Skip to main content
Log in

Parameter Uncertainty Propagation in a Rainfall–Runoff Model; Case Study: Karoon-III River Basin

  • Water Resources and the Regime of Water Bodies
  • Published:
Water Resources Aims and scope Submit manuscript

Abstract

Conceptual hydrological models are popular tools for simulating land phase of hydrological cycle. Uncertainty arises from a variety of sources such as input error, calibration and parameters. Hydrologic modeling researches indicate that parametric uncertainty has been considered as one of the most important source. The objective of this study was to evaluate parameter uncertainty and its propagation in rainfall-runoff modeling. This study tried to model daily flows and calculate uncertainty bounds for Karoon-III basin, Southwest of Iran, using HEC-HMS (SMA). The parameters were represented by probability distribution functions (PDF), and the effect on simulated runoff was investigated using Latin Hypercube Sampling (LHS) on Monte Carlo (MC). Three chosen parameters, based on sensitivity analysis, were saturated-hydraulic-conductivity (Ks), Clark storage coefficient (R) and time of concentration (t c ). Uncertainty associated with parameters were accounted for, by representing each with a probability distribution. Uncertainty bounds was calculated, using parameter sets captured from LHS on parameters PDF of sub-basins and propagating to the model. Results showed that maximum reliability (11%) resulted from Ks propagating. For three parameters, underestimation was more than overestimation. Maximum sharpness and standard deviation (STD) was resulted from propagating Ks. Cumulative Distribution Function (CDF) of flow and uncertainty bounds showed that as flow increased, the width of uncertainty bounds increased for all parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Benke, K.K., Lowell, K.E., and Hamilton, A.J., Parameter uncertainty, sensitivity analysis and prediction error in a water-balance hydrological model, Math. Comp. Model., 2008, vol. 47, pp. 1134–1149.

    Article  Google Scholar 

  2. Bennett, T.H., Development and application of a continuous soil moisture accounting algorithm for the Hydrologic Engineering Center Hydrologic Modeling System (HEC-HMS), MSc Thesis, Dept. Civil Environ. Engineering, Univ. California, 1998.

    Google Scholar 

  3. Beven, K.J. and Freer, J., Equifinality, data assimilation, and uncertainty estimation in mechanistic modeling of complex environmental systems using the GLUE methodology, J. Hydrol., 2001, vol. 249, nos. 1–4, pp. 1–29.

    Google Scholar 

  4. Boughton, W. and Droop, O., Continuous simulation for design flood estimation—A review, Env. Model. Soft., 2003, vol. 18, pp. 309–318.

    Article  Google Scholar 

  5. Cosby, B.J., Hornberger, G.M., Clapp, R.B., and Ginn, T.R., A statistical exploration of the relationship of soil moisture characteristics to the physical properties of soils, Water Resour. Res., 1984, vol. 20, pp. 682–690.

    Article  Google Scholar 

  6. Cunderlik, J.M. and Simonovic, S.P., Calibration, verification and sensitivity analysis of the HEC-HMS hydrologic model, CFCAS project, Univ. Western Ontario, Project Rep. IV, 2004.

    Google Scholar 

  7. Da Ros, D. and Borga, M., Adaptive use of a conceptual model for real time flood forecasting, Nord, J. Hydrol., 1997, vol. 28, pp. 169–188.

    Google Scholar 

  8. Dalbey, K., Patra, A.K., Pitman, E.B., Bursik, M.I., and Sheridan, M.F., Input uncertainty propagation methods and hazard mapping of geophysical mass flows, J. Geophys. Res., 2008, vol. 113, B05203.

    Article  Google Scholar 

  9. Diaz-Ramirez, J.N., Johnson, B.E., McAnally, W.H., Martin, J.L., Alarcon, V.J., and Camacho, R.A., Estimation and propagation of parameter uncertainty in lump hydrological models: a case study of HSPF model applied to Luxapallila Creek watershed in southest USA, J. Hydrogeol. Hydraul. Eng., 2013, vol. 2, no. 1, 1000105.

    Google Scholar 

  10. Dongquan, Zh., Jining, Ch., Haozheng, W., and Qingyuan, T., Application of a sampling based on the combined objectives of parameter identification and uncertainty analysis of an Urban Rainfall-Runoff Model, J. Irrig. Drain. Eng., 2013, vol. 139, no. 1, pp. 66–74.

