Methodology for reconstructing wind direction, wind speed and duration of wind events from aeolian cross-strata

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117,, doi: /2012jf002368, 2012 Methodology for reconstructing wind direction, wind speed and duration of wind events from aeolian cross-strata Erin N. Eastwood, 1,2 Gary Kocurek, 1 David Mohrig, 1 and Travis Swanson 1 Received 7 February 2012; revised 27 July 2012; accepted 30 July 2012; published 21 September [1] A methodology for reconstructing wind direction, speed, and event duration from aeolian dune cross-strata was developed from analysis of crescentic dunes at White Sands, New Mexico, during wind events. Dune lee faces were surveyed, lee-face deposits mapped, deposition rates measured, grain size sampled by stratification type, and winds characterized from meteorological and field data. The spatial distribution of lee-face stratification styles is a function of the incidence angle formed between the wind and the brinkline, with secondary controls by wind speed and dune sinuosity and height. Sets of wind-ripple strata form at incidence angles of 25 40, grainfall/grainflow foresets over wind-ripple bottomsets at 40 70, and grainflow/grainfall foresets at Erosional reactivation surfaces form at incidence angles up to 15 ; bypass surfaces up to 25. The total sediment load is fractionated within lee-face stratification types. Wind speed can be reconstructed from relationships between grain size, transport mode, shear velocity and grain-settling velocity. Where the full range of grain transport modes occurs and grain size is limited by shear stress, the shear velocity and grain-size range in each transport mode can be estimated by assuming the coarse fraction in grainflow strata traveled in creep, and the coarse fraction in grainfall traveled in saltation. The minimum duration of a wind event can be estimated using measures of shear velocity, dune height and dune forward migration. Method limitations arise with source-area control on grain size, extremes in wind events, and severe truncation of sets of cross-strata. Citation: Eastwood, E. N., G. Kocurek, D. Mohrig, and T. Swanson (2012), Methodology for reconstructing wind direction, wind speed and duration of wind events from aeolian cross-strata, J. Geophys. Res., 117,, doi: /2012jf Introduction [2] Aeolian dune cross-strata are the most direct stratigraphic record of continental winds and house a climatic record of the wind events that gave rise to the cross-strata. Aeolian cross-strata, which represent dune lee-face deposition, are inherently complex because: (1) most wind regimes are not unidirectional, (2) most dunes are too large to reform with each directional component of the wind regime, (3) the wind is rarely uniform or steady, and (4) the wind (i.e., primary flow) is strongly modified by the dunes themselves (i.e., secondary flow). Despite these complexities, geologists have long used the orientation of cross-strata (i.e., strike and dip) to interpret wind direction and compared these interpretations to models of regional or global circulation [e.g., Parrish and Peterson, 1988; Loope et al., 2001; Rowe et al., 2007]. In some examples, the types and orientations of cross-strata and 1 Department of Geological Sciences, Jackson School of Geosciences, University of Texas at Austin, Austin, Texas, USA. 2 Now at Shell Oil Company, New Orleans, Louisiana, USA. Corresponding author: G. Kocurek, Department of Geological Sciences, Jackson School of Geosciences, University of Texas at Austin, 2275 Speedway, M.S. C9000, Austin, TX 78712, USA. (garyk@jsg.utexas.edu) American Geophysical Union. All Rights Reserved /12/2012JF bounding surfaces have been used to interpret cyclic components of the wind regime [e.g., Hunter and Rubin, 1983; Kocurek et al., 1991; Scherer and Goldberg, 2010]. In other examples, the average dip direction of the cross-strata has simply been taken as the wind direction [e.g., Tanner, 1965; Parrish and Peterson, 1988; Mountney and Jagger, 2004]. As discussed below, this simplifying assumption is correct in only the special case where the total wind regime is unidirectional, and making this assumption may yield an inaccurate and incomplete picture of the wind regime. In addition, the wind speed associated with cross-strata has only rarely been addressed in a quantitative manner [Jerolmack et al., 2006, 2011], and although daily [Hunter and Richmond, 1988] and annual cycles [e.g., Hunter et al., 1983; Hunter and Rubin, 1983; Crabaugh and Kocurek, 1993] have been interpreted in sets of cross-strata, the duration of given wind events has not been explored. [3] The purpose of this paper is to build upon the existing understanding of sediment transport and airflow over aeolian dunes using data from the White Sands Dune Field in New Mexico to develop a quantified methodology for the reconstruction of wind direction, wind speed, and duration of wind events from sets of aeolian cross-strata. Determination of the wind direction is based upon the spatial distribution of lee-face stratification types. Determination of wind speed is based upon the distribution of grain sizes within stratification 1of20

2 types. Determination of the duration of wind events is based upon the volume of sediment transported during a wind event. 2. Theory 2.1. Reconstruction of Wind Direction [4] Experiments [Rubin and Hunter, 1987; Rubin and Ikeda, 1990], analytical solutions [Werner and Kocurek, 1997] and computer models [Werner, 1995; Bishop et al., 2002] all indicate that the crestlines of aeolian dunes are oriented to be as perpendicular as possible to all constructive wind directions within the total wind regime. This gross bedform-normal crest orientation [terminology of Rubin and Hunter, 1987] applies to any bedform where the duration of sediment-transporting flow from a given direction is shorter than the reconstitution time of the bedform, and applies to all but the smallest of aeolian dunes [Rubin and Ikeda, 1990]. In a wind regime that is not unidirectional, therefore, wind directional components of the total wind regime may not strike the dune crestline at right angles. In addition, because most dunes are sinuous, a variety of incidence angles occur along the crestline for any given wind direction. [5] Current