Downloaded from geology.gsapubs.org on May 23, 2012 Storm and fair-weather wave base: A relevant distinction? Shanan E. Peters and Dylan P. Loss Department of Geoscience, University of Wisconsin, Madison, Wisconsin 53706, USA ABSTRACT fair-weather wave base intersects the seafl oor Surface waves are an important mechanism for the redistribution of sediment on shallow and is associated with a change from wave marine shelves, and are commonly interpreted as comprising two distinct populations: fair- ripples and dunes with trough and swaley cross- weather waves and storm waves, the latter of which are generally thought to penetrate to stratifi cation above to hummocky cross-stratifi - greater water depths. Here we used >2.3 × 106 spectral density estimates for the surface ocean cation (HCS) below, the latter of which forms collected between 1996 and 2008 from 32 buoys in the Caribbean, the Gulf of Mexico, and under storm conditions (Dott and Bourgeois, the western Atlantic to test the hypothesis that surface waves in the modern ocean comprise 1982; Duke, 1985; McCave, 1985). The tran- two size modes. Although distinct wave size classes occur in some individual measurements sition to the offshore zone is defi ned by mean and over the time scales of some individual storms, time-averaged frequency distributions of storm wave base and is represented in strati- wave size are unimodal. Thus, there is no empirical basis for presupposing a distinct bimodal graphic successions by a change from HCS in separation in the size of fair-weather and storm waves, or in the manifestation of such differ- muddy and/or silty sediments to mud-dominated ences in stratigraphic successions. Instead, there is a continuously increasing probability that intervals that lack HCS below (Sageman, 1996). a wave will reach the bottom with decreasing water depth and a separate probability that The sedimentary structures that are used to describes the hydrodynamic state of the sediment-water interface. Wave size does, however, subdivide shelf deposits refl ect hydrodynamics, exhibit signifi cant geographic bimodality. Locations in the relatively protected Gulf of Mexico which in standing bodies of water is typifi ed by and Caribbean regions have modal wavelengths that are ~50 m less than waves at locations the passage of surface gravity waves that cause along the western Atlantic. Time-integrated estimates of the depth of wave penetration pro- oscillatory fl ow at the sediment-water inter- vide empirical constraints on the paleo-water depths of ancient sedimentary deposits and face. There may also be a component of super- highlight differences between sheltered shelf environments, such as those that characterized imposed unidirectional fl ow, a hydrodynamic many ancient epeiric seas, and open-ocean–facing, narrow continental shelves. condition known as oscillatory-combined fl ow (Allen, 1985; Duke et al., 1991). In order for a INTRODUCTION and storm wave base, at discrete and clearly surface gravity wave to entrain sediment, water The textbook shelf profi le (Fig. 1A) is intro- separated water depths. Wave base in the sedi- depth must be less than or equal to about one- duced to most students in sedimentology and mentary record is identifi ed by the characteris- half of its wavelength (Reading and Collinson, stratigraphy (e.g., Coe et al., 2003; Reading and tic structures and bedform relationships that are 1996). This depth is known as wave base. Oscil- Collinson, 1996). However, critical conceptual formed by water motion and sediment entrain- latory fl ow is the most common hydrodynamic inaccuracy may be inherent in the practice of ment. The shoreface to offshore transition zone state of the surface ocean and is associated with placing two important boundaries, fair-weather boundary is defi ned as the depth at which mean fair-weather (normal) waves. Waves character- ized by oscillatory-combined fl ow are typically associated with storms. Many studies have con- A nected one or both of these hydrodynamic states Mean sea level to the formation of HCS, and there are three Backshore postulated mechanisms for its formation: oscil- Foreshore Fair-weather wb latory fl ow (Dott and Bourgeois, 1982; Walker Shoreface Storm wb et al., 1983), unidirectional-dominated com- Transition zone bined fl ow (Allen, 1985; Swift et al., 1983), and Offshore oscillatory-dominant combined fl ow (South- BCard et al., 1990; Duke et al., 1991; Dumas and Hourly bimodal Hourly unimodal Arnott, 2006). observation 2007-8-29 observation 1996-1-3 Beginning in the 1800s (Gulliver, 1899), geoscientists used wave base terminology to describe and interpret sedimentary deposits (Dietz, 1963; Diem, 1985; Aigner, 1985; Sage- man, 1996). However, sedimentary structures do not correspond directly to water depth, but refl ect instead the interactions between the Spectral density Spectral density physical properties of sediment