hydrologic model in teaching hydrologic processes. Int. J. Eng. Educ. 26,  963–973.
Beven, K.. and Binley. A. (1992). The future of distributed models: Model calibration and uncertainty prediction. Hydrol. Process., 6, 279-298.
Bezdek, J.C. (1974a). Numerical taxonomy with fuzzy sets. Journal of Mathematical Biology, 1: 57–71.
Bezdek, J.C. (1974b). Cluster validity with fuzzy sets. Journal of Cybernetics, 3 (3), 58–72.
Breiman, Leo. (2001). Random forests. Mach. Learn, 45 (1), 5– 32.
Chang, C. H., Yang J.C. and Tung, Y.K. (1993). Sensitivity and uncertainty analysis of a sediment transport models: a global approach. Stochastic Hydrological Hydraulics, 7 (4), 299- 314 .
Dogulu,  N., López López, P., Solomatine, D. P., Weerts, A. H. and Shrestha, D. L. (2015). Estimation of predictive hydrologic uncertainty using the quantile regression and UNEEC methods and their comparison on contrasting catchments. Hydrol. Earth Syst. Sci., 19, 3181–3201.
Evin, G., Thyer, M. Kavetski, D. McInerney D. and Kuczera, G. (2014). Comparison of joint versus postprocessor approaches for hydrological uncertainty estimation accounting for error autocorrelation and hetero-scedasticity. Water Resour. Res, 50 (3), 2350– 2375.
Fukuyama, Y. and Sugeno, M. (1989). A new method of choosing the number of clusters for the fuzzy c-means method. Proceedings of Fifth Fuzzy Systems Symposium, pp. 247–250 (in Japanese)
Houska, T., Multsch, P., Kraft, H., Frede, G. and Breuer, L. (2014). Monte Carlo-Based calibration and uncertainty analysis of a coupled plant growth and hydrological model. Biogeosciences, 11, 2069-2082.
Khu, S.T. and Werner, M.G.F. (2003). Reduction of monte-carlo simulation runs for uncertainty estimation in hydrological modeling. Hydrology and Earth System Sciences. 7 (5),  680-692.
Koenker, R. (2005). Quantile Regression, Cambridge University Press.
Koenker, R. and Bassett, J.r. (1978). Regression Quantiles, Econometrica, 1, 33–50.
López López, P., Verkade, J.S., Weerts, A .H. and Solomatine, D.P. (2014). Alternative configurations of quantile regression for estimating predictive uncertainty in water level forecasts for the Upper Severn River: a comparison. Hydrol. Earth Syst. Sci. Discuss. 11 (4), 3811 – 3855.
Malone, B.P., McBratney, A.B. and Minasny, B. (2011). Empirical estimates of uncertainty for mapping continuous depth functions of soil attributes. Geoderma, 160 (3– 4), 614-626.
Matott, L.S., Babendreier, J.E. and Purucker, S.T. (2009). Evaluating uncertainty in integrated environmental models: A review of concepts and tools. Water Resources Research, 45, W06421.
Montanari, A. (2011). Uncertainty of Hydrological Predictions. In: Peter Wilderer (ed.) Treatise on Water Science, vol 2. pp. 459–478 Oxford: Academic Press.
Rouhani, H. and Farahi Moghadam, M. (2014). Application  of the Genetic  Algorithm Technique  for  Optimization  of the Hydrologic  Tank and  SIMHHYD Models’ Parameters. Journal Of Range and Watershed Management (Iranian Journal Of Natural Resources). 66(4), 521-533.
 In Farsi).
Shrestha, D. L., and D. P. Solomatine (2006). Machine learning approaches for estimation of prediction interval for the model output , Neural Networks , 19 (2), 225 – 235, doi: 10.1016/ j.neunet. 2006. 01. 012.
Siebert, J. and Vis, M. J. P. (2012). Teachinghydrological modeling with a userfriendly catchment runoff-model software package, Earth Syst. Sci. 16, 3315-3325.
Solomatine, D. P. and Siek, M. B. (2006). Modular learning models in forecasting natural phenomena. Neural Networks, 19(2), 215-224.
Solomatine, D. P. and Shrestha, D. L. (2009). A novel method to estimate model uncertainty using machine learning techniques, Water Re-sour. Res., 45, W00B11.
Walker, W.E., Harremoës, P., Rotmans, J., Van der Sluis, J.P., Van Asselt, M.B.A., Janssen, P. and Krayer von Krauss M.P. (2003). Defining uncertainty a conceptual basis for uncertainty management in model-based decision support. Integrated Assessment, 4 (1), 5-17
Weerts, A. H., Winsemius, H. C. and Verkade, J. S. (2011). Estima-tion of predictive hydrological uncertainty using quantile re-gression: examples from the National Flood Forecasting Sys-tem (England and Wales), Hydrol. Earth Syst. Sci., 15, 255–265.
Xu, T., and Valocchi, A .J.(2015). Data-driven methods to improve base flow prediction of a regional groundwater model. Computers & Geosciences. 85(B), 124–13.