Water Circulation, Sediment Transport, and Pollutant Dynamics in Southern Iberia Waters: A Review on Numerical Modelling Studies
Abstract
Southern Iberian Peninsula coastal waters have a high ecologic and economic value. The objective of this work has consisted of describing numerical models which simulate the dispersion of particle-reactive tracers in these waters and reproducing measured concentration levels in water and bed sediment samples. Additionally, information on suspended matter concentration distributions and sedimentation rates is obtained. In the Alboran Sea, the model has been applied to simulate the transport of radionuclides introduced from atmospheric fallout. Transport pathways of heavy metals discharged from three rivers draining a large mining area have been obtained for the Gulf of Cadiz. It has been found that these rivers constitute a source of trace elements to the Mediterranean through the Strait of Gibraltar. Some characteristic times have been calculated, as well as fluxes of isotopes through the Strait of Gibraltar, as additional results of environmental interest.
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Hindawi Publishing Corporation ISRN Oceanography Volume 2013, Article ID 424572, 27 pages http://dx.doi.org/10.5402/2013/424572 Review Article Water Circulation, Sediment Transport, and Pollutant Dynamics in Southern Iberia Waters: A Review on Numerical Modelling Studies R. Periáñez Departamento de Física Aplicada I, Escuela Técnica Superior de Ingeniería Agronómica (ETSIA), Universidad de Sevilla, Carretera Utrera km 1, 41013 Sevilla, Spain Correspondence should be addressed to R. Periáñez; rp[email protected] Received 22 August 2012; Accepted 9 October 2012 Academic Editors: C. W. Brown and C. Lamborg Copyright © 2013 R. Periáñez. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Southern Iberian Peninsula coastal waters have a high ecologic and economic value. e objective of this work has consisted of describing numerical models which simulate the dispersion of particle-reactive tracers in these waters and reproducing measured concentration levels in water and bed sediment samples. Additionally, information on suspended matter concentration distributions and sedimentation rates is obtained. In the Alboran Sea, the model has been applied to simulate the transport of radionuclides introduced from atmospheric fallout. Transport pathways of heavy metals discharged from three rivers draining a large mining area have been obtained for the Gulf of Cadiz. It has been found that these rivers constitute a source of trace elements to the Mediterranean through the Strait of Gibraltar. Some characteristic times have been calculated, as well as �uxes of isotopes through the Strait of Gibraltar, as additional results of environmental interest. 1. Introduction e Gulf of Cadiz (GoC) is responsible for 5–10%of �sh and shell-�sh catches of Spain and Portugal [1], holding important living resources of commercial and ecological interest. Similarly, the Alboran Sea (AS) is one of the most productive areas in the Mediterranean Sea [2]. is whole area (Figure 1) has a high ecological and economic value as it constitutes the only connection between the Mediterranean Sea and the Atlantic Ocean. e region is also exposed to potential pollutant discharges given the intense shipping activities through the Strait of Gibraltar, connecting the GoC and AS, and the usual adverse meteorological conditions here. We must also consider the presence of large industrial areas in the Spanish shores. Finally, the Guadalquivir, Guadiana, and Odiel-Tinto rivers, in the southern Iberian Peninsula (Figure 2(a)), present strongly enhanced heavy metal concentrations since they drain the Iberian Pyrite Belt [3], one of the most important mining areas in the south of Europe. Mineral resources have been extracted in the last 5000 years during two main periods: the Roman age and the last two centuries. During the last period, intensive exploitation has led to a relevant environmental impact, with vast surfaces covered with mining residues and subjected to erosion [3]. Consequently, it is relevant to study and understand geochemistry and dispersion patterns of contaminants in the system, since this will help assessing the potential in�uence of pollutants on ecosystem functioning. us the main objective of the present work has consisted of reviewing appropriate numerical models developed in the University of Seville, which simulate the dispersion of particle-reactive tracers in southern Iberian Peninsula waters and reproducing measured concentration levels in water and bed sediment samples [4, 5]. As an additional result, information on suspended matter distributions and sedimentation rates is obtained. Valuable environmental results concerning tracer �uxes through the Strait of Gibraltar and characteristic times in the Alboran Sea, not published before, are also obtained carrying out numerical experiments. is highlights the usefulness of this type of dispersion models for reactive pollutants. Dispersion models are based upon appropriate hydrodynamic models which provide water circulation in each system
2 ISRN Oceanography 40 N 37.5 N 35 N 32.5 N 30 N 10 W 7.5 W 5W 2.5 W 0 ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ F 1: General map of the study area. (GoC and AS). Tracers which can be easily identi�ed in each system are used for the study. us, heavy metals (Zn and Cu) have been simulated in the GoC. ese metals are introduced by the three rivers mentioned above. Fallout radionuclides ( 137Cs, 239,240Pu, and 210Pb) are considered for the AS. Ideally, for a proper testing and validation of a dispersion model, we would need a well-known point source of pollutants. In the GoC, metal inputs from rivers may be used. In the AS we had to use fallout radionuclides due to the lack of such a well-de�ned source. Also ideally, we would need an spatial array of measurements to appreciate if the spatial distribution of pollutants is reproduced by the model. ese re�uirements are satis�ed in the GoC since there are metal measurements in water and in bed sediments, along the Spanish coast, where a clear spatial structure appears, but data is more limited in the AS. e situation is even more complicated since time variations will be apparent as well, more in the dissolved phase than in bed sediments. Only in limited cases there is enough information to allow a complete model validation. is is the case, for instance, of authorized discharges from nuclear fuel reprocessing plants to the sea, where wide monitoring programs are undertaken and the source term is well known [6–8]. But in practice, it is rather di�cult that these re�uirements are satis�ed and model results and validations have to be interpreted with care. Published models describing trace metal dispersion in the GoC consider metals as conservative tracers, no interacting with sediments and without any other sources and sinks [1, 9]. Similarly, models describing trace elements dispersion in the AS, including water/sediment interactions, are not found in literature. ese reactive tracers may provide information not only on water circulation, but on sediment processes as well. Some background oceanography is provided in Section 2. Aer, models are described (Section 3). Next, results arepresentedanddiscussedfortheASandtheGoCin Sections 4.1 and 4.2, respectively. Models have also been applied to evaluate radionuclide �uxes through the Strait of Gibraltar and characteristic times of the AS system. Some sensitivity analysis are �nally presented. 2. Background Physical Oceanography 2.1. Alboran Sea. e water circulation in the Strait of Gibraltar is characterized by a surface in�ow of Atlantic water and a deep out�ow of more dense Mediterranean water. �xchanged �ows are of the order of 1 Sv with a net in�ow into the Mediterranean Sea of about 0.05 Sv [10]. is net in�ow compensates the excess of evaporation over precipitation and river supply in the Mediterranean. e exchanged �ows show some variability. In particular, Tsimplis and Bryden [10] gave an estimation of 0.66 ± 0.47Sv for the Atlantic in�ow, where the large error is due to seasonal variability, and 0.57±0.26Sv for the out�ow. Nevertheless, these values are about 10% lower than the lowest previous estimates [11].Areviewon transport estimations through the Strait of Gibraltar may be seen in such reference: from the very �rst carried out in 1877 and the widely cited value of 1.2 Sv for both out�ow and in�ow [12], to their own estimations of 0.72 and 0.68 Sv for in�ow and out�ow, respectively. e water masses that may identi�ed in the Alboran Sea are: the Surface Atlantic Water (SAW) that has its origin in the North Atlantic Central Water (NACW) that has been modi�ed by air-sea interactions, thus strictly speaking is not a water mass [13]; the Surface Mediterranean Water (SMW) which occupies the surface layer in areas not reached by the SAW; the Levantine Intermediate Water (LIW) that �ows from the Mediterranean to the Atlantic at depths between some 200 and 600 m and, �nally, the Western Mediterranean Deep Water (WMDW), below the LIW and also �owing towards the Atlantic. �owever, this description may be simpli�ed to a twolayer system with water �owing in opposite directions [14– 16]. us, from an operative point of view, SAW and MSW constitute the upper layer, and LIW and WMDW constitute the bottom layer, �owing to the west. Indeed, a steady westward �ow of LIW and WMDW has been recorded in several experiments [14, 17]. is approach has already been used to study the water exchanges between the Atlantic and the Mediterranean by means of numerical models [18–21]. e surface circulation in the Alboran Sea is as follows. e in�owing surface Atlantic water penetrates the Strait of Gibraltar (see Figure 2(b) for geographic names) and reaches mean velocities of the order of 0.6 m/s. is water forms a jet that enters the Alboran Sea in a east-northeast direction. e jet �ows along the Spanish coast and curves to the south at about −3.5∘longitude. en part of it �ows to the west, incorporating to an anticyclonic gyre, while the remainder �ows to the African coast between Cape Tres Forcas and Alboran Isle [22]. e anticyclonic gyre is known as the Western Alboran Gyre (WAG). A detailed description may be seen for instance in [23, 24] and references cited in these papers, which include the classical works carried out since the 70s. e WAG is an almost permanent feature, although presents variations in intensity and even there are periods in which disappears [23].espatialscaleoftheWAGisabout 100 km in diameter and some 200 m in depth. Bryden and Stommel [25]havefoundthattheout�owof water from the Mediterranean to the Atlantic occurs along the Moroccan continental slope, and that this circulation appears
