Uncertainty assessment and optimization of hydrological model with the Shuffled Complex Evolution Metropolis algorithm: an application to artificial neural network rainfall-runoff model

Assessment of parameter and predictive uncertainty of hydrologic models is an essential part in the field of hydrology. However, during the past decades, research related to hydrologic model uncertainty is mostly done with conceptual models. As is accepted that uncertainty in model predictions arises from measurement errors associated with the system input and output, from model structural errors and from problems with parameter estimation. Unfortunately, non-conceptual models, such as black-box models, also suffer from these problems. In this paper, we take the artificial neural network (ANN) rainfall-runoff model as an example, and the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) is employed to analysis the parameter and predictive uncertainty of this model. Furthermore, based on the results of uncertainty assessment, we finally arrive at a simpler incomplete-connection artificial neural network (ICANN) model as well as with better performance compared to original ANN rainfall-runoff model. These results not only indicate that SCEM-UA can be a useful tool for uncertainty analysis of ANN model, but also prove that uncertainty does exist in ANN rainfall-runoff model. Additionally, in some way, it presents that the ICANN model is with smaller uncertainty than the original ANN model.

[1]  Kaoru Takara,et al.  Hydrological model performance comparison through uncertainty recognition and quantification , 2007 .

[2]  Karel J. Keesman,et al.  Uncertainty propagation and speculation in projective forecasts of environmental change - a lake eutrophication example. , 1991 .

[3]  C. Diks,et al.  Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation , 2005 .

[4]  George M. Hornberger,et al.  Sustainable water resource management under hydrological uncertainty , 2008 .

[5]  Soichi Nishiyama,et al.  A comparative study of artificial neural networks and neuro-fuzzy in continuous modeling of the daily and hourly behaviour of runoff , 2007 .

[6]  Hoshin Vijai Gupta,et al.  Model identification for hydrological forecasting under uncertainty , 2005 .

[7]  Chuntian Cheng,et al.  A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series , 2009 .

[8]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .

[9]  Chuntian Cheng,et al.  A new indirect multi-step-ahead prediction model for a long-term hydrologic prediction , 2008 .

[10]  Martyn P. Clark,et al.  Ensemble Bayesian model averaging using Markov Chain Monte Carlo sampling , 2008 .

[11]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information , 1998 .

[12]  Soroosh Sorooshian,et al.  Calibration of rainfall‐runoff models: Application of global optimization to the Sacramento Soil Moisture Accounting Model , 1993 .

[13]  G. C. Tiao,et al.  Bayesian inference in statistical analysis , 1973 .

[14]  K. Beven,et al.  Bayesian Estimation of Uncertainty in Runoff Prediction and the Value of Data: An Application of the GLUE Approach , 1996 .

[15]  Hafzullah Aksoy,et al.  Artificial neural network models for forecasting monthly precipitation in Jordan , 2009 .

[16]  L. Rabiner,et al.  An introduction to hidden Markov models , 1986, IEEE ASSP Magazine.

[17]  Keith Beven,et al.  A manifesto for the equifinality thesis , 2006 .

[18]  H. Scholten,et al.  Prediction Uncertainty in an Ecological Model of the Oosterschelde Estuary , 1991 .

[19]  K. Beven,et al.  Model Calibration and Uncertainty Estimation , 2006 .

[20]  Patrick Willems,et al.  Uncertainties in Rainfall–Runoff Modeling , 2005 .

[21]  Reza Maknoon,et al.  Assessment of flood forecasting lead time based on generalized likelihood uncertainty estimation approach , 2006 .

[22]  K. P. Sudheer,et al.  A neuro-fuzzy computing technique for modeling hydrological time series , 2004 .

[23]  K. Beven,et al.  Comment on “Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling?” by Jasper A. Vrugt, Cajo J. F. ter Braak, Hoshin V. Gupta and Bruce A. Robinson , 2009 .

[24]  J. Stedinger,et al.  Appraisal of the generalized likelihood uncertainty estimation (GLUE) method , 2008 .

[25]  Qingyun Duan,et al.  An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction , 2006 .

[26]  Mohammad Bagher Menhaj,et al.  Training feedforward networks with the Marquardt algorithm , 1994, IEEE Trans. Neural Networks.

[27]  Henrik Madsen,et al.  Automatic calibration of a conceptual rainfall-runoff model using multiple objectives. , 2000 .

[28]  B. Bates,et al.  A Markov Chain Monte Carlo Scheme for parameter estimation and inference in conceptual rainfall‐runoff modeling , 2001 .

[29]  Jasper A. Vrugt,et al.  Comparison of point forecast accuracy of model averaging methods in hydrologic applications , 2010 .

[30]  S. Sorooshian,et al.  Effective and efficient algorithm for multiobjective optimization of hydrologic models , 2003 .

[31]  Martyn P. Clark,et al.  Multi‐objective calibration of forecast ensembles using Bayesian model averaging , 2006 .

