1293 00994 6249 )V1ESI.} RETURNING MATERIALS: Place in book drop to LJBRARJES remove this checkout from J-I-Kjl-IL your record. FINES will be charged if book is returned after the date stamped below. APR 174299 NEARSHORE WAVE ENERGY AND BLUFF RECESSION RATES ALONG LAKE HICHIGAN’S SOUTHEASTERN SHOREZONE By Jeffrey P. LaMoe A THESIS Submitted to Pfichigan State University in partial fulflHlment of the requirements for the degree of MASTER OF SCIENCE Department of Geography 1987 ABSTRACT Bluff crest recession along the southeastern shore zone of Lake Mhflfigan is examined cohufldent to wave energy probabiuties associated with storms recurrent at 5, 10, 20, 50, and 100-year intervals. The investigation considers twenty three previously studied sites composed of unconsoudated sediments. Recession rates are based on measured crest retreat whfle wave energy values are derived through computation. Corredation and regression tests suggest that the total effect of redatively frequent storms of moderate intensity is morphological”! more signhficant than that of rare,lfigh energy events. lmproved results may be possible with refinements in the experimental design. To my brothers Ted and Eric who have always challenged and inspired me. ii ACKNOWLEDGMENTS This study would have been impossible without the selfless contributions of several people. I am humbly grateful and indebted to those who invested their time and experience in this endeavor; I am enriched academically, professionally, and personally. Lieutenant Colonel Thomas E. Farewell made me look toward the future and personally insured that I had the opportunity to pursue a Master’s degree. Without his assistance 1 may never have come to graduate school. I am truly grateful to Professor Harold A. Winters whose personal interest, uncompromising standards, and complete dedication elevated my experience at Michigan State University above the classroom. Dr. Winters challenged me academically and packed more teaching, field work, and valuable experiences into two years than I thought possible. I am honored to have worked for Dr. Winters who spares nothing in teaching his students. I am also grateful to his wife Marjorie for her terrific sense of humor, gracious hospitality, and expert editing of the final manuscript. 1 thank Professor Jay R. Harman and Colonel William Reynolds for carefully reading and improving the thesis and their help throughout this study. Mr. Thomas Nuttle of the Detroit District, U.S. Army Corps of Engineers fostered my interest in Coastal Engineering, opened his files and office for assistance, recommended the Coastal Engineering Course, and invited me along iii on field studies. This investigation could not have been compdeted without his assistance. My very special thanks to Dr. Timothy Antaya who patiently taught me how to understand science and research. His help was invaluable in making field measurements, verifying numerical procedures, and calming frayed nerves when the whole project seemed impossible. Tim and his wife Ann helped in more ways than I can express and I am indebted more than I can possibh/ repay. Finally, I thank my loving wife Kathi, her support and encouragement never faiL She is always there and I could not have done this without her. iv Chapter 1 Chapter 2 Chapter 3 Chapter 4 cm LITERATURE REVIEW,OBJECTIVES,AND METHODS Introduction Literature Review Objectives and Hypothesis Study Area General Criteria The General Land Office Surveys The Buckler Study The Section 111 Studies Site Selection Criteria Measurement Procedures Wave energy Estimation SHOREZONE CHARACTERISTICS AND COASTAL PROCESSES Introduction Terminology Shorezone Characteristics Beaches Longshore Bars Bathymetry Lake Level Fluctuations Waves Littoral Transport Storms Ice Summary DATA AND ANALYSIS RESULTS Introduction Recession Rates Wave Energy Analysis Summary DISCUSSION, SUGGESTIONS FOR FUTURE RESEARCH, AND CONCLUSION Introduction Discussion Suggestions for Future Research Conclusion 11 12 12 13 14 14 17 18 20 24 24 25 26 28 29 31 31 35 39 44 46 48 49 49 51 55 59 61 62 62 63 69 71 GLOSSARY OF TERMS APPENDIX A Site Locations and Measurement Data Recession Rates Spring Wave Data Fall Wave Data Hindcast, Site Locations, and Nearshore Slope APPENDIX B List of Wave Variables and Equations LIST OF REFERENCES vi 72 85 85 87 88 89 90 91 91 94 Figure 10 11 12 13 14 LIST OF FIGURES Subject Study areas and site locations. Section 111 project locations. Locations of grid points for two- dimension deep water wave spectra. Location map for the Great Lakes. Visual definition of terms describing a typical beach profile. Map showing variations in surficial formations along the east shore of Lake Michigan. From Davis 1976. Longshore bar profile under rising lake level. From Hands 1980. Long term average annual water levels of Lake Michigan. Wave characteristics and direction of water particle movement. From the Shore Protection Manual. Schematic diagram of waves in the breaker zone. From the Shore Protection Manual. Schematic diagram of offshore transport by storm wave attack on beach and dune From the Shore Protection Manual. Rapid accretion of ridge-and-runnel at Lake Michigan (Holland, Michigan). From the Shore Protection Manual. Direction of net longshore transport along the eastern shore of Lake Michigan. Not all sources are in agreement. From Hands 1980. Percentage of ice cover on Lake Michigan. vii Page 15 16 22 24 25 27 30 33 36 38 4O 41 43 46 15 16 17 18 19 20 21 A flow diagram for analyzing the relationship between bluff recession and wave energy. Statistical and geographic distribution of bluff recession rates. Site number 2. Site number 18. Site number 21. Locations of hindcast points and observation sites. Work accomplished by spring waves at site number 18. viii 50 52 53 54 54 57 67 Table LIST OF TABLES Subject Wave energies. Pearson product-moment correlation coefficients analyzing long term annual recession rates with storm wave energies for various return periods. Linear regression results; predic- ting long term annual recession rate with mean energy flux for various return periods. Site locations and measurement data. Recession rates. Spring wave data. Fall wave data. Hindcast and site locations/ nearshore slope. ix Page 57 58 59 85 87 88 89 90 Chapter 1 LITERATURE REVIEW, OBJECTIVES, AND METHODS Introduction Landowners spend millions of dollars annually to preserve lake front property. Even so, in 1986 record high levels on Lake Michigan brought high erosion rates and staggering economic losses. In response, Michigan allocated $12 million in low interest loans and community grants to aid areas of severe erosion in seventeen counties. During March, 104 applications were made to the Emergency Home Moving Program; sixty-three houses had already been certified ”in imminent danger.” By April an estimated 800 homes were within 20 feet of the waterline. Such threats to property and resulting high expenditures by the private sector and government agencies justify research to better understand coastal erosion. The interaction of physical factors involving erosion along Lake Michigan’s coastline is complex and not fully understood. The purpose of this study is to examine the relationship between long-term bluff erosion, storm intensity, and nearshore wave energy. Comparing the energy associated with severe fall and spring storm waves with long-term recession rates may help reveal and define interrelationships between these two factors. Literature Review The Lake Michigan coastline has interested investigators and authors since the late 18005 (Andrews 1870; Brater n.d.; Buckler 1981; Powers 1958). Numerous scientists have studied many different aspects of coastal processes. Recent research and publications on Great Lakes’ shorezones demonstrate continuing interest in coastal phenomena, especially those contributing to erosion. A variety of investigations reflects the complexity of the shoreline. Some observers have inventoried and described subaerial, physical attributes and geomorphic processes (Birkemeier 1981; Brater and Seibel 1973; Buckler 1973a, 1981; Buckler and Winters 1983; Davis 1976; Davis, Fingleton, and Pritchett 1975; Gilbert 1985; Powers 1958). Others have studied the subaqueous, nearshore environment with most concentrating on the formation and behavior of longshore bars (Hands 1976, 1980; Orme 1985). A sediment or volumetric balance is commonly considered in engineering-oriented studies (Davis n.d.; Hands 1980, 1981, 1984; U.S. Army Corps of Engineers 1986a, b, c, d, e). Other engineering studies focus on the structural protection of shorezones (U.S. Army Corps of Engineers 1984; 1986a, b, c, d, e). The use of vegetation as an inexpensive, natural means of erosion abatement is discussed by Clemens (1977) and Hall and Ludwig (1975). Wave energy is considered a key factor in coastal zone modification. To better understand their climate and distribution, Liu (1970) and Liu and Housley (1970) presented some qualitative characteristics of waves from visual observations. Resio and Vincent (1976) rendered wave data based on a numerical hindcast model simulating storm-generated waves of varying intensity. Allender et al. (1981) and Paddock and Ditmars (1981) developed and tested numerical methods for modeling nearshore circulation and sediment transport. The advent of more advanced computer techniques has fostered interest in modeling the coastal environment numerically to simulate storm waves and evaluate designs that may mitigate coastal erosion (Allender et al. 1981; Allsop, Franco, and Hawks 1985; Paddock and Ditmars 1981). Powers (1958) conducted a comprehensive study of Lake Michigan’s shorezone in order to group coastal terrains based on type and association. He also determined some long-term recession rates by remeasuring distances coincident with section lines established by the original land survey conducted between 1820 and 1860. Powers resurveyed 134 section line locations; 23 of these are incorporated into this study. Seven of Powers’s points were reexamined in 1973 (Buckler 1973). During 1976 and 1977 many more were resurveyed (Buckler 1981; Buckler and Winters 1983) to examine the relationship between differential recession rates and selected physiographic characteristics. Buckler hypothesized that recession on the eastern shore exceeded that on the western shore--attributable 4 to prevailing westerly winds and predominant easterly cyclonic passage. But he was unable to explain differential recession rates based on physical attributes; further, he found recession rates to be slightly greater along southern shores when compared to northern shores and relatively similar on both the east and west sides of the lake. Both Powers (1958) and Buckler (1981) include a summary of studies conducted as early as 1847. A recent study of Thompson Island, Boston Harbor, Massachusetts (Jones, Fisher, and Reigler 1985) is similar to Buckler’s investigations. Thompson Island, which is composed of unconsolidated Quaternary sediments (as is much of the Lake Michigan coast), was studied specifically to establish the relationship between beach erosion and seacliff recession considering various geologic and environmental factors. Jones, Fisher, and Reigler found that coarser-grained cliffs receded faster than finer-grained cliffs whereas Buckler (1981) and Buckler and Winters (1983) were unable to confirm a relationship between sediment size and bluff recession. The assertion that beaches oriented north and east would recede faster, because they are exposed to greater storm energy (similar to Buckler’s hypothesis that the east shore receded faster than the westL could not be substantiated by Jones, Fisher, and Reigler. Buckler’s observation of higher recession rates toward the south may support speculation by Hands (1978a, 1978b) that accelerated southern shoreline retreat in Lake Michigan could be attributable to apparent coastal subsidence. This subsidence is actually submergence resulting from a continuing crustal rebound 5 of the Lake Michigan basin, which began near the end of Pleistocene glaciation. Hands demonstrated with geodetic survey and lake level data that the northern portion of the basin is rebounding faster than the southern region, effecting an emerging coastline in the north and a submerging coastline in the south. Hands (1976, 1980, 1981, 1984) further investigated the consequences of submerging coastlines using fluctuating levels on Lake Michigan as a surrogate to rising sea level conditions. Longshore bars were shown to migrate landward while maintaining constant depths beneath the gradually rising lake surface (Hands 1980). Testing and refinement of the Brunn rule led to development of sediment and volumetric balance procedures (Hands 1980, 1981, 1984). That is, a rise in mean surface elevation tends to shift the equilibrium profile landward. Eroded material from the upper beach supplies materials to build up the lower profile (beneath the water level). The method predicts long-term profile adjustments under rising level conditions based on an empirically verified model. A recent investigation of longshore bars by Orme (1985) demonstrated the existence of stationary and nonstationary longshore bars on the Ventura, California, coast. Orme indicated that stationary bars are strongly associated with the breaker zone, the location of which in turn reflects wave steepness, nearshore slope, and tidal stage. Nonstationary bars are generally asymmetric and move landward over several days to a few weeks before they are destroyed by a changing wave climate 6 or accumulating sediment to the point of instability. A number of investigations were conducted in the early to middle 19705 during a period of unusually high lake levels (Birkemeier 1981; Brater n.d.; Brater and Seibel 1973; Brater, Armstrong, and McGill 1975; Davis 1976; Davis, Fingleton, and Pritchett 1975). These studies all incorporate an engineering approach that evaluated the relationship between several factors influencing erosion. Attributes commonly analyzed were lake level fluctuation, storm frequency, sediment trans- port/littoral drift, protective structures, slope stability, and grain size. 