A Preliminary Cellular Model for Sand Coastal Erosion and Experimental Contrast with Porto Cesareo Case Maria Vittoria Avolio1 , Claudia Roberta Calidonna2 , Marco Delle Rose3 , Salvatore Di Gregorio1, Valeria Lupiano4 , Tiziano Maria Pagliara5, and Anna Maria Sempreviva2 1
Dept. of Mathematics, University of Calabria (UNICAL), 87036 Rende (CS), Italy 2 CNR-ISAC Inst. of Climate and Atmospheric Science, Industrial Area Comp. 15,88046 Lamezia Terme (CZ), Italy 3 CNR-IBAM Ins. for Archaeological and Monumental Heritage, Prov.le Lecce-Monteroni,73100 Lecce, Italy 4 Dept. of Earth Science, UNICAL, 87036 Rende (CS), Italy 5 Nautilus Puglia, Campi Salentina (LE), Italy
[email protected] Abstract. The phenomenon of sand erosion is recently spreading in Mediterranean beaches in a worrisome way. Cellular Automata modelling such a phenomenon involves many difficulties for adopting a convenient time and space scale (minute and decimeter), that can permit temporally reasonable simulations. A very preliminary model RUSICA was developed in association with an experimental work in order to test hypotheses, to receive suggestion separately for some basic processes and to learn from past occurred cases. During this contamination phase, some experimental applications were succesfully projected in order to contrast sand erosion on the coast. This paper presents the current initial version of RUSICA for sand erosion/transport/deposition and describes the results obtained at Porto Cesareo coast in the Italian Apulia Region. Complete simulations by RUSICA will soon follow this preparatory work.
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Introduction
An extension of classical Cellular Automata (CA), the Macroscopic CA [5], were developed in order to model many complex macroscopic fluid-dynamical phenomena, that seem difficult to be modeled in other CA frames (e.g. the lattice Boltzmann method), because they take place on a large space scale. Macroscopic CA can need a large amount of states describing properties of the cells (e.g. temperature of bottom sea, thickness of sand cover,...); such features may be formally represented by means of substates, that specify the characteristics to be attributed to the state of the cell and determining the CA evolution. In the case of surface flows, quantities concerning the third dimension, i.e. the height, may be easily included among the CA substates (e.g. the altitude). This is an easier and effective way to deal with third dimension and simplifying the problem in a two dimensional one. The phenomenon is very complex as it includes G.C. Sirakoulis and S. Bandini (Eds.): ACRI 2012, LNCS 7495, pp. 273–278, 2012. c Springer-Verlag Berlin Heidelberg 2012
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granular flows problem class, in this case, time dynamics is very important. In the past the erosion problem by CA approach was described and modeled by: [3] soil erosion by rain (SCAVATU model); [2] transport, deposit and erosion by sand and snow; [2,6], subaerial-subaqueous flow-like landslides [1]. We can summarize consideration in the previous approaches as follows: phenomenon, when approached as sandpile + waves, requires naturally a microscopic approach. That means cells smaller than mm and time step smaller than s, i.e. problems about data precision and validation. Two-dimensional Chopard model for snow/sand transport, deposit and erosion would be extended. The aim of this contribution is to show, how, by means of CA, to model and simulate dynamics of the coastal erosion complex phenomenon. In the following sections the CA RUSICA (RUdimental SImulation of Coastal erosion by cellular Automata) model is introduced and then experimental results are described. Finally some conclusions and perspectives of this work are outlined.
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The Model RUSICA Phenomenological Considerations and Hypothesis
The underlying ideas in modeling coastal erosion is to approach it according a macroscopic view on the base of a simplified phenomenology. Equivalent sand cover (an average type of sand) may be assumed without a continuous variation of sand properties. Water covers the shore on the sea level up to a height dependent on wind intensity and direction or/and tide height or/and sea current intensity and direction without explicit wave movement. Sand flows are averaged in time (no explicit turbulence and movement alternation), but along a computed direction between slope, wind and current directions.
