Problems of scale in the modeling and interpretation ...

Marine

Geology

124 (1995) 339-349

Problems of scale in the modeling and interpretation coastal dunes

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Douglas J. Sherman Department of Geography, University of Southern California, Los Angeles, CA 90089-0255, USA Received 11 March 1994; revision accepted 13 June 1994

Abstract Coastal dune systems are studied at time scales from seconds to millennia, and space scales from millimeters to kilometers. Present approaches to the study of coastal dunes make it difficult to integrate models and interpretations of these systems over these scale ranges and arrive at reasonable conclusions. It is argued that identification of key controls on dune development, measurement of those controls, and synthesis of data, describing past and present conditions and used as calibration points, will improve the viability of coastal dune models. Theoretical and empirical advances are necessary to improve the reliability of predictions across a range of geomorphological scales. Attempts at linking theoretical (systematic) models, process (synoptic) measurement, and historical or paleoenvironmental (synthetic) approaches make explicit the recognition that at time scales of more than a few hours, and space scales greater than a few hundred meters, deterministic models become unstable vis&vis prototype environments. Process “climatologies” provide one means to link process-based work with broader-scaled analysis. As scales increase, such climatologies will become less appropriate as the data become less reliable, or as the systems change, or as the scales become too large relative to the process record lengths. In these conditions, specific data (i.e. samples) representing points in time and space become check points for calibrating models. It should be possible, ideally, to integrate both up and down time and space scales. This is not yet possible.

1. Introduction A coastal sand dune, or dune system, represents the integration of a suite of geomorphic processes and sedimentary responses over a particular span of time and space. The interpretation of what occurs across those scales comprises a major challenge for geomorphologists, geologists, and engineers, and it is a critical goal toward understanding the development of these forms. Studies of coastal dunes usually adopt one of two perspectives: either beginning at a micro-scale, with the study of duneforming processes, leading to the development of the landform; or beginning at a macro-scale, with the dune itself and attempting to reconstruct the process and environmental history. For the most 0025-3227/95/$9.50 0 1995 Elsevier Science B.V. All rights reserved SSDZ 0025-3227(95)00048-8

part, the two approaches are conceptually and methodologically incompatible. This divergence is not unique to the study of coastal systems, but appears to be inherent in the nature of modern geomorphology (e.g., Lewin, 1980). However, in an attempt to understand coastal dunes as landforms, this schism, and possible means of bridging it, demands attention. There has been a rapid expansion in knowledge of aeolian sediment transport processes and associated landform responses. Most of this work evolves from studies in arid environments (e.g., Bagnold, 1941), and theories concerning wind-blown sand and dune development reflect this orientation. However, in terms of potential value to society, coastal dune systems are of arguably greater

importance than desert systems. Desert dunes are usually located where people are not: coastal dunes are frequently located within or adjacent to large populations. Coastal dunes are important geomorphologically (e.g.. Psuty. 1992). biologically and ecologically (e.g.. McLachlan. 1990). and as a resource and land use base (Gares et al.. 1979: Nordstrom, 1990: Pye, 1990). Additionally, there is a critical need for scientific information concerning the dynamics of coastal dune systems to give managers and planners a sound basis for decisionmaking. This is particularly true when environmental change threatens to pose additional stresses on coastal systems. Unfortunately. as Carter et al. (1990, p. 3) note ‘....coastal dune research is still at a rather primitive stage.” The purpose of this paper is to review\, concepts of aeolian sediment transport and foredune development, to identify process-oriented problems, and especially to discuss barriers to applying dune models across ranges of scale. Present approaches to the study of coastal dune systems make it difficult to integrate process-based models across a range of scales and arrive at reasonable results. Similar problems inhibit the interpretation of process details based upon large-scale conceptual models. Problems arise because the scale domains of dune systems are typical of those for most geomorphological systems, with time scales ranging from seconds to millennia. and space scales that range from millimeters to kilometers ( Fig. I ). The coastal dune system is different from many typical geomorphic systems in that the rates of change are relatively fast, and substantial changes can occur over periods of hours. However. the general form of a dune system may persist foi centuries or longer. Therefore micro-scale is defined here as comprising time and space scales of seconds to months, and millimeters to hundreds of meters, respectively. Meso-scale spans months to decades and hundreds of meters to tens of kilometers. Macro-scales are longer than decadal and larger than tens of kilometers. These scale definitions differ substantially from those usually specified for geomorphic systems. For example. Cullingford et al. (1980) define short time scales as about 1 to 100 years, and long time scales as exceeding 10,000 years. The compression of time