'The studies, up to three years in length, varied in duration and involved up to seventeen sites along the eastern shore of Lake Michigan. Most of the reports have similar findings. Recession rates are proven to vary at different locations along the coast but are apparently unrelated to bluff height or composition although bluffs with a high clay content are generally thought to be more cohesive and able to support steeper slopes (Brater and Seibel 1973). Clemens (1977) and Hall and Ludwig (1975) reported on the use of vegetation to moderate shore erosion. They concluded that vegetation alone would not protect against wave-induced erosion. Vegetation is best used on barren areas to stabflize unconsour dated soils by reducing surface runoff and destructive aeolian processes. High lake levels decrease beach widths and allow wave action to reach the base of bduffs and dunes, thereby accelerating erosion rates. Some investigators speculate about the 7 relationship between erosion rates and various factors influencing wave energy; however, they present no quantitative evidence to support their claims. The interrelationship of varying fetch distances and depths with shore juxtaposition to storm wave climate and cyclonic movement across Lake Michigan is also discussed empirically in some studies. There is abundant evidence linking the most damaging erosion events with high energy storms, but not mean wave activity. Much has been written on both wave and storm characteris- tics and their combined effect on the Great Lakes shorezone (Birkemeier 1981; Brater and Seibel 1973; Buckler 1981; Buckler and Winters 1983; Davis 1976; Davis, Fingleton, and Pritchett 1975; Gilbert 1986; Hands 1976, 1980; Powers 1958). There is a general consensus that major erosion events are produced by high energy storms, as well as an acknowledged relationship between high water elevations and accelerated erosion rates. Wave properties are even more dynamic than the shoreline conditions, but they are more difficult to measure and observe quantita- tively. Liu (1970) and Liu and Housley (1970) presented a summary of visual wave observations for Lake Michigan compiled during two consecutive autumns in 1966-1967 and one autumn in 1965, respectively. They observed greater wave heights along the northern shore and longer wave periods to the south. At the time of his study, Liu (1970) noted that theoretical models showed little quantitative agreement with observed waves. 8 andcastz’ng is a means of calculating past wave characteristics using historic synoptic wind charts. In 1976 Resio and Vincent hindcasted wave information for 64 points along the Lake Michigan shoreline. To do this, they used a model developed primarily by Barnett at the Scripps Institute of Oceanography which uses a theoretical representation of energy transfer mechanisms to compute energy spectra at grid points. The Resio and Vincent model yields significant wave heights and periods for severe storms with probable return periods of 5, 10, 20, 50, and 100 years. Their model further subdivides the information for spring, summer, fall, and winter storms. More recently, Paddock and Ditmars (1981) and Allender et al. (1981) developed and tested numerical models to evaluate nearshore coastal processes. In general, they conclude that the nearshore wave environment is hydraulically complex and further complicated by longshore bars. Although numerically feasible, the Paddock and Ditmars (1981) model is constrained by an enormous computer requirement which makes it impractical to simulate more than a few minutes of activity. The model developed by Allender et al. (1981) seems to underestimate wave height decay within the breaker zone which is believed attributable to inadequate representation of wave behavior in the region of bar-trough topography. The Michigan Department of Natural Resources has classified the Michigan shoreline as either high risk erosion areas, flood risk areas, or environmentally sensitive areas (Michigan Division of Land Resource Programs 1982). Classification of high risk 9 erosion areas is accomplished by comparing historic and recent aerial photos and extensive field survey. Areas are designated as high risk if their average, long-term recession rate (determined photogrametrically over a period of twenty to forty years) exceeds 1 foot per year. High risk erosion areas are then subject to management and zoning, emphasizing a nonstructu- ral approach. The program is primarily an administrative policy which requires set back distances, from the bluff line, to protect new construction or improvements to existing structures. The U.S. Army Corps of Engineers maintains several harbor structures along the eastern shore of Lake Michigan. Section 111 of the River and Harbor Act of 1968 authorizes the investigation and construction of projects to prevent or mitigate shore damages resulting from federal navigation works (Larson 1981). Under the provisions of Section 111, the Detroit District (U.S. Army Corps of Engineers) monitors shorezone reaches north and south of their harbor projects to evaluate ongoing beach nourishment efforts designed to moderate erosion induced by structural blockage of littoral drift (Larson 1981; U.S. Army Corps of Engineers 1986a, b, c, d, e). Their reports address the extent of coast affected by harbor jetties, present volume balance estimates, percentage of total coastal erosion directly attributable to Corps-administered works, and an appraisal of beach nourishment effectiveness. In summary, these references confirm the complex nature of shorezone interactions and erosion. More specifically, these studies recognize the influence of several factors contributing 10 to different recession rates including nearshore topography, storm frequency and intensity, vegetation, structures, lake level, and wave climate. The relationship between available wave energy and rates of bluff recession has often been asserted but seldom investigated in detail. It is possible that heterogeneous wave energies may account for different bluff recession rates, and that is the focus of this study. If so, this relationship could be useful in further understanding the dynamics of coastal morphology and guiding future shorezone management decisions. 11 Objectives and Hypothesis The objectives of this study are 1. To reexamine sites previously used to determine long-term bluff recession (Powers 1958; Buckler 1981) that coincide with shore reaches monitored annually by aerial photography (U.S. Army Corps of Engineers 1986a, b, c, d, e). And to update long-term bluff recession rates for selected sites along the eastern shore of Lake Michigan, from St. Joseph to White Lake, Michigan. 2. To examine the hypothesis that recession rates at those sites are positively related to nearshore wave energy associated with storm events. The hypothesis is a deduction based on the following observations: (a) Shorezone erosion is frequently attributed to wave action during high energy fall and spring cyclonic storms (Brater and Seibel 1973; Birkemeier 1981; Davis, Fingleton, and Pritchett 1975; Hands 1980). (b) Bluff recession rates vary at different locations along the coast but are apparently not related primarily to shore composition or physiography (Buckler 1981; Buckler and Winters 1983). (c) Because development of deep water waves depends on wind velocity and duration combined with fetch and depth, the wave energy varies at different locations along the shore (Resio and Vincent 1976). Therefore, it is possible that nearshore attenuation of deep water wave energy may partially explain differential bluff recession rates. 12 Study Area The study area encompasses a portion of shoreline along the west coast of southern Michigan between St. Joseph, in the south, to White Lake, in the north (Figure 1). The shorezone consists of unconsolidated Quaternary sediments. General Criteria The intersection of some U.S. Public Land Survey section lines with the Lake Michigan bluff line provides a means for determining long-term bluff recession. A record of the distance between bluff crest and the nearest section corner is contained in the original General Land Office (GLO) survey notes (1827-1852). By comparing the distance established in the GLO survey with a recently measured distance, over the same transect, long-term recession rates can be calculated. Furthermore, several of these sites were resurveyed within the last thirty years by both Powers (1958) and Buckler (1981), providing an opportunity to determine short-term recession data. Deep water wave heights and periods are given for similar locations along the Lake Michigan coast by Resio and Vincent (1976) (Figure 3 and Appendix A, Tables 6 and 7). The data are numerically generated and tabulated for seasonal wave values associated with storms of 5, 10, 20, 50, and 100 year return periods. Breaking wave energies are calculated with solitary and linear wave theories using data from the Resio / Vincent model. 13 The two data sets, long-term bluff recession and nearshore wave energy, can be compared statistically. The amount of variance in recession rates accounted for by storm intensity wave energy can be discerned with correlation and regression testing. The General LandjOfficg Surveys The first governmental surveys of Michigan, conducted between 1827 and 1852 by the General Land Office (GLO), may constitute the oldest, reliable, quantitative record for the Lake Michigan shoreline. Consistent with the U.S. Public Land Survey system, Michigan is divided into townships, generally 36 miles square and 6 miles on a side. Each township is further subdivided into 36 sections, 1 mile on each side. The Michigan meridian, or principal meridian, is located approximately 6 miles east of East Lansing, Michigan and provides one basis for surveying boundaries of townships and extending the grid system to the Lake Michigan shore. The partitioning ends at the last full section or quarter section grid adjacent to the lake. The remaining distance from the last section corner (or quarter corner) to the ”meander line” is recorded in the GLO notes. Powers (1958, p. 89-90) observes, ”the ’meander line’ was never precisely defined, but clearly it was seldom, if ever, identified as the water line. In many cases the measurements were obviously made to some point at or near the edge of the bluff, where present.” Measurements of questionable accuracy were 14 eliminated by both Powers and Buckler to maximize reliability. This study utilized data from sites where successive surveys were judged to be precise and correct. The Buckler Study Buckler (1981) reexamined Michigan sections, in the original GLO survey, searching for remeasurable township lines that intersected shorezone bluffs. Buckler refined the data by eliminating sites that did not meet this criterion as well as those with a ”questionable relationship between the meander line and the bluff crest” (Buckler 1981, p. 6). Buckler’s work identifies numerous sites in Michigan suitable for studying long-term bluff recession. The Section 111 Studies The U.S. Army Corps of Engineers, in compliance with Section 111 of the River and Harbor Act of 1968, monitors nearshore processes in the vicinity of their Lake Michigan harbor structures (Figure 2). Annual measurements include bathymetric soundings and observations from current aerial photographs. Several sites identified in Buckler’s work are also covered by this aerial photography, which extends several miles north and south of each harbor project. This circumstance makes it possible to observe annual changes at some sites where long-term recession rates are known. 15 is. V'\."-.\_ “)5 x .A f ‘v Study Area and Site Locations ) \4 L on . .. .. ‘ s all!“ Q g I S north 1" 5 Big Sable Point ' Ludington Sheboygan 2 2 Little Sable Point 2 e White Lake 21 ' Muskegon WISCONSIN 2' 19 Grand Haven 1 : 17 0 Holland 16 1 ~—--—--—-- 14 eSouth Haven 13 12 7:— Benton Harbor 1‘ StJoseph 'LL'NO'S ‘ MICHIGAN 7 ______ ,___- .._. 6 -- '5 ' ‘ INDIANA ! 3 i 2 l Figure 1. Study areas and site locations. 165 T“ -\‘.\_\ "\ I I1. ’- muss north WISCONSIN ILLINOIS ba——-.—- Section 111 Projects in the Study Area \I C? 5‘ I s 1‘? 3 e White Lake Grand Haven 0 Holland eSouth Haven .Stdoseph MICHIGAN -——--—--—"—--—-1 INDIANA Figure 2. Section 111 project locations. 17 Site Selection Criteria Twenty sites from Buckler’s 1981 study are in the area monitored by the Corps of Engineers, and all but one are included in this study. The one site (M-38) was eliminated because of its isolated northern location several miles from the other 19 sites clustered south of Little Sable point. In addition, sites M-11 to M-14 previously measured by Powers (1958) and Buckler (1981) were added to provide a continuity of sampling points between St. Joseph and White Lake, even though they are not within the area of Corps of Engineers aerial photographs. Each of these sites represents the intersection of a section line with a shorezone bluff known to have experienced recession. Bluff definition and measurement are described by Buckler (1981, p. 5): A bluff is defined as a lakeward-facing steep bank or sharp slope composed of unconsolidated material landward of the shoreline. Bluff crests provide reliable standardized lines to which measurements can be made. Water lines are less acceptable because the surface altitude of Lake Michigan fluctuates to a considerable degree. Measurements of bluff change refer to the landward displacement or lakeward accretion of the top edge of the bluffs. It should be recognized, however, that changes may take place on the bluff slope that do not necessarily affect the position of the crest. With only one exception, none of the sites are directly fronted by a protective structure. The protected site, M-2, has been fortified with heavy rock armor at the water line. The long-term recession value used for M-2 was calculated by Buckler (1981) prior to placement of the revetment. 