Uncertainty modelling in Rainfall-Runoff simulations based on parallel Monte Carlo method

Martin Golasowski, Martina Litschmannová, Štěpán Kuchař, Michal Podhorányi, Jan Martinovič


This article describes statistical evaluation of the computational model for precipitation forecast and proposes a method for uncertainty modelling of rainfall-runoff models in the Floreon+ system based on this evaluation. The Monte-Carlo simulation method is used for estimating possible river discharge and provides several confidence intervals that can support the decisions in operational disaster management. Experiments with other parameters of the model and their influence on final river discharge are also discussed.


rainfall-runoff; uncertainty modelling; kernel density estimation; Monte Carlo method; high performance computing

Full Text:



BEVEN K. Rainfall-Runoff Modelling – The Primer. 2nd ed. UK: Wiley-Blackwell, 2012, doi: 10.1002/9781119951001.

BOGNER K., PAPPENBERGER F., CLOKE H.L. Technical Note: The Normal Quantile Transformation and its application in a flood forecasting system. Hydrology and Earth System Sciences Discussions. 2011, 8(5), pp. 9275–9297, doi: 10.5194/hessd-8-9275-2011.

BRESLOWN. A generalized Kruskal-Wallis test for comparing K samples subject to unequal patterns of censorship. Biometrika, 1970, 57(3), pp. 579–594, doi: 10.1093/biomet/57.3.579.

CRHOVA L., HOLTANOVA E., KALVOVA J., FARDA A. Performance of ALADIN-Climate/CZ over the area of the Czech Republic in comparison with ENSEMBLES regional climate models. Stud Geophys Geod. 2013, 58(1), pp. 148–169, doi: 10.1007/s11200-013-1107-0.

FARDA A., DEUE M., SOMOT S., HORANYI A., SPIRIDONOV V., TOTH H. Model ALADIN as regional climate model for Central and Eastern Europe. Stud Geophys Geod. 2010, 54(20), pp. 313–332, doi: 10.1007/s11200-010-0017-7.

HOLTANOVA E., KALVOVA J., MIKSOVSKY J., PISOFT P., MOTL M. Analysis of uncertainties in regional climate model outputs over the Czech Republic.Stud Geophys Geod. 2010, 54(3), pp. 513–528, doi: 10.1007/s11200-010-0030-x.

IT4INNOVATIONS. IT4Innovations Anselm Cluster Documentation [online]. VSB – Technical University of Ostrava, 2014. [viewed 2014-09-01]. Available from: https://docs.it4i.cz/anselm-cluster-documentation/hardware-overview.

KOBOLD M., SUSELJ K. Precipitation forecasts and their uncertainty as input into hydrological models. Hydrology and Earth System Sciences. 2005, 9(4), pp. 322–332, doi: 10.5194/hess-9-322-2005.

KROESE D.P., TAIMRE T., BOTEV Z.I. Handbook of Monte Carlo Methods. USA and Canada: John Wiley & Sons, Inc., 2011, doi: 10.1002/9781118014967.

KRZYSZTOFOWICZ R. Bayesian theory of probabilistic forecasting via deterministic hydrologic model. Water Resour. Res. 1999, 35(9), pp. 2739–2750, doi: 10.1029/1999wr900099.

MARTINOVIC J., KUCHAR S., VONDRAK I., VONDRAK V., SIR B., UNUCKA J. Multiple Scenarios Computing In The Flood Prediction System FLOREON. In: A. BARGIELA, S.A. ALI, D. CROWLEY, E.J.H. KERCKHOFFS, eds. Proceedings of the 24th European Conference on Modelling and Simulation, Simulation Meets Global Challenges (ECMS 2010), Kuala Lumpur. ECMS, 2010, pp. 182–188, doi: 10.7148/2010-0182-0188.

MONTANARI A. Large sample behaviors of the generalized likelihood uncertainty estimation (GLUE) in assessing the uncertainty of rainfall-runoff simulations.Water Resour. Res. 2005, 41(8), doi: 10.1029/2004wr003826.

MONTANARI A. What do we mean by ‘uncertainty’? The need for a consistent wording about uncertainty assessment in hydrology. Hydrol. Process. 2007, 21(6), pp. 841–845, doi: 10.1002/hyp.6623.

MONTANARI A., BRATH A. A stochastic approach for assessing the uncertainty of rainfall-runoff simulations. Water Resour. Res. 2004, 40(1), doi: 10.1029/2003wr002540.

NASH J., SUTCLIFFE J. River flow forecasting through conceptual models part I – A discussion of principles. Journal of Hydrology. 1970, 10(3), pp. 282–290, doi: 10.1016/0022-1694(70)90255-6.

R CORE TEAM. R: A Language and Environment for Statistical Computing [online]. R Foundation for Statistical Computing, Vienna, Austria, 2014. [viewed 2014-09-01] Available from: http://www.R-project.org/.

SCHWARZ C. J. Sampling, regression, experimental design and analysis for environmental scientists, biologists, and resource managers. Canada: Department of Statistics and Actuarial Science, Simon Fraser University 57, 2011.

STEENBERGEN N.V., RONSYN J., WILLEMS P. A non-parametric data-based approach for probabilistic flood forecasting in support of uncertainty communication. Environmental Modelling & Software. 2012, 33, pp. 92–105, doi: 10.1016/j.envsoft.2012.01.013.

VIEUX B.E. Distributed Hydrologic Modeling Using GIS. Springer Netherlands, 2004, doi: 10.1007/1-4020-2460-6.

VONDRAK I., MARTINOVIC J., KOZUSZNIK J., STOLFA S., KOZUBEK T., KUBICEK P., VONDRAK V., UNUCKA J. A Description of a Highly Modular System for the Emergent Flood Prediction. In: Proceedings of the 7th conference on Computer Information Systems and Industrial Management Applications (CISIM 2008), Ostrava, Czech Republic. IEEE, 2008, pp. 219–224. doi: 10.1109/cisim.2008.22.

ZIDEK D., LIPINA P. CHMI Manual for the observers of the meteorological stations [online]. Methodological regulations [viewed 2014-09-01]. 2003, 13. In Czech. Available from: http://www.meteoopava.estranky.cz/file/7/navod-pro-pozorovatele.pdf.

ZUCCHINI W. Applied smoothing techniques. Part I: Kernel Density Estimation [online]. Philadephia, PA: Temple University, 2003, pp. 15–19 [viewed 2014-09-01]. Available from: http://staff.ustc.edu.cn/ zwp/teach/Math-Stat/kernel.pdf.

DOI: http://dx.doi.org/10.14311/NNW.2015.%25x


  • There are currently no refbacks.

Should you encounter an error (non-functional link, missing or misleading information, application crash), please let us know at nnw.ojs@fd.cvut.cz.
Please, do not use the above address for non-OJS-related queries (manuscript status, etc.).
For your convenience we maintain a list of frequently asked questions here. General queries to items not covered by this FAQ shall be directed to the journal editoral office at nnw@fd.cvut.cz.