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Analysing the Sub-processes of a Conceptual Rainfall-Runoff Model Using Information About the Parameter Sensitivity and Variance

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Abstract

Sensitivity analyses are often carried out for the main model output and using a predefined evaluation period. It is possible, however, to get much more knowledge about how the system works when estimating the sensitivity for the output of individual modules for each time step (time-varying sensitivity analysis). This is shown here using a variance-based sensitivity analysis for a conceptual rainfall-runoff model applied to a mountainous catchment. The first-order and total sensitivities were computed using Sobol’s method. Since the parameter ranges used in the sensitivity analysis were obtained through a Markov chain Monte Carlo (MCMC) sampling, the sensitivity indices reflect the parameter uncertainty and make a good use of the previous available information. As a first step, the variance of each flow component was calculated. The flow component with the highest variance at each time step can be regarded as the ‘dominant physical control’, which has been defined as the parameter to which the model output reacts in a highly sensitive way when the parameter varies within realistic ranges. This information about the dominant processes can be used for facilitating model calibration by identifying the periods on which to focus when calibrating different parameters. It also can be useful for estimating the amount of data available for calibrating each process. The second part presents the total sensitivity indices and interactions for individual flow components considering a 2-year period. The results show large differences in the time-varying sensitivity patterns of the flow components. It is concluded that such a high-resolution sensitivity analysis for each flow component is a good complement to a sensitivity analysis of the total discharge, increasing our understanding about the internal functioning of individual modules which can be helpful when comparing different model formulations.

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References

  1. Refsgaard, J. C., & Hansen, J. R. (2010). A good-looking catchment can turn into a modeller’s nightmare. Hydrological Sciences Journal, 55(6), 899–912. doi:10.1080/02626667.2010.505571.

    Article  CAS  Google Scholar 

  2. Jakeman, A. J., Letcher, R. A., & Norton, J. P. (2006). Ten iterative steps in development and evaluation of environmental models. Environmental Modelling & Software, 21, 602–614. doi:10.1016/j.envsoft.2006.01.004.

    Article  Google Scholar 

  3. Hartebrodt, C. H., Aichholz, R., & Braasch, M. (2011). Analyzing and predicting forestry accountancy network variables with Bayesian Belief Networks as compared to traditional analyzing methods. Small-Scale Forestry, 10, 163–183. doi:10.1007/s11842-010-9124-0.

    Article  Google Scholar 

  4. Judd, B.R., North, D.W., & Pezier, J.P. (1974). Assessment of the probability of contaminating Mars. Final Report of the Stanford Research Institute for the NASA Planetary Programs Division, Grant NASW-2535, 161p.

  5. Sumner T. (2010). Sensitivity analysis in systems biology modelling and its application to a multi-scale model of blood glucose homeostasis. PhD thesis, Centre for Mathematics and Physics in the Life Sciences and Experimental Biology, University College London, 162p.

  6. Baroni, G., & Tarantola, S. (2014). A General Probabilistic Framework for uncertainty and global sensitivity analysis of deterministic models: A hydrological case study. Environmental Modelling & Software, 51, 26–34. doi:10.1016/j.envsoft.2013.09.022.

    Article  Google Scholar 

  7. Cloke, H. L., Pappenberger, F., & Renaud, J.-P. (2008). Multi-method global sensitivity analysis (MMGSA) for modelling floodplain hydrological processes. Hydrological Processes, 22, 1660–1674. doi:10.1002/hyp.6734.

    Article  Google Scholar 

  8. Guse, B., Reusser, D., & Fohrer, N. (2014). How to improve the representation of hydrological processes in SWAT for a lowland catchment—temporal analysis of parameter sensitivity and model performance. Hydrological Processes, 28, 2651–2670. doi:10.1002/hyp.9777.

    Article  Google Scholar 

  9. Herman, J. D., Kollat, J. B., Reed, P. M., & Wagener, T. (2013). From maps to movies: High-resolution time-varying sensitivity analysis for spatially distributed watershed models. Hydrology and Earth System Sciences, 17, 5109–5125. doi:10.5194/hess-17-5109-2013.

