Application of neuro fuzzy technique in streamflow forecasting

APPLICATION OF A NEURO - FUZZY TECHNIQUE IN STREAMFLOW FORECASTING by Chau Nguyen Xuan Quang A thesis submitted in partial fulfillment of the requirements for the degree of Master of Engineering Examination Committee: Prof Tawatchai Tingsanchali (Chairman) Dr Roberto S Clemente Dr Manukid Parnichkun Nationality Previous Degree : : Vietnamese Bachelor of Civil Engineering Hochiminh City University of Technology Hochiminh, Vietnam Scholarship Donor : Government of the Netherlands Asian Institute of Technology School of Civil Engineering Thailand April 2004 i ACKNOWLEDGEMENT First of all, the author wishes to express his deepest gratitude to his advisor, Professor Tawatchai Tingsanchali, for his invaluable advice, continuous guidance and encouragement in the accomplishment of this thesis Grateful acknowledgements are extended to Dr Roberto S Clemente and Dr Manukid Parnichkun who served as Examination Committee Members, for their valuable suggestions, comments, guidance and inspiration during period of this study The author also would like to express his appreciation to Royal Irrigation Department (RID) for their help providing data The financial support of the Government of Netherlands through a scholarship award is gratefully acknowledged His study at the Asian Institute of Technology (AIT) would have been impossible without this financial support Finally, grateful acknowledgements are extended to his family, for their eternal love, dedications, constant encouragement, and moral support throughout his education and study at AIT ii ABSTRACT The neuro - fuzzy technique (NFT), called the Adaptive Neuro - Fuzzy Based Inference System (ANFIS) was employed to forecast daily and weekly streamflow for four gauging stations, namely Y17, Y4, Y6 and Y20 of the Yom River Basin in Thailand The model is proposed to forecast the streamflow of one, two and three days and one week in advance Various inputs of different types and length of training data were tried, using observed daily and weekly discharges, water level and mean areal rainfall series from 1990 to 1999 for calibration (training) and from 2000 to 2001 for verification (testing), to obtain the most accurate results The accuracy of flood forecast is evaluated by using statistical efficiency index (EI), and root mean square error (RMSE) The results obtained from NFT model were found to be very satisfactory in both daily and weekly streamflow forecasting The model accuracy decreases when the time of forecasting ahead is increased However, the accuracy of results of two and three days ahead forecasting are much better when using successive day to day forecast of previous day as the input of the next days forecast The NFT model results are very close to the results obtained by using multilayer perceptron (MLP) model and are better than the results obtained from multi variable regression (MVR) model This study presented the application of NFT for daily and weekly streamflow forecasting with promising results The results also indicate that NFT perform slightly better than MLP and much better than MVR in flood forecasting in terms of accuracy Both NFT and MLP are strongly recommended for streamflow forecasting due to their capacity in nonlinear relationship modeling iii Tables Of Contents Chapter Title Page Title page Acknowledgement Abstract Table of Contents List of Figures List of Tables List of Abbreviation i ii iii iv vi ix x INTRODUCTION 1.1 General 1.2 The Study Area 1.3 Statement of the Problem 1.4 Objectives of the Study 1.5 Scope of the Study 1 LITERATURE REVIEW 2.1 Neural Network Approach 2.2 Fuzzy Sets Approach 2.3 Neuro-Fuzzy Approach 7 THEORETICAL CONSIDERATIONS 3.1 Introduction 3.2 Fuzzy Logic 3.2.1 Definition of Fuzzy Sets 3.2.2 Basic Relations and Logical Operations 3.2.3 Membership Functions 3.2.4 Fuzzy If-Then Rules 3.2.5 Takagi-Sugano Model 3.2.6 Fuzzy Inference Systems 3.3 Adaptive Network 3.3.1 Architecture 3.3.2 Gradient Descent Learning Algorithm 3.3.3 Hybrid Learning Rule: (Off – line learning) 3.3.4 Hybrid Learning Rule: (On – line learning) 3.4 ANFIS 3.4.1 ANFIS Architecture 3.4.2 Hybrid Learning Algorithm for ANFIS 3.4.3 Computation Complexity 3.5 Performance Statistics 10 10 10 10 11 12 13 13 14 14 15 16 18 18 18 21 22 22 iv Tables Of Contents (Continued) Chapter Title Page DATA COLLECTION AND MODELING PROCEDURE 4.1 Data Collection 4.2 Data Processing 4.3 Input Selection 4.3.1 Selection of Input and Output Variables 4.3.2 Selection of Relationship Function of Input and Output 4.3.3 Selection of Training Patterns 4.4 ANFIS Modeling 4.4.1 Membership Function 4.4.2 Initial Parameters 4.4.3 Training Algorithm 4.5 Performance Statistics 4.6 Stop Criteria 24 26 26 26 28 28 28 28 29 29 29 RESULTS AND DISCUSSIONS 5.1 Relationship Function of Output and Input 5.2 Training Data Selection 5.3 Separation of Training Period 5.4 Flood Forecasting Models 5.4.1 Daily Discharge Forecasting Model 5.4.2 Daily Water Level Forecasting Model 5.4.3 Mean Weekly Discharge Forecasting Model 5.5 Comparison of NFT Model to MLP and MVR Models 30 31 32 33 33 35 38 41 CONCLUSIONS AND RECOMMENDATIONS 6.1 Conclusions 6.2 Recommendations 49 50 References Appendix A Appendix B Appendix C v List of Abbreviations Abbreviation ANN ANFIS EI MF MVR NFT MLP OLS Q R RID RMSE RBF SSARR USGS W Description Artificial Neural Network Adaptive Neuro - Fuzzy Based Inference System Efficiency Index Membership Function Multi Variables Regression Neuro-Fuzzy Technique Multilayer Perceptron Orthogonal Least Squares Algorithm Discharge Rainfall Royal Irrigation Department Root Mean Square Error Radius Basis Function Streamflow Synthesis and Reservoir Regulation U.S Geological Survey Water Level x List of Figures Figure Title Page 1.1 Map of Yom River Basin, Thailand 3.1a Triangular Membership Function 11 3.1b Trapezoidal Membership Function 11 3.2a Gaussian Membership Function 12 3.2b Bell Membership Function 12 3.3 Sigmoid Membership Function 12 3.4 Fuzzy Inference System 13 3.5 Commonly Used Fuzzy If – Then