Modelling the distribution of suspended matter and the sedimentation process in a marine environment

Ecological Modelling, 71 (1994) 197-219

197

Elsevier Science B.V., Amsterdam

Modelling the distribution of suspended matter and the sedimentation process in a marine environment 1 J.M. Abril and M. Garda

Le6n

Facultad de Fisica, Uniuersidad de Seuilla, Apdo. 1065, 41080 Seuilla, Spain (Received 24 February 1992; accepted 23 February 1993)

ABSTRACT Abril, J.M. and Garcia Le6n, M., 1994. Modelling the distribution of suspended matter and the sedimentation process in a marine environment. Ecol. Modelling, 71: 197-219. A computational model for the study of suspended matter distribution in a marine environment is presented. It involves four main processes: the horizontal transport, the external sources of suspended matter, and its deposition and resuspension from the sea bed. As an immediate consequence of the calculations with such a model, the sedimentary regime at the studied marine scenario is also obtained. The model has been applied to the Irish Sea where we get a reasonably good description of the residual advection and diffusion and, at the same time, a detailed implementation of the sea bed structure and of the continental water runoff for each coastal sector has been done. The values for resuspension and deposition velocities are taken from the literature and the whole model is calibrated against field data. The corresponding sensitivity tests have also been carried out. The results confirm that the physical assumptions made for model development are adequately realistic. It also shows the predictive power of the model when studying the sedimentary processes in a given environment.

1. I N T R O D U C T I O N T h e r e a r e s o m e g o o d p h y s i c a l a n d c o m p u t a t i o n a l m o d e l s in t h e a r e a s o f oceanography and engineering to describe sea dynamics (Backhaus and H a i n b u c h e r , 1987; N i h o u l a n d D j e n i d i , 1987). T h e s e m o d e l s c a n r e p r o d u c e

Correspondence to (present address): J.M. Abril, Dpto. Fisica Aplicada, E.U. Ingenieria T~cnica Agricola, Ctra. Sevilla-Utrera km 1, 41014 Sevilla, Spain. i Work partially supported under contract PB89-0621 of the Spanish CICYT. 0304-3800/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 3 8 0 0 ( 9 3 ) E 0 0 2 1 - T

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J.M. ABRIL AND M. GARCIA LEON

the variation in height of the water and in the current system, induced by tides and wind, by solving the hydrodynamic equations with typical time steps of a few minutes or some seconds (Prandle, 1984; Backhaus and Hainbucher, 1987; Nihoul and Djenidi, 1987). Furthermore, they can be used to simulate the particulate matter tracks under specific conditions. Nevertheless, such models are not appropriate for predictive studies which involve large time scales (dispersion of radionuclide discharges in the sea, heavy metals and other environmental degradation processes produced by human industrial activities, red tides, greenhouse effect, etc.). There are several reasons for that, the first being the actual computational limitations. Thus, for such studies, new models based on residual circulation and, consequently, using time steps of a few hours are required. This, on the other hand, supposes a certain degree of limitation about the expected accuracy of model predictions. The knowledge of water movements is not enough to make predictions about the dispersion of non-conservative substances in the sea. In fact, every chemical substance in the sea has some affinity to the suspended particulate matter in the water column. Obviously, the amount, distribution and dynamics of suspended matter, its interaction with the sediment phase, the growth or erosion of the latter in our sea area, will influence the behaviour of non-conservative substances. The description of these processes is the first objective of the present paper. The ionic exchanges among the different phases which play an important role in the dynamics of the non-conservative substances are introduced by using radiological information, which is presented in two separate papers (Abril and Garcla-Le6n, 1993a,b). This way some new and suggestive possibilities are now open in the ecohydrodynamic modelling. It is interesting to mention some of them; for instance: modelling of oligoelement (and other nutrients) dispersion in the marine environment, phytoplankton growth and, consequently, the toxin production in red tides or the CO 2 exchange in photosynthesis, with its implications in the greenhouse effect. It is interesting also to clear that we use a 2D model. Such models are useful only for well-mixed, deep waters. This is an important restriction indeed. Nevertheless we can easily imagine that in the majority of the cases, the study area will be defined over the continental shelf where the application of a 2D model is totally admissible. The reason for emphasis on these zones is the stronger impact which they receive from human activities. This, together with the abundance of suspended matter and biological activity, makes such zones the first objective when any risk-evaluation program is to be implemented. In Section 2 we present the mathematical description of our model as well as a selection of input parameters. Some considerations about sensitiv-