ISRN Oceanography 3 Longitude Latitude Gibraltar St. Guadiana 33 33.5 34 34.5 35 35.5 36 36.5 37 37.5 −8 −7 −6 Odiel-Tinto Morocco Guadalquivir −2500 −2000 −1500 −1000 −500 (a) GoC. e localization of Guadiana, Odiel-Tinto, and Guadalquivir rivers is also shown Latitude Morocco 36.8 36.6 36.4 36.2 36 35.8 35.6 35.4 35.2 35 −5.5 −5 −4.5 −4 −3.5 −3 −2.5 Longitude Spain Strait of Gibraltar Atlantic Jet Alboran Trough Alboran Island Western Alboran Gyre −200 −400 −600 −800 −1000 −1200 −1400 −1600 −1800 (b) AS. Arrows indicate surface circulation F 2: Topography of both model domains (m). to be a nearly permanent feature of the southern side of the Alboran Sea. With respect to the tides in the area, an important feature of the tidal �ow in the Strait is that it can be considered, as a �rst approach, as barotropic. Indeed, 93%of the variance of current velocity in the semidiurnal band has a barotropic character in the Strait [26]. Tsimplis and Bryden [10] have pointed out that tidal currents are barotropic and larger than the mean in�ow or out�ow. e semidiurnal tide dominates ADCP records in the Strait, obscuring the expected two-layer character of the mean �ow. e tidal signal is so strong that itreversesthecurrentsnearthebottomforapartofeach tidal cycle. As a consequence, 2D depth-averaged models have already been applied to simulate surface tides in the Strait [27]. Tsimplis et al. [28] have even used a 2D barotropic model for simulating tides in the whole Mediterranean Sea. In the case of the main tidal constituent, 𝑀𝑀 2, tide amplitude at the Atlantic entrance of the Strait is about 0.8 m. is amplitude decreases towards the east. us, at the Mediterranean entrance is only about 0.3 m. e amplitude of the tide is reduced more in the Alboran Sea, reaching 0.09 m at the east limit of our domain (see map in Figure 2(b)). e 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 Alboran Sea basin. Similar behaviour is observed for the 𝑆𝑆2constituent. Turning now to sedimentology, it has been reported [29] that essentially all the western Alboran basin and southern part of the eastern one (which indeed is the whole domain of the model) are covered with muds, with less than 7%of coarse material (>63 𝜇𝜇m). e composition of these muds is controlled by river inputs, marine carbonate production in shallow areas, biogenic production in surface water, and water mass circulation [30]. Lithogenic particles are mostly introducedtotheAlboranSeaby�uvialandeolianmechanisms and, to a small extent, by coastal erosion (less than 5% of the total; see [31]). Eolian supply is strongly controlled by the proximity of the Sahara Desert. us, some episodes of atmospheric dust deposition, mostly of Saharan origin, have been recorded [31]. e �uvial input of particles has been extensively investigated by Liquete et al. [32]. ese authors havefoundthatsupplyfromthenorthcoastisatleastone order of magnitude larger than from the southern one. ey provide detailed data on sediment supply by the main rivers discharging into the Alboran Sea. 2.2. Gulf of Cadiz. Recently,theGoChasbeenthesubject of oceanographic studies dealing with surface and deep circulation, aimed at understanding the mechanisms of water exchange between the Atlantic Ocean and the Mediterranean Sea; as well as the behaviour of the dense plume of Mediterranean water [13, 33–35]. Figure 3 shows a TS diagram obtained aer a cruise in the GoC [13]. e different waters found in the samplings can be listed as follows. (1) North Atlantic Central Water (NACW): the linear behaviour in the TS diagram, characteristic of NACW, is found for the following 𝑇𝑇and 𝑆𝑆ranges: 11.0∘≤ 𝑇𝑇 ≤ 1𝑇.0∘C; 35.6 ≤ 𝑆𝑆 ≤ 36.5 (although its most super�cial region will be called SAW henceforth). Below a certain depth (from a certain isopycne), the TS diagram diverges from its former linear behaviour due to mixing with the underlying, salty Mediterranean Water (MW). (2) Surface Atlantic Water (SAW): this water has its origin in shallow NACW that has been modi�ed by air sea interactions so, strictly speaking, SAW is not a water mass. In the Gulf of Cadiz, SAW can be characterized for practical purposes as a region of the TS diagram with temperatures above 16.0∘C and salinity 𝑆𝑆 𝑆 36.𝑆, which is found between the surface and a depth of approximately 100 m over the entire region except for the continental shelf.
4 ISRN Oceanography 4 6 8 20 18 16 14 12 10 Salinity 35 35.5 36 36.5 37 37.5 Temperature ( ∘ C) F 3: TS diagram obtained aer a cruise in the GoC. (3) Warm Shelf Waters (SW): at some of the sampled stations, mainly over the continental shelf, water warmer and fresher than SAW has been detected at the surface. is water comes from SAW that has been noticeably in�uenced by continental shelf processes, including heating and fresh water inputs from land. It corresponds to the points of the TS diagram between temperatures of 14.0 ∘C and 18.0∘C. (4) Mediterranean Water (MW): the analysis of the thermohaline properties of MW shows two main maxima in the TS diagram corresponding to two cores (upper and lower) with different densities, centered near 800 and 1200 m. (5) North Atlantic Deep Water (NADW): at a reduced number of deep stations (depth > 1500m) in the southwest part of the surveyed region, NADW, which is characterised by its depth-decreasing thermohaline properties [36], has been found. e surface circulation of the Gulf of Cadiz, less studied than its deep circulation, is integrated into the general circulation of the Northeast Atlantic: the Azores Current, which transports some 15 Sv between latitudes 35.1∘N and 40.1∘N to feed the Canary Current, frequently forms meanders that separate themselves from the main �ow [37]. us, the surface circulation of the Gulf of Cadiz could be understood as the last meander of the said Azores Current. Part of this meander enters the Mediterranean Sea through the Strait of Gibraltar to balance evaporation and buoyancy losses within this Sea. e residual surface circulation in the northern GoC is characterized by a current directed to the SE [13, 35] along the Spanish coast. is circulation is a rather constant pattern duringmostoftheyear.Partofthe�owenterstheStraitof Gibraltar and part is de�ected to the south. Below the surface, the Mediterranean waters �ow into the Atlantic and mainly direct to the NW [38, 39]. e amplitude of the 𝑀𝑀2tide is about 1 m over all the GoC, decreasing near the Strait of Gibraltar. Associated currents are weak, with amplitudes below 0.10 m/s over most of the GoC. Indeed at the RAP (Red de Aguas Profundas, Spanish Institute of Oceanography) buoy position (see Figure 16), the 𝑀𝑀2barotropic tidal current is less than 0.03 m/s [33]. e current amplitude increases as approaching the Strait entrance, where currents about 0.8 m/s are produced. A similar behaviour is observed for the 𝑆𝑆2tide. With respect to sediments, schematically, it may be said that sand and sandy mud dominate to a depth of 30 m. e middle shelf, to a depth of 100 m, is characterized by an extensive mud belt. Finally, outer sediments below 100 m are dominated by mixtures of sand and clay [40]. 3. Model Descriptions e tracer transport model is based upon an advection/ diffusion equation with terms describing the exchanges of contaminants between the dissolved and the solid phases (suspended matter particles and bed sediments). Suspended matter concentrations and sedimentation rates are consequently required. ey are obtained from a sediment transport model developed for this purpose. Water currents in theareaarerequiredtosolvetheadvectivepartsofthe equations and to calculate bed stress, which is needed to evaluate deposition and resuspension of particles from the seabed. Two computational domains were de�ned, Figures 2(a) and 2(b),fortheGoCandAS,respectively. 3.1. Hydrodynamics. e water current at any position is obtained through the addition of the instantaneous barotropic tidal current plus a residual (mean or long-term) circulation. Both in the GoC and the AS, tides are computed using a 2D depth-averaged model, which is a reasonable approach [41, 42] already used successfully in the Strait of Gibraltar [43, 44]. Tidal equations are standard and may be seen, for instance, in [45]. e solution of these equations provides the water currents at each point in the model domain and for each time step. Currents are treated through standard tidal analysis [46] and tidal constants are stored in �les that will be read by the transport models. e two main tidal constituents, 𝑀𝑀2and 𝑆𝑆2, are considered. us, the hydrodynamic equations are solved for each constituent and tidal analysis is also carried out for each constituent separately. Tidal constants allow a very fast calculation of the tidal current at any time and point in the domain. From an operative point of view, circulation in the Strait of Gibraltar and the AS may be simpli�ed to a twolayer system with water �owing in opposite directions, as commented above. Consequently, a 2-layer model has been adopted to calculate the residual circulation in the AS. Equations may be seen in Izquierdo et al. [18]. Complex mixing processes between several water masses occur in the GoC [13], thus a full 3D primitive-equation baroclinic hydrodynamic model is used. It is based upon the hydrostatic and Bousssinesq approximations on a 𝛽𝛽plane. e model includes equations for salinity and temperature evolution and water density is calculated from them using a standard state equation. A one-equation turbulence model has been used to calculate the vertical eddy viscosity. Details on the 3D equations may be seen, for instance, in Kowalick
