TECHNICAL REPORT CERC-85-4 EXTREMAL ANALYSIS OF HINDCAST rengiece AND MEASURED WIND AND WAVE DATA AT KODIAK, ALASKA by Michael E. Andrew, Orson P. Smith Jane M. McKee Coastal Engineering Research Center DEPARTMENT OF THE ARMY Waterways Experiment Station, Corps of Engineers PO Box 631 Vicksburg, Mississippi 39180-0631 June 1985 Final Report Approved For Public Release; Distribution Unlimited Prepared for US ARMY ENGINEER DISTRICT, ALASKA Pouch 898 Anchorage, Alaska 99506 . Destroy this report when no longer needed. Do not return it to the originator. The findings in this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents. The contents of this report are not to be used for advertising, publication, or promotional purposes. Citation of trade names does not constitute an official endorsement or approval of the use of such commercial products. Unclassified SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO.| 3. RECIPIENT'S CATALOG NUMBER Technical Report CERC-85-4 5. TYPE OF REPORT & PERIOD COVERED 4. TITLE (and Subtitle) EXTREMAL ANALYSIS OF HINDCAST AND Final report MEASURED WIND AND WAVE DATA AT KODIAK, ALASKA 6. PERFORMING ORG. REPORT NUMBER 8. CONTRACT OR GRANT NUMBER(s) 7- AUTHOR(a) Michael E. Andrew Orson P. Smith Jane M. McKee 9. P F ING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASK ERP ORMING'S oy AREA & WORK UNIT NUMBERS US Army Engineer Waterways Experiment Station Coastal Engineering Research Center PO Box 631, Vicksburg, Mississippi 39180-0631 11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATE US Army Engineer District, Alaska eine ee 15. SECURITY CLASS. (of this report) 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) Unclassified DEG PASS EI CATIONADOWNIG RSD ING 15a, SCHEDUL 16. DISTRIBUTION STATEMENT (of this Report) Approved for public release; distribution unlimited. 17. DISTRIBUTION STATEMENT (of the abetract entered in Block 20, if different from Report) 18. SUPPLEMENTARY NOTES Available from National Technical Information Service, 5285 Port Royal Road, Springfield, Virginia 22161. 19. KEY WORDS (Continue on reverse side if necessary and identify by block number) Water wave hindcasting (WES) Ocean waves--Measurement (LC) Winds--Alaska--Measurement (LC) St. Paul Harbor (Kodiak, Alaska) (LC) Wind waves--Alaska--Measurement (LC) =>, 20. ABSTRACT (Continue am reverse side ff neceasary and identify by block number) == The purpose of this study is to provide an analysis of hindcast and mea- —-,; sured wave and wind data to estimate the long-term extreme wave heights for SSS the St. Paul Harbor area at Kodiak, Alaska. This study included the develop- 4 ment of the deepwater extreme wave climate, the derivation of a wave energy _—-, attenuation factor for deep- to shallow-water transition of extreme waves, =F (Continued) = =o —— DD ‘uaa 1473 ~—s Er TIow OF 1 NOV 6515 OBSOLETE nel ee n sci SECURITY CLASSIFICATION OF THIS PASE (When Data Entered) Unclassified SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) 20. ABSTRACT (Continued): and an analysis of collateral wind data to support the results of the analysis of hindcast wave data. The Wave Information Study (WIS) hindeast data applicable to the Kodiak area was surveyed for extreme wave conditions. This survey resulted in a sample of 62 significant wave heights for the years 1956 through 1975 (Appen- dix A). The 62 significant wave heights were scaled and plotted according to several extreme probability models. The Extremal Type I or Fisher-Tippett Type I model demonstrated a better fit with the data than did the other models (Figure 1). Extrapolated significant wave heights based on the Extremal Type I model are listed versus return period in Table 7. The extreme wave predictions computed using monthly maximum significant wave height values from measured wave data (Table 9) tended to be smaller than the hindcast predic- tions. This difference was best explained by the fact that the measured data covered a time span of about 2 years; whereas, the hindcast data represented 20 years of wave climate. The longer record had a better chance of capturing a representative sample of extreme events than the short record. Extreme wave heights computed with long-term wind data provided by the National Weather Service agreed well with results from the analysis of WIS hindeast data and supported the overall validity of the study. Measured wave data provided by the Alaska Coastal Data Collection Pro- gram were analyzed to obtain a wave energy attenuation factor for the long- period swell crossing the reefs into St. Paul Harbor at Kodiak. The atten- uation factor represented the fraction of deepwater wave energy that is not dissipated in the transition across the reefs into St. Paul Harbor. The at- tenuation factor had a value of 0.374; therefore, a significant wave height of 1m in deep water corresponded to 0.374 m inside the harbor. The long-term extreme wave height prediction from the analysis of hind- cast data was adjusted to represent the long-term wave climate inside St. Paul Harbor by means of the attenuation factor. Values for attenuated long-term significant wave heights are listed in Table 24. These estimates represented the best estimates for the extreme wave climate at St. Paul Harbor, based on analyses of all the presently available data. Unclassified SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) PREF ACE Authority for the US Army Engineer Waterways Experiment Station (WES) to conduct this study was contained in Intra-Army Order for Reimbursable Ser- vices No. E86-84-0018, dated 8 February 1984. The study was sponsored by the Alaska District Office of the Corps of Engineers, NPAEN-DL-P. The study was conducted by personnel of the Coastal Engineering Research Center (CERC), WES, under the direction of Dr. R. W. Whalin, Chief, CERC, and Dr. F. E. Camfield, Acting Chief, Engineering Development Division. The study was performed under the direct supervision of Dr. Dennis R. Smith, Chief, Pro- totype Measurement and Analysis Branch, and Dr. Michael E. Andrew, assisted by Mr. Orson P. Smith and Ms. Jane M. McKee. Commanders and Directors of WES during the conduct of the study and the preparation of this report were COL Tilford C. Creel, CEH, and COL Robert C. Lee, CH. COL Allen F. Grum, CE, was Director of WES during the publication of this report. Technical Directors were Mr. Fred. R. Brown and Dr. Robert W. Whalin. CONTENTS PREFACE CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OF MEASUREMENT . PART I: INTRODUCTION Purpose of Study . us Physical Description of Kodiak and Wileniteyn PART II: HINDCAST EXTREMAL ANALYSIS . Hindeast Data Selection Probability Distribution for the Number “of Storms per “Year Extremal Theory Extremal Plotting Estimate Reliability . Wave Period Distribution . PART III: ANALYSIS OF MEASURED WAVE DATA Data Description . Data Selection... Extremal Plotting of Monthly Maxima Discussion . Saha De ta, Wiener k meen ae PART IV: ENERGY ATTENUATION FACTOR Analytical Procedures Wave Data Analysis . PART V: ANALYSIS OF MEASURED WIND DATA .......... NWS Data . 