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ity studies and calibration methods are also given. In Section 3 our model is applied to solve the suspended m a t t e r distribution and the sedimentary regimen in the Irish Sea. Finally, the results are presented and discussed in Section 4. 2. EQUATIONS FOR THE MODEL The real system, in which the dynamics of suspended matter is to be studied, will be r e p r e s e n t e d by a grid containing a certain n u m b e r of grid-cells or compartments. Each c o m p a r t m e n t i contains a certain amount, m i, of suspended m a t t e r in ppm (parts per million). However, some remarks concerning such matter have to be done. Obviously, the behaviour of the particulate matter depends on its specific weight, or m o r e simply, on its size - which is in practice the available observed p a r a m e t e r - if m a t t e r density does not vary too much over the studied marine system. Nevertheless, in order to simulate its dynamics we have to accept a simplification, which is usual in other geological or modelling studies (Belderson, 1964; G u b u r t et al., 1987; Howorth and Kirby, 1988). Indeed, one normally assumes the existence of two kinds of particulate matter. That with a diameter < 62.5/xm and that of diameter >/62.5 p~m. We will assume that the first class can remain as suspended matter, while the second will rapidly be attached to the sediments. Consequently, we will not consider the horizontal dispersion for this second class of particulates, since those introduced by the runoff of continental waters will quickly be deposited in the shoreline. Although this imposes a rough simplification, we cannot elude it since, as far as we know, there are no measured data which could support a m o r e complex description. But, on the other hand, this simplification does not limit the model applications as we will see in what follows, since we are interested only in the very basic aspects of suspended m a t t e r dynamics over large time scales (e.g. annually averaged distributions, and m e a n sedimentation or erosion rates). Several processes contribute to the change along the time of mi in a given compartment: the deposition of particulate material onto the sea bed, the resuspension of fine particulates from the top layers of the sediment in contact with c o m p a r t m e n t i, the exchange of suspended m a t t e r with the different compartments placed at the borders of c o m p a r t m e n t i and, finally, the inputs of suspended matter from runoff of continental waters, provided that c o m p a r t m e n t i is in contact with the coast line. The first two processes provoke a vertical m o v e m e n t of m i inside c o m p a r t m e n t i, while the third contributes to a horizontal displacement of the material. The fourth process will represent the source term for our calculations. In the following these contributions will be discussed in detail.

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J.M, ABRIL AND M. GARCIA LEON

2.1. T h e v e r t i c a l m o v e m e n t

The particulate m a t t e r in a water column of height h i falls down with a m e a n settling velocity v s. In the case of well mixed waters, an homogeneous distribution of m i can be assumed for modelling purposes. Therefore, a fraction At

Vs hi

(1)

of m i will be deposited onto the sediment in contact with c o m p a r t m e n t i, during a time interval At. The resuspension effect is produced by physical or biological agents, such as fluctuations in water currents, bioturbation or even ship traffic. This resuspension effect will affect the small size particulate m a t t e r ( < 62.5 /xm) situated along a m e a n depth L in the sediment. Such m a t t e r will move up from the top of the sediment with a m e a n resuspension velocity v r. Let us call d i the weight fraction of small particulates in the top layer of the sediment in contact with c o m p a r t m e n t i. If Pm is the dry m a t t e r density of the sediment and S is the area of the bottom of c o m p a r t m e n t i, vrSPmd i will give us the amount of fine m a t t e r (in kg) resuspended per unit time in our compartment. Such m a t t e r will be incorporated, and homogeneously distributed, into the water column, of section S and height h i, corresponding to the studied compartment. A n d it will contribute to the variation of m i through the time with an a m o u n t in ppm of