18 Measurement Procedures Except for locations M-11 to M-14, which were examined in the field using standard surveying techniques, distances at sites M-2 to M-23 were measured from photographs taken in April 1986. Sites M-24, M-28, and M-29 were examined from photography dated April 1985. All aerial photographs were obtained from the Detroit District, U.S. Army Corps of Engineers and have an unrectified approximate scale of 1:6,000. The true scale of each photograph was calculated by determining the distance between two points of known separation. By comparing the actual ground distance between the points to the length measured on the photograph, the scale can be determined. The location of section and quarter corners is revealed by the intersection of certaholinear cultural features and/or boundary markers. This procedure is consistent with techniques described by Powers (1958, p. 90): In no case was an original corner or quarter post recovered, but the position of long established fence lines and other boundary indications checked closely with the chained distances given in the original survey. It is believed that most if not all points of origin used for remeasurement were correct to within 3 to 5 feet of their true position. And followed by Buckler (1981, p. 7): In a few cases where records were lacking and field monuments could not be found it was possible to determine section corner locations by fence and road patterns fairly accurately (within three to five feet). Where the corner or quarter corner was not obvious, an intermediate landmark was used. In several cases the remaining 19 distance between a road intersection to the corner of interest had already been measured either by Buckler or registered land surveyors. Summing the measures to the intervening control point yielded the total distance of interest. The estimated accuracy of identifying points of origin on the aerial photography, under magnification, is .01 inch; at a scale of 1:6,000 this translates to a possible ground error of 5 feet. The distance from most section corners or quarter corners to the bluff crest was then measured along the section line, which is often easily identifiable as a fence row or road center line. Where there were no linear features marking the section line, measurement was made due west to the bluff line. The bluff crest is defined as ”the point or line of abrupt change in slope at the top of the bluff” (Buckler 1981, p. 143). Stereopairs of aerial photographs were used to identify the location of the bluff crest along selected section lines. At places where the crest is notched by human disturbance, projecting an imaginary line connecting the bluff edge on either side of the site inferred the natural position of the crest. Distance on the aerial photography was measured with a TEKTRONIX 4956 digital graphics tablet to 0.005 inch (manufactur- ers specified resolution). Each length was measured three times; an average of the three measurements constituted the accepted value. Assuming the final value is accurately measured to 0.005 inch, the error on a 1:6,000 scale photograph is plus or minus 2.5 foot. 20 To establish a control for photo-interpretation accuracy, 20% of the sites were also measured in the field using the same criteria. Distance was measured with a 100 foot steel tape and surveyor’s compass utilizing standard surveying procedures as described by Kissam (1971). Comparing the ground measured distance to that calculated from the aerial photographs yields an accuracy within 1.2% or an average of eight feet. Wave Energy Estimation Deep water wave data are given by Resio and Vincent (1976) from a model designed to calculate significant wave heights and periods for waves generated by synaptic-scale systems, such as extratropical storms. Significant wave height is defined as ”the average of the one-third highest waves in an observation period and was intended to correspond to that wave height estimated visually by an observer.” Deep water refers to the depth that waves are unconstrained by frictional lake bottom influence usually defined as one-half the deep water wave length (L./2). The accuracy of waves projected by the model is described by Resio and Vincent (1976, p. 32): The agreement between hindcast wave maxima and observed wave maxima for cases involving fetches over 20 miles and for wave propagation toward shore was extremely good. All the hindcast maxima were within 1.5 feet of observed maxima. The root-mean-square error in estimating peak wave heights for this set of conditions is about 1 foot. Resio and Vincent provide wave statistics at 64 locations on Lake Michigan (Figure 3). Points 16 through 26 areused in 21 this study. Values for specific study sites, between points where wave data are given, are calculated by linear interpola- tion. Fall and spring values for waves approaching obliquely and parallel to the shore are considered in this study. Periods associated with the wave heights are given as the average across all possible angles (of incidence to the shore) that correspond to the particular wave height (Sam Corson 1986, personal communication). Breaking wave height (H.) and mean energy flux are calculated using the computer program SINWAVES (MACE-11) for linear wave theory predictions (U.S. Army Corps of Engineers 1985). The program applies Snell’s law of refraction (U.S. Army Corps of Engineers 1984, p. 2-64) to calculate the refraction coefficient, assuming straight and parallel bottom contours. This assumption is a good approximation of the nearshore bathymetry throughout the study area and is consistent with procedures used in recent Section 111 studies (U.S. Army Corps of Engineers 1986a, b, c, d, e). Wavelengths are evaluated at different depths using a subroutine that solves the linear dispersion equation by iteration. Breaking height and depth are also determined by iteration using equations 2-92, 2-93, and 2-94 (a modified solitary wave theory) from the Shore Protection Manual (U.S. Army Corps of Engineers 1984, p. 2-130) and the above mentioned wavelength subroutine. This process assumes that linear wave theory applies up to the point of breaking (U.S. Army Corps of Engineers 1985). $222 Wave Hindcast Data Locations 0 o I. o 8 \0 ISI 62 63 64 ° g; so» ‘F e .7 2o! 0 SS 56 0‘ ‘3 r 55‘ . o 53 5‘ 052 .5 0 SI 7 . j . 5° 8 e E? 0 I l0 0 47 9 l O 1 Q - 3 12 0 46 e 045 13. O 4‘ Lu 1‘ . O ‘3 § 15 . —J ‘42 16 0 4I 17 0.10 Ia '39 19 e 38 2, HINDCAST POINTS 16 TO 26 e 37 2‘ USED IN THIS STUDY 0 36 22 o 35 23 '3‘ 24 O 33 25 ' 32 26 27 O 0 3i 0 mm 30 29 28 ° . . 0 25 30 mules Figure 3. Locations of grid points for tvo-dinenslonal deep water vave spectra. Froe Resio and Vincent 1976. 23 Estimating nearshore wave energy requires an approximation of shorezone bathymetric slope in addition to values for deep water wave height and period. ‘The nearshore slope is estimated on the basis of data from the U.S. Army Corps of Engineers, Section 111 studies and information from certain 7.5 minute U.S. Geological Survey topographic maps. Detailed bathymetric surveys are conducted annually as part of the Section 111 studies. Transects run orthogonally from the shoreline and record bottom variations at 1 foot intervals to a depth of 30 feet. Slope is calculated using elevation values from the shore and the 30-foot depth. 1Tus procedure,1flfich normauzes nearshore topography, he necessary because the SINWAVES program cannot accommodate wave behavior in the longshore bar complex. At study sites where Section 111 survey data are unavailable, the slopes are estimated from U.S. Geological Survey, 7.5 minute topographic maps which record contour intervals to the 30-foot depth. Chapter 2 SHOREZONE CHARACTERISTICS AND COASTAL PROCESSES Introduction Lakes, Lake Michigan is second only to Lake Of the Great It is the third Superior in water volume -- 1,181 cubic miles. Lakes in terms of surface area, 22,300 the Great largest of lake’s maximum square miles, and mean depth of 279 feet. The 118-mile width spans 3° of longitude from 85° west to 88° west. of latitude from not It is 306 miles long, spanning about 4° 42° north to 46° north. At this latitude Lake Michigan is quite storms that in the westerly wind belt and subject to wave action along its 1,362-mile coast. cyclonic may generate vigorous <0 <3 <2 ::3 .5 ' s / z a \ s e 5 ‘8: 0 7’ 30 jg \f\ Lu :: I< \ .4 ‘20 105 90 75 {:} -._--_...!_.____ norlh i Q___EP mIles Figure 4. Location lap for the Great Lakes. 24 25 Varying precipitation and evaporation rates impart both seasonal and annual lake-level fluctuations. Coastal erosion is generally most severe during periods of high lake levels when the beaches are narrow or nonexistent. Under these circumstances, the unconsolidated, Quaternary sediments that comprise the shorezone may be eroded directly by storm waves. Terminology Terminology used in this study is defined in the glossary of terms and graphically represented in Figure 5. Coastal area Shorezone Nearshore zone )1 Coast Beach or shore (defines area of nearshore currents) Backshore Foreshore Inihore or Shoretace VOIIshore L—BIU" crest 8:; ch (extends through breaker zone) face or escarpment /"-Berms Beach scarp’ Breakers _ High water level Ordinary low water level Plunge point/“I Bottom Typical Beach Profile Figure 5. Visual definition of terns describing a typical beach profile. 26 Shorezone Characteristics The shorezone in the study area is composed entirely of low to high banks of unconsolidated Quaternary sediments. Bedrock is not exposed anywhere in the study area. Sediments are primarily glacial drift, eolian sand, and postglacial lacustrine and stream deposits. Several investigators have discussed the relation of this material to erosion rates (Birkemeier 1981; Brater and Seibel 1973; Buckler 1973a, 1981; Buckler and Winters 1983; Davis 1976; Hall and Ludwig 1975; among others). In some areas, the bluffs are composed of one sediment type, while in others there may be an intricate mosaic of interbedded, stratigraphic layers. At some places a combination of permeable glacial-fluvial sediments comingled with relatively impermeable till or lacustrine clays forms perched water tables and affects ground water flow, possibly causing seepage on the bluff face. Dune topography varies from that of low relief to heights exceeding 150 feet. Dunal tracts may be a mile in width and extend several miles along the coast. Elsewhere, bluffs constructed of cohesive till stand very steeply over of 100 feet high. 27 Surface Geology along the East Shore of Lake Michigan nonh 0 25 50 - .1" mlles - 5:3?” Big Sable Point ":Ltldington , ‘3 2 5% Little Sable Point :5 g. 5 I33! White Lake 3 E - y ‘9 Holland g“? Surface Geology WISCONSIN 9: South - Moralnes Haven - Till plains ILLINOIS j / enton HarborD Outwash 153 St. Jose h p . gLake beds and dunes J MICHIGAN INDIANA LAKE —-—- Hap shoving variations in surficial {creations along the east shore of Lake flichigan Figure 6. After Davis 1976. 28 We The character of Lake Michigan beaches is highly variable and subject to several influences including wave climate, lake level, littoral drift, and shorezone physiography. Furthermore, and especially during times of low lake level, wide, sandy beaches contribute fine-grained eolian material to the landward shorezone. Fore dunes may develop from ordinary beach sediments or ephemeral sand bars that are successively pushed ashore to accrete on the beach (Davis 1976; Gilbert 1986; Hands 1984). Conversely, when lake levels are high, beaches are narrow or even absent, limiting the supply of eolian sand. Beaches react in basically two modes to wave motion: a response to typical waves and in adjustment to storm conditions. Under normal circumstances, wave energy dissipates largely along and across the beach. In some cases, generally in the summer, an ephemeral bar may form close to shore and migrate onto the beach to become part of the beach; this seems to provide limited protection to the backshore during future storms. HWXES, however, may evoke extraordinary changes. These large waves reach farther into the backshore, and their correspondinglyh higher energycanflmovefl larger-sized particles [byhboth traction and suspension. Storms may also increase the capacity of the littoral current to transport more sediment because higher waves widen the transport zone offshore. Consequently, during severe storms, large sections of 29 heat?“ 329-311.039991be lashioln timeoths .beacmmay .reeeveri.__eut usually not without permanentmbluff recession. -—— __. ~o. Longshore Bars Longshore bars are a sequence of submerged offshore sand ridges, parallel to the strand line, in the nearshore zone. The there may be as many as five in places. Numerous investigators have reported on longshore bars (Allender et al. 1981; Davis, Fingleton, and Pritchett 1975; Gilbert 1986; Hands 1976, 1978b, 1980, 1984; Orme 1985; among others). According to the U.S. Army Corps of Engineers (1986a), In areas where there is a supply of transferable material, the existence of well developed longshore bars* is an indicator of sediment available for movement in the nearshore transport system. The absence of such bars generally indicates a disequili- brium and a nearshore sediment deficit. Hands (1984) showed that when lake levels are rising, the entire bar complex migrates toward shore while maintaining constant depths beneath the lake surface. The bars seem to be stable during storms, although Davis (1976) believes that they may be modified by high amplitude waves during the storm and return to equilibrium, with no apparent changes, as the storm subsides. Wave dynamics in this zone are extremely complex and little understood-~linear wave theory is not applicable in the ridge and runnel topography. During storms, waves break on all bars in a multiple bar system, the largest waves breaking on the deepest bar and progressively smaller breakers occurring on the [levellon (In) IGLD 30 inner bars. The waves which finally reach the shoreline are thus reduced in size. When smaller waves prevail, they pass over the deep bars and do not break until they reach the shallow water over the inner bar (Komar 1976). Station 20 7 ‘3. '9’5 ----- 26 In 059 — fi—rfi’TfrTYYTY‘Y" ‘ 1 1 1 1 I L l 4 1 1 4 A 1 1 A l 1 1 1 l 1 J 1 1 '00 (OD 300 ‘00 500 600 ’00 (IOU 90’.) LOGO IJUO I300 L300 LCW '.590 “.00 Dislonce tIom Bose Line In) E O r- Figure 7. Longshore bar profile under rising lake level. Frol Hands 1980. 31 Bathymetry Lake Michigan can be divided into four bathymetric regions: a southern, central, and northeastern basin, and Green Bay. The study area is along the eastern edge of the southern basin, which extends from the southern shore to a rise that crosses beneath the lake between Sheboygan, Wisconsin and Ludington, Michigan. This ridge is thought to be one or more submerged moraines of the Lake Michigan glacial lobe (Powers 1958). The deepest part of the southern basin is mid-lake, west of Holland, Michigan, where the maximum depth ranges from 490 to 650 feet. Water depths gradually decrease along relatively smooth bottom profiles shoreward of the mid-basin area. Bathymetry is a relatively important dimension when considering erosion. Basin topography and shoreline geometry govern wave development, by limiting depth and fetch, and are also linked to ice formation and break up. Lake Level Fluctuations The level of Lake Michigan is always changing; fluctuations may be measured in hours, seasons, decades, or in terms of geologic time. Lake Michigan’s elevation vacillates because of natural forces. Variation in lake level is the product of several factors and is manifested in three noticeable regimes superimposed on one another. Short-term fluctuations are H _ “ _ u .- ----- ~..—.—~ ‘ F....._. 