0 0 Puffin Island Data BoM : Comparison of NWS and Puffin Island ‘Data i Analysis of Annual Maxima for NWS Data . Wave Forecasts Based on NWS Wind Data PART VI: WATER DEPTH AND WAVE BREAKING CONSIDERATIONS . PART VII: SUMMARY AND CONCLUSIONS . REFERENCES . APPENDIX A: KODIAK STORM DATA, 1956-1975. APPENDIX B: DATA PLOTS FOR PROPOSED EXTREMAL MODELS . APPENDIX C: EXTREMAL DISTRIBUTIONS OF WIND VELOCITIES FOR WOMENS BAY AND GULF OF ALASKA . CONVERSION FACTORS, NON-SI TO SI (METRIC) UNITS OF MEASUREMENT Non-SI units of measurement used in this report can be converted to SI (metric) units as follows: Multiply By To Obtain feet 0.3048 metres miles (US nautical) 1.852 kilometres miles (US statute) 1.609347 kilometres square miles (US statute) 2589 .988 square kilometres yards 0.9144 metres EXTREMAL ANALYSIS OF HINDCAST AND MEASURED WIND AND WAVE DATA AT KODIAK, ALASKA PART I: INTRODUCTION Purpose of Study 1. This study was conducted to provide an analysis of hindcast and measured wave and wind data for Kodiak, Alaska. The purpose of the analysis was to obtain long-term extreme wave conditions for the St. Paul Harbor at Kodiak. This study was accomplished by means of extremal analyses of deep- water hindecast data from the nearest Wave Information Study (WIS) grid point outside Chiniak Bay. Long-term wind measurements were used to validate the results obtained from the analyses of the hindecast data. The local wave cli- mate and attenuation factor for swell crossing the reef into St. Paul Harbor were derived using measured wave data from the area. Physical Description of Kodiak and Vicinity 2. The city of Kodiak is located on the northeastern shore of Kodiak Island, on the western Gulf of Alaska, about 1,250 air miles* northwest of Seattle and 250 miles southwest of Anchorage. Kodiak Island is 3,588 square miles in area and is mostly mountainous terrain rising to over 4,000 ft in places. Its shoreline is characterized by deep glacial fiords separated by rocky peninsulas and many smaller islands. The center of the city lies on the Kodiak Island side of a narrow channel defined by Near Island. The Port of Kodiak's deep-draft facilities are southwest of the city on the northwest shore of that 50- to 60-ft-deep area of Chiniak Bay known as St. Paul Harbor. St. Paul Harbor is defined by a series of small islands and submerged rocky reefs a few feet deep extending from the offshore side of Near Island 2 miles to the southwest to just beyond Puffin Island. Further to the southwest of St. Paul Harbor is Womens Bay, the site of the US Coast Guard Kodiak Air * A table of factors for converting non-SI units of measurement to SI (metric) units is presented on page 3. Station. Chiniak Bay, offshore of the city and St. Paul Harbor, is defined by Cape Chiniak and Long Island and is exposed to the northern half of the Gulf of Alaska. Cape Chiniak offers protection from the Pacific Ocean to the south. 3. The specific area of interest to this study is the deep-draft termi- nal operated by the Port of Kodiak on St. Paul Harbor. This container dock is fully exposed to St. Paul Harbor, and its operations are intermittently dis- rupted by long-period swell which passes during bad weather over the reefs defining St. Paul Harbor. 4. Developments by the State of Alaska in Dog Bay on the southwest side of Near Island are under way; they were proposed in 1976 by the Corps of Engineers and are also of interest in this study. Dog Bay is sheltered from Chiniak Bay by the southern tip of Near Island but is exposed to occasional strong winds out of Womens Bay, which generate seas that are hazardous to small craft. The map of the area given in Figure 1, taken from the Alaska Coastal Data Collection Program Data (ACDCP) report, shows the locations of measurement devices and other features discussed in this report. “70 amcnorace City of Kodiak Buoy No. 2 KODIAK ISLAND oe ‘ef naneOR, __ Anemometer ea mOOIAK AIRPORT TAUMEA CLIFF 4. CHINIAK BAY © Buoy No. 1 Figure 1. Kodiak area map and data collection and telemetry system PART II: HINDCAST EXTREMAL ANALYSIS Hindeast Data Selection 5. The hindeast wave data set used in this study was provided on mag- netic tape by WIS. The data consisted of one record of wave climate charac- teristics including significant wave height, period, and direction for every 3 hr for the years from 1956 to 1975 for a total of approximately 58,400 rec- ords (Ragsdale 1983). A computer program was developed to search this tape for records having specific directions and magnitudes. The program writes tabular listings of the selected data records for further data reduction. The WIS grid point (Point 17) that is nearest to the Chiniak Bay area is 120 nautical miles east of Kodiak (see Figure 2). Events producing signif- icant wave heights of 6 m or more were chosen and maximum significant wave height and associated period were then selected for each event. Appendix A provides a listing of the 78 resulting maximum significant wave heights, each with its date of occurrence and period. The choice of 6 m as a selec- tion criterion was arbitrary. However, the choice was modified and vali- dated in terms of the resulting extremal analysis. The data were surveyed for significant storm events with wave directions corresponding to a direc- tion window defined by Cape Chiniak to the south and Long Island to the north. This window was taken to be approximately 95 to 140 degrees relative to True North for waves traveling from the north and 90 degrees for waves from the east. The direction window was constructed using the approximate center of the St. Paul Harbor area (a little to the northwest of Puffin Island) as the vertex of a triangle with the other two vertices defined by Cape Chiniak and Long Island. Probability Distribution for the Number of Storms per Year 6. The number of storms per year producing significant wave heights of 6 m or more is listed in Table 1. Note that for 1957 there was no event pro- ducing significant wave heights of 6 m or more; whereas 1963, 1968, and 1969 each produced seven such events. The number of storms per year is listed with its observed frequencies in Table 2. A common assumption for studies of this type is that the number of storms per time interval is distributed according g 2 E SL £7 SOK LLL 170 ey Boa FADS ee ee eo epaee geoceee he See tuvectieeaeretii 2a GSS eee case enecnes TetcEae | Ean EERE EEE EEE pueipebinnetaceeecseeststaterecters \etiet netasucnactarseretetarics en sag SSN SOHN SOs SRe S. ~ 130 120 110 100 140 Point 17 used for this study 180 170W MERCATOR PROJECTION OF PACIFIC OCEAN 170E WIS hindcast grid points. 160 Figure e. 140 130 Table 1 Annual Number of Storms Producing Significant Wave Heights of 6 m or More Number of Year Storms 1956 1 1957 (0) 1958 5 1959 3 1960 5 1961 3 1962 5 1963 7 1964 mM 1965 2 1966 3} 1967 5 1968 7 1969 T 1970 3 1971 1 1972 5 1973 6 1974 3 1975 ns) 78 = N Table 2 Frequency Table for the Number of Storms per 1-Year Interval Producing Significant Wave Heights of 6 m or More Number of Storms Frequency 0) 1 1 2 2 1 3 6 4 1 5 5 6 1 Uf 3 to a Poisson probability distribution (Borgman and Resio 1982). The Poisson distribution has probability density aka Ol ae All) 852) ane Shuts: Woless (1) The variable x is the number of storms per year and the parameter u is the average number of storms per year in this case, and u = 78 storms/20 years or WM 2 39) ¢ 7. The chi square goodness of fit test is used to test the validity of the Poisson assumption (Miller and Freund 1977). The test is based on the statistic x where 2 n 0), o Je, 2 ( i ‘| i eer ee (2) i=] i and 0; = observed frequency of years with i - 1 storms E; = Poisson expected frequency of years with i - 1 storms If x is small when compared to theoretical chi square values, then the probability that the Poisson assumption is valid will be great. Table 3 lists the values for 0; and E; and the resulting value for ra Table 3 Chi Square Test for the Poisson Model Number of Storms i i it i ee Fe ie 2 17 3:08 7.09 0.001 Gis Cana ee i) xo = 0.928 Some of the cells have been combined in the test to minimize the impact of small cell counts on the resulting statistic. The theoretical chi