    Article  Google Scholar 

  11. Gabellani, S., Boni, G., Ferraris, L., Handerberg, J.V., and Provenzale, A., Propagation of uncertainty from rainfall to runoff: A case study with a stochastic rainfall generator, Adv. Water Res., 2007, vol. 30, pp. 2061–2071.

    Article  Google Scholar 

  12. Garcia, A., Sainz, A., Revilla, J.A., Alvarez, C., Juanes, J.A., and Puente, A., Surface water resources assessment in scarcely gauged basins in the north of Spain, J. Hydrol., 2008, vol. 356, pp. 312–326.

    Article  Google Scholar 

  13. Gourley, J.J. and Vieux, B.E., A method for identifying sources of model uncertainty in rainfall-runoff simulation, J. Hydrol., 2006, vol. 327, pp. 68–80.

    Article  Google Scholar 

  14. Govindaraju, R.S., Morbidelli, R., and Corradini, C., Areal infiltration modeling over soils with spatially correlated hydraulic conductivities, J. Hydrol. Eng., 2001, vol. 6, no. 2, pp. 150–158.

    Article  Google Scholar 

  15. Gupta, H.V., Beven, K.J., and Wagner, T., Model calibration and uncertainty estimation, in Encyclopedia Hydrol. Sci., Anderson, M., Ed., John Wiley and Sons, 2005.

    Google Scholar 

  16. Hromadka, T.V., Yen, C.C., and Seits, M.H., A comparison of techniques for evaluating hydrologic model uncertainty, Prob. Eng. Mech., 1987, vol. 2, no. 1, pp. 25–37.

    Article  Google Scholar 

  17. Hwang, Y., Clark, M.P., and Rajagopalan, B., Use of daily precipitation uncertainties in stream flow simulation and forecast, Stoch. Env. Res. Risk Ass., 2011, vol. 25, pp. 957–972.

    Article  Google Scholar 

  18. Janssen, H., Monte-Carlo based uncertainty analysis: Sampling efficiency and sampling convergence, Rel. Eng. Sys. Safe., 2013, vol. 109, pp. 123–132.

    Article  Google Scholar 

  19. Jia, Y., Robust Optimization for Total Maximum Daily Load Applications, Univ. Virginia, 2004.

    Google Scholar 

  20. Jin, X., Xu, Ch-Yu., Zhang, Qi., and Singh, V.P., Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model, J. Hydrol., 2010, vol. 383, pp. 147–155.

    Article  Google Scholar 

  21. Kitanidis, P. and Bruce, R., Real-time forecasting with a conceptual hydrologic model. 2: Application and results, Water. Resour. Res., 1980, vol. 16, pp. 1034–1044.

    Article  Google Scholar 

  22. Law, J.A., Statistical Approach to the Interstitial Heterogeneity of Sand Reservoirs, Trans. AIME, 1994, p. 155.

    Google Scholar 

  23. Melching, C.S., Reliability estimation, in Computer Models of Watershed Hydrology, Water Res. Pub. Littelton., 1995, pp. 69–118.

    Google Scholar 

  24. Mishra, S., Uncertainty and sensitivity analysis techniques for hydrologic modelling, J. Hydroinf., 2009, vol. 11, pp. 282–296.

    Article  Google Scholar 

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

    Book  Google Scholar 

  26. Moulin, L., Gaume, E., and Obled, C., Uncertainties on mean areal precipitation: assessment and impact on streamflow simulations, Hydrol. Earth Sys. Sci., 2009, vol. 13, pp. 99–114.

    Article  Google Scholar 

  27. Razmkhah, H., Comparing performance of different loss methods in rainfall-runoff modeling, Water Res., 2016, vol. 43, no. 1, pp. 207–224.

    Article  Google Scholar 

  28. Razmkhah, H., Akhound Ali, A.M., Radmanesh, F., and Saghafian, B., Evaluation of rainfall spatial correlation effect on rainfall-runoff modeling uncertainty, considering 2-copula, Arab. J. Geosci., 2016, vol. 9, no. 323.

    Google Scholar 

  29. Razmkhah, H., Saghafian, B., AkhoundAli, A.M., and Radmanesh, F., Rainfall-Runoff modeling considering soil moisture accounting algorithm, case study: Karoon III river basin, Water Resour., 2016, vol. 43, no. 4, pp. 699–710.

