Skip to main content
Log in

Statistical Analysis of Parameters and Residuals of a Conceptual Water Balance Model – Methodology and Case Study

  • Published:
Water Resources Management Aims and scope Submit manuscript

Abstract

Statistical analysis of parameters and residuals of conceptual hydrological models has received little effort in the hydrological research, certainly by orders of magnitude less than on many other problems like development and comparison of automatic calibration methods, optimisation algorithms, etc. Much more work is required than is presently undertaken to investigate the properties of model residuals. There is a need of an easily understandable and applicable statistical analysis scheme. In this article, a procedure is presented through which two basic issues of model evaluation are accounted for. First, different techniques used for parameter analysis are discussed. Second, methodology of residual analysis is discussed and the general behaviours of residuals are examined. To illustrate the procedure, a simple water balance model was applied to the Stabbybäcken River Basin in central Sweden.

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

  • Aitken, A. P.: 1973, Assessing systematic errors in rainfall-runoff models, J. Hydrol. 20, 121-136.

    Google Scholar 

  • Alley, W. M.: 1984, On the treatment of evapotranspiration, soil moisture accounting and aquifer recharge in monthly water balance models, Wat. Resour. Res. 20(8), 1137-1149.

    Google Scholar 

  • Bergström, S.: 1976, Development and Application of a Conceptual Model for Scandinavian Catchments, The Swedish Meteorological and Hydrological Institute (SMHI), Report RHO 7, Norrköping, Sweden.

    Google Scholar 

  • Bergström, S.: 1992, The HBV Model — Its Structure and Applications, SMHI Report RH No. 4, Norrköping, Sweden.

    Google Scholar 

  • Clarke, R. T.: 1973, ‘A review of some mathematical models used in hydrology, with observations on their calibration and use’, J. Hydrol. 19(1), 1-20.

    Google Scholar 

  • Crawford, N. H. and Linsley, P. K.: 1966, Digital simulation in Hydrology: Stanford Watershed Model IV, Technical Report 39, Stanford University, Stanford.

    Google Scholar 

  • Dawdy, D. R. and O'Donnell, T.: 1965, Mathematical models of catchment behaviour, Proceedings of American Society of Civil Engineers. Journal of the Hydraulics Divisions of the ASCE, 91(HY4), 123-137.

    Google Scholar 

  • Duan, Q., Sorooshian, S. and Gupta, V. K.: 1992, Effective and efficient global optimisation for conceptual rainfall-runoff models, Water Resour. Res. 28(4), 1015-1031.

    Google Scholar 

  • 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.

    Google Scholar 

  • Gupta, V. K. and Sorooshian, S.: 1985, The relationship between data and the precision of estimated parameters, J. Hydrol. 81, 57-77.

    Google Scholar 

  • Haan, C. T.: 1977, Statistical Methods in Hydrology, The Iowa State University Press, Ames, Iowa, 378 pp.

    Google Scholar 

  • Hendrickson, J., Sorooshian, S. And Brazil, L. E.: 1988, Comparison of Newton-type and direct search algorithms for calibration of conceptual rainfall-runoff models, Water Resour. Res. 24(5), 691-700.

    Google Scholar 

  • Kruskal, W. H. and Wallis, W. A.: 1952, Use of ranks in one criterion variance analysis, J. Amer. Stat. Assoc. 47, 583-621.

    Google Scholar 

  • Kuczera, G.: 1983, Improved parameter inference in catchment models 1. Evaluating parameter uncertainty, Water Resour. Res. 19(5), 1151-1162.

    Google Scholar 

  • Kuczera, G.: 1997, Efficient subspace probabilistic parameter optimisation for catchment models, Water Resour. Res. 33(1), 177-185.

    Google Scholar 

  • Moore, R. J. and Clarke, R. T.: 1981, A distribution function approach to rainfall runoff modelling, Water Resour. Res. 17(5), 1367-1382.

    Google Scholar 

  • Nash, J. E. and Sutcliffe, J.: 1970, River flow forecasting through conceptual models. Part I. A discussion of principles, J. Hydrol. 10, 282-290.

    Google Scholar 

  • Pickup, G.: 1977, Testing the efficiencies of algorithms and strategies for automatic calibration of rainfall-runoff models, Hydrological Science Bulletin 22(2), 257-274.

    Google Scholar 

  • Sefe, F. T. and Boughton, W. C.: 1982, Variation of model parameter values and sensitivity with type of objective function, J. Hydrol. 21(1), 117-132.

    Google Scholar 

  • Servat, E. and Dezetter, A.: 1991, Selection of calibration objective functions in the context of rainfall-runoff modeling in a Sudanese Savannah area, Hydrol. Sci. J. 36(4), 307-330.

    Google Scholar 

  • Sorooshian, S. and Dracup, J. A.: 1980, Stochastic parameter estimation procedures for hydrologic rainfall-runoff models. Correlated and Heteroscedastic error cases, Water Resour. Res. 16(2), 430-442.

    Google Scholar 

  • Sorooshian, S. and Gupta, V. K.: 1983, Automatic calibration of conceptual rainfall-runoff models: The question of parameter observability and uniqueness, Water Resour. Res. 19(1), 251-259.

    Google Scholar 

  • Sorooshian, S., Duan, Q. and Gupta, V. K.: 1993, Calibration of rainfall-runoff models: Application of global optimisation to the Sacramento soil moisture accounting model, Water Resour. Res. 29(4), 1185-1194.

    Google Scholar 

  • Spiegel, M. R.: 1980, Theory and Problems of Probability and Statistics, McGraw-Hill Book Company, 372 pp.

  • Thornthwaite, C. W. and Mather, J. R.: 1955, The Water Balance, Publications in Climatology, Laboratory of Climatology, Centerton, NJ, 8(1).

    Google Scholar 

  • Vandewiele, G. L., Xu, C.-Y. and Ni-lar-win: 1992, Methodology and comparative study of monthly water balance models in Belgium, China and Burma, J. Hydrol. 134, 315-347.

    Google Scholar 

  • Vertessy, R. A., Hatton, T. J., O'Shaughnessy, P. J. and Jayasuriya, M. D. A.: 1993, Predicting water yield from a mountain ash forest catchment using a terrain analysis based catchment model, J. Hydrol. 150, 665-700.

    Google Scholar 

  • Wang, Q. J.: 1991, The generic algorithm and its application to calibrating conceptual rainfall-runoff models, Water Resour. Res. 27(9), 2467-2471.

    Google Scholar 

  • Xu, C.-Y. and Singh, V. P.: 1998, A review on monthly water balance models for water resources investigation and climatic impact assessment, Water Resources Management 12, 31-50.

    Google Scholar 

  • Xu, C.-Y., Seibert, J. and Halldin, S.: 1996, Regional water balance modelling in the NOPEX area: Development and application of monthly water balance models, J. Hydrol. 180(1–4), 211-236.

    Google Scholar 

  • Yapo, P. O., Gupta, H. V. and Sorooshian, S.: 1996, Automatic calibration of conceptual rainfallrunoff models: Sensitivity to calibration data, J. Hydrol. 181, 23-48.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, Cy. Statistical Analysis of Parameters and Residuals of a Conceptual Water Balance Model – Methodology and Case Study. Water Resources Management 15, 75–92 (2001). https://doi.org/10.1023/A:1012559608269

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1012559608269

Navigation