square values are found in The Handbook of Mathematical Functions (Abramowitz and Stegun 1972). For a chi square with 5-degrees of freedom (n = 4) 2 Pr(xj > 0.711) = 0.95 2 Pr(xi, > 1.064) = 0.90 and by means of linear interpolation Pr (xj 2 0.928) 0.92 Since the computed statistic is small compared to 92 percent of all possible chi square values, it is concluded that the Poisson assumption is valid. This result will be instrumental in defining such quantities as return period and nonencounter probability in the following sections of this report. Extremal Theory 8. There are several theoretical probability distributions that have been successfully used in the fitting and subsequent extrapolation of extreme wave conditions. These are the Extremal or Fisher-Tippett Type I distribution, the Lognormal distribution, the Log Extremal distribution, and the Weibull distribution. These distributions have cumulative probability functions as listed in Table 4. Table 4 Extremal Models Extremal Type I: F(x) = exp je [2] (3) -~7<¢ X¥ ¢ @ (Continued) 10 Table 4 (Concluded) Lognormal: x 2 1 1 1 f/gn h = F(x) = — — exp [ = a) dh (4) (Bi ° oh 2 (oj d Log Extremal: -u F(x) = exp [ =) (5) Weibull: F(x) = 1.0 - exp [- (<4) | (6) 9. The theoretical cumulative probability function is fit to data by means of the plotting position formula. If the data sample given by X14 Xp yeeey Xp is ranked in ascending order denoted by Y(1) < Y(2) aan Y(n) where T(x) is called the th order statistic, then the plotting position formula Dees en (7) represents the estimate of the data cumulative probability function. If this is set equal to the proposed theoretical cumulative probability function F(x) from Table 4 then FL -—“_: FLAY ,) ; B | (8) where A and B are scale and location parameters, respectively. The in- verse of the function in Equation 8 is F'(f)=Be Yop) + A (9) If the plot of F-'(k/n + 1) with Y(K) approximates a straight line with slope A and intercept B then the proposed theoretical distribution is ac- cepted. Sometimes more than one of the possible distributions will yield a straight line fit. In this case, the better of these is usually that which best fits the upper tail of the function Fy . However, some subjective judgment is required in such cases. 10. The quantity known as the return period, R , is defined to be the mean value of the random number of observations preceding and including the first exceedence of a specified wave threshold x . In terms of the cumula- tive probability function and the Poisson model parameter u 1 o 9 Ti Sse Another useful measure is the nonencounter probability, NE(x) , or the prob- ability that for a design life L the largest wave condition is less than or equal to x in value. For the Poisson model NE(x) = exp (=) ; 1) Note that if L = R_ then NE(x) = 0.37 Thus the probability of encountering a condition larger than the R year re- turn period condition in R years is 0.63. This demonstrates the misleading nature of the return period in that during R years, there is a 63 percent chance of encountering an R year extreme condition. Care should be taken when using return period as the only criterion for extremal prediction. Extremal Plotting 11. A computer software package called EXPLOT was developed at the US Army Engineer Waterways Experiment Station (WES) on the Honeywell DPS1 system to plot the formula given in Equation 9. The plotting was performed for each 12 of the functions listed in Table 4. The Weibull distribution was computed for values of C = 1.0 and C = 2.0 from Equation 6. These values represent the general range of Weibull shape parameters that are applicable to wave condi- tions. Note that if C = 1.0 , the Weibull reduces to an exponential distri- bution and if C = 2.0 , the Rayleigh distribution (Petrauskas and Aagaard 1971). The slope and intercept from Equation 9 are estimated by computing the least squares linear regression line corresponding to Equation 9 (Issacson and Mackenzie 1981). For a listing of estimated values of A and B along with the corresponding parameter estimates for each specific function see Table 5: Table 5 Estimated Parameters for the Hypothesized Extremal Models Model A B m 0 Extremal Type I -6.804 0.981 6.936 1.019 Lognormal -8.058 1.128 7.144 0.886 Log Extremal -14.952 7.742 7.742 6.898 Weibull, C = 1.0 -4.615 0.745 6.195 1.342 Weibull, C = 2.0 -1.839 0.363 5.066 Bo (SD 12. Appendix B contains the resulting data plots for each of the pro- posed extremal models. The horizontal axis entitled Cumulative Probability Seale denotes the actual values of the function F(x) from Table 4 that cor- respond to the data values on the vertical axis. The other horizontal axis is the return period as defined in Equation 10. By inspection it is seen that the Lognormal model does not fit. The Weibull with C = 1.0 , or exponential, also displays significant curvature. The Log Extremal model shows less curva- ture, but the plot still deviates from linearity in the upper and lower tails of the distribution. The Extremal Type I and the Weibull with C = 2.0 (Rayleigh) both look fairly linear except for the lowest 16 points. Since the choice of 6 m for the data selection threshold was arbitrary, it is in- tuitively appealing to recompute the analysis without the lower 16 points. This results in a total of 62 storm events with maxima greater than or equal to 6.4 m and a revised Poisson parameter of u = 3.1 storms per year. The chi square goodness of fit test for the Poisson distribution of storms per year was recomputed with the reduced data set. The chi square value was Xi = 1.35 and (er Xi > 1.35) x 0.85 . The chi square statistic is still smaller than 85 percent of all possible chi square values; therefore, it is 13 concluded that the Poisson model still holds. The extremal plots for the re- duced data sets are displayed in Figures 3 and 4. The Extremal Type I and the Weibull C = 2.0 both appear to fit the largest 62 data points well. The Ex- tremal Type I is the preferred model because (a) it appears to fit better in the upper tail of the data, (b) it is one of the three possible extremal as- ymptotes (Borgman and Resio 1982), of which the Weibull is not a member and, therefore, has a better theoretical basis than does the Weibull, and (c) the Extremal Type I is a two-parameter model whereas the Weibull has three param- eters. The Weibull shape parameter C makes it possible to fit the distribu- tion to data with a higher degree of accuracy than for two-parameter models. This fact does not necessarily mean that extrapolations beyond the data extent will be improved by the higher precision fit. The extrapolations could be very unreliable if the Weibull were used when a simpler model was more appro- priate. Results will be given for both models, but it is believed that the Extremal Type I is qualitatively the better model. Table 6 contains the val- ues of A and B and the resulting distribution parameters. The return periods and associated significant wave heights were computed for both models and are presented in Table 7. RETURN PERIOD IN YEARS 5 10 20 40 60 100 SIGNIFICANT WAVE HEIGHT IN METERS 1.0 50-0 80.0 90.0 95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE Figure 3. Extremal plot for 62 largest maximum significant wave heights, Extremal Type I 14 SIGNIFICANT WAVE HEIGHT IN METERS RETURN PERIOD IN YEARS 5 10 20 40 60100 1.0 50.0 80.0 90.0 95.0 98.0 939.0 CUMULATIVE PROBABILITY SCALE Figure 4. Extremal plot for 62 largest maximum significant wave heights, Weibull, C = 2.0 Table 6 Estimated Parameters for the Selected Extremal Models Model A B u oj Extremal Type I -7.567 1.036 7.304 0.965 