[32]  Bellie Sivakumar,et al.  Characterization and prediction of runoff dynamics: a nonlinear dynamical view , 2002 .

[33]  J. Vrugt,et al.  A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic, and non‐Gaussian errors , 2010 .

[34]  Kuolin Hsu,et al.  Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using the particle filter , 2005 .

[35]  Soroosh Sorooshian,et al.  Toward improved calibration of hydrologic models: Combining the strengths of manual and automatic methods , 2000 .

[36]  Hubert H. G. Savenije,et al.  Model complexity control for hydrologic prediction , 2008 .

[37]  Martyn P. Clark,et al.  Rainfall‐runoff model calibration using informal likelihood measures within a Markov chain Monte Carlo sampling scheme , 2009 .

[38]  George Kuczera,et al.  Monte Carlo assessment of parameter uncertainty in conceptual catchment models: the Metropolis algorithm , 1998 .

[39]  Henrik Madsen,et al.  An evaluation of the impact of model structure on hydrological modelling uncertainty for streamflow simulation , 2004 .

[40]  Patrick M. Reed,et al.  How effective and efficient are multiobjective evolutionary algorithms at hydrologic model calibration , 2005 .

[41]  Dong-Jun Seo,et al.  Towards the characterization of streamflow simulation uncertainty through multimodel ensembles , 2004 .

[42]  Karel J. Keesman,et al.  Membership-set estimation using random scanning and principal componet analysis , 1990 .

[43]  Breanndán Ó Nualláin,et al.  Parameter optimisation and uncertainty assessment for large-scale streamflow simulation with the LISFLOOD model , 2007 .

[44]  Feyzan Misirli Baysal.  Improving efficiency and effectiveness of Bayesian recursive parameter estimation for hydrologic models , 2003 .

[45]  Lucy Marshall,et al.  Towards dynamic catchment modelling: a Bayesian hierarchical mixtures of experts framework , 2007 .

[46]  P. Mantovan,et al.  Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology , 2006 .

[47]  Bo Liu,et al.  Projected streamflow in the Huaihe River Basin (2010–2100) using artificial neural network , 2010 .

[48]  Chuntian Cheng,et al.  Long-Term Prediction of Discharges in Manwan Hydropower Using Adaptive-Network-Based Fuzzy Inference Systems Models , 2005, ICNC.

[49]  Cajo J. F. ter Braak,et al.  Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling? , 2009 .

[50]  M. Trosset,et al.  Bayesian recursive parameter estimation for hydrologic models , 2001 .

[51]  Saman Razavi,et al.  Long‐lead seasonal rainfall forecasting using time‐delay recurrent neural networks: a case study , 2008 .

[52]  Henrik Madsen,et al.  Parameter estimation in distributed hydrological catchment modelling using automatic calibration with multiple objectives , 2003 .

[53]  Ashish Sharma,et al.  A comparative study of Markov chain Monte Carlo methods for conceptual rainfall‐runoff modeling , 2004 .

[54]  Keith Beven,et al.  The future of distributed models: model calibration and uncertainty prediction. , 1992 .

[55]  Bruce A. Robinson,et al.  Treatment of uncertainty using ensemble methods: Comparison of sequential data assimilation and Bayesian model averaging , 2007 .

[56]  S. Sorooshian,et al.  Effective and efficient global optimization for conceptual rainfall‐runoff models , 1992 .

[57]  Willem Bouten,et al.  Information content of data for identifying soil hydraulic parameters from outflow experiments , 2001 .

[58]  K. Beven.  Rainfall-Runoff Modelling: The Primer , 2012 .

[59]  R. Lippmann,et al.  An introduction to computing with neural nets , 1987, IEEE ASSP Magazine.

[60]  Steven M. Gorelick,et al.  Framework to evaluate the worth of hydraulic conductivity data for optimal groundwater resources management in ecologically sensitive areas , 2005 .

[61]  S. Sorooshian,et al.  A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters , 2002 .

[62]  Wesley W. Wallender,et al.  Inverse modeling of large-scale spatially distributed vadose zone properties using global optimization / W06503, doi:10.1029/2003WR002706 , 2004 .

[63]  Keith Beven,et al.  So just why would a modeller choose to be incoherent , 2008 .

[64]  Frank T.-C. Tsai,et al.  Bayesian model averaging assessment on groundwater management under model structure uncertainty , 2010 .

[65]  Ozgur Kisi,et al.  Wavelet regression model as an alternative to neural networks for monthly streamflow forecasting , 2009 .

[66]  Soroosh Sorooshian,et al.  Multi-objective global optimization for hydrologic models , 1998 .

[67]  Henrik Madsen,et al.  Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling , 2008 .

[68]  O. Kisi.  Neural Networks and Wavelet Conjunction Model for Intermittent Streamflow Forecasting , 2009 .

[69]  S. P. Neuman,et al.  Maximum likelihood Bayesian averaging of uncertain model predictions , 2003 .