Uncertainty analysis for the forecast of lake level fluctuations using ensembles of ANN and ANFIS models

In this study various ANN and ANFIS models were developed to forecast the lake level fluctuations in Lake Urmia in northwest of Iran. In addition to the time series of lake levels, the time series of three most effective variables in the water budget of the lake namely, the rainfall, evaporation and inflow were also used to find the best input variables to the models. Furthermore the uncertainty due to the error in measuring the hydrological variables and also the uncertainty in the outputs of ANN and ANFIS models which stems from their sensitivity to the training sets used to train these models and also the initial configuration before commencement of training were estimated. Comparing the outputs and confidence intervals of the two types of models it was found that the results of ANFIS model are superior to those of ANN' in that they are both more accurate and with less uncertainty.

[1]  Tom Heskes,et al.  Practical Confidence and Prediction Intervals , 1996, NIPS.

[2]  Dimitar Filev,et al.  Generation of Fuzzy Rules by Mountain Clustering , 1994, J. Intell. Fuzzy Syst..

[3]  K. Abbaspour,et al.  Estimating Uncertain Flow and Transport Parameters Using a Sequential Uncertainty Fitting Procedure , 2004 .

[4]  Ping Li,et al.  Application of Back-Propagation Artificial Neural Network Models for Prediction of Groundwater Levels: Case study in Western Jilin Province, China , 2008, 2008 2nd International Conference on Bioinformatics and Biomedical Engineering.

[5]  Alejandro Ramirez-Serrano,et al.  Adaptive fuzzy control for a quadrotor helicopter robust to wind buffeting , 2011, J. Intell. Fuzzy Syst..

[6]  K. P. Sudheer,et al.  A data‐driven algorithm for constructing artificial neural network rainfall‐runoff models , 2002 .

[7]  B. S. Thandaveswara,et al.  A non-linear rainfall–runoff model using an artificial neural network , 1999 .

[8]  James M. Ehrman,et al.  Using neural networks to assess the influence of changing seasonal climates in modifying discharge, dissolved organic carbon, and nitrogen export in eastern Canadian rivers , 1998 .

[9]  Z. Şen,et al.  Stochastic Modeling of the Van Lake Monthly Level Fluctuations in Turkey , 2000 .

[10]  Ian Flood,et al.  Neural Networks in Civil Engineering. I: Principles and Understanding , 1994 .

[11]  Stephen L. Chiu,et al.  Fuzzy Model Identification Based on Cluster Estimation , 1994, J. Intell. Fuzzy Syst..

[12]  Soichi Nishiyama,et al.  Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool. , 2007, Journal of environmental management.

[13]  Roger Jones,et al.  Modelling historical lake levels and recent climate change at three closed lakes, Western Victoria, Australia (c.1840–1990) , 2001 .

[14]  K. Abbaspour,et al.  Modelling hydrology and water quality in the pre-alpine/alpine Thur watershed using SWAT , 2007 .

[15]  James C. Bezdek,et al.  Fuzzy mathematics in pattern classification , 1973 .

[16]  A. Shamseldin Application of a neural network technique to rainfall-runoff modelling , 1997 .

[17]  P. Hall The Bootstrap and Edgeworth Expansion , 1992 .

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

[19]  L. Bengtsson,et al.  Using rainfall-runoff modeling to interpret lake level data , 1997 .

[20]  Donald Gustafson,et al.  Fuzzy clustering with a fuzzy covariance matrix , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[21]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[22]  Sobri Harun,et al.  Rainfall-Runoff Modeling Using Artificial Neural Network , 2001 .

[23]  Paulin Coulibaly,et al.  Groundwater level forecasting using artificial neural networks , 2005 .

[24]  Slobodan P. Simonovic,et al.  Short term streamflow forecasting using artificial neural networks , 1998 .

[25]  A. W. Minns,et al.  Artificial neural networks as rainfall-runoff models , 1996 .

[26]  Rafael Marcé,et al.  A neuro‐fuzzy modeling tool to estimate fluvial nutrient loads in watersheds under time‐varying human impact , 2004 .

[27]  Alan F. Murray,et al.  Confidence estimation methods for neural networks : a practical comparison , 2001, ESANN.

[28]  Kim N. Irvine,et al.  Multiplicative, Seasonal ARIMA Models for Lake Erie and Lake Ontario Water Levels , 1992 .

[29]  A. Tokar,et al.  Rainfall-Runoff Modeling Using Artificial Neural Networks , 1999 .

[30]  P. C. Nayak,et al.  Groundwater Level Forecasting in a Shallow Aquifer Using Artificial Neural Network Approach , 2006 .

[31]  M. Vaziri Predicting Caspian Sea Surface Water Level by ANN and ARIMA Models , 1997 .

[32]  E. Mizutani,et al.  Neuro-Fuzzy and Soft Computing-A Computational Approach to Learning and Machine Intelligence [Book Review] , 1997, IEEE Transactions on Automatic Control.

[33]  Chuen-Tsai Sun,et al.  Neuro-fuzzy modeling and control , 1995, Proc. IEEE.

[34]  Leo Breiman,et al.  Bagging Predictors , 1996, Machine Learning.

[35]  A. Soldati,et al.  River flood forecasting with a neural network model , 1999 .

[36]  Padraig Cunningham,et al.  Confidence and prediction intervals for neural network ensembles , 1999, IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339).

[37]  A. Altunkaynak Forecasting Surface Water Level Fluctuations of Lake Van by Artificial Neural Networks , 2007 .

[38]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

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

[40]  S. T. Buckland,et al.  An Introduction to the Bootstrap. , 1994 .

[41]  Peter K. Dunn,et al.  Bootstrap confidence intervals for predicted rainfall quantiles , 2001 .