on the possibility of using the commercially available ecos model to simulate cd distribution in the...

EISEVIER Marine Chemistry 58 (1997) 163- 172

On the possibility of using the commercially available ECoS model to simulate Cd distribution in the Gironde estuary (France)

M.K. Pham a, J.M. Martin a3 * , J.-M. Garnier a, Z. Li a, B. Boutier b, J.F. Chiffoleau b a Institut de Biogiochimie Marine URA CNRS 386, Ecole Normale Supe’rieure, I, rue Maurice Amoux, 92120 Montrouge, Frunce

b Lahoratoire de Chimie des Contaminants, Unite’ de Recherches Marines No. 6, IFREMER, Centre de Names, Nantes, France

Accepted 7 April 1997

Abstract

The ECoS model (estuarine contaminant simulator) from Plymouth Marine Laboratory (UK) was used to simulate the distribution of salinity, turbidity and cadmium (Cd) contaminant in the Gironde estuary (France). The Cd distribution (local dissolved concentration and location of the maximum) in this mixing zone during different seasons is well described by this 1D model which can be used to predict the Cd distribution along the estuary and to estimate the residence time of this contaminant in this estuary. 0 1997 Elsevier Science B.V.

1. Introduction

The progress achieved in the understanding of estuarine processes allowed the development of vari-

ous numerical models to predict the distribution of conservative elements such as salinity and in some

cases of suspended sediments.

In the present state of knowledge, it is possible to

implement 2D and 3D numerical models to simulate the hydrodynamics of macrotidal estuaries. The coupling of such models with chemical models is badly

needed to improve our capacity for forecasting the

distribution and the effects of pollutants discharged into the coastal zone.

However, due to a lack of knowledge of the kinetics of the main reactions controlling the distribution in estuarine systems of major pollutants, both

* Corresponding author. Present address: Joint Research Center,

European Commission, Environment Institute, I-21020. Italy.

organic and inorganic and to practical difficulties to validate such kinds of coupled chemical/dynamical numerical models, most estuarine chemists consider

that simple models such as box models (Officer, 1980) and 1D models are presently the most appro-

priate.

With this perspective, several models have been developed, some of them such as ECoS (commer-

cially available as ID model) aim to simulate the

distribution of contaminants in a theoretical estuary. The simulated estuary has a rectangular cross-section

which increases exponentially in the seawards direc- tion. Its bed is covered by a layer of mobile sedi-

ment. Particles, some of which are exchanged with bottom material, are suspended in the water-column. Contaminants within the estuary may be transported either dissolved or attached to suspended particles or trapped with the bottom sediment.

The aim of this work is to test the applicability of this simple model to a natural system: the Gironde

0304-4203/97/$17.00 0 1997 Elsevier Science B.V. All rights reserved. PI1 SO304-4203(97)00032-7

164 M.K. Pham et d/Marine Chemistry 58 (1997) 163-172

estuary (France). Initially, the profile of salinity calculated from the Cl- concentration (known to be a conservative element) and of turbidity in this estuary have been simulated by the model for different sea-

sons. Subsequently, Cd which has been shown to be

a major trace metal contaminant of this estuary (Elbaz-Poulichet et al., 1982, 1987) and is character-

ized by a non-conservative estuarine behaviour has

been selected for simulation.

2. The Gironde estuary

The Gironde estuary (Fig. 1) is located between

the French Atlantic coast (Bay of Biscay) and its two tributaries: the Garonne and the Dordogne rivers. Its

total surface from the inlet at Royan to the upper limit of the tidal intrusion (170 km landward) is 560

km* including well-developed inter-tidal areas and a

few sand-bars and islands.

The average fresh-water discharge from the Garonne and Dordogne rivers is 2.4 X 10” m3/year

with the annually-averaged river discharge (1961-

1970) amounts to 760 m3/s (Jouanneau and La- touche, 1981). Seasonal variations may significantly bias this mean value and greatly affect the estuarine

regime: the average monthly discharge varies from 200 m’/s during low water to 2200 m3/s during

flood periods. The time required to replace the fresh-water of the estuary is equal to 20 days in

flood and 86 days during the low water (for average

tidal conditions). The tide at the inlet is semi-diurnal and its ampli-

tude ranges from 2.5 m to 4.9 m. In this macrotidal estuary, the tidal processes strongly influence water

mixing (Allen et al., 1980). The fluctuating limit of saline intrusion (defined by the 0.1 g/l Cl isopleth)

is located 40 km upstream the inlet during flood, 100 km or more during low water.