Weibull, C = 2.0 -2.130 0.384 5.547 2.604 Table 7 Predicted Significant Wave Heights and Associated Return Periods for the Selected Models Return Period Significant years Wave Height, m Extremal Type I 5 9.92 10 10.60 20 11.28 Oo 11.95 (Continued) 15 99 9 Table 7 (Concluded) Return Period Significant years Wave Height, m Extremal Type I (Continued) 50 12.17 60 12.35 100 12.84 Weibull, € = 2.0 5 9.86 10 10.37 20 10.84 ho 11.26 50 11.39 60 11.50 100 11.78 13. The concept that we refer to as "return period" has been shown to be prone to misinterpretation (Borgman 1963). The statement "50-year wave" may be taken to mean that waves of magnitude greater than or equal to the 50-year value occur on the average of once every 50 years. The phrase "on the average" is the key to interpreting this concept. As was seen in the discus- sion of nonencounter probabilities, the chance of encountering a 50-year wave in any given 50-year interval is about 63 percent. The nonencounter probabil- ities given in Table 8 are defined to be the probabilities for any given de- Sign life L that an R year wave is not encountered. These values can be used to give further meaning to the return periods and associated significant wave heights reported in Table 6. Table 8 Estimated Nonencounter Probabilities for the Extremal Type I Model Design Life, Return Period, years (R) years (L) 20 oO 50 60 100 20 ORSii 0.61 0.67 0.72 0.82 HO 0.14 0.37 0.45 0.51 0.67 50 0.08 0.29 0.37 0.43 0.61 60 0.05 0.22 0.30 0.37 0.55 100 0.01 0.08 0.14 0.19 0.37 16 Estimate Reliability 14. Methods for computing the reliability of extreme wave condition estimates can be found in various reports and articles (Petrauskas and Aagaard 1971, Isaacson and Mackenzie 1981, Borgman 1983). The method given by Borgman requires relatively little computation while the other methods either do not apply to prediction or entail extensive numerical simulations. The method used here has been successfully applied to the extremal analysis of hindcast data on the coast of California (Borgman 1982). 15. The first step in computing the estimate reliability is to calcu- late an upper bound on the error (standard deviation) o, from estimating F the function F(x) from Table 4. This upper bound is approximated by the Kolmogorov-Smirnov (KS) limit for the quantity [F, - F(x)| (12) for Fr from Equation 7. The KS upper bound is the value D(a,n) such that pR|max|Fp - F(x)| > D(a,n) | =a for a = a small number. In other words, the number D(a,n) is such that the maximum absolute difference between the cumulative probability function F(x) and its estimated value FR will be greater than D(a,n) only with small probability a. The value D(a,n) is then assumed to represent a 20/2 x OF error where 20/2 is the standard normal variate such that Pr(Z < Z0/2) = a/2 ; thus, an approximate value for the error op is computed to be on . D(a,n) (13) F Z a/2 For samples of n > 35 and a = 0.05 an approximate value for D(a,n) given n= 62 is D(0.05,n) = 1:38 4/62 and 29.025 = 1.96 then Op = 0.09 (14) The value for oF represents the approximate sampling error or standard de- viation involved in the estimation of F(x) . In order to state this error in terms of the Y-year significant wave height, it is necessary to define the quantity known as the coefficient of variation or CV. The CV is the standard deviation of a variable divided by the mean of the variable. At the median where F(x) = 0.5 , the CV for the quantity F(x) will be approximately oF CVE = 0.5 (15) CVE = 0.18 (16) The CV for F(x) is approximately equal to the CV for Fy (x) , the cumu- lative probability density for the Y-year significant wave height (Borgman 1982); thus, if o, is the standard deviation for Fy (x) and since Fp(x) R = 0.37 for the R-year wave, then tye = 0.37CV,. (17) = 0) 0f/ 16. The final step in the reliability analysis is to express the error in terms of the R-year significant wave height error GG This is accom- plished by means of the approximate formula lo} XR Oy a (18) R R where 9p = the slope of Fp evaluated at Xp. The formula for ap is aF(X,) an = uR ax C&P {unt - F(x) 1 (19) 18 for u = the Poisson parameter or the mean number of storm events per year. The slope ap for the Extremal Type I is approximately a, = 1.03 R (20) for all values of R from 20 to 100. 17. The error due to the hindcast model can also be included in the reliability analysis. The WIS hindcast model when compared to measured data shows at most a difference of about 0.04 for percent occurrence of signifi- cant wave heights larger than 6 m (Figure 11, Corson and Resio 1981). If this value is assumed to be the error in estimating F(x) due to the hind- cast model then a F from Equation 14 becomes On = 0.09 + 0.04 = 0.13 (21) Recomputing Equations 15 through 17, the result is G, 8 On10 (22) FR and then by Equation 18 for the Extremal Type I oem 20810 (23) Xp 18. The error in the extremal prediction to a very rough approximation is about one-tenth of a meter. It is not yet known how accurate this error estimation technique is, and its results should be used with some subjective consideration. Wave Period Distribution 19. The joint probability distribution for significant wave height ver- sus period is listed in Table 9. For the extreme wave condition, the periods tend to be larger than 12 sec with periods at 14.3 sec for the three most ex- treme conditions in the 20-year period. This tendency suggests the use of a period of near 14.3 sec for the computation of design conditions. Table 9 Joint Frequency Distribution of Wave Period Versus Significant Wave Height Significant Wave Height Wave Period, sec on Be 8 AE 1 ENS SNS RS a eee EN) © < bs < 7 6 14 9 (0) 3 7 < is < & 4 9 2 5 i} < hiss < Y) 0) 4 8 4 OO SL°RE I 19 6 6 6 SG UD CPR hrs 88 2 £ ¥222 gI I I I I I I I I I I I I + I I + 82°SL I 16 2 6 2 € I € Y G 9S #¥¥ao ee 92S dI I I I I SS I I I I + I I + L7°St I I I I I I I I I I » | 2 * * I I I I I + I I YAS (SC I I I I I I I I I I I I I I I I + I I @ . 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The most significant statistical relationship, following prelimi- nary analyses, appeared to be the reduction of significant wave height between buoy 1 and buoy 2, as revealed by the scattergrams. SPSS procedures, which computed multiple stepwise regression of HS2 with factors including HS1, HS12, HS13, TP1, and TP1° were executed. Table 16 is a summary of a run where cases with TP1 < 4 sec were excluded. The independent variables are listed in order of their relative significance in the regression equation: Y = A + ByX, + BoX5 +...+ BX, (24) where A and Ba are constants and XxX, is the independent variable. The changes in the correlation (R2) indicate that HS1 provides the only important correlation, with TP1 as next most important though comparatively insignifi- cant. Nonlinear correlations were not revealed by inclusion of the HS12, HS13, or TP12 terms. Table 16 Regression Summary for the Multiple Linear Regression of HS2 with HS1, HS1°, HS13, TP1, and TP1© for TP1 > 4 sec Multiple R RSQ Simple Variable R Square Change R B Beta HS1 - Sig Wave Ht 1 0.74649 0.55725 0.55725 0.74649 0.44623 1.11870 TPH - Peak Period 1 0.76011 0.56266 0.00542 -0.02561 -0.02978 -0.30323 TP1SQ - TPeak1 Squared 0.75218 0.56578 0.00312 -0.05501 0.00108 0.24627 HS1SQ - HSIG1 Squared 0.75358 0.56788 0.00209 0.67612 -0.07965 -0.66127 HS1CU - HSIG1 Cubed 0.75513 0.57022 0.00235 0.56785 0.01090 0.33109 (Constant) 0.26593 33. Scattergrams of HS2 with HS1 which excluded cases with TP1 values below an increasing lower limit showed increasing correlation. Figure 16 is a scattergram of HS2 with HS1 where cases with TPA < 12 sec were excluded. The Re computed was 0.73 with 405 cases included. The grouping near axes intersection and along the HS2 = HS1 line is typical of all the scatter- grams where only lower TP1 values were excluded. Figure 17 is a scattergram of HS2 with HS1 where the following conditions were specified: TP1 > 12 sec bisa 2 Oo ii 5 eiel Sl > 165 mo Was Re computed was 0.75 with 38 cases 38 o£ °0 27°0 s9°0 28°0 66°0 9L°b ££°b ts*t 89°L se°l das Z| < spotued yeed uoz (Z2SH) Aong usuuy ayq 4e 4YUSTOEY BAEM JUOTJTUSTS snsuaa (|SH) Aong ueqno euq 4e 4UusTeY eAeM AUROTJTUSTS Jo weuduEq\eOS “9, auNZTY 22°S S8°? 