Rules and Fuzzy Reasoning Mechanisms 14 3.6 An Adaptive Network 15 3.7 Type-3 Fuzzy Reasoning 19 3.8 Equivalent ANFIS (type-3 ANFIS) 19 3.9a Type-1 Fuzzy Reasoning 20 3.9b Equivalent ANFIS (type-1 ANFIS) 20 3.10a Two-Input Type-3 ANFIS with Nine Rules 21 3.10b Corresponding Fuzzy Subspaces 21 4.1 The Distribution of Rainfall and Gauging Stations in Yom River Basin 25 4.2 Arrangement of Gauging Stations for Streamflow Forecasting 25 4.3 The diagram for Selection the Relationship Function of Input and Output 27 4.4 Bell Membership function 28 4.5 Overtraining Behavior of Training Process 29 5.1 RMSE vs Relationship Functions of Input and Output of Stations Y17, Y4, Y6, Y20 30 Comparison of Observed and Day Ahead Forecasted Discharge at Station Y17, (Testing Period: 1/April/2000 – 31/March/2002) 34 Comparison of Observed and Day Ahead Forecasted Discharge at Station Y4, (Testing Period: 1/April/1997 – 31/March/1999) 35 Comparison of Observed and Day Ahead Forecasted Discharge at Station Y6, (Testing Period: 1/April/2000 – 31/March/2002) 35 Comparison of Observed and Day Ahead Forecasted Discharges at Station Y20, (Testing Period: 1/April/2000 – 31/March/2002) 35 5.2 5.3 5.4 5.5 vi 5.6 5.7 5.8 5.9 5.10 RMSE vs Relationship Functions of Input and Output of Stations Y17, Y4, Y6, Y20 36 Comparison of Observed and Day Ahead Forecasted Water Level at Station Y17, (Testing Period: 1/April/2000 – 31/March/2002) 38 Comparison of Observed and Day Ahead Forecasted Water Level at Station Y4, (Testing Period: 1/April/1997 – 31/March/1999) 38 Comparison of Observed and Day Ahead Forecasted Water Level at Station Y6, (Testing Period: 1/April/2000 – 31/March/2002) 39 Comparison of Observed and Day Ahead Forecasted Water Level at Station Y20, (Testing Period: 1/April/2000 – 31/March/2002) 39 5.11 Comparison of Mean Weekly Observed and Week Ahead Forecasted Discharge at Station Y17, (Testing Period: 1/April/2000 – 31/March/2002) 40 5.12 Comparison of Mean Weekly Observed and Week Ahead Forecasted Discharge at Station Y6, (Testing Period: 1/April/2000 – 31/March/2002) 40 Comparison of Mean Weekly Observed and Week Ahead Forecasted Discharge at Station Y6, (1/April/2000 – 31/March/2002) 40 5.13 5.14 Comparison of Mean Weekly Observed and Week Ahead Forecasted Discharge at Station Y20, (Testing Period: 1/April/2000 – 31/March/2002) 41 5.15 Comparison of Observed and Day Ahead Forecasted Discharges Obtained from NFT, MLP and MVR at Station Y17, (Testing Period: 1/April/2001– 31/March/2002) 43 5.16 Comparison of Observed and Day Ahead Forecasted Discharge Obtained from NFT, MLP and MVR at Station Y4, (Testing Period: 1/April/1998 – 31/March/1999) 44 5.17 Comparison of Observed and Day Ahead Forecasted Discharge Obtained from NFT, MLP and MVR at Station Y6, (Testing Period: 1/April/2001 – 31/March/2002) 44 5.18 Comparison of Observed and Day Ahead Forecasted Discharge Obtained from NFT, MLP and MVR at Station Y20, (Testing Period: 1/April/2001 – 31/March/2002) 44 5.19 Comparison of Observed and Day Ahead Forecasted Water Level Obtained from NFT, MLP and MVR at Station Y17, (Testing Period: 1/April/2001 – 31/March/2002) 45 5.20 Comparison of Observed and Day Ahead Forecasted Water Level Obtained from NFT, MLP and MVR at Station Y4, (Testing Period: 1/April/1997 – 31/March/1998) 45 5.21 Comparison of Observed and Day Ahead Forecasted Water Level Obtained from NFT, MLP and MVR at Station Y6, (Testing Period: 1/April/2001 – 31/March/2002) 45 5.22 Comparison of Observed and Day Ahead Forecasted Water Level Obtained from NFT, MLP and MVR at Station Y6, (Testing Period: 1/April/2001 – 31/March/2002) 46 vii 5.23 5.24 5.25 5.26 6.1 Comparison of Mean Weekly Observed and Week Ahead Forecasted Discharge Obtained from NFT, MLP and MVR at Station Y17, (Testing Period: 1/April/2000 – 31/March/2002) 46 Comparison of Mean Weekly Observed and Week Ahead Forecasted Discharge Obtained from NFT, MLP and MVR at Station Y4, (Testing Period: 1/April/1997 – 31/March/1999) 46 Comparison of Mean Weekly Observed and Week Ahead Forecasted Discharge Obtained from NFT, MLP and MVR at Station Y6, (Testing Period: 1/April/2000 – 31/March/2002) 47 Comparison of Mean Weekly Observed and Week Ahead Forecasted Discharge Obtained from NFT, MLP and MVR at Station Y20, (Testing Period: 1/April/2000 – 31/March/2002) 47 RMSE and EI vs Days of Forecast 49 viii List of Tables Table Title Page 3.1 Two passes in the hybrid learning procedure for ANFIS 22 4.1 List of the Rainfall Stations 24 4.2 List of the Gauging Stations 24 5.1 Results of Selected the Training Pattern for Station Y17, Y4, Y6 and Y20 32 5.2 Results of the Separation of Training Data into Two Sets: High Flow (July to November) and Low Flow (December to June of following year) 32 5.3 Results of Daily Discharge Forecasting of Stations Y17, Y6, Y4 and Y20 5.4 Results of Daily Water Level Forecasting of Stations Y17, Y6, Y4 and Y20 36 5.5 Results of Mean Weekly Discharge Forecasting 38 5.6 Comparison of Results of NFT, MLP and MVR Models for Station Y17 41 5.7 Comparison of Results of NFT, MLP and MVR Models for Station Y4 42 5.8 Comparison of Results of NFT, MLP and MVR Models for Station Y6 42 5.9 Comparison of Results of NFT, MLP and MVR Models for Station Y20 43 ix 33 Table A11 MF p The Parameters of Output Membership Functions of One Day Ahead Discharge Forecasting at Station Y17 using NFT Model (continued) q r m n e MF p q r m n e MF77 0.000 0.001 0.008 0.007 0.007 0.000 MF128 0.000 0.000 0.000 -0.001 -0.001 0.000 MF78 0.000 0.000 0.001 0.001 0.001 0.000 MF129 0.000 0.000 0.000 0.000 0.000 0.000 MF79 0.000 0.000 0.000 0.000 0.000 0.000 MF130 0.000 0.000 0.000 0.000 0.000 0.000 MF80 0.000 0.000 0.000 0.001 0.001 0.000 MF131 0.000 0.000 -0.003 0.009 0.009 0.000 MF81 0.000 0.000 0.000 0.000 0.000 0.000 MF132 0.001 0.000 0.005 0.011 0.013 0.000 MF82 0.156 0.058 0.052 0.187 0.587 0.000 MF133 0.000 0.000 0.000 0.000 0.000 0.000 MF83 0.118 0.015 0.289 0.697 0.810 0.002 MF134 0.000 0.000 0.002 0.004 0.004 0.000 MF84 0.003 0.001 0.012 0.016 0.020 0.000 MF135 0.000 0.000 0.002 0.005 0.006 0.000 MF85 