ISRN Oceanography 5 T 1: Summary of hydrodynamic model characteristics. 2D model 2-layer model 3D model Domain GoC, AS AS GoC Objective tides Mean circulation Mean circulation Spatial resolution 2 minutesa2 minutesa2 minutesa Features Barotropic 2 water layers with constant density Hydrostatic, Boussinesq Depth-averaged Baroclinic 𝑀𝑀2,𝑆𝑆2constituents Equations for 𝑇𝑇and 𝑆𝑆 Forcing Tidal analysis 1-equation turbulence model Tide amplitude and phase Water exchanges through Water exchanges through along open boundaries Gibraltar Strait Gibraltar Strait and 𝑇𝑇,𝑆𝑆from climatology Forcing data source [47, 48] [20] [20] [28] WOA05 climatologyb Additional boundary condition where required RadiationcRadiationcRadiationc a In both longitude and latitude. b World Ocean Atlas 2005, National Ocean and Atmosphere Administration, available online. Seasonal values have been used for climatology and wind stress. c See [49]. and Murty book [50]. A summary of the main characteristics of hydrodynamic models may be seen in Table 1 and detailed descriptions and equations may also be seen in [44]. Residual circulations in the GoC and AS are again stored in �les which are appropriately read by the dispersion codes. It must be noted that the simplest approach (2-layer for AS, 3D for GoC) capable of reproducing the most relevant features of circulation in each area has been adopted. 3.2. Sediment Transport. e transport of sediments is described by an advection-diffusion equation to which some terms are added. ese are external sources of particles (river supply), terms describing particle deposition on the seabed and resuspension from the bed to the water column, and vertical settling. e formulation of these processes is based upon standard formulae. us, the erodability constant is used for the resuspension term. Particle settling and deposition are described using the settling velocity, which is obtained from Stoke’s law. Critical resuspension and deposition stresses are applied as usually. Details on the mathematical formulation may be seen elsewhere [51–54]. Finally, it is also possible to calculate net sedimentation rates (SR) as the balance between the deposition and resuspension terms. All equations and terms are appropriately written both for the 2-layer and the full 3D approaches. ey are presented in Appendix A, for illustrative purposes, in the full 3D form. A number of approximations had to be assumed in both domains, mainly because the lack of �eld data to feed the model and to validate it. us, episodes of heavy rains, atmospheric deposition, and bedload transport are not included. Moreover, only the lithogenic particle fraction, that isabout80%of the total suspended load [30, 31], is simulated. Finally, atmospheric deposition events of particles coming from the Sahara Desert have not been considered in the model since they cannot be easily quanti�ed [31]. 3.3. Tracer Transport. Nonconservative pollutants are those which do not remain dissolved in the water column, but have a certain affinity to be �xed to particles (suspended matter and bed sediments) and/or those which may suffer any decay process (radioactive, biodegradation, and so forth). us, three phases are included in the model: dissolved, suspended particles and bed sediments. Only �ne sediments are considered (particles with diameter <62.5 𝜇𝜇m) since metals and radionuclides are predominantly �xed to these [55]. e exchanges between the dissolved and solid phases may be described in terms of kinetic transfer coefficients. us, assuming that adsorption/release reactions are governed by a single reversible reaction, a coefficient 𝑘𝑘1governs the transfer from the liquid to the solid phase and a coefficient 𝑘𝑘2governs the inverse process. Also, the migration of tracers to the deep sediment is included. us, tracers deposited on the sediment surface will be buried by particle deposition and will migrate below the mixed sediment layer which directly interacts with the dissolved phase. is effect may be easily treated as a decay process with constant 𝜆𝜆burial given by 𝜆𝜆burial =SR 𝜌𝜌𝑠𝑠𝐿𝐿,(1) where 𝐿𝐿is the sediment mixing depth (the distance to which the dissolved phase penetrates the sediment), 𝜌𝜌𝑠𝑠is the sediment bulk density (dry mass divided by wet volume), and SR is the sedimentation rate provided by the sediment transport submodel. Note that the model implicitly assumes an instantaneous pollutant mixing over this sediment layer with thickness 𝐿𝐿. A summary of all the processes involved may be seen in Figure 4, in the case of a 2-layered sea. ere is advection and diffusion of suspended particles and contaminants in both water layers, as well as uptake/release reactions between dissolved pollutants and suspended sediments. ere will also be some diffusion through the pycnocline, direct uptake/release reactions between the bottom
6 ISRN Oceanography Seabed Pycnocline Atmospheric deposition Sea surface Suspended particles Kinetic exchanges Kinetic exchanges Dissolved radionuclides Settling Settling Deep sediment Burial Deposition Mixed layer Diffusion Horizontal advection/diffusion Horizontal advection/diffusion F 4: Processes affecting the dispersion of nonconservative pollutants in a two-layer sea. Black circles are suspended particles and the red ones are radionuclides. water layer and bed sediments, and deposition of suspended particles on the seabed. It is known that adsorption depends on the surface of particles per water volume unit at each point and time. is quantity has been denoted as the exchange surface [6, 7, 45, 56]. us, the kinetic coefficient 𝑘𝑘 1is written as 𝑘𝑘1=𝜒𝜒𝑆𝑆𝑚𝑚+𝑆𝑆𝑠𝑠𝛿𝛿𝑏𝑏=𝑘𝑘 𝑚𝑚 1+𝑘𝑘𝑠𝑠 1,(2) where 𝑆𝑆𝑚𝑚and 𝑆𝑆𝑠𝑠are the exchange surfaces for suspended matter and bottom sediments respectively (dimensions [𝐿𝐿𝐿−1) and 𝜒𝜒is a parameter with the dimensions of a velocity denoted as the exchange velocity (see references cited above). e delta function is introduced to take into account that only the deepest water layer interacts with the bed sediment. us 𝛿𝛿𝑏𝑏=1for the deepest layer and 𝛿𝛿𝑏𝑏=0elsewhere. Assuming spherical particles, the exchange surfaces are written as (again see references cited above) 𝑆𝑆𝑚𝑚=3𝑚𝑚 𝜌𝜌𝜌𝜌,(3) 𝑆𝑆𝑠𝑠=3𝐿𝐿𝐿𝐿𝐿𝐿1−𝑝𝑝 𝜌𝜌𝑅𝑅 ,(4) where 𝜌𝜌and 𝜌𝜌are particle radius and density, respectively, 𝑚𝑚is the suspended matter concentration, 𝐿𝐿is the fraction of �ne particles in the sediment, 𝑝𝑝is sediment porosity, and 𝐿𝐿 is a correction factor that takes into account that part of the sediment particle surface may be hidden by other sediment particles. Finally, 𝑅𝑅is the thickness of the deepest water layer. is formulation has been successfully used in all modelling works cited above. Real particles are not spheres, but with this approach it is possible to obtain an analytical expression for the exchange surface [57]. e kinetic coefficient 𝑘𝑘2is considered to be constant. Tracer dispersion equations are summarized in Appendix B, where they are presented in a general 3D form. ey are appropriately modi�ed in the case of the 2-layer AS model. 3.4. Numerical Solution. e topography of both domains was obtained from the NOAA (US National Ocean and Atmosphere Administration) GEODAS database, available on-line, with a resolution of two minutes in both longitude and latitude. Fiy vertical levels are considered in the GoC 3D model. Topography of both domains is presented in Figures 2(a) and 2(b). All the equations were solved using explicit �nite difference schemes. Details on the solution of the hydrodynamic equations are given in [44] and are not repeated here. It is worth commenting that the simple addition of tidal and long-term currents implies that nonlinear interactions between both �ow components are neglected. However, this is a common practice in pollutant transport modelling (see for instance [58]). e second-order accuracy MSOU (Monotonic Second Order Upstream) scheme [59] is applied for all advective terms and a second-order scheme is used for diffusion as well [50]. Mass conservations has been careffully checked for all numerical schemes. Time-step in the different submodels is selected with care to assure that stability conditions are satis�ed. A timesplitting procedure was used to treat the water-sediment pollutant interactions. is is essentially the same as in hydrodynamic models, when time-splitting is used to solve the external and internal modes. e procedure is required because a very restrictive stability condition is introduced by such interaction terms [45]. Essentially, it consists of using a smaller time step to solve water-sediment tracer interactions. us, for each advection/diffusion time step, a number of smaller steps are needed to solve tracer partition. Appropriate boundary conditions must be de�ned as well. ey are described below. Finally, it must be commented that both tidal and residual currents are used in the sediment transport models, in order to describe appropriately deposition and resuspension events. However, only residual currents and mean SRs provided by the sediment models are