thinking is that secondary flow on the lee face of a dune is primarily a function of the incidence angle (i.e., the angle formed between the primary wind and the local crestline orientation), but also of dune morphology and, to a lesser extent, atmospheric stability [Sweet and Kocurek, 1990; Walker and Nickling, 2003]. For steep dunes (i.e., dunes with slipfaces) during neutral atmospheric conditions that characterize most sand-transporting events [Frank and Kocurek, 1994], secondary flow is thought to be controlled by incidence angle. Based upon a variety of dunes in nature and a rotating experimental dune, Sweet and Kocurek [1990] classified lee secondary flow as a function of the incidence angle: transverse (70 90 ), oblique (10 70 ), and longitudinal (0 10 ). With a longitudinal configuration, the secondary lee flow is attached, undeflected and transport is entirely by tractional processes. As the incidence angle becomes greater (i.e., oblique), the lee flow is deflected to blow alongslope. Flow separation in the form of a vortex with components of alongslope and reversed flow [e.g., Allen, 1982] develops as the incidence angle increases. A 2-D roller with crestnormal return flow occurs as the incidence angle approaches 90. Wind speed along a lee face is approximately the crestal wind speed times the cosine of the incidence angle: secondary flow speed approaches the primary wind speed at longitudinal incidence angles and approaches zero at transverse incidence angles [Tsoar, 1983]. The general result is the dominance of tractional transport at longitudinal incidence angles, gravitydriven processes at transverse incidence angles, and the coexistence of both gravity-driven and tractional processes at oblique incidence angles. [6] Lee-face processes and the resultant stratification types result from the secondary flow configurations. The basic aeolian lee-face processes from Hunter [1977] are: (1) grainfall in which grains blown past the dune brink settle to the surface in paths that can be strongly modified by lee turbulence [Nickling et al., 2002]; (2) grainflow in which sediment deposited immediately downslope from the dune brink reaches the angle of initial yield, avalanches and flows down the dune slipface, and (3) wind ripples in which lee sediments of any origin are incorporated into and transported by the ripples. Grainfall and grainflow are gravity-driven processes and their exclusive presence indicates a transverse flow configuration where there is a general absence of tractional transport. Wind ripples are indicative of a flow configuration where tractional transport dominates, becoming increasingly prominent with decreasing incidence angles. Lee ripples typically have crests oriented parallel to the dip direction of the lee face as a function of alongslope transport and gravity [Howard, 1977]. With oblique flow, both grainfall/grainflow and wind ripples can occur, depending upon the spatial dominance of gravity-driven versus tractional transport. Typically, gravity-dominated processes on the upper lee face yield downslope to ripples migrating alongslope where tractional transport dominates. [7] In aeolian cross-strata, the stratification types are generally distinct and easily recognized in trenches or outcrops (e.g., Hunter, 1977, 1981; Kocurek and Dott, 1981). Grainflow cross-strata are tabular, tapering-upward wedges at the angle of repose and typically show inverse grading as a result of sorting during the avalanche process. Grainfall deposits are typically indistinctly laminated and range in dip from horizontal bottomsets to foresets that approach the angle of repose. Wind-ripple deposits are very distinctive, and consist of typically thin (i.e., millimeter scale), inversely graded laminae in which each lamina represents the migration of one wind ripple. In nature a variety of styles in the arrangement of the basic stratification types in sets of cross-strata occurs as a function of the total wind regime, the most common configurations are shown by Kocurek [1991]. [8] In summary, the current state of understanding is as follows. Because dune crestline orientation is the product of all constructive primary winds, the average dip direction of cross-strata within a set reflects the overall dune migration direction as measured normal to the generalized crest orientation. Unless the total wind regime is unidirectional, however, this average dip direction alone is insufficient to determine all the constructive primary wind directions that gave rise to the cross-strata. Because any given cross-strata orientation shows the local crestline orientation, a coupling of local crest orientation with stratification style brackets the local incidence angle into broad categories of transverse, oblique and longitudinal configurations. A compilation of pairs of local cross-strata orientation and stratification style all along a set reveals the overall crestline shape and orientation, and the range of incidence angles along the crestline. The correlation between incidence angle and stratification style, however, is known in only the broad categories of transverse, oblique and longitudinal. A primary goal in developing the methodology here is to provide a more precise correlation between incidence angle and style of stratification types, and to examine the extent to which other parameters may impact the distribution of lee-face surface processes Reconstruction of Wind Speed [9] The three end-member modes of sediment transport by the wind are creep, saltation and suspension, and these arise because of the balance between grain properties and the surface forces that cause motion [Bagnold, 1941]. For sand dunes, saltation is the primary mode of transport and is characterized by grains that rise from the surface in 2of20