0.095 0.012 0.139 0.451 0.538 0.001 MF136 0.000 -0.003 0.016 0.032 0.034 0.000 MF86 0.259 0.034 0.590 0.294 0.438 0.003 MF137 0.001 0.004 0.015 0.034 0.035 0.000 MF87 0.038 0.021 0.364 0.470 0.609 0.000 MF138 0.000 0.000 0.002 0.005 0.005 0.000 MF88 0.002 0.000 0.007 0.014 0.015 0.000 MF139 0.001 0.004 0.015 0.034 0.035 0.000 MF89 0.005 0.004 0.155 0.280 0.240 0.000 MF140 0.023 0.060 0.401 0.859 0.896 0.001 MF90 0.025 0.012 0.264 0.710 0.749 0.001 MF141 0.007 0.016 0.108 0.236 0.249 0.000 MF91 0.037 0.014 0.102 0.295 0.337 0.000 MF142 0.000 0.000 0.002 0.004 0.004 0.000 MF92 0.033 0.008 0.242 0.233 0.266 0.001 MF143 0.004 0.010 0.069 0.150 0.157 0.000 MF93 0.001 0.000 0.009 0.012 0.015 0.000 MF144 0.001 0.003 0.020 0.046 0.048 0.000 MF94 0.024 0.006 0.108 0.136 0.161 0.000 MF145 0.000 0.000 0.005 0.004 0.004 0.000 MF95 0.032 0.006 0.254 0.363 0.477 0.001 MF146 0.000 0.001 0.006 0.010 0.010 0.000 MF96 0.024 0.009 0.196 0.419 0.514 0.000 MF147 0.000 0.000 0.001 0.002 0.002 0.000 MF97 0.000 0.000 0.004 0.005 0.006 0.000 MF148 0.000 0.001 0.006 0.010 0.011 0.000 MF98 0.003 0.001 0.047 0.124 0.126 0.000 MF149 0.011 0.026 0.171 0.373 0.390 0.000 MF99 0.008 0.006 0.034 0.162 0.200 0.000 MF150 0.003 0.007 0.046 0.100 0.105 0.000 MF100 0.001 0.000 -0.011 0.004 0.005 0.000 MF151 0.000 0.000 0.001 0.002 0.002 0.000 MF101 0.001 0.000 0.057 0.019 0.020 0.000 MF152 0.002 0.004 0.029 0.063 0.066 0.000 MF102 0.000 0.000 0.002 0.001 0.001 0.000 MF153 0.001 0.001 0.009 0.020 0.021 0.000 MF103 0.001 0.000 0.041 0.013 0.014 0.000 MF154 0.000 0.000 0.000 0.000 0.000 0.000 MF104 0.005 0.000 0.350 0.106 0.115 0.000 MF155 0.000 0.000 0.000 0.000 0.000 0.000 MF105 0.001 0.000 0.013 0.011 0.013 0.000 MF156 0.000 0.000 0.000 0.000 0.000 0.000 MF106 0.000 0.000 0.001 0.000 0.000 0.000 MF157 0.000 0.000 0.000 0.000 0.000 0.000 MF107 0.000 0.000 0.009 0.005 0.005 0.000 MF158 0.000 0.001 0.005 0.008 0.009 0.000 MF108 0.000 0.000 0.002 0.007 0.007 0.000 MF159 0.000 0.000 0.001 0.002 0.002 0.000 MF109 0.144 0.111 0.113 0.675 0.747 0.003 MF160 0.000 0.000 0.000 0.000 0.000 0.000 MF110 0.028 0.024 0.105 0.145 0.135 0.001 MF161 0.000 0.000 0.001 0.001 0.001 0.000 MF111 0.002 0.001 0.012 0.026 0.029 0.000 MF162 0.000 0.000 0.000 0.000 0.000 0.000 MF112 0.029 0.025 0.106 0.172 0.166 0.001 MF163 0.130 -0.004 0.299 0.437 0.468 0.002 MF113 MF114 MF115 MF116 -0.021 0.055 0.001 0.013 0.010 0.050 0.001 0.025 0.637 0.527 0.006 0.195 0.646 1.160 0.014 0.431 0.647 1.341 0.014 0.453 0.000 0.001 0.000 0.000 MF164 MF165 MF166 MF167 0.065 0.001 0.063 0.082 0.000 0.000 0.000 0.003 0.115 0.005 0.108 0.181 0.337 0.012 0.331 0.564 0.343 0.014 0.336 0.602 0.001 0.000 0.001 0.001 MF117 0.017 0.013 0.190 0.474 0.516 0.000 MF168 0.025 0.008 0.166 0.373 0.469 0.000 MF118 0.012 0.006 0.227 0.145 0.153 0.000 MF169 0.001 0.000 0.002 0.005 0.005 0.000 MF119 0.006 0.006 0.115 0.065 0.066 0.000 MF170 0.002 0.001 0.014 0.032 0.038 0.000 MF120 0.001 0.001 0.007 0.011 0.013 0.000 MF171 0.007 0.002 0.047 0.107 0.132 0.000 MF121 0.005 0.006 0.103 0.063 0.065 0.000 MF172 0.012 0.000 0.040 0.041 0.044 0.000 MF122 0.018 0.050 0.134 0.726 0.767 0.001 MF173 0.005 0.000 0.024 0.032 0.033 0.000 MF123 0.024 0.022 0.218 0.503 0.584 0.001 MF174 0.000 0.000 0.002 0.004 0.004 0.000 MF124 0.000 0.000 0.004 0.005 0.006 0.000 MF175 0.005 0.000 0.020 0.029 0.030 0.000 MF125 0.006 0.011 0.075 0.180 0.190 0.000 MF176 0.008 0.001 0.040 0.081 0.095 0.000 MF126 0.008 0.006 0.089 0.228 0.249 0.000 MF177 0.011 0.004 0.074 0.165 0.208 0.000 MF127 0.001 0.001 0.016 0.006 0.007 0.000 MF178 0.000 0.000 0.000 0.001 0.001 0.000 A-8 Table A12 MF p MF179 0.001 MF180 0.003 MF181 The Parameters of Output Membership Functions of One Day Ahead Discharge Forecasting at Station Y17 using NFT Model (continued) q r m n e MF p q r m n e 0.000 0.006 0.013 0.016 0.000 MF212 0.000 0.000 0.001 0.001 0.001 0.000 0.001 0.020 0.048 0.059 0.000 MF213 0.000 0.000 0.001 0.003 0.003 0.000 0.000 0.000 0.001 0.002 0.002 0.000 MF214 0.000 0.000 0.000 0.000 0.000 0.000 MF182 0.000 0.000 0.002 0.002 0.002 0.000 MF215 0.000 0.000 0.000 0.000 0.000 0.000 MF183 0.000 0.000 0.000 0.000 0.000 0.000 MF216 0.000 0.000 0.000 0.001 0.001 0.000 MF184 0.000 0.000 0.002 0.001 0.001 0.000 MF217 0.000 0.000 0.001 0.001 0.002 0.000 MF185 0.000 0.000 0.008 0.004 0.005 0.000 MF218 0.000 0.000 0.000 0.001 0.001 0.000 MF186 0.000 0.000 0.002 0.004 0.005 0.000 MF219 0.000 0.000 0.000 0.000 0.000 0.000 MF187 0.000 0.000 0.000 0.000 0.000 0.000 MF220 0.000 0.000 0.000 0.001 0.001 0.000 MF188 0.000 0.000 0.000 0.000 0.000 0.000 MF221 0.000 0.001 0.005 0.012 0.013 0.000 MF189 0.000 0.000 0.000 0.001 0.001 0.000 MF222 0.000 0.000 0.003 0.007 0.008 0.000 MF190 0.005 0.002 0.014 0.026 0.028 0.000 MF223 0.000 0.000 0.000 0.000 0.000 0.000 MF191 0.003 0.001 0.007 0.016 0.017 0.000 MF224 0.000 0.000 0.001 0.002 0.002 0.000 MF192 0.000 0.000 0.002 0.005 0.007 0.000 MF225 0.000 0.000 0.001 0.002 0.002 0.000 MF193 0.003 0.001 0.007 0.017 0.018 0.000 MF226 0.000 0.000 0.000 0.000 0.000 0.000 MF194 0.007 0.002 0.040 0.089 0.106 0.000 MF227 0.000 0.000 0.000 0.000 0.000 0.000 MF195 0.018 0.006 0.120 0.270 0.339 0.000 MF228 0.000 0.000 0.000 0.000 0.000 0.000 MF196 0.000 0.000 0.000 0.001 0.001 0.000 MF229 0.000 0.000 0.000 0.000 0.000 0.000 MF197 0.001 0.001 0.010 0.022 0.026 0.000 MF230 0.000 0.000 0.002 0.005 0.005 0.000 MF198 0.005 0.002 0.033 0.075 0.093 0.000 MF231 0.000 0.000 0.001 0.003 0.004 0.000 MF199 0.001 0.000 0.005 0.004 0.004 0.000 MF232 0.000 0.000 0.000 0.000 0.000 0.000 MF200 0.000 0.000 0.004 0.003 0.003 0.000 MF233 0.000 0.000 0.000 0.001 0.001 0.000 MF201 0.000 0.000 0.001 0.002 0.003 0.000 MF234 0.000 0.000 0.000 0.001 0.001 0.000 MF202 0.000 0.000 0.003 0.003 0.003 0.000 MF235 0.000 0.000 0.000 0.000 0.000 0.000 MF203 0.002 0.001 0.017 0.039 0.047 0.000 MF236 0.000 0.000 0.000 0.000 0.000 0.000 MF204 0.008 0.003 0.053 0.119 0.150 0.000 MF237 0.000 0.000 0.000 0.000 0.000 0.000 MF205 0.000 0.000 0.000 0.000 0.000 0.000 MF238 0.000 0.000 0.000 0.000 0.000 0.000 MF206 0.001 0.000 0.004 0.010 0.012 0.000 MF239 0.000 0.000 0.000 0.000 