Modelling surface radioactive spill dispersion in the Alboran Sea

Modelling surface radioactive spill dispersion in the Albora ´n Sea R. Peria ´n ˜ez* Dpto. Fı´sica Aplicada I, E.U. Ingenierı´a Te´cnica Agrı´cola, Universidad de Sevilla. Ctra. Utrera km 1, 41013 Sevilla, Spain Received 22 February 2006; received in revised form 25 April 2006; accepted 5 June 2006 Available online 24 July 2006 Abstract The Strait of Gibraltar and the Albora ´n Sea are the only connection between the Atlantic Ocean and the Mediterranean Sea. Intense shipping activities occur in the area, including transport of waste radionuclides and transit of nuclear submarines. Thus, it is relevant to have a dispersion model that can be used in an emergency situation after an accident, to help the decision-making process. Such dispersion model requires an appropriate description of the physical oceanography of the region of interest, with simulations of tides and residual (average) circulation. In this work, a particle-tracking dispersion model that can be used to simulate the dispersion of radionuclides in the system Strait of GibraltareAlbora ´n Sea is described. Tides are simulated using a barotropic model and for the average circulation a reduced-gravity model is applied. This model is able to reproduce the main features of the Albora ´n circulation (the well known Western Albora ´n Gyre, WAG, and the coastal circulation mode). The dispersion model is run off-line, using previously computed tidal and residual currents. The contamination patch is simulated by a number of particles whose individual paths are computed; diffusion and decay being modelled using a Monte Carlo method. Radionuclide concentrations may be obtained from the density of particles per water volume unit. Results from the hydrodynamic models have been compared with observations in the area. Several examples of dispersion computations under different wind and circulation conditions are presented. Ó2006 Elsevier Ltd. All rights reserved. Keywords: Dispersion; Numerical modelling; Hydrodynamic models; Particle-tracking; Albora ´n Sea * Fax: þ34 954486436. E-mail address: [email protected] 0265-931X/$ - see front matter Ó2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jenvrad.2006.06.009 Journal of Environmental Radioactivity 90 (2006) 48e67 www.elsevier.com/locate/jenvrad 1. Introduction The area of the Strait of Gibraltar has a high ecological value, being essential in marine and aerial migratory processes. As the only connection between the Mediterranean Sea and the Atlantic Ocean, marine turtles and mammals (dolphin, porpoise, sperm whale, killer whale) travel through the Strait and the Albora ´n Sea. Also, the region has a high tourist interest, since many kilometers of sand beaches in the area of the Strait and the Costa del Sol (Ma ´laga) attract thousands of tourists each year. Finally, there are also some important towns. A release of radioactivity in the area as a consequence of an accident (or a deliberate release) can lead to relevant ecological and economic impacts. Shipping activities in the area of interest are very intense, again due to the fact that it is the only connection between the Atlantic and the Mediterranean. There is a traffic over 70,000 merchant vessels per year, 30% of them declaring hazardous cargos. Transit of nuclear submarines and vessels transporting radioactive waste must also be considered. Only in the Strait of Gibraltar there are over 12,000 vessels per year (mostly passenger ferries) crossing between the north and south coasts (Nav42, 1998). Connections between the towns of Ma ´laga and Almerı ´a (Spain) and the north African coast must be added (see Fig. 1 for locations). It is usual to have adverse meteorological conditions in the Strait, with more than 54% of days of moderate to poor visibility and 13% of days with persistent fog conditions. Winds must be added, with frequent east and west gales. East winds (levantes) blow on an average of 165 days per year, predominantly from April to October, with an average speed of the order of 50 km/h. Maximum speed reaches 125 km/h. Gusts of winds can remain up to 7e10 days. West winds ( ponientes) blow on an average of 60 days per year, from November to March predominantly. Minimum and maximum speeds are 30 and 90 km/h. West winds are not as persistent as levantes, lasting for about 12e36 h. −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.2 35.4 