ISRN Oceanography 7 used to simulate tracer dispersion, given the generally small tidal currents in the domains. 3.5. Parameters. e horizontal diffusion coefficient, 2.0 m2/s in both domains, has been selected according to the horizontal grid resolution [44]. e vertical diffusion coefficient in the 3D model is set equal to the vertical viscosity provided by the one-equation turbulence model, as usual in most models. Suspended particles (diameter <63 𝜇𝜇m) are characterized by a mean size that is considered to be representative of suspended matter in the considered environment. e particle size controls, through Stoke’s law, the settling velocity of particles and, as a consequence, affects the sedimentation rate as well. It also affects the adsorption of tracers from the dissolved phase ((3) and (4)). e value used for particle diameter was 8 𝜇𝜇mforboththeGoCandAS.Freitasand Abrantes [60] have found that particles with diameter <10 𝜇𝜇m are dominant in all water masses in the Gulf of Cadiz. e GoC re�ects the AS since surface waters in the �rst �ow into the second and �editerranean waters �ow, in the deep layer, from the AS into the GoC. A sensitivity analysis (not shown) has also been carried out, trying different particle sizes. e best results were obtained with a diameter of 8 𝜇𝜇m. e critical deposition stress typically ranges between 0.04 and 0.1 N/m2[61], while the critical resuspension stress ranges 0.1–1.5 N/m2[61]. In the present applications intermediate values of 0.06 and 1.0 N/m2have been taken for the critical deposition and resuspension stresses, respectively. e erodability constant is �xed as 𝐸𝐸 𝐸 𝐸𝐸𝐸 𝐸 𝐸𝐸−3 kg/m2s. is parameter typically varies between 2 𝐸 𝐸𝐸−4 and 3𝐸 𝐸𝐸−3 kg/m2s[61]. e fraction 𝑓𝑓of �ne particles in bed sediments must be de�ned over the model domain. In the case of the GoC, this information has been compiled from [40]. As already mentioned, sand and sandy mud dominate to a depth of 30 m. e middle shelf, to a depth of 100 m, is characterized by an extensive mud belt. Finally, outer sediments below 100 m are dominated by mixtures of sand and clay. For the AS, since less than 7%of the bed sediments consists of coarse material [29], it has been taken an uniform value of 𝑓𝑓 𝐸 𝐸𝐸𝑓𝑓. e equilibrium distribution coefficient, 𝑘𝑘𝑑𝑑, concept is used to estimate the exchange velocity as explained below. e 𝑘𝑘𝑑𝑑describes the partition of a tracer between the dissolved and solid phases at equilibrium: 𝑘𝑘𝑑𝑑𝐸𝐶𝐶𝑠𝑠 𝐶𝐶𝑑𝑑,(5) where 𝐶𝐶𝑠𝑠and 𝐶𝐶𝑑𝑑are tracer concentrations in the solid and dissolved phases, respectively. is parameter is of course depending on the tracer geochemical behaviour and on environmental conditions, thus it is a site-speci�c parameter. As described before [62], 𝑘𝑘2is very similar even for elements with a rather different geochemical behaviour, being 𝜒𝜒(see (2)) the essential parameter describing the tracer geochemical behaviour. us, the same value is given to 𝑘𝑘2 for all simulated tracers, which is 𝑘𝑘2𝐸 𝐸𝐸𝐸𝐸 𝐸 𝐸𝐸−𝑓 s−𝐸. is value has been successfully used in earlier simulations in the Odiel-Tinto estuary, in the GoC [63]. It was measured for Cs by Nyffeler et al. [62]. e exchange velocity for each tracer is obtained from the equation relating this parameter with 𝑘𝑘2and its corresponding equilibrium distribution coefficient, 𝑘𝑘𝑑𝑑[45]: 𝑘𝑘𝑑𝑑𝐸𝜒𝜒 𝑘𝑘2 3 𝜌𝜌𝜌𝜌𝐸(6) e 𝑘𝑘𝑑𝑑mean values recommended by the International Atomic Energy Agency [64] for coastal waters have been used. is procedure has been widely used before [7, 51, 63, 65]. Distribution coefficients may vary in more than one order of magnitude depending on environmental conditions. Consequently, the model sensitivity to this parameter has been studied and some results are presented below (Section 4.2.4). For some tracers, the 𝑘𝑘𝑑𝑑had to be obtained from calibration if there is not information about it or if results with the recommended value are not satisfactory. is may occur due to environmental 𝑘𝑘𝑑𝑑variability. Values for other parameters as 𝐿𝐿,𝜌𝜌and 𝜙𝜙have been obtained from previous modelling works. A summary of model parameters and their sources may be seen in Table 2. 4. Results and Discussion Results are presented for the AS and for the GoC separately. In both cases results of the hydrodynamic model are initially discussed, later sediment transport results are presented. For the AS, dispersion patterns of 𝐸37Cs and 23𝑓,24𝐸Pu are presented in one Section 4.1.3 and, in a following one (4.1.4), 2𝐸𝐸Pb results are shown. Later, �uxes through the Strait of Gibraltar (Section 4.1.5) and characteristic times (Section 4.1.6) are analyzed. In the case of the GoC metal dispersion is studied in Section 4.2.3 and, in the next Section 4.2.4, sensitivity analysis results are discussed. It should be highlighted that results from hydrodynamic models have been successfully implemented on rapidresponse particle tracking models for radioactive, chemical andoilspillsalreadydevelopedfortheASandGoC[44, 66– 68]. 4.1. Alboran Sea 4.1.1. Hydrodynamics. Computed values of the amplitude and phase of the water surface elevation due to the 𝑀𝑀2and 𝑆𝑆2tides have been compared with observed values [28, 69] at different locations in the Strait of Gibraltar and the Alboran Sea. Results are given in Table 3. Locations may be seen in the map in Figure 5. 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 𝑀𝑀2tide is shown in Figure 6. e same color joins points with the same tide amplitude (corange chart). e amplitude decreases quickly in the Strait of Gibraltar, from some 0.75 m in the Atlantic entrance to 0.30 in the section of Gibraltar. ere is a further, although slower, amplitude reduction in
8 ISRN Oceanography T 2: Summary of model parameters. In the cases of 𝐸𝐸and the critical stresses for resuspension and deposition, the selected values correspond to intermediate values within their range of variation commonly found in literature. A reference [61]isgivenasanexample.Note that some parameters may differ for the GoC and AS. Parameter description Value Source Water kinematic viscosity 𝜈𝜈 𝜈 𝜈𝜈𝜈𝜈𝜈𝜈 𝜈𝜈−𝜈 m2/s Standard value Vertical diffusion coefficient 𝐾𝐾= variable Turbulence equation (GoC) Diffusion through pycnocline 𝐾𝐾= 1.0 𝜈10−5 m2/s Standard value (AS) Horizontal diffusion 𝐴𝐴= 2.0 m2/s [44] Sediment mixing depth 𝐿𝐿= 0.1 m [7] (GoC) 𝐿𝐿= 0.035 m [30] (AS) Particle density 𝜌𝜌= 2600 kg/m3Standard value Particle radius 𝑅𝑅= 4.0 𝜇𝜇m [60] Fraction of small 𝑓𝑓= variable [40] (GoC) Particles in sediment 𝑓𝑓= 0.95 [29] (AS) Correction factor 𝜑𝜑= 0.1 [7] Sediment porosity 𝑝𝑝= 0.6 [29] Erodability 𝐸𝐸= 1.6 𝜈10−3 kg/m2s [61] Critical resuspension stress 𝜏𝜏ce = 1.0 N/m2[61] Critical deposition stress 𝜏𝜏cd = 0.06 N/m2[61] Desorption kinetic coefficient 𝑘𝑘2= 1.16 𝜈10−5 s−𝜈 [62] Zn distribution coefficient 𝑘𝑘𝑑𝑑= 7.0 𝜈104[64] Cu distribution coefficient 𝑘𝑘𝑑𝑑= 2.6 𝜈104Calibration Cs distribution coefficient 𝑘𝑘𝑑𝑑= 2.0 𝜈103Calibration (similar to [64]) Pu distribution coefficient 𝑘𝑘𝑑𝑑= 1.0 𝜈105[64] Pb distribution coefficient 𝑘𝑘𝑑𝑑= 2.0 𝜈105[64] T 3: Observed (subindex obs) and computed (subindex comp) amplitudes (𝐴𝐴, cm) and phases (𝑔𝑔, deg) of tidal elevations at several locations indicated in Figure 5. Station 𝑀𝑀2𝑆𝑆2 𝐴𝐴obs 𝑔𝑔obs 𝐴𝐴comp 𝑔𝑔comp 𝐴𝐴obs 𝑔𝑔obs 𝐴𝐴comp 𝑔𝑔comp Tarifa 42 57 41 45 14 85 16 79 Ceuta 30 50 32 52 11 76 12 86 M alaga 17 59 18 42 7 72 8 77 Alhucemas 18 58 18 56 780 789 Almer ia 9 51 9 49 4 78 4 77 Gibraltar 30 46 29 41 11 72 12 77 the Alboran Sea, reaching only some 0.10 m at the eastern boundary. It can be seen that corange lines are oriented in a south-north direction, while cotidal lines (not shown) are essentially in a northeast direction, in agreement with observations and the earlier computations in [28]. e spatial distribution of the 𝑀𝑀2current amplitude is presented in Figure 7 as an example, and a comparison of computed current ellipse parameters with those deduced from measurements [70] is presented in Table 4. In general, there is a good agreement between both set of data. Returning to Figure 7, the current amplitude in most of the Alboran Sea is some 0.03 m/s. Only in some speci�c areas larger currents are obtained. is is the case of the south-north section going from Cape Tres Forcas to Alboran Isle and the Spanish coast. Currents of the order of 0.06 to 0.09 m/s are computed close to the Cape, around Alboran Isle and close to the Spanish coast. is is in good agreement with the earlier computations presented in [28]. 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 Figure 7 is limited to 0.2 m/s. In the case of the 𝑆𝑆2tide, results show a similar decrease in the tide amplitude, from some 0.25 m at the Atlantic entrance of the Strait to some 0.04 m at the eastern open boundary of the domain. Current 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 Alboran Sea. e calculated geostrophic �ows for the upper and lower layers, for the mean water exchanges through the Strait of Gibraltar, are presented in Figure 8.Intheupperlayer,the jet of Atlantic water entering through the Strait of Gibraltar �ows towards the east along the Spanish coast and partially curves to the south before reaching Alboran Island. Part of