22°99 oe’s 42°s G2°2 £2°e az°t Bel $9°0 £1°O a ee ees Oa ha mh an panna pan nm ba mn a han mn ha nn ta an tn nt nt Hn an $a pa pt + I I = #66666+ I I I * 2*276662 I I I I * $9£769922 I I I I * e2s 2e2e2Eux2 I I I I * 2252 vuvQue I + I I * 2 es 8 + I I I Ce OC TS oxy 2 I I I I * ¥ * * * I I I I 2 2 I I I I ae I * I * I 2s * + I I s I 2s Beas s s I I I T2 * * I I I I * » ee # * I I ¢ 1 as s ae I + I I a2 * + I I » * Is ae * I I-2-efrerere CO OG OO ae Ors CO 1 OO OOO OOS OS SS I I » I * 2 I I I I I + I » I * 2 + I I * * I * I I T I Bees I I I * I 2s I I I I ss I + I * I ue + I * I * mM I ae I I I * IT £ I I I of I I I I a) * I * I + I I + I I I * I I I I I Ie = - eee ee ee we ee Ke mee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee ee I I I * I + I I + I I I * I I I I I I I * I I I I I I + * » I + I I I I I * * I I I I I « I I I* I I I + I I + I I I I I I I I I * I I I I I I I + * I + Om pn pn pn mm pn mm mpm mn pn am pn nm pm am a ha an ta an pa a tn tnt = = $e tH =H * Lies gs°4 90°? 9S°¢ to°s 67°2 96°L 97°L 26°0 6<°0 L LH 3AWM SIS LSH (SSO¥IW) 2 LH JAVA SIS 2SH (NMOG) (98/92/90 = 31V0 NOTLV34N)) 3WV v] 39Vd 98/72/90 £1°O o£ °O 29°O $9°0 28°0 66°0 9LrL £o°b ts*L 8971 ser NON JO W¥NSNSLLWIS 3113 SISATVNVY Wivd 3AVM XWVIGOX 39 ts°O 79°0 82°0 t6°0 so°L BLek tee So°L es°t 22°b SerL w G°O < ZSH ‘Ww S*| < LSH pue das 2, < spotued yeed soz (2SH) Aong ueuuy ay} 4e 4YUSTEY aAeM queotyrusTs snsuaa (|SH) Aong uagng eyq 4e 4UsTeY SAEM YUROTJTUZTS Jo weus19843e0S 2e°s 66°9 t9°9 22°9 78°s 99°¢ 8o°s 02° te°2 £6° Ss°L Bo ee ee eee ee ee eee See See ee ts = » B+ ® os * s eee ee ee oe ee eo oe ee oe ee en ee en) * * * Oe ee ee eo ee See ee ee ee eo eo re woe woe) x x 2 2 ee ee ee ee ne ee noe | » Hen mh mn a ha nnn ha nn pn nm Fa nn hn nn mh nn pen npn enn tan nn npn nnn Henne ta cnn tee cate nn nt ons ntereetocentacnnt BL°s 08° 27°9 £0°? $9°s 22° 68°2 Ls°2 22 92°b tL 2H 3AWA OTS LSH (SSO¥DV) 2 LH 3AWM OTS 2@SH (NAOQ) 40 ee eo oe ee ee ee ee er oe en oe a ee bs°O 79°O 82°0 t6°O so°t BLeb beers $7°t gs°L 22°h sent “LL ean3tg WVEYSUILIVIS (98/08/90 = 31VGd NOTLV3UI) 3WVNON 3713 9 39Vd 98/05/90 SISATVNY WivGd JAVA AWIGOX 4O included. The complete regression statistics for this condition are presented in Table 17. The linear regression equation resulting from this analysis is: HS2 = 0.003 + 0.374 HS1 (25) The intercept is notably very near zero indicating that an attenuation factor of 0.37 for the conditions stated above has significance. In fact the 90 per- cent confidence interval on the intercept, given by (-0.17, 0.18), contains zero indicating that the intercept is not significantly different from zero in a statistical sense. The slope or attenuation factor has 90 percent con- fidence interval (0.31, 0.43). Table 17 Linear Regression Summary for Inner Buoy Significant Wave Height (HS2) and Outer Buoy Significant Wave Height (HS1) Variable(s) Entered on Step Number 1 Multiple R 0.86888 R Square 0.75495 Adjusted R Square 0.74814 Standard Error 0.19925 Analysis of Sum of Mean Variance DF Squares Square F Regression 1 4.40304 4.40304 110.90697 Residual 36 1.42921 0.03970 Variables in the Equation Standard Variable B Beta Error B F HS1 0.37425 0.86888 0.03554 110.907 (Constant) 0.00311 44 PART V: ANALYSIS OF MEASURED WIND DATA NWS Data 34. The NWS anemometer is located at the Coast Guard Station within Womens Bay. The anemometer is approximately 100 yd from the water line at mean sea level, elevation 10 m. Prior to 1973, a Navy anemometer was at the same location, but at an elevation of 5 m. The NWS/Navy anemometer provided hourly data from November 1945 through December 1982. Data adjustment 35. Using the method presented in the Coastal Engineering Technical Note CETN-I-5, "Method of Determining Adjusted Windspeed, U, , Forecasting," WES personnel adjusted the data. The adjustments included the for Wave following: a. Correction to 10-m level for data prior to 1973. b. Correction to hourly averages from 5-min averages every hour. ec. Adjustment of overland readings to overwater readings. d. Correction for nonconstant coefficient of drag. e. Correction for instability due to air-sea temperature differ- ences for directions where the fetch is greater than 10 miles (an unstable condition was assumed, since no temperature data were available). These corrections were made so that the wind data could be applied directly to wave forecasting curves. Wind summary 36. A computer program was developed to produce summaries of the hourly winds and of the 3-, 6-, 8-, and 10-hourly winds. The summaries relate wind speed and duration to recurrence probability for 16 directional sectors. The maximum annual wind was also found for use in an extremal analysis to be pre- sented later. 37. The procedure to compute the N-hour average wind was as follows: a. Delete bad observations (less than 1 percent of the 325,050 observations were bad). b. Compute arithmetic average of all wind speeds in consecutive N-hour intervals to estimate wind speed (calm values were counted as zero wind speeds). c. Compute vector sum of all noncalm observations in the N-hour interval. ry) d. Compute direction of vector sum from c to estimate wind direction. 38. The distribution of the hourly winds with respect to direction is shown as a wind rose (Figure 18). The wind rose shows the distribution of winds in 16 directional sectors as a percent of all winds. The bars in each direction are broken into 10-mph intervals. 39. The distributions of wind speed and duration relating to return period are presented in Figure 19. Figure 19 shows combined data from all sectors (0-360 deg). The curves represent the visual best fit to the data. From these curves, the wind speed for a given return period can be obtained. In general, these curves should not be extrapolated beyond twice the period of record (37 years). Puffin Island Data 40. The Puffin Island anemometer is part of the ACDCP. Puffin Island is located 1.5 miles offshore in Chiniak Bay. The anemometer is located at an elevation of 23 m (island elevation) plus 6.1 m (elevation of sensor above the island). The anemometer supplied about 16 months of usable data starting late in 1981. The anemometer was not working in October and November of 1981 nor in October of 1982, months when major storms are expected. The anemometer was also out during other extreme events, so the data for extreme events are un- reliable. The observations were 1-hr averages at 3-hr intervals. Data adjustments 41. Again, the raw data were adjusted using the method presented in CETN-I-5. The adjustments included: a. Correction to 10-m level. b. Adjustment of overland readings to overwater readings. ce Correction for nonconstant coefficient of drag. d. Correction for instability due to air-sea temperature differ- ences for directions where the fetch is greater than 10 miles (an unstable condition was assumed, since no temperature data were available). A calibration correction factor of 1.06 was also applied as recommended by the Alaska District. An additional adjustment was made to account for the influ- ence of the island height and shape on the airflow (Simiu and Scanlon 1978). 