Computer simulation of the dynamics of a dune system

Computer simulation of the dynamics of a dune system

Ecological Modelling 78 (1995) 205-217 Computer simulation of the dynamics of a dune system Francisco de Castro Departamento de Biabgiiz Vegetal y Ec...

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Ecological Modelling 78 (1995) 205-217

Computer simulation of the dynamics of a dune system Francisco de Castro Departamento de Biabgiiz Vegetal y Ecologi’a, Facultad de Biologia, Universidad de Sevilla, Aptdo. 1095, 41080 Sevilla, Spain

Received 11 May 1993; accepted 2 November 1993

Abstract The mobile dune system of the Doiiana National Park (southwest Spain) covers an area of 100 km2. It is formed by several transverse dune fronts 5-20 m high, lying parallel to the beach, and separated by flat slacks covered by scrub vegetation. Dunes move from the beach inland at a rate of 2.5 m per year, burying the slack vegetation as they progress. The vegetation is well adapted to the dune dynamics, colonizing the slacks in the wake of a dune at the same rate the next front covers the old part of the slacks. A computer model simulating the dune dynamics is presented. The model parameter values were estimated in accordance with the sensitivity test, thus suggesting the key points of the dune dynamics. Only certain sets of values for the parameters of the model produce a topography fitting the actual one. The erosion rate, and the growth of vegetation are the parameters which most deeply affect the appearance of the simulated dunes. Under the assumptions of the model, a simulated descent of the groundwater table may produce the disappearance of the slack vegetation for more than 200 years. Keywords: Dune dynamics; Dune front; Groundwater;

1. Introduction

Park (southwest Spain), with an area of 50720 ha, includes three major types of ecosystems: marshes, stabilized sands and mobile dunes (Garcia Novo, 1981). The latter is a great dune field 25 km long and some 4 km wide, dominated by massive parabolic dunes. Several dune fronts (from three to six depending on the sector) running parallel to the shoreline, move inland at an average rate of 2.5 m/yr (for a full description of the site see Garcia Novo et al., 1976, 1977; Garcia Novo and Merino Ortega, 1993). Dvo successive dune fronts are separated by a slack, locally called “corral” (Fig. l), which is covered by vegetation dominated by pinus pineu Dofiana

National

Simulation;

Slack

(umbrella pine) and several shrub species (Corema album, Halimium halimifolium, Ulex minor, Artemisia chritmifoia, etc.). The composition of

the shrub communities varies from one slack to another. The advance of the dune fronts buries all vegetation, with the occasional exception of some the tallest individuals of P. pinea, which survive because the dune does not entirely cover their crowns. On the other extreme of the dune the vegetation continuously colonizes the tail of the dunes as soon as the sand substratum erosion ceases due to the proximity to the water table. The active dune movement produces a highly dynamic system, with vegetation colonization keeping pace with dune displacement. The setting in motion of the mobile dune

0304-3800/95/%09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0304-3800(93)E0090-P

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F. de Castro /Ecological

system took place in the 18th century. Before then the main vegetation was a forest dominated by Quercw suber, Olea europaea and Juniperus oophora (Allier et al., 1974; Rivas Martinez et al., 1980). pinus pinea was introduced in the mobile

Modelling 78 (I 995) 205-217

dune system about 1850, although it was planted in near zones from 1737. The causes of the initial movement of the dunes could have been an overexploitation which destroyed primitive forest cover coinciding with a period of severe drought

Fig. 1. Aerial photograph of the dune system. The sea is situated at the upper left comer of the image. The white zones are naked sand (v.g., dune fronts without vegetation) while the dark ones are slacks covered by vegetation.

F. de Castro / Ecobgical Modelling 78 (199.5)205-217

and climatic instability (Granados Corona, 1985; Granados Corona et al., 1988). The dune field has experienced numerous pulses of activity (Pou, 1976). The dunes present a parabolic morphology and dune fronts may extend for several hundred of meters with heights ranging from 5 to 20 m. The sand is mainly composed of rounded quartz grains (80%) with less than 5% calcium carbonate content. The objective of this paper is to present a computer model which simulates the movement of the dunes and their interaction with the vegetation. The model covers the sand erosion and transport, the growth of the vegetation, the supply of sand by the sea and the depth of the water table, which is the major source of water for plants in this area and strongly influences the species distribution (Garcia Novo et al., 1976). Through the sensitivity analysis of the model, the most important processes in the system have been identified, and the influence of each one on the characteristics of the system were revealed. Despite of the simplicity of the model, simulations closely resembling the morphology of the real dunes can be obtained.