The average solid discharge of the Garonne and Dordogne rivers which flow into the Gironde estuary are 1.5 X lo6 and 0.7 X lo6 tons/year, respectively. This suspended matter is accumulated in the ‘turbid-

ity maximum’ in the middle part of the estuary where the concentration may reach 10 g/l or more in the bottom water. This is a permanent feature with a longitudinal extension of turbidity maximum reaching usually several tens of kilometres. The turbidity

Fig. 1. The Gironde estuary (France). PK: downstream distance

from Bordeaux (km).

maximum is well developed in the saline waters and

can also reach the fresh water zone. During periods of high river discharge, strong

fluvial advection reduces the effect of flood tides in

the upper estuary and pushes the tidal limit downstream. On average, IO6 tons/year escape to the

turbidity maximum and may reach the sea. During periods of low river discharge, a well-developed

turbidity maximum is still maintained. Density gradi-

ents and circulation are reduced in the estuary, which is well mixed and tidal transport plays a more important role acting to trap resuspended sediment at the

null residual velocity point. It appears, therefore, that resuspension processes dominate the trapping processes during high river flow while tidal processes dominate during periods of low river flow. In the former case, the turbidity maximum is limited to the PKSO while in the latter, it extends upstream to the

PK40 (Allen, 1973). As far as chemical elements are concerned, the

estuary is polluted by Cd originating from a mining

M.K. Phmn et al./Marine Chemistry 58 (1997) 163-172 165

area which was still operating in 1987 (Cossa and

Lassus, 1989). The river concentration of dissolved Cd contaminant varies between 4 nM in the winter and 3 nM in the summer (Boutier et al., 1989).

Cd is transported from the drainage basin to the

Gironde estuary mainly in particulate form: 23 tons per year, against approximately 2 tons as dissolved

form. Conversely Cd is introduced into the ocean

predominantly in the dissolved form (20 tons/year). Therefore in the estuary a mechanism is controlling

the yearly mobilization of about 20 tons. The most accepted explanation of this phenomenon is the parti-

tion of Cd between the dissolved and particulate phases through heterogeneous complexation reac-

tions (Comans and van Dijk, 1988; Turner et al.,

1993). Cl- and (to a lower extent) SO:- are the

most efficient dissolved inorganic ligands for Cd*+

complexation in sea water (Long and Angino, 1977; Gamier et al., 1996). They become more and more

concentrated seaward and compete more and more strongly with surface particulate sites for Cd’+. This

results in an increase of dissolved Cd in the low salinity part of the mixing zone. After reaching a

maximum for a salinity of 15-20%0 in the Gironde,

the dissolved Cd concentrations decrease by simple dilution.

3. The ECoS model

The main characteristics of ECoS are summarised below:

ECoS requires data which describe both the phys- ical conditions of the estuary and the local chemistry

of the contaminants. The length of the estuary (100 km from Bordeaux to the mouth) is divided longitu-

dinally into 25 equal-length segments. Its cross-sec-

tion area increases exponentially seawards (Allen,

1973). Within each box the water-column and the bottom sediment are assumed to be perfectly mixed.

ECoS determines tidally-averaged movements of ma-

terial between these segments and between the water-column and the bottom. The movements of water and materials are represented as two separate components: advection (flow) and dispersion (mixing). These components are combined additively: ECoS represents these processes using an implicit numeri-

cal scheme designed after Richtmyer and Morton

(1967). The advective component represents the average

transport of material (water or suspended particles). For example, the permanently suspended particles

(turbidity) are assumed to move exactly as the water

and dissolved materials (ECoS, 199 1). The turbidity of river water entering an estuary frequently in-

creases with river discharge. Such an increase might

be allowed for by setting:

Pf=a*Qb

where Pf is the turbidity of river water (g/l), Q is the river discharge (m3/s) and a and b are regres-

sion correlation coefficients obtained from actual

data. In the case of tidal intrusion, the distribution of

turbidity or contaminant will be influenced by tidal

range.

For average flow conditions, the dispersive component embodies the stirring and the mixing pro-

cesses of the estuary. This process is defined by three different dispersive coefficients:

(i) The water dispersive coefficient K, (m2/s> reflects the water mixing due to the tidal action and

the fresh water discharge. K, can be expressed as a

function of salinity, river water flow and tidal range as follows:

K,=c+(dxUxSxR)

where U is the net water velocity (m/s), S is the

salinity (o/00), R is the tidal range (m) and c and d are regression correlation coefficients obtained from

actual data. For the Gironde estuary K, is about

250-400 m2/s. Due to numerical dispersion caused by the discrete nature of the estuarine segments, simulated dispersion is somewhat higher than that

indicated by this coefficient. We have observed that

this effect can be reduced by increasing the number of estuary segments.

(ii) The dispersive coefficient of bed exchange-

able particles (BEP) K, (m2/s> reflects the dispersion of these particles in the water-column. This

dispersive effect increases linearly with both fresh water velocity and tidal range (ECoS, 1991). K, influences horizontally the extension of the turbidity maximum. Fig. 2 shows the effect of K, calibrated with different parameters for different days of simulation.

166 M.K. Pham et al./Marine Chemistry 58 (1997) 163-172

COtIlL Turbidity (gil)

' X l.EtOO

50 PK 100km

Turbidity (g/l) b)

' X l.EtOO

0 50 PK IOOkm

Fig. 2. Extension and evolution of the turbidity maximum for the

Gironde estuary [simulated with different calibration parameters:

(a) small K,; (b) low Kpl. Solid line: 15 days simulation, dotted

line: 75 days simulation.

