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Flood Forecasting Using Copula Entropy Method

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Copulas and Its Application in Hydrology and Water Resources

Part of the book series: Springer Water ((SPWA))

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Abstract

Artificial neural networks (ANNs) have proved to be an efficient alternative to traditional methods for hydrological modeling. One of the most important steps in the ANN development is the determination of significant input variables. This chapter proposes a new method based on the copula entropy (CE) theory to identify the inputs of an ANN model. Two tests are carried out for verifying the accuracy and performance of the CE method. The CE theory-based input determination methodology is applied to identifying suitable inputs of flood forecast models for case studies. Different kinds of ANN models, including multi-layer feed-forward networks (MLF), radial basis function (RBF) and general regression neural network (GRNN), are also discussed. Results indicate that the CE method could effectively identify inputs for the ANN with smallest RMSE values for training and validation data, and the ANN models coupled with the CE method perform better than the traditional linear correlation analysis (LCA) method.

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References

  • Abrahart RJ, See L (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(4):655–670

    Article  Google Scholar 

  • Angulo JM, Madrid AE, Ruiz-Medina MD (2011) Entropy-based correlated shrinkage of spatial random processes. Stoch Env Res Risk A 25(3):389–402

    Article  Google Scholar 

  • Berntson J, Espelid TO, Genz A (1991) An adaptive algorithm for the approximate calculation of multiple integrals. ACM Trans Math Softw 17:437–451

    Article  MathSciNet  Google Scholar 

  • Birikundavyi S, Labib R, Trung HT, Rousselle J (2002) Performance of neural networks in daily streamflow forecasting. J Hydrol Eng 7(5):392–398

    Article  Google Scholar 

  • Bowden GJ, Dandy GC, Maierb HR (2005a) Input determination for neural network models in water resources applications. Part 1-background and methodology. J Hydrol 301:75–92

    Article  Google Scholar 

  • Bowden GJ, Maierb HR, Dandy GC (2005b) Input determination for neural network models in water resources applications. Part 2. Case study: forecasting salinity in a river. J Hydrol 301:93–107

    Article  Google Scholar 

  • Calsaverini RS, Vicente R (2009) An information-theoretic approach to statistical dependence: copula information. Europ Phys Lett 88(6):3–12

    Article  Google Scholar 

  • Castellano-Méndeza M, González-Manteigaa W, Febrero-Bande M, Prada-Sáncheza MJ, Lozano-Calderón R (2004) Modeling of the monthly and daily behavior of the runoff of the Xallas river using Box-Jenkins and neural networks methods. J Hydrol 296:38–58

    Article  Google Scholar 

  • Chen L, Ye L, Singh VP, Zhou J, Guo S (2014a) Determination of input for artificial neural networks for flood forecasting using the copula entropy method. J Hydrol Eng 19(11):04014021

    Article  Google Scholar 

  • Chen L, Singh VP, Guo S, Zhou J, Ye L (2014b) Copula entropy coupled with artificial neural network for rainfall–runoff simulation. Stochastic environmental research and risk assessment. Stoch Env Res Risk 28(7):1755–1767

    Article  Google Scholar 

  • Davies L, Gather U (1993) The identification of multiple outliers. J Am Statist Assoc 88(423):782–792

    Article  MathSciNet  Google Scholar 

  • de Vos NJ, Rientjes THM (2005) Constraints of artificial neural networks for rainfall-runoff modelling: trade-offs in hydrological state representation and model evaluation. Hydrol Earth Syst Sci Discuss 2:365–415

    Article  Google Scholar 

  • Elman JL (1988) Finding structure in time, In: CRL Technical Report 8801, University of California at San Diego, Centre for Research in Language

    Google Scholar 

  • Fernando TMKG, Maier HR, Dandy GC (2009) Selection of input variables for data driven models: an average shifted histogram partial mutual information estimator approach. J Hydrol 367:165–176

    Article  Google Scholar 

  • Hecht-Nielsen R (1987) Counterpropagation networks. Appl Opt 26:4979–4984

    Article  Google Scholar 

  • Hopfield JJ (1987) Learning algorithms and probability distributions in feed-forward and feed-back networks. P Natl Acad Sci USA 84:8429–8433

    Article  MathSciNet  Google Scholar 

  • Hsu KL, Gupta HV, Sorooshian S (1995) Artificial neural network modeling of the rainfall–runoff process. Water Resour Res 31(10):2517–2530

    Article  Google Scholar 

  • Islam MN, Liong SY, Phoon KK, Liaw C-Y (2001) Forecasting of river flow data with a general regression neural network. Integrated water resources management (Proceedings of a symposium held at Davis. California. IAHS Publ. no. 272

    Google Scholar 

  • Jain SK, Das A, Drivastava DK (1999) Application of ANN for reservoir inflow prediction and operation. J Water Resour Plann Manage 125(5):263–271

    Article  Google Scholar 

  • Jayawardena DA, Fernando AK, Zhou MC (1997) Comparison of multilayer perceptron and radial basis function networks as tools for flood forecasting. Destructive water: water-caused natural disasters, their abatement and control (Proceedings of the conference held at Anaheim, California, June 1996). IAHS Publ. no. 239

    Google Scholar 

  • Jeong DI, St-Hilaire A, Ouarda TBMJ, Gachon P (2012) Comparison of transfer functions in statistical downscaling models for daily temperature and precipitation over Canada. Stoch Env Res Risk A 26(5):633–653

    Article  Google Scholar 

  • Karunanithi N, Grenney WJ, Whitley D, Bovee K (1994) Neural networks for river flow prediction. J Comput Civil Eng 8:201–219