3 quasi-parabolic arcs to again collide with the surface and eject other grains. Saltating grains, once ejected from the surface, are driven by fluid drag and gravity, with negligible effects from fluid lift by turbulent eddies. The heaviest grains move in creep, characterized by sliding, rolling or short hops, and are driven by the combination of the fluid stresses acting on grains and the kinetic energy transfer associated with impacts from saltating grains. The lightest grains are suspended, carried into the flow when vertical velocities associated with turbulent eddy motions exceed grain settling velocities, and have only rare surface contact. In nature, however, there is significant gradation between the endmember modes of transport, especially between pure saltation and pure suspension. This gives rise to motions best described as modified saltation and incipient suspension [e.g., Nishimura and Hunt, 2000; Nino et al., 2003]. [10] Attempts to characterize sediment transport all utilize basic relationships between fluid forces and grain properties. Fluid forces are characterized by the shear stress, t, exerted on the bed by the flowing fluid. This boundary shear stress is commonly presented as a shear velocity,, where r ffiffiffiffiffiffiffiffi. ¼ t rf ð1þ and r f is the density of the moving fluid. Shear velocity is then typically estimated from a measured velocity profile by application of the law of the wall u z ¼ u * k n z where u z is the wind speed at height z above the surface, k is von Kármán s constant (equal to in neutral atmospheric conditions), and z 0 is the surface roughness height where zero velocity occurs. Neglecting sorting, the transportability of a grain is a function of properties such as volume, shape and density. These grain properties can be characterized by grain settling velocity, w s, and the critical shear velocity to initiate movement, c. Bagnold [1941] observed that once grain motion is established, saltation continues and creep begins to occur at a lower than that required to initiate motion as a result of momentum transfer from the impact of saltating grains. From wind tunnel data, this critical impactaugmented shear velocity, i, is approximately 0.7 c [Bagnold, 1941; Nishimura and Hunt, 2000]. [11] Although developed for grains settling in water, the equation by Ferguson and Church [2004], as modified by Jerolmack et al. [2006], can be applied to air: w s ¼ z 0 ðs 1Þgd 2 C 1 v þ ð0:75c 2 ðs 1Þgd 3 Þ 1 2 where s ¼ r s r f is the relative density of sediment where r s is the sediment density, g is the acceleration due to gravity, d is the nominal grain diameter, v is kinematic viscosity for the fluid, and C 1 and C 2 are constants with values of 18 and 1, respectively, for natural sand. [12] We follow Jerolmack et al. [2006] in adopting the equation by Shao and Lu [2000] for c, which is based upon ð2þ ð3þ data from Iverson and White [1982] for a range of grain sizes that includes most aeolian sand: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c ¼ 0:0123 sgd þ 3! u t 10 4 kg= s 2 : ð4þ r f d [13] Given values for w s, c and, the range of near-bed conditions associated with the different modes of sediment transport have been described as a function of the ratios /c and w s /, as summarized in Figure 1a. Values of /c best serve to address the boundary between creep and saltation, as originally defined by Bagnold [1941], in which grains begin to saltate once c is exceeded (i.e., /c > 1), but creep occurs (and saltation continues) until /c = 0.7 (Figure 1a). Using high-speed videos, Nishimura and Hunt [2000] found that particle trajectories in saltation begin to be distorted by turbulent eddies when /c 1.5. This change in grain paths, although described by Nishimura and Hunt [2000] as the onset of suspension and adopted as such by Jerolmack et al. [2006, 2011], is probably best described as the onset of modified saltation. This change in grain paths would not be ordinarily detectable in the field, and is not a practical definition for suspension. In this study we adopt the relationship that creep occurs when 0:7 < 1:0; ð5þ c beyond which saltation occurs with an upper limit that is best characterized by the ratio w s (Figure 1b). [14] Values of w s are most appropriate to define partitions u in the gradation between * saltation and suspension because the downward grain settling velocity must be balanced by the upward velocities associated with turbulent eddies, which scale with shear velocity at small distances above the bed [e.g., Bagnold, 1966; Nino et al., 2003]. Attempts to define this gradation in both air and water, summarized in Figure 1a, are subject to differing experimental methods and terminology, as well as making judgmental determinations within a clearly gradational process. The onset of deviations in saltation paths (described above) by Nishimura and Hunt [2000] begins when w s 10, with greater values of the ratio reflecting pure bedload. More conservatively, Shao [2000] gives the boundary between saltation and modified saltation as w s / 2, with suspension occurring when w s / < 0.5 Using high-speed videos for transport in water, Nino et al. [2003] give the boundary between saltation and incipient suspension at w s 2.5, and the boundary between incipient suspension and full suspension as w s 1. These values agree with earlier works by van Rijn [1984] and Laursen [1958] where significant numbers of grains are advected into the flow interior by turbulent eddies when w s 2.5, and by 3of20

4 Figure 1. Summary diagram of experimentally derived boundaries for grain transport in creep, saltation, modified saltation, incipient suspension and suspension modes. (a) Summary of experimental results defining modes of grain transport by u and w s. Note that modified saltation and incipient suspension u c u are used by different authors to define the same mode of transport positioned between saltation and suspension. (b) Grain-transport boundaries adopted for this study as justified in the text. Bagnold [1966] where a measurable concentration profile of suspended sediment develops at w s 1. Laursen [1958] and Smith and Hopkins [1972] argued that the transition to suspension transport is complete when w s =0.3. [15] For field studies, a definition of suspension based upon a measurable sediment concentration profile is the most appropriate definition for the onset of suspension, and we adopt suspension as occurring when w s 1 (Figure 1b). All experimental work agrees that the transition from saltation to suspension is well underway in the range of w s = , and we adopt incipient suspension as occurring when 1 < w s < 2:5 (Figure 1b). Modified saltation would be largely undetectable from saltation in the field, and we combine these modes ð6þ ð7þ of transport, using the definition that pure saltation is tied to conditions where w s 2:5 (Figure 1b), whereas Jerolmack et al. [2011] adopt w s / 3.0 for this same boundary. u [16] Given ranges of * and w s associated with the c u different modes of grain transport, the * basis for our approach is the hypothesis that the total grain population traveling over a dune brink is sorted on the dune lee face as a function of lee processes (see section 2.1). Because the preserved aeolian rock record almost exclusively represents the lowermost portions of dune lee faces [Rubin and Hunter, 1982; Kocurek, 1981], we are concerned with the grain-size range in the stratification types that are found there. Although grains traveling in saltation can have trajectories that extend to basal portions of small aeolian dunes, we hypothesize that grainfall that accumulates on the basal lee of larger dunes is enriched in grains that traveled in incipient suspension and is depleted in grains that traveled in creep in comparison to the other lee-face deposits. In contrast, grainflow is hypothesized to ð8þ 4of20

5 Figure 2. (a) Location of the White Sands Dune Field in south-central New Mexico, USA. (b) Portion of the dune field within the White Sands National Monument, showing the zone of active crescentic and parabolic dunes, deflationary Alkali Flat, and playa Lake Lucero. The wind resultant toward N65E was determined from wind data recorded at Holloman AFB by Jerolmack et al. [2011]. (c) Dunes 1, 2 and 3 monitored in this study and the adjacent Dunes Drive, as indicated in (b). The lines define the brink and top of each lee face for the three studied bedforms. be more representative of the entire transport range of grains traveling over the dune. Because lee wind ripples reflect tractional transport of any grain population that has passed the dune brink, we hypothesize that wind ripples possess the least diagnostic distributions of grain sizes, with the exception that coarse grain sizes should be associated with deflationary surfaces. [17] Our approach in determining wind speed largely follows that of Jerolmack et al. [2006, 2011], also at White Sands, but differs in objectives. Jerolmack et al. [2011] systematically sampled dune stoss, crest and lee face in order to determine the mean grain size in transport, from which the characteristic for the dune-forming wind could be derived. The dune-forming wind, by a combination of magnitude and frequency, does the most work in dune-field construction [Jerolmack and Brzinski, 2010]. This parameter is important, but because dune grain size is similar throughout the Phanerozoic on Earth [e.g., Kocurek, 1996], significant ranges in wind speeds are most likely to be found in the extremes of the grain-size range for each mode of grain transport as preserved in dune cross-strata. Our methodology is focused, therefore, upon characterization of specific wind events as recorded in lee-face stratification, the most common of which will reflect the typical wind regime. 3. Study Area and Methods 3.1. Study Area Overview [18] Data for this study were collected from the gypsum dune field within White Sands National Monument, New Mexico (Figure 2a). The White Sands Dune Field is situated within the Tularosa Basin and consists of a core of crescentic and barchan dunes, which is rimmed to the north, east and south by parabolic dunes. To the west the dune field yields abruptly to an extensive gypsum plain, Alkali Flat 5of20

6 (Figure 2b). Further to the west, occupying the lowest elevations of the basin, are active playa lakes, the largest of which is Lake Lucero. Analysis of the decades-long wind record recorded at nearby Holloman Air Force Base (AFB) by Fryberger [ parks/whsa/] and Jerolmack et al. [2011] yields a transport resultant of 060 and 065, respectively (Figure 2b). Dominant winds are from the WSW and are strongest during the winterspring, a second mode of winds from the N-NW occurs during the fall and winter, and a third mode of winds from the S- SE occurs during the spring and summer. [19] Aspects of the White Sands Dune Field have been addressed in a number of studies, and a much fuller description and interpretation of its history, geomorphology and sedimentology are given collectively by Kottowski [1958], McKee [1966], McKee and Douglass [1971], Allmendinger [1972], McKee and Moiola [1975], Langford [2003], Jerolmack et al. [2006, 2011], Kocurek et al. [2007], Langford et al. [2009], Ewing and Kocurek [2010], Reitz et al. [2010], Szynkiewicz et al. [2010], and Fryberger [ nature.nps.gov/geology/parks/whsa/] Methods [20] Three crescentic dunes were chosen for this study because of their relatively high sinuosity (Figure 2c). The dunes were similar in height, with average brinkline heights of 10.6 m for Dune 1, 9.7 m for Dune 2, and 9.1 m for Dune 3. The brinkline and lee-face base of each dune were surveyed using a Trimble S3 (2 ) Robotic Total Station during calm periods before sand-transporting wind events during March and April During the surveying process, dowel rods (3 mm in diameter) were set into the dune lee faces at 2 m intervals from the base of the lee face to the dune brink, forming transects oriented perpendicular to the brinkline. The lateral spacing of these transects was such that representative segments of the curving dune lee faces were sampled. [21] Both the March and April wind events were 24 hours in duration with winds above threshold speed and significant sand transport. Lee-face deposits were identified and mapped along the entire lee faces at a sub-meter scale for Dunes 1 and 2 after the March wind event, and along Dune 3 after the April wind event. Primary wind directions were determined by the average orientation of wind ripples on the upper stoss slopes of the dunes, and compared to the wind data recorded at Holloman AFB during the same intervals. The weather station at Holloman AFB is located 14 km ENE of the study area, and wind data, collected at a height of 10 m, consist of average wind speed and direction over 2 minute intervals and the maximum wind gust during 10 minute intervals. [22] The incidence angle for each approximately straightline segment of the lee face was determined based upon the primary wind directions, and lee-face deposits were plotted by incidence angle. Dune