0.000 0.000 MF207 0.002 0.001 0.015 0.034 0.042 0.000 MF240 0.000 0.000 0.000 0.000 0.000 0.000 MF208 0.000 0.000 0.000 0.000 0.000 0.000 MF241 0.000 0.000 0.000 0.000 0.000 0.000 MF209 0.000 0.000 0.000 0.000 0.000 0.000 MF242 0.000 0.000 0.000 0.000 0.000 0.000 MF210 0.000 0.000 0.000 0.000 0.000 0.000 MF243 0.000 0.000 0.000 0.000 0.000 0.000 MF211 0.000 0.000 0.000 0.000 0.000 0.000 A-9 Table A13 Input a 21.81967 21.84638 21.64332 Input a 555.62041 555.64614 555.62496 Parameter MF1 MF2 MF3 Parameter MF1 MF2 MF3 Table A14 MF The Parameters of Input Membership Functions of One Day Ahead Discharge Forecasting at Station Y4 using NFT Model p b 1.75729 2.14812 2.55393 c 0.02861 43.47627 87.11263 Parameter MF1 MF2 MF3 b 0.67058 1.67703 2.17945 c -0.00895 1111.23287 2222.49989 Parameter MF1 MF2 MF3 Input a 21.81536 21.63969 21.71176 Input a 80.88364 80.79708 80.90862 b 1.95480 2.58676 2.25731 c 0.05329 43.62700 87.07165 b 2.37902 2.79285 2.17708 c 0.00708 161.81736 323.52731 The Parameters of Output Membership Functions of One Day Ahead Discharge Forecasting at Station Y4 using NFT Model q r m n MF p q r m n MF1 0.0916 -0.0278 -0.4511 1.1350 -0.2080 MF42 0.0430 0.0051 0.0096 0.2247 0.0008 MF2 0.1798 -0.1431 0.8977 0.1014 -0.0085 MF43 0.0016 -0.0009 0.0075 0.0003 0.0000 MF3 0.2472 0.2074 0.6049 0.1998 -0.0024 MF44 0.0007 -0.0003 -0.0045 0.0011 0.0000 MF4 0.0815 0.0130 4.2564 0.6405 -0.0013 MF45 -0.0010 -0.0012 -0.0831 -0.0084 0.0000 MF5 0.0304 0.0036 0.3629 -0.5124 0.0023 MF46 0.0121 0.0702 0.0245 0.0035 0.0005 MF6 0.1699 0.3245 -0.0404 0.7609 0.0000 MF47 0.0041 0.0196 0.0453 0.0402 0.0002 MF7 0.0019 0.0001 0.1008 0.0170 -0.0006 MF48 0.0024 0.0083 0.0717 0.0407 0.0001 MF8 0.0002 0.0003 0.1325 0.0120 0.0001 MF49 0.0011 0.0044 0.0035 0.0005 0.0000 MF9 0.0028 0.0036 0.0361 0.2936 0.0009 MF50 0.0009 0.0022 0.0115 0.0080 0.0000 MF10 -0.2938 0.1355 -0.0816 0.7450 -0.0069 MF51 0.0017 0.0050 0.0390 0.0284 0.0001 MF11 0.0801 0.4325 0.8362 0.2762 0.0080 MF52 0.0001 0.0002 0.0001 0.0000 0.0000 MF12 0.0338 -0.0191 0.7929 0.2017 0.0001 MF53 0.0000 0.0001 0.0000 0.0002 0.0000 MF13 -0.0171 0.0095 0.1911 0.0862 0.0001 MF54 0.0000 0.0001 -0.0010 0.0003 0.0000 MF14 0.0236 0.0197 -0.0506 -0.0435 0.0009 MF55 0.1249 0.0213 0.1449 0.0469 0.0015 MF15 0.0155 -0.0232 -0.0251 0.4992 0.0013 MF56 0.0795 0.0192 0.2151 0.1892 0.0014 MF16 -0.0009 0.0004 0.0045 0.0035 0.0000 MF57 0.0405 0.0121 0.3741 0.1928 0.0007 MF17 0.0004 0.0001 -0.0264 -0.0053 0.0000 MF58 0.0090 0.0017 0.0223 0.0061 0.0002 MF18 -0.0015 -0.0035 0.0924 0.0747 0.0002 MF59 0.0120 0.0036 0.0629 0.0401 0.0002 MF19 0.0057 0.1034 0.0346 0.0618 0.0010 MF60 0.0453 0.0130 0.4302 0.2290 0.0008 MF20 0.0033 0.3118 0.4770 0.6173 0.0039 MF61 0.0005 0.0001 0.0008 0.0002 0.0000 MF21 0.0085 0.0737 0.4862 0.3038 0.0011 MF62 0.0004 0.0001 0.0016 0.0012 0.0000 MF22 0.0006 0.0070 0.0142 0.0069 0.0001 MF63 0.0010 0.0002 0.0097 0.0054 0.0000 MF23 0.0010 0.0285 0.0591 0.0618 0.0004 MF64 0.0268 -0.0133 0.1628 0.0547 0.0004 MF24 0.0059 0.0401 0.3030 0.1994 0.0007 MF65 0.3065 0.1636 0.3770 0.5540 0.0036 MF25 0.0000 0.0004 0.0004 0.0003 0.0000 MF66 0.0290 0.0123 0.1585 0.0997 0.0004 MF26 0.0000 0.0014 0.0017 0.0029 0.0000 MF67 0.0034 0.0002 0.0158 0.0048 0.0001 MF27 0.0001 0.0008 -0.0002 0.0047 0.0000 MF68 0.0250 0.0129 0.0476 0.0517 0.0003 MF28 -0.2136 -0.4029 1.6866 -0.7052 -0.0287 MF69 0.0168 0.0050 0.1467 0.0820 0.0003 MF29 0.4999 0.1726 0.8601 0.1433 -0.0031 MF70 0.0002 0.0000 0.0007 0.0003 0.0000 MF30 0.0605 0.1030 0.8217 0.1381 0.0003 MF71 0.0014 0.0007 0.0018 0.0026 0.0000 MF31 0.0143 -0.0228 0.5140 0.0000 -0.0003 MF72 0.0004 0.0001 0.0022 0.0018 0.0000 MF32 0.0770 0.0747 -0.1537 0.0264 0.0001 MF73 -0.0008 -0.0007 0.0029 0.0029 0.0000 MF33 0.0880 0.0976 -0.0108 0.4605 0.0013 MF74 0.0223 0.0130 0.0268 0.0418 0.0003 MF34 -0.0002 -0.0011 0.0162 -0.0012 -0.0001 MF75 0.0015 0.0010 0.0064 0.0048 0.0000 0.0000 MF35 0.0020 0.0016 -0.0204 -0.0047 0.0000 MF76 0.0000 0.0000 0.0003 0.0002 MF36 -0.0007 -0.0019 0.0685 0.0323 0.0001 MF77 0.0017 0.0010 0.0026 0.0034 0.0000 MF37 MF38 MF39 MF40 0.2035 0.0769 0.0670 0.0426 -0.3681 -0.0870 0.0172 -0.0122 1.5348 0.7453 0.7998 0.1758 0.0002 0.1401 0.3564 0.0060 -0.0087 -0.0010 0.0013 -0.0001 MF78 MF79 MF80 MF81 0.0005 0.0000 0.0001 0.0000 0.0003 0.0000 0.0001 0.0000 0.0049 0.0000 0.0001 0.0001 0.0028 0.0000 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 MF41 0.0330 0.0021 0.3378 0.1647 0.0007 A-10 Table A15 The Parameters of Input Membership Functions of One Day Ahead Discharge Forecasting at Station Y6 using NFT Model Input Parameter MF1 MF2 MF3 a 406.16850 406.18056 406.17527 Parameter MF1 MF2 MF3 a 555.61892 555.62940 555.62549 b 1.97326 2.34372 2.18440 c 0.79332 813.14423 1625.49940 Parameter MF1 MF2 MF3 b 1.99291 2.51682 2.15281 c -0.00641 1111.24285 2222.49922 Parameter MF1 MF2 MF3 Input a 555.62254 555.62111 555.62561 Input a 555.62481 555.63127 555.62384 Input Table A16 MF p b 2.13251 2.71480 2.18211 c -0.00201 1111.25033 2222.49909 b 1.62368 2.00386 2.32200 c -0.00191 1111.24431 2222.50040 The Parameters of Output Membership Functions of One Day Ahead Discharge Forecasting at Station Y6 using NFT Model q r m n MF p q r m n MF1 0.1508 0.1357 -0.7617 1.5547 -0.0553 MF42 -0.3251 -0.2501 -0.0404 0.3341 MF2 1.0817 0.6873 -0.3356 0.5569 -0.0031 MF43 -0.0111 -0.0142 -0.0128 -0.0042 0.0000 MF3 0.0594 0.0519 0.0901 0.1830 0.0000 MF44 -0.1647 -0.0936 -0.1276 -0.2079 -0.0001 MF4 0.4959 0.3598 0.2425 0.3463 -0.0020 MF45 -0.3582 0.0139 0.5976 1.1399 0.0003 MF5 0.4335 0.1782 -0.2330 0.3091 -0.0003 MF46 -0.0062 -0.0022 -0.0016 0.0110 0.0000 MF6 0.3987 0.3622 1.0071 1.8065 0.0010 MF47 0.0093 0.0413 0.0281 0.0383 0.0000 MF7 0.0102 0.0061 0.0013 0.0097 -0.0002 MF48 -0.0001 0.0016 0.0008 0.0014 0.0000 MF8 0.0128 0.0061 -0.0031 0.0080 0.0000 MF49 -0.0074 0.0512 0.0339 0.0303 0.0000 MF9 0.0312 0.0492 0.0978 0.1421 0.0001 MF50 0.2104 0.9133 0.5532 0.5581 0.0005 MF10 0.5461 -0.1904 -0.0590 0.3985 -0.0022 MF51 -0.0375 -0.0203 -0.0447 -0.0378 0.0000 MF11 0.4777 0.4492 0.4044 0.6635 0.0007 MF52 0.0035 0.0176 0.0183 0.0107 0.0000 MF12 0.0209 0.0190 0.0331 