scales here reelects the dynamic nature of many dune systems (and coastal systems in general ) relative to hill slope or tluvial processes, for example. Micro-scale. process-based approaches emphasire the importance of understanding sediment transport systems as a key to landform development. These approaches rely heavily upon empiricism and attempt to develop deterministic models based on theoretical relationships. Meso-scale approaches are frequently associated with sediment budget calculations or littoral cell assessments (Illenberger and Rust, 1988). and information at this scale is usually of a type most relevant to environmental managers and planners. Macroscale approaches are used mainly by quaternary geomorphologists to reconstruct dune field chronologies. frequently in relation to sea-level changes (Orme and Tchakerian, 1986; Shulmeister et al., 1993 ). The definitions of micro-, meso-, and macro-scales used here are roughly analogous, at least in concept, to the ‘steady’. ‘graded’, and ‘cyclic’ time scales of Schumm and Lichty (1965). In ideal circumstances, it would be possible to ‘slide’ information and concepts across time and space scales. It would be possible to identify and to use a universal set of concepts and methods. In reality. however, the task is difficult, and, in fact, seldom attempted. Approaches to the study of coastal dunes remain essentially scale-dependent. because research methodologies are partly scaledependent. This research compartmentalization inhibits the development of clear understanding of dune system behavior and limits our ability to predict dune development except at very small scales or at a very coarse resolution. This problem can be addressed. and the viability of dune models enhanced, by a systematic identification of key controls on dune development, synoptic measurement of the system processes and responses, and .v~xthr.sis of data describing past and present conditions. The linkage of systematic, synoptic, and synthetic approaches makes explicit the recognition that deterministic dune models, based on sediment transport processes, usually become unstable when applied at larger time and space scales. This is illustrated through a discussion

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of the simplest coastal foredune.

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2. The systems approach The systems approach assumes that development of foredunes is predictable with an understanding of processes, and through application of the principles of physics and fluid dynamics. The approach requires models of wind-blown sand transport based on the identification and quantification of key system attributes and interactions. The systems approach represents the logical evolution of the methods first employed by Bagnold (1936). A first step is recognizing that the foredune system comprises three main subsystems: the wind system; the sediment system; and the vegetation system. Characteristics of these subsystems, and the interactions between them, will determine the dune formation potential. The wind system has six basic attributes that relate to foredune development: speed, spatial variability, temporal variability, direction, duration, and aerosol content. The first five relate to sand transport potential, whereas aerosol content is associated with nutrient supply to dune vegetation. If transport potential is considered for one location at one point in time, only wind speed and direction are important.

The sediment system is more complicated, and is considered here to include representative components of the local beach and dune morphology. The basic attributes of the sediment system include: grain size, shape and composition; grain population characteristics; inter-grain cohesion; local bed slope; beach-dune morphology; and the geometry of bedforms. In some environments, it is also important to consider changes in the surfacesediment attributes through time (e.g., Carter, 1976). For most laboratory studies of simple transport systems, this variable list may collapse to grain size alone. The vegetation system is usually the least considered component of the transport/dune system. The basic system attributes are species composition, age, and plant density. These are usually modeled as elements of surface roughness geometry: height; silhouette area; and spacing (or roughness density). It is the set of interactions between these systems that causes sand transport and dune formation. The interaction between the wind and sediment systems can be expressed in terms of shear velocity, roughness length, and sediment transport rate (Bagnold, 1936; Horikawa et al., 1986). For fully developed turbulent flow in thermally neutral conditions, one set of interactions is described using the ‘law of the wall’. During saltation, the roughness length fluctuates with shear velocity to maintain an equilibrium relationship (Sherman, 1992).