(iii) The dispersion of bed material K, (m’/s> is assumed to occur over a constant 1 m layer of mobile sediment. It can thus be expressed in analo- gous way to that of BEP dispersion (ECoS, 1991).

As far as the chemistry of contaminants is concerned, it is assumed that suspended particles adsorb dissolved contaminants and that this process is fast enough to achieve an equilibrium between the adsorbed and dissolved phases. This equilibrium is characterized by a partition coefficient K, (kg 1-l > which is defined as the ratio between the concentration of contaminant on the particles to its dissolved concentration in the water column.

Particulate bed material which is occasionally resuspended in the water-column, constitutes a reser- voir of mobile sediment within the estuary. It is assumed that there is no net transport of particles from the bottom to the water-column or vice versa, but these particles are exchanged between these two reservoirs at a rate determined by one exchange coefficient Ex (kg/m2/s>. In the model, this coefficient is defined as an alometric function of the concentration of suspended particles:

As described above, there is a proportion of Cd adsorbed on particles desorbing when the activity of chloride and sulfate becomes sufficient and hence its particle-water partition coefficient K, declines rapidly as the salinity increases (Salomons, 1980). In the Gironde estuary, K, is well described by a simple power function such as:

K,=K,X(S+ 1)”

where K, is the particle-water partition coefficient in river water and k is a negative constant to show that K, is a decreasing function of salinity S.

Ex = m X PE”

where PE is particulate suspended concentration (g/l) and m is the sinking rate of BEP (m/s> which is about 0.001 m/s (ECoS, 1991). If n = 1, the exchange is directly proportional to BEP concentration Ex is generally found to increase with increasing particulate concentrations and can be modelled by setting IZ greater than one.

Using data of dissolved and particulate Cd (Bou- tier et al., 1989), we have computed the regression of log( Kd) as a function of salinity to obtain the values of K, = 67.5 l/g and k = - 1.3 with a coefficient of regression R2 = 0.82 (Pham, 1993). By coupling this chemical parameter with the physico- and hydro-dynamical conditions calibrated for the model in the Gironde estuary, we attempted to simulate the evolution of Cd in different phases (dissolved, suspended and sediment) in this estuary.

Fresh water input can be introduced into each It should be noted that K, is a useful parameter estuarine segment. For the Gironde estuary, an an- to describe the processes of physicochemical adsorp-

nual geometric mean of river water discharge (Q = 700 m3/s> is introduced at the first segment. Both seasonal and daily variations can be simulated. ECoS superimposes these variations on the mean fresh water discharge specified above by entering two other parameters: one for seasonal variation which is determined by the ratio between the river water discharge in mid-winter (2200 m3/s) and in mid- summer (200 m3/s> (ratio r = 11) and one for daily variation which is determined by the value of the standard deviation of log ,a Q ( = 0.31, which corresponds approximately to a range of Q/3 to Q * 3. This means that if the geometric mean at a particular time of the year is Q, = 300 m3/s, the daily cycle will lie between 100 and 900 m3/s.

M.K. Phan et al./Marine Chemistry 58 (1997) 163-172 167

tion/desorption of Cd following the saline gradient along the Gironde estuary since in this estuary, almost all particulate Cd is mobilizable i.e. the residual fraction of particulate Cd is small. If this was not the case, it would be necessary to take it into account

in the model. Like the movements of water and materials from

which they are derived, the concentrations of Cd in

different phases which are calculated by the model should be considered tidally averaged.

4. Results and discussion

4. I. Salinity

The salinity variation of an estuary depends on

three parameters: tidal cycle, tidal range and river water discharge.

4.1.1. Salinity and its variation in the Gironde estu-

ary during one tidal cycle

The field data show one maximum of salinity in

the flood period and one minimum during the ebb period. The variation of salinity in the navigation channel at the beginning of the flood period for a mean tidal coefficient shows a marked asymmetry of

the saline curve during one tidal cycle (Allen, 1973). This phenomenon is not considered in the model.

4. I .2. The salt intrusion as function of tidal range

The volume of saline water input during the flood period changes according to the tidal coefficients.

This also determines the variation of salinity (some

unities per thousand only) at a given point in the Gironde estuary and the saline intrusion is maximum when the tidal coefficient reaches its maximum (Al- len, 1973). Fig. 3 shows the longitudinal profiles of

salinity obtained from the model for different tidal coefficients applied for one lunar month in winter

(on the right) and in summer (on the left). The observed change of saline intrusion is well repro-

duced by the model. Indeed, when the coefficient is maximum (spring tide) the saline intrusion moves

up-stream (solid line) and when the tidal coefficient

is minimum (neap tide), it shifts seawards (dotted line). The calculated distance between these two extremes is about 4 km. It is in good agreement with

the observed data (5 km between spring tide and neap tide).

4.1.3. The variation of salinity as a function of the

fresh water discharge

Fig. 4 shows the longitudinal profiles of salinity

for different seasons in the Gironde estuