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Along the Holland Coast dunes have important functions in flood protection, recreation and as a habitat. The dynamics of coastal foredunes at timescales of years to decades (the engineering timescales) are characterized by alternating periods of erosion and accretion. Whereas coastal foredunes erode mainly due to marine forces, their accretion is mainly due to aeolian processes. Dune erosion is the most important failure mechanism of dunes as a flood defence system. Much research therefore focuses on predicting dune erosion, which has led to tools enabling quantitative prediction of this phenomenon. The capability to quantitatively predict dune accretion, however, is less established and predictive tools are still lacking. Although several models to predict aeolian sediment transport in desert-type situations are available, the complex physics on a beach are less well understood.

This lack of quantitative knowledge on dune accretion makes it difficult to describe or predict the dynamics of dunes including both erosion and accretion. Moreover, where long-term data on the temporal and spatial development of dunes are available (e.g. the JARKUS dataset of the Dutch coast), measured behaviour is difficult to reproduce.

The research described herein aims to "identify and quantify the processes governing the development of coastal dunes at the engineering timescales" by analysing collected morphological and process data and formulating a conceptual model.

    Measured dune behaviour

    Along the Holland coast, foredune, beach and foreshore morphology have been measured in almost 600 transects every year since 1963. The data are stored in the JARKUS dataset (JAaRlijkse KUSTmeting / Annual Coastline Monitoring). From this dataset yearly to decadal dune behaviour such as dune volume changes can be derived. These dune volume changes can be correlated with wind time series and additional morphological parameters.

    Observations

    1. Since the start of the JARKUS monitoring scheme, measured dune volumes in many transects show a positive linear trend. For the transects where this holds true, a constant mean dune accretion rate can be assumed. This allows for a simple predictive model of long-term dune behaviour.
    2. The magnitude of the measured accretion rate varies between transects. Spatial and temporal variations in dune volume change can easily be correlated with parameters of interest. The present knowledge page focuses on wind conditions and beach slope, but other parameters of interest can be considered.
    3. At none of the locations considered, a correlation can be found between interannual or decadal dune behaviour and wind forcing. This casts doubt upon the use of decadal-scale dune behaviour models with wind as the main forcing.
    4. There is a significant negative correlation between dune volume change and beach slope. The latter may represent a supply-limiting factor, which would mean that dune behaviour be governed by sediment supply rather than wind forcing.
    5. Annual mean erosion volumes as a result of extreme marine events are found to be of a similar order of magnitude as the aeolian growth. This means that the observed volume changes represent a relatively small difference between two large quantities.

    Aeolian transport measurements

     

    Wind-driven aeolian sediment transport is the result of a complex interaction between wind and erodible sediment. In order to test generic relations between wind and aeolian sediment transport rates, field experiments were conducted. Data of wind velocity and sediment fluxes were collected during a 5-day field campaign at Vlugtenburg beach, part of the Holland coast, the Netherlands. Adjacent photo's show the saltiphone and the wind station used.