    Article  Google Scholar 

  • Kasiviswanathan KS, Sudheer KP (2013) Quantification of the predictive uncertainty of artificial neural network based river flow forecast models. Stoch Env Res Risk A 27(1):137–146

    Article  Google Scholar 

  • Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69

    Article  MathSciNet  Google Scholar 

  • Lachtermacher G, Fuller JD (1994) Backpropagation in hydrological time series forecasting. In: Hipel KW, McLeod AI, Panu US, Singh VP (eds) Stochastic and statistical methods in hydrology and environmental engineering. Kluwer Academic, Dordrecht

    Google Scholar 

  • Lekkas DF, Onof C, Lee MJ, Baltas EA (2004) Application of Artificial Neural networks for flood forecasting. Global Nest: Int J 6(3):205–211

    Google Scholar 

  • Li X, Guo SL, Liu P, Chen GY (2010) Dynamic control of flood limited water level for reservoir operation by considering inflow uncertainty. J Hydrol 391:124–132

    Article  Google Scholar 

  • Liang GC, Kachroo RK, Kang W, Yu XZ (1992) Applications of linear modeling techniques for flow routing on large basins. J Hydrol 133:99–140

    Article  Google Scholar 

  • Maier Holger R, Dandy Graeme C (2000) Neural networks for the prediction and forecasting of water resources variables: a review of modeling issues and applications. Environ Model Softw 15:101–124

    Article  Google Scholar 

  • May Robert J, Dandy Graeme C, Maier Holger R, Nixon John B (2008a) Application of partial mutual information variable selection to ANN forecasting of water quality in water distribution systems. Environ Model Softw 23:1289–1299

    Article  Google Scholar 

  • May Robert J, Maier Holger R, Dandy Graeme C, Fernando TMK (2008b) Non-linear variable selection for artificial neural networks using partial mutual information. Environ Modell Softw 23:1312–1326

    Article  Google Scholar 

  • McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in nervous activity. B Math Biol 5:115–133

    MathSciNet  MATH  Google Scholar 

  • Ministry of Water Resources (MWR) (2006) Regulation for calculating design flood of water resources and hydropower projects. Chinese Shuili Shuidian Press, Beijing (in Chinese)

    Google Scholar 

  • Mishra AK, Singh VP (2009) Analysis of drought severity-area-frequency curves using a general circulation model and scenario uncertainty. J Geophys Res 114:D06120. https://doi.org/10.1029/2008JD010986

    Article  Google Scholar 

  • Mishra AK, Ines AVM, Singh VP, Hansen JW (2013) Extraction of information content from stochastic disaggregation and bias corrected downscaled precipitation variables for crop simulation. Stoch Env Res Risk A 27(2):449–457

    Article  Google Scholar 

  • Park J, Sandberg IW (1991) Universal approximations using Radial-Basis-Function networks. Neural Comput 3(2):246–257

    Article  Google Scholar 

  • Powell MJD (1987) Radial basis functions for multivariable interpolation: a review. In: Mason JC, Cox MG (eds) Algorithms for approximation. Clarendon Press, Oxford, pp 143–167

    Google Scholar 

  • Raman H, Sunilkumar N (1995) Multivariate modeling of water resources time series using artificial neural networks. Hydrol Sci J 40(2):145–163

    Article  Google Scholar 

  • Rumelhart DE, Hinton E, Williams J (1986) Learning internal representation by error propagation. Parallel Distrib Process 1:318–362

    Google Scholar 

  • Shamseldin AY (1997) Application of a neural network technique to rainfall-runoff modeling. J Hydrol 199:272–294

    Article  Google Scholar 

  • Sharma A (2000) Seasonal to interannual rainfall probabilistic forecasts for improved water supply management: Part 1 a strategy for system predictor identification. J Hydrol 239:232–239

    Article  Google Scholar 

  • Specht DF (1991) A general regression neural network. IEEE Trans Neural Netw 2(6):568–576

    Article  Google Scholar 

  • Svozil D, KvasniEka V, Pospichal J (1997) Introduction to multi-layer feed-forward neural networks. Chemometr Intell Lab 39:43–62

    Article  Google Scholar 

  • Thirumalaiah K, Deo MC (2000) Hydrological forecasting using neural networks. J Hydrol Eng 5(2):180–189

    Article  Google Scholar 

  • Tongal H, Demirel MC, Booij MJ (2013) Seasonality of low flows and dominant processes in the Rhine River. Stoch Env Res Risk A 27(2):489–503

    Article  Google Scholar 

  • Wu CL, Chau KW (2011) Rainfall–runoff modeling using artificial neural network coupled with singular spectrum analysis. J Hydrol 18:394–409

    Article  Google Scholar 

  • Zhao N, Linb WT (2011) A copula entropy approach to correlation measurement at the country level. Appl Math Comput 218(2):628–642

    MathSciNet  MATH  Google Scholar 

  • Zupan J, Gasteiger J (1993) Neural networks for chemists: an introduction. In: Zupan J, Gasteiger J (eds) Weinheim, VCH (Germany)

    Google Scholar 

Download references

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Authors and Affiliations

  1. School of Hydropower & Information Engineering, Huazhong University of Science and Technology, No. 1037 Luoyu Road, Wuhan, 430074, Hubei, China

    Lu Chen

  2. State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, No. 299 Bayi Road, Wuhan, 430072, Hubei, China

    Shenglian Guo

Authors
  1. Lu Chen
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  2. Shenglian Guo
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Chen, L., Guo, S. (2019). Flood Forecasting Using Copula Entropy Method. In: Copulas and Its Application in Hydrology and Water Resources. Springer Water. Springer, Singapore. https://doi.org/10.1007/978-981-13-0574-0_10

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