    Article  Google Scholar 

  10. Herman, J. D., Reed, P. M., & Wagener, T. (2013). Time-varying sensitivity analysis clarifies the effects of watershed model formulation on model behavior. Water Resources Research, 49, 1400–1414. doi:10.1002/wrcr.20124.

    Article  Google Scholar 

  11. Massmann, C., Wagener, T., & Holzmann, H. (2014). A new approach to visualizing time-varying sensitivity indices for environmental model diagnostics across evaluation time-scales. Environmental Modelling & Software, 51, 190–194. doi:10.1016/j.envsoft.2013.09.033.

    Article  Google Scholar 

  12. Reusser, D. E., Buytaert, W., & Zehe, E. (2011). Temporal dynamics of model parameter sensitivity for computationally expensive models with the Fourier amplitude sensitivity test. Water Resources Research, 47, W07551. doi:10.1029/2010WR009947.

    Google Scholar 

  13. Atkinson, S. E., Woods, R. A., & Sivapalan, M. (2002). Climate and landscape controls on water balance model complexity over changing timescales. Water Resources Research, 38(12), 1314. doi:10.1029/2002WR001487.

    Article  Google Scholar 

  14. Montanari, L., Sivapalan, M., & Montanari, A. (2006). Investigation of dominant hydrological processes in a tropical catchment in a monsoonal climate via the downward approach. Hydrology and Earth System Sciences, 10(5), 769–782. doi:10.5194/hess-10-769-2006.

    Article  Google Scholar 

  15. Grayson, R., & Blöschl, G. (2000). Summary of pattern comparison and concluding remarks. In R. Grayson & G. Blöschl (Eds.), Spatial patterns in catchment hydrology: Observations and modelling (pp. 355–367p). Cambridge: Cambridge University Press.

    Google Scholar 

  16. Scherrer, S., & Naef, F. (2003). A decision scheme to indicate dominant hydrological flow processes on temperate grassland. Hydrological Processes, 17, 391–401. doi:10.1002/hyp.1131.

    Article  Google Scholar 

  17. Schmocker-Fackel, P., Naef, F., & Scherrer, S. (2007). Identifying runoff processes on the plot and catchment scale. Hydrology and Earth System Sciences, 11, 891–906. doi:10.5194/hess-11-891-2007.

    Article  Google Scholar 

  18. Reszler, C., Komma, J., Blöschl, G., & Gutknecht, D. (2008). Dominante Prozesse und Ereignistypen zur Plausibilisierung flächendetaillierter Niederschlag-Abflussmodelle [Dominant processes and event types for checking the plausibility of spatially distributed runoff models]. Hydrologie und Wasserbewirtschaftung, 52(3), 120–131.

    Google Scholar 

  19. Casper M. (2002). Die Identifikation hydrologischer Prozesse im Einzugsgebiet des Dürreychbaches (Nordschwarzwald) [The identification of hydrological processes in the Dürreychbach catchment (northern Black Forest)]. Mitteilungen des Institutes für Wasserwirtschaft und Kulturtechnik, Universität Karlsruhe (TH) Nr, 210

  20. van den Bos, R., Hoffmann, L., Juilleret, J., Matgen, P., & Pfister, L. (2006). Regional runoff prediction through aggregation of first-order hydrological process knowledge: A case study. Hydrological Sciences Journal, 51(6), 1021–1038. doi:10.1623/hysj.51.6.1021.

    Article  Google Scholar 

  21. Wagener, T., McIntyre, N., Lees, M. J., Wheater, H. S., & Gupta, H. V. (2003). Towards reduced uncertainty in conceptual rainfall-runoff modelling: Dynamic identifiability analysis. Hydrological Processes, 17, 455–476. doi:10.1002/hyp.1135.

    Article  Google Scholar 

  22. Shin, M.-J., Guillaume, J. H. A., Croke, B. F. W., & Jakeman, A. J. (2013). Addressing ten questions about conceptual rainfall-runoff models with global sensitivity analyses in R. Journal of Hydrology, 503, 135–152. doi:10.1016/j.jhydrol.2013.08.047.