Fig. 1. Vertical scheme according to model substates, expliciting the third dimension
The wind transmits energy from the sea surface possibly up to the sea bottom, depending on its intensity, type and depth of sea bottom. Shallow sandy/ porous/rock-solid but irregular bottom involves larger energy loss. Such an energy permits (by turbulence) sand suspension in water up to a maximum possible
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quantity, if the wind intensity is not sufficient, sand sedimentation occurs. Sand erosion occurs when enough wind energy passes on sandy bottom sea. Sand sedimentation and erosion may occur contemporary. Free wind generates surface wind by propagation from the borders of CA: it implies that updating needs a shortest time step (less than a minute) only when the wind changes: this problem may be solved by introducing a coupled CA, that works only when wind changes. Obstacles (cliffs, artificial barriers of different type) can locally affect wind direction-intensity and sea current directionintensity. Third dimension substates are made explicit as depicted in the Fig. 1. 2.2
The CA Model
The RUSICA model is a two-dimensional CA with hexagonal cells, with substates and the transition function defined as follows: RU SICA = R, G, X, S, P, τ, Γ – R identifies the set of regular hexagons, where the phenomenon evolves. – G represents the cell at the border of R, where the wind could be generated. – X = {(0, 0), (0, 1)(0, −1)(1, 0)(−1, 0), (1, 1), (−1, −1)} are the neighbors of the central cell according to hexagonal grid. – S = {SA ×SD ×ST H ×SW E ×SSW E ×SC ×SF ×SXC ×SY C ×SXF W ×SY F W × SXSW × SY SW × SW L × SW A × SXW C × SY W C } is the finite set of states (of the finite automaton embedded in the cell) respectively: the cell altitude (or sea bottom depth), the cell sea water depth, the sand layer thickness, the average (for a step) kinetic energy of wind inside the cell, the average kinetic energy of sea water inside the cell, the sea water average sand concentration, the suspended sand flows, normalized to a thickness, from the central cell toward any adjacent cell, the x − y components of sea current speed, the x − y components of free wind speed, the x − y components of surface wind speed. Furthermore wavelenght, wave amplitude, and x-component and ycomponent wave celerity address for sea waves considered properties. – P = {pa , pt , pd , pet1 , pet2 , pslv , psm , psd } is the set of the global physical and empirical parameters, which account for the general frame of the model and the physical characteristics of the phenomenon, respectively considering: the apothem of the cell, the time interval corresponding to a CA step, is the decay parameter for kinetic energy variation according the sea depth, the two energy transfer coefficients; parameter for sea level variation; two parameters of sand mobilization and deposit. – τ : S 7 → S is the deterministic transition function, composed by the following elementary processes: • σ1 suspended sand outflows determination; the motion of a suspended sand particle may be described as a combination of an elliptical and translational motion with a drift along the composed wind and sea current directions, ellipsis and translation size increase depending on wave
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energy and decrease top-down, ellipsis (a circle for deep waters) flattens in shallow waters; sand outflows are computed by accounting of back and forth motion and by considering the hexagonal discretization of plane and variations in height: σ1 : (SA × SD × ST H )7 × SSW E × SC × SXC × SY C × SXSW × SY SW × SW L × SW A × SXW C × SY W C → SF6 • σ2 variation of sand cover thickness and suspended sand concentration by sand cover mobilization and sand deposit; if the water energy of sea bed overcomes a threshold psm dependent on sand granulosity, a sand quantity proportional to energy overcoming the threshold (this is a first rough approximation [3]) is added to suspended sand, then the sand deposit is computed by considering that sea water energy density in the cell can proportionally (by psd dependent on sand granulosity) support a maximum suspended sand concentration, if the concentration overcomes such a maximum, sand deposit occurs in order to re-establish equilibrium; sand deposit and mobilization may occur simultaneously: σ2 : SA × SD × ST H × SSW E × SC → SA × SD × ST H × SC • σ3 variation of suspended sand concentration in the water inside the cell; it consists trivially by composition of new suspended sand concentration from remaining (because of outflows) suspended sand in the cell more suspended sand from the inflows; control of possible deposits is performed according the sand deposit computation in σ2 and correspondent variation in sand layer thickness, depth etc.: σ3 : SA × SD × ST H × SSW E × SC × SF6 → SA × SD × ST H × SC • σ4 surface wind intensity, direction variation by free wind intensity, direction and altitude (if rocks or structures emerge from the sea, then the other coupled CA must work when at most direction and/or intensity changes of wind occur, otherwise free and surface wind coincide without coupled CA): σ4 : (SA × SD × ST H )7 × SXSW × SY SW → SY W C × SXW C • σ5 water depth variation by altitude, wind and sea current; wind and sea current involve wave formation, that is complicated by form (altitude) of sea bed: σ5 : (SA × SD × ST H )7 × SXC × SY C × SXSW × SY SW → SA × SD × ST H × SW A – external influences Γ : γ1 • γ2 account for generating step by step (historical, statistical, hypothetical) data of: • sea current velocity components offshore: γ1 : N × G → SXC × SY C , (N is the set of natural number accounting for CA steps). • free wind velocity components: γ2 : N × G → SXF W × SY F W