    During the campaign the wind was onshore directed. In order to identify transport gradients in the direction of the wind a cross-shore array of 4 saltiphones was used. Figure 1 shows the cross shore profile and the locations of the saltiphones, together with the high and low tide marks.
    The measurements show a significant temporal variability of the sediment transport rate. Figure 2 shows data measured at location C; the top panel shows the wind speed time series, the middle panel the measured sediment transport rates and the bottom panel the tidal elevation. From this figure it is evident that the measured variability of the transport rate is related to the variability of the tide elevation, rather than the wind speed. As a result it is unclear if the wind-driven sediment transport capacity is reached at any point in time.
    There can be two reasons why the wind-driven sediment transport is not reached: limited sediment supply or a lag between aeolian forcing and sediment pick-up. The latter is often referred to as a fetch effect (Delgado-Fernandez, 2010), i.e. a gradual increase of sediment transport rate in the direction of the wind and can be interpreted as spatial variability of the transport. The array of saltiphones is meant to distinguish the fetch effect from spatial variation due to other causes.
    Figure 3 shows the spatial transport variation measured by the saltiphone array. Wind direction is from left to right and the data points correspond to the locations indicated in Figure 3. Each dot in the figure represents the mean sediment transport over a 30 min time interval at a specific location, dots are connected by lines to indicate simultaneous measurements. At the location closest to the upwind boundary (waterline), hardly any transport is measured. The measured transports increase in the direction of the wind, which indicates a fetch effect. During all measured 30 min intervals, the measured transport rates at the most downwind saltiphones are different, though of comparable magnitude. This means that there is no evidence that wind driven transport capacity is reached. Supply limitations could explain the apparent fetch effects if it is assumed that sediment transport is a function of upwind supply. The increase of sediment transport in downwind direction is then governed by the supply magnitude in the direction of the wind. This fetch effect due to supply limitations is likely to overshadow fetch effects due to the lag between aeolian forcing and sediment pick-up processes.
    Supply limitations are not well addressed in traditional sediment transport formulations: generic formulae for wind-driven transport often relate sediment transport rates to the third power of the wind speed, which means that they refer to the transport capacity. Figure 4 shows collected data at three locations where traditional 3rd power functions are fitted, as well as linear ones and the two give comparable results. The linear function can be described as the wind speed times a linearly increasing sediment concentration due to a constant supply from the bed. At this stage we propose to use linear relationships between wind speed and aeolian sediment transport, and to focus on the supply magnitude. The resulting transport relations may be used to predict wind-blown sediment fluxes on this type of beaches.

    Results

    1. The variation in measured transports is strongly correlated to the tidal elevation. This indicates an explicit link between aeolian sediment transport rates and the intertidal area. During the measurements, the sediment supply in and around the intertidal area is measured to be of larger magnitude than at the upper beach. The limited supply at the upper beach could be explained by armouring of the surface due to aeolian sediment sorting and the presence of shells. Armouring is the capture of smaller sediments under larger sediments resulting in a lower possibility of movement and subsequently a total sediment transport decrease. Armouring in the intertidal area is of less importance due to the mixing of the sediment surface due to marine processes.
    2. According to conventional fetch theory, sediment transport increases downwind until the wind driven transport capacity is reached (Delgado-Fernandez, 2010). Although fetch-like effects are measured, conventional fetch theories are not confirmed because it is unclear if the wind driven transport capacity is reached, at any stage during the experiment. If this capacity is not reached, the relationship between wind speed and sediment transport rates does not follow traditional capacity formulations.
    3. Traditional sediment transport capacity formulae relate the sediment transport rate to the wind speed to the third power. These relationships, however, are unable to explain measured behaviour. Therefore, an alternative model is proposed which expresses the transport rate as a linear function of the wind speed. This model allows for a particular implementation of supply limitations and, when properly tuned, can successfully reproduce the measured data. Two tuning parameters are used: the threshold wind speed for transport and the mean sediment concentration.
    4. For this particular dataset the tuned threshold velocities do not show much spatial and temporal variability, whereas the tuned mean sediment concentrations do.

    A conceptual model

    To explain and reproduce the process measurements, we propose a new model for aeolian sediment transport in supply-limited situations (De Vries et al., 2012). It is based on a 1D linear advection model to compute sediment transport rates as a function of wind speed using traditional sediment transport formulae, but with limited sediment supply explicitly taken into account. The linear advection model reads:

    Where C c is the sediment transport concentration, u the advection speed, h the heigth of the sediment transport layer, E is the erosion and S the sedimentation. Erosion (E) and Sedimentation (S) are calculated as functions of wind capacity and sediment supply.

    For pragmatic reasons the spatial domain of the model is simplified towards a supply and a no supply zone. This spatial domain could represent a cross shore beach profile where there is a zone of relatively large supply and a zone of no supply. Such a situation can happen in beach settings where sediment exchange between the marine and aeolian zones is mainly occurring in the intertidal zone. The main sediment supply is therefore in the intertidal zone (and lower beach). At the upper beach sediment supply can be limited due to sediment sorting processes and surface armoring due to lag deposits. Such a situation is similar to the one described in the measurements section. Figure 5 shows the spatial representation of the conceptual model with the wind direction and the supply (lower beach) and no supply zones (upper beach) indicated.