VrPmdi

- -

X 10 6,

(2)

hiPa Pa being the water density. Although these formulations for deposition and resuspension are common, they are not necessarily exact. Indeed, the assumption of a homogeneous distribution of small particles in the water column and in the surface sediments may introduce some inaccuracy. We remark, however, that our interest is to calculate the m e a n - annually averaged - suspended matter distribution. This, together with an "effective m e a n settling velocity" and an "effective m e a n resuspension velocity" produces a m e a n - annually averaged - distribution of sedimentation or erosion rates. 2.2. T h e h o r i z o n t a l m o v e m e n t The suspended m a t t e r can remain in the water column for a long time. Consequently, it will participate in the water movements, that is, it will

S U S P E N D E D M A T P E R A ND S E D I M E N T A T I O N PROCESS IN M A R I N E E N V I R O N M E N T

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behave as a conservative substance. Therefore, some exchange of susp e n d e d matter among neighbouring compartments will occur. Such exchange can be described by a transfer coefficient formalism. Thus, the variation of m i due to this reason will be

~m i --=

Y'~ ( k j i m j - k i j m i ) ,

Ot

j~e(i)

(3)

where e(i) is the set of all the other compartments in physical contact with compartment i, and kij is the transfer coefficient from compartment i to j. As was shown in Abril and Garcla-Le6n (1991),

~)ijPijSij kij=

Vi

uijSij +

Vi

,

(4)

V~ being the volume of compartment i, and Sij is the surface of contact between compartment i and j. ~ij is the average value of the projection of the diffusional velocity over a direction normal to S~j, and from i to j. pij is the probability that a fine particulate in compartment i has v~j ~ 0. Finally, uij is the residual advective velocity at such direction and sense, uij can be defined as the time-averaged water flux through Sij, while v~j will be obtained by subtracting uij from the real velocity field. But a more consistent m e t h o d can be used to calculate the advective part (second term of Eq. 4) and the diffusive part (first term of Eq. 4) of kii (Abril and Garcla-Le6n, 1992). Indeed, the residual circulation, u, can be obtained from the stream function, ~ ( x , y), evaluated in a given compartment placed at the point (x, y) of our grid. This function verifies (Howorth and Kirby, 1988) that

Ox - u y h ( x '

y),

and oqt

~y

(5) -

ugh(x, y),

u x and ur, respectively being the component along the X- and Y-axis of the residual velocity averaged over compartmenl~ depth, h(x, y). The stream function may be evaluated from conventional tidal modelling (Prandle, 1984) or first estimated from field observations and then calibrated by modelling the salinity distribution in a given marine scenario, as shown in Abril and Garcla Le6n (1992). This • will be used to calculate the advective part of kij and will be described in the next section for our real case.

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J.M. ABRIL AND M. GARCJA LEON

The diffusive part of kij, k.rD, can be written as kTD =

(6)

kb A x A y '

Ax and Ay being the dimensions of the compartment. Here, h is the mean depth of the contact surface between compartments, while k b is the diffusion coefficient. In the above mentioned reference (Abril and Garcia Le6n, 1992), k b is described by the following formula, evaluated over each compartment contour kb=f×(81a.3×e

(km 2 y - a ) .

+30Fij)

(7)

The second term in this sum is proportional to the water flux from compartment i to j, since F,.j=uijhAx. This corresponds to a usual formulation of the Shear effect (Bowden, 1965). The first term represents the remaining turbulent diffusion. Such term will strongly depend on the current system and, therefore, can change from one part of the grid to another. As will be seen in the next section, this variability will be reproduced by the parameter e. The factor f can be varied to obtain global changes in k b. 2.3. The source term

The amount of material incorporated into the compartment i from runoff of continental waters will be represented by (8)

a R i,

a being a constant factor which can be fixed after a calibration exercise as will be referred later. R i is the total volume of continental waters (in km 3) which yearly enters the compartment. R i will be different from zero when the compartment is situated along the coast line. 2.4. The general equation

Consequently, the equation which describes the dynamics of suspended matter, mi, in compartment i, will be obtained by summation of all the above mentioned terms, that is, those of Eqs. 1, 2, 3, and 8. Thus, am/ Ot

( ~( =

j

) i)

kjimy - k i j m i +

1( hi

)

vrPmdi X 10 6 - Vsm i + otR i Pa

with an obvious meaning for the notation.