43 eJep SMN UOJ JOTd potuad uungjau snsuea paeads putm Ol NOILVYNG YH-OL @ NOILVYNG YH-8 B NOILVYNG YH-9 Y NOILVYNG YH-E O NOILVYNG YH-l O GN3941 oO! YA ‘GOIY3Sd NYNL3SY ,-Ol SYOLOAS 11V - SMN Ah LE "6, eun3T 4 WY 5-01 p-Ol St oe Sv 09 GZ 06 Sol Oct HdW ‘G33dS GNIM 45 This correction is where 2/L | hoin Pray (xo 2) (e) Raa 1+ (26) p Lin 2) E (2) + inf Zz QL Zz fo) in which h = height of the hill GO =P lO L = factor of island length Zo = roughness length i° = dimensionless quantity representing the perturbation of the upwind velocity due to the presence of the hill N Ty anemometer height above the island 9 = thickness of the internal boundary layer This correction assumes that L is much larger than h and that it is rural terrain. A maximum correction of 0.65 was applied in the direction of the short axis of the island, and a minimum correction of 0.85 was applied in the direction of the long axis of the island. These corrections were made so wind data could be applied directly to wave forecasting curves. Wind summary 42. The same computer program used to analyze the NWS data was used for the Puffin Island data. Data were available for only the 3-hr averages, so summaries were produced for the 3- and 6-hr winds. Of the 4,800 observations, 17 percent were bad. 43. The distribution of the hourly wind with respect to direction is shown as a wind rose (Figure 20). The wind rose shows the distribution of winds in 16 directional sectors as a percent of all winds. The bars are broken into 10-mph intervals. 44. The short period of record for the data from Puffin Island anemom- eter makes it difficult to create reliable curves for wind speed and duration versus return period. The best use for this data is for comparison with the NWS data. 46 15% WIND ROSE PUFFIN ISLAND KODIAK, ALASKA 1981 - 1983 10% Figure 20. Wind rose plot for Puffin Island data Comparison of NWS and Puffin Island Data 45. The Puffin Island data seem to compare well in velocity, direc- tion, duration, and return period with the NWS data. Figure 21 shows the distribution of wind speed and duration relative to return period (3- and 47 ejep PUeTS] UTJJng sOJ potued uunjeu snsuaa paeds puTtM NOILVYNG YH-9 GNV-€ SMN —— NOILVYNG YH-9 NOILVYNG YH-E GQN3941 YA ‘GOIHSd NYNL3Y 90 1-01 SYOLOAS 11V - GNVISI NidaNd 2-01 "Le aun3ty e-0l Lo SL 10} Sv 09 SL 06 SOL OZL HdW ‘G33dS GNIM 48 6-hr duration). The solid curves represent the distribution for the NWS data (see Figure 19). The Puffin Island data follow the NWS distribution closely in the lower parts of the curves. This is the region where the Puffin Island data are most reliable. This implies that the NWS wind data are a good esti- mate of the Puffin Island wind conditions which would give a good estimate of the open water conditions in St. Paul Harbor and Chiniak Bay at Kodiak. The following section presents the extremal analysis of the winds using the NWS wind data. The extremal curves are recommended for design purposes. Analysis of Annual Maxima for NWS Data 46. The NWS data for 1-, 3-, 6-, 8-, 10-, 12-, 15-, 18-, 21-, 24-, 27-, and 30-hr wind speed averages were searched for yearly maxima for input to the extremal plotting routine, EXPLOT. The resulting plots are provided in Appen- dix C. It is apparent for all but the 1-hr averages that the smaller eight data points have been smoothed out and can no longer be considered extremes. For this reason the points in question were not used when fitting the least Squares lines to the data, and therefore, do not affect the resulting extrap- olated wind speeds. Table 18 contains a full listing of the predicted wind speeds for given return periods and hourly averages. The analysis was com- puted for all directions, the offshore exposure (45-180 deg relative to 0 deg from North) and Womens Bay (202.5-247.5 deg) separately as indicated in Appen- dix C and Table 18. The Extremal Type I or Fisher-Tippett I distribution was used in this analysis. The Fisher-Tippett or Extremal Type II distribution results were also computed and found to be unsatisfactory. In general, the chosen extremal model fits the data very well as is demonstrated by the plots. Wave Forecasts Based on NWS Wind Data 47. The long-term (extremal) distributions of wind velocities averaged over varying durations for all directions for 247.5-292.5 deg (Womens Bay), and for 45-157.5 deg (Gulf of Alaska) are presented in Appendix C. This in- formation can be used to derive equivalent significant wave heights and peak spectral periods, given appropriate assumptions of water depth and fetch. Two sectors of interest were defined which correspond to the 7-mile fetch of 49 Table 18 Maximum Windspeeds, Miles per Hour with Hours Averaged and Return Period Hours Return Period, years Averaged 5 10 20 HO 50 60 100 All Directions 1 94.0 103.4 112.4 121.3 124.1 126.4 132 3 80.1 89.2 98.0 106.5 109.2 W165 117 6 74.0 83.1 91.8 100.3 103.1 105.3 111 8 70.9 79.4 87.5 95.5 98.0 100. 1 105 10 68.4 76.8 85.0 92.9 95.4 97.5 103 12 49.3 56.2 62.3 68.3 70.2 71.8 76 15 46.2 52.3 58.2 64.0 65.9 67.4 71 18 44.8 50.5 56.1 61.5 63.2 64.6 68 21 42.9 48.4 53.6 58.7 60.4 O67 65 a4 41.5 47.2 52.6 57.9 59.6 61.0 64 27 37.8 41.8 45.6 49.3 50.5 51.5 54 30 36.9 41.4 45.7 50.0 51633 52.4 55 Offshore Exposure 1 72.2 19.7 86.8 93.8 96.0 97.8 102 3 62.1 Oat 78.9 87.0 89.5 91.6 97 6 56.1 63.5 70.7 Ti os 80.0 81.9 87 8 53.0 59.5 65.8 72.0 74.0 75.6 80 10 50.1 56.1 62.0 67.6 69.4 71.0 15 Womens Bay 1 52.5 Gileie 70.5 719.1 81.8 84.1 90 3 37.2 NT 4 56.7 66.0 69.0 1105 78 6 26.5 34161 35.5 39.7 H1.1 42.2 45 8 26.1 31165 36.7 41.8 43.5 44.8 48 10 24.3 29.8 35.1 40.2 41.9 43.2 N7 TM OF DAW OVNWO o-OWwo OUWW Womens Bay to Dog Bay, and the virtually unlimited fetch across the Gulf of Alaska. The depths along the Womens Bay fetch vary from a few feet to over 50 ft. Shallow water forecasting curves (Vincent and Lockhart 1983) for an assumed constant 35-ft depth and 7-mile fetch were used to translate veloc- ities and durations at selected return periods from Figures C1-C5 to equiva- lent significant wave heights and peak periods for the Womens Bay fetch, as presented in Table 19. The fetch limitation makes the higher velocities of 1-hr duration the extreme condition in terms of wave height. 50 Table 19 Wave Forecast for Womens Bay Fetch Based on NWS Wind Data Duration Return Period, year vealitg 5 10 20 4O 50 60 100 1 Ios Ue ROM Aeron) (250, 0) esOne O.ON ein oe On Veco one 3 Vet Sat ete AO MTs ees) Ae ly AO” esmall. tacos We enon dg Note: First number under Return Period indicates Significant Wave Height, m; second number indicates Peak Period, sec. 48. A similar translation of winds from the Gulf of Alaska (Figures C6- C17) was performed using the deepwater forecasting curves with duration as the only limitation. Table 20 indicates a duration of 24 hr as the extreme condi- tions in this case with low probability deepwater significant wave heights Table 20 Wave Forecast for Gulf of Alaska Based on NWS Wind Data Duration Return Period, year hr 5 10 20 hO 50 60 100 12 Giese Wee) Gallis “Well. ThBh 12.0. = eee 128 . ee, TRA Ga, TBM ~— Gay. 1963 15 Bie Wh Gals 1222 Ws9, Io Bel, 1 Osi 1.0 9.5, 10 10.0, a8 18 Geis As G5 TE BS, Wii Op Met =~ Wale 1Ss0" WON, 15.9 11.0, 15.5 21 1405 (os G25 Wee ~ On, 15.0 TO, 15.8 1.75 15.9 11.0, 16.9 11595 16.6 24 feOn Wee) Bs55 UKG Teds 15s Tiled, Tes VieG5 1G. 17.9, 16.9 12.8, 17.8 27 UO, Wie Ba Ws GE 1G. Oo, Wel Moi, 16.3 10.8, 1.0 1.0, 17.0 30 Ooty 1B) 3.2, Bee Ox 1Gs2 Ay IO WSS Wal» Web, 17.2 12:5, 17.9 Note: First number under Return Period indicates Significant Wave Height, m; second number indicates Peak Period, sec. very close to those predicted using the WIS data base (see Table 21). The duration over 21 hr for the low probability events have corresponding fetches on the order of 300 to 400 nautical miles. Though no physical barriers to the wind exist, this distance is on the scale of the synoptic weather patterns. The variations of velocity across weather patterns of this scale are modeled by the WIS data base, but are not using the NWS point source of data. This inadequacy, along with the other measurement errors inherent in land-based anemometers, indicates that the statistics from the WIS data base are more reliable, as applied here, for wave conditions at Kodiak. 