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Sediment transport represents the most important of all the systems interactions, in terms of foredune development. Virtually all modern sediment transport models are expressed as functions of the magnitude of shear velocity exceeding a threshold value, usually predicted following Bagnold’s (1936) expression. For a given sedimentary environment, the threshold condition is essentially a function of mean grain size only. There are many models for predicting aeolian sediment transport, and these have been reviewed extensively (e.g., Horikawa et al., 1986; Sarre, 1987; or Sherman and Hotta, 1990). Most of these models assume that the transport rate is mainly a function of shear velocity and mean grain size, thus presuming an overly simplified sediment sediment system. Other factors, including grain shape and density (Willetts, 1983), or the presence of cohesive salts (Nickling, 1984) may have substantial effects on transport conditions. The effects of local surface slope and surface-moisture content frequently exert important controls on transport rates. The Hardisty and Whitehouse (1988) model, for example, predicts that a 2” upslope will reduce the transport rate by about 33%. Surface-moisture content increases threshold shear velocity as a result of surface tension. Although the moisture content models diverge considerably in their predictions, they all indicate that potential moisture effects are large (Namikas and Sherman, in press). For example, at low moisture contents, Belly’s (1964) model produces mid-range estimates (relative to other models) for moisture-enhanced threshold shear velocity. Nevertheless, for 0.27 mm sands with a 1% moisture content (for example), Belly’s conservative model predicts that the threshold shear velocity will be approximately doubled. Interaction between the wind and vegetation systems also involves shear velocity and roughness length, but includes a finite displacement height and nutrient transport (Bressolier and Thomas, 1977; McLachlan, 1990; Niedoroda et al., 1991). The main effect of a vegetation-produced displacement height is to move the mean zero stress plane away from the surface, thereby reducing the transport potential. Direct nutrient transport by wind

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or with sea spray supports the vegetation system in an otherwise inhospitable environment. Interactions between sediment and vegetation systems include sediment trapping, habitat creation, and nutrient transport (Willis, 1989). Experiments by Fay and Jeffrey (1992) suggest that some of the nutrients required by dune vegetation, nitrogen in particular, are transported on sand grains directly, rather than being borne by sea spray. There are a host of lesser controls on dune development that may be occasionally or locally important through their influence on the transport system. These include the effects of air-temperature gradients, air density, rain splash, and surface obstructions (such as seaweed or other wrack), and other vegetation system attributes (Thomas and Tsoar, 1990). These above considerations describe in general terms the attributes and interactions of the wind, sediment, and vegetation systems controlling the aeolian component of foredune development. Many of these factors are common to the study of aeolian processes in arid environments, e.g., shear velocity or grain size. However others are of enhanced importance in coastal systems, e.g., moisture content or vegetation density. In order to verify and use models based upon these process characteristics, synoptic measurements of these factors in coastal systems must be undertaken.

3. The synoptic approach The primary goal of the synoptic approach is to obtain ‘simultaneous’ field or laboratory measurements of a completely specified transport system in order to quantify relationships and calibrate models. Although there have been many experiments designed to assess aspects of the aeolian system, none have been successful in obtaining high-quality, comprehensive data sets of both the wind regime and the geomorphic/sediment system. Field experiments, especially, are constrained by the need to measure, or control for, numerous parameters under complex and unsteady conditions. It is therefore common to ‘assume away’ the importance of many of the system attributes

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described above. Table 1 summarizes the general status of field synoptics. It can be seen that seldom is there complete specification of the aeolian system. For example, in the field experiment and modeling project of Mikkelsen ( 1989), one of the most thorough efforts for coastal dune synoptics, the vegetation field is only roughly specified, and moisture effects are ignored. Bauer et al. (1990) did not measure, or did not consider, moisture or slope effects, and Nordstrom and Jackson (1992) did not measure the velocity profile or moisture content. Although these factors may have been unimportant to the respective studies, the actual magnitude of effects remains unknown. There are two main reasons why experiments only incompletely measure the transport system. First, the magnitude of the potential effects of Table 1 An outline of the system parameters controling aeolian sediment transport across beaches, and indications of how often these factors are included in empirical studies Attributes that we measure (fairly) well or often

