Incorporating Prior Knowledge in the Calibration of Hydrological Models for Water Resources Forecasting

  • Julien LeratEmail author
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 28)


The management of water resources in Australia faces increasing challenges due the rise of conflicting demands and a highly variable climate. In this context, the Bureau of Meteorology developed a dynamic seasonal forecasting service providing probabilistic forecasts of river flow at selected locations across Australia by coupling rainfall forecasts from a Global Circulation Model with a rainfall–runoff model. The chapter presents a method to improve the Bayesian inference of the rainfall–runoff model parameters by using an informative prior derived from the calibration of the model on a large sample of catchments. This prior is compared with a uniform prior that is currently used in the system. The results indicate that the choice of the prior can have a significant impact on forecast performance for both daily and monthly time steps. The use of an informative prior generally improved the performance, especially for one test catchment at daily time step where prediction intervals were narrowed without compromising forecast reliability. For other catchments and time steps, the improvement was more limited.


Seasonal streamflow forecasts Rainfall–runoff modelling Bayesian inference Prior distribution Importance sampling 


  1. 1.
    B.C. Bates, E.P. Campbell, A Markov chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall-runoff modeling. Water Resour. Res. 37(4), 937–947 (2001)CrossRefGoogle Scholar
  2. 2.
    Bureau of Meteorology, Seasonal Climate Outlook (2016a), Accessed 20 Sep 2016
  3. 3.
    Bureau of Meteorology, Seasonal Streamflow Forecasts (2016b), Accessed 20 Sep 2016
  4. 4.
    G. Evin, D. Kavetski, M. Thyer, G. Kuczera, Pitfalls and improvements in the joint inference of heteroscedasticity and autocorrelation in hydrological model calibration. Water Resour. Res. 49(7), 4518–4524 (2013)CrossRefGoogle Scholar
  5. 5.
    H. Hersbach, Decomposition of the continuous ranked probability score for ensemble prediction systems. Weather Forecast. 15(5), 559–570 (2000)CrossRefGoogle Scholar
  6. 6.
    D. Huard, A. Mailhot, Calibration of hydrological model GR2M using Bayesian uncertainty analysis. Water Resour. Res. 44(2) (2008)Google Scholar
  7. 7.
    E. Jeremiah, S.A. Sisson, A. Sharma, L. Marshall, Efficient hydrological model parameter optimization with Sequential Monte Carlo sampling. Environ. Model. Softw. 38, 283–295 (2012)Google Scholar
  8. 8.
    D. Kavetski, G. Kuczera, S.W. Franks, Bayesian analysis of input uncertainty in hydrological modeling: 2. application. Water Resour. Res. 42(3) (2006)Google Scholar
  9. 9.
    G. Kuczera, D. Kavetski, S. Franks, M. Thyer, Towards a bayesian total error analysis of conceptual rainfall-runoff models: characterising model error using storm-dependent parameters. J. Hydrol. 331(1), 161–177 (2006)Google Scholar
  10. 10.
    F. Laio, S. Tamea, Verification tools for probabilistic forecasts of continuous hydrological variables. Hydrol. Earth Syst. Sci. 11(4), 1267–1277 (2007)Google Scholar
  11. 11.
    J. Lerat, C. Pickett-Heaps, D. Shin, S. Zhou, P. Feikema, U. Khan, R. Laugesen, N. Tuteja, G. Kuczera, M. Thyer, D. Kavetski, Dynamic streamflow forecasts within an uncertainty framework for 100 catchments in Australia, in 36th Hydrology and Water Resources Symposium: The Art and Science of Water, Engineers Australia (2015), p. 1396Google Scholar
  12. 12.
    D. McInerney, M. Thyer, D. Kavetski, G. Kuczera, J. Lerat, Evaluation of approaches for modelling heteroscedasticity in the residual errors of hydrological predictions. Water Resour. Res. accepted (2017)Google Scholar
  13. 13.
    C. Perrin, C. Michel, V. Andréassian, Improvement of a parsimonious model for streamflow simulation. J. Hydrol. 279(1), 275–289 (2003)CrossRefGoogle Scholar
  14. 14.
    G. Schoups, J.A. Vrugt, A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non-gaussian errors. Water Resour. Res. 46(10) (2010)Google Scholar
  15. 15.
    A.F. Smith, A.E. Gelfand, Bayesian statistics without tears: a sampling-resampling perspective. Am. Stat. 46(2), 84–88 (1992)MathSciNetGoogle Scholar
  16. 16.
    T. Smith, A. Sharma, L. Marshall, R. Mehrotra, S. Sisson, Development of a formal likelihood function for improved bayesian inference of ephemeral catchments. Water Resour. Res. 46(12) (2010)Google Scholar
  17. 17.
    N. Tuteja, D. Shin, R. Laugesen, U. Khan, Q. Shao, E. Wang, M. Li, H. Zheng, G. Kuczera, D. Kavetski, G. Evin, Experimental evaluation of the dynamic seasonal streamflow forecasting approach. Technical Report (Australian Bureau of Meteorology, 2012)Google Scholar
  18. 18.
    Q. Wang, D.L. Shrestha, D. Robertson, P. Pokhrel, A log-sinh transformation for data normalization and variance stabilization. Water Resour. Res. 48(5) (2012)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Bureau of MeteorologyCanberraAustralia

Personalised recommendations