    Article  Google Scholar 

  23. Estrada, V., & Diaz, M. S. (2010). Global sensitivity analysis in the development of first principle-based eutrophication models. Environmental Modelling & Software, 25, 1539–1551. doi:10.1016/j.envsoft.2010.06.009.

    Article  Google Scholar 

  24. Zeug, S. C., Bergman, P. S., Cavallo, B. J., & Jones, K. S. (2012). Application of a life cycle simulation model to evaluate impacts of water management and conservation actions on an endangered population of Chinook salmon. Environmental Modeling and Assessment, 17(5), 455–467. doi:10.1007/s10666-012-9306-6.

    Article  Google Scholar 

  25. Vezzaro, L., & Mikkelsen, P. S. (2012). Application of global sensitivity analysis and uncertainty quantification in dynamic modeling of micropollutants in stormwater runoff. Environmental Modelling & Software, 27–28, 40–91. doi:10.1016/j.envsoft.2011.09.012.

    Article  Google Scholar 

  26. Nossent, J., Elsen, P., & Bauwens, W. (2012). Sobol’ sensitivity analysis of a complex environmental model. Environmental Modelling & Software, 26, 1515–1525. doi:10.1016/j.envsoft.2011.08.010.

    Article  Google Scholar 

  27. Zhang, C., Chu, J., & Fu, G. (2013). Sobol’s sensitivity analysis for a distributed hydrological model of Yichun River Basin, China. Journal of Hydrology, 480, 58–68. doi:10.1016/j.jhydrol.2012.12.005.

    Article  Google Scholar 

  28. Kostka, Z., & Holko, L. (2000). Vplyv klimatickej zmeny na priebeh odtoku v malom horskom povodí [Impact of climate change on runoff in a small mountain catchment]. National Climate Program of the Slovak Republic, 8, 91–109.

    Google Scholar 

  29. Holko, L., & Kostka, Z. (2006). Hydrologický výskum vo vysokohorskom povodí Jaloveckého potoka [Hydrological research a high-mountain catchment of the Jalovecky creek catchment]. Journal of Hydrology and Hydromechanics, 54(2), 192–206.

    CAS  Google Scholar 

  30. Holko, L., & Kostka Z. (2010). Hydrological processes in mountains—knowledge gained in the Jalovecky Creek catchment, Slovakia. In: Status and perspectives of hydrology in small basins, IAHS Publ, 336

  31. Han, D., & Bray, M. (2006). Automated Thiessen polygon generation. Water Resources Research, 42, W11502. doi:10.1029/2005WR004365.

    Article  Google Scholar 

  32. Thornthwaite, C. W. (1948). An approach toward a rational classification of climate. Geographical Review, 38(1), 55–94.

    Article  Google Scholar 

  33. Holzmann, H., & Nachtnebel, H. P. (2002). Abflussprognose für mittelgroße Einzugsgebiete – Methodik und Anwendungen [Runoff forecast for medium sized basins—methods and applications]. Österreichische Wasser- und Abfallwirtschaft, 54(9–10), 142–153.

    Google Scholar 

  34. Matott, L. S., Babendreier, J. E., & Purucker, S. T. (2009). Evaluating uncertainty in integrated environmental models: A review of concepts and tools. Water Resources Research, 45, W06421. doi:10.1029/2008WR007301.

    Article  Google Scholar 

  35. Lilburne, L., & Tarantola, S. (2009). Sensitivity analysis of spatial models. International Journal of Geographical Information Science, 23(2), 151–168. doi:10.1080/13658810802094995.

    Article  Google Scholar 

  36. Tang, Y., Reed, P., van Werkhoven, K., & Wagener, T. (2007). Advancing the identification and evaluation of distributed rainfall-runoff models using global sensitivity analysis. Water Resources Research, 43, W06415. doi:10.1029/2006WR005813.