ISRN Oceanography 9 T 4: Computed and measured current ellipse parameters for the 𝑀𝑀2tide at points indicated with numbers in Figure 5. 𝑀𝑀and 𝑚𝑚are the magnitudes of the major and minor semiaxes, respectively, and dir is the direction of the major semiaxis measured anticlockwise from east. Point Measured values Computed values 𝑀𝑀(cm/s) dir (deg) 𝑚𝑚(cm/s) 𝑀𝑀(cm/s) dir (deg) 𝑚𝑚(cm/s) 1 65 15 3 68 2 2 2 21 20 6 34 22 1 3 9 54 2 14 57 1 4 6 4 0.5 5 7 0.1 5 3 22 1 3 −5 0.03 6 7 22 2 6 −8 0.4 7 4 45 2 2 67 1 8 2 40 0.2 4 2 1 9 1 −5 0.5 2 17 0.1 Longitude Latitude 36.8 36.6 36.4 36.2 36 35.8 35.6 35.4 35.2 35 −5.5 −5 −4.5 −4 −3.5 −3 −2.5 Alboran Island Tarifa Malaga Almeria Guadalhorce Cape Tres Forcas Guadiaro Ceuta Gibraltar 89 7 5 46 3J Q1L2M PE BCD AN HG F Alhucemas F 5: Map of the Alboran Sea showing position of sampling points and geographical sites mentioned in the text. e two main rivers discharging in the area, Guadiaro and Guadalhorce, are also shown. Numbers indicate points where computed current ellipses have been compared with observations and letters are the same but for sedimentation rates and radionuclide concentrations. Longitude 35 35.2 35.4 35.6 35.8 36 36.2 36.4 36.6 36.8 Latitude −5.5 −5 −4.5 −4 −3.5 −3 −2.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 F 6: Corange chart for the 𝑀𝑀 2 tide. Amplitude of the tide is given in m. this �ow continues to the east between Cape Tres Forcas and Alboran Island and the remaining rotates towards the west. A gyre of anticyclonic circulation is thus completed. Surface water velocity in the Strait reaches 0.53 m/s, in agreement with the current speeds of the order of 0.6 m/s reported from measurements [22] and models [71]. In the jet, along the 35 35.2 35.4 35.6 35.8 36 36.2 36.4 36.6 36.8 Latitude Longitude −5.5 −5 −4.5 −4 −3.5 −3 −2.5 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 F 7: Calculated current amplitude (m/s) for the 𝑀𝑀 2 tide. Spanish coast, maximum surface velocities are of the order of 0.4 m/s. Measurements of Perkins et al. [22] in this area range between 0.1 and 0.53 m/s and the model of Werner etal.[72] produces maximum currents in the north of the gyre of 0.25 m/s. Vargas-Yáñez et al. [23] have measured eastward geostrophic velocities in the passage between Cape tresForcasandAlboranIsland(pointFinFigure 5). ey are 11 ± 5,5±3and 1±3cm/s at depths of 74, 117, and 178 m, respectively, (all depths correspond to the surface layer). Computed current at the same point for the surface layer is 3.8 cm/s. A westward circulation is obtained for the bottom layer. In the western Strait of Gibraltar computed velocities are of the order of 0.20 m/s, in good agreement with the 0.15 m/s obtained by Béranguer et al. [73]. Maximum out�ow current calculated in the Strait is 0.36 m/s; Sannino et al. [74] obtained a �gure of 0.35 m/s. In the Alboran Sea, water velocities are reduced to some 0.1 m/s in the southern area and less in the northern part of the basin. is circulation pattern for the deep layer is in good agreement with the earlier calculations in [20],thatalsoshowthatmostofthedeep water �ows along the south coast with speed below 0.15 m/s, and with measurements in [14], which give velocities in the southern shelf, near the Strait, of 0.1 m/s. As commented before, Bryden and Stommel [25]havealsofound,from CT� transects, that the westward deep �ow occurs along the Moroccan continental slope. ese authors have measured
16 ISRN Oceanography T 10: Flushing times (days) for 137Cs and 239,240Pu in the surface and deep layers, for the dissolved phase and suspended matter. e regression coefficient of the numerical �tting to the double exponential decay function is also given. 137Cs 239,240Pu Surface Bottom Surface Bottom Water 𝑇𝑇𝑓𝑓(days) 292 121 3720 814 𝑟𝑟20.966 0.992 0.989 0.999 SPM 𝑇𝑇𝑓𝑓(days) 248 123 4422 893 𝑟𝑟20.974 0.992 0.997 0.999 0 1000 2000 3000 4000 5000 Time (days) 10 1 10 0 10 −1 10 −2 10 −3 10 −4 137 Cs surface 137 Cs bottom 239,240 Pu surface 239,240 Pu bottom #RN F 15: Computed temporal evolution of Cs and Pu mean dissolved concentrations (Bq/m 3 ) for the numerical experiments carried out to determine characteristic times of the AS system. In the case of dissolved 137Cs in the surface layer, for instance, a �ushing time of 176 days is obtained if the cor� responding curve in Figure 15 is �tted to a single exponential decay and the regression coefficient is 𝑟𝑟2= 0.636. However, if the double exponential is used (7), the regression coefficient increases to 𝑟𝑟2= 0.966 and the �ushing time is 292 days. Flushing times have been determined for 137Cs and 239,240Pu, for both water layers. Results are summarized in Table 10. It can be seen that Pu �ushing time is about one order of magnitude larger than for Cs, specially for the surface layer. is is again due to the higher affinity of Pu to be �xed to the solid phase, which makes it less mobile than Cs. Essentially the same values are obtained for the dissolved phase and suspended matter. Inthecaseofconstant�owthrougharegion,asisthe case in our simulations, the �ushing time can be obtained as 𝑉𝑉𝑉𝑉𝑉 [91], where 𝑉𝑉is the region volume and 𝑉𝑉is the �ow. A �ushing time of some 80 days is obtained if this equation is applied to the surface water layer with 𝑉𝑉 = 1.2𝑞Sv. Longitude Latitude 33 33.5 34 34.5 35 35.5 36 36.5 37 37.5 −8 −7 −6 Ayamonte Huelva Faro 1 •2 RAP 3 4 Rabat Chipiona Rota Cadiz Casablanca F 16: Map of the GoC showing all locations mentioned in the text. is is shorter than the �ushing times presented in Table 10 because two reasons: �rstly the fact that the WAG traps water (which stays longer in the AS) and, secondly, radionuclide interactions with the solid phase make them less mobile, which is of course more evident for 239,240Pu than for 137Cs. 4.2. Gulf of Cádiz 4.2.1. Hydrodynamics. A map showing the different locations and sampling points mentioned in the paper is presented in Figure 16. Computed tidal constants have been compared with established values for both 𝑀𝑀2and 𝑆𝑆2tides. Results are shown in Table 11, and it may be seen that, generally, there is a good agreement between both set of data. As an example, maps showing the 𝑀𝑀2tide amplitude and the amplitude of the tidal current are presented in Figure 17. e amplitude of the tide is about 1 m over all the GoC, decreasing near the Strait of Gibraltar. Associated currents are weak, with amplitudes below 0.10 m/s over most of the GoC. Indeed at the RAP (Red de Aguas Profundas, Spanish Institute of Oceanography) buoy position (see Figure 16), the 𝑀𝑀2barotropic tidal current is less than 0.03 m/s [33]. e computed current at this position is 0.034 m/s. e current amplitude increases as approaching the Strait entrance, where currents about 0.8 m/s are produced (the color scale in Figure 17 is limited to 0.5 m/s for more clarity). A similar behaviour is observed for the 𝑆𝑆2tide. e residual surface circulation in the northern GoC is characterized by a current directed to the SE [13, 35] along the Spanish coast. is circulation is a rather constant pattern during most of the year. Part of the �ow enters the Strait of Gibraltar and part is de�ected to the south. e residual
ISRN Oceanography 17 T 11: Established, index obs, [95] and computed, index comp, amplitudes (𝐴𝐴, cm), and phases (𝑔𝑔, deg) of tidal elevations at several locations indicated in Figure 16. Station 𝑀𝑀2𝑆𝑆2 𝐴𝐴obs 𝑔𝑔obs 𝐴𝐴comp 𝑔𝑔comp 𝐴𝐴obs 𝑔𝑔obs 𝐴𝐴comp 𝑔𝑔comp Faro 92 94 99 68 32 125 36 91 Chipiona 102 54 104 62 41 82 38 85 Rota 105 52 103 62 37 78 38 85 Cadiz 100 87 99 61 37 110 36 83 Ayamonte 100 59 101 65 32 88 36 89 Huelva 102 56 105 65 38 82 38 88 Casablanca 99 56 92 53 35 81 36 77 Rabat 88 59 98 57 35 83 36 78 Longitude Latitude 33 33.5 34 34.5 35 35.5 36 36.5 37 37.5 0.8 0.85 0.9 0.95 1 1.05 −8 −7 −6 (a) Latitude 33 33.5 34 34.5 35 35.5 36 36.5 37 37.5 Longitude −8 −7 −6 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 (b) F 17: Amplitude of the 𝑀𝑀 2 tide in m (a) and current amplitude in m/s (b). circulation computed with the baroclinic model at the sea surface is presented in Figure 18. e current is effectively directed to the SE over the continental shelf and part of this �ow enters the Strait of Gibraltar. �aximum currents are of the order of 0.3 m/s, in agreement with [33]. e anticyclonic eddyattheeastofFaro(seeFigure 16) has been described by [34]. Also, the cyclonic eddy in front of the Strait of Gibraltar appears clearly in models [1, 96]. ese last authors have attributed it to the strong convergence occurring in this area. �elow the surface, the �editerranean waters �ow into the Atlantic and mainly direct to the NW [38, 39, 97]. As an example, the computed circulation 590 m below the surface is presented in Figure 19. Only the northern part of the GoC is shown to appreciate details more clearly. ese currents are in agreement with the geostrophic velocities below 400 m, referenced to 300 m, provided in [13], and withthecalculationsin[96] for summer. Water velocity is higher close to the Strait and then slows to about 0.1 m/s, in agreement with [97]. Temperature and salinity pro�les in the water column calculated by the model have been compared with those obtained from observations carried out under the TOROS project [9] in summer 1997. Examples for 4 points shown in Figure 16 may be seen in Figure 20. ere is an acceptable agreement between model results and experimentally obtained vertical pro�les of 𝑇𝑇and 𝑆𝑆. Finally, two vertical south-north sections of water salinity are presented in Figure 21, at longitudes of −6.87 ∘and −6.05∘. In the �rst case, the core of more dense �editerranean water is clearly seen, with the salinity maximum below 600 m. is �ow is aligned with the Spanish continental slope, in agreement with [96, 98]. Close to the Strait, the situation may be characterized as a two-layer exchange �ow, with the interface tilted down southward [98]. Although seasonally averaged values have been used for open boundary conditions and wind stress, the main features of water circulation in the GoC are, generally speaking, reproduced by the model.