1,... '— “-— 32 attributable to meteorological phenomena, and not volumetric change. Contrasting barometric pressures over different lake locations or strong winds can, in effect, tilt the lake surface, causing locally higher levels in one area and correspondingly lower levels simultaneously elsewhere. Annual variations on the order of 1.1 feet are predictably cyclic. Changes in precipitation, evaporation, andmruwnoff raise Lake Michigan _. to a yearlygwhigh about,,July or August; and subseque’ntlowl around Decembermor_99993rx1 Longer-term Holocene fluctuations are the major concern of coastal inhabitants. Since lake level monitoring began around the middle 18005, Lake ~Michigan has variedk_nealrl4ym16_Afeet_ in elevation (Figure 8). , This is particularly significantwsince a iffootr‘ise in elevation can decrease beach width, by anaverage 201feet. Longer-term variations largely reflect climatic trends in precipitation throughout the Lake Michigan/Huron drainage basin over several years (Buckler 1973b; Harris 1986). Lake Michigan and Lake Huron are hydraulically a single unit. A deep, wide channel at the Straits of Mackinac connects the two. Levels of the entire Great Lakes system remain predominantly self- regulated despite artificial outlets and diversions. ”Under natural outlet conditions, the lake’s levels and outflows adjust continually to maintain a balance between the quantity of water supplied to it and the quantity of water leaving it” (Harris 1986). Lake Level (feet) 5K3 LAKE LEVELS 1900-1986 seo - I“ II. '1 i\‘~ i I / ff. {\1‘ "i I \ I I A, I 579* i I. ,II II II I] Hi! ”i \‘I' I I. II ,N‘\ I l !' ‘1’ I iiU ‘\. l1 i' 1.! a '1 1 57a »- '1' I. j I I II \ H / ' I A ' H I l / \. . I. A! If I = an r I! l I: i. I I . . I ' g = . \le \'.f' I! 576 l— \./ I?! 1900 1910 1920 1930 1940 1950 1960 1970 1980 Years —--- Leke Level Aver-eye Level Figure 8. Long-tern average annual vater levels of Lake Michigan. 34 In the context of geologic time, there has been considerable fluctuation in the level of Lake Michigan. Largely a result of Pleistocene glacial events, the most common evidence of former lake stages is sand or gravel beach deposits, similar to beaches of the present Lake Michigan but lying inland from them at a higher altitude (Hough 1958). At least 12 stages of Lake Michigan have been proposed with elevations ranging from 230 to 640 feet above sea level. , . ._ ._._ a.» __.‘..-4——~‘—._.. .i.-—.—- hig‘hfllake levelsand accelerated erosion rates (Birkemeier 1981; ,. 1 7-,” “I 5.", Brater and Seibel 1973; Brater, Armstrong, and McGill 1975; Davis 1976; Davis, Fingleton, and Pritchett 1975; Hall and Ludwig 1975; Hands 1981, 1984; among others). Although high‘lake levels accelerate erosion, the bluffs may also erode during periods of rEEQEQJPX- levels (Brater n.d.). Davis (1976) asserted that a mean annual elevation of 580.0 feet is a threshold above which erosion on Lake Michigan is universal. Cohn and Robinson, in an attempt to predict lake elevations, determined prominent cycles of 1, 8, 11, 22, and 36 years through a Fourier analysis of historic records between 1860 and 1970 (110 years) (Birkemeier 1981). Predictions by this method, however, have not proven viable because either the system is not cyclic or a complete cycle has not yet been recorded. The intricacies of this vast system are not fully understood. Predictions of lake level fluctuation are generally considered only on a yearly basis by observing watershed catchment and runoff. At present predictions beyond a year or more into the future are not reliable. 35 ' \ ’3 f : Waves The effects of water waves are of paramount importance in coastal morphology. Haves accumulate wind .EDEI‘SY.LEPI_9EJ§«~LII-en transform_ed__into‘flui‘dhmofitio‘n. Most wave energy is ultimately attenuated in the nearshore regnnn where it shapes the geometry and composudon of the beach. Wave magnitude is a function of wind velocity and duration. Wind duration is governed both by the duration of a certain significant wind speed and by the available distance across open water (fetch). Both wave height and period on Lake Michigan are limited by fetch. Regardless how great the velocity, there is only a finite distance that the wind can blow across an open water surface..Average Lake Mnflugan fetches are from 70 to 100 miles. Given these distances and using the SMB method (Sverdrup, Munk, and Bretschneider), a sustained 30 knot wind over 7 hours can produce 5-foot waves in deep water; a 40-knot wind, of comparable duration, would generate 14'f00t, deep water waves. Haves affect sediment in three ways that, in turn, influence shore erosion and beach profiles: I»i.ewaves that approach the shore obliquely create 719085.091? ”currents . and ”corresponding sedimentw”transport; 2 breaking wave turbulencemsuspend‘shsome PRPFQEMSEQIQBDII53 and _3. orbital motions. in theeygavewfprms,.,. move sediment _back Hand forth Hin_a wide band, offshorebeyond_the PITEBLKQRLZQDQJKIDS 1959). The depth at which waves effect bed motion depends on both wave height and length (Figure 9). 36 Direction of wave travel I- : Wavelength Wave crest \ H =Wave Hei ht Createlégnngtll ' ‘ Wave Trough I Still-w ---Trough Length ater level Region 6 3 Depth Lake Bottom\:\ J L,,/2 l I i . . . d |I Direction of orbital movement of water lI particles in different parts of a i deep-water wave. l I Small motion of water below I-o/2 Direction of Wave TraveL ‘— L A ..................... a...........-...........a.-.-...-.-.-..no.-neeruvv .........-.-......-..-..«.......«.o...-uocue-an.coo...eoo-n-e-aoaoopnouo-e-i eeeee i -------- .... ... .. .. .. . . .. .. . . e e e. le- enteoelolbee ape-u....on..co-e-..nceeneo-.neo--neIa- r vvvvvvv ................................................................................................................................................................................................................ ............................................................................................................................................................................... ............................................................................................................................................................. .................................................................................................................................................................................................................... ............................................................................................................... eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee .............. of water particles under various parts of a shallow-water wave. Wave Characteristics telecoms”) Figure 9. Have characteristics and direction of water particle love-ant. Fro: the Shore Protection hrnral. 37 The deeper the water, the lower the wave bottom velocity. According to linear wave theory for a deep water wave (L./2), the bottom orbital velocity is approximately 4% of surface velocity. Waves may travel hundreds of miles before reaching the coast. As a wave moves progressively toward shallower depths, the bottom eventually imparts a frictional drag on the wave, causing it to slow, steepen, and eventually break (Figure 10). Waves that break on the outer bars often reorganize to break again closer to shore. After a wave breaks, however, linear wave theory no longer applies; in its place cnoidal or solitary wave models (among others) may be suitable. Nevertheless, actual water-wave behavior after the breaking point is complex and difficult to describe mathematically because of nonlinearities, three-dimensional characteristics, and apparent random behavior (Allender et al. 1981; U.S. Army Corps of Engineers 1984). 38 L sort or Breaker zone I Wave peaked up but I normally do nol .c I break on this bar ‘5! m‘ms MI.» mwes —— 0. 3I Inner “"9 Re-tormed OUIG' ""9 Waves flatten 3' I r k rs oscillatory f k r a ain E w -| ‘I I l Uprush I Still-wale/r level V l x I -- ‘ . ‘ \ V I MLLW -reaker depth'lsu Back rush Beach lace nner oar WEIR?— Deep bar Wave Activity in the Breaker Zone Figure 10. Scheeatic diagral of waves in the breaker zone. Free the Shore Protection Manual. 39 Littoral Transport Littoralmtransportfl is thekgmovement of‘sedjfigflf-MEYJHEXES afind CUP?€Q£§.,-_J.H_£Q§ nearsboreflzoflne; The process can be subdivided flue”... 0’ .L A... ._. _ ..__- into two categories: 1. lmovementperpendicular to the shoreline (onshore-offshore transport [Figure 11])7and 2. movement parallel to the shoreline (longshore transport). Sediments carried in the nearshore zone ~ are called littoral drift (U.S. Army Corps of Engineers 1984). Wave steepness (the ratio of wave height to wave width), s edimefint size , and“ “beach.” “51913.9, . .r eggelitee ”HODSLQQEQLQff‘sfigh‘ore ...._.,.._~ - I i- M,“ ._M transport. Migh, w”steep" Awaves generally transport material offshore, ~while1094'1°98:ng‘19‘?,3§‘.{&§ movesediments on shore. ltis this process, that may remove“beacheshwduringa 5t9tnI§v,--§Dd rebu_ild_ themdu‘riflng afinormal wavegclimate. Uaves observed along the Lake Michigan shore, during autumn of 1966 and 1967, had greater heights in the north and longer wave periods toward the south (Liu and Housley 1970). This may be due to the fact that long-period waves are dispersive in the wave spectrum. For example, if a cyclonic storm passes over northern Lake Michigan, only the longer-period waves will reach the southern shores (Dag Nummendal 1986, personal communication). “"8599? II‘Z'II'IS‘F’W‘t is “git-5'3. 9):- Haves..-w.impinainsfieeéiiaesly ‘q. Wm‘h -.. m-J‘f—’ on the~ shorelineL“ As the waves break in the nearshore zone, me w "m-mI _,_ sediment is entrained by the turbulence, then transported by the alongshore wave energy component and the current generated by successive breaking waves. The direction of longshore transport 4O Dune Crest /-- Benn _ _ . ......". ' M H w Profile A - Normal wave action Crest ' ' o . . l .. . Lowering Profile C - Storm wave'a'ttack .- Crest of toredune I I ... I ' : h 9/7\‘ - Recession . X \ ACCRETION —’ . ' “"-" ‘52: ': 5,5.I27}.--.13-'.'..'-".3i.':':_.-."..1".s;--" Profile 0 - After storm wave attack, ‘ normal wave action ‘.' ACCRETION \ <- Offshore Transport by Storm Waves Figure 11. Scheeatic diagraa of offshore transport by store vave attack on beach and dune. Fro- Shore Protection Hanna). 41 2| July l970 Loke Level .. .) .‘1' .fw , . ' h 22 July l970 25 July l970 \ \\ \ \ ['31. ' “w; . 1% x 27 J“, .970 \Q 30 July (970 °- N e 2.] -- .3 O I so it mom Davis et al.. 19m l I 1 l l J 0 5 10 15 20 25 Figure 12. Rapid accretion of ridge-and-runnel at Lalre l‘lichigan (Holland, flichigan). Fran Shore Protection Hanual. 42 is a function of the angle of wave incidence to the shoreline. Thedirectionofwlittoralwtransport changes as! oblique waves. approaching the Ashore ’changeangle and direction. Consequently longshore transport may vary hourly and seasonally. if sediment ‘5 @3199“!-reeov_se_fr.ee 8mm .elens.-the__ shoreuaod never replenished, thatwrparticular ”logationd will. _ experience erosion. Accretion occurs at places where W more sediment is supplied r--..,.__-- t -._1- .—.....-~ AL- Au“.--w:..._:‘ : ,... . 1 ,.A r“ 9190}? removed. Some contend that long-term convergence may account for the development of Big and Little Sable Points (Hands 1980). However, the long-term direction of longshore transport on Lake Michigan is not clear; not all sources agree (Figure 13). Recent studies by the Corps of Engineers (1986a, 1986d) assert that at some places net transport may be to the south for some years, then reverse northward. For example, at Grand Haven, Michigan, From 1975 to 1984, seven years showed northward movement and three years showed southward movement. Within most years, the movement tended to be northward from spring to summer, and southward from fall to winter. (U.S. Army Corps of Engineers 1986d). Rates of sediment supply at different sites depend on local shore conditions and shore alinement, as well as the energy and direction of wave approach. 43 LITTORAL TRANSPORT STUDIES 1. Geomorphology (Hands, 1970) 2. Extreme Storms (Resio and Vincent, 1976) . 3-year Hindcast (Seville. 1953) . LEO Currents (Weggel, 1979) . LEO Waves (Weggel, 1979) ‘ . Section 111 Reports (U.S. Army Engineer District, Detroit, 1975; 1976) . Sediment Characteristics (Hulsey. 1962) . Sediment Characteristics (Saylor and Hands, 1970) 001‘“ (”‘1 _. Indicates Direction of Net Transport. 9 Indicates a Balance Between Longshore Transport Directions riOrlh miles Figure 13. Direction of net longshore transport along the eastern shore of Lake Michigan. Not all sources are in agree-eat. Froe Hands 1980. 44 Storms Ther most erosive force acting v on Lake Michigan’s 39.9"? comes fromhdghnmenergy "EYES: generated“ by Hstorm systems (Brater and Seibel 1973). Many researchers note the connection between intense cyclonic disturbances and severe erosion on Lake Michigan (Birkemeier 1981; Brater n.d.; Brater and Seibel 1973; Buckler 1981; Buckler and Winters 1988; Davis 1976; Gilbert 1986; Hands 1980; Powers 1958; among othersL The harshest storms occur from fallto spring. Between November and April two dominant cycknfic tracks converge on the Great Lakes: one from western Canada and the other from the southwestern United States. The consequence of these merging tracks is recurrent cyclonic passage that maintains an elevated wave climate and frequent surges in wave energy that may resuhzin dramath: erosion. 5139.51-19.83awhsigfltellmresarg leases. .9.f._.l.a_lss_i.l.s.v.slo Naturally. when levels are high, the potential for erosion is greater. Nevertheless, the vertical rise in still-water level on the leeward side of the lake, caused by surface wind stress (wind setuph is suffkfient to transmit wave energy into backshore regions and cause significant erosion. Fortunately whengwater levels are at an annual high inHJuly or Augus, ,.,.th9.,-_t!a,\l§ Apiimate is generally moderate compared with conditions between fall and 5.2.17.1 ne- 45 Storms are historically linked to erosion. Brater (n.d., p. 3) includes a 1940 storm account by Norman Billings, hydrogeologist for the Department of Conservation: Foredune ridges were completely eroded and the waves actually attacked the land mass behind them. Great pine trees, whose locations attested the previous stability of their foundation, were undermined and felled into the lake.... cottage yards disappeared, leaving dwellings which had formerly occupied modest terraces now standing precariously only a few feet from nearly vertical banks. The severe erosion described in Billings’s account occurred during a period of below normal lake levels. Brater (n.d.) emphasized that rapid shore erosion is associated with wave action during large storms that attack and erode the toes of bluffs. Although increased recession rates are a response to high lake levels, the amount is dependent on storm events (Hands 1980). Birkemeier (1981) recorded an average 5.2 feet of recession at 11 out of 17 study sites (on Lake Michigan) following a March storm in 1973. He further observed that high recession occurred during late fall and early spring but was low or nonexistent during summer and periods of ice cover. Brater and Seibel (1973) contended that about 90% of all movement of littoral material during a three year period may be caused by the two or three largest storms, although others disagree. These large, infrequent storms introduce much more energy to the coastal system than the largest monthly waves (that are not associated with storms) because wave energy (in foot-pounds per foot of wave crest per wave length) increases as the square of wave height (King 1959). Therefore as wave height increases, energy increases rapidly. 