35.6 35.8 36 36.2 36.4 36.6 36.8 37 longitude latitude Gibraltar Málaga Almería Ceuta Alborán Isle Cape Tres Forcas Tarifa ALBORAN SEA SPAIN MOROCCO Alhucemas Strait of Gibraltar Fig. 1. Map of the Strait of Gibraltar and Albora ´n Sea. 49R. Peria´n˜ez / J. Environ. Radioactivity 90 (2006) 48e67 The particular conditions in the area (intense traffic and adverse meteorology) make navigation difficult. Indeed, several accidents have occurred in the last years (Nav42, 1998). Due to the particular water circulation patterns in the area, a spill occurring in the Strait is introduced into the Albora ´n Sea basin in a time scale ranging from some hours to some days (Echevarrı ´a et al., 2002). Thus, the area of the Albora ´n Sea may be affected by an accident occurring not only inside the Albora ´n Sea itself, but in the Strait of Gibraltar as well. The objective of this work consists of describing a spill model that covers the Strait of Gibraltar and the Albora ´n Sea that can be applied to radioactive contaminants. This work may be considered as the natural continuation of Peria ´n ˜ez (2005a), where a radionuclide dispersion model covering only the Strait of Gibraltar was described. The hydrodynamic is solved in advance. A 2D depth-averaged barotropic model is used to obtain tidal currents in the region. A reduced-gravity model is applied to obtain the average water circulation in the upper water layer, since only spills occurring at the surface will be considered by the moment. Tidal and average circulations are stored in files that will be read by the dispersion code to compute water current at any time and position. Dispersion is solved using a particle-tracking method. Thus, the spill is simulated by a number of particles, each of them equivalent to a number of units (for instance Bq), whose paths are followed in time. Radioactive decay and turbulent diffusion are simulated by means of Monte Carlo methods. Contaminant concentrations may be obtained at the desired time from the density of particles per water volume unit. Some characteristics of the physical oceanography of the region are briefly described in the next section. The hydrodynamic and dispersion models are next presented. Some examples of calculations are then given and, finally, some discussion is included. 2. The Albora ´n Sea The water circulation in the Strait of Gibraltar is characterized by a surface inflow of Atlantic water and a deep outflow of more dense Mediterranean water. Exchanged flows (Tsimplis and Bryden, 2000) are of the order of 0.7 sverdrup (1 sverdrup ¼10 6 m 3 /s) with a net inflow into the Mediterranean Sea of about 0.05 sverdrup. This net inflow compensates the excess of evaporation over precipitation and river supply in the Mediterranean. This description of the exchange as a simple two-layer system flowing in opposite directions is a good first approximation (Farmer and Armi, 1988; Echevarrı ´a et al., 2002). The surface circulation in the Albora ´n Sea is as follows. The Atlantic water penetrates the Strait of Gibraltar and reaches mean velocities of the order of 0.6 m/s. This water forms a jet that enters the Albora ´n Sea in a east-northeast direction. The jet flows along the Spanish coast and curves to the south. Part of it flows to the west, incorporating to an anticyclonic gyre, while the remainder flows to the African coast between Cape Tres Forcas and Albora ´n Isle (Perkins et al., 1990). This is known as the Western Albora ´n Gyre (WAG). Another gyre, more elusive, fills the eastern basin of the Albora ´n Sea: it is the Eastern Albora ´n Gyre (EAG) that is out of domain of our model. A detailed description may be seen for instance in Vargas-Ya ´n ˜ez et al. (2002),Ve ´lez-Belchı ´et al. (2005) and references cited in these works, which include the classical works carried out since the 1970s. The WAG fills the western Albora ´n Sea between the Strait of Gibraltar and the Albora ´n Isle (Perkins et al., 1990), thus extending some 200 km in the westeeast direction. The WAG extends towards the south, reaching the coast of Morocco (Perkins et al., 1990; Werner et al., 1988). The vertical scale of the gyre is about 200 m. It has also been suggested (Preller, 50 R. Peria´n˜ez / J. Environ. Radioactivity 90 (2006) 48e67 1986) that a coastal feature (Cape Tres Forcas) acts as a barrier to the gyre growth. The variability of circulation in the Albora ´n Sea has been investigated by Vargas-Ya ´n ˜ez et al. (2002). These authors conclude, from their results and from the revision of previous works, that the gyre is the dominant circulation pattern in summer and the coastal mode is more likely in winter. In this coastal mode, the Atlantic current flows close to the African coast once it exits the Strait of Gibraltar and no gyre is apparent. Nevertheless, it has to be clearly pointed out that this bimodal behaviour is not perfectly defined, as can be seen for instance in the data presented by Heburn and La Violette (1990). In fact, there are transitions between the two commented behaviours (Va ´zquez-Cuervo et al., 1996; Ve ´lez-Belchı ´et al., 2005 and references here included). In this work, the presence of the WAG and the coastal model will be sometimes referred as the usual summer and winter conditions, respectively. However, it must be kept in mind that an absolutely clear annual cycle does not exist. We will return to this point later. With respect to the tides in the area, an important feature of the tidal flow in the Strait is that it can be considered, as a first approach, as barotropic. Indeed, 93% of the variance of current velocity in the semidiurnal band has a barotropic character in the Strait (Man ˜anes et al., 1998). Tsimplis and Bryden (2000) have pointed out that tidal currents are barotropic and larger than the mean inflow or outflow. The semidiurnal tide dominates ADCP records (acoustic Doppler current profiler) in the Strait, obscuring the expected two-layer character of the mean flow. The tidal signal is so strong that it reverses the currents near the bottom for a part of each tidal cycle. As a consequence, 2D depth-averaged models have already been applied to simulate surface tides in the Strait (Tejedor et al., 1999). Tsimplis et al. (1995) have even used a 2D barotropic model for simulating tides in the whole Mediterranean Sea. The success of these models indicates that the baroclinic component is of secondary importance. In the case of the main tidal constituent, M 2 , tide amplitude at the Atlantic entrance of the Strait is about 0.8 m. This amplitude decreases towards the east. Thus, at the Mediterranean entrance it is only about 0.3 m. The amplitude of the tide is reduced more in the Albora ´n Sea, reaching 0.09 m at the east limit of our domain (see map in Fig. 1). The associated currents decrease in a similar way: from tidal currents of the order of 1 m/s in the Strait to currents of a few cm/s in the Albora ´n Sea basin. Similar behaviour is observed for the S 2 constituent. From this analysis it seems evident that tides are relevant, for the transport of pollutants in water, in the area of the Strait of Gibraltar. However, once those pollutants enter the Albora ´n Sea the main mechanism is the residual (average) circulation. Contaminants may remain trapped in the WAG, and an appropriate description of this average circulation is thus required for a realistic calculation of contaminant dispersion. 3. Model description 3.1. Hydrodynamics The hydrodynamics of the area is described by means of two models: a barotropic model is used to calculate tides and a reduced-gravity model is applied to obtain the residual (average) circulation. A 2D depth-averaged model is used to calculate tidal currents over the domain; as commented in the previous section, it is a good approach. Equations are standard and may be seen for instance in Peria ´n ˜ez (2005b). The solution of these equations provides the water currents at each point in the model domain and for each time step. Currents are treated by standard tidal analysis and tidal constants are stored in files that will be read by the dispersion code to 51R. Peria´n˜ez / J. Environ. Radioactivity 90 (2006) 48e67 calculate the advective transport of particles. The model includes the two main tidal constituents, M 2 and S 2 . Thus, the hydrodynamic equations are solved for each constituent and tidal analysis is also carried out for each constituent separately. Some open boundary conditions must be provided to solve the hydrodynamic equations. Surface elevations are specified, from observations, along open boundaries of the computational domain. A radiation condition is applied to the water velocity component that is normal to the open boundary (Jensen, 1998; Peria ´n ˜ez, 2005b). Equations are solved using an explicit finite difference scheme. The computational domain (Fig. 1) extends from 35000Nto36 