2. Description of the model The basic process the model deals with is the sand movement. The dune area is assumed to be divided into square “cells” or units. Each cell is represented by an element of a two-dimensional array (Fig. 2a). The upper part of the array (the first line) corresponds to the shoreline, and the bottom part (the last line) corresponds to the inner front of the system. The value represented by each element is the height of sand at that point, the thickness of the sand stratum (see Fig. 2b). The actual area corresponding to each element is one of the input parameters. By changing this parameter the resolution of the model can be varied. Thus, an array of 100 x 100 elements, each one standing for a square of 10 x 10 m, represents a surface of 1000 X 1000 m (1 km2). It is to be noted that if elements represented a smaller area, the model gained in precision but, on the other hand, more elements were needed

207

a Shoreline

Wind DirectIon

INLAND

One \element

‘s

N

of the array

tielgrltof sand I

Fig. 2. Representation of the dunes system as they are considered in the model (a). The value stored in each element represents the height of sand at that point (b). The first row of the array represent the shoreline. The actual area covered by the whole array depends on the number of rows and columns and on the assumed size of each element.

to simulate the same total area and so the computing time largely increased. In the Doiiana dune field the sand is transported inland by dominant southwestern winds, a direction almost perpendicular to the shoreline. In the simulated model the sand “moves” from the uppermost part of the array (the beach) to the bottom part (inner front). The initial situation for all the simulations is assumed to be a stratum of sand 50 m deep. This value is assigned, at the start of the program, to every element of the array. The first few lines of the array (those equivalent to 50 m) are maintained at their initial values, as to simulate a beach surface.

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F. de Castro /Ecological Modelling 78 (I 995) 205-217

2.1. Parameters of the model

1. Sea sand supply: Represents the amount of sand (in meters of sand height per cell per year) supplied by the beach to the dunes every year. 2. Erosion rate: Represents the amount of sand removed in each cell every cycle (m/yr). It is provided to the program as two thresholds between which a value is chosen at random when needed during the calculations. 3. Transport distance: Represents the distance (m) up to which the sand eroded in a cell can be moved in the direction of the wind. As erosion, it is provided to the computer as two limits. A value between these limits is chosen automatically at random. 4. Slide-down slope: The maximum stable slope allowed between two adjacent cells. It is set to 32” for all the simulations because this is the stable free slope for the Doiiana grain size of the sand (Garcia Novo et al., 1976, 1977) and it corresponds to the grain size of aeolian sands (Zenkovich, 1967; Young, 1972). 5. Maximum climbing slope: Stands for the maximum slope the sand is able to get over, impulsed by the wind. Steeper slopes prevent the movement of sand. Its actual average value is 4” (Garcia Novo et al., 1976, 1977). The meaning of other parameters will be explained later. The model proceeds by applying a sequence of six computations in turn to each cell of the array a given number of times. Each iteration represents one year. The values stored in the array are kept unchanged until all the cells have been examined, then all the values are updated. The six steps are as follows. 2.1.1. Accumulation of sand All the sand entering the system is assumed to be supplied by the sea. By each iteration the value of all the elements in the first line of the array is increased by a figure corresponding to the height (in cm) that a given amount of sand would reach if deposited in a cell (sea sand supply). This figure simulates the amount of sand the sea deposits on the beach every year. The real dunes near the beach show different characteris-