18 ISRN Oceanography Longitude Latitude 33 33.5 34 34.5 35 35.5 36 36.5 37 37.5 0.3 m/s −8 −7.5 −7 −6.5 −6 F 18: Computed surface residual currents. Only one of each 4 vectors is drawn. 4.2.2. Suspended Particle Transport. e sediment transport model is run until steady particle distribution and SR are obtained. Open boundary conditions are the same as in the AS domain. As expected, the river-discharged suspended matter is transported to the southeast along the Spanish coast, which is the residual current direction in this area of the GoC. As widely discussed [40], there is a dominant eastward transport throughout the entire northern GoC. Some authors [99] have postulated the existence of some westward transport of sediments released by the Guadalquivir River in the inner shelf, although little indication of it has been found in other works [40]. Maps of suspended matter concentrations at the surface and in the deepest water layer are presented in Figure 22. Logarithmic scale is used to appreciate differences. e suspended particle plumes produced by the three rivers can be clearly seen in the maps. Indeed, concentrations of the order of 10 g/m3are obtained near the river mouths. Concentrations of the order of 10−1 g/m3are obtained in part of the northern GoC and much smaller values are apparent to the south. Computed surface particle concentrations are in agreement, by order of magnitude, with measured surface concentrations. Indeed, concentrations of the order of 10−1 g/m3have been measured at the surface in the northern GoC [100]. Also, concentrations in the range 20–45 g/m3have been detected in the Guadiana River plume [101]overanarrow area (<10 km from the coast). In the deepest water layer concentrations are slightly higher than at the surface over most of the northern GoC, in agreement with [100].Insome areasastheStraitofGibraltarandtheSpanishcontinental slope, concentrations are more signi�cantly enhanced in the Latitude Longitude −8 −7.8 −7.6 −7.4 −7.2 −7 −6.8 −6.6 −6.4 −6.2 −6 36 36.5 37 37.5 0.3 m/s F 19: Computed residual currents 590 m below the surface in the northern GoC. Only one of each 4 vectors is drawn. deep water. is is probably due to resuspension produced by stronger tidal currents (in the area of the Strait) and also produced by the Mediterranean Water current. Computed net sedimentation rates (not shown) are larger, as expected, in the vicinity of the river mouths, wheretheyareoftheorderof10−3 g/cm2year. Much smaller values are obtained far from the river discharge in�uence. In particular, there is a region where no sedimentation occurs atthewestoftheStraitofGibraltar.isisduetothe strong currents in the Mediterranean out�ow water, which keep particles in suspension. Nevertheless, all these results have to be interpreted with care due to the approximations which have been made in the model (the same as in the AS), described in Section 3.2. Also, although constant suspended matter concentrations have been de�ned in the three estuaries, there will be seasonal variations depending on pluviometry, for instance. It must be taken into account that suspended particles will affect tracer transport only close to the coast, given the extremely low suspended matter concentrations which are measured offshore [100], and river supply is the main sediment source in this coastal area. 4.2.3. Metal Transport. Metal concentrations in the dissolved phase have been de�ned at the three main sources: Guadalquivir, Guadiana, and Odiel-Tinto estuaries. Values are given in [1] and may be seen in Table 12. e metal transport model is started from background dissolved concentrations, which correspond to the open Atlantic Ocean metal concentrations reported in [9]. e corresponding background in the solid phase is obtained from the metal 𝑘𝑘𝑑𝑑through (5). Equations are integrated until steady metal distributions are obtained in all phases. Open boundary conditions are again the same as in the AS domain. e concentrations of several metals have been measured in the �ne sediment fraction (<63 𝜇𝜇m) along the Spanish coast from the Guadiana to the Guadalquivir mouths [3, 102]
ISRN Oceanography 19 Depth (m) Point 1 10 15 20 10 15 20 Point 2 Point 3 10 15 20 25 36 37 38 Point 4 −350 −300 −250 −200 −150 −100 −50 Depth (m) −350 −300 −250 −200 −150 −100 −50 Depth (m) Depth (m) −350 −300 −250 −200 −150 −100 −50 Depth (m) −350 −300 −250 −200 −150 −100 −50 Depth (m) −350 −300 −250 −200 −150 −100 −50 Depth (m) −350 −300 −250 −200 −150 −100 −50 35.5 36 36.5 35.5 36 36.5 35.5 36 36.5 37 −200 −150 −100 −50 Depth (m) −200 −150 −100 −50 10 15 20 QTV Ӣ $ QTV Ӣ $ QTV Ӣ $ QTV Ӣ $ F 20: �o�puted (lines) and �easured (points) salinity and te�perature pro�les in points indicated in Figure 16. 0 −100 −200 −300 −400 −500 −600 −700 −800 −900 −1000 −1100 Depth (m) 36.4 36.3 36.2 36.1 36 35.9 35.8 35.7 35.6 34 35 36 37 Latitude (a) Depth (m) 0 −50 −100 −150 −200 −250 −300 −350 −400 −450 Latitude 37.4 37.2 37 36.8 36.6 36.4 36.2 35.4 35.6 35.8 36 36.2 (b) F 21: Vertical south-north salinity sections at longitudes −6.87 ∘ and −6.05 ∘ ((a) and (b), resp.).