sinuosity, s, was calculated based upon the surveys using the definition that s = L / L, where L is the measured brinkline length and L is the straight-line distance. Points of divergence in the lee-face secondary flow field were used as the end points for dune segments for which local brinkline sinuosity was also calculated. [23] During the April wind event, wind speed was measured over a 2 hour period using robust hot-wire anemometers mounted on a staff at heights of 4 cm, 10 cm, 30 cm and 80 cm above the bed at the crest of Dune 3. This wind profile was subsequently compared to the wind record for the same time interval as recorded at Holloman AFB. [24] The amount of deposition/erosion that occurred on the lee faces during the wind events was measured off of the dowel rods after the wind events, and these changes in surface elevation were converted to lee-face deposition rates by dividing by the length of time during which the wind was above threshold speed. [25] Grain-size samples were taken at dowel locations. Care was taken to sample the entire lamina/stratum formed by a given lee-face process, such that the entire thickness of windripple laminae and grainflow tongues were taken. Grainfall deposits were sampled by scraping off and collecting only those grains from the immediate surface. Grain-size analysis was performed using a Retsch Technology CamSizer (www. retsch-technology.com), which digitally images and measures most grains in each sediment sample. Errors associated with measuring grain size using this device are significantly less than those associated with sieving techniques. The grain-size distribution for each sediment sample is composed of 50 bins spaced logarithmically over the diameter range of mm and was plotted by lee-face stratification type. The range in grain size for each mode of grain transport (e.g., creep, saltation, incipient suspension, full suspension) as predicted from equations (5) (8) was calculated for both wind events. 4. Results 4.1. Primary Wind Direction and Incidence Angles [26] The primary wind directions determined from the average orientation of wind ripples on the stoss slopes of Dunes 1 3 were 069 for the March wind event, and 068 for the April wind event (Figure 3). These values compare to 061 and 059, respectively, as recorded at Holloman AFB. The differences in primary wind directions as measured at Holloman AFB compared to those measured within the dune field probably occur because: (1) the weather station at Holloman AFB is situated leeward of the dune field, closer to the Sacramento Mountains, and may not experience exactly the same wind regime as that within the dune field, and (2) dune topography affects the orientation of the nearbed flow. The average orientation of stoss-slope wind ripples is taken as the more accurate indicator of the primary wind within the dune field, especially as it relates to the incidence angle, and is used in our analysis. [27] Calculated dune sinuosity ranges from 1.31 for Dune 3, to 1.44 for Dune 1, to 1.61 for Dune 2 (Figure 3). Given the primary wind directions, local incidence angles for approximately straight-line segments of the brinkline range from 2 90 (Figure 3). Local brinkline sinuosity, defined by points of divergence in the lee-face secondary flow field, ranges from (Figure 3) Lee-Face Processes, Stratification and Incidence Angles Basic Styles of Lee-Face Processes and Stratification [28] Seven basic styles of lee-face processes and their resultant stratification were identified and are designated as Styles A G in Figure 4. Within these basic styles, there was 6of20

7 Figure 3. Maps of the lee faces of Dunes 1 3 showing the spatial distribution of styles of lee-face stratification (see Figure 4) as mapped after the March (Dunes 1 2) and April (Dune 3) wind events. Uncolored areas represent dune segments where the lee face was not defined by a brinkline; these segments were not considered in this study. Primary wind directions were determined by the orientation of stoss-side wind ripples. Local incidence angles along approximately straight-line segments of the brinkline are noted to the left of each segment. Sinuosity for entire dunes is given; local segment sinuosity is shown to the right of the segments, with segments of particularly high sinuosity in red. Black dots mark the location of lee-face traverses where sediment erosion/deposition was measured off of dowel rods, and where grain-size samples were taken. significant variation, which is thought to represent stages of development. For example, grainflow deposits varied from pristine to subdued ( ghosts ) where grainflow tongues had been partly blanketed by subsequent grainfall deposits or partly mantled by wind ripples. The seven basic styles of lee-face stratification represent a distillation that would be recognizable in the rock record. [29] Style A (wind ripples) characterized entire segments of lee faces, ranging from those experiencing erosion to bypass to deposition (Figure 4a). At White Sands, ripples on erosional surfaces, which typically exposed weakly cemented dune cross-strata, were coarser grained than those on surfaces undergoing sediment deposition. Wind-ripple stratification is probably the most common stratification type 7of20

8 Figure 4. Field photos and diagrammatic renderings (used as symbols in Figure 3) of the 7 styles of lee-face stratification recognized on Dunes 1 3 after the March and April wind events. (a) Style A wind ripples (wr) occurring on net erosional, bypass and depositional surfaces. (b) Style B wind ripples and grainfall (ga). (c) Style C wind ripples, grainfall and grainflow (gf). (d) Style D grainfall only. (e) Style E grainfall and grainflow with basal wind ripples. (f) Style F grainfall and grainflow. (g) Style G grainflow only. in the aeolian rock record [e.g., Hunter, 1981, Figures 3 4; Kocurek and Dott, 1981, Figure 8], and consists of the translatent strata of Hunter [1977]; the very thin subcritically climbing variety referred to as pin-stripe laminations by Fryberger and Schenk [1988]. [30] Style B (wind ripples and grainfall) occurred on surfaces of bypass to deposition and is characterized by grainfall on the upper lee face passing downward to wind ripples (Figure 4b). These lee faces, therefore, show a mix of gravity-driven and traction-driven processes. Grainfall deposits are largely prevented from building to the angle of initial yield and avalanching by alongslope reworking by the wind ripples. At White Sands, Style B ranged from patchy grainfall deposits on largely rippled lee surfaces to lee 8of20