tics than those situated far from the shoreline. The former are small, embryo dunes originated from the direct supply of sand by the sea. This is coarser grained sand than the rounded aeolian sand of the rest of the dune system. The erosion of these embryo dunes and the transport of the smaller sand particles inland will promote the formation of the great dune ridges which constitute the main part of the system. The model can not simulate that difference because it does not consider spatial variations in the quality of sand, so the zone of embryo dunes is modeled as a flat band, 50 m wide, where the supply of sand is considered to be uniform. 2.1.2. Erosion For each element the amount of eroded sand per year is chosen randomly between two limits. These limits are input parameters as explained above. The eroded sand is removed from the element (so its height decreases) provided that the slope between this and the next element is lower than 4” (maximum climbing slope). This is the slope of the dune’s tail cited in the literature and was therefore used as a first approximation. It is assumed that, under the average wind conditions in the zone, the sand does not climb steeper slopes. 2.1.3. Transport The amount of sand removed from an element is transported within the limits of a given distance in the direction of dune’s advance. All the elements on the path are checked. If in this process a slope between two adjacent elements is found to exceed the maximum set value (see above), the transport does not proceed any further. In that case all transported sand is deposited in the element being checked. No sand is considered to be retained in any of the previous cells. This is obviously an oversimplification, undoubtely some amount of sand is deposited along the transport path, which was not included in order to keep the model simple. To simulate such a process accurately would require to include several new parameters. The transport distance is randomly chosen between two limits (transport distance) which are, as in the previous case, input data.

F. de Castro /Ecological Modelling 78 (1995) 205-217

2.1.4. Slide down

Wind

At each iteration the slope between every element and each one of its eight nearest neighbors is checked. If the steepest of the eight slopes surpasses a critical value (input parameter), part of the sand in the element being examined is moved to the neighbor with the steepest slope. In the simulations that critical slope (slide-down slope) was assumed to be 32” (Garcia Novo et al., 1976, 1977; Warren, 1979). The amount of sand displaced because of slide down depends on the difference in height between the two elements and the size of the cells (Fig. 3), and is computed as follows: D = H, - [II,

+ (tan 32*d)],

(1)

where D is the height of sand displaced, H, is the height of the higher element, H, represents the lower one and d is the cell size of the elements of the array (in m). The critical slope (32”) is also included as a parameter. The value of D is subtracted from H, and added to Hz. In some cases this procedure could result in Hz becoming greater than H,. If that situation occurs, both elements are set to the same value, the average of H, and Hz. 2.1.5. Wind shelter It is assumed that a column of sand of height H stops the wind within a distance equal to 3

a

209

b

Fig. 3. The situation depicted in (a) is unstable due to the difference in the height of the sand between the two contiguous elements. Part of the sand in the higher element slides down to the lower one (b). The amount of sand displaced (D) is such that the final slope between both elements is 32” (see text for the calculation of D).

Potential

shadow of “A”

(3*H)

-i

Fig. 4. The elements 1, 2, 3, 4 and 5, are assumed to be protected from the wind, and so from the erosion, due to the element A. The latter sheds a wind shelter up to a distance equal to 3 times its height (Zf) in the direction of the wind. The height of the “shadow” decreases with the distance. The element B is higher than such limit and so it does present erosion.

times H (Warren, 1979). Thus some elements may be sheltered from the wind by others lying windward, and in them no erosion takes place. Prior to calling the erosion routine, these elements have to be computed as follows. Let A represent the element providing shelter. Its effective height in this case is calculated as the difference with respect to the contiguous cell placed windward (Fig. 4). In case the difference was negative the current cell is skipped. First the number of cells equivalent to a distance 3 times the effective height of A is calculated (which depends on the “cell size” assigned to the elements of the array). That number is called “potential shadow of A” (Fig. 4), and all the elements closer to A than the calculated figure are assumed to be sheltered from the wind provided they do not surpass a given height (calculated by trigonometry) which depends on their relative distances to A. If any of those elements is higher than the mentioned limit (as is the element B in the figure), it is assumed that only the cells placed between A and B are protected from the erosion. The same process is performed on every cell of the array. 2.1.6. Vegetation

In order to include the vegetation in the model, a second array must be considered. This array has the same number of elements as the previous one