20 ISRN Oceanography Latitude Longitude 35 35.5 36 36.5 37 37.5 −8 −7.5 −7 −6.5 −6 −3 −2 −1 0 1 2 (a) Latitude 35 35.5 36 36.5 37 37.5 Longitude −8 −7.5 −7 −6.5 −6 −3 −2 −1 0 1 2 (b) F 22: Computed suspended matter concentrations (g/m 3 ) in logarithmic scale at the surface (a) and bottom (b) of the water column in the GoC. and also at some points closer to the Strait of Gibraltar [103]. Samples were collected at an approximate distance of 500 m from the shoreline. A comparison of measured and computed metal concentrations along the northern coast of the model domain can be seen in Figure 23.Ingeneral,thereisagood agreement between the measured and calculated concentrations. Metal concentrations are very low westward from the Guadiana River. ere is an increase in concentrations here T 12: Values of river discharge metal concentrations (nM). metal Guadiana Guadalquivir Odiel-Tinto Cu 42 58 214 Zn 49 33 129 0 100 200 300 400 500 600 700 Zn 0 100 200 300 400 Cu Longitude −8 −7.8 −7.6 −7.4 −7.2 −7 −6.8 −6.6 −6.4 −6.2 −6 Longitude −8 −7.8 −7.6 −7.4 −7.2 −7 −6.8 −6.6 −6.4 −6.2 −6 NHLH NHLH F 23: Measured (circles) and computed (lines) metal concentrations in sediments along the northern coast of the GoC model domain. e mouths of the Guadiana, Odiel-Tinto and Guadalquivir rivers are located, respectively, at the longitudes of −7.4 ∘ ,−6.9 ∘ , and −6.4 ∘ . since, as has already been mentioned, the three rivers drain the Iberian Pyrite Belt. Maximum concentrations exist in the mouth of the Odiel-Tinto rivers. Although river �ows are much smaller than those of the Guadiana and Guadalquivir, the Odiel-Tinto rivers are considerably more contaminated [40] and, indeed, they have been recognized as the main sourceofmetalsalongthecoast[102]. A map of computed dissolved Zn concentrations at the surface for summer 1997 is presented in Figure 24 together with a contour plot obtained from empirical data [104], which shows essentially the same banded structure. It may be clearly seen that the impacts from river out�ow are restricted to a narrow band along the shore. Samples were not collected in the coastal area from Cadiz to the Strait, thus the impact is apparently restricted (in the case of observations) in Figure 24 to the zone located to the north of Cadiz. e highest concentrations are obtained in the mouth of the Odiel-Tinto rivers, obviously as in the case of bed sediments. e plume of dissolved metals, however, reaches the Strait of Gibraltar. Indeed, it has already been found [9] that coastal waters transport dissolved metals from the Odiel-Tinto rivers to a distance of more than 200 km. Moreover, it has been found that these rivers constitute a source of natural radionuclides into the Mediterranean through the Strait of Gibraltar [81]. Once it seems that the model is giving a realistic representation of reactive transport in the GoC, a numerical experiment has been carried out to assess the effect of the out�ow of Mediterranean �ater on the Pu contamination of bed sediments in the GoC. e model is started from clean
ISRN Oceanography 21 33.7 14.4 49.1 3.9 6.7 5.7 3.5 32.1 26.6 66.8 124.7 105.1 2.5 2.1 1.9 5.8 12.2 0.1 33.1 5.7 2.9 17.8 35 16 Longitude Latitude Zn 5 10 15 20 25 30 35 40 45 50 55 60 35.8 36 36.2 36.4 36.6 36.8 37 37.2 37.4 −8 −7.8 −7.6 −7.4 −7.2 −7 −6.8 −6.6 −6.4 −6.2 −6 30 30 10 10 5 5 Cadiz Zn (nM) Jun 97 F 24: Up: measured and computed (color scale) metal concentrations (nM) in surface waters of the northern GoC. Down: contour plot showing surface dissolved Zn concentrations (nM) in June 1997 from experimental data [104]. water, suspended matter, and bed sediments. Pu concentration in water is speci�ed, as a boundary condition, in the Mediterranean Water entering the GoC through the Strait of Gibraltar. Such Pu concentration is obtained from the output of the AS model: 0.012 Bq/m3. e model is integrated until a steady situation is achieved. e computed Pu distribution in bed sediments is presented in Figure 25. ese results could not be compared with measurements. However, the path followed by the Mediterranean Water is clearly marked on the bed sediment as a tongue of enhanced Pu concentrations directed to the noth-west. Its shape is in agreement with the computations in [38], Figure 4(b) in this paper, for salinity. 4.2.4. Sensitivity Analysis. e main parameter which describes the geochemical behaviour of tracers is the exchange velocity 𝜒𝜒, obtained from the equilibrium distribution coefficient 𝑘𝑘𝑑𝑑through (6), as already described. e model sensitivity to changes in this last parameter has been investigated since the 𝑘𝑘𝑑𝑑is poorly de�ned and presents a high natural variability depending on environmental conditions (mainly pH, temperature and salinity, although other parameters as light intensity may be relevant as well). Obviously, a higher 𝑘𝑘𝑑𝑑means that the substance has a higher affinity to be �xed to the solid phase and vice versa. us, surface sediment metal concentrations are linearly correlated with the 𝑘𝑘𝑑𝑑, as should be expected from the model formulation. e distribution of metals in coastal sediments obtained with several 𝑘𝑘𝑑𝑑values have been computed and are presented in Figure 26 in the case of Zn as an example. e value 2.0 × 105has been measured in coastal waters of the USA [105]. A smaller value, by one order of magnitude, has also been tested (2.0 × 104). Effectively, too high metal concentrations, when compared with empirical data, are obtained with 2.0×105. On
22 ISRN Oceanography Longitude Latitude 33 33.5 34 34.5 35 35.5 36 36.5 37 37.5 −8 −7.5 −7 −6.5 −6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 F 25: Computed distribution of 239,240 Pu (Bq/kg) in surface bed sediments of the GoC resulting from the out�ow of Mediterranean Waters. 0 200 400 600 800 1000 1200 1400 1600 1800 Longitude −8 −7.8 −7.6 −7.4 −7.2 −7 −6.8 −6.6 −6.4 −6.2 −6 7 × 10 4 (nominal) 2 × 10 5 2 × 10 4 NHLH F 26: Model sensitivity to the distribution coefficient in the case of Zn. Results in Figure 23 are presented for three 𝑘𝑘 𝑑𝑑 values. e nominal simulation corresponds to 𝑘𝑘 𝑑𝑑 =7×10 4 . the other hand, concentrations are too low if a 𝑘𝑘 𝑑𝑑of 2.0×104 is used. e best agreement between measured and computed metal concentrations are obtained with the 𝑘𝑘𝑑𝑑recommended by IAEA [64], which is indicated in Figure 26 as the nominal simulation. e sensitivity of the formulation of the water-sediment interaction processes to other parameters as particle size, and density, sediment mixing depth, fraction of small particles and the correction factor 𝜙𝜙has already been studied in detail [56, 106]andwillnotberepeatedhere. 