(9)

S U S P E N D E D MA'Iq'ER A ND S E D I M E N T A T I O N PROCESS IN M A R I N E E N V I R O N M E N T

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As mentioned before, we are interested in the mean - annually averaged suspended matter distribution over the Irish Sea. So no seasonal variations will be considered in the model. If no significant variations take place in the input of matter and in the transport processes from one year to another, no substantial changes will appear in such a mean suspended matter distribution from one year to another, so we can reasonably assume that, for the time scale of our problem, such a mean suspended matter distribution is in a steady-state situation. Eq. 9 must be solved during a simulation time period t of the order of the typical fluxing time for the marine area under study, so as to obtain the steady state distribution of suspended matter over the system. For instance, in the case of the Irish Sea, t = 1 year (Prandle, 1984). However, it is important to note that this equation can also provide valuable information on the sedimentation processes which take place in the area. Indeed, the sedimentation rate, w i, or erosion rate (w i < 0) at compartment i can be obtained as a net balance between deposition and resuspension. Expressing w i in kg m-2 y-1 results in -

W i = UsmiP a X

10 - 6 --

UrPmd i.

(10)

Or alternatively, it can be evaluated from the net matter balance in compartment i as

w i = ( Y'. k j i m j - k i j m i +otRi)hiPa× lO -6. jEe(i)

(11)

The second method being true only if a steady state for m i has been reached. It is just the agreement between Eqs. 10 and 11 that gives support to ensure that such steady state has been reached in the calculation. 3. A P P L I C A T I O N OF T H E MODEL: T H E CASE OF T H E IRISH SEA

3.1. Geological structure of the Irish Sea Testing of our model has been done by studying the suspended matter distribution in the Irish Sea where this study has a special relevance for modelling the dispersion of non-conservative radionuclides released by the nuclear reprocessing plant of Sellafield (Cumbria, UK). A map of the area is given in Fig. 1, where the grid used for our calculations is also represented. It includes 2200 compartments. Each compartment is described by their spatial coordinates (x, y) and the depth h(x, y), which is read from marine charts. The compartments were rectangular with dimensions Ax = Ay = 5.16 km.

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Fig. 1. Batimetry of the Irish Sea and the grid used in our numerical model, with grid lengths Ax = Ay = 5.16 km. Numbers in the X and F" directions are the index used to label each grid-cell. Black boxes represent land and the white ones water. Eq. 1 is solved in the center 9f each grid-cell at every time step.

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54*

"+' + ,o

0

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l 6*W

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5*

4*

3*

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Fig. 2. Distribution (in % dry weight) of small particles (qb ~<62.5 /zm) in the top sediment layer for the Irish Sea.

There are some observational data for d i in the Irish Sea (Belderson, 1964, Pentreath et al., 1985; M A F F , 1987; H o w o r t h and Kirby, 1988). F r o m them we developed the map of Fig. 2, in which the distribution of d i over our environment is presented.

206

J.M. ABRIL AND M. GARCIA LEON

The geological structure of the Irish Sea shows several sedimentary basins formed by Carbonifer and Triassic rocks. Superficial sediments have been deposited from the Pleistocene. In some recent studies (Smith et al., 1980) it has been shown that the eastern part of the Irish Sea consists of a Permo-Triassic rock basin, strongly eroded in glacial periods. Later this zone was covered by the Holocene sea and, as a result, several metres of fine sediments were accumulated forming a mud bank which in our days lies opposite Cumbrian coasts. A larger m u d bank lies north of Dublin Bay, and a small one extends north of Anglesey (see Fig. 2). The eastern part of the Irish Sea shows an important bioturbation in the sea bed sediments, which makes the interpretation of sediment cores sampled from this region not easy. As far as we know no conclusive results over the existence of a net accumulation or erosion rate on this region has been presented.