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F. de Castro /Ecological

with sand height data. The values in this new array represent the abundance of vegetation in each cell. A value of 0 means no vegetation, which is the initial state for all the elements. The growth of vegetation strongly depends on the availability of water. In the study area, the main source of water for plants is the soil water table. Due to the sandy soil texture, if the water table was too deep, the vegetation could not reach it and would die, which is the rationale underlying the procedure that the program uses to simulate the dynamics of vegetation. The maximum water depth allowing for the vegetation to survive is set at 2 m. The choice of this value is based on personal observations and personal communications. In the model the phreatic level is arbitrary set 3 m below the initial surface of the sand, 47 m above the zero base level and it is maintained unchanged along the simulations for simplicity. If, at any moment during the simulation, the difference between the surface of the sand and the phreatic level surpasses 2 m, the vegetation in that cell dies. Also when a dune ridge slides down to a cell, the vegetation in that cell is considered to be buried and dies (i.e. its value is set to 0). Since each model cycle represents one year, it is assumed that the slide down of sand over such period is enough to bury all the vegetation. The specified cell will not be colonized until the dune ridge has passed away and the erosion makes the surface close enough to the phreatic level as to supply water to plants. Vegetation is seen as a single entity. No different species are considered. By each iteration the values stored in the vegetation array are increased by one unit provided the condition explained above is satisfied. Also it is assumed that when the amount of vegetation in a cell reaches a certain threshold it prevents the sand erosion in it, and the transport of sand through it, and thus, in those cells “densely” covered by plants neither erosion nor transport takes place. The threshold cover needed to stop the transport and the erosion of the sand is one of the parameters of the model. It can be considered as the lapse time needed to develop the threshold cover. Actually the natural vegetation represents an obstacle for the transport of sand, the degree of which depends strongly on the

Modelling 78 (1995) 205-217

species and the density of the stand. Some species are more effective than others in trapping the sand. This difference between species was not included in the model since only one theoretical species of plant is considered. In order to maintain the model as simple as possible the retention of sand by the vegetation is simulated as a switch, a discrete process with only two states. The vegetation’s array is completely updated by each iteration accordingly with the rules expressed before, so the distribution of plants is continually changing as dunes advance. 2.2. Variables used to test the model The characteristics of the real dune system used to test the results of the model are: the advance rate of the foredunes (their speed in meters per year) and the number of the observed fronts along a distance of 1 km from the beach inland. The latter is used instead of the width of the dunes because this measure is very variable and difficult to estimate precisely. Both variables are characteristics of the system, not being involved in any of the calculations, and so they are appropriate to test the behavior of the model. It is not easy to find out the number of ridges that exist in the real dune system. In many places they are joined, due to the different speed at the different points. The fronts are not straight segments, but irregular undulations. In spite of that, from aerial photographs and satellite images, a certain number of ridges can be distinguished, ranging from 3 at the narrowest part of the dune system (some 2 km wide from the beach to the innermost ridge), to 6 at the broadest zone, 4 km wide (this latter value is close to the theoretical maximum of 7-11 suggested by Zenkovich, 1967). From the values above, the number of observable fronts per km, from the beach to inland, can be estimated as 1.5. The speed of the fronts has been measured by two different methods: comparison of aerial photographs taken with an g-year interval, and by direct measurement with fixed marks on the ground, over two years (Garcia Novo et al., 1976). From these measurements the speed can be estimated as 2.5 m/yr on average. A third method, involving the estimation of the

F. de Castro /Ecological Modelling 78 (1995) 205-217 Table 1 Values used in the sensitivity test of the model for the different parameters. They amount a total of 125 (5 X 5 X 5) runs of the program Erosion rate (m/yr)

Transport distance (m/yr)

0.08-0.1 0.2-0.3 0.4-0.5 0.6-0.7 0.9-1.0

15- 20 80- 100 3Oc- 400 700- 800 800-1000

Thershoid cover 2 5 10 20 40

The values for the rest of the parameters were: 32” Slide down slope: 4” as initial value. 2” as final Maximum climbing slope: value same as the minimum value Sea sand supply: for erosion rate each case 10xlOm Cell size: 3 times Wind shelter

211

mates in the rate computations, the first mentioned experimental methods were preferred for this model. 2.3. Sensitiuity test of the model The model’s behavior has been tested through the sensitivity test. Those variables for which actual values were known were maintained constant, while the unknown ones were varied, each in turn, along a set of different values (Table 0, and the program was run for each combination of input parameters. This procedure allows us to examine the behavior of the model and shows the variables that have the greatest influence on the results.

3. Results and discussion

ages of pinus individuals in the slacks, yields a much higher value of over 5 m/yr (Garcia Novo et al., 1976). Due to the inclusion of age esti-

The results obtained and explained here should be taken as suggestions of the model. The values

Fig. 5. Result obtained when the transport distance is set to 15-20 m. No dune fronts are developed. Instead, a surface of sand slowly advances, covering the vegetation. The assigned values to other parameters do not affect the result in this case. The figure depicted represents an array of 100 X 100 elements. The cell size is set to 10 m, thus the total area simulated is 1 km*. The sea is placed at the right hand side, while the sand is transported to the left. The vertical scale is magnified 4.5 times.