5. Conclusions and Future Work Tracer dynamics in the Gulf of Cadiz and Alboran Sea have been studied through numerical modelling. Water circulation, required to solve dispersion, is obtained from appropriate hydrodynamic models for each domain. ese models have been tested by means of comparisons of computed tides and currents with measurements in the GoC and the AS. Sediment transport models are also needed. An interesting effect has been observed. It consists of an enhancement of radionuclide concentrations in the WAG. is effect has also been observed in the centre of oceanic gyres in the Atlantic and Paci�c. It is due to the fact that water remains trapped in the gyre region, remaining relatively isolated from the surroundings, and thus accumulating radionuclides introduced from the atmosphere. In the case of the AS, the model has been applied to three radionuclides: 137Cs, 239,240Pu, and 210Pb. ey are mainly introduced from atmospheric deposition. Generally speaking, the model produces results in agreement with measurements. A correct estimation of 137Cs levels in bed sediments and in the water column is obtained. Also, the model reproduces the observed fact that essentially the same Cs concentrations exist in both water layers. Although the model slightly underestimates Pu concentrations in the water column, concentrations in the deep water layer are essentially a factor 2 higher than in the surface layer because of the efficient removal of dissolved plutonium by settling suspended particles. Excess 210Pb inventories in the sediment have been calculated. ey are underestimated with respect to measurements, although this is due to the difficulties in modelling 210Pb: this is a natural radionuclide which is also produced by in situ radioactive decay of its parent radionuclide 226Ra. Also, initial conditions for the simulation cannot be appropriately de�ned. Radionuclide �uxes through the Strait of Gibraltar have beenevaluated.eyareinrelativegoodagreementwith previous estimations based upon radionuclide concentration measurements in the Strait. Finally, system time-scales that are useful from a management perspective have been calculated. ey are the sediment half-life and the systemwide �ushing time. Both time scales are signi�cantly larger for 239,240Pu than for 137Cs, which is due to the fact that reactive elements are less mobile in the environment than those remaining dissolved. us, �ushing time for 239,240Pu in the surface water layer is one order of magnitude larger than that of 137Cs, for instance. Also, it has been found that the presence of the WAG increases the �ushing time in the surface layer. In the case of the GoC, the contamination of bed sediments by metals discharged by the main rivers draining the southern Iberian Peninsula has been adequately reproduced. eimpactfromriverout�owisrestrictedtoanarrowband
ISRN Oceanography 23 along the shore, the area of the Odiel-Tinto river mouth being the more contaminated. e plume of dissolved metals reaches the Strait of Gibraltar, con�rming that coastal waters transport dissolved metals from the Odiel-Tinto rivers to adistanceofmorethan200kmandthattheseriversmay constitute a source of metals and radionuclides into the Mediterranean through the Strait of Gibraltar. e dispersion of Pu entering the Gulf of Cadiz with the out�ow of Mediterranean Water has been simulated with the model. e path followed by the Mediterranean Water is clearly marked on the bed sediment as a tongue of enhanced Pu concentrations. Its shape is in agreement with earlier salinity computations. Although both models give a generally good overview of pollutant dynamics in GoC and AS, a clear weak point is that they run using steady residual circulations. Models should be adapted to run with evolving circulation. is would be interesting to evaluate, for instance, the role of Mediterranean mesoscale eddies in pollutant and suspended sediment dynamics. Of course, modelling the behavior of the biotic components of the ecosystem would also be of great interest, given the high productivity of the region. Appendices A. Sediment Transport Model In an three-dimensional form, the equation which provides the suspended matter concentration, 𝑚𝑚, is 𝜕𝜕𝑚𝑚 𝜕𝜕𝜕𝜕 +𝑢𝑢𝜕𝜕𝑚𝑚 𝜕𝜕𝜕𝜕 +𝑣𝑣𝜕𝜕𝑚𝑚 𝜕𝜕𝜕𝜕 +𝑤𝑤𝑤𝑤𝑤𝑠𝑠𝜕𝜕𝑚𝑚 𝜕𝜕𝜕𝜕 =𝐴𝐴𝜕𝜕2𝑚𝑚 𝜕𝜕𝜕𝜕2+𝜕𝜕2𝑚𝑚 𝜕𝜕𝜕𝜕2+𝜕𝜕 𝜕𝜕𝜕𝜕𝐾𝐾𝜕𝜕𝑚𝑚 𝜕𝜕𝜕𝜕,(A.1) where 𝑤𝑤𝑠𝑠is the settling velocity of suspended particles and 𝐴𝐴and 𝐾𝐾are, respectively, the horizontal and vertical diffusivities. 𝑢𝑢,𝑣𝑣and 𝑤𝑤are water velocities along the 𝜕𝜕, 𝜕𝜕- and 𝜕𝜕-axis. e deposition and resuspension terms are incorporated into the sea bed boundary condition of the equation. e deposition rate is written as 𝐷𝐷𝐷𝐷=𝑤𝑤𝑠𝑠𝑚𝑚(𝑏𝑏)1𝑤𝜏𝜏𝑏𝑏 𝜏𝜏𝑐𝑐𝑐𝑐,(A.2) where 𝑚𝑚(𝑏𝑏) is particle concentration evaluated at the sea bottom, 𝜏𝜏𝑏𝑏is bottom stress due to tides and the residual current, and 𝜏𝜏𝑐𝑐𝑐𝑐is a critical deposition stress above which no deposition occurs since particles are maintained in suspension by water turbulence. e settling velocity is determined from Stokes’s law: 𝑤𝑤𝑠𝑠=𝜌𝜌𝑤𝜌𝜌𝑤𝑤 𝜌𝜌𝑤𝑤𝑔𝑔𝐷𝐷2 18𝜈𝜈,(A.3) where 𝜌𝜌and 𝐷𝐷are suspended particle density and diameter, respectively, 𝜈𝜈is kinematic viscosity of water and 𝜌𝜌𝑤𝑤its density. e resuspension rate is written in terms of the erodability constant: 𝐸𝐸𝐸𝐸=𝐸𝐸𝐸𝐸𝜏𝜏𝑏𝑏 𝜏𝜏𝑐𝑐𝑐𝑐 𝑤1,(A.4) where 𝐸𝐸is the erodability constant, 𝐸𝐸gives the fraction of �ne particles in the bed sediment, and 𝜏𝜏𝑐𝑐𝑐𝑐is a critical resuspension stress below which this process does not occurs. e model can also calculate sedimentation rates (SR) as the balance between the deposition and resuspension terms. B. Tracer Dispersion Model e equation that gives the time evolution of tracer concentration in the dissolved phase, 𝐶𝐶𝑐𝑐, is 𝜕𝜕𝐶𝐶𝑐𝑐 𝜕𝜕𝜕𝜕 +𝑢𝑢𝜕𝜕𝐶𝐶𝑐𝑐 𝜕𝜕𝜕𝜕 +𝑣𝑣𝜕𝜕𝐶𝐶𝑐𝑐 𝜕𝜕𝜕𝜕 +𝑤𝑤𝜕𝜕𝐶𝐶𝑐𝑐 𝜕𝜕𝜕𝜕 =𝐴𝐴𝜕𝜕2𝐶𝐶𝑐𝑐 𝜕𝜕𝜕𝜕2+𝜕𝜕2𝐶𝐶𝑐𝑐 𝜕𝜕𝜕𝜕2+𝜕𝜕 𝜕𝜕𝜕𝜕𝐾𝐾𝜕𝜕𝐶𝐶𝑐𝑐 𝜕𝜕𝜕𝜕 𝑤𝑘𝑘1𝐶𝐶𝑐𝑐+𝑘𝑘2𝑚𝑚𝐶𝐶𝑠𝑠+𝛿𝛿𝑏𝑏𝑘𝑘2𝐿𝐿𝜌𝜌𝑠𝑠𝜙𝜙𝐸𝐸𝐴𝐴𝑠𝑠 𝜓𝜓, (B.1) where 𝐶𝐶𝑠𝑠and 𝐴𝐴𝑠𝑠are, respectively, the concentrations of tracers in suspended matter and the �ne fraction of bottom sediments (particles with diameter <62.5 𝜇𝜇m, as mentioned in Section 3.3). All remaining parameters have been de�ned before (Section 3.3). e last three terms of the equation correspond to the tracer transfer from water to suspended matter and bed sediment, from suspended matter to the dissolved phase and from the bed sediment to the deepest water layer dissolved phase. e equation that gives the time evolution of tracer concentration in suspended matter is 𝜕𝜕𝑚𝑚𝐶𝐶𝑠𝑠 𝜕𝜕𝜕𝜕 +𝑢𝑢𝜕𝜕𝑚𝑚𝐶𝐶𝑠𝑠 𝜕𝜕𝜕𝜕 +𝑣𝑣𝜕𝜕𝑚𝑚𝐶𝐶𝑠𝑠 𝜕𝜕𝜕𝜕 +𝑤𝑤𝑤𝑤𝑤𝑠𝑠𝜕𝜕𝑚𝑚𝐶𝐶𝑠𝑠 𝜕𝜕𝜕𝜕 =𝐴𝐴𝜕𝜕2𝑚𝑚𝐶𝐶𝑠𝑠 𝜕𝜕𝜕𝜕2+𝜕𝜕2𝑚𝑚𝐶𝐶𝑠𝑠 𝜕𝜕𝜕𝜕2 +𝜕𝜕 𝜕𝜕𝜕𝜕𝐾𝐾𝜕𝜕𝑚𝑚𝐶𝐶𝑠𝑠 𝜕𝜕𝜕𝜕 +𝑘𝑘𝑚𝑚 1𝐶𝐶𝑐𝑐𝑤𝑘𝑘2𝑚𝑚𝐶𝐶𝑠𝑠𝑤𝛿𝛿𝑏𝑏𝑆𝑆𝐸𝐸𝐷𝐷, (B.2) where 𝑤𝑤𝑠𝑠is the particle settling velocity. e last three terms are the tracer transfer from the dissolved phase to suspended matter, from suspended matter to the dissolved phase and the deposition of metals (�xed to suspended particles) from the deepest water layer to the sediment, evaluated according to 𝑆𝑆𝐸𝐸𝐷𝐷=SR𝐶𝐶𝑠𝑠(𝑏𝑏) 𝜓𝜓.(B.3) Note that (𝑏𝑏)means that the corresponding magnitude is evaluated at the deepest water layer.
24 ISRN Oceanography e equation for the temporal evolution of tracer concentration in the bottom sediment mixed layer is 𝜕𝜕𝜕𝜕𝑠𝑠 𝜕𝜕𝜕𝜕 =𝑘𝑘 𝑠𝑠 1𝐶𝐶𝑑𝑑(𝑏𝑏)𝜓𝜓 𝐿𝐿𝐿𝐿𝑠𝑠𝑓𝑓−𝑘𝑘2𝜕𝜕𝑠𝑠𝜙𝜙−𝜙𝜙burial𝜕𝜕𝑠𝑠+𝑆𝑆𝑆𝑆𝑆𝑆𝑆 (B.4) where deposition is now calculated as 𝑆𝑆𝑆𝑆𝑆𝑆 = SR𝐶𝐶𝑠𝑠(𝑏𝑏) 𝐿𝐿𝑠𝑠𝐿𝐿𝑓𝑓 .(B.5) e total tracer content, 𝜕𝜕𝑝𝑝, in the sediment below the mixed depth is given by the following equation: 𝜕𝜕𝜕𝜕𝑝𝑝 𝜕𝜕𝜕𝜕 =𝜙𝜙 burial𝐿𝐿𝐿𝐿𝑠𝑠𝑓𝑓𝜕𝜕𝑠𝑠.(B.6) Radioactive decay, −𝜙𝜙𝐶𝐶, should be added to the equations to simulate a radioactive isotope. Acknowledgments e author is indebted to the Agencia Española de Cooperación Internacional for partially funding this work and to the Spanish Ministerio de Educación y Ciencia for a fellowship to stay during three months at the University of Wales, Bangor, where part of this work was carried out. is work is partially supported through the project “Determination of scavenging rates and sedimentation velocities using reactive-particle radionuclides in coastal waters; application to pollutants dispersion modeling,” Ref. CTM2009-14321- C02-01-02, funded by the Spanish Ministerio de Ciencia e Innovación. References [1] J. M. Beckers, E. P. Achterberg, and Ch. Braungardt, “Comparison of high spatialresolution trace metal distributions with model simulations for surface waters of theGulf of Cadiz,” Estuarine, Coastal and Shelf Science, vol. 74, pp. 599–609, 2007. [2] X. A. G. Morán and M. 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