0.0594 0.0000 MF53 0.1128 0.4728 0.5358 0.3381 0.0003 MF13 0.3346 0.1110 0.0621 0.2986 0.0002 MF54 -0.0813 -0.0352 -0.0758 -0.1361 -0.0001 MF14 0.3990 0.0178 -0.0111 0.4337 0.0008 MF55 -0.0240 0.6553 0.4732 0.9099 -0.0003 MF15 0.1019 0.0182 0.2329 0.4954 0.0002 MF56 1.0861 0.2529 0.1917 0.3282 0.0007 MF16 0.0034 0.0115 0.0058 0.0106 0.0000 MF57 0.0173 0.0056 0.0049 0.0080 0.0000 MF17 0.0427 0.1653 0.2637 0.1785 0.0001 MF58 0.3053 0.0291 0.0114 0.0895 0.0001 MF18 0.2207 0.4232 0.7726 0.9959 0.0004 MF59 0.1457 0.0094 0.0026 0.0336 0.0001 MF19 0.0125 0.0118 0.0087 0.0202 -0.0001 MF60 0.0022 0.0004 0.0035 0.0129 0.0000 MF20 0.0205 0.0578 0.0363 0.0377 0.0000 MF61 0.0077 0.0024 0.0016 0.0041 0.0000 MF21 0.0009 0.0013 0.0015 0.0022 0.0000 MF62 0.0047 -0.0003 -0.0011 -0.0004 0.0000 MF22 0.0469 0.3275 0.2413 0.1371 0.0002 MF63 -0.0035 -0.0037 -0.0045 -0.0041 0.0000 MF23 0.1350 0.0753 -0.0941 -0.1084 0.0002 MF64 0.4326 -0.0424 -0.0396 0.1009 0.0001 MF24 -0.0021 -0.1198 -0.0808 -0.0547 0.0000 MF65 0.2219 0.0089 0.0053 0.0440 0.0001 MF25 0.0050 0.0262 0.0298 0.0122 0.0000 MF66 0.0037 -0.0010 -0.0015 -0.0005 0.0000 MF26 0.0564 0.0337 0.3457 0.1370 0.0001 MF67 -0.1322 -0.1164 -0.0990 -0.0497 -0.0002 MF27 0.0390 0.2961 0.3173 0.1816 0.0001 MF68 -0.0270 -0.0413 -0.0456 -0.0185 0.0000 MF28 0.3129 -0.6003 -0.8948 2.2055 -0.0048 MF69 -0.0721 -0.0921 -0.1211 -0.1254 -0.0001 MF29 1.1184 0.1980 -0.2056 1.6455 0.0020 MF70 -0.0020 -0.0036 -0.0038 -0.0027 0.0000 MF30 0.0337 0.0339 0.0521 0.1063 0.0001 MF71 -0.0261 -0.0325 -0.0445 -0.0501 0.0000 MF31 -0.6603 -0.0181 -0.1461 -0.0471 -0.0006 MF72 -0.1153 -0.1430 -0.1861 -0.1951 -0.0001 MF32 -0.3073 0.1670 0.4569 1.1147 0.0003 MF73 0.0126 0.0022 0.0016 0.0051 0.0000 MF33 0.1107 0.1791 0.4660 0.9564 0.0006 MF74 0.0080 0.0018 0.0013 0.0023 0.0000 MF34 -0.0110 -0.0021 -0.0049 0.0048 0.0000 MF75 0.0000 -0.0001 -0.0002 -0.0002 0.0000 MF35 -0.0100 -0.0014 -0.0003 0.0161 0.0000 MF76 -0.0003 0.0000 -0.0003 0.0003 0.0000 MF36 0.0162 0.0719 0.1365 0.1953 0.0001 MF77 0.0029 0.0134 0.0063 0.0064 0.0000 MF37 MF38 MF39 MF40 -0.0186 0.1511 0.0126 -0.0408 0.4581 0.5403 0.0211 -0.0459 0.3340 0.4802 0.0325 0.0441 0.5129 0.7805 0.0617 0.2592 0.0005 0.0009 0.0001 0.0004 MF78 MF79 MF80 MF81 -0.0066 0.0000 0.0002 -0.0111 -0.0086 0.0003 0.0062 -0.0122 -0.0119 0.0003 0.0072 -0.0177 -0.0127 0.0001 0.0025 -0.0209 0.0000 0.0000 0.0000 0.0000 MF41 0.5043 0.1320 0.1598 0.9376 0.0012 A-11 0.0000 Table A17 Input a b 36.560240 2.033274 36.425132 2.743177 36.527950 2.258407 Input a b 225.978519 2.513482 226.002966 2.411005 225.997458 2.214778 Parameter MF1 MF2 MF3 Parameter MF1 MF2 MF3 Table A16 MF The Parameters of Input Membership Functions of One Day Ahead Discharge Forecasting at Station Y20 using NFT Model p Input c 0.022275 73.161578 146.171293 Parameter MF1 MF2 MF3 a 36.419289 36.664723 36.523571 c 0.783033 452.795018 904.801366 Parameter MF1 MF2 MF3 a 225.984991 226.005116 225.996037 b 2.010523 2.383475 2.329792 c -0.122949 72.945093 146.172814 b 2.369943 2.180410 2.296855 c 0.787883 452.792925 904.802022 Input The Parameters of Output Membership Functions of One Day Ahead Discharge Forecasting at Station Y6 using NFT Model q r m n MF p q r m n MF1 0.2947 0.5932 -0.3457 1.1964 -0.0214 MF42 0.0114 0.0072 0.1132 0.2467 0.0003 MF2 0.1734 0.2262 0.3530 0.8558 0.0035 MF43 0.0007 0.0010 0.0050 0.0046 0.0000 MF3 0.0069 0.0055 0.0289 0.0777 0.0001 MF44 0.0032 0.0049 0.1036 0.0869 0.0001 MF4 0.0886 0.2626 0.1261 0.4318 -0.0004 MF45 0.0067 0.0088 0.2268 0.1917 0.0003 MF5 -0.0168 0.3096 0.3676 -0.0339 0.0014 MF46 0.0032 0.0078 0.0049 0.0069 0.0001 MF6 0.0284 0.0210 0.3055 0.6255 0.0007 MF47 0.0012 0.0011 0.0051 0.0103 0.0000 MF7 0.0023 0.0068 0.0171 0.0207 0.0000 MF48 0.0001 0.0001 0.0006 0.0015 0.0000 MF8 0.0053 0.0204 0.2045 0.0969 0.0003 MF49 0.0003 0.0007 0.0019 0.0021 0.0000 MF9 0.0257 0.0302 0.5400 0.4788 0.0006 MF50 0.0005 0.0008 0.0048 0.0073 0.0000 MF10 0.2280 0.4948 0.9564 1.0562 0.0108 MF51 0.0004 0.0002 0.0037 0.0081 0.0000 MF11 0.0660 0.1467 0.8627 0.8774 0.0040 MF52 0.0000 0.0000 0.0001 0.0001 0.0000 MF12 0.0023 0.0037 0.0246 0.0340 0.0001 MF53 0.0001 0.0001 0.0022 0.0019 0.0000 MF13 0.0578 0.1726 1.0954 1.0001 0.0046 MF54 0.0002 0.0002 0.0053 0.0046 0.0000 MF14 0.1250 0.3506 2.6039 2.6719 0.0088 MF55 0.3858 0.0269 0.0402 0.0836 0.0027 MF15 0.0099 0.0125 0.1568 0.2287 0.0004 MF56 0.0289 0.0035 0.0156 0.0358 0.0003 MF16 0.0017 0.0049 0.0342 0.0296 0.0001 MF57 0.0012 0.0002 0.0017 0.0041 0.0000 MF17 0.0125 0.0232 0.4349 0.3550 0.0006 MF58 0.0202 0.0023 0.0038 0.0074 0.0002 MF18 0.0225 0.0344 0.8300 0.6685 0.0009 MF59 0.0020 0.0015 -0.0011 0.0054 0.0000 MF19 0.0067 0.1250 0.0307 0.0301 0.0010 MF60 0.0010 0.0006 0.0097 0.0212 0.0000 MF20 0.0016 0.0097 0.0160 0.0178 0.0001 MF61 0.0011 0.0001 0.0002 0.0004 0.0000 MF21 0.0001 0.0004 0.0006 0.0010 0.0000 MF62 0.0002 0.0002 0.0025 0.0022 0.0000 MF22 0.0012 0.0099 0.0203 0.0182 0.0001 MF63 0.0004 0.0003 0.0097 0.0095 0.0000 MF23 0.0020 0.0065 0.0416 0.0425 0.0002 MF64 0.0277 0.0057 0.0079 0.0107 0.0003 MF24 0.0003 0.0003 0.0038 0.0064 0.0000 MF65 0.0025 0.0011 0.0056 0.0083 0.0000 MF25 0.0000 0.0005 0.0007 0.0006 0.0000 MF66 0.0001 0.0001 0.0004 0.0010 0.0000 MF26 0.0002 0.0005 0.0083 0.0067 0.0000 MF67 0.0017 0.0009 0.0048 0.0046 0.0000 MF27 0.0005 0.0007 0.0169 0.0138 0.0000 MF68 0.0008 0.0017 0.0120 0.0136 0.0000 MF28 0.4553 0.1114 0.3986 1.1466 0.0078 MF69 0.0003 0.0002 0.0027 0.0055 0.0000 MF29 0.2437 0.0927 0.7465 1.8434 0.0054 MF70 0.0001 0.0000 0.0002 0.0002 0.0000 MF30 0.0153 0.0068 0.0811 0.2038 0.0003 MF71 0.0001 0.0002 0.0033 0.0027 0.0000 MF31 0.0377 0.0260 0.0668 0.1572 0.0009 MF72 0.0002 0.0003 0.0069 0.0058 0.0000 MF32 0.0461 0.0384 -0.1365 0.2771 0.0008 MF73 0.0011 0.0005 0.0002 0.0004 0.0000 MF33 0.0471 0.0254 0.4519 0.9993 0.0012 MF74 0.0001 0.0000 0.0001 0.0002 0.0000 MF34 0.0018 0.0008 0.0038 0.0072 0.0000 MF75 0.0000 0.0000 0.0000 0.0000 0.0000 MF35 MF36 MF37 MF38 MF39 MF40 MF41 0.0045 0.0177 0.1605 0.0441 0.0032 0.0150 0.0229 0.0048 0.0121 0.2039 0.0374 0.0020 0.0258 0.0424 0.0910 0.4054 0.2319 0.1949 0.0194 0.1076 0.2866 