1. Committees of hydrological models specialized on high and low flows Dimitri Solomatine 1,2 (presenting) and Nagendra Kayastha 1 Vadim Kuzmin 3 1 UNESCO-IHE Institute for Water Education, Delft,The Netherlands 2 Delft University of Technology, The Netherlands 3 Russian State Hydrometeorological University

2. Motivation Theory of modelling: Complex systems (processes) are comprised of multiple components (simpler sub-processes) Simple models often cannot adequately reflect complexity Idea: instead of one, use several specialised models, each representing such a sub-process (hydrometeorological situation) Optimize the way they are combined This may allow for better response in changing conditions Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 2

3. 3 Outline Committee modelling: examples and experiences Building specialized models Fuzzy committee of specialized models Case studies: Leaf catchment, USA Lissbro, Sweden Results and conclusions Ideas for future work

4. 4 Combination of models (committees, ensembles, modular models): earlier work Shamseldin, A. Y., K. M. O'Connor and G. C. Liang (1997). Methods for combining the outputs of different rainfall–runoff models. J. Hydrol. 197(1–4): 203-229. Xiong, L., Shamseldin, A. Y. and O’Connor, K. M. (2001). A nonlinear combination of the forecasts of rainfall-runoff models by the first-order Takagi-Sugeno fuzzy system, J. Hydrol., 245(1), 196–217. Abrahart, R. J. and See, L. M. (2002). Multi-model data fusion for river flow forecasting: an evaluation of six alternative methods based on two contrasting catchments, Hydrol. Earth Syst. Sci., 6, 655–670. Solomatine, D. P. and Siek, M. (2006). Modular learning models in forecasting natural phenomena, Neural Networks, 19, 215–224. Oudin L., Andréassian V., Mathevet T., Perrin C. & Michel C.,(2006), Dynamic averaging of rainfall-runoff model simulations from complementary model parameterization. Water Resources Research, 42. G. Corzo and D.P. Solomatine (2007). Baseflow separation techniques for modular ANN modelling in flow forecasting. Hydrol. Sci. J., 52(3), 491-507. Fenicia, F., Solomatine, D. P., Savenije, H. H. G. and Matgen, P. Soft combination of local models in a multi-objective framework. HESS, 11, 1797-1809, 2007. Toth E. (2009). Classification of hydro-meteorological conditions and multiple artificial neural networks for streamflow forecasting, HESS, 13, 1555–1566. Kayastha N., Ye J., Fenicia F., Solomatine D.P. (2013). Fuzzy committees of specialised rainfall-runoff models: further enhancements, HESSD, 10, 675-697, doi:10.5194/hessd-10-675-2013. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013

5. 5 Limitations of “single model” approach Complexity of the hydrological processes The simplicity of the “conceptual” modelling paradigm often leads to errors in representing all the different complexity of the physical processes in the catchment A single model often cannot capture the full variability of the system response varying order of magnitude in flow value variance of error dependent on flow value A single aggregate measure criteria of model performance is traditionally used Divide and conquer… Small is beautiful…

6. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 6 Steps in building a committee of RR models Identification of specialized models, e.g.: “soft separation” scheme to identify “low flows” and “high flows” (Fenicia et al., 2007) baseflow separation (Corzo and Solomatine, 2006) identifying rising and falling limbs (Jain and Shrinivasulu, 2006) separation by threshold value of flow (Willems, 2009) Transformation of flow (Oudin et al. 2006) Objective functions (errors) definition Calibration of specialised models (Multi-objective, Single objective) Models combination (committees, ensembles, averaging) Check performances

7. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 7 Complex process Modular models for modelling sub-processes Splitting into sub-processes: Domain experts (humans) specify such processes Computational intelligence algorithms discover “hidden” processes based on observed data Combination of both approaches Sub-process 1 Sub-process K Sub-process 2 D.P. Solomatine (2006). Optimal modularization of learning models in forecasting environmental variables. iEMSs 3rd Biennial Meeting: Summit on Environmental Modelling and Software (A. Voinov, A. Jakeman, A. Rizzoli, eds.) Solomatine & Xue. (2004) M5 model trees compared to neural networks: application to flood forecasting in the upper reach of the Huai River in China. ASCE J. Hydrologic Engineering, 9(6), 491-501. … Papers by Shamseldin et al.,1997; Abrahart & See 2002; Jain et al., 2006; Oudin et al., 2006; etc.

8. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 8 Modular models: Methods of data splitting Using machine learning methods to group (cluster) data corresponding to different hydrometerological regimes: k-means, Fuzzy c-means Self-organising maps Applying hydrological knowledge for flow separation: Tracer-based methods Threshold-based flow separation Constant-slope method for baseflow separation Recursive filter for baseflow separation G. Corzo and D.P. Solomatine. (2007) Baseflow separation techniques for modular artificial neural network modelling in flow forecasting. Hydrological Sciences J., 52(3), 491-507.

9. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 9 Modular models using clustering Modular Models are built for each cluster of data K-means cluster (Bagmati training data set) P (current precipitation) Q (current discharge) Q t+1 (forecast discharge)

10. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 10 Optimal model structure using recursive filter for baseflow separation Parameter a=0.01 (Recession coefficient) Parameter a= 0.99 (Recession coefficient ) Parameter BFI max =0.5 (Chapman and Maxwell 1996) Ekhardt 2005 G. Corzo and D.P. Solomatine (2007). Knowledge-based modularization and global optimization of ANN models in hydrologic forecasting. Neural Networks, 20, 528–536

11. 11 Performance of the Modular Model using recursive filter vs Single (global) model Bagmati catchment Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013

12. 12 Committee models States- based dynamic averaging i) Soil moisture accounting (Oudin et al., 2006) ii) Other states: quick and slow flows Inputs-based dynamic averaging Outputs-based dynamic averaging i) Fuzzy committee (Fenicia et al., 2007, Kayastha et al., 2013) ii) Weights based on observed and simulated flows 12 Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 A B C

13. Specialized models Two models are built – for low and high flows Each objective functions (wRMSE) weights flows differently Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 13 Error on low flows Error on high flows By applying weighting factors to the model residuals Fenicia, F., Solomatine, D. P., Savenije, H. H. G. and Matgen, P. Soft combination of local models in a multi- objective framework. HESS, 11, 1797-1809, 2007.

14. Fuzzy committee of specialised models (1) The membership functions are subject to the accurate optimization of the parameters (γ, δ), 14 Low-flow model Combiner (fuzzy committee) High-flow model QcQc Q LF Q HF R, E For this range of flow both models work Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013

15. 15 Fuzzy committee of specialised models (2) Further enhancements (2012-2013): optimization all parameters of - weighted schemes and fuzzy membership functions Experiments conducted on calibration data, and model verification on test data Tested optimization algorithms Multi- objective – NSGA II (Deb, 2001) Single objective: Genetic algorithm – GA (Goldberg, 1989), Adaptive cluster covering – ACCO (Solomatine, 1999) Tested on three case studies Alzette, Bagmati and Leaf catchment Kayastha, Ye, Fenicia, Solomatine. (2013) Fuzzy committees of specialised rainfall-runoff models: further enhancements, HESSD, 10, 675-697, doi:10.5194/hessd-10-675-2013

16. 16 Fuzzy committee of specialised models (3) Influence of different weighting schemes used in objective functions for calibration of high and low flow models: Quadratic, N=2 Cubic, N=3 Cont. Kayastha et al., (2013) Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013

17. 17 Fuzzy committee of specialised models (4) The shape of membership functions are subjected to the parameters (γ, δ), which switch the flow regimes (between low flow and high flow). Cont. Kayastha et al., (2013) Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013

18. 18 Case study : Leaf catchment Area - 1924 km2, 10 years of daily data, 6 yrs calibration / 4 yrs verification One of the identified Pareto-optimal front corresponding to model parameterisations using weighting scheme to separate flow regimes and the objective function value in calibration and verification periods Calibration Verification