Attributes that we do not measure well or often

wind speed wind direction mean grain size- and sorting vegetation type

Usually important:

spatial variations in the wind field wind velocity profile sediment transport rate sediment moisture content (including ice) local bed slope Occasionally or locally important:

grain shape sediment composition (density variations) sediment salts content changes in surface conditions morphology bedform geometry vegetation geometry temperature gradients evaporation rates surface obstructions (including seaweed and snow)

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many of the system attributes listed in Table 1 have only been recently appreciated, or are ambiguously specified. The variation in moisture content models illustrates this problem (Namikas and Sherman, in press). However the over-riding consideration has been the level of effort necessary to account for all of the parameters listed in the table. The personnel, instrumentation and equipment requirements are substantial, and the value of many of the measurements can only be established after the fact. Logistics and practical considerations often dictate a ‘least risk’ approach to experimental design, so that effort is concentrated to maximize the likelihood of success in at least part of a project. One attempt to address the suite of usually important parameters has been the development of the Aeolus Project, a multi-institution research program designed to bring an array of resources to bear on the problem (described in Gares et al., 1993; and Sherman at al., 1994). The Aeolus Project experiments, conducted in Canada, Ireland, and the USA, have aimed to improve experimental design, equipment and methods, and models of the sediment transport system. With larger personnel and equipment resources available, projects such as this enhance the likelihood that suitably comprehensive data sets can be acquired. It is also important to recognize that some of the critical attributes, such as surface-sediment moisture content, and the sediment transport rate itself, are difficult to measure. Other interaction attributes, such as shear velocity and roughness length, are often difficult to derive, even with high quality measurements and careful environmental control (Bauer et al., 1992). For example, estimates of shear velocity are commonly derived from measurements of the velocity-profile gradient, based upon the assumption of the development of a logarithmic velocity profile through the elevation range measured by an anemometer array (typically of the order of meters). This requires that boundary-layer conditions remain constant, over a spatially variable surface, for a distance long enough to allow sufficient vertical growth to envelope the anemometers. In many coastal environments this condition is never met across beach and dune systems

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(Sherman and Bauer, 1993). Therefore, measurement of log-normal velocity profiles, a common key to shear velocity derivation, remains a difficult matter. Despite these concerns, because the dune systematics can be relatively well specified, at least in theory, it is possible to design a series of field or laboratory experiments to measure or derive estimates for all of the recognized key parameters. The missing element is an appropriate level of research support. Pragmatically, the ‘perfect’ experiment cannot be designed, much less executed. However, great improvements over present efforts are possible. Data from such experiments should accelerate the development of deterministic. process-based models for foredunes. It should then be possible to simulate the growth and evolution of a foredune system. By running such models ‘into the future’ useful predictions at management scales are attainable. Similarly these models could be run backwards to test their viability against historical records.

4. The synthetic approach The intent of the synthetic approach is to provide the data needed to integrate systematic models to larger time and space scales, especially to those scales appropriate for management decisionmaking. Synthetic in this context refers to the drawing together of diverse data, from a variety of sources, representing process and response systems at meso- and macro-scales. Short-term synthesis is appropriate for meso-scale studies, and it requires the establishment of either a process climatology, a dune sediment budget, a dune form chronology, or combinations of these types of data sets. A process climatology is developed using a frequency distribution of a time series of measurements. For aeolian systems, data, including wind, temperature, precipitation, and solar radiation measurements, are acquired from weather stations. Dune morphology data are acquired through field mapping, or more commonly, through analysis of maps, air photos, satellite imagery, or other remote sensing methods. Therefore, short-term synthetic investigations can only consider dunes across his-

