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The Direct Joint Probability Method for Estimating

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The Direct Joint Probability Method for Estimating THE DIRECT JOINT PROBABILITY METHOD FOR ESTIMATING EXTREME SEA LEVELS by JOAN C. H. LIU B. A. Sc., The University of British Columbia, 2002 A THESIS SUBMITTED IN A PARTIAL COMPLETION OF THE REQUIREMENTS FOR THE DEGREE OF THE MASTERS OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Civil Engineering) We accepted this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August 2004 ©Joan C. H. Liu, 2004 THE UNIVERSITY OF BRITISH COlUMRifl FACULTY OK GRADUATE STUDIES Library Authorization for scho,arly purposes may be granled 6ylhe te ™*' ""^^ Permission extensile copyin9 of lhis lhesj ^^^^^ Name of Author (please print) Date (dd/mm/yyyy) Title of Th6SiS m^ck SX C > 3~ Degree: Year: Departmentof _?£^lL_£ww^^ The University of BritisrTcdur^te t/~ Q" Vancouver, BC Canada grad.ubc.ca/forms/?formlD=THS page 1 of 1 ABSTRACT The design of coastal structures includes the key element of estimating crest elevation. A crest height designed to protect against specified return periods avoids damages due to overflowing and overtopping. In order to avoid overflowing, the design sea levels should be at least at the design flood level, also referred to as the extreme flood level, which is usually composed of tides and storm surges. The extreme flood level can be determined by several approaches, such as the Annual Maxima, Simple Addition, Joint Probability, and Revised Joint Probability Methods. These methods have various limitations in terms of the required amount of data, the representation of contributing factors in sea level fluctuations, the ability to assess the joint probability of these factors, and the degree of independence required of the data. To minimize overtopping, in addition to considering tides and storm surges, the design sea levels should also include wave run-up. The design sea level, also referred to as the extreme sea level, includes the effects of tides, storm surges, and wave run-up. Wave run-up estimates are generally based on the design flood level and design wave climate, data for which are often dependent. This thesis develops the Direct Joint Probability Method for estimating extreme sea levels which simultaneously considers tides, storm surges, and wave run-up. This method has fewer limitations than the previously mentioned methods in terms of the assumption of independent variables and the required amount of data. Data for the City of Richmond, British Columbia, Canada, are used to demonstrate the Direct Joint Probability Method, and results show that the method provides a reasonable estimate of extreme sea levels, that is, the resulting estimates are within the same range as other traditionally applied methods. The results also indicate a large difference between design sea levels required for preventing overflowing and those for preventing overtopping. The sea levels at Richmond are also increasing due to the ii climatic and geologic effects. A hybrid of the Direct Joint Probability and the Simple Addition Methods is also applied in this thesis and is used to estimate extreme sea levels for regions facing long-term increases in sea levels. The results of the hybrid approach indicate that the contribution to extreme sea level due to wave run-up increases with long-term increases in sea levels. This can dramatically affect estimates of extreme sea levels. 111 TABLE OF CONTENTS ABSTRACT ii TABLE OF CONTENTS iv LIST OF TABLES vii LIST OF FIGURES viii LIST OF APPENDICES x ACKNOWLEDGEMENTS xi 1 INTRODUCTION 1 2 COASTAL STRUCTURES AND FLUCTUATIONS IN SEA LEVELS 6 2.1 Impacts of Sea Floods 6 2.2 Coastal Structures 8 2.2.1 Types of Coastal Structures 8 2.2.1.1 Seawalls 9 2.2.1.2 Revetments 10 2.2.1.3 Dykes 11 2.2.2 Modes and Consequences of Failures 11 2.2.2.1 Overtopping and Overflowing 11 2.2.2.2 Instability of Outer Slope 13 2.2.2.3 Instability of Inner Slope 13 2.2.2.4 Scour 14 2.2.2.5 Geotechnical Failures 14 2.2.3 Design of Coastal Structures 15 2.2.3.1 Crest Elevation 17 2.2.3.2 Other Design Considerations 18 2.3 Fluctuations of Sea Levels 19 2.3.1 Scientific Classification Scheme 21 2.3.2 Engineering Classification Scheme 22 2.3.3 Wind Waves 23 2.3.3.1 Characteristics of Wind Waves 24 2.3.3.2 Statistical Analysis of Waves 24 2.3.3.2.1 Statistical Analysis of Wave Height and Period 25 2.3.3.2.2 Wave Spectrum Analysis