51 Table 21 Comparison of Extremes Predicted from WIS Hindcast Data and NWS Wind Data Analysis Significant Wave Return Period Height, m years WIS NWS 5 9.92 7.0 10 10.6 8.5 20 11.28 10.1 4O 11.95 11633 50 12.17 11.6 60 12.35 11.9 100 12.84 12.8 52 PART VI: WATER DEPTH AND WAVE BREAKING CONSIDERATIONS 49. The outer buoy location water depth is about 77 m. For linear Waves with periods of 12 sec and longer, this does not constitute deep water. The deepwater assumption holds for h/Lo > 0.5 where h = water depth and Lo = deepwater wavelength. Values for h/Lo with h = 77m and periods of 12 sec and longer are h/Lo < 0.34 ; thus, the waves traveling from deep Water will be somewhat affected by the water depth. Corrections for this are available in wave tables (Skovgaard et al. 1974) that report the ratio of wave height to deepwater wave height as a function of h/Lo . Values for this ratio are listed in Table 22 for the range of wave periods of interest. Wave breaking limits were computed using a controlling depth of 7.5 m for the area between Puffin Island and Popov Island. It was found that for the ex- treme waves of this study the attenuation factor does not need to be modified using an upper limit of significant wave height. Table 22 Ratio of Wave Height Over Deepwater Wave Height for a Water Depth of 77 m Versus Wave Period Wave Period H_ sec Ho 14.0 0.932 14.3 0.929 14.5 0.929 14.8 0.926 15.0 0.923 oS 0.920 15.5 0.920 15.8 0.918 16.0 0.916 16.3 0.916 16.5 0.914 16.8 0.914 17.0 ils) 50. The peak wave period that most accurately represents the local weather conditions comes from the WIS hindcast data set. The WIS hindcast period for the 20-year event is 14.3 sec. This value is also sufficient for 53 the 50- and 100-year wave conditions. The ratio of wave height in 77 m of water to deepwater wave height for waves with 14.3-sec periods is 0.929; thus, the 50- and 100-year deepwater significant wave heights given in Table 7, 12.17 and 12.84, respectively, will be 11.3 and 11.9 m at the outer buoy location. 54 PART VII: SUMMARY AND CONCLUSIONS 51. The WIS hindeast data applicable to Chiniak Bay were surveyed for extreme wave conditions. The resulting 62 significant wave heights were found to fit the Extremal Type I distribution. The resulting extrapolated significant wave heights are reported in Table 7. The associated reliability analysis indicates that if the Extremal Type I is the proper model, then the standard error in estimating the extremes is about one-tenth of a meter. It should be stressed that the major source of error is due to the choice of the model and is thus not included in this number. 52. Measured data from the area were also found to fit an Extremal Type I distribution. The results from this analysis tend to underestimate long-term conditions such as the 10- to 50-year events. This is mostly due to the short data record length (2 years). Extremes computed using the NWS wind data are similar to those given by the hindcast analysis. For the 50-year event they differ by about six-tenths of a meter, and for the 100-year event they are approximately the same. 53.. The peak wave period that most accurately represents the local weather patterns is that computed by the WIS hindcast. The wave period asso- ciated with the 20-year extreme event is 14.3 sec. This value should be suf- ficient for the 50- and 100-year events as well. The deepwater to intermedi- ate water depth (77 m at the outer buoy) wave height correction for 14.3-sec periods is 0.929. This correction was applied to the significant wave heights listed in Table 7 and the values listed in Table 23 were obtained. Table 23 Depth Corrected to Outer Buoy (77 m) Significant Wave Heights Versus Return Period Return Period Significant Wave years Height, m 5 9.22 10 9.85 20 10.48 HO 11.10 50 lbiersi 60 11.47 100 11.93 55 54. The deep- to shallow-water attenuation factor from Equation 25 is 0.374. The values in Table 23 multiplied by this factor result in the inner- buoy or shallow water extreme values given in Table 24. Table 24 Attenuated Significant Wave Heights Versus Return Period Return Period Significant Wave years Height, m 5 3.45 10 3.68 20 3.92 ho 4.15 50 4.23 60 4.29 100 4.46 The values given in Table 24 along with the wave period of 14.3 sec are the estimates for the long-term extreme events pertaining to the St. Paul Harbor area, based on analyses of all the currently available data. 56 REFERENCES Abramowitz, M., and Stegun, I. A. 1972. Handbook of Mathematical Functions aS SS SS SE EEE Dover, N. Y. Borgman, L. E. 1963 (Aug). "Risk Criteria," Journal, Waterway, Port, Coastal and Ocean Division, American Society of Civil Engineers, Vol 89, No. WW3. . 1982. "Extremal Analysis of Wave Hindcasts for the Diablo Canyon Area, California," report prepared by L. E. Borgman, Inc. Borgman, L. E., and Resio, D. T. 1982. "Extremal Statistics in Wave Clima- tology," Topics in Ocean Physics, LXXX Corso, Soc. Italiana di Fisica, Bologna, Italy. Carter, D. J. T., and Challenor, P. G. 1978. "Return Wave Heights at Seven Stones and Famita Estimated from Monthly Maxima," Report No. 66, Institute of Oceanographic Sciences. Challenor, P. G. 1982. "A New Method for the Analysis of Extremes Applicable to One Years' Data," Report No. 142, Institute of Oceanographic Sciences. Corson, W. D., and Resio, D. T. 1981 (May). "Comparisons of Hindcast and Measured Deepwater, Significant Wave Heights," WIS Report 3, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Isaacson, M., and MacKenzie, N. 0. 1981 (May). "Long Term Distributions of Ocean Waves: A Review," Journal, Waterway, Port, Coastal and Ocean Division, American Society of Civil Engineers, Vol 107, No. Wwe. Miller, I., and Freund, J. F. 1977. Probability and Statistics for Engi- neers, 2d ed., Prentice-Hall, Englewood Cliffs, N. J. Petrauskas, C., and Aagaard, D. M. 1971. "Extrapolation of Historical Storm Data for Estimating Design Wave Heights," Journal, Society of Petroleum Engi- neering, Vol 11. Ragsdale, D. S. 1983 (Aug). "Sea State Engineering Analysis System (SEAS)," WIS Report 10, US Army Engineer Waterways Experiment Station, Vicksburg, Miss. Simiu, E., and Scanlan, R. H. 1978. "Wind Effects on Structures," An Intro- duction to Wind Engineering, Wiley, New York. Skovgaard et al. 1974. "Sinusoidal and Cnoidal Gravity Waves Formulae and Tables," ISVA Technical University of Denmark. US Army Engineer District, Alaska. 1983a. "Alaska Coastal Data Collection Program (ACDCP)," Report 1, State of Alaska Department of Transportation and Public Facilities, Anchorage, Alaska. 1983b. "Alaska Coastal Data Collection Program (ACDCP)," Report 2, State of Alaska Department of Transportation and Public Facilities, Anchorage, Alaska. US Army Engineer Waterways Experiment Station. 