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toric time scales, and the maximum synthesis period is restricted by the pertinent data set of shortest duration. In rare cases this may extend to a century scale, but it is more typically decadal in length. These data can be used to calibrate deterministic models if the foredunes can be considered as time- and space-integrating sand traps. Under these conditions, changes in foredune volume represent the net transport into the dunes, and can be used to establish a net sediment budget. There have been, however, few rigorous attempts to use dune-volume change, with detailed dune measurements, and local climatic data to assess the aeolian transport system (e.g., Davidson-Arnott and Law, 1990). The work of Sarre ( 1989) along the Devon coast of the UK is one example of a study that employs local and regional wind data with shortterm transport data and longer-term dune accretion rates to try to address the larger issue of dune development characteristics. There are fewer ongoing efforts to measure dune development over meso-scale periods, although this does represent one component of the Aeolus Project (e.g., Gares et al., 1993). Foredune systems at sites in New Jersey and California have been surveyed repetitively to monitor their evolution. The Castroville, California site has been mapped with a 3D grid on an annual basis since 1987. The Island Beach, New Jersey site has been mapped since 1981, but at less regular intervals. These data sets are just beginning to approach the scale length to allow interpretation of more general relationships controlling dune development. A major drawback associated with attempting to calibrate systematic models in this manner, aside from the challenge of obtaining good data sets, is the propensity of foredune systems to ‘leak’ sediments. Leakage of sand from the foredunes occurs mainly through erosion of the dune front by waves or by landward movement of sand through blowouts or parabolic dune migration (Carter et al., 1990), or combinations of the above (Fig. 2). In these cases, to the extent that the foredune ‘trap’ leaks sand offshore or onshore, it becomes difficult to relate the information concerning the aeolian transport system from the beach alone to the changes in foredune volume. The foredune volume, therefore, will represent a mini-

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IDUNES

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"LEAK"

JLANDWARD~

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FOREDUNES “LEAK” SEDIMENT TONEARSHORE (DUNE SCARPING) Fig. 2. Modeling foredune development landward migration of sand.

is complicated by sediment leakage from the dunes resulting from wave erosion and

mum estimate of net sand transport. In terms of using these data for model calibration, such estimates must be considered to be conservative. The sand leakage issue also implies that if mesoscale, quantitative foredune models are to succeed, they must include terms to describe wave erosion and scarping (e.g., Kriebel et al., 1991), and landward losses. It is most likely that these terms will be estimated using sediment budget approaches (as per Illenberger and Rust, 1988), as deterministic specification would be extremely difficult with the present state of knowledge. The greater complexity of the dune system at increasing scales is again a common characteristic of geomorphic systems. This results from increased interactions with other environmental systems. Long-term synthesis involves the reconstruction of dune chronologies at time scales that are long relative to historic data records-i.e. decades (centuries) to millennia. Synthesis at this scale involves sediment sampling and dating, or stratigraphic mapping, of modern and relict dune systems to

both describe the systems and to provide evidence of depositional processes. The approach includes establishment of depositional environments via stratigraphic interpretation (McCann and Byrne, 1989) or the recognition and identification of depositional events via absolute or relative dating chronologies (Tooley, 1990; Shuhneister et al., 1993). At these longer time scales, the dune system reflects not only the interactions of the transport system as described above, but also the strong interactions resulting from long-term sediment budget changes and sea-level changes. However, dune system models at this scale remain largely conceptual rather than empirical or deterministic. Psuty (1992) and Sherman and Bauer ( 1993) have proposed sediment budget models for dune development. Pye and Bowman (1984) have presented similar models reflecting sea-level controls on dune development. These approaches are limited to broad description, and assume constancy of many process and response parameters. Resolution of

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the ambiguities in these models requires better specification of the dominant controls on dune development at large scales; a task not readily accomplished with the present state of understanding.

5. Discussion There are several scale dependent discontinuities that inhibit broad spectrum modeling of coastal dune systems, and prevent the successful integration of the approaches outlined above. Two key discontinuities occur at the conceptual boundaries between micro- and meso-scales, and meso- and macro-scales. When deterministic models are used to predict future dune development at meso-scales, it will be necessary to substitute probability functions for specific variable estimates. The point at which this substitution is required represents the conceptual passage from micro- to meso-scale. It is also the point at which confidence in modeling results drops substantially. Part of the loss of confidence results from increased uncertainty in the modeling process when using probability distributions. For example, we understand very little about the effects of event sequences, e.g., stormj non-storm ordering, on the transport system, a potential first-order effect in some circumstances (see general discussion by Church, 1980). The effects of event sequences are not addressed adequately in the application of probability distributions alone. Wind speed, roughness length, grain size and density, surface slope, and moisture content, are the primary controls of wind-blown sand transport across beaches, All of these parameters vary through time, and the variability of each is expected to increase through time. Many of these controls are codependent (for example wind speed, roughness length and shear velocity), but many also seem independent of one another (for example moisture content and surface slope). Unfortunately, there may also be interdependence of many of these other variables. For example, coastal storm events may generate fast winds, heavy rains, and dissipative surf conditions, with low-angle slopes. The complexity of these system