    The model is capable of reproducing two types of apparent fetch effects. Both of which are shown in the case presented in Figure 6. When supply is small with respect to wind driven 'demand', the sediment transport rates at any location are governed by the total supply in upwind direction. Therefore sediment transport increases until no supply is available in downwind direction. When supply is relatively large, wind driven demand and pick up speed determine the sediment transport rates. Analysing measured fetch effects in the field can be biased by these separate causes.

    Focussing more on the relevance of supply limitations, Figure 7 shows an example of model output where supply is threaded as only variable. In this conceptual model winds are randomly varied between 0-10 m/s to create some variability in wind speed and sediment transport rates. The top panel shows results of three model runs. The top left shows a situation where supply is very limited. The middle panel shows a situation where supply is in the same order than the wind driven transport capacity. Right panel shows a situation with abundant supply. Given a time series of wind, the sediment transport rates at the downwind model boundary are calculated an plotted. For all three runs traditional third power models and linear models are fitted and the quality of the fit is indicated by the correlation coefficient (R). The middle panel shows the difference in fit quality (given by correlation coefficient R) between the traditional third power model vs the new linear model where sediment supply is varied. It shows that the linear model is better when supply is limited and traditional formulations are better when supply is abundant. The bottom panel shows that in supply limited situations, the linear fit provides an estimate of the supply magnitude.

    Modelling exercise conclusions

    The following conclusions can be drawn from this modelling exercise.

    1. The presented model successfully explains several physical observations such as the occurrence of a fetch effect, intermittency in sediment transport and a dominant role of supply.
    2. Limited supply can cause fetch effects where sediment transport rates increase in the direction of the wind. The distance over which these fetch effects occur (critical fetch distance) is dependent on magnitude of the supply per unit downwind length.
    3. When supply is limited, measured sediment transport rates are poorly correlated with the results of traditional sediment transport capacity formulae. A linear relationship between wind and sediment transport rate does performs just as well under these conditions.
    4. The tuning paprameters of the linear model, when fitted to the measured data, provide information on the supply rate and the threshold wind speed.
    5. Field data collected at supply-limited locations (beaches) provide evidence that linear relationships between wind speed and transport rate can also be found in the field and are governed by the supply magnitude.
    6. For the model to be applicable to predict aeolian sediment transport in other situations, threshold wind speeds and supply magnitudes should be known. Gaining knowledge on these quantities and how they can be estimated is of crucial importance.

    Synthesis

    Processes of dune development and aeolian sediment transport rates were investigated  by:

    1. Analysing interannual and decadal dune behavior using the JARKUS dataset.
    2. Collecting process data on wind and aeolian sediment transport rates.
    3. Formulating a conceptual model for aeolian sediment transport rates in supply- limited conditions.

    The main finding is that neither aeolian sediment transport rates nor long-term dune volume changes are primarily governed by wind velocities. Both are reflected by the lack of correlation of their variations with the prevailing wind conditions. Aeolian transport rate variations and dune volume changes are rather governed by variations in the sediment supply rate. At a beach, supply is generally limited and the transport capacity of the wind is not saturated. On the other hand, the transport rate increases with the wind speed. Therefore, it must be the combination of supply rate and wind speed that governs the actual transport.

    At present, the supply rate is a relatively abstract parameter which is difficult to quantify. Yet, we know that variations in supply (in function of surface moisture content, beach slope and tidal elevation) have a significant effect on sediment transport magnitudes. Predicting the sediment supply rate is therefore key to predicting aeolian sediment transport and dune behaviour. A method to predict sediment supply using in situ data is presented herein, but generic knowledge on this phenomenon needs further research.

    Another subject of further research concerns the receiving end, especially how sediment is transported and trapped between dune vegetation. This is a non-trivial issue, since vegetation not only reduces the bed shear stress, thus reducing the sediment pick-up capacity of the wind, but it also enhances turbulence, thus increasing the wind’s suspension capacity (Baptist, 2005).

    References

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