1981 (Mar). "Method of Deter- mining Adjusted Windspeed: VA, for Wave Forecasting," CETN-I-5, Vicksburg, Miss. 1984. Shore Protection Manual (2 vols), 4th ed., Vicksburg, Miss. 57 Vincent, C. L., and Lockhart, J. H., Jr. 1983 (Sep). "Determining Sheltered Water Wave Characteristics," ETL 1110-2-305, Department of the Army, Office, Chief of Engineers, Washington, DC. Wang, S., and LeMéhauté, B. 1983 (May). "Duration of Measurements and Long Term Wave Statistics," Journal, Waterway, Port, Coastal and Ocean Engineering, American Society of Civil Engineers, Vol 109, No. 2. 58 APPENDIX A: KODIAK STORM DATA, 1956-1975 Kodiak Storm Data Period Date Homax, Ww sec 01-18-56 6.20 12.50 01-28-58 8.80 12.50 02-12-58 6.60 11.10 02-24-58 6.90 11.10 11-20-58 7.80 11.10 12-10-58 6.30 10.00 01-16-59 11.70 14.30 01-21-59 7.20 10.00 11-16-59 7.40 11.10 01-31-60 9.90 14.30 02-07-60 8.90 14.30 10-24-60 7.50 11.10 11-22-60 7.00 11.10 12-20-60 6.70 11.10 01-19-61 9.20 12.50 01-24-61 6.20 11.10 11-26-61 6.30 11.10 10-27-62 8.10 12.50 11-07-62 6.30 11.10 11-23-62 7.20 10.00 11-28-62 6.30 10.00 12-30-62 6.00 11.10 02-08-63 8.40 12.50 10-21-63 6.80 11.10 10-31-63 9.30 12.50 11-11-63 6.70 14.30 11-22-63 6.50 12.50 11-25-63 7.20 11.10 12-21-63 8.50 11.10 01-12-64 6.90 11.10 01-24-64 6.60 10.00 01-20-64 9.40 12.50 12-01-64 8.20 12.50 10-02-65 6.30 11.10 10-05-65 7.60 11.10 01-13-66 7.30 12.50 01-26-66 8.60 12.50 11-01-66 7.40 11.10 01-10-67 7.10 14.30 02-27-67 6.00 12.50 (Continued) A2 Kodiak Storm Data (Concluded) Period Date Hsmax, na sec 12-02-67 6.30 12.50 12-07-67 6.00 12.50 12-23-67 7.70 14.30 01-16-68 6.60 12.50 01-22-68 6.50 10.00 03-21-68 6.90 14.30 11-04-68 7.70 11.10 11-18-68 8.20 11.10 11-28-68 6.70 10.00 12-14-68 7.40 12.50 02-07-69 6.40 10.00 02-11-69 6.10 11.10 10-11-69 7.10 10.00 11-19-69 6.50 11.10 12-02-69 8.50 12.50 12-19-69 8.80 12.50 12-23-69 9.10 12.50 01-20-70 8.00 11.10 10-31-70 6.30 111.10 11-11-70 9.10 12.50 01-17-71 6.60 14.30 01-15-72 6.70 12.50 03-09-72 7.20 11.10 11-25-72 10.20 14.30 12-17-72 7.00 14.30 12-24-72 10.10 14.30 01-27-73 7.80 14.30 12-06-73 6.10 12.50 12-13-73 6.30 12.50 12-19-73 8.60 14.30 12-23-73 7.10 10.00 12-27-73 10.00 12.50 01-17-74 8.00 14.30 04-13-74 6.10 11. 1@ 10-30-74 8.40 14.30 01-12-75 7.40 14.30 11-19-75 8.20 12.50 12-21-75 8.10 1. 10 A3 vi seas | i‘ ; ‘ Dat Bagley DP sak oe pra pboypliasah Rh Dentin a ag ame a a eSB Hs aa oa ae | SOP es Ate area pa co) iy 7 ; Yr WF rs ee vi ; { i eis ‘ , ; ui ied i a oily Lies Ww gts eteh eae lsh 7 i rey ath pat Be ui a ORT aah Wven ita inenk } 4 iv s POE eee ees Oa QE e a Ls A ee ee . i aa | o \ i te i ail i i i | i Ee aes AAA ey NN % th tg af here te i ep Dey Hees Hay y 4 | Wi Ie . 5 i v a? i hei Th LF He , ih hy Ma Ae Bes cae eT rid "i it tee Ney ti8 a we, Cel Shp et tsk AS ae We: a Lal re ea: Cin tava Wa ‘ e oatoey waa evens 4 nays Be re iy O hys i fe Fe fi \ Wi i 5 i i ay ; / Gr 4 if | 1 * F te ; ; r 1 Fiteanes std aol Aho eS Mh ehabinenid sea Laie tact tet i - lens ; ries A ‘ i ; ii 4) i] APPENDIX B: DATA PLOTS FOR PROPOSED EXTREMAL MODELS RETURN PERIOD IN YEARS 5 10 20 40 60 100 14.0 12.0 SIGNIFICANT WAVE HEIGHT IN METERS 8.0 6.0 -& 1.0 90.0 95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE LOGNORMAL RETURN PERIOD IN YEARS 5 10 20 40 60 100 14.0 w ao lu — (1260) = — a) oO 1040 WwW > cx =z — 738 = 8.0 i= z o o 6.0 TOM SOLO BOLOMESOFONUSS OES GEOMmGGhO 99.9 CUMULATIVE PROBABILITY SCALE WEIBULL. C = 1-0 B2 LN SIGNIFICANT WAVE HEIGHT IN METERS SIGNIFICANT WAVE HEIGHT IN METERS RETURN PERIOD IN YEARS 5 10 20 4060 100 14.0 10.0 50.0 80.0 90.0 95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I RETURN PERIOD IN YEARS 5 10 20 4060 100 50.0 60.0 90.0 /95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I! B3 SIGNIFICANT WAVE HEIGHT IN METERS 14.0 12.0 10.0 8.0 RETURN PERIOD IN YEARS 5 10 20 4060 100 50.0 80.0 90.0 95.0 96-.099.0 CUMULATIVE PROBABILITY SCALE WEIBULL. C = 2.0 BY 99.9 APPENDIX C: EXTREMAL DISTRIBUTIONS OF WIND VELOCITIES FOR WOMENS BAY AND GULF OF ALASKA GONE HR AVERAGE MAX WIND SPEED IN MPH THREE HR AVERAGE MAX WIND SPEED IN MPH 100.0 80.0 60.0 40.0 20.0 60.0 60.0 40.0 20-0 RETURN PERIOD IN YEARS 5 10 20 40 60 100 50-0 80.0 90.0 95.0 98.0 99.0 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C1. Womens Bay, 1-hr averages RETURN PERIOD IN YEARS i) 10 20 4060 100 50.0 80.0 90.0 95.0 98.0 99.0 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C2. Womens Bay, 3-hr averages C2 99.9 99.9 SIX HR AVERAGE MAX WIND SPEED IN MPH EIGHT HR AVERAGE MAX HIND SPEED IN MPH RETURN PERIOD IN YEARS 5 10 20 4060 100 40.0 30.0 20.0 10.0 0.0 1-0 50.0 80.0 90.0 95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C3. Womens Bay, 6-hr averages RETURN PERIOD IN YEARS 5 10 20 40 60 40.0 #00 30.0 20.0 10.0 0.0 1.0 50.0 60.0 90.0 95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C4. Womens Bay, 8-hr averages C3 TEN HR AVERAGE MAX WIND SPEED IN MPH ONE HR AVERAGE HAX WIND SPEEDO IN MPH 45.0 36.0 25.0 15.0 5.0 120.0 100.0 60.0 60.0 40.0 RETURN PERIOD IN YEARS by} 10 20 4060 100 1.0 50.0 680.0 90-0 95-0 98.0 99.0 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C5. Womens Bay, 10-hr averages RETURN PERIOO IN YEARS 5 10 20 40 60 100 1.0 50.0 60.0 90.0 95.0 98.0 99.0 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C6. Gulf of Alaska, 1-hr averages c4 99.9 99.9 THREE HR AVERAGE MAX WIND SPEED IN MPH SIX HR AVERAGE MAX HIND SPEED IN MPH RETURN PERIGD IN YEARS tS) 10 20 40 60 100 60.0 b 60.0 40.0 20.0 1.0 50.0 80.0 90-0 95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C7. Gulf of Alaska, 3-hr averages RETURN PERIOO IN YEARS 5 10 20 4060 100 60.0 60.0 40.0 20.0 0.0 1.0 50.0 60.0 90.0 95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE 1! Figure C8. Gulf of Alaska, 6-hr averages C5 EIGHT HR AVERAGE MAX WIND SPEED IN MPH TEN HR AVERAGE MAX WIND SPEED IN MPH RETURN PERIOD IN YEARS i) 10 20 40 60 100 80.0 60.0 40.0 20.0 1.0 50.0 80.0 90.0 95-0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE IJ Figure C9. Gulf of Alaska, 8-hr averages RETURN PERIOD IN YEARS 5 10 20 40 60 100 60.0 60.0 40.0 1-0 50.0 60.0 90.0 95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C10. Gulf of Alaska, 10-hr averages C6 TWELVE HR AVERAGE MAX WIND SPEED IN MPH FIFTEEN HR AVERAGE MAX WIND SPEED IN MPH RETURN PERIGO IN YEARS ) 10 20 40 60 100 80. 60. 40. 20.0 1.0 50.0 80.0 90-0 95.0 98-0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE J Figure C11. Gulf of Alaska, 12-hr averages RETURN PERIOO IN YEARS tS) 10 20 40 60 100 80.0 60.0 20.0 1.0 50.0 80.0 90.0 95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C12. Gulf of Alaska, 15-hr averages C7 EIGHTEEN HR AVERAGE MAX WIND SPEED IN MPH TWENTY ONE HR AVERAGE MAX WIND SPEED IN MPH RETURN PERIOD IN YEARS 5 10 20 40 60 100 80.0 60.0 40.0 20.0 1.0 50.0 60-0 90-0 95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C13. Gulf of Alaska, 18-hr averges RETURN PERIGD IN YEARS 5 10 20 40 60 100 60.0 60.0 40.0 20.0 1.0 50-0 680.0 90-0 95.0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C14. Gulf of Alaska, 21-hr averages c8 TWENTY FOUR HR AVERAGE MAX WIND SPEED IN MPH THENTY SEVEN HR AVE MAX WIND SPEED IN MPH RETURN PERIOD IN YEARS 5 10 20 40 60 100 60.0 60.0 40.0 20.0 0.0 1.0 50.0 go0-0 90.0 95-0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C15. Gulf of Alaska, 24-hr averages RETURN PERIOD IN YEARS 5 10 20 4060 100 50.0 40.0 30.0 20.0 10.0 1.0 60.0 60.0 90.0 95-0 98.0 99.0 99.9 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE I Figure C16. Gulf of Alaska, 27-hr averages C9 THIRTY HR AVERAGE MAX WIND SPEED IN MPH 1.0 50.0 Figure C17. RETURN PERIGD IN YEARS 5 10 20 4060 100 60-0 90.0 95.0 98.0 99.0 CUMULATIVE PROBABILITY SCALE EXTREMAL TYPE J Gulf of Alaska, 30-hr averages C10 99.9 et Pilih i Thi =) iy i an ; incall F Nay Re gt ee