0.0924 0.4073 0.2839 0.3513 0.0454 0.1096 0.3594 0.0001 0.0005 0.0047 0.0013 0.0001 0.0007 0.0011 MF76 MF77 MF78 MF79 MF80 MF81 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0002 0.0001 0.0000 0.0001 0.0002 0.0001 0.0003 0.0002 0.0000 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 A-12 Table B-1: Architecture of Multilayer Perceptron Neural Network for One Day Ahead Discharge Forecasting at Stations Y17, Y4, Y6 and Y20 Station Y17 Station Y4 No RMSE (m /s) Architecture 5-5-4-1 5-6-4-1 (*) No RMSE (m3/s) Architecture Training Training 6.381 5.771 4-6-4-1 5.011 5.638 4-8-6-1 (*) Training Training 11.068 9.822 10.996 9.223 9.106 8.651 5-8-6-1 5.208 5.828 4-10-8-1 5-8-10-1 5.148 5.683 4-6-6-4-1 12.302 9.866 5-8-8-6-1 5.489 5.902 4-8-8-6-1 11.494 9.222 Station Y6 Station Y20 No Architecture 4-5-1 4-6-5-1 4-6-6-4-1 (*) RMSE (m /s) No Architecture Training Training 32.221 35.406 4-6-1 32.003 34.514 4-6-5-1 (*) RMSE (m3/s) Training Training 25.984 30.160 23.242 27.537 20.928 22.014 28.205 30.789 4-7-5-4-1 4-8-6-5-1 28.233 30.862 4-8-6-4-1 20.816 22.375 4-10-8-5-1 29.208 31.713 4-10-6-4-1 21.325 22.071 (*): Selected Architecture Table B-2: Architecture of Multilayer Perceptron Neural Network for One Day Ahead Water Level Forecasting at Stations Y17, Y4, Y6 and Y20 Station Y17 No RMSE (m) Architecture 3-4-2-1 3-4-4-1 (*) Station Y4 No Training Training 0.127 0.148 3-4-3-1 0.103 0.136 3-6-3-1 Training Training 0.184 0.236 0.133 0.201 0.124 0.189 (*) 0.096 0.114 3-6-4-4-1 3-6-6-4-1 0.098 0.117 3-6-5-4-1 0.130 0.199 3-7-6-4-1 0.095 0.121 3-7-5-5-1 0.121 0.204 3-5-5-4-1 Station Y6 No RMSE (m) Architecture Architecture Station Y20 RMSE (m) Training Training No Architecture RMSE (m) Training Training 2-3-3-1 0.257 0.339 2-3-1 0.165 0.294 2-4-3-2-1 2.226 0.310 2-4-4-1 (*) 0.153 0.277 0.213 0.308 2-5-3-1 0.157 0.290 2.09 3.125 2-6-4-1 0.150 0.301 2-5-4-3-1 2-6-5-3-1 (*) (*): Selected Architecture B-1 Table B-3: Architecture of Multilayer Perceptron Neural Network for One Week Ahead Mean Weekly Discharge Forecasting at Stations Y17, Y4, Y6 and Y20 Station Y17 Station Y4 No Architecture 5-6-4-1 5-6-4-4-1 (*) 5-8-6-5-1 5-10-7-5-1 RMSE (m /s) Training Training 20.663 29.114 No Architecture 4-5-4-1 (*) RMSE (m3/s) Training Training 35.698 20.371 31.189 14.823 18.425 22.704 4-5-4-4-1 14.339 20.630 4-6-5-4-1 30.998 15.327 14.502 20.933 4-8-6-5-1 31.307 15.011 Station Y6 Station Y20 No Architecture 4-5-3-1 4-6-4-1 4-7-5-4-1 4-8-5-4-1 RMSE (m /s) No Architecture Training Training 8.724 6.19 4-5-3-1 8.255 5.987 4-6-4-3-1 (*) 6.258 4.721 4-6-6-4-1 6.287 4.805 4-8-7-5-1 RMSE (m3/s) Training Training 26.400 37.894 21.688 36.151 20.178 34.965 (*) 20.177 35.039 (*): Selected Architecture Table B4: Best Weight Factors of Multilayer Perceptron Model for One Day Ahead Discharge Forecasting at Station Y17 From Hidden Layer To Hidden Hidden Hidden Hidden Input -0.3028 1.1736 0.7746 6.1900 -12.8589 -0.5977 Input 0.3226 0.9082 8.3164 -28.5767 -2.6409 8.5886 Input 7.1565 11.9512 -14.5386 0.4656 -1.6269 -11.8186 Input -1.2112 -29.7896 1.7230 -7.1464 -5.4153 -4.3973 Input 0.6592 6.1459 -12.1393 19.9688 -0.1893 -26.6056 Bias 1.1092 -0.4790 -0.1169 0.1529 3.5274 18.6754 From Hidden Layer To Hidden Hidden From To Output Layer Output Hidden Hidden Hidden Hidden Hidden 2.1329 1.2873 0.8963 2.0000 Hidden -1.4822 Hidden 1.3706 0.3106 -2.0367 -0.5692 Hidden 3.4146 Hidden -1.4420 -0.8529 -3.1468 -4.8656 Hidden -2.8928 Hidden 4.1075 2.8247 -1.0642 2.6199 Hidden -1.8346 Hidden 1.2603 0.6241 0.3396 1.9620 Bias Hidden 4.3542 1.7303 -2.1256 -4.1464 -2.1754 5.9153 -4.1423 -0.5156 Bias B-2 0.3482 Table B5: Best Weight Factors of Multilayer Perceptron Model for One Day Ahead Discharge Forecasting at Station Y6 From Hidden Layer To Hidden Hidden Hidden Hidden Hidden Hidden Input 2.392 -0.479 5.647 -14.778 3.394 -0.247 Input -13.865 10.288 -6.719 -4.809 -7.666 -13.301 Input 6.108 0.794 -2.548 12.156 -6.913 -0.211 Input -1.693 0.205 -7.266 -5.881 -8.149 -16.603 Bias -0.527 -3.212 -0.830 -9.805 0.990 0.332 From Hidden Layer To Hidden Hidden Hidden Hidden Hidden Hidden Hidden -2.502 2.368 -0.991 3.584 -1.295 -1.358 Hidden 2.449 -1.210 1.610 -2.573 0.515 1.983 Hidden 1.969 -1.577 1.716 -2.310 0.568 1.920 Hidden 2.374 -1.694 2.109 -2.640 0.999 2.808 Hidden 1.473 -1.231 1.668 -2.841 0.990 1.807 Hidden 1.978 -1.413 2.332 -2.714 0.999 2.551 -0.302 -1.064 -0.767 -1.431 -0.585 -1.243 Bias From Hidden Layer To Hidden Hidden Hidden Hidden Hidden From To Output Layer Output Hidden -2.087 1.025 0.703 1.336 0.823 Hidden Hidden 0.960 0.408 -0.135 -0.215 -0.190 Hidden Hidden 0.000 -0.302 -2.114 0.516 1.041 Hidden Hidden 1.032 0.608 1.118 -1.857 0.773 Hidden Hidden 0.681 1.222 0.789 1.083 1.924 Hidden Hidden -0.775 -0.231 -1.194 -0.648 -0.918 Bias -1.035 0.050 -0.708 -0.953 0.471 Table B6: 0.190 Best Weight Factors of Multilayer Perceptron Model for One Day Ahead Discharge Forecasting at Station Y20 From Hidden Layer Bias -1.501 0.300 -1.252 -1.274 1.272 To Hidden Hidden Hidden Hidden Input -0.571 -0.878 -1.060 -1.791 -8.073 -1.970 3.134 Input -12.979 -3.983 19.598 -1.616 -0.095 3.115 0.610 Input -1.060 6.213 -4.613 0.476 -7.492 -14.966 -4.105 Input -6.735 -1.389 -9.192 4.601 6.497 -12.862 -19.301 Bias -1.117 2.998 -2.769 -0.436 1.129 9.385 0.637 B-3 Hidden Hidden Hidden From To Hidden Layer Hidden Hidden Hidden Hidden Hidden 0.513 2.374 -2.990 -2.224 3.709 Hidden 0.452 4.014 0.057 1.753 -1.275 Hidden -1.038 1.707 1.278 2.037 -0.143 Hidden 2.213 -1.135 -1.117 1.840 1.545 Hidden 1.781 -0.387 -2.009 3.199 0.823 Hidden -1.752 -3.721 -2.308 0.060 -2.563 Hidden 3.147 0.492 -2.423 -3.831 -2.323 -3.596 -1.048 -1.480 0.353 0.656 Bias From Hidden To Hidden Layer From To Hidden Hidden Hidden Hidden Hidden 2.360 1.067 0.845 -1.833 Hidden -1.632 Hidden -2.078 0.909 0.178 0.216 Hidden -0.160 Hidden -0.946 -0.768 1.528 0.853 Hidden -0.830 Hidden 0.697 -1.519 -1.494 2.414 Hidden -1.630 Hidden 0.462 1.152 -1.771 -2.246 -0.681 -0.204 -0.620 -0.521 Bias Table B7: Output Layer Bias 1.008 Best Weight Factors of Multilayer Perceptron Model for One Week Ahead Mean Weekly