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The Experimental Site: Porto Cesareo
The study area, Porto Cesareo site, is a special Italian coastal zone in Apulia, on the east side, Jonian sea, which represents a significant example of Mediterranean type low-lying coastal landscape with different kinds of human activities and some important areas of environmental and archaeological interest. Such a region, similar in geomorphology to some second-order physiographic unit in
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south-western Apulia Adriatic coast, is particularly prone to coastal erosion and marine inundation [4]. From a morpho-sedimentological characteristic, gently sloping carbonate ramp are present as well as discontinues dunes, coastal dolines and water basin along the coast. The coastal site was in equilibrium for several decades not showing particular and intense erosion phenomenon until 2009 year (see Fig. 2.a). The intertidal bars and coastal line were at first modified and then destroyed in a very short temporal range. Analising meteorological and oceanographic data (2009-2011) some observation arised: 1)there was not an evident correlation between wind intensity and direction and wave height in the open sea and erosion events/sand deposit, 2)different wind direction from south direction in some cases arised in erosion or sand accumulation.
Fig. 2. A particular of sand deposition after experimental intervention and turbulence effect after slopes a) before erosion b)eroded beach c) removable contrast barrier d) erosion after a storm e) sand deposit after barrier intervention f) turbulence effect
At beginning of 2011 year a contrast intervention was experimented, in the south zone of the bay, for three months in order to allow the intertidal bar reconstruction. It was built a barrier under sea level with some controlled exits in order to modulate outflow currents (see Fig 2.b). The removable barrier (height 70 cm considering a 90 cm height bathymetry) was built with special bags (propylene 1000 lt capacity) filled with sands (2,1 t each weight). After about 45 days, in which the barrier was stable, the estimation of accumulated sands in the bay was about 2500m3 (see Fig. 2.e). The accumulation occurred during three main severe storms (February - April 2011) with Southern direction winds whose intensity was 17Kn. In particular during one of them there was an additional effect as the sea level was very high (+ 0,17 m on zero elevation IGM). With removable bags it was possible to tune the suitable control of outflows currents in the bay. The experimental intervention was guided by the turbulence behavior in presence of obstacles/slopes (see Fig 2.f). The measured bathymetry allow us to refine the model described in the previous section and actually still in development.
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Observations and Future Works
Adopting an interdisciplinary approach and analysing the complex phenomenon of the sand erosion/transport/deposition allowed us to project and experiment a low impact method. This gave us such results in contrasting erosion and also individuating emerging processes for the whole complex system. CA RUSICA is a new preliminary empirical way to approach and simulate the coastal erosion complex phenomenon and tacking into account its emerging phenomena. This permits to define a simplified model when opportune temporal scale and discrete steps in order to overcome turbulence regimes. Considering turbulence regime and related dynamics gave us the way to exploit the properties of the turbulent energy when a slope is present (see Fig 2.f). Taking into account this last issue, according the shoreline orientation and wind and marine currents directions, it was possible to put opportunely the contrast disposable structures in order to transform a usual erosive event into an accumulation one. Our first experimentation results comfort us; there is an ongoing work on data elaboration to populate the RUSICA model input. That will permit to tune, refine and validate RUSICA on the base of other site experimentations. Acknowledgements. This research was partially funded by PON (Operational National Plan) 2007 − 2013 from MIUR (Italian Research Ministry of Research) project ”SIGIEC: Integrated management system for Coastal erosion ” ID: PON01 02651.
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