    Article  Google Scholar 

  30. Refsgaard, J.C., Thorsen, M., Jensen, J., Kleeschulte, S., and Hansen, S., Large scale modelling of groundwater contamination from nitrate leaching, J. Hydrol., 1999, vol. 221, pp. 117–140.

    Article  Google Scholar 

  31. Rogowski, A.S., Watershed physics: soil variability criteria, Water. Resour. Res., 1972, vol. 8.

    Google Scholar 

  32. Rousseau, M., Cerdan, O., Ern, A., Maitre, O.L., and Sochala, P., Study of overland flow with uncertain infiltration using stochastic tolls, Adv. Water. Resour., 2012, vol. 38, pp. 1–12.

    Article  Google Scholar 

  33. Sharma, M.L., Gander, G.A., and Hunt, C.G., Spatial variability of infiltration in a watershed, J. Hydrol., 1980, vol. 45, nos. 1–2, pp. 101–22.

    Article  Google Scholar 

  34. Sheikh, V., Van Loon, E., Hessel, R., and Jetten, V., Sensitivity of LISEM predicted catchment discharge to initial soil moisture content of soil profile, J. Hydrol., 2010, vol. 393, nos. 3–4, pp. 174–185.

    Article  Google Scholar 

  35. Straub, T.D., Melching, Ch.S., and Kocher, K.E., Equations for Estimating Clark Unit-Hydrograph Parameters for Rural Watersheds in Illinois, Water-resources Investigation Rep. 00-4184, USGS, 2000.

    Google Scholar 

  36. Taibi, A.E. and Elfeki, A., Modeling hydrologic responses of the Zwalm catchment using the REW approach: Propagation of uncertainty in the soil properties to model output, Arab. J. Geosci., 2011, vol. 4, pp. 1005–1018.

    Article  Google Scholar 

  37. Tung, Y.K., Uncertainty and reliability analysis, in Water resources Handbook, Mays, L.W., Ed., McGraw-Hill, 1996, pp. 7.1–7.65.

    Google Scholar 

  38. Vorechovskey, M. and Vovak, D., Correlation control in small-sample Monte Carlo type simulations I: A simulated annealing approach, Prob. Eng. Mech., 2009, vol. 24, pp. 452–462.

    Article  Google Scholar 

  39. Wagner, T. and Gupta, H.V., Model identification for hydrological forecasting under uncertainty, Stoch. Env. Res. Risk Ass., 2005, vol. 19, pp. 378–387.

    Article  Google Scholar 

  40. Wu, F.-Ch. and Tsang, Y.-Ph., Second-order Monte Carlo uncertainty/variability analysis using correlated model parameters: Application to salmonid embryo survival risk assessment, Ecol. Model., 2004, vol. 177, pp. 393–414.

    Article  Google Scholar 

  41. Xiong, L. and O’Connor, K.M., An empirical method to improve the prediction limits of the GLUE methodology in rainfall–runoff modeling, J. Hydrol., 2008, vol. 349, nos. 1–2, pp. 115–124.

    Article  Google Scholar 

  42. Yang, J., Reichert, P., Abbaspour, K.C., and Yang, H., Hydrological modelling of the Chaohe basin in China: statistical model formulation and bayesian inference, J. Hydrol., 2007, vol. 340, pp. 167–182.

    Article  Google Scholar 

  43. Ye, M., Pan, F., Wu, Y.-Sh., Hu, B.-X., Shirley, C., and Yu, Zh., Assessment of radionuclide transport uncertainty in the unsaturated zone of Yucca Mountain, Adv. Water Resour., 2007, vol. 30, pp. 118–134.

    Article  Google Scholar 

  44. Yu, P.-Sh., Yang, T.-Ch., and Chen, Sh.-J., Comparison of uncertainty analysis methods for a distributed rainfall-runoff model, J. Hydrol., 2001, vol. 244, pp. 43–59.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Homa Razmkhah.

Additional information

The article is published in the original.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Razmkhah, H. Parameter Uncertainty Propagation in a Rainfall–Runoff Model; Case Study: Karoon-III River Basin. Water Resour 45, 34–49 (2018). https://doi.org/10.1134/S0097807817050074

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0097807817050074

Keywords

Navigation