9 Figure 4. surfaces mostly covered by grainfall deposits with minor basal wind ripples. The representation of this stratification style in the rock record is a function of original dune size and preserved set thickness. On small dunes, where grainfall typically reaches the base of the lee face, Style B shows a dominance of grainfall deposits in the upper portion of the set passing downward to interlaminated wind-ripple and grainfall laminae, the former commonly showing a high angle of climb [e.g., Hunter, 1981, Figures 5a and 6; Hunter and Richmond, 1988, Figure 19; Kerr and Dott, 1988; Figure 3a]. On large dunes or where only the most basal lee face has been preserved, Style B may be indistinguishable from Style A except for the intercalation of some grainfall laminae. [31] Style C (wind ripples, grainflow and grainfall) typically represented a more depositional surface than Style B and one which was more dominated by gravity-driven (continued) processes (Figure 4c). Either higher rates of grainfall or less tractional reworking by wind ripples allowed the grainfall deposits to build to the point of avalanching, yielding grainflow tongues. Wind ripples, however, mantled the entire surface between avalanches, and dominated on lower portions of the lee face. Style C is common in the rock record, and is represented by grainflow cross-strata that both (1) intertongue with bottomsets of ripple laminae, and (2) are intercalated with ripple laminae that extend to the top of the sets [e.g., Blakey and Middleton, 1983, Figure 11c; Hunter and Richmond, 1988, Figure 21; Mountney and Jagger, 2004, Figure 5a]. [32] Style D (grainfall) is characterized by lee faces showing only grainfall deposits, which may extend as aprons onto the interdune floor (Figure 4d). This stratification style should be inherently ephemeral because the grainfall deposits should build to the angle of initial yield and 9of20

10 Figure 5. Styles of lee-face stratification (Styles A G) plotted by their range of incidence angles on Dunes 1 3, as indicated by data point color. Local dune-segment length over which the lee-face stratification style occurred is shown by data point size. Data points circumscribed by dashed ovals represent lee-face processes that occurred on dune segments with high local sinuosity (marked in red on Figure 3). Note the occurrences of first grainfall, first grainflow, and the last occurrence of wind ripples. avalanche (Style F). At White Sands this stratification style occurred along tapering segments of transverse dune terminations. Although not common, cross-strata consisting largely of grainfall laminae have been described [e.g., Hunter, 1981, Figure 5b; Clemmensen and Abrahamsen, 1983, Figure 6a]. [33] Style E (grainflow, grainfall, and basal ripples) is similar to Style C, with the important difference that wind ripples occur only at the base of the lee face (Figure 4e). Style E, therefore, represents a gravity-dominated slipface except for the basal portion where traction still dominates. In the rock record, this stratification style is identified by grainflow cross-strata that intertongue with bottomsets of ripple laminae [e.g., Chandler et al., 1989, Figures 3a and 3c; Clemmensen and Blakey, 1989, Figure 11]. Ripple laminae intercalated with the grainflow strata, a characteristic of Style C, are largely absent. [34] Style F (grainflow and grainfall) is characterized by slipfaces in which grainfall mantles some or much of the surface between avalanches and wind ripples are absent (Figure 3f). The extent to which grainfall is carried down the lee face is a function of dune size, wind speed and turbulence associated with lee eddies. In the rock record, Style F is represented by grainfall laminae intercalated with grainflow cross-strata [e.g., Kocurek and Dott, 1981, Figures 5 6; Clemmensen and Abrahamsen, 1983, Figure 6b], but it may be indistinguishable from Style G where slipface height or other factors precluded grainfall on the lower lee face. [35] Style G (grainflow) is characterized by slipfaces where pristine avalanche tongues extended from the lee base to the dune brink (Figure 4g). The difference between Style G and Style F is that although grainfall occurred in Style G, it was confined to the uppermost slipface and the frequency of avalanching in Style G was much greater than in Style F. Style G is common in the rock record and consists of sets of cross-strata composed exclusively of grainflow strata [e.g., Hunter, 1981, Figure 6d; Kocurek et al., 1991, Figure 10; Loope, 1984, Figure 5b; Taggart et al., 2010, Figure 6a] Distribution of Styles of Lee-Face Stratification by Incidence Angles [36] The mapping of the styles of lee-face stratification (Styles A G) on Dunes 1 3 after the March and April wind events illustrates the diversity of stratification that may form along the lee faces of sinuous dunes during single wind events (Figure 3). The simple plotting of these stratification styles by incidence angle shows a general trend from Style A through Style G corresponding to progressively higher incidence angles (Figure 5). Wind ripples and their stratification where the surface was depositional (Style A) dominate at low incidence angles, and grainflow and grainfall stratification (Styles F and G) dominate at high incidence angles. Between these end-members there is a progression in Styles B E from the first occurrence of gravity-driven surface processes (grainfall at 16 in Style B and grainflow at 22 in Style C), to the last occurrence of tractional transport (wind ripples disappear at 70 in Style E) Characterization of Wind Speed [37] Wind speed is directly characterized by: (1) the velocity profile measured at the crest of Dune 3 during the April wind event, and (2) wind data recorded at Holloman AFB during both wind events. Wind speed is indirectly characterized by: (3) dune migration rates during the wind events, and (4) the grain-size distributions within the lee stratification types Direct Characterization of Wind Speed [38] The wind velocity profile measured at the crest of Dune 3 during the April wind event shows = 0.36 m/s as calculated from the equation (2), with z o = 0.2 mm (Figure 6). Wind data recorded at Holloman AFB during the same interval shows an average wind speed of 6.5 m/s, with an average gust speed of 10.3 m/s (Figure 6). The projection of the velocity profile measured at the crest of Dune 3 to the 10 of 20