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F. de Castro /Ecological

obtained for some of the parameters of the model from the sensitivity test have not been tested against direct measurements. Different input values produce different dune topographies on the screen. Only certain combinations of those values result in the banded pattern of dunes and vegetation which fit the actual one. Other values outside the tested range will produce other kinds of dune morphology.

Modehg

78 (1995) 205-217

result obtained is a undulated surface of small elevations (Fig. 5). The sand advance covering the vegetation is extremely slow. The same result is obtained with a transport distance between 80 and 100 m and a low erosion rate (from 0.08 to 0.1 m/yr). This suggests that if the movement of the sand is not intense enough, separated dune fronts can not be formed (Goldsmith, 1978). 3.2. Erosion rate

3.1. Transport distance The transport distance does not exert noticeable influence on the characteristics of the system (Tables 2 and 3). The variations in the value of this parameter do not promote changes either in the number of fronts nor in their speed, except in one case. If the transport distance is very short (15-20 m), no fronts can be obtained in any case, independently of the rest of the parameters. The

The erosion rate has the greatest influence on the two characteristics used to test the behavior of the model: number of fronts and speed. If the erosion is very intense (0.9 to 1 m/yr>, the dune fronts, as in the previous case, are not formed. In spite of this, the resultant topography is different from that of the one previously mentioned. The topography becomes more uneven, with large accumulations of sand in irregular dunes, separated

Fig. 6. Result of the simulation with a high erosion rate (0.9-l m). The dunes do not form separated fronts. They are randomly placed with small slacks with vegetation between them. The area represented is the same as in Fig. 5 (1000 X 1000 m). The vertical scale is magnified 4.5 times.

F. de Castro /Ecological Modelling 78 (1995) 205-217

by small vegetated slacks. The dunes, however, do not form parallel ridges. Their distribution is completely irregular (Fig. 6) (Goldsmith, 1978). In most other cases the result is a variable number of dune ridges, more or less neatly apart from each other, with flat slacks covered by vegetation between two successive ridges. As can be seen in Table 2, an increase in the erosion rate promotes an increase in the speed of the fronts (so agreeing with Bangold, 1954). The speed ranges from 0.6 m/yr to 3 m/yr depending on the values of another parameter (the threshold cover>. The reason is that the advance of the dune fronts takes place only by the accumulation of sand at the top of the ridge and the subsequent slide of the sand when it reaches an unstable slope. A greater erosion rate promotes a greater accumulation of sand on the top of the ridges and, so, a more frequent sliding. The width of the ridges decreases as the erosion increases, and, thus, the number of fronts per km increases. In Table 3 the number of fronts

213

per km for different values of erosion is shown. It is easier to count fronts on the screen than to estimate their width, which is highly variable. As the erosion rate increases, greater amounts, of sand are displaced every year and the sand removal in the tail of the dune is more intense. This promotes a narrowing of the ridges and also a higher number of fronts per km. 3.3. Vegetation The main effect of the vegetation is to constitute an obstacle for the movement of the sand, allowing its progressive accumulation and the formation of dunes (Wartena et al., 1991). Without the presence of vegetation no dunes are formed in any case. Instead, the sand is dragged along until it disappears and a smoothly undulated surface is maintained where no structure is recognisable. If vegetation exists, the formation of discontinuous dune fronts is possible. The threshold cover

Table 2 Advance rate of simulated dune fronts. It is expressed in meters per year for each combination of erosion rate (columns) and transport distance (rows). Each sub-table correspond to a different value of threshold cover (no units). A dash means that no neat fronts develooed. Values in brackets mean that the estimation was difficult due to the fraarnentation of the dune fronts Transport distance Cm) 15- 20 80- 100 300- 400 700- 800 800-1000

Erosion rate

Erosion rate 0.08-0.1

0.2-0.3

Threshold cover: 2 1.56 0.64 1.67 0.71 1.64 0.68 1.60

0.4-0.5

0.6-0.7

0.9-1.0

15- 20 80- 100 300- 400 700- 800 800-1000

0.66 2.00 0.63 1.93 0.63 1.93 Threshold cover: 40

0.68 0.65

-

0.2-0.3

0.4-0.5

0.6-0.7

0.9-1.0

2.7 2.05 2.11 2.09

2.57 2.60 2.64

(3.04) (3.13) (3.08)