Discharge Forecasting at Station Y17 From Hidden Layer Hidden Input 0.762 -1.412 -7.862 -0.774 -6.104 Input 11.680 -4.864 -1.105 -0.424 Input -0.118 -1.852 0.256 Input -8.127 2.001 Input -15.398 Bias From Hidden Layer -0.232 To Hidden Hidden Hidden Hidden Hidden Hidden Hidden 3.273 -1.600 0.947 -0.103 -0.954 -1.917 -3.061 -6.161 -3.488 -3.525 -7.289 -4.844 6.712 8.181 0.969 10.055 -0.756 -0.868 -6.109 -11.198 -0.721 2.014 0.702 -4.140 -10.077 -2.411 -1.249 2.693 0.326 -16.490 1.373 3.185 To Hidden Hidden Hidden Hidden Hidden Hidden Hidden 1.023 1.480 -0.087 0.845 1.127 -3.163 Hidden 2.133 1.315 0.940 1.308 0.372 0.774 Hidden 1.298 -2.840 2.366 0.587 0.980 1.507 Hidden 0.239 0.945 1.123 -2.836 2.006 1.151 Hidden -1.285 -1.518 -0.246 -1.585 -1.523 3.311 Hidden -1.822 -1.326 1.530 0.352 0.145 -0.007 Hidden 2.025 -2.916 3.508 1.124 -0.555 -0.694 Hidden 0.188 -1.405 -0.963 2.702 -0.805 -1.310 -1.206 -1.699 -1.436 0.995 -2.467 0.920 Bias Output B-4 From Hidden Layer To Hidden Hidden Hidden Hidden From Output Layer Hidden To Output Hidden 0.661 1.622 1.222 -2.056 1.781 Hidden -1.637 Hidden -1.022 1.360 0.964 0.886 -2.446 Hidden -1.437 Hidden 1.469 -0.670 -0.475 0.355 -0.128 Hidden 0.308 Hidden -0.094 0.232 0.048 1.291 1.177 Hidden -1.25 Hidden 1.235 -1.860 0.974 -1.325 0.734 Hidden -0.421 Hidden 0.156 0.412 -1.308 1.094 -1.154 -1.473 -1.126 0.293 -0.997 -0.250 Bias Table B8: From Hidden Layer Bias Best Weight Factors of Multilayer Perceptron Model for One Week Ahead Mean Weekly Discharge Forecasting at Station Y4 Hidden Hidden To Hidden Hidden Hidden Input 6.812 -4.561 -12.905 -25.027 -8.160 Input 4.835 2.340 -17.599 2.398 -3.113 Input -10.096 -5.071 -2.756 2.217 -13.727 Input -8.118 -2.039 2.017 0.274 -16.695 1.067 1.299 7.186 5.000 15.700 Bias From Hidden Layer 1.315 Hidden Hidden Hidden To Hidden Hidden 1.618 1.137 1.958 1.703 Hidden 2.708 -1.435 -0.868 -3.100 Hidden -1.613 -5.344 5.393 3.171 Hidden 0.748 0.588 0.767 3.114 Hidden 3.353 2.406 1.196 1.635 3.455 -5.491 To Hidden Hidden -4.807 Bias From Hidden Layer -3.017 Hidden Hidden From Output Layer To Output Hidden -1.039 2.409 -1.975 -1.938 Hidden 2.294 Hidden 0.766 -1.982 2.321 2.080 Hidden -1.837 Hidden 1.201 -2.008 2.261 2.228 Hidden -2.000 Hidden 0.868 -1.141 0.769 0.272 Hidden -0.328 Bias 1.323 -1.726 -1.906 -0.214 Table B9: From Hidden Layer Bias 0.760 Best Weight Factors of Multilayer Perceptron Model for One Week Ahead Mean Weekly Discharge Forecasting at Station Y6 Hidden Hidden Hidden To Hidden Hidden Hidden Hidden Input -5.654 -4.100 -8.395 -11.051 3.386 5.671 4.465 Input -5.704 -0.845 -2.524 6.366 -10.270 -5.600 -5.383 Input -10.560 -13.614 -5.750 -5.209 -8.634 -11.164 3.369 Input -2.236 2.330 7.737 -4.430 -2.577 -5.888 -7.140 Bias From -0.400 0.908 0.586 To 0.429 -0.383 -10.036 -2.634 B-5 Hidden Layer Hidden Hidden Hidden Hidden Hidden Hidden 2.472 1.001 2.537 2.159 1.935 Hidden -3.309 1.283 -1.431 -1.736 -2.459 Hidden -1.700 -0.736 5.374 -0.870 1.437 Hidden 1.308 2.462 1.817 1.656 -3.626 Hidden 1.000 1.194 1.264 1.747 1.355 Hidden 1.235 -2.722 0.959 1.537 1.340 Hidden 2.507 2.512 2.250 -3.047 1.486 0.423 -1.895 To Hidden Hidden -1.573 -2.381 Bias From Hidden Layer -1.955 Hidden From Output Layer Hidden To Output Hidden 0.982 -2.576 1.328 0.533 Hidden -0.979 Hidden 1.204 1.860 -2.850 0.939 Hidden -1.335 Hidden 0.885 1.023 1.324 -2.861 Hidden -1.899 Hidden 1.954 0.409 1.962 1.500 Hidden -1.546 Hidden -2.633 1.530 0.951 1.354 Bias Bias -1.007 -1.189 -1.695 -1.616 Table B10: From Hidden Layer 2.321 Best Weight Factors of Multilayer Perceptron Model for One Week Ahead Mean Weekly Discharge Forecasting at Station Y20 Hidden Hidden Hidden To Hidden Hidden Hidden Input 2.662 -1.399 -3.665 8.387 3.152 -2.699 Input 4.111 -12.286 -1.642 2.643 -13.287 -21.277 Input -4.486 -3.726 -2.295 -8.020 -2.189 -0.069 Input -9.950 -15.531 -2.181 -1.322 -7.573 -10.050 Bias From Hidden Layer -0.051 0.514 -0.039 12.371 -0.912 -2.218 Hidden Hidden Hidden To Hidden Hidden Hidden Hidden 0.521 -2.273 -1.628 -4.561 -1.538 -0.952 Hidden -1.988 2.025 3.139 1.593 2.086 1.554 Hidden 0.995 -1.779 -2.109 -4.779 -1.130 -0.754 Hidden -1.350 1.729 1.038 2.136 0.933 0.683 Hidden -1.293 1.445 1.860 2.439 1.261 1.618 Hidden -1.193 1.798 3.487 1.986 3.137 2.204 -2.348 1.783 To Hidden Hidden -1.231 -2.229 -3.356 Bias From Hidden Layer 2.172 Hidden Hidden From Output Layer To Output Hidden -0.786 0.185 -0.948 0.351 Hidden -0.275 Hidden 0.313 0.631 -2.255 1.297 Hidden -2.130 Hidden -1.991 0.400 1.359 2.070 Hidden 2.441 Hidden 1.949 -1.442 2.122 -1.023 Hidden -1.757 Hidden -0.859 -1.243 -2.288 1.059 Hidden -2.223 0.880 1.384 1.053 Bias -0.391 -0.652 0.364 -0.105 B-6 Bias 0.492 Table B11: Best Weight Factors of Multilayer Perceptron Model for One Day Ahead Discharge Forecasting at Station Y4 From Hidden Layer To Hidden Hidden Hidden Hidden Hidden Hidden Hidden Hidden Input -13.532 2.540 -4.470 -20.043 -0.889 -2.578 15.180 -3.268 0.214 0.162 Input -17.326 -16.495 2.293 1.149 -17.556 -4.437 1.718 -2.152 -8.997 -0.714 Input -8.312 -3.704 -21.010 -0.877 -3.303 -1.715 41.265 -22.213 -16.788 2.318 Input -12.954 -14.991 -0.993 1.050 25.042 8.081 0.088 -0.536 -6.354 -11.259 Bias From Hidden Layer 4.463 -0.758 2.519 2.422 6.530 1.880 5.866 -5.033 From Output Layer 5.572 To Hidden Hidden 10 12.361 To Hidden Hidden Hidden Hidden Hidden Hidden Hidden Hidden Hidden 0.905 0.417 1.334 -0.455 -0.551 -0.268 0.088 -0.289 Hidden -0.234 Hidden -0.775 -0.122 -2.667 1.346 -0.325 -1.626 -0.664 -2.199 Hidden 0.952 Hidden 3.808 -3.200 1.059 -1.484 0.132 -1.997 -0.317 0.798 Hidden 1.355 Hidden 0.084 2.327 -5.219 1.488 1.448 -0.904 2.428 -2.231 Hidden -1.506 Hidden 2.894 2.797 1.518 1.753 -8.869 0.383 -3.694 1.926 Hidden -0.867 Hidden 2.503 -1.120 0.018 0.960 1.092 2.650 -4.327 3.097 Hidden -0.924 Hidden -1.110 1.900 2.876 1.682 1.507 -0.936 -0.565 0.664 Hidden -2.120 Hidden -1.772 2.795 -3.043 1.775 2.107 -0.078 5.785 -0.501 Hidden 0.757 Hidden -0.510 1.394 -0.537 -3.435 -2.163 -0.344 -1.640 0.004 Bias 0.752 Hidden 10 -0.838 0.022 -0.137 -0.348 2.284 -1.444 1.053 -3.065 Bias -1.802 1.045 0.507 -1.466 -0.947 -0.262 -2.665 0.161 B-7 Output Table C-1: Coefficients of Multi Variable Regression Equation for Daily Discharge Forecasting at Station Y17 Relationship Function day ahead Relationship Function days ahead Relationship Function days ahead QY17(t+1) = f(R1m(t-1), R1m(t), QY6(t), QY17(t-1), QY17(t)) Intercept R1m(t-1) R1m(t) QY6(t) QY17(t-1) QY17(t) x x -0.6124 0.0358 0.2741 0.0114 -0.4907 1.4792 x x QY17(t+2) = f(R1m(t-1), R1m(t), QY6(t), QY17(t-1), QY17(t), QY17(t+1)) Intercept R1m(t-1) R1m(t) QY6(t) QY17(t-1) QY17(t) QY17(t+1) x -0.0044 -0.0218 0.0165 0.0003 -0.2026 0.2748 0.9270 x QY17(t+3) = f(R1m(t-1), R1m(t), QY6(t), QY17(t-1), QY17(t), QY17(t+1), QY17(t+2)) Intercept R1m(t-1) R1m(t) QY6(t) QY17(t-1) QY17(t) QY17(t+1) QY17(t+2) -0.0510 -0.0001 -0.0011 -0.0005 -0.0286 0.0093 0.0293 0.9901 Table C-2: Coefficients of Multi Variable Regression Equation for Daily Discharge Forecasting at Station Y4 Relationship Function day ahead Relationship Function day ahead Relationship Function day ahead QY4(t+1) = f(R2m(t-1), R2m(t), QY6(t), QY4(t)) Intercept R2m(t-1) R2m(t) QY6(t) QY4(t) x x 1.4996 0.3717 0.0821 0.0314 0.9010 x x QY4(t+2) = f(R2m(t-1), R2m(t), QY6(t), QY4(t), QY4(t+1)) Intercept R2m(t-1) R2m(t) QY6(t) QY4(t) QY4(t+1) x 1.7175 0.7814 0.2740 0.0277 0.3712 0.5005 x QY4(t+3) = f(R2m(t-1), R2m(t), QY6(t), QY4(t), QY4(t+1), QY4(t+2)) Intercept R2m(t-1) R2m(t) QY6(t) QY4(t) QY4(t+1) QY4(t+2) 10.2108 4.6105 2.2461 0.1527 1.7192 3.5355 -5.0289 Table C-3: Coefficients of Multi Variable Regression Equation for Daily Discharge Forecasting at Station Y6 Relationship Function day ahead Relationship Function days ahead Relationship Function days ahead QY6(t+1) = f(QY20(t), QY6(t-2), QY6(t-1), QY6(t)) Intercept QY20(t) QY6(t-2) QY6(t-1) QY6(t) x x 0.9942 0.3104 0.1402 -0.6720 1.3388 x x QY6(t+2) = f(QY20(t), QY6(t-2), QY6(t-1), QY6(t), QY6(t+1)) Intercept QY20(t) QY6(t-2) QY6(t-1) QY6(t) QY6(t+1) x -3.0264 0.0271 0.0195 -0.2599 0.4896 0.7710 x QY6(t+3) = f(QY20(t), QY6(t-2), QY6(t-1), QY6(t), QY6(t+1), QY6(t+2)) Intercept QY20(t) QY6(t-2) QY6(t-1) QY6(t) QY6(t+1) QY6(t+2) -2.6026 0.3293 0.0113 -0.1361 0.2755 1.2546 -0.5665 C-1 Table C-4: Coefficients of Multi Variable Regression Equation for Daily Discharge Forecasting at Station Y20 Relationship Function day ahead Relationship Function days ahead Relationship Function days ahead QY20(t+1) = f(R4m(t-1), R4m(t), QY20(t-1), QY20(t)) Intercept R4m(t-1) R4m(t) QY20(t-1) QY20(t) x x -0.6982 0.6148 1.7451 -0.0381 0.8497 x x QY20(t+2) = f(R4m(t-1), R4m(t), QY20(t-1), QY20(t), QY20(t+1)) Intercept R4m(t-1) R4m(t) QY20(t-1) QY20(t) QY20(t+1) x 1.3690 0.3594 2.4629 0.0978 0.5105 0.1054 x QY20(t+3) = f(R4m(t-1), R4m(t), QY20(t-1), QY20(t), QY20(t), QY20(t+2)) Intercept R4m(t-1) R4m(t) QY20(t-1) QY20(t) QY20(t+1) QY20(t+2) 5.3526 -0.1318 2.0813 0.1210 0.4131 0.1209 0.0255 Table C-5: Coefficients of Multi Variable Regression Equation for One Week Ahead Mean Weekly Discharge Forecasting at Station Y20 Station Y17 Relationship Function Coefficients Relationship Function Coefficients Relationship Function Coefficients Relationship Function Coefficients QY17(T+1) = f(R1m(T-1), R1m(T), QY6(T), QY17(T-1), QY17(T)) Intercept -1.0364 R1m(T-1) R1m(T) -1.2596 2.8625 Station Y4 QY6(T) 0.2047 QY17(T-1) -0.3981 QY17(T) 1.2071 QY6(T) 0.035503 QY4(T) 0.910874 x x QY6(T) 1.876996 x x QY20(T) 1.543571 x x QY4(T+1) = f(R2m(T-1), R2m(T), QY6(T), QY4(T)) Intercept 0.528922 R2m(T-1) R2m(T) 0.924985 -0.34922 Station Y6 QY6(T+1) = f(QY20(T), QY6(T-2), QY6(T-1), QY6(T)) Intercept -0.06573 QY20(T) QY6(T-2) 0.199118 0.43822 Station Y20 QY6(T-1) -1.42632 QY20(T+1) = f(R4m(T-1), R4m(T), QY20(T-1), QY20(T)) Intercept -0.21997 R4m(T-1) -0.88606 R4m(T) 1.202728 C-2 QY20(T-1) -0.57059 Table C-6: Coefficients of Multi Variable Regression Equation for Daily Water Level Forecasting at Station Y17, Y4, Y6 and Y20 Station Y17 Relationship Function WY17(t+1) = f(R1m(t), QY17(t), WY17(t)) days ahead Relationship Function days ahead WY6(t+1) = f(WY20(t), WY6(t)) Intercept R1m(t) QY17(t) WY17(t) x x Intercept WY20(t) WY6(t) 0.589 0.012 0.000 0.981 x x -29.366 0.215 0.837 day ahead Relationship Function Station Y6 WY17(t+2) = f(R1m(t), QY17(t), WY17(t), WY17(t+1)) day ahead Relationship Function days ahead Relationship Function days ahead x x WY6(t+2) = f(WY20(t), WY6(t), WY6(t+1)) Intercept R1m(t) QY17(t) WY17(t) WY17(t+1) 0.618 0.016 0.000 0.973 0.008 x WY17(t+3) = f(R1m(t), QY17(t), WY17(t), WY17(t+1), WY17(t+2)) Intercept WY20(t) WY6(t) WY6(t+1) x 27.405 -0.195 -2.031 3.168 x WY6(t+3) = f(WY20(t), WY6(t), WY6(t+1), WY6(t+2)) Intercept R1m(t) QY17(t) WY17(t) WY17(t+1) WY17(t+2) Intercept WY20(t) WY6(t) WY6(t+1) WY6(t+2) -0.884 -0.018 0.000 -1.474 0.000 2.502 -123.156 0.911 2.584 -3.142 0.842 x x x Station Y4 Relationship Function x Station Y20 WY4(t+1) = f(WY6(t), QY4(t), WY4(t)) WY20(t+1) = f(QY20(t), WY20(t)) Intercept WY6(t) QY4(t) WY4(t) x x -11.217 0.212 -0.003 0.969 x x WY4(t+2) = f(WY6(t), QY4(t), WY4(t), WY4(t+1)) -11.212 -0.001 1.062 WY20(t+2) = f(QY20(t), WY20(t), WY20(t+1)) Intercept WY6(t) QY4(t) WY4(t) WY4(t+1) x Intercept QY20(t) WY20(t) WY20(t+1) x -5.319 0.108 -0.002 -0.058 1.034 x -12.387 -0.002 0.484 0.584 x WY4(t+3) = f(WY6(t), QY4(t), WY4(t), WY4(t+1), WY4(t+2)) WY20(t+3) = f(QY20(t), WY20(t), WY20(t+1), WY20(t+2)) Intercept WY6(t) QY4(t) WY4(t) WY4(t+1) x Intercept QY20(t) WY20(t) WY20(t+1) WY20(t+2) 19.846 -0.379 0.006 -0.779 -1.253 3.091 4.403 0.000 -1.401 2.030 0.348 C-3 ... maps Nestor Sy (2003) applied neuro - fuzzy techniques in plot – scale rainfall runoff modeling using rainfall simulator data In this study the Adaptive Neuro – Fuzzy Inference Systems (ANFIS) was... 2001) In this study, a neuro- fuzzy technique (NFT), which combines the learning capacity of ANNs and flexible capability of knowledge representation of fuzzy logic in order to overcome many of shortcomings... Type-1 Fuzzy Reasoning 20 3.9b Equivalent ANFIS (type-1 ANFIS) 20 3.10a Two-Input Type-3 ANFIS with Nine Rules 21 3.10b Corresponding Fuzzy Subspaces 21 4.1 The Distribution of Rainfall and Gauging