and the hydro- 0.02 0.04 0.06 0.08 dynamic state of the fl uid above the sediment- water interface. This is an important distinction because there need not be a simple relationship 0.00 0.05 0.10 0.15 0.00 0 50 100 150 200 250 0 50 100 150 200 250 between the hydrodynamic state of the ocean λ/2 (m) λ/2 (m) and the depth of wave penetration, as suggested by the typical conceptualization of fair-weather Figure 1. Standard depiction of shelf profi le and example hourly measurements of spectral density in surface ocean. A: Standard shelf profi le (after Coe et al., 2003) subdivided by tidal and storm wave bases (Fig. 1A). This issue is range and wave base. B, C: Individual hourly observations from buoy 42040 off coast of particularly relevant because wave base termi- Louisiana showing power as function of wave size and wave base (wb) (λ/2). nology is widely used to describe and interpret © 2012 Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or [email protected]. GEOLOGY,Geology, June June 2012; 2012 v. 40; no. 6; p. 511–514; doi:10.1130/G32791.1; 2 fi gures; Data Repository item 2012149. 511 Downloaded from geology.gsapubs.org on May 23, 2012 sedimentary successions. As of December 2011, λ=g2πf 2 , (1) quency scales. One scale ranges from 0.02 to ( ) GeoRef (www.georef.org/) returned 635 journal 0.4850 Hz in varying increments while the other articles with the phrase “wave base” in the title where g is gravitational acceleration and f is ranges from 0.03 to 0.4 Hz in even increments and/or abstract. Many more make use of the wave frequency measured in Hz. Non-breaking of 0.01 Hz. Most of the buoys followed one of concepts of storm and fair-weather wave bases waves change in profi le as they encounter the these scales for their entire observation interval. even though the terms are not used in their title bottom, but their frequency remains constant. However, some buoys switched between scales. or abstract. The goal of this study is to better Thus, the buoy spectral density estimates used In these cases, data for the longest continuous understand the meaning of these two descrip- here are useful for estimating wave size even interval were used, though results are insensitive tive and interpretive concepts for sedimentary in shallow water locations where waves may to this convention. successions and to test whether there is any encounter the bottom. Buoy data for signifi cant After converting individual hourly measure- signifi cant bimodality in wave size in nature. wave height, a historically and nautically preva- ments to wavelength, the time-averaged power It is taken into account that, at any given time, lent measure of wave size, were also compiled. spectrum for each site, which combines all many different sizes of waves may exist in the Each buoy analyzed had as much as 13 yr of data observations into a single composite measure- surface ocean, all of which fall into two catego- starting in 1996, though several buoys operated ment of the mean state of the ocean, was cal- ries, locally generated wind waves and swell. for only 1 yr. The combined data set consists of culated in two ways. The fi rst normalized each The latter are wind waves, commonly formed 2.39 × 106 individual spectral density observa- hourly observation by scaling the sum of the during storms, that have traveled long distances, tions. Each observation summarizes the power power across all wavelengths to unity (row nor- thereby undergoing sorting and organization by associated with spectral densities in wave fre- malization). This method forces each observa- wavelength (Snodgrass et al., 1966). quencies ranging from 0.02 to 0.485 Hz. Signifi - tion to contribute equally to the time-integrated cant wave-height estimates are not emphasized signal. The second method summed all of the METHODS here because only one data point exists for each hourly data for each frequency class and then Data were downloaded from the National observation and because signifi cant wave height normalized the resultant vector to unity (col- Data Buoy Center (http://www.ndbc.noaa.gov/) refl ects only the average size of the upper one- umn normalization). This method allows indi- in the fall of 2009. The buoys utilized in this third of all waves. Data for each buoy were com- vidual measurements with large power at some study all have spectral density estimates for bined into a single fi le and analyzed using the wavelengths to contribute disproportionately to the surface ocean, which are central for analy- R language (R Development Core Team, 2008). the time-averaged signal for a buoy. Because sis of wave size. The buoys are dispersed from Raw buoy data contain invalid and missing row normalization is more representative of the the Gulf of Mexico through the Caribbean and data due to episodic instrument malfunctions time averaged state of the ocean, it is used here, extend along the western Atlantic (Fig.