46 15g; lce normally begins to form on the Lake Michigan shorezone in December and generally persists until March (Figure 14). But during severe winters the ice may cover up to 90% of the lake and endure infidl the end of ApriL In contrast, more ndld winters are characterized by less than 15% coverage which melts by March (Assel et al. 1983). Lake Michigan Ice Cover 100 - 90 - 80 — 70 L 50 - 50 - 40 m Percent Ice Cover 30 b 20 - 10I— J1 J2 F1 F2 M1 M2 A1 Time (half months) Maximu- —-'-- Hormel —-- Minim- Figure 14. Percentage of ice cover on Lake Michigan. 47 Ice first forms in northern, shallow areas followed by other shallow and restricted portions along the perimeter of the lake. The most rapid increase in ice extent occurs the last half of February. lce formation tends to cease in the southern two-thirds of Lake Michigan by March as below-freezing temperatures recede northward. The greatest decrease in ice cover occurs from 1—15 March as ice dissipates shoreward and northward from mid-lake areas (Assel et al. 1983). Ice accumulates to form a series of ridges parallel to the strand line. Some sand is incorporated into the ice ridges during their formation by wave turbulence. As the ridges grow, they may be held fast by strong, onshore winds and their great mass until, in places, they actually rest on the lake bottom (Davis 1976). No significant erosron is caused by the “extensive g ”ice -.. -,__ -I-.. ,W— ‘1‘- V H- ___.-.._.. - complex, instead the ice forms a protective armor that guards -‘_“A __ _ ‘ -v ”ya-H‘s- r‘w ,W. n--— F“..— the shore against fierce wave attack. January, -EEQEPEELHLEDCI .g r _,.m‘.-—a -~._..~-——-L_~...a (_ “Hfi,,—a—A—~ -‘ "M March have the most frequent storms _of_ any three- month period ‘_ -Hn—Fh ”a —- (Buckler 1981; Buckler and Winters 1983; Davis 1976), but. the.“ .ef.fscts.-_-.9twthese S’wrms a??- VittuaIIYnssatf—id... 9X-P339_.__Pr...e§9139.? ww-c-a-N-u, of ice, which commonly extends one wqfluarteflr tho_ 1__/2 __’ mile from n... 'm *1. shore. Thus $1192-93? Michigan shoreline is essentially static during theWmostmudynamicW”waive , cl__imates-._._..where-.. swinter. ”mice, structures are fully developed. 48 Summary FeesMeeiifltxumgurinz ”nigh.:1133eneitx-surefseamefl, is the vamp. .hsu. “ ' u fundamental causesof ”Lake - innichiganw 51.19119. _ fir?$3$1,399,“?{Eff eeeeeeiee- SmJexeewePPerimeeeedmez.Eiah,,.le!<.e_.3eye}:..._.e-"e Peten'eiellx-the_meet.-dsn1ae..ins.-. ngwever: during summer. months. when Lake Michigan is at an annual high, stormsIIaIreI infrequent and of low intensity. Annual-Wlo-w-‘water periods between fall and spring are a time of recurrent, extreme storminess. Ice development protests the Shereline eeainst-renaissent ”winter storm ”attack. Consequently, .3319 storms most associated with .,\‘_- F...—_..—.—--_ _ , coastal erosionIoccur in theIfIall prior toIIiIce formation and in the spring after the ice breaks up. Long-term high lake levels exacerbate erosion along the coastline; however, violent storms have caused severe erosion even during times of record low lake levels (Brater n.d.). Less common high energy storms are considered more important than more frequent monthly storms of low to intermediate intensity in bluff recession (Buckler 198i; Birkemeier 1981; Brater and Seibel 1973). Separate areas of shoreline typically experience intermittent recession. Thus, coastal erosion that threatens personal property and communities, as well as railway and road networks, is largely the product of severe fall and spring storms. Chapter 3 DATA AND ANALYSIS RESULTS Introduction In this study bluff recession rates are based on measure- ments of bluff crest retreat while wave energy values are derived through computation. Subsequent analysis is designed to examine the dependence between bluff recession and wave energies associated with fall and/or spring storms (Figure 15). To this end, individual recession rates for 23 sites are compared to wave energies projected for storms with return periods of 5, 10, 20, 50, and 100 years. Pearson’s product-moment correlation coefficient is used to measure the extent of association while regression testing indicates how the variables are associated. 49 50 RECESSION DATA PHYSICALLY MEASURED WAVE DATA DERIVED THROUGH COMPUTATION I I I I I I I I I ' ' ' GLO and . I I A" Photo Measurmont I DeepwaIer Wave I I 33'? and Field Survey I I Heights and Periods “gm° l I I I 90! FaIJvlnd SWING Measurement I I am I I I ' I I I \ I I \ / I I arxmm ' . New“ I a e a I Sites ' I Theory I I I I l I I I I I l l Moan Energy Flux I I I I 01 Breaking Waves I L____.___._..._.__._____ .I L ________ _..__..__..._...___._.__J CORRELATION AND REGRESSION TESTING FLOW DIAGRAM FOR ANALYSING THE RELATIONSHIP BETWEEN BLUFF RECESSION AND WAVE ENERGY Figure 15. A flow diagral for analyzing the relationship between bluff recession and nearshore wave energy. 51 Rece§§ion Rates Both short and long-term recession rates are known for 23 sites. The ten-year period between observations made by Buckler in 1976 and measurements completed during this investigation, irI 1986, constitute the short-term increment. Long-term intervals generally cover 150 years, the time elapsed since the initial General Land Office survey. The sites and their recession rates are shown in Figure 16. Values exceeding one standard dewdation above and below the mean are highughted to lend scale to the degree of variation among values. Erosion rates over the past ten years, for all sites, show greater variation than for long-term observations. In the short term, four sites registered no bluff recession while the bluff crest at site number 12 retreated 192.48 feet, more than any of the others, and along with sites 18 and 20 was greater than one standard devdation above the mean. 'The recession rates do not show any apparent geographic pattern (Figure 16). Long-term recession rates are relatively consistent with those established by Buckler (1981). Recession rates vary from near zero (sites 21 and 23) to an average of -4.53 feet per year at site 4. The long-term rates are of greater interest because they tend to compensate for fluctuating water levels and may show more clearly the overall influence of storms with varying intensity and frequency, consistent with the return periods incorporated in the wave hindcast model. north Long Term New Long Recent Rate Term Site Recession (Buckler, Rate Number 1976-198 1976) (This study) 29 «0.72 3 ’ 41.45 ' 4.41 28 ‘2.“ . f1 .59 '-‘I.56 24 {40.81 -2.17 ; g «2.47 ‘- 23 ; +0.30, . - «0.36 r 12% 22 «0.50 . * 4.00 ‘ 098 21 . “ +5.31 ‘ “..fiié “ii: ‘ 20 . 4 0.30 .1 .04. * 19 j’; ,‘ ‘4179 4174‘. 18 44.88 «0.89 4.,52 17 41.77 ' .103 .- g-1.07..f<; 16 .e.oaf}_,;.g. are»- 2.0.0019; 15 +0.00 - «0.00 4175 14 0.00 . 0.93 0.81 g; 13 _—5.10 . «0.94 5.1.105}; 12 .21.33 - 0.92 4.1013"? 11 iv-1.?o" (~4193 14198;; a ;_ -2.07 .209 42.70 7 }_ -1 .10 4.53 , ' 41.51;:- e -8.18 .239 -2.69 5 “ 43.21 .2.92 0.20 4 I 0.24 «1.30 4.53 3 91.71 , 4.42. ; 41.271121 2 IOJXI,., 14LIB.~‘ ..4l16jg mean 4.87 -1 .36 -1 .55 std. dev. 5.53 1.03 1.05 Big Sable Point ’ Ludington ittie Sable Point ‘— e White Lake ‘ Muskegon __ Grand Haven 0 Holland eSouth Haven Less than one standard deviation below the mean Within one standard deviation of the mean standard deviation above the mean Figure 16. Statistical and geographic distribution of bluff recession rates in feet per year. 513 The long-term recession rates show no gradational spatial trend, either increasing or decreasing along the shore (Figure 16L However, an apparent clustering of higher rates in the south and lower rates in the north seems in agreement with values reported by Buckler (1981) and may support his finding of greater overall recession at the southern end of Lake Michigan. Seventy-eight percent of the observations fall within one standard deviation of the mean (-L55 feet per year» which suggests a normal distribution. Furthermore, there is no compelung indication that the values are not normaHy distributed. Two observations (sites 21 and 23) are less than one standard deviation below the mean, and three observations (sites 4, 5, and 6) are greater than one standard deviation above the mean. Figures 17 through 19 are representative of the study area and variabflity in recession rates. Additional data concerning site observations are given in appendix A. Figure 17. Site nulber 2 has experienced n0 recession since elplacelent of heavy llaestone block revetlent and groin systel in 1971. Photo date: August 1986. 5511 Figure 18. The bluff at site nuaber 18 has receded 176.10 feet in 10 years. Although a recession rate of -14.88’/year is high for the short tern. the long-tern rate of -i.52'/year is close to the lean (-1.55’/year). Note the close proxility of houses to the bluff crest and the effect of individual structures that front private property at the strand line. The barge in the foreground is equipped with a pile driver and laterial to construct or repair shore protection structures. Photo date: August 1986. Figure 19. Site nunber 21 has an ertreaely lov, long-tern recession rate of -0.16'/year. Still, after several years, houses are dangerously close to the shoreline. South is to the right in this photo; note that little or no sand is accuaulated in the groins along the shore. Littoral drift appears to have been to the north recently. Photo date: August 1986. 55 Wave Energy Have energy data for this study are calculated using linear wave theory, values from the Resio and Vincent hindcast model, and a normalized nearshore slope at each site. Deep water wave heights and periods are interpolated for observation sites between hindcast points (Figure 20). Heights and periods for spring and fall waves of 5, 10, 20, 50, and 100 year return periods (Appendix A) combine with the nearshore slope at each site to yield wave energy values given as mean energy flux in Table 1. The mean energy flux, which is in units of foot-pounds/foot-second, can be thought of as the amount of energy that is transmitted horizontally landward by a wave when it first breaks. Table 1 presents the wave energy associated with storm events of varying frequency and the long-term, average annual recession rate at each observation site. Since wave energy is a function of both storm intensity and lake geometry, these values (unlike bluff recession) exhibit a gradational trend along the shore. In general, highest spring energy values are found in the northern part of the study area for frequent return periods (5 years) and toward the central part for the more infrequent events (100 years). Fall wave energies tend to be greater along the central and northern portion of shore for 5-year storms but lower along the central reach for loo-year storms. Resio and Vincent (1976, p. 47) suggest that the disparity between time limitation and fetch limitation may explain the distribution of wave values at this 56 end of the lake. Fall storms generally show intensities about four times greater than spring storms of the same return period. This could result from instability between the warm, autumn lake surface and cooler air aloft, which may create a greater. tendency for coupling between surface and upper atmospheric winds. 57 Ix “\‘fl‘r- Study Site Locations and N Wave Hindcast Data Locations .8 v’ (f L'- 0 25 50 ‘ é m... S); cf I \ O -? 1‘? 5 2 HINDCAST POINTS 16 TO 26 2 USED IN THIS STUDY 2 16 2 ‘—— 17 21 18 WISCONSIN I 19 19 I 20 17 21 16 22 15”’/’,,/”" '''''''' 14 23 I3 24 12 —_- 25 11 26 ll.LJId(3IE§ : 7 --..--Yl°.*.".‘it'§L-_. s . 5 i; INDIANA i2 1 Figure 20. 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The amount of association or interdependence is assessed with Pearson's product-moment correlation coefficient in a pair-wise test. Pearson’s coefficients are actually calculated, using the recession rate at each site paired with the corresponding wave energy value for each return period. Results are presented in Table 2. Table 2. PEARSON PRODUCT-NONENT CORRELATION COEFFICIENTS ANALYZING LINIG-TERN ANNUAL RECESSION RATES IIITII STORII IIAVE ENERGIES FOR VARIOUS RETURN PERIODS. SPRING UAVES FALL HATES STR iOYR ZOYR SOYR 100TR SYR 10YR ZOYR l SOYR 100R 0.522 0.579 0.600 0.491 0.415 0.477 0.341 046410.380 0.244 Correlation coefficients are a leasure of association or interdependence betveen sets of variables. Values range iron -1 (perfect negative correlation) to +1 (perfect positive correlation). If there is no association, the coefficient is 0. The results of linear regression techniques used to evaluate how the variables are related are shown in Table 3. Wave energy is the independent variable, used to predict the dependent variable -- bluff recession rate, in seeking a linear functional relationship. A second analysis using the natural logarithm of wave energy values to linearize a power law relationship gives slightly better results. The logarithmic transformation implies a nonlinear relationship between bluff EH3 wave energy. This means a change in the form of recession and the regression equation from: tax: + t: y=m(1nx)+b where: predicted value of bluff recession rate ‘< II wave energy value 3‘ II In and b = regression coefficients. Table 3. LINEAR REGRESSION RESULTS; PREDICTING LONG-TERN ANNUAL RECESSION RATE UITN NEAN ENERGY FLUX FOR VARIOUS RETURN PERIODS. SPRING UAVES FALL UAVES SYR 1012 201R SOYR 100YR STR 1078 2018 SOYR 1001R Adjusted 9’ 0.238 0.304 0.330 0.205 0.133 0.191 0.074 0.178 0.104 0.015 Significance Level 0.011 0.004 0.002 0.017 0.049 0.021 0.111 0.026 0.074 0.281 In SPRING UAVES In FALL UAVES Adjusted R’ 0.283 0.308 0.340 0.214 0.152 0.200 0.087 0.209 0.129 0.021 Significance Level 0.005 0.004 0.002 0.015 0.038 0.019 0.093 0.018 0.052 0.240 In general 8’ is the proportion of variance in the dependent variable explained by the independent variable and regression equation. assuling a knovn distribution. Significance reflects area outside a confidence interval, For era-pie if significance=0.05; this leans 5% (of the distribu- tion) is outside the confidence interval, or there is a 95! confidence that R’ is correct. 