    Article  Google Scholar 

  37. Ratto, M., Young, P. C., Romanowicz, R., Pappenberger, F., Saltelli, A., & Pagano, A. (2007). Uncertainty, sensitivity analysis and the role of data based mechanistic modeling in hydrology. Hydrology and Earth System Sciences, 11, 1249–1266. doi:10.5194/hess-11-1249-2007.

    Article  Google Scholar 

  38. Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., & Tarantola S. (2008). Global sensitivity analysis. The primer. Wiley & Sons, 292p.

  39. Saltelli, A. (2002). Making best use of model evaluations to compute sensitivity indices. Computer Physics Communications, 145(2), 280–297. doi:10.1016/S0010-4655(02)00280-1.

    Article  CAS  Google Scholar 

  40. Cibin, R., Sudheer, K. P., & Chaubey, I. (2010). Sensitivity and identifiability of stream flow generation parameters of the SWAT model. Hydrological Processes, 24, 1133–1148. doi:10.1002/hyp.7568.

    Article  Google Scholar 

  41. Massmann, C., & Holzmann, H. (2012). Analysis of the behavior of a rainfall-runoff model using three global sensitivity analysis methods evaluated at different temporal scales. Journal of Hydrology, 475, 97–110. doi:10.1016/j.jhydrol.2012.09.026.

    Article  Google Scholar 

  42. Hario, H., Laine, M., Mira, A., & Saksman, E. (2006). DRAM: Efficient adaptive MCMC. Statistics and Computing, 16, 339–354. doi:10.1007/s11222-006-9438-0.

    Article  Google Scholar 

  43. Chib, S., & Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. The American Statistician, 49(4), 327–335. doi:10.2307/2684568.

    Google Scholar 

  44. Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7(4), 457–511. doi:10.1214/ss/1177011136.

    Article  Google Scholar 

  45. Link, W. A., & Eaton, M. J. (2012). Forum: On thinning of chains in MCMC. Methods in Ecology and Evolution, 3, 112–115. doi:10.1111/j.2041-210X.2011.00131.x.

    Article  Google Scholar 

  46. Shein, K. A. (2006). Assessing the long-term representativeness of short wind records. Proceedings 18 th Conference of Probability and Statistics in the atmospheric Sciences 2006, Atlanta.

  47. Bennett, N. D., Croke, B. F. W., Guariso, G., Guillaume, J. H. A., Hamilton, S. H., Jakeman, A. J., et al. (2013). Characterising performance of environmental models. Environmental Modelling & Software, 40, 1–20. doi:10.1016/j.envsoft.2012.09.011.

    Article  Google Scholar 

  48. Singh, S. K., & Bárdossy, A. (2012). Calibration of hydrological models on hydrologically unusual events. Advances in Water Resources, 38, 81–91. doi:10.1016/j.advwatres.2011.12.006.

    Article  Google Scholar 

  49. Beven, K., & Westerberg, I. (2011). On red herrings and real herrings: Disinformation and information in hydrological inference. Hydrological Processes, 25, 1676–1680. doi:10.1002/hyp.7963.

    Article  Google Scholar 

  50. Saltelli, A., Tarantola, S., & Campolongo, F. (2000). Sensitivity analysis as an ingredient of modeling. Statistical Science, 15(4), 377–395. doi:10.1214/ss/1009213004.

    Article  Google Scholar 

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Acknowledgments

This work was funded by the Austrian Academy of Sciences through the project Domina_HyPro ‘Development and testing of a modular conceptual hydrological model to identify dominating hydrological processes’. The data of the Jalovecky catchment were provided by Ladislav Holko from the Slovak Academy of Sciences.

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  1. Institute of Water Management, Hydrology and Hydraulic Engineering, University of Natural Resources and Life Sciences, Vienna, Austria

    Carolina Massmann & Hubert Holzmann

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Correspondence to Carolina Massmann.

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Massmann, C., Holzmann, H. Analysing the Sub-processes of a Conceptual Rainfall-Runoff Model Using Information About the Parameter Sensitivity and Variance. Environ Model Assess 20, 41–53 (2015). https://doi.org/10.1007/s10666-014-9414-6

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