2.41 2.32 2.39 2.39

(2.61) (2.71) (2.71)

Threshold cover: 5 2.10 2.05 2.02 2.04

2.96 2.62 2.56 2.54

3.00 -

Threshold cover: 10 15- 20 80- 100 300- 400 700- 800 800-1000

0.08-0.1

0.71 0.71 0.71

2.17 1.79 1.75 1.79

Threshold cover: 20 2.24 2.19 2.22 2.16

2.66 2.67 2.77 2.72

(3.34) (3.16) _

_

_

I 0.65 0.65 0.65

I -

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F. de Castro /Ecological Modelling 78 (1995) 205-217

of the vegetation (expressed as the number of iterations needed for the vegetation to stop the sand displacement) has some influence on the characteristics of the simulated dune system. The threshold cover also does influence the advance rate as can be seen in Table 2. The greater the threshold cover, the quicker the dune movement. The reason for this is that, when the threshold couer is large, a smaller number of places (i.e. cells) become covered by a vegetation dense enough to stop the erosion and the transport. Thus the movement of sand is possible in more places and so the whole dynamics is increased. As the threshold cover decreases, the number of fronts per km tends to increase, because they are narrower. This is shown in Table 3. When the threshold cover is great (more than 20) the total number of distinguishable fronts drops. The cause is that, when a front starts moving and moves away from the “beach”, the vegetation colonizes

the zone between the beach and the front which is progressing. If the threshold cover is small, the vegetation reaches it before being buried by the sand which is continuously deposited from the beach. This process promotes that, when a ridge is just coming apart form the shoreline, a vegetation “barrier” is easily formed behind it, so stopping the transport of sand from the beach to the front. The final consequence is numerous, narrow fronts. If the threshold cover is large, the fronts will be wider, each with a larger amount of sand. The effect of that is, given an erosion rate, the speed will be higher with “slow-growing” vegetation. If the threshold cover is too high (> 40), no fronts are obtained. All the dunes coalesce in many points and no separation between the dunes can be observed. The erosion rate producing an adequate advance rate (around 2 m/yr) lies between 0.3 and 0.5 m/yr. With those values, an advance rate

Fig. 7. Representation obtained with an erosion lying between 0.4 and 0.5 m/yr. The figure represents an area of 1 km wide (in the direction of dune fronts) and 2 km long. Seven dune fronts are clearly appreciable, so about 3.5 per km. This is approximately two times the real value. The vertical scale is magnified 4.5 times, as in previous figures.

F. de Castro /Ecological

Moa’elling 78 (1995) 205-217

215

Table 3 Number of observable dune fronts per km for each combination of erosion rate (columns) and transport distance (rows). One dune ridge plus a slack is considered as one unit. Thus each number is calculated as the number of ridge + slack units divided by the total length represented by the cells of the array in each simulation. Each sub-table correspond to a different value of threshold cover (no units). A dash means that no neat fronts developed. Values in brackets mean that the estimation was difficult due to the fragmentation of the dune fronts Transport distance Cm) 15-

20

80-

100 300- 400 700- 800 80&1000 15-

20

80-

100 300- 400 700- 800 800-1000 1580-

20

100 300- 400 700- 800 800-loo0

Erosion rate 0.08-0.1

Erosion rate 0.2-0.3

0.4-0.5

Threshold cover: 2 -

_

2.5 3 3.5

4.5 5 5.5 5.5

(3) 3 3.5 3.5

0.2-0.3

0.4-0.5

0.6-0.7

4.5 5 5.5 5.5

J.5 5.5 5.5 5.5

5.5 6 -

0.9-1.0

_

5.5 6 -

_ 2.5 3 3.5

_

_

Threshold couer: 20 _ _

_

_

_

_ 2.75 2.75 2.75

3 3 3 3

(3.5) (3.5)