61 W Bluff recession rates within the area studied seem to constitute a normal distribution but show no geographic patterns in their ordering along the shoreu in contrast, estimates of wave energy exhibit a gradational trend between high and low values along the coast. Bluff recession rates, the dependent variable of interest, are compared with wave energies (the independent variable) to examine this relationship. Statistical tests show a moderate relationship between recession rates and wave energies associated with storms of certain return periods. Spring waves of 20, 10, and 5 year return periods have the highest correlation coefficients. Regression testing suggests a nonlinear relationship, using the natural logarithm of wave energy to predict bluff recession yields the highest R2 values. The strongest relationships from this study are spring 20, 10, and 5 year waves, which account for 34%, 31%, and 28% of the variance in bluff recession rates, respectively. Chapter 4 DISCUSSION AND CONCLUSIONS Introduction The two objectives of this study are 1. to obtain long and short-term bluff recession data at previously studied sites and 2. to examine the hypothesis that the variability in recession rates are related to storm intensity and nearshore wave energy. Significant results are addressed in the following discussion. Additional findings, pertinent to both the technical design of the investigation and coastal morphology, are also considered. 62 63 W Short and long-term recession data for 23 sites, previously investigated by Powers (1958) and more recently by Buckler (1973a, 1981), provide a basis for several findings. Variation in recession rates among sites is greater over short periods (1976-1986) than long periods (middle 1800’s to 1986). The standard deviations for short and long-period observations are 5.53 and 1.05 (feet/year), respectively. This suggests that, although the crest line as a whole is receding, erosion occurs sporadically at individual locations. Certain sites may loose several feet during a few years and then remain somewhat more stable while other locations begin to recede. Even though the long-term recession rates are five times less variable than short-term rates, and subsequently more closely distributed about their mean, they nevertheless express a degree of variation. Since the values are in fact rates, the longer the observation period, the greater the difference in actual recession. For example, neither site 11 (rate = -0.98 feet/year) or site 8 (rate = -2.70 feet/year) shows statistically significant variation from the mean (rate = ~1.55 feet/year). However, over a 100-year period, site 8 would lose 270 feet of bluff compared to only 98 feet at site 11. Exactly how great the difference is may be a matter of scale and perspective. A property owner at site 8 would certainly regard losing 270 feet a substantially greater loss than 98 feet. Yet in a geomorphic 64 context of hundreds of miles of coastline shaped over thousands of years, the difference may be less consequential. The second objective is to examine the hypothesis that bluff recession is related to wave energy. Acceptable significance levels for correlation and regression coefficients were not set in advance because there are no similar investigations to provide a comparative measure or indicate appropriate values. Therefore, this research examines rather than tests these relationships. The analysis indicates a nonlinear relationship. Spring storm waves with return periods of 20, 10, and 5 years can each account for approximately 30% of the variance in bluff recession rates, but waves associated with spring 50 and 100 year storms explain a much lower proportion of the variance (13-20%). Although fall waves are not as strongly related to recession as spring waves, the R2 values indicate a similar pattern (5 and 20-year return intervals accounting for more variance than 50 and 100-year phenomena). Less than half of the variation in bluff recession rates is explained by the regression equation. Thus, using this model to predict bluff recession as a function of wave energy is not practical; predictions based on established, long-term recession rates would yield better results. On the other hand, the R2 values are high enough to suggest that there is a relationship between bluff recession and wave energy. With appropriate refinements in this model, the association may emerge more clearly. Therefore, the regression results are considered EH5 moderately successful and encouraging. .Assuming that there is a relationship between wave energy and bluff recession, there are at least two possibilities that might explain the stronger association with frequent storms of moderate intensity rather than infrequent, high energy (50 and 100-year) events.’ First, nearshore wave energies, for this study, are caunnated from deep water wave values projected by Resio and Vincent (1976). Their hindcast model is based on 62 years of wind data. Naturally the margin of error about infrequent 50 and 100-year wave projections, based on only 62 years of data, is greater than the error about 5, 103 and 20 year wave predictions. It is therefore possible that the values for 50 and 100-year waves are not representative of actual conditions. If this is the case, any error in the Resio and Vincent model would be incorporated into this study and affect the regression tests and subsequent results. The second possibflity is that the Resio and Vincent 50 and 100-year wave values do approximate actual conditions. In this case, the lower association between high wave energy and bluff recession may impty that storm waves of moderate intensity and frequency (of occurrence) are morphologically more influential in shaping the coast line than infrequent, high energy waves. This notion is consistent with postulations by Holman and Miller (1960) in their article, Magnitude and frequency of forces in geomorphic processes. ' The 5, 10, 20, 50, and iOO-year store events are probabilities. For instance, a 100-year store has a 15 likelihood of occurrence any given year. 66 As applied to bluff recession, the rate at which a coast-line, composed of unconsolidated material, is shaped by wave energy at various locations along the shore depends on the distribution of wave energy in time as well as in magnitude. The enormous wave energies associated with rare or infrequent storms are not implicitly the most significant forces shaping the coast. As Holman and Miller (1960, p. 5) indicate, The relative amount of ”work” done during different events is not necessarily synonymous with the relative importance of these events in forming a landscape or a particular feature of a landscape. The effectiveness of an event of a given frequency in terms of its performance of work is measurable both by its magnitude and by the frequency with which it recurs. Work, in this sense, is the product of frequency times magnitude. In the specific instance of bluff recession on Lake Michigan, work = return period it mean energy flux. A literal interpretation of wave return periods may help illustrate this concept. During the course of a century, the coast may experience 100-year storm waves only once; and in the process of the same 100 years potentially be exposed to five 20 year storms, ten 10-year storms, and twenty 5-year storms. Erosion during these relatively moderate but more frequent events may exceed the changes made by the rare, high energy storms and thus become the dominant geomorphic force. As an example, Figure 21 shows the relative amounts of potential work accomplished over a 100-year period at site 18 for spring waves of different return periods. This (in thousands) Applied Stress 300 250 200 150 100 50 SITE 18 67 SPRING WAVES Analted Stress Figure 21. Uork accoaplished by spring vaves at site nuaber 18. \\ \I _ \‘ \\ \\ L \\ \\ I— ‘ \ ‘ .\\ \\ .\\ .\\ L ‘\\ \\H‘§- P - L l l l l J l__ J J 10 20 30 40 50 60 70 80 90 Spring Have Return (years) 100 68 generalization can only hold true providing that the wave magnitude during recurrent events exceeds some threshold value to move sediments and induce bluff erosion. For instance, if 5-year storms do not generate enough energy to produce significant offshore and longshore transport, the concept of geomorphic work cannot be applied. Consequently the effect of 5-year storms would be negligible compared with storms that do exceed the threshold energy requirement. An important distinction between Holman and Miller’s research (1960) and this study is that they cited examples of geomorphic events that were both constructional and destructional. Although waves may impart erosional and depositional change in the beach profile, only destructional processes occur on the bluffs examined. Holman and Miller (1960, p. 72) note, ”There is a notable lack of examples demonstrating effectiveness of moderate events of frequent occurrence in molding erosional landforms.” This study may be one such example. Finally, the low correlation between potential wave energy and bluff crest recession rates reinforces the findings of other similar studies that concentrated on shorezone geomorphology. In combination, other investigations indicate that erosion is a complex process involving several variables. The influence of other factors such as soil cohesion, lithology, lake level fluctuations, runoff, and destablization due to ground water should not be discounted. Thus, a simple bivariate relationship is not likely to relate or explain the intricacies of a dynamic system with numerous other forces impinging on it. Yet the 69 development of techniques to study and quantify these simple relationships contribute significantly, by describing fundamental interactions necessary to construct more comprehensive and dimensionally correct models. Suggestions for thure Research This study provides a first iteration model to investigate the association between wave energy and Lake Michigan coastal erosion. The model is restricted to a small sample area and based on probabilities for wave energy. During the course of this study certain improvements became apparent which deserve further investigation. Several assumptions are incorporated into the study as a result of using the hindcasting concept. Have return periods are based on the statistical probability of storms, with certain magnitudes, recurring in a 100-year interval. Since these storms do not actually recur according to this schedule, error is introduced into this design. A model that includes actual meteorological data may produce more accurate results. By researching historic synoptic wind charts, storms with magnitudes that correspond to the hindcast storm intensities could be identified. Approximations of deep water wave parameters, calculated with procedures described by Resio and Vincent (1976), could be improved by using actual storm track and 7O wind speed information. Better estimations of nearshore wave magnitude and incidence, including longshore energy flux, could be determined using true storm track data. Actual storm dates could then be referenced to an exact lake elevation, on those dates, to estimate beach width and wave proximity to the toe of the bluff slopes. lmproved accuracy of nearshore, wave energy estimates would greatly enhance this model and may help to clarify the connection between waves and erosion. 71 Conclusion The Lake Michigan shoreline forms a dynamic interface between land and water where numerous physical forces continually interact. Bluff erosion is a destructional coastal process which is caused, in part, by wave energy. This study is one of the first to examine quantitatively the relationship of wave energy and bluff recession at numerous sites. Significant findings of this investigation can be summarized in three main points. First, the results show only moderate success in linking bluff recession to wave energy, but future improvements in design may reveal more about the association. Second, the data suggest that relatively frequent storms (5 to 20-year return periods) of moderate intensity are morphologically more significant than rarer events of greater magnitude. This notion is consistent with a similar concept by Holman and Miller (1960) that, over a period of time, landscapes are a function of ”work,” which is the product of the frequency of an event times its magnitude. Finally, the low correlation level is a reminder that coastal processes are complex. Bluff recession results from the. interaction of numerous physical factors and cannot be fully explained by simply investigating one of them. However, this study provides a basis to understand further the relationship between wave energy and bluff recession and may contribute, in the future, to more comprehensive investigations. GLOSSARY OF TERMS 72 GLOSSARY OF TERMS' ACCRETION. May be either natural or artificial. Natural accretion is the buildup of land, solely by the action of the forces of nature, on a beach by deposition of water- or airborne material. Artificial accretion is a similar buildup of land by reason of an act of man, such as the accretion formed by a groin, breakwater, or beach fill deposited by mechanical means. ALLUVIUM. Soil (sand, mud, or similar detrital material) deposited by streams, or the deposits formed. ALONGSHORE. Parallel to and near the shoreline; LONGSHORE. ARMOR UNIT. A relatively large quarrystone or concrete shape that is selected to fit specified geometric characteristics and density. It is usually of nearly uniform size and usually large enough to require individual placement. In normal cases it is used as primary wave protection and is placed in thicknesses of at least two units. ARTIFICIAL NOURISHMENT. The process of replenishing a beach with material (usually sand) obtained form another location. ATTENUATION. (1) A lessening of the amplitude of a wave with distance from the origin. (2) The decrease of water-particle motion with increasing depth. Particle motion resulting from surface oscillatory waves attenuates rapidly with depth, and practically disappears at a depth equal to a surface wavelength. BACKSHORE. That zone of the shore or beach lying between the foreshore and the coastline comprising the berm or berms and acted upon by waves only during severe storms, especially when combined with exceptionally high water. BANK. A landward-facing steep bluff or sharp slope of unconsolidated material landward of the shoreline; the bluff. BAR. A submerged or emerged embankment of sand, gravel, or other unconsolidated material built on the lake floor in shallow water by waves and currents. BATHYMETRY. The measurement of depths of water in oceans, seas, and lakes; also information derived from such measurements. ' All definitions from the Shore Protection Manual (1984) and Buckler (1981). 