of Wave Height and Period 26 2.3.3.3 Wave Prediction : 27 2.3.4 Storm Surges 29 2.3.4.1 Generation of Storm Surges 29 2.3.4.2 Characteristics of Storm Surges 30 2.3.4.3 Estimation of Storm Surges 30 2.3.4.3.1 Indirect Measurement of Storm Surges 30 2.3.4.3.2 Numerical Models of Storm Surges 31 2.3.5 Astronomical Tides 32 2.3.5.1 Generation of Tides 33 2.3.5.2 Characteristics of Tides 33 2.3.5.3 Measurements of Tides and Establishment of Datum 34 2.3.5.4 Prediction of Astronomical Tides 35 2.3.6 Tsunami 36 2.3.6.1 Generation of Tsunami 37 2.3.6.2 Characteristics of Tsunami 38 iv 2.3.7 El Nino 38 2.3.8 Climatologic and Geologic Effects 39 3 QUANTITATIVE METHODS FOR ESTIMATING EXTREME CONDITIONS 50 3.1 Methods for Estimating Flood Levels 50 3.1.1 Probability of Exceedance and Return Period 51 3.1.2 Annual Maxima Method 52 3.1.2.1 Application 53 3.1.2.2 Data Requirements 54 3.1.2.3 Assumptions 55 3.1.2.4 Advantages and Disadvantages 56 3.1.3 i?-Largest Maxima Method 56 3.1.3.1 Advantages and Disadvantages 58 3.1.4 Simple Addition Method 58 3.1.4.1 Advantages and Disadvantages 60 3.1.5 Joint Probability Method (JPM) 60 3.1.5.1 Application 62 3.1.5.2 Data Requirements 64 3.1.5.3 Assumptions 65 3.1.5.4 Advantages and Disadvantages 66 3.1.6 Revised Joint Probability Method (RJPM) 67 3.1.6.1 Advantages and Disadvantages 68 3.2 Estimation of Extreme Wave Conditions 69 3.2.1 Long-Term Distribution of Sea States 70 3.2.2 Long-Term Distribution of Individual Wave Height 70 3.3 Joint Probability of Flood Levels and Extreme Wave Conditions 71 3.4 Wave Run-up and Overtopping Discharges 72 3.4.1 Wave Transition in Shallow Water 73 3.4.2 Prediction of Wave Run-Up 74 3.4.2.1 Shore Protection Manual (SPM) Method 75 3.4.2.2 Van Der Meer-Janssen (VDMJ) Method 77 3.4.3 Overtopping Discharge 79 3.4.3.1 Estimation of Overtopping Discharges 79 3.4.3.1.1 Shore Protection Manual (SPM) Method 80 3.4.3.1.2 Van Der Meer (VDM) Method 81 3.4.3.1.3 Owen's Method 82 3.4.3.1.4 Comparison of Methods for Predicting Overtopping Discharges 83 3.4.3.2 Allowable Overtopping Discharge 84 4 DIRECT JOINT PROBABILITY METHOD (DJPM) 95 4.1 Description of the DJPM 95 4.2 Data Requirements 98 4.3 Assumptions 99 4.4 Advantages and Disadvantages 99 5 SEA FLOOD PROTECTION IN RICHMOND, B.C 103 5.1 Surroundings 104 5.2 Settlements 104 5.3 Flood Concerns 105 5.3.1 River Floods 106 5.3.2 Sea Floods 106 5.3.3 Excessive Amount of Rain 107 v 5.4 Current Dyke System 108 5.4.1 Legislation 108 5.4.2 Description of the Dyke System 109 5.4.3 Dyke Maintenance Program 110 5.5 Sea Level Variations 112 5.6 Data Availability 114 6 METHODOLOGY 120 6.1 Input Parameters 120 6.2 Assessment of the DJPM for Estimating Extreme Flood Levels 123 6.2.1 Application of the DJPM for Estimating Extreme Flood Levels 123 6.2.2 Application of the Annual Maxima Method for Estimating Extreme Flood Levels 124 6.2.3 Application of the Simple Addition Method for Estimating Extreme Flood Levels 125 6.3 Estimating Extreme Sea Levels for Richmond 126 6.3.1 Application of the DJPM for Estimating Extreme Sea Levels 126 6.3.1.1 Application of DJPM for Combining Observed Sea Levels and Wave Run-up 127 6.3.1.2 Application of DJPM for Combining Tides, Storm surges, and Wave run-up 129 6.3.2 Application of the Hybrid of the DJPM and Simple Addition Method for Combining Tides, Storm surges, Wave Run-up, and Long-term Sea Level Rises 130 7 RESULTS AND DISCUSSION 137 7.1 Assessment of the Direct Joint Probability Method 137 7.1.1 Estimation of Extreme Flood Levels Using the Direct Joint Probability Method 137 7.1.2 Estimation of Extreme Flood Levels Using the Annual Maxima Method 138 7.1.3 Estimation of Extreme Flood Levels Using the Simple Addition Method 139 7.1.4 Assessment of the Direct Joint Probability Method for Estimating Extreme Flood Levels 139 7.2 Estimation of Extreme Sea Levels using the DJPM and Hybrid DJP-Simple Addition Method 141 7.2.1 Estimations of Extreme Sea Levels Using the Direct Joint Probability Method 141 7.2.1.1 DJPM Application to Observed Sea Levels and Wave Run-up 141 7.2.1.2 DJPM Application to Tides, Storm Surges, and Wave Run-up 142 7.2.2 Hybrid DJP-Simple Addition Method Application to Tides, Storm Surges, Wave Run-up, and Long-term Sea Level Changes 143 7.2.3 Discussion of the Estimations of Extreme Sea Levels for Richmond 143 7.3 Sources of Error for Estimates of Extreme Flood and Sea Levels 145 8 CONCLUSIONS AND RECOMMENDATIONS 161 REFERENCES •.
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