3. 2. Hydrodynamics of the Irish Sea Values f o r kij have been obtained by modelling the distribution of salinity in the Irish Sea. The details of this work can be found in Abril and Garcia Le6n (1992). Such transfer coefficients should be considered as representative of water movements, since salinity is a conservative substance. The stream function used in our calculations was based on that of Prandle (1984) and on observational studies (MAFF, 1987). This, first estimated, ~ ( x , y) was calibrated in the same modelling work referred to above, and the final one is presented in Fig. 3. From this, the depth-averaged residual velocity field is obtained. On the other hand, the parameters for Eq. 7 were f = 2, e = 2 for x >~ 24, and e = 1 elsewhere. This way, values for k b ranged from 1.5 × 10 5 to 5.0 × 10 6 c m 2 s - 1 . In Fig. 4 the salinity distribution calculated with these qb and k b is shown, together with experimental data. The agreement is particularly good. A relevant consequence of the mentioned work is that kij s o obtained can be used to model the distribution of any conservative substance, as, for instance, 137Cs (Abril and Garcla-Le6n, 1992). The comparisons between observed and computed 137Cs presented in this latter reference show quite good agreement, which supposes an additional validation of our hydrodynamical model. It is also important to note that modelling the salinity distribution required a simulation study of the dispersion of river water discharges, treated as a conservative substance, as well as the net balance evaporation-precipitation. The result of such a study is presented in Fig. 5,

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'

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t o g e t h e r w i t h t h e e s t i m a t e d river d i s c h a r g e s in k m 3 y - 1 for e a c h c o a s t a l sector. T h e s e d a t a h a v e b e e n u s e d in o u r p r e s e n t c a l c u l a t i o n as s o u r c e t e r m R/.

208

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3.38 54 °

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53'

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3.3. Parameters for source terms and the uertical mouement Experimental studies (McKay et al., 1987) have shown values of some 3000 m y-1 for uS. This quantity, however, should be considered as an upper limit for u s, since the suspended matter studied contained a high fraction of sand grains. Our calculations have revealed that a value of uS = 1000 m y-~ for the whole system of the Irish Sea very well reproduces the available m e a s u r e d values of suspended m a t t e r concentrations.

210

J.M. ABRIL AND M. GARCIA LEON

m (ppm)

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Fig. 6. The suspended matter (1), the dry matter density, am (2), the mean resuspension velocity, v r (3), and the log Pm and log vr against the sea bed composition (di). Information corresponding to samples from the Irish Sea area (Kershaw and Young, 1988).

As for v r and Or,, it can be said, in principle, that these parameters will change from one part of the sea b e d to another, depending on, for instance, the sea b e d composition. F r o m the study of Kershaw and Young (1988), it is possible to evaluate v r from the estimated resuspension rates (kg m -z y-~) and the m e a s u r e d P,, and d i data. The results, plotted in Fig. 6, can help us to analyse v r and Pm" W e plotted m (6.1), Pm (6.2) and v r (6.3) versus d. There does not s e e m to exist a clear correlation b e t w e e n m and d. However, an exponential decay of p,, and v r when d increases is suggested from Fig. 6.2 and 6.3. This d e p e n d e n c e is a little more clear