73 BEACH. The zone of unconsolidated material that extends landward from the low water line to the place where there is marked change in material or physiographic form, or to the line of permanent vegetation (usually the effective limit of storm waves). The lakeward limit of a beach-- unless otherwise specified-- is the mean low water line. A beach includes FORESHORE and BACKSHORE. See also SHORE. BEACH EROSION. The carrying away of beach materials by wave action, tidal currents, littoral currents, or wind. BEACH HIDTH. The horizontal dimension of the beach measured normal to the shoreline. BLUFF. A lakeward-facing steep bank or sharp slope of unconsolidated material landward of the shoreline; the bank. BLUFF BASE. The point or line of abrupt change in slope at the bottom of the bluff; the bluff toe. BLUFF CREST. The point of line of abrupt change in slope at the top of the bluff; the bluff line. BLUFF FACE. The lakeward facing inclined surface of the bluff; the bluff slope. BLUFF LINE. The point or line of abrupt change in slope at the top of the bluff; the bluff crest. BLUFF TOE. The point or line of abrupt change in slope at the bottom of the bluff; the bluff base. BOTTOM. The ground or bed under any body of water; the bottom of the lake. BOTTOM (nature of). The composition or character of the bed of a lake or other body of water (e.g., clay, coral, gravel, mud, ooze, pebbles, rock, shell, shingle, hard, or soft). BOULDER A rounded rock more than 10 inches in diameter; larger than a cobblestone. 74 BREAKER. A wave breaking on a shore, over a reef, etc. Breakers may be classified in four types: SPILLING-- bubbles and turbulent water spill down front face of wave. The upper 25% of the front face may become vertical before breaking. Breaking generally occurs over quite a distance. PLUNGING-- crest curls over air pocket; breaking is usually with a crash. Smooth splash-up usually follows. COLLAPSING-- breaking occurs over lower half of wave, with minimal air pocket and usually no splash-up. Bubbles and foam present. SURGlNG-- wave peaks up, but bottom rushes forward from under wave, and wave slides up beach face with little or no bubble production. Hater surface remains almost plane except where ripples may be produced on the beach face during runback. BREAKER DEPTH. The still-water depth at the point where a wave breaks. Also called BREAKING DEPTH. BREAKER ZONE. The area a water bounded by the beach and the plunge line; the plunge line is the line along which the highest waves break. CELERITY. Have speed. CHANNEL. (1) A natural or artificial waterway of perceptible extent which either periodically or continuously contains moving water, or which forms a connecting link between two bodies of water. (2) The part of a body of water deep enough to be used for navigation through an area otherwise too shallow for navigation. CHART DATUM. The plane or level to which soundings (or elevation) or tide heights are referenced (usually LOH HATER DATUM). CLIFF. A high, steep face of rock; a precipice. CNOIDAL HAVE. A type of wave in shallow water (i.e., where the depth of water is less than 1/8 to 1/10 the wavelength). The surface profile is expressed in terms of the Jacobial elliptic function on u; hence the term cnoidal. COAST. A strip of land of indefinite width (may be several kilometers) that extends from the shoreline inland to the first major change in terrain features. 75 COASTAL AREA. The land and lake area bordering the shoreline. COASTLINE. (1) Technically, the line that forms the boundary between the COAST and SHORE. (2) Commonly, the line that forms the boundary between the land and the water. CONTOUR. A line on a map or chart representing points of equal elevation with relation to a DATUM. It is called an isobath when connecting points of equal depth below a datum. Also called DEPTH CONTOUR. CONVERGENCE. (1) In refraction phenomena, the decreasing of the distance between orthogonals in the direction of. wave travel. Denotes an area of increasing wave height and energy concentration. (2) In wind-setup phenomena, the increase in setup observed over that which would occur in a equivalent rectangular basin of uniform depth, caused by changes in planform of depth; also the decrease in basin width or depth causing such increase in setup. CREST OF HAVE. (1) The highest part of a wave. (2) That part of the wave above still-water level. CURRENT, LITTORAL. Any current in the littoral zone caused primarily by wave action; e.g., LONGSHORE CURRENT, RIP CURRENT. CURRENT, LONGSHORE. The littoral current in the breaker zone moving essentially parallel to the shore, usually generated by waves breaking at an angle to the shoreline. CURRENT, NEARSHORE. A current in the NEARSHORE ZONE. DECAY DISTANCE. The distance waves travel after leaving the generating area (FETCH). DECAY OF HAVES. The change waves undergo after they leave a generating area (FETCH) and pass through a calm, or region of lighter winds. In the process of decay, the significant wave height decreases and the significant wavelength increases. DEEP HATER. Hater so deep that surface waves are little affected by the lake bottom. Generally, water deeper than one-half the surface wavelength is considered deep water. DEPTH. The vertical distance form a specified tidal datum to ‘ the sea floor. DEPTH OF BREAKING. The still-water depth at the point where the wave breaks. Also BREAKER DEPTH. 76 DIFFRACTION (of water waves). The phenomenon by which energy is transmitted laterally along a wave crest. Hhen a part of a train of waves is interrupted by a barrier, such as a breakwater, the effect of diffraction is manifested by propagation of waves into the sheltered region within the barrier’s geometric shadow. DIVERGENCE. (1) In refraction phenomena, the increasing of distance between orthogonals in the direction of wave travel. Denotes an area of decreasing wave height and energy concentration. (2) In wind-setup phenomena, the decrease in setup observed under that which would occur in an equivalent rectangular basin of uniform depth, caused by changes in planform or depth. Also the increase in basin width or depth causing such decrease in setup. DOHNDRIFT. The direction of predominant movement of littoral materials. DUNES. Ridges or mounds of loose, windblown material, usually sand. DURATION. In wave forecasting, the length of time the wind blows in nearly the same direction over the FETCH (generating areaL DURATION MINIMUM. The time necessary for steady-state wave conditions to develop for a given wind velocity over a given fetch length. EMBANKMENT. An artificial bank such as a mound or dike, generally built to hold back water or to carry a roadway. EMBAYED. Formed into a bay or bays, as an embayed shore. EMBAYMENT. An indentation in the shoreline forming an open bay. ENERGY COEFFICIENT. The ratio of the energy in a wave per unit crest length transmitted forward with the wave at a point in shallow water to the energy in a per crest length transmitted forward with the wave in deep water. On refraction diagrams this is equal to the ratio of the distance between a pair of orthogonals at a selected shallow-water point to the distance between the same pair of orthogonals in deep water. Also the square of the REFRACTION COEFFICIENT. EOLIAN SANDS. Sediments of sand size or smaller which have been transported by winds. They may be recognized in marine deposits off desert coasts by the greater angularity of the grains compared with waterborne particles. 77 EROSION. The wearing away of land by the action of natural forces. On a beach, the carrying away of beach material by wave action, littoral currents, or by deflation. ESCARPMENT. A more or less continuous line of cliffs or steep slopes facing in one general direction which are caused by erosion or faulting. FEELING BOTTOM. The initial action of a deepwater wave, in response to the bottom, upon running into shoal water. FETCH. The area in which waves are generated by a wind having a fairly constant direction and speed. Sometimes used synonymously with FETCH LENGTH. FETCH LENGTH. The horizontal distance (in the direction of the wind) over which a wind generates waves or creates a HIND SETUP. FOREDUNE. The front dune immediately behind the backshore. FORESHORE. The part of the shore, lying between the crest of the lakeward berm (or upper limit of wave wash) and the mark that is ordinarily traversed by the uprush and backrush of the waves. GENERATION OF HAVES. (1) The creation of waves by natural or mechanical means. (2) The creation and growth of waves caused by a wind blowing over a waver surface for a certain period of time. The area involved is called the GENERATING AREA or FETCH. GEOMETRIC SHADOH. In wave diffraction theory, the area outlined by drawing straight lines paralleling the direction of wave approach through the extremities of a protective structure. It differs from the actual protected area to the extent that the diffraction and refraction effects modify the wave pattern. GEOMORPHOLOGY. That branch of geography and geology which deals with the form of the Earth, the general configuration of its surface, and the changes that take place in the evolution of landform. GRADIENT (GRADE). Hith reference to winds or currents, the rate of increase or decrease in speed, usually in the vertical; or the curve that represents this rate. GROIN. A shore protection structure built (usually perpendicu- lar to the shoreline) to trap littoral drift or retard erosion of the shore. 78 GROUND HATER. Subsurface water occupying the zone of saturation. In a strict sense, the term is applied only to water below the water table. GROUP VELOCITY. The velocity of a wave group. In deep water, it is equal to one-half the velocity of the individual waves within the group. HINDCASTING, HAVE. The use of historic synoptic wind charts to calculate characteristics of waves that probably occurred at some past time. JETTY. On open coasts, a structure extending into a body of water, which is designed to prevent shoaling of a channel by littoral materials and to direct and confine the stream or tidal flow. Jetties are built at the mouths of rivers or tidal inlets to help deepen and stabilize a channel. KINETIC ENERGY (OF HAVES). In a progressive oscillatory wave, a summation of the energy of motion of the particles within the wave. LAKESHORE. A general term used to denote the margin of the lake or a particular side of the lake. it does not refer to a specific area within the shorezone; the lakeside. LEE. (1) Shelter, or the part or side sheltered or turned away from the wind or waves. (2) (Chiefly nautical) The quarter or region toward which the wind blows LEEHARD. The direction toward which the wind is blowing; the direction toward which waves are traveling. LENGTH OF HAVE. The horizontal distance between similar points on two successive waves measured perpendicularly to the crest. LITTORAL. Of or pertaining to a shore. LITTORAL CURRENT. See, CURRENT LITTORAL. LITTORAL DEPOSITS. Deposits of littoral drift. LITTORAL DRIFT. The sedimentary material moved in the littoral zone under the influence of waves and currents. LITTORAL TRANSPORT. The movement of littoral drift in the littoral zone by waves and currents. Includes movement parallel (longshore transport) and perpendicular (on-offshore transport) to the shore. 79 LITTORAL TRANSPORT RATE. Rate of transport of sedimentary material parallel or perpendicular to the shore in the littoral zone. Usually expressed in cubic meters (cubic yards) per year. Commonly synonymous with LONGSHORE TRANSPORT RATE. LITTORAL ZONE. In beach terminologyr an indefinite zone extending lakeward from the shoreline to just beyond the breaker zone. LOAD. The quantity of sediment transported by a current. It includes the suspended load of small particles and the bedload of large particles that move along the bottom. LONGSHORE. Parallel to and near the shoreline; ALONGSHORE. LONGSHORE BAR. A bar running roughly parallel to the shoreline. LONGSHORE CURRENT. See CURRENT, LONGSHORE. LONGSHORE TRANSPORT RATE. Rate of transport of sedimentary material parallel to the shore. Usually expressed in cubic meters (cubic yards) per year. Commonly synonymous with LITTORAL TRANSPORT RATE. MASS TRANSPORT. The net transfer of water by wave action in the direction of wave travel. MONOCHROMATIC HAVES. A series of waves generated in a laboratory; each wave has the same length and period. NEARSHORE (zone). In beach terminology an indefinite zone extending lakeward from the shoreline well beyond the breaker zone. It defines the area of NEARSHORE CURRENTS. NEARSHORE CURRENT SYSTEM. The current system caused primarily by wave action in and near the BREAKER ZONE; four main components comprise the system: the shoreward mass transport of water, longshore currents, lakeward return flow, including rip currents, and the longshore movement of the expanding heads of rip currents. NOURISHMENT. The process of replenishing a beach. It may be brought about naturally by longshore transport, or artificially by the deposition of dredged materials. OFFSHORE. (1) In beach terminology, the comparatively flat zone of variable width, extending from the breaker zone' to the seaward edge of the Continental Shelf. (2) a direction lakeward from the shore. OFFSHORE CURRENT. (1) Any current in the offshore zone. (2) Any current flowing away from shore. 80 ONSHORE. A direction landward from the lake. ORBIT. In water waves, the path of a water particle affected by the wave motion. In deepwater waves the orbit is nearly circular, and in shallow water waves the orbit is nearly elliptical. In general, the orbits are slightly open in the direction of wave motion, giving rise to MASS TRANSPORT. ORBITAL CURRENT. The flow of water accompanying the orbital movement of the water particles in a wave. Not to be confused with wave-generated LITTORAL CURRENTS. ORTHOGONAL. On a wave-refraction diagram, a line drawn perpendicularly to the wave crests. PARTICLE VELOCITY. The velocity induced by wave motion with which a specific water particle moves within a wave. PERCOLATION. The process by which water flows through the interstices of a sediment. Specifically, in wave phenomena, the process by which wave action forces water through the interstices of the bottom sediment and which tends to reduce wave heights. PHASE. In surface wave motion, a point in the period to which the wave motion has advanced with respect to a given initial reference point. PHASE VELOCITY. Propagation velocity of an individual wave as opposed to velocity of a wave group. PLANFORM. The outline or shape of a body of water as determined by the stillwater line. PLUNGE POINT. (1) For a plunging wave, the point at which the wave curls over and falls. (2) The final breaking point of the waves just before they rush up on the beach. POTENTIAL ENERGY OF HAVES. In a progressive oscillatory wave, the energy resulting from the elevation or depression of the water surface from the undisturbed level. PROFILE, BEACH. The intersection of the ground surface with a vertical plane; may extend from the top of the dune line to the lakeward limit of sand movement. PROPAGATION OF HAVES. The transmission of waves through water. REFLECTED HAVE. That part of an incident wave that is returned lakeward when a wave impinges on a steep beach, barrier, or other reflecting surface. 