Subhash Chandra Y210338 M Tech IIT Kanpur 2004 RR Modelling ANN

Slide 1:

Evaluation of Techniques for Modeling the Event-Based Rainfall-Runoff Process A Thesis Submitted In Partial Fulfillment of the Requirements for the Degree of MASTER OF TECHNOLOGY by Subhash Chandra Y210338 to the DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY, KANPUR JULY, 2004 CERTIFICATE It is certified that the work contained in the thesis entitled “Evaluation of Techniques for modeling the Event-Based Rainfall-Runoff Process” by Subhash Chandra (Roll No. Y210338) has been carried out under my supervision and that this work has not been submitted elsewhere for any degree. Dr. Ashu Jain Assistant Professor Dept. of Civil Engineering Indian Institute of Technology Kanpur, India July 15, 2004 ABSTRACT The focus of present research work is on the modeling of the event-based rainfall-runoff (R-R) process using a variety of conventional and new techniques. Conceptual rainfall-runoff (CRR) models were used as conventional techniques and Artificial Neural Network (ANN) was used as a new techniques. Among the CRR model four widespread conceptual models, the Unit hydrograph model, Nash conceptual model, Clark conceptual model and simple non-linear Tank model, were developed. Among the ANNs, twenty different architectures having single hidden layer were explored. An attempt has also been made to develop new guidelines and methodologies for the development of the ANN models. The back propagation algorithm of MATLAB toolbox was used to develop ANN models in this study. The stream flow and rainfall data from Kentucky River Basin (KRB), USA were employed to develop all these models. The worth of multi-criteria validation for evaluating model consistency was emphasized. All models were capable to simulate runoff adequately after calibration. Among the CRR models, UH model was found to perform best during both calibration and validation. ANN 3-10-1 was found best the ANN model when the data from many storms are combined into one training set. The evaluation results in terms of standard statistical parameters between CRR model simulation result and ANN models were found to be comparable. It was observed that rather than relying on a few performance statistics such as correlation coefficient, efficiency and root mean square error, a wide variety of error statistics including average absolute relative error, normalized mean bias error, and threshold statistics should be used to evaluate the predictive capability of the developed models. The use of such methods enables assessment of the reliability of model predictions. It also supports the further development of models by identification of weak parts and evaluation of improvements. ACKNOWLEDGEMENT I take this opportunity to express my deep sense of gratitude to Dr. Ashu Jain for his constant inspiration, support and encouragement given to me from time to time. His guidance, cooperation and meticulous scientific attitude inspired and immensely benefited me for the completion of this work. It was indeed a great privilege for me to have worked under his supervision. I also pay my sincere gratitude to Dr. T. Gangadharaiya, Dr. Rajesh Srivastva, Dr. Bithin Datta and Dr. Pranab Mahapatra for their encouragement and affection throughout my stay in IIT Kanpur. I am fortunate to have nice and so helpful friends at IITK. In fact it was their support, inspiration and love that made my stay memorable and delightful here. Their concern, love and support during crisis are some of the things that I will never forget in my life. To list them is a Herculean task for me. Simply words are not sufficient to acknowledge their kind help. I wish to extend my thanks to all the friends in Hydraulics and water resources engineering group in IIT-Kanpur. I acknowledge the help received from my seniors, juniors and my batch mates. I enjoyed partying, joking, discussing problem with them. In their company, I always relaxed from the tension of work and enjoyed most. I would like to thank all of the HWRE lab members. I would like to express my deepest gratitude to my parents for their love, care blessings, throughout and unconditional in my whole academic career. Thanks to all people who have helped me directly or indirectly throughout the thesis work and have helped me in completing the job successfully. Last but not least, I would like to express my thanks and gratitude to the almighty, the most beneficent and merciful, for granting me an opportunity to be here in world’s one of the best educational institute. I will cherish its memories lifelong. July 15, 2004 Subhash Chandra Indian Institute of Technology Kanpur CONTENTS ABSTRACT……………………………………………………………………..