S U S P E N D E D MA'VFER A ND S E D I M E N T A T I O N PROCESS IN M A R I N E E N V I R O N M E N T

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w h e n a semi-logarithmic scale is used (see Fig. 6.4). Nevertheless, the scarcity of available experimental data does not invite us to explicitly include such d e p e n d e n c e in our model, and so to make it m o r e complex. On the other hand, u r and Pm always appear together in our equations as UrP m. So, we have p r e f e r r e d to keep this product constant over the whole system as a basic approach. This is compatible with the fact that u r and Pm can change separately. The chosen value for urp,,, was 13.2 kg m 2 y-1. Finally, it can be said that an optimum value for a of 2.2 × 10 6 kg km 3 for the whole Irish Sea coast has been used. It was obtained after a calibration exercise which will presented in the next section. 4. RESULTS AND DISCUSSION 4.1. Suspended matter distribution and sedimentary regimes

The steady state distribution of suspended matter in the Irish Sea obtained by solving Eq. 9 during a simulation period of 1 year is presented in Fig. 7a. As expected, higher concentrations of m i appear over the mud banks north of Dublin Bay and on the Cumbrian coasts. As expected also, there are relatively high concentrations of mi along the coasts, which continuously decrease w h e n entering into the open sea. In the same Fig. 7a, the experimental sampling points of Kershaw and Young (1988), are represented as asterisks. The a g r e e m e n t between experimental and calculated data is reasonably good, as is shown with more detail in Fig. 8a. Calculated sedimentation or erosion rates are given in Fig. 7b. Our results reveal that the three m u d banks in the Irish Sea are actually suffering an erosion process in the greater part of their extension. However, this process seems to be slow as confirmed by the low value of w i -- - 0 . 2 5 g cm 2 y-1. In contrast, an also slow process of net accumulation of material is observed along the coast line (wi ~< 0.5 g cm -2 y - l ) . Nevertheless it is important to note that in the same shore line one can find higher values for wi, related to the deposition of material greater than 62.5 tzm in size, which are not considered explicitly in our model. All these results for w confirm the general accepted impression about the sedimentary processes taking place at the Irish Sea. In that sense the conclusions of IOS and M A F F are interesting (Kirby et al., 1983). In such works no evidences were found of net erosion or sedimentation in the mud bank of Cumbria, concluding that the sedimentary regime in this area is relatively stable and dominated by bioturbation processes. We note that our result of a slow erosion process of the two main m u d banks which takes place u n d e r our actual conditions is not contradictory with the existence of the mud banks themselves, since they originated during an earlier geological time (see Section 3.1).

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As far as we know, there are not more published data on suspended load distribution in the Irish Sea. So a more extensive validation of our model results is not possible at the moment. Nevertheless, our model of suspended matter dynamics has been implemented in a more complex model which includes the ionic exchanges of non-conservative substances among the dissolved phase, the suspended matter and the small- and large-fraction matter of the top sea bed sediments. This model has been applied to study the dispersion of the 137Cs and 239+24°pu in the Irish Sea (Abril and Garcla-Ledn, 1993a,b). An extensive validation of this large model is presented in the last two references by comparing observed and computed

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radionuclide distributions in dissolved seawater, top sea bed sediments and total inventory (depth integrated) in sediments. This, from our point of view, can be regarded as an additional validation of our suspended matter dynamics submodel.

4.2. Sensitivity tests W e have explored the changes in the m e a n suspended matter concentrations and in the net deposition when modifying settling and resuspension velocities, doubling and halving the source terms, and also when modifying the b o u n d a r y conditions. The situation will be illustrated by plotting the s u s p e n d e d load and the net deposition rate from the Cumbrian coast to the Irish coast-line along

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the transversal section defined by the four sampling sites marked with asterisks in Fig. 7a. In Figs. 8a and b we plot, respectively, the suspended load and the net deposition against the distance from the Cumbrian coast-line. The continuous line corresponds to our model results by using our selected set of p a r a m e t e r values (Section 3). The dashed line corresponds to a double value of u s and the point-dashed one to a half value for us. W e can see how in the first case the s u s p e n d e d load decreases (it falls more quickly) in such a way that the increase in v s is c o m p e n s a t e d with the decrease of m. This results in no appreciable changes in the net deposition rate. W h e n u s is halved, m is practically doubled and again no appreciable changes in w take place. In both cases the general structure of the suspended load pattern along this transversal section is preserved. In Figs. 9a and b we present the same as in Figs. 8a and b, but now by using a double (dashed line) and a half (point-dashed line) value of u~. In