11 Figure 6. Velocity profile (blue) for wind measured by hot-wire probes at 4 cm, 10 cm, 30 cm and 80 cm above the bed at the crest of Dune 3 during the April wind event. Each point represents the average speed for a 2-hour sampling interval, with wind speed measured every 10 sec. The range bars on each mean velocity is +/ one standard deviation. The surface roughness height, z o, is the Y-intercept at 0.2 mm. Using equation (2), the calculated is 0.36 m/s. The measured profile is projected up to a height of 10 m, the height at which wind data is collected at Holloman AFB. For the same period as our measurements, the mean and range for average and gust wind speeds recorded at Holloman AFB are shown (green triangle = average, red square = gust). Note that the projected wind speed at 10 m is most closely approximated by the average gust speed measured at Holloman AFB. In contrast, the velocity profile (red) defined by gust speeds measured at the crest of Dune 3 projects well beyond gusts recorded at Holloman AFB, and yields a calculated of 0.59 m/s, with a z o of 0.8 mm. The best fit to each velocity profile is presented in the law of the wall (equation (2)) format. The p-value for the regression equation using the average wind data is and for the regression equation using the gust data is , indicating a statistically significant relationship between the variables in each equation at the 5% significance level. 10 m height at which data are collected at Holloman AFB yields 9.7 m/s, which is within the gust range recorded at Holloman AFB. Indeed, using the average gust speed at 10 m (10.3 m/s) and z o = 0.2 mm yield = 0.38 m/s, which is 5% greater than the measured crestal. In contrast, the velocity profile for the average gust speed, using the highest 10% of wind speeds measured at the crest of Dune 3, projects well beyond the range recorded at Holloman AFB, and yields = 0.59 m/s with z o = 0.8 mm (Figure 6). Note that the increase in the value of z o over the same surface with the increase in is expected because of the greater intensity of saltation and momentum extracted from the wind [Owen, 1964; Wiberg and Rubin, 1989]. [39] Because the primary wind is modified as it travels over the dune topography, including acceleration up stoss slopes and deceleration on the lee slopes, the appropriate dune wind speed to compare to that recorded at meteorological stations is not straight-forward. For the White Sands example, the calculated at the dune crest is approximated by the calculated using the average wind gust as recorded by meteorological data collected at 10 m, and provides a convenient reference point for characterizing the wind event. The average wind gust speed during the monitoring period (23 hrs) for the April wind event was 12.1 m/s, yielding = 0.45 m/s, using z o = 0.2 mm. The average wind gust speed during the monitoring period (14 hrs for Dune 1, 22 hrs for Dune 2) for the March wind event was 9.4 m/s, yielding = 0.35 m/s, using z o = 0.2 mm. These values of shear stress are adopted here as approximations that characterize their respective wind events. The formative shear velocity f = 11 of 20

12 Figure 7. Dimensionless lee-face sediment deposition as a function of local incidence angle for Dunes 1, 2 and 3. First the average amount of sediment deposition measured from dowels (Figure 3) on roughly transverse segments of lee face for Dune 1, 2 and 3 was calculated. Then the value for deposition at each transect site was made dimensionless by dividing it by the appropriate mean transverse value for Dune 1, 2 or 3. Measurements for transects on all three dunes are plotted here. Negative values for deposition represent sites of net sediment erosion from the lee face of a dune. The figure includes two trend lines. The thick solid line is the best fit to the data points. The thinner dashed line depicts the control of incidence angle on dune migration speed as first proposed by Rubin and Hunter [1985, equation 2]. Notice that incidence angle alone (dashed line) does a reasonably good job of predicting the relative amount of lee-face deposition tied to dune migration. However, including a shift of twelve degrees (solid line) provides a better fit to data and captures the lee-face erosion measured at transects with low incidence angles. The p-value for this regression equation is smaller than 10 4, indicating a statistically significant relationship between the sine of incidence angle and dimensionless lee-face sediment deposition m/s for the White Sands Dune Field determined by Jerolmack et al. [2011] falls between the values for our March and April events Lee-Face Sediment Deposition as a Function of Incidence Angle [40] Sediment deposition on the dune lee faces during the March and April wind events, as determined from measurements taken off of the dowel rods after each wind event, are not uniform but rather trend with incidence angle (Figure 7). Greatest deposition rates occurred at high (transverse) incidence angles, and deposition rates generally decreased with incidence angle, with examples of bypass (i.e., zero deposition) occurring at incidence angles of and erosion dominating where the incidence angle is less than 15.This relationship between lee-face deposition and incidence angle occurs because the lee face in transverse configurations is unmodified by alongslope transport, whereas alongslope transport of sediment progressively increases and reworks the lee faces of dunes with decreasing incidence angles characteristic of oblique and longitudinal flow configurations. [41] For the White Sands data the relationship between standardized deposition on the lee face, f, and incidence angle is presented in Figure 7. In order to determine f for all transects on Dunes 1, 2 and 3 (Figure 3) the average amount of sediment deposition measured from the dowels on transverse segments of each dune was calculated, z trans. Then the value for deposition at each transect site, z local, was divided by its associated dune value for z trans. Measurements for transects on all three dunes are plotted together in Figure 7. Negative values for deposition represent sites of net sediment erosion from the lee face of a dune. This figure includes two trend lines: and f ¼ z local ¼ sin a ð9þ hz trans i f ¼ z local h i z trans ¼ sinða 12Þ ð10þ 12 of 20