…(iii) LIST OF FIGURES……………………………………………………………….(vii) LIST OF TABLES…………………………………………………………………(X) Introduction General……………………………………………………………………1 Statement of Problem……………………………………………………..1 Research Objectives………………………………………………………4 Organization of Thesis……………………………………………………4 Literature Review General……………………………………………………………………6 CRR Models………………………………………………………………6 ANN Models……………………………………………………………...9 Artificial Neural Network General…………………………………………………………………..12 The Artificial Neuron……………………………………………………12 Architecture of ANNs…………………………………………………..13 Learning………………………………………………………………….14 The Back-propagation….………………………………….……...14 The ANN Tool Box………..…………………………………………….16 Model Development General…………………………………………………………………..21 Study Area And Data……………………………………………………21 Model Development……………………………………………………..26 Unit Hydrograph Model………………………………………….28 4.3.1.1 Calculation of - Index……………………………………...30 4.3.2 Nash Conceptual Model………………………………………….35 4.3.3 Clark Model………………………………………………………41 4.3.4 Nonlinear Tank Model…………………………………………...45 4.3.4.1 Determination of Parameters…………………………………46 4.3.4.2 Calculation of Excess Rainfall ()…………………………..47 ANN Model……..………………………………………………..50 4.3.5.1 Selection of Input and Outputs……………………………….50 4.3.5.2 Training of ANN Models…………………………………….51 Results and Discussions General…………………………………………………………………..62 Statistical Parameters……………………………………………………62 Discussion of Results……………………………………………………66 Results for Combined Input ……………………………………..66 Results for Category-wise Input ……..………………………….67 Analysis of Various Performance Statistics……………………...70 Summary, Conclusions and Scope of Future Work ………………………92 APPENDIX A Performance of Various Models in Terms of Standard Statistical Parameters APPENDIX B Performance of Various Models-Scatter Plots REFERENCES LIST OF FIGURES Figure 3.1 Model of an Artificial Neuron………………………………………..13 Figure 3.2a MATLAB window…………………………………………………...16 Figure 3.2b Neural Network Tool…………………………………………………17 Figure 3.2c Network type and different function…………………………………18 Figure 3.3a Log sigmoid Transfer function……………………………………….18 Figure 3.3b Tan sigmoid Transfer function……………………………………….19 Figure 3.3c Linear Transfer function……………………………………………...19 Figure 3.4a 2-5-1 Architecture……………………………………………………19 Figure 3.4b Training Window…………………………………………………….20 Figure 3.4c Plot-Error v/s Training cycle…………………………………………20 Figure 4.1 Kentucky River Basin………………………………………………..22 Figure 4.2 Rainfall and streamflow for the storm of S1 (May 1960)……………23 Figure 4.3 Rainfall and streamflow for the storm of S2 (May 1961)……………23 Figure 4.4 Rainfall and streamflow for the storm of S10 (April 1970)………….24 Figure 4.5 Rainfall and streamflow for the storm of S13 (May 1972)…………..24 Figure 4.6 Relationship Between Effective Rainfall and Peak Flow from Calibration Storms……………………………………………..……..25 Figure 4.7 Relationship Between Effective Rainfall and Peak Flow from All 13 Storms…………………………………………………………25 Figure 4.8 Model development procedures……………………………………...27 Figure 4.9 Rainfall-Runoff Processes UH Conceptual Model…………………..29 Figure 4.10 Behaviour of -Index With Ground Water Flow Magnitude………..31 Figure 4.11 Behaviour of -Index With Total Rainfall (2-days previous)……….32 Figure 4.12 Behaviour of -Index With Total Rainfall (3-days previous)……….32 Figure 4.13 Behaviour of -Index With Total Rainfall (4-days previous)……….32 Figure 4.14 Behaviour of -Index With Total Rainfall (5-days previous)……….32 Figure 4.15 Calibrated UHs……………………………………………...………..34 Figure 4.16 NASH Model-Cascade of n Linear Reservoirs………………………37 Figure 4.17 UHs for Nash model………………………………………………….39 Figure 4.18 Isochrones and TA histogram for a watershed……………………….41 Figure 4.19 UHs for Clark model…………………………………...…………….45 Figure 4.20 Determination of Parameters of Tank Model: kg, ks, ko, Qg and Qs ……………………………….………………...47 Figure 4.21 Schematic Plot of Recession Curves on Semi logarithmic Graph…...48 Figure 4.22 Auto-correlation function v/s Lag……………………………………51 Figure 4.21 Plot of Acceptable level of global error and Difference Between Training and Testing AARE (training S6) from ANN 2-5-1 Model…55 Figure 4.15 Plot of Acceptable level of global error and Difference Between Training and Testing E (training S6) from ANN 2-5-1 Model………56 Figure 4.16 Difference In Performance During Training And Testing For ANN 2-5-1 Model For Different Initial Set Of Weights……………..56 Figure 4.17 Difference In Performance During Training And Testing For ANN 2-5-1 Model For Different Initial Set Of Weights……………..57 Figure 4.27 Scatter Plot of Observed