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J.M. ABRIL AND M. GARCIA LEON

the first case, the resuspension increases noticeabily over the two m u d banks, where the net erosion becomes higher, while no significant changes in w appear elsewhere. Just the opposite effect is observed when v r is halved, and again the general structure of the suspended load pattern is preserved in both cases. In Figs. 10a and b we analyse the effect of using a double value for a (dashed line) and its half value (point-dashed line). In the first case an increase of m and w appears only near the Cumbrian coast-line (and a decrease in the case of a / 2 ) where the advective transport is not too high (see Fig. 3). This effect does not appear in the Irish coasts, since here the advective transport is stronger (see Fig. 3) and the inputs of suspended load are quickly transported towards the North Channel. Finally, it is especially interesting to study the influence of the choice of boundary conditions at St. George's Channel. By using the boundary conditions of Abril and Garcla Le6n (1992), typical values of m i 0.5 p p m are found at St. George's Channel (see Fig. 7a). If we now assume a Dirichlet boundary condition in the Southern border of our grid, it is possible to simulate a hypothetical input of suspended matter from the French or Cantabrian coasts. Such additional input could change, in principle, the whole sedimentary regime in this zone. This calculation has been done by fixing a value of m i 2 p p m in such area. The results appear in Figs. l l a (m i) and b (wi). It can be concluded that such hypothetical input should affect only a small zone in the south of the region, while no apparent changes occur north of Anglesey, which is an additional support for the obtained results in these last regions. =

=

4.3. C o n c l u s i o n s

The water transport model has been widely validated against observed distributions of salinity and 137Cs. The sea bed structure (particle size distribution) is known and, on the other hand, changes in boundary conditions are affecting only a narrow zone close to the boundary itself. Seasonal variations in the suspended matter inputs from land will produce smooth changes in rn and w, but only over a few kilometres near the Cumbrian coasts where advective transport is slow. The two main governing parameters of the suspended matter dynamics are the mean settling and resuspension velocities. Both influence the suspended matter concentrations, but only the second produces some appreciable changes in the net accumulation rate. Values for v r have been obtained from field observations (Kershaw and Young, 1988; Section 3), some of them done far away enough from the Cumbrian coasts. Conse-

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J.M. ABRIL AND M. GARCIA LEON