13 Table 1. Transport Modes for March and April Wind Events a Transport Mode Creep 0.7 c < 1.0 Saltation w s 2.5 c > 1.0 Incipient Suspension 1.0 < w s < 2.5 Suspension w s 1.0 March Wind Event u* = 0.35 m/s mm mm mm 117 mm Total Volumetric Sediment Load 27.3% 64.4% 6.9% 1.4% Grainflow Fraction 31.2% 64.5% 3.4% 0.8% Grainfall Fraction 15.3% 71.6% 11.6% 1.5% Wind Ripple Fraction 35.9% 57.1% 5.3% 1.7% April Wind Event u* = 0.45 m/s mm mm mm 136 mm Total Volumetric Sediment Load 3.9% 76.3% 15.5% 4.2% Grainflow Fraction 6.0% 79.8% 10.9% 3.3% Grainfall Fraction 0.9% 76.0% 18.8% 4.2% Wind Ripple Fraction 3.0% 71.5% 19.8% 5.6% a Summary of equations defining the boundaries for grain transport modes of creep, saltation, incipient suspension and suspension. For each mode of transport, the predicted grain-size ranges are given for the March and April wind events. Based upon the grain-size data, the percentages for each grainsize range are given for the total volumetric sediment load and the lee-face processes. Estimates for for each wind event were based upon average gust speed at 10 m as recorded at Holloman AFB during each event using equation (2) with z o = 0.2 mm. Estimates of w s were calculated from equation (4). Estimates for c were calculated from equation (3). where a is incidence angle. Equation (9) describes the control of incidence angle on lee-face deposition and, hence, dune-migration speed as first proposed by Rubin and Hunter [1985, equation 2]. In Figure 7, equation (9) does a reasonably good job of predicting the relative amount of lee-face deposition, but over-estimates the observed deposition at lower incidence angles. Equation (10) is the best-fit line to the data set presented in Figure 7. Including a shift of 12 captures both the zone of lee-face bypass and the zone of erosion at low incidence angles. The inclusion of this phase shift in equation (10) indicates the relative amount of sediment deposition on the lee faces dunes is not simply a matter of incidence angle. There is a measurable correction associated with lee-face processes that are not a function of incidence angle alone. Resolving these processes is an important avenue of ongoing and future research Indirect Characterization of Wind Speed by Measured Dune Migration Rate [42] The measured, lee-face deposition rate indirectly characterizes the wind events by providing a measure of the sediment transported during the events. The required to transport this sediment over the duration of the wind event is effectively the characteristic of the wind event. Because of the potential for alongslope sediment transport in all but the most transverse flow configurations, those deposition rates occurring within measured incidence angles of provide the most accurate measure of the event sand transport rate. The average volume flux of sediment, q s (m 2 /s), can be estimated for transverse segments of the observed dunes (incidence angles >70 )as q s ¼ ɛc H = 2Þ ð11þ where C is dune forward migration rate, H is dune height (10.6 m for Dune 1, 9.7 m for Dune 2, 9.1 m for Dune 3), and ɛ is sediment concentration of the bed (1 porosity). Given the grain size and grain sorting found at White Sands, ɛ is taken as 0.7 [Beard and Weyl, 1973]. Dune forward migration is the horizontal displacement associated with the lee-face deposition as measured off of the dowel rods. Migration rate is this same horizontal shift divided by the time wind speed was above threshold ( 0.29 m/s, assuming r gypsum = 2320 kg/m 3 ) as measured at Holloman AFB during the wind events. During the March wind event, in which the dowel rods were emplaced in Dune 1 for 14 hrs, yielding q s = m 2 /s, whereas the dowel rods were emplaced in Dune 2 for 22 hrs, yielding q s = m 2 /s. During the April wind event, dowel rods were emplaced in Dune 3 for 23 hrs, yielding q s = m 2 /s. [43] A volume flux of sediment can be converted to a mass flux of sediment, Q s, simply by multiplying the former parameter by the appropriate grain density. For this study, Q s = r gypsum q s. The characteristic can then be calculated from Q s using the White [1979] formulation of the Kawamura [1951] equation, as corrected by Namikas and Sherman [1997] Q s ¼ 2:61 r f u 3 * g 1 u! * c 1 þ u! 2 * c ð12þ The calculated characteristic for the March event is 0.36 m/s for Dune 1 and 0.34 m/s for Dune 2. The average value of 0.35 m/s is the same as that based upon the average gust speed (Section 4.3.1). The calculated for the April event is 0.39 m/s, under-estimating the = 0.45 m/s based upon the gust speed by 15% Indirect Characterization of Wind Speed by Grain Size [44] Table 1 shows a compilation in which the grain-size ranges for: (1) creep ( mm for March, mm for April) were determined using equation (5), (2) saltation ( mm for March, mm for April) 13 of 20

14 Figure 8. Cumulative grain-size curves for deposits occurring at the base of the lee faces of Dunes 1 3 following the March (Dunes 1 2) and April (Dune 3) wind events. (a) Grainflow. (b) Grainfall. (c) Wind Ripples. The curves are portioned into modes of grain transport based upon the empirical relationships shown in Figure 1. Table 1 shows the ranges of grain sizes for each mode of transport and their percentage within each lee-face process. Statistics given with each set of curves are mean values for these curves. Sorting is given as the Trask coefficient. were determined using equation (8), (3) incipient suspension ( mm for March, mm for April) were determined using equation (7)), and (4) full suspension ( 117 mm for March, 136 mm for April) were determined using equation (6) for the March ( = 0.35 m/s) and April ( = 0.45 m/s) wind events. These values bracket those of Jerolmack et al. [2011], who used somewhat different definitions (see section 2.2) for the formative wind ( = 0.39 m/s) at White Sands to determine grain-size ranges for 14 of 20