560N and from 5540Wto2 100W. Resolution of the grid is Dx¼2972 m and Dy¼3341 m. Water depths were downloaded from the NOAA Geodas database. Time step, limited by the CFL (CouranteFriederichseLewy) stability condition is Dt¼10 s. Once a stable periodic solution is achieved, tidal analysis is carried out to determine tidal constants that are used by the particle-tracking code. The reduced-gravity model is the simplest model able to simulate the major features of circulation above the pycnocline. Essentially it is a two-layer model in which the lower layer is infinitely deep and at rest. Thus, the interface between the two layers may deform without any resulting motion in the lower layer. In spite of this relative simplicity, reduced-gravity models are used at present to study different problems in oceanography (Cummins and Lagerloef, 2004; Chern and Wang, 2005; Morales-Maqueda et al., 1999; Arruda et al., 2004). Equations may be seen in the above indicated references. They are very similar to those of the barotropic motion, but the upper layer thickness replaces the surface elevation in the continuity equation and in the gravity term of the momentum equations. Also, the reduced gravity, g0, replaces gravity, g, in these equations: g0¼gr2r1 r2 ð1Þ where r 1 and r 2 are the densities of the upper and lower layers, respectively. The reduced gravity is fixed as 0.010 m/s 2 , the same as in the model of Heburn and La Violette (1990). The same numerical scheme as in the barotropic model was used to solve the reducedgravity equations. The CFL stability condition is less restrictive in this case than in the barotropic model. Thus, time step for the explicit integration is increased to Dt¼800 s. The model is integrated specifying water currents along the open western boundary until a steady solution is achieved. The computed steady current and upper layer thickness over the domain are stored in files that will be read by the dispersion code. Two average water circulation patterns have been obtained with the reduced-gravity model: one corresponding to the usual summer situation (existence of the gyre) and the other one corresponding to the usual winter situation (coastal circulation). As will be discussed in some more detail below, different circulation patterns are obtained by changing the surface inflow through the Strait of Gibraltar. 3.2. Particle-tracking dispersion model The dispersion of radionuclides is calculated by using a particle-tracking method. Essentially, the radionuclide discharge is simulated by a number of discrete particles. The path followed by each particle is computed; turbulent diffusion being modelled as a three-dimensional random walk process. Advection is calculated through the addition of the tidal and the residual 52 R. Peria´n˜ez / J. Environ. Radioactivity 90 (2006) 48e67 currents. Radioactive decay is also simulated using a Monte Carlo method (Peria ´n ˜ez and Elliott, 2002). The density of particles per water volume unit is finally computed to obtain radionuclide concentrations over the domain at the desired time. Both instantaneous and continuous releases of particles can be simulated. It must be noted that the particle-tracking model is threedimensional, while the hydrodynamic module provides depth-averaged currents. Thus, a current profile is generated from the depth-averaged currents at each location by the dispersion code (see for instance Pugh, 1987), which is a common approach in rapid-response particle-tracking models (Riddle, 1998). The effect of wind is included as usual in particle-tracking models. Thus, it is assumed that the water surface moves in the direction of wind at a speed equal to 3% of the wind speed 10 m above the sea surface. This current decreases logarithmically to zero at a depth usually defined as 20 m (Pugh, 1987; Proctor et al., 1994; Elliott, 1986). Date and time of the discharge (and duration in the case of continuous releases) must be given. Thus, the appropriate phase of each tidal constituent at t¼0 must be specified. The values used in this model correspond to the origin of time, January 1, 2003 at 0:15 hours Greenwich time. The adsorption of pollutants by suspended and bottom sediments can also be simulated with a particle-tracking model (Peria ´n ˜ez and Elliott, 2002). However, these processes are neglected in the present study since suspended matter concentrations are very low in the area, typically 0.1e0.5 mg/L (Leo ´n-Vintro ´et al., 1999). Also, since the pycnocline is acting as a barrier for vertical mixing, interactions of pollutants with bed sediments can be neglected. There is no stability criterion equivalent to the CFL condition in the particle-tracking calculations, although it is wise to ensure that each particle does not move through a distance that exceeds the grid spacing during each time step. Thus, time step was fixed as Dt¼300 s. All the equations involved in the particle-tracking dispersion model, as well as the numerical aspects of their solution, may be seen for instance in Peria ´n ˜ez (2005b). The dispersion code automatically reads six files which contain the topography of the Albora ´n Sea, amplitudes and phases of the two tidal constituents included in the model (M 2 and S 2 ), and the residual circulation (for gyre or coastal circulation modes). These files are generated by the hydrodynamic module that has been run off-line, as noted before. The user must also include some information for each simulation, related to the release characteristics. This information is summarized in Table 1. Wind conditions are also defined in a file that must be edited before running the model. Variable winds can be included. The reduced-gravity model provides the residual current in the domain, as already noted. Nevertheless, residual currents are controlled by the water inflow through the Strait of Gibraltar that, as will be discussed in some more detail below, presents some variability. Thus, a factor that acts as a modulator of the residual current amplitude must be introduced. If 1 is used, the residual current for the average water inflow (for gyre or coastal modes) through the Strait is used in the calculations. These average currents may be slightly amplified or reduced by specifying values for the modulator larger or smaller than 1, respectively. The dispersion model provides several output files. It gives the coordinates of each particle at several times during the simulation. Thus, snapshots of particles can be drawn to study the temporal evolution of the discharge. In particular, 12 snapshots at constant intervals along the simulation are provided. Another file contains a map of the final contaminant concentration over the domain computed from the density of particles per water volume unit. Optionally, the time evolution of radionuclide concentrations at desired points over the domain can be obtained. 53R. Peria´n˜ez / J. Environ. Radioactivity 90 (2006) 48e67 4. Results Results of the hydrodynamic models are presented first. Next, some examples of dispersion calculation are given. Computed values of the amplitude and phase of the water surface elevation produced by the M 2 and S 2 tides have been compared with observed values (Tsimplis et al., 1995; Manzella and Elliott, 1991) at different locations in the Strait of Gibraltar and the Albora ´n Sea. Results are given in Table 2. Locations may be seen in the map in Fig. 1. It can be observed that generally there is a good agreement between the measured and computed tidal constants for both constituents. A tidal chart for the M 2 tide is shown in Fig. 2. The same color joins points with the same tide amplitude (corange chart). The amplitude decreases quickly in the Strait of Gibraltar, from about 0.75 m in the Atlantic entrance to 0.30 in the section of Gibraltar. There is a further, although slower, amplitude reduction in the Albora ´n Sea, reaching only about 0.10 m at the eastern boundary. It can be seen that corange lines are oriented in a southenorth direction, while cotidal lines (join points with the same tidal phase, not shown) are essentially in a northeast direction, in agreement with observations and the earlier computations by Tsimplis et al. (1995). The spatial distribution of the M 2 current amplitude is presented in Fig. 3 as an example. The current amplitude in most of the Albora ´n Sea is about 0.03 m/s. Only in some specific areas larger currents are obtained. This is the case of the southenorth section going from Cape Tres Forcas to Albora ´n Isle and the Spanish coast. Currents of the order of 0.06e0.09 m/s are computed close to the Cape, around Albora ´n Isle and close to the Spanish coast. This is Table 1 Information required by the model to be introduced by the user Release point coordinates Select instantaneous/continuous release option Wind file name Release date (day, month, year) Release time, UTC (hours, minutes) Select circulation mode (gyre/coastal) Simulation time (days) Magnitude of the release in the corresponding units Radionuclide decay constant Residual current modulator Table 2 Observed (subindex obs) and computed (subindex comp) amplitudes (A, cm) and phases ( g, deg) of tidal elevations at several locations indicated in Fig. 1 Station M 2 S 2 A obs g obs A comp g comp A obs g obs A comp g comp Tarifa 42 57 41 45 14 85 16 79 Ceuta 30 50 32 52 11 76 12 86 Ma ´laga 17 59 18 42 7 72 8 77 Alhucemas 18 58 18 56 7 80 7 89 Almerı ´a 9 51 9 49 4 78 4 77 Gibraltar 30 46 29 41 11 72 12 77 54 R. Peria´n˜ez / J. Environ. Radioactivity 90 (2006) 48e67 in good agreement with the earlier computations presented by Tsimplis et al. (1995). Current amplitude increases as approaching Gibraltar Strait, where, as expected, maximum values are obtained. Indeed, currents of the order of 0.8 m/s are computed in some locations. For clarity reasons, however, the scale maximum in Fig. 3 is limited to 0.2 m/s. In the case of the S 2 tide, results show a similar decrease in the tide amplitude, from about 0.25 m at the Atlantic entrance of the Strait to about 0.04 m at the eastern open boundary of the domain. Current −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.2 35.4 35.6 35.8 36 36.2 36.4 36.6 36.8 Longitude Latitude 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Fig. 2. Corange chart for the M 2 tide. Amplitude of the tide is given in meters. −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.2 35.4 35.6 35.8 36 36.2 36.4 36.6 36.8 Longitude Latitude 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 Fig. 3. Current amplitudes (m/s) for the M 2 tide. 55R. Peria´n˜ez / J. Environ. Radioactivity 90 (2006) 48e67 amplitudes decrease from maximum values of the order of 0.25 m/s in the Strait of Gibraltar to currents weaker than 1 cm/s in the Albora ´n Sea. Residual currents provided by the reduced-gravity model are presented in Fig. 4 for both circulation conditions (existence of the gyre and coastal mode). The different situations are obtained by simply changing the inflow through the Strait of Gibraltar. The collapse of the WAG may be related to its westward advection, that is caused by an enhanced transport towards the Atlantic in the deep water layer (Heburn and La Violette, 1990). Recently another mechanism (Ve ´lez-Belchı ´et al., 2005), consisting of an eastward advection of the WAG, has been observed for its disappearance. It is also related to a decrease in the Atlantic inflow after an initial increase of water velocity in the Strait of Gibraltar. Nevertheless, other different mechanisms have been proposed to explain WAG disappearances (see discussion in Ve ´lez-Belchı ´et al., 2005). Usually in summer, the jet of Atlantic water entering through the Strait of Gibraltar flows towards the east along the Spanish coast and partially curves to the south before reaching Albora ´n Island. Part of this flow continues to the east between Cap Tres Forcas and Albora ´n Island and the remaining rotates towards the west, flowing along the African coast. A gyre −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.5 36 36.5 Longitude Latitude −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.5 36 36.5 Longitude Latitude 10 cm/s 10 cm/s Fig. 4. Steady currents computed with the reduced-gravity model showing the WAG (up) and the coastal circulation mode (down). 56 R. Peria´n˜ez / J. Environ. Radioactivity 90 (2006) 48e67 is not possible to have an answer. Thus, it is recommended to carry out calculations under the most probable conditions in a first guess: WAG in summer, coastal mode in winter. Additional simulations may then be carried out using the other circulation mode and different current modulators (to increase and reduce water velocities). This method will, at least, allow to estimate if there is any chance that a given sensible point (a coastal town for instance) is affected by contamination. 6. Conclusions A particle-tracking model that simulates the dispersion of radioactive spills in the Albora ´n Sea has been developed. The contamination release is simulated by a number of particles whose paths are computed. Diffusion and decay are simulated by a Monte Carlo method. The currents required to calculate the advective transport are obtained from appropriate hydrodynamic models. Radionuclide concentrations are obtained from the density of particles per water volume unit. −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.5 36 36.5 −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.5 36 36.5 latitude −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.5 36 36.5 longitude Release point Fig. 11. Snapshots showing the position of particles: 7.5, 15 and 27.5 (from top to bottom) days after a continuous radionuclide release occurring off Gibraltar harbour. 