I -

4 4 4 4

Threshold cover: 40 -

_

_

2.5 2.5 -

_ _

_ -

-

0.08-O. 1

5.5 5.5 5.5 5.5

4 4 4 4

-

0.9-1.0

Threshold cover: 5

Threshold couer: 10 -

2 2.5 2

0.6-0.7

_

(3) 3 3.5 3.5

_ _ _ _

_ _

Fig. 8. Simulation obtained setting the value of the maximum climbing slope (see text for definition) to 2”, instead of the 4” cited in the literature. The area simulated in this figure is 2 km (from left to right) and 4 km wide (200 x 400 cells of 10 x 10 m). The number of fronts per km fit the actual one (1.5). The advance rate varied accordingly with the erosion, transport distance and the threshold cover (see Table 2). If the erosion is set to 0.6-0.7 m/yr, an advance rate around 2.6 m/yr is obtained, which is very close to the real value (2.5 m/yr). Other parameters do not affect as much as the erosion.

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F. de Castro /Ecological

ranging from 2 to 2.4 m/yr is obtained in the simulation, the exact value depending on the threshold cover. Unfortunately, such values of erosion lead to the formation of 3 to 4.5 fronts per km (Fig. 71, which clearly exceeds the real value (around 1.5). Through several runs of the program it has been shown that the only way to solve this conflict is to reduce the maximum climbing slope (see above for definition) from 4” to 2”. If this last value is used, the ridges get wider and less ridges per km are formed. The obtained result can be regarded as close enough to the real situation (Fig. 8). The adoption of the lower value seems justified as the average value cited by Garcia Novo et al. (1976) was based on only four measurements, and Garcia Novo and Merino Ortega (1993) cite a windward slope of less than 5”. 3.4. Simulation of a water table drop After a simulation ends, the program stores all the information about the levels of sand (i.e. the topography) and the amount of vegetation in such a way that they can be used as the initial situation for subsequent simulations. This procedure allows the modification of some of the input parameters and then to continue with the simulation, in order to observe the effect of the change. After the second run is completed, the modifications made in the parameters can be reverted and thus test if the changes produced in the system are reversible or not. The method described above has been used to simulate the effect that a hypothetical descent in the phreatic level has on the characteristics of the mobile dune system. After a stable situation is reached (like that depicted in Fig. 7) the phreatic level (initially 3 m below the surface of the sand) was lowered by 1 m. After that change the simulation was continued. The immediately observable change is that most of the vegetation present at the start of the simulation will die out. As a consequence, a great part of the surface is now exposed to wind erosion and there are no obstacles to sand transport. Now the available amount of sand is greater

Modelling 78 (1995) 205-217

and the dunes grow higher and speed up. After some time the erosion again makes the surface close enough to the water table to permit the growth of vegetation. The slacks slowly appear again near the beach, while they are not regenerated in the rest of the area. Using the same values for the parameters as those explained above, it takes the first slack 80 iterations to develop, and over 200 for the second to be restored. It is only after 700 iterations that all the previous slacks are fully regenerated. Although it is only a simulation, this result suggests that the whole equilibrium of the mobile dune system can be severely altered by a small drop in the water table. A similar statement is made by Noest (1991). It is to be pointed out that the situation described in the simulations is stable. The dunes are continuously developing at the beach and disappearing at the opposite side. The vegetated zones advance, colonizing the tails of the dunes as the dunes bury the old parts of the slacks, just as it occurs in reality. The model remains stable for at least 1500 iterations (say 1500 years), which is the longest period simulated. With the model presented here it has been shown that to simulate the main features of the Doiiana mobile dune system, only a few variables are needed. The sensitivity test of the model reveals that the transport distance does not affect much the characteristics of the dune ridges, the intensity of the erosion being what determines their dynamics and morphology. The value the model suggests the erosion rate to lie between 0.3 and 0.5 meters per year. From measurements of wind speed in the zone it can be stated that the assumed values of erosion and transport are reasonable ones. The model also suggests that the value of the windward slopes of the dunes cited in the literature may have been overestimated, being more close to 2” than to 4”. The model points out the role of the vegetation in the formation and control of the dunes, suggesting that their morphology may depend not only on geomorphological or ecological processes, but on a combination of both and also that changes affecting the growth of the vegetation could promote long-term changes in the system.

F. de Castro/Ecological Modelling78 (1995) 205-217

Acknowledgements Valuable criticism and manuscript revisions by Professor Dr. F. Garcia Novo are gratefully acknowledged.

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