19. 19 Current study: Lissbro, Sweden (1) Lissbro catcment, 97.0 km², Sweden, 17 years of daily data HBV model (13 parameters) was used Optimization algorithm used for calibration: Adaptive cluster covering – ACCO (Solomatine, 1995, 1999) All experiments are conducted on calibration data, and verified on test data Complete period: 01/01/1984 - 31/12/2010 Calibration periods: P1: 01/01/1984 - 31/12/1988 P2: 01/01/1989 - 31/12/1993 P3: 01/01/1994 - 31/12/1998 P4: 01/01/1999 - 31/12/2003 P5: 01/01/2006 - 31/12/2010 Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013

20. 20 Current study: Lissbro, Sweden (2) Statistical properties of data Statistical properties Period1Period2Period3Period4Period5Period5+1 Period from (day/month/year) '01-Jan-1984''01-Jan-1989''01-Jan-1994''01-Jan-1999''01-Jan-2006''01-Jan-1984' Period to (day/month/year) '31-Dec-1988''31-Dec-1993''31-Dec-1998''31-Dec-2003''31-Dec-2010' Number of data18271826 10076 Stremflows Average (m 3 /s)0.980.901.061.291.301.10 Minimum(m 3 /s)0.070.01 0.050.040.01 Maximum (m 3 /s)6.206.746.357.307.7410.50 Standard deviation(m 3 /s)1.030.941.221.20 1.14 Precipitation Average (m 3 /s)2.182.042.152.252.342.19 Minimum(m 3 /s)0.00 Maximum (m 3 /s)33.3041.8037.4057.3052.2067.70 Standard deviation(m 3 /s)3.743.954.024.104.224.04 Temperature Average (m 3 /s)5.687.216.507.287.056.81 Minimum(m 3 /s)-23.90-13.20-17.20-16.90-17.30-23.90 Maximum (m 3 /s)21.2024.6024.2023.7024.70 Standard deviation(m 3 /s)7.936.677.717.467.707.52 Evapotranporation Average (m 3 /s)1.321.411.381.44 1.40 Minimum(m 3 /s)0.00 Maximum (m 3 /s)4.505.004.90 5.00 Standard deviation(m 3 /s)1.271.291.311.331.341.31

21. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 21 Conceptual model: HBV Conceptual model: HBV Conceptual lumped model 3 tanks 13 parameters to calibrate Parameters’ nameDescriptionsUnitsLowerUpper FCMaximum soil moisture contentmm 100300 LPLimit for potential evapotranspiration - 0.11 ALFAResponse box parameter - 02 BETAExponential parameter in soil routine - 14 KRecession coefficient for upper tankmm/d 0.0050.5 K4Recession coefficient for lower tankmm/d 0.0010.3 PERCPercolation from upper to lower response boxmm/d 05 CFLUXMaximum value of capillary flowmm/d 02 MAXBASTransfer function parameterd 16 RCFRefreezing coefficient - 11.2 SCFSnowfall correct factor - 0.51.2 CFMAXDegree day factormm/ºC/d 14 TTThreshold temperaturesºC -21

22. 22 Objective functions used Nash and Sutcliffe Efficiency (NSE) Root mean squared error (RMSE) Log transformed flows (Oudin et al. 2006) Weighted RMSE on high flows (Fenicia et al. 2007) Weighted RMSE on low flows (Fenicia et al. 2007) 22 Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013

23. 23 Experiment -1: Level 2: single model, calibration on 5 subsets Single model performance (NSE) over the 5 pre-defined periods) 23 Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 NSE(NSE is used for optimization) Period1Period2Period3Period4Period5Period5+1 Period10.660.820.780.770.69 Period20.610.870.750.730.64 Period30.600.810.780.700.66 Period40.600.710.700.810.69 Period50.540.750.690.770.67 Period5+1 (whole) 0.77 Mean Calibration Verification NSE0.760.70 Log NSE0.840.67 RMSE HF 0.290.28 RMSE LF 0.350.36 Means of 5 performances

24. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 24 Experiment-1: Comparing committee models to the single one A) State-based dynamic averaging (Oudin et al., 2006) B) Output-based dynamic averaging using fuzzy committee (Fenicia et al., 2007 ; Kayastha et al., 2013) C) Output-based dynamic averaging using observed flows Period1Period2Period3Period4Period5Period5+1 Period10.560.730.700.720.63 Period20.490.740.590.640.59 Period30.540.78 0.760.69 Period40.510.660.670.760.60 Period50.530.710.650.750.66 Period5+1 0.72 Period1Period2Period3Period4Period5Period5+1 Period10.690.830.790.740.66 Period20.590.860.70 0.62 Period30.610.810.770.750.67 Period40.600.740.700.810.70 Period50.610.730.710.810.71 Period5+1 0.77 Period1Period2Period3Period4Period5Period5+1 Period10.690.850.780.740.67 Period20.580.860.700.690.62 Period30.630.860.790.700.65 Period40.620.800.710.800.72 Period50.620.770.730.820.74 Period5+1 0.76 Mean of NSE ModelsCalibrationVerification Single model0.760.70 Cmte A0.700.65 Cmte B0.770.70 Cmte C0.770.71

25. 25 Experiment-2: single model, calibration on 1+2+3 Model performance (NSE) over the 2 pre-defined periods Calibration period – Periods 1 + 2 + 3 Verification period – Periods 4 + 5 25 Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 Models Period 1+2+3Period 4+5 CalibrationVerification Single parameterized0.780.66 A0.750.70 B0.790.67 C 0.790.72 P1: 01/01/1984 - 31/12/1988 P2: 01/01/1989 - 31/12/1993 P3: 01/01/1994 - 31/12/1998 P4: 01/01/1999 - 31/12/2003 P5: 01/01/2006 - 31/12/2010 In verification Committees are better than the single models

26. 26 Experiment -2: fragments of hydrograph The fragments of hydrograph (Experiment -2) 26 Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013

27. 27 Model errors for various years: the committee model is more robust Single model vs Committee model (Fuzzy) 27 Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 lower SD for Committee model Yearly NSE Yearly NSE low flow Yearly Bias (Qsim/Qobs)

28. 28 Model errors for different periods: the committee model is more robust Single model vs Committee model (Fuzzy) 28 Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 lower SD in Committee model NSE

29. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 29 Conclusions (1) Splitting of data into small subsets does not allow for committee models to become significantly better than a single model However using larger sets (P1+P2+P3) for calibration, makes committee models more accurate than a single model Models Experiment 1Experiment 2 P1,P2,P3,P4,P5 separatelyP1+P2+P3P4+P5 CalibrationVerificationCalibrationVerification Single parameterized0.760.700.780.66 A0.700.650.75 0.70 B0.770.700.790.67 C0.770.710.79 0.72 Mean of NSE Lowe r than single param. model

30. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 30 Conclusions (2) Committees of specialized models can be used when an overall model fails to identify triggers and thresholds in the catchment behavior is seen as a natural way of introducing additional complexity and hence adaptivity Committee models were initially developed for improving accuracy of short-term forecasts, and they do it well. However our hypothesis is: inherent capacity of committee models to react to short- term changes in hydrometeorologic condition may provide the mechanism for capturing the long-term changes as well

31. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 31 Further work Defining what is a “hydrometeorological regime” at different time scales To try to deal with non-stationarity by using non- stationary parameters (and machine-learning them) Developing more adaptive dynamic combination schemes able to deal with the long term changes in regimes “Philosophical questions” to think about: When several models are combined the notion of “state” seem to disappear – is it a problem? Some combination schemes are not conservative, i.e. may generate or loose water (“violates physics”) - is it bad ? We calibrate models knowing data is bad (especially for peaks) – is it right ?

32. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 32 Welcome to our COURSES on Flood Risk Management (July, 3 weeks) New data sources for flood modelling (September, 1 week) KULTURisk Summer School Flood risk reduction: perception, communication, governance Delft (The Netherlands) 9-12 September 2013 Erasmus Mundus Flood Risk Management Masters 2013-2015 www.FloodRiskMaster.org

33. Solomatine and Kayastha : Committee models, IAHS, Gothenburg, 2013 33