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parameters and their interactions makes it extremely difficult to recognize the correct manner for establishing and using probability distributions to drive transport models. The second significant discontinuity occurs at the stage when historical records are no longer available, at the juncture of meso- and macroscales. Deterministic models can be used to cross this discontinuity, but confidence in the results will be minimal. The degree of uncertainty is magnified because the process regime must be expected to change as time scales, especially, increase. Attempts at using dating or stratigraphic techniques to move toward smaller-scale understanding is similarly encumbered because understanding of modern processes and responses is used as the basis for interpreting depositional environments. Given the errors associated with measuring, correlating, and modeling micro-scale systematics in the present, it is particularly difficult to infer anything other than the general nature of past processes. This difficulty can be illustrated by considering the ambiguous relationships established between sealevel changes and coastal dune behavior (e.g., Bird, 1993; or Pye and Bowman, 1984), whereby dune development may be enhanced by rising, falling, or static sea levels. In some cases there are specific sea-level thresholds that control dune system behavior, thresholds that can only be identified through careful, site specific research (e.g., Shulmeister et al., 1993). Many of these scale-induced problems are probably intractable. For example, deterministic models will not be able to make predictions of detailed dune development that span tens of years (much less thousands) and hundreds of kilometers. However, first approximations of dune development, using such models, may be well employed for planning purposes over decadal scales. If the models can be specified to the point of putting error terms on the predictions, then best case, worst case, and most likely scenarios can be established. With a proliferation of monitoring efforts aimed at increasing meso-scale data bases, empirical assessment of these models will be possible by running the model through ‘historical’ data sets beginning with boundary conditions established in the record. Even relatively coarse resolution pre-

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dictions will represent improvements over the status quo, and successful efforts will have immediate management applications. There are also methodological developments that promise to narrow the gap between mesoand macro-scale studies. Especially important have been the development of sediment dating techniques using such properties of quartz (and other) sands as thermoluminescence, and perhaps more importantly, optically-stimulated luminescence. Optically-stimulated luminescence (OSL) is capable of dating some aeolian deposits at time scales ranging from decades to millennia. Refined OSL techniques have the potential to remove some of the methodological barriers between empirical (historical) records and reconstructed records. These methods will also remove some of the methodological constraints to interpreting the stratigraphic record, especially the requirements of a non-erosional system with temporally repetitive bedding (e.g., Church, 1980). Sequences of dates from a given dune system can be used to create a development chronology and estimate minimum accretion rates, which are, in turn, a function of sand transport rates.

6. Conclusions The issues described above are not unique to the study of coastal dune systems, but are typical of geomorphological systems where multiple interacting controls, internal and external to the system, occur at different scales. Scaling problems, in particular, present a substantial barrier to processbased prediction of landform development over periods of years to about a decade, a time frame of interest to coastal managers. These same problems limit the resolution of paleoenvironmental reconstructions, especially in terms of interpreting the magnitude and duration of processes. Whereas it is likely that major advances in understanding both large- and small-scale aspects of coastal dune systems will occur in the next decade, it is unlikely that we will see similar advances in meso-scale understanding. This last conclusion arises from the largely unmet need for longitudinal studies of contemporary dune systems. Although some such

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studies have been initiated, they are few in number, and may portray strong, site-specific characteristics. The pressing need for additional work at all scales of examination promises an exciting research agenda.

Acknowledgements Thanks go to the Department of Geography, University College, Cork, Ireland, for providing research facilities during the writing of this paper. This work was partially supported by a Fulbright Scholarship, a Grant from the North Atlantic Treaty Organization (CRG 900540), and a contract from the California Department of Boating and Waterways (91- 100-200-26). Robin DavidsonArnott and Paul Gares made valuable comments on an earlier version of the paper. Mr. Mike Murphy drafted the figures. This paper is a contribution to the International Geological Correlation Programme (IGCP) Project 274, Coastal Evolution in the Quaternary. It is adapted from a presentation made at the final meeting of the UK Working Group for Project 274.

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