q u e n t l y , t h e y a r e n o t t o o m u c h a f f e c t e d b y s e a s o n a l c h a n g e s in m a t t e r i n p u t rates. T h e s a m e c a n b e said f o r v s. T h u s , it c a n b e c o n c l u d e d t h a t , even having a preliminary character, the general structure of the mean annually averaged - distributions of suspended matter and net deposition r a t e s o v e r t h e w h o l e I r i s h S e a c a n b e c o n s i d e r e d as t h e b e s t p o s s i b l e e s t i m a t i o n s w i t h t h e a c t u a l a v a i l a b l e field i n f o r m a t i o n . O n t h e o t h e r h a n d , the model predictions on w agree with the general accepted impression a b o u t s e d i m e n t a r y p r o c e s s e s in t h e I r i s h Sea. A n d t h e s e c o m p u t e d distrib u t i o n s o f m a n d w h a v e b e e n u s e d in o u r 2 D - 4 P h a s e s m a r i n e d i s p e r s i o n m o d e l f o r n o n - c o n s e r v a t i v e r a d i o n u c l i d e s w i t h r e a s o n a b l y g o o d results. This supposes an additional support for our present suspended-matter dynamics submodel. REFERENCES Abril, J.M. and Garcla Le6n, M., 1991. A mathematical approach for modelling radionuclide dispersion in the marine environment. J. Environ. Radioact., 13: 39-54. Abril, J.M. and Garcla Le6n, M., 1992. A marine dispersion model for radionuclides and its calibration from non radiological information. J. Environ. Radioact., 16: 127-146. Abril, J.M. and Garcla Le6n, M., 1993a. A 2D-4Phases marine dispersion model for non conservative radionuclides. Part 1: Conceptual and computational mode: J. Environ. Radioact., 20: 71-88. Abril, J.M. and Garcla Le6n, M., 1993b. A 2D-4Phases marine dispersion model for non conservative radionuclides. Part 2: Two application cases, 137Csand 239+24°pudispersion in the Irish Sea. J. Environ. Radioact., 20: 89-115. Backhaus, J.O. and Hainbucher, D., 1987. A finite difference general circulation model for shelf seas and its application to low frequency variability on the North European Shelf. In: J.C.J. Nihoul and B.M. Jamart (Editors), Three-Dimensional Models of Marine and Estuarine Dynamics. Oceanography Series. Elsevier, Amsterdam, pp. 221-244. Belderson, R.H., 1964. Holocene sedimentation in the Western half of the Irish Sea. Marine Geol., 2: 147-163. Bowden, K.F., 1965. Horizontal mixing in the sea due to a shearing current. J. Fluid Mech., 21: 83-95. Guburt, P.A., Kershaw, P.J. and Durance, J.A. 1987. Modelling the distribution of soluble and particle-adsorbed radionuclides in the Irish Sea. In: J.C. Guary, P. Guegueniat and R.J. Penthreath (Editors), Radionuclides. A Tool for Oceanography. Elsevier Appl. Sci. Publ., pp. 395-407. Howorth, J.M. and Kirby, C.R., 1988. Studies of environmental radioactivity in Cumbria. Part 11: Modelling the dispersion of radionuclides in the Irish Sea. AERE, R 11734. Kenosha, P.J. and Young, A., 1988. Scavenging of 234Oh in the Eastern Irish Sea. J. Environ. Radioact., 6: 1-23. Kirk, R. et al., 1983. Sedimentation studies relevant to low-level radiative effluent dispersal in the Irish Sea. Part 3. An evaluation of possible mechanisms for the incorporation of radionuclide into marine sediments. I.O.S. Report 178. Mucky, W.A. et al., 1987. Studies of environmental radioactivity in Cumbria. Part 10: Some radionuclides in near-shore seawater 1980-1984. AERE, R 11912.

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MAFF. Radioactivity in Surface and Coastal Waters of the British Isles. Aquatic Environmental Monitoring Report. Reports from 1970 to 1987. Ministry of Agriculture, Fisheries and Foods, Directorate of Fisheries, Lowestoff, UK. MAFF, 1987. Aquatic Environment Monitoring Report, No. 17. Irish Sea Status Report of the Marine Pollution Monitoring Management Group. M A F F Directorate of Fisheries, Lowestoft, UK. Nihoul, J.C. and Djenidi, S., 1987. Perspective in three-dimensional modelling of the marine system. In: J.f.J. Nihoul and B.M. Janart (Editors), Three-Dimensional Models of Marine and Estuarine Dynamics. Oceanography Series. Elsevier, Amsterdam, pp. 1-33. Pentreath, R.J. et al., 1985. Behaviour of radionuclides released into coastal waters. IAEA-TECDOC-329. I A E A Vienna. Prandle, D., 1984. A modelling study of the mixing of 137Cs in the seas of the European continental shelf. Phil. Trans. R. Soc. Lond. A, 310: 407-436. Ramster, J.W. and Hill, H.W., 1966. Current system in the Northern Irish Sea, Nature, 224: 59-61. Roache, P.J., 1976. Computational Fluid Dynamics. Hermosa, Albuquerque, NM. Roger, T. and Wilson, S., 1974. Caesium-137 as a water movement tracer in the St. George's Channel. Nature, 248: Smith, J. et al., 1980. Sedimentation studies relevant to low-level radioactive effluent dispersal in the Irish Sea. 1. Radionuclides in Marine Sediments. Institute of Oceanographic Sciences Report, 110, 50 pp.