and Difference Between Observed and Predicted Streamflow from UH Model During Validation……...57 Figure 4.28 Scatter Plot of Observed and Difference Between Observed and Predicted Streamflow from NASH Model During Calibration….58 Figure 4.29 Scatter Plot of Observed and Difference Between Observed and Predicted Streamflow from NASH Model During Validation…..58 Figure 4.30 Scatter Plot of Observed and Difference Between Observed and Predicted Streamflow from ANN 3-10-1 Model During Training…..59 Figure 4.31 Scatter Plot of Observed and Difference Between Observed and Predicted Streamflow from ANN 3-10-1 Model During Testing…....59 Figure 4.32 Behaviour of e1 With Flow Magnitude from UH Model…………….60 Figure 4.33 Behaviour of e1 With Flow Magnitude from ANN 2-5-1 Model…....60 Figure 4.34 Behaviour of e2 With Flow Magnitude from UH Model…………….61 Figure 4.35 Behaviour of e2 With Flow Magnitude from ANN 2-5-1 Model…....61 Figure 5.1 Scatter Pot for UH-c Model During Calibration ..………….………..78 Figure 5.2 Scatter Pot for UH-c Model During Validation .…………………….78 Figure 5.3 Scatter Plot for ANN 2-8-1c During Training ...……………………..79 Figure 5.4 Scatter Plot for ANN 2-8-1c During Testing ...……………………...79 Figure 5.5 Scatter Plot for ANN 3-10-1c During Training ...……………………80 Figure 5.6 Scatter Plot for ANN 3-10-1c During Testing .……………………...80 Figure 5.7 UH Model Validation from Category-I Storms ..……………………81 Figure 5.8 UH Model Validation from Category-II Storms ..…………………...81 Figure 5.9 UH Model Validation from Category-III Storms ……………………82 Figure 5.10 UH Model Validation from Category-IV Storms ……………………82 Figure 5.11 Scatter Plot for Category-I storms from ANN 2-5-1 Model During Training ………………………………….………………….83 Figure 5.12 Scatter Plot for Category-I storms from ANN 2-5-1 Model During Testing ……………………………………..………………...83 Figure 5.13 Scatter Plot for Category-II storms from ANN 2-6-1 Model During Training ……………………………..……………………….84 Figure 5.14 Scatter Plot for Category-II storms from ANN 2-6-1 Model During Testing ………………………………………………….…...84 Figure 5.15 Scatter Plot for Category-III storms from ANN 2-10-1 Model During Training …………………………………………..………….85 Figure 5.16 Scatter Plot for Category-III storms from ANN 2-10-1 Model During Testing ……………………………………………………….85 Figure 5.17 Scatter Plot for Category-IV storms from ANN 3-6-1 Model During Training ……………………………………………………...86 Figure 5.18 Scatter Plot for Category-IV storms from ANN 3-6-1 Model During Testing …………………………………….………….……...86 Figure 5.19 During Calibration/Training Combined Input ……………………….87 Figure 5.20 During Validation/Testing Combined Input ………………………...87 Figure 5.21 Category-I Storm During Calibration/Training .…………………….88 Figure 5.22 Category-I Storm During Validation/Testing ..……………………...88 Figure 5.23 Category-II Storm During Calibration/Training …………………….89 Figure 5.24 Category-II Storm During Validation/Testing ...…………………….89 Figure 5.25 Category-III Storm During Calibration/Training .…………………...90 Figure 5.26 Category-III Storm During Validation/Testing .……………………..90 Figure 5.27 Category-IV Storm During Calibration/Training .…………………...91 Figure 5.28 Category-IV Storm During Validation/Testing .……………………..91 LIST OF TABLES Table 4.1 Runoff depth and index for the calibration storms………………..30 Table 4.2 Computation of 24-hour UH by UH theory………………………….33 Table 4.3 Calibrated UHs from UH model….………………………………….33 Table 4.4 Runoff Depth And Index For Validation Storms………………….34 Table 4.5 Calculation of and of Nash’s Model………………………38 Table 4.6 Calculation of and of Nash’s Model………………………38 Table 4.7 Nash’s Model Parameters- n and K …………………………………..39 Table 4.8 Calibrated UHs from NASH Model………………………………….40 Table 4.9 Calculation 24-hour UH by NASH model…………..……………….40 Table 4.10 CLARK Model Parameters- C1, C2 and K…………………………...43 Table 4.11 Calculation of UH Clark’s method…………………………………...44 Table 4.12 Calibrated UHs from Clark-2 Model…………………………………44 Table 4.13 Recession Coefficient of Tank Model………………………………..46 Table 4.14 Calculation of Flow Hydrograph by Tank model……………………49 Table 4.17 Auto-correlation coefficients…………………………………………50 Table 5.1 Performance Evaluation Criteria from Various Models (Combined Input)…………………………………………………….73 Table 5.2 Performance Evaluation Criteria from Various Models: Category I…………………………………………………………….74 Table 5.3 Performance Evaluation Criteria from Various Models: Category II………………………………...………………………….75 Table 5.4 Performance Evaluation Criteria from Various Models: Category III….……………………………………………………….76 Table 5.5 Performance Evaluation Criteria from Various Models: Category IV…………………………………………………………..77