63R. Peria´n˜ez / J. Environ. Radioactivity 90 (2006) 48e67 A 2D barotropic model is used to calculate tidal currents over the domain. This model provides the tidal constants that are used by the dispersion model to reconstruct the tidal current at any time and position in the model domain. This model has been validated through the comparison of computed tidal elevations and phases with measurements in the area. The residual circulation is obtained from a reduced-gravity model. This is the simplest approach which is able to simulate the major features of circulation above the pycnocline. Essentially it is a two-layer model in which the lower layer is infinitely deep and at rest. It was not possible to carry out a quantitative validation of this model, but computed currents are, at least, in qualitative agreement with observations available in the region. In particular, the main circulation features (the WAG and the coastal mode) are reproduced by the model. Equations in both the models are solved by standard explicit finite difference schemes. Some experiments concerning hypothetical radioactivity releases in the region have been carried out. The average speed of a radionuclide patch released in the Strait of Gibraltar as it travels towards the eastern boundary of the domain is of some 9 and 1 cm/s for usual −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.5 36 36.5 −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.5 36 36.5 latitude −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.5 36 36.5 longitude Fig. 12. Snapshots showing the position of particles: 2.5 (up), 12.5 (middle) and 27.5 (down) days after an instantaneous release of a long-live radionuclide in the central part of the Strait. A 10 m/s wind blowing from the east is included. 64 R. Peria´n˜ez / J. Environ. Radioactivity 90 (2006) 48e67 summer and winter conditions, respectively (existence of the gyre and coastal circulation mode). If the accident occurs in the central part of the Albora ´n Sea, particles are trapped in the WAG (if present). The time required to complete a rotation has been estimated to be two months. The simulation of a continuous release has been illustrated with the case of an accident occurring off Gibraltar harbour. The model predicts that a significant portion of the Spanish coast is contaminated. Winds have a significant effect on the dispersion patterns in the area. Thus, dominant east winds tend to retain contaminants inside the Albora ´n Sea, also enhancing mixing along the transverse direction (northesouth). On the other hand, west winds produce a faster cleaning of the sea. As a final conclusion, it can be said that this kind of model is a very useful tool that may be used to support the decision-making process in response to an emergency situation. −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.5 36 36.5 −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.5 36 36.5 latitude −5.5 −5 −4.5 −4 −3.5 −3 −2.5 35 35.5 36 36.5 longitude Release point Fig. 13. Snapshots showing the position of particles: 22.5 (up), 25 (middle) and 90 (down) days after an instantaneous release of a long-live radionuclide off Ceuta harbour with the coastal mode for residual circulation (usual winter conditions). 65R. Peria´n˜ez / J. Environ. Radioactivity 90 (2006) 48e67 In the near future, the reduced-gravity model will be replaced by a two-layer model able to simulate deep outflow from the Albora ´n Sea to the Atlantic. This way, the model could deal not only with accidents occurring at the surface, but also at any depth (for instance leakage from a sunken nuclear submarine). Acknowledgement This work is supported by the Research Project of Excellence RNM-419 Te´cnicas Ultrasensibles para la Determinacio´n de Radionucleidos en Muestras Ambientales, Junta de Andalucı ´a, Spain. References Arruda, W.Z., Nof, D., O’Brien, J.J., 2004. Does the Ulleung eddy owe its existence to band norlinearities? Deep Sea Research I 51, 2073e2090. 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