81 REFRACTION (of water waves). (1) The process by which the direction of a wave moving in shallow water at an angle to the contours is changed: The part of the wave advancing in deeper water, causing the wave crest to bend toward alinement with the underwater contours. (2) The bending of wave crests by currents. REFRACTION COEFFICIENT. The square root of the ratio of the distance between adjacent orthogonals in deep water to their distance apart in shallow water at a selected point. Hhen multiplied by the SHOALING FACTOR and a factor for friction and percolation, this becomes the HAVE HEIGHT COEFFICIENT or the ratio of the refracted wave height at any point to the deepwater wave height. Also, the square root of the ENERGY COEFFICIENT. REVETMENT. A facing of stone, concrete slabs, etc. built to protect a scarp, embankment, or shore structure against erosion by wave action or currents. RIP CURRENT. A strong current flowing lakeward from the shore. RUNNEL. A corrugation or trough formed in the foreshore or in the bottom just offshore by waves or currents. SCOUR. Removal of underwater materials by waves and currents, especially at the base or toe of a shore structure. SETUP, HAVE. Superelevation of the water surface over normal surge elevation due to onshore mass transport of the water by wave action alone. SHALLOH HATER. (1) Commonly, water of such depth that surface waves are noticeably affected by bottom topography. It is customary to consider water of depths less than one-half the surface wavelength as shallow water. (2) More strictly, in hydrodynamics with regard to progressive gravity waves, water in which the depth is less than 1/25 the wavelength; also called VERY SHALLOH HATER. SHOAL (noun). A detached elevation of the lake bottom, comprised of any material except rock which may endanger surface navigation. SHOAL (verb) (1) to become shallow gradually. (2) to cause to become shallow. (3) to proceed from a greater to a lesser depth of water. SHOALING COEFFICIENT. The ratio of the height of a wave in water of any depth to its height in deep water with the effects of refraction, friction, and percolation eliminated. 82 SHORE. The narrow strip of land in immediate contact with the lake, including the zone between high and low water lines. A shore of unconsolidated material is usually called a BEACH. SHORELINE. The intersection of a specified plane of water with the shore or beach (e.g., the high water shoreline would be the intersection of the plane of mean high water with the shore or beach» SIGNIFICANT HAVE. A statistical term relating to the one-third highest waves of a given wave group and defined by the average of their heights and periods. The composition of the higher waves depends upon the extent to which the lower waves are considered. Experience indicates that a careful observer who attempts to establish the character of the higher waves will record values which approximately fit the definition of the significant record values which approximately fit the definition of the significant wave. SIGNIFICANT HAVE HEIGHT. The average height of the one-third highest waves of a given wave group. Note that the composition of the highest waves depends upon the extent to which the lower waves are considered. In wave record analysis, the average height of the highest one-third of a selected number of waves, this number being determined by dividing the time of record by the significant period. SIGNIFICANT HAVE PERIOD. An arbitrary period generally taken as the period of the one-third highest waves within a given group. Note that the composition of the highest waves depends upon the extent to which the lower waves are considered. In wave record analysis, this is determined as the average period of the most frequently recurring of the larger well defined waves in the record under study. SLOPE. The degree of inclination to the horizontal. Usually expressed as a ratio, such as 1:25 or 1 on 25, indicating 1 unit vertical rise in 25 units of horizontal distance; or in a decimal fraction (0.04); degrees (2° 18’); or percent (4%). STILL-HATER LEVEL. The elevation that the surface of the water would assume if all wave action were absent. STORM SURGE. A rise above normal water level on the open coast due to the action of wind stress on the water surface. SUSPENDED LOAD. The material moving in suspension in a fluid, kept up by the upward components of the turbulent currents or by colloidal suspension. SYNOPTIC CHART. A chart showing the distribution of meteoro- logical conditions over a given area at a given time. 83 TROUGH OF HAVE. The lowest part of a waveform between successive crests. Also, that part of a wave below still-water level. UPDRIFT. The direction opposite that of the predominant movement of littoral materials. HATERLINE. A juncture of land and sea. This line migrates, changing with fluctuations in the water level. Hhere waves are present on the beach, this line is also known as the limit of backrush. (Approximately, the intersection of land and the still-water level. HAVE. A ridge, deformation, or undulation of the surface of a liquid. HAVE DIRECTION. The direction from which a wave approaches. HAVE HEIGHT. The vertical distance between a crest and the preceding trough. HAVE HEIGHT COEFFICIENT. The ratio of the wave height at a selected point to the deepwater wave height. The REFRACTION COEFFICIENT multiplied by the shoaling factor. HAVE PERIOD. The time for a wave crest to traverse a distance equal to one wavelength. The time for two successive wave crests to pass a fixed point. See also SIGNIFICANT HAVE PERIOD. HAVE PROPAGATION. The transmission of waves through water. HAVE SPECTRUM. In ocean wave studies, a graph, table, or mathematical equation showing the distribution of wave energy as a function of wave frequency. The spectrum may be based on observations or theoretical considerations. Several forms of graphical display are widely used. HAVE STEEPNESS. The ratio of wave height to wave length. (H/L). HAVE TRAIN. A series of waves from the same direction. HAVE TROUGH. The lowest part of a wave form between succes- sive crests. Also that part of a wave below still-water level. WAVELENGTH. The horizontal distance between similar points on two successive waves measured perpendicular to the crest. HIND 84 SETUP. On reservoirs and smaller bodies of water (1) the vertical rise in the still-water level on the leeward side of a body of water caused by wind stresses on the surface of the water; (2) the difference in still-water levels on the windward and the leeward sides of a body of water caused by wind stresses on the surface of the water. STORM SURGE (usually reserved for use on the ocean or large bodies of waterL HIND HAVES. (1) Haves being formed and built up by the wind. (2) Loosely, any wave generated by wind. APPENDICES APPENDIX A DATA TABLES 85 8...... 8.: 3.8. 8... E... .8. 8 .9. a. . .8 8 8.522(80885. 5:8 8 2.3.. #88 8.8.. 28. 2.2 .8. 8 .9. 8 c .8 c\. 8 85.22.8588,... 5:8 ca 8.5 8...! 5.28 8.8%. 8.88 ms... to. .8. m... .9. a. {A .8 .\. m E.¢.i....\808\oc.. 5:8 8 , 2898:: :38 289.83 8.8. 8.2.. 8.8. 8.... 2.... «8. 8 .9. S 8 .8 i. w 8.z.§~noo:\oc.. 5:8 2 .o and... 2.8.. 8...? 8... 2.... NS. 8 .9. S .v .8 8 8.x.z....\...08\oc.. 5:8 - .o 21.8.. .188 8.3: 23. 82.. NS. 8 .9. 2 8:8 .8 1. m 82.2..{808x82 5:8 .~ 8.8m. «~68. 8.8.: 88. E... .8. 8...... 2 8 .8 .\. m 8....Enmoflxoc: 5:8 2. 355. 936 8...... 8.2.. 8.5. 8.. 2.... R... 8 .9. a. .n .8 .x. 8 52.2808}... 5:8 8. 8...: 8.88 3.8.. 8... E... 3: 8 .9. S R .8 .x. m BESEMURR... 5:8 o. 8.28 8.28 8...: 8... to. 2... 8 .9. s. cm .8 ex. 8 82.28.}...{32 5:8 2 2.8. 2.8. 8...... 8.... F... 2... 8 .9. a. 3 .8 ex. 8 ESSEKOSR... 5:8 o. 8.26 888 8.8.. .8. 2.... 2a. 8 .2 2 S .8 .x. 8 83.23.0885. 5:8 8. 9.58: .560 £25 2...... 8...... 3.88 8... E... .8. .8 .x. m $3.22.}..oooxoc: 5:8 I 2.8.: 9...... ~32... 8a. 2.... .2: .8 ex. 8 5.x..fl..\o~08\oc.. 5:8 n. .0 2.2: 8.88.. 2.2.. 8... F... .8. .8 8 82.8(20885. 5:8 2 3.68 8.2.. 2.8.: one. 2.5 .3. .8 v) w 58.8.(30805. 5:8 .— 585.635 8.58 263.... 288 8.2.... 3.8.. 8... Km. :8. 8 .9. S Di. .8 8 8.52880885. 5:8 a 2.8... 22.8 8.2:. 8... .8. c8. 8 .9. S m. .8 ex. 8 2.2.2.}...0885. 5:8 a 355. :58 B280 55.. ,2: 252. .83.. 2.8.... 8... 2.... c8. 8 .9. a. a. .8 .\. m 8.58:.5885. 5:8 8 8...: 2.2.8 3.2.8 8.... R... :8. 8 .9. a. 2 .8 8 8282\80882 5:8 8 .n 3.8.. 2.8.. 3.8... 8... 2.... :8. 8 .9. a. 2 .8 a: 8.x.mvtooflxoc: 5.02 v 8.2... 868. 8.22 8... E... :8. 8 .9. a. .n .8 .\. m 88.82508}... 5:8 n .u 2.88 2.8.... S82. 8... 2.... 8.: 8 .9. a. .o .8 .x. z 8.u.8.\n08\0c.. 5.8 u .58.. .5 .558 ESE—o .3... 0...... 5.96:: So .58 SE. «.95.... Q8 E2: 5.52 25.8 22.58 58.! 52.8 E... 8:88 a...» .86 25.... B 825...... 5.55.5... 8 as: 2...... a... <53 EEK—unfit Q: war—.18. Prum 3:. 2.8288- 2. 2338.: 23 .c 02a... 86 ..00. c. 0.0 0.5.5.0000... .3 .~ $0.600 050.... :3 002. 00.. .5800... 630225.... 0.0 0030.1 ..0 0.0.! .. .003 0903.0 0 .0 0030250... 05 5... 2.2 0. 0030.0: 0.! .00.... 0E. .00: 003000 05 .0 000.0 503 ..0 30.0 :03 05 003005.00 0.... 0 03 03-. 0!. .5500... .0 . .05. 0:0 2.2 0003.03 .00. 2o .0 000. 500.0 .33 0 3.00:... :03... 3.000... 8.3... 0 5... 8309.00 6030.000 .0: 0.0020. >03... 2.. 390333 .0... 00.0.. .0303 .0 .0302 0000.0... 2.0.2.505... 30..) 3000.5 05:... 0 .0 0003 0.05.00 05 5... 0020500 0:: 003000 0.... .0 .0333 0 00 0.030 .0 3000. 03. in... .0303 33030... 0. 0.3 0.5 .0. 0.... 00.0000... .503 one. 0.2. 6.0.2.000 0:0... 0033.5 0.50 9.0 953 00.0. 0 0.0.1. :03 0... 03000.03... 0:: 00308 08.. .3 4.2... c. .0303 .3 003033500 00...: 05 00 00...... 0. 00... 00.8000. 03. 8.0.05 32.2 00.... 3.50.... c003 00.. 00.00000. .33 .0003»... 030.0208... 0 5.60 0... 5.8 8.0.8.0 .0: .58 2... 80.0.. .5002... .8... 80.02... :8 0.... .00.. a 5...... :2 .35 5.8000. .8... 0.0... 088 .._.2. .0380 .a "E ....==...oo. . 0.... 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D c~.ml -.wu ~a.~u 06.ncml u~.nbl aa.aNVI m mm.v| v~.ml am.v| Bu.oahn Q~.vhl No.~mol v h~.—I ~5.~I vN.—I ou.coml mw.mul mm.~0~a n w—.~I 56.8 e~.~| mm.o~ml 50.0 Nm.a~mu N wag was: 2.13.2 wman mead 332.2 flag: 9—. >m>~5m 0.5 On. shuwa— 9—. >m>~5m Q5 9—. >m>~5m Qflu Oh. thwhau Oh. agm Qflu Wham EF<¢ ZO—wmmuca J<322< m0<¢w>< flUZ¢=U.FmD¢U.hb=JD .uoea. WWFta zonwmwumm cewmmmoom .m ~_pm~ Spring wave dab. Table 6. SPRING WAVE DATA 88 O a: mm HHHssmha~mavmmmr~hhr~@mwwmvmmvvvv vm I]: 00.000.000.00 00.000.000.000000000 3 v-4 . NNSGGma‘thmvthva-vvmmmuhmmwmmma‘m—a E" O O O. O O O O O O O O O O O O O O I O O O O O O O O. O O O O O. I mmmmmvvoohmmhwwwhhhhhhhhwwmmmmhspwm HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHv-‘HHH O a: O‘fiwml‘hr‘HwaNO\VI-OHNMMMMMV'MHQQQQO‘O‘OG E O O O O O O O O 0 O O O O O O O O O O O O O O O O. O O O O O. mwmmmwma~o~c~ma~wwmwmc~mmmaxo‘mmmwmmmmmmas E mmmmmmmmmNNwNoNNwhhbwwmQ'HIN—dwmaaxbhd O O O O O O O O O O O O O O O O O I C O O O O O O O O O. O O O O 0. E mmmmmmmcvmommvvvmmmmmmmmmvvmmvvvvv HHHHHHHHHHHHHo—Odo—d—l—(HHHHHHHHHHHHHHHH . vvmmmmmvvvmfiaa‘hbhhhbwomanhommmvmmb m 0 O O O O O O O O O O O O O I O I O O O I O O O O O O. O O O O O O a: E Qmwmmmwmmmmmmhbbmwwmmwmwmommwmmwmw an: u: E? 8 a H N E oovvvmmmstVQMNvafl-vMMNN—aasr‘wwhN—‘Hm m 0 O I D O O C O O I O O O. O O O O O I O O O O O O O O. O O O O C O [- HHHHHHHHNNNNNNNNMMMMMMMMMNNNNNMMMN g :1: HHHHHHHHHHHH—lu—OHHHHHHHHHHHHHu—CHHHHHH U) E . H a: webmaxmmmhhhommvvvmmmmmmmmmmmmmmaNNm E I O 0 O O O O O O .0 O O O O I I O O O O O O O O. O O O O O O E m hhhhhbhhr‘hhhr‘bhhmmmmmmmmwmmmmwwmmm E E 3 S U H a . mmo~a~o~m¢mwmm vmmo~mwmmr~hww00mwmmmmmm a E 00000000000000.0000.00000000000000 a. O\U\O\O\O\O\O\O\O\O\O\SSGDGHHHHHHHHHHHHHHHHHH m HHHHHHHHHHHHHHHHHHHHHHH O a: HowmmmmmmmvMMNNNmmmwmmmmmuH—daaa‘as—d a 0 O O O I O I O O O I O. O O O I O O O O O O O O O O. I O O O O O hhhhbhhhhhhhhhhhhhhhhhhbhmmmmmhmmm g In . m'mbwwmmmaxmasNvmmmmmmmmmmmammmmmmmmm O O O O O C O O O O O .0 C O O O O O O O O O C O O C O O O O O O O E wmmmmmmmmowmcsaamammaaaacxaasaaaaaaa v-IHHHHHHHHH a: g [— vamw hm r-Nm <- mwbmc‘ GHNM «- max :3 I-b-(H H HHHHH NNNN N mm 2 8 E \D Inq- M N H G cnco f‘ \D H N NN N N N N HH .4 H z 8 H I NOTE: Wave heights are given in feet and wave periods are given in seconds. 89 .250me 5 53¢ 3m 3330 963 can umwu E 530 mun mun—Em: 263 «ED: N.a~ u.- 0.5H h.a~ m.a~ h.mH u.a~ v.5H o.a H.wH ma m.aH h.- 9.5H ~.HN c.m w.aH h.m b.h~ m.a H.@H an m.aH h.NN m.a~ H.~N m.m w.mH m.¢ 5.5H ~.¢ H.0H an 5.8H a.m~ ¢.u~ m.- $.m v.m~ m.m m.h~ H.m H.wH ha m.HH m.m~ N.HH a.H~ w.s~ h.aa u.a~ a.mH o.a v.9a VN n.da e.mm m.HH u.- 9.5H h.aH a.aH u.w~ w.a v.@~ ma N.HH a.mm a.a~ n.H~ ~.aH v.a~ a.a u.oH w.m h.wH ad N.HH a.- m.uH N.H~ N.aH n.a~ a.a 0.5H o.m 9.9H MN ~.HH m.- Q.u~ a.- n.8H a.¢~ h.¢ m.hu m.m N.w~ NN N.HH N.- o.a~ m.a~ m.oa a.a~ h.a n.5H v.0 m.mH AN ~.HH H.~N o.a~ b.5N m.aH 0.0H w.a ~.bH v.m o.m~ aw ~.HH a.NN «.3H h.aN m.a~ h.o~ w.m fi.h~ v.m b.mH am m.s~ m.HN m.u~ N.uN H.a~ m.m~ u.a a.mH m.m h.md ma m.a~ N.H~ m.aH H.uN $.5H N.mH a.o m.wH m.m b.ma ma szH H.~N v.3H u.s~ 5.5H ~.c~ w.m a.w~ m.¢ h.mH ha m.uH w.a~ n.a~ h.ma m.¢ a.h~ m.m m.o~ N.a h.mH ma m.a~ w.a~ n.5H h.ma w.m $.5H m.» w.mH N.a h.ma ma v.5a m.eN H.9H v.o~ h.m b.5H m.h b.oH ~.m h.mH AN m.a a.- n.a h.a~ 5.0 9.0H o.m h.wa v.o v.mH #H w.a a.AN m.a b.¢~ u.a a.mH o.w 5.9H 9.x v.m~ NN m.m ~.HN >.m m.a~ ~.m w.h~ o.w w.o~ w.m ¢.m~ ma m.aH m.HN c.3H ¢.a~ v.o o.hH H.¢ ¢.w~ a.m «.mH ~H m.a~ h.- 3.5H m.mH m.¢ v.hH ~.m m.wH u.m v.mH HA ~.HA H.N~ b.5H H.aN o.a H.hH m.a H.@H m.a v.mH MN s.HH v.HN v.5a v.m~ m.m ~.hH m.a A.@H m.m v.m~ m a.aH H.- n.5a H.a~ m.a H.h~ m.m H.@H m.m v.mH h w.a~ m.a~ ~.sa w.mH m.m H.h~ m.m H.@H m.m ¢.mH vN m.a~ m.s~ o.s~ w.o~ v.a b.oH ~.a b.mH a.a o.vH mN m.u~ h.a~ s.a~ h.mH v.a h.w~ ~.o h.m~ a.¢ ¢.mH w m.aH w.u~ a.uH h.ma m.m w.o~ «.o h.mH a.¢ m.vH m m.u~ m.a~ 5.3H o.m~ m.m w.w~ m.m h.mH ~.¢ m.v~ v m.ua v.5N c.3H m.mH m.¢ o.wa m.m h.mH H.¢ w.va m m.aH a.m~ 5.5H ~.wH w.¢ v.o~ v.m >.m~ ~.m m.v~ N m.sH m.m~ n.3H H.mH w.¢ «.wa ¢.¢ h.m~ ~.m w.qH wN «mm .9: .mmn .9: .mma .9: .mmn .9: .mmm .9: mmmzaz fizuon «(my 55H m¢m> am «(my am “(aw 5H mdua m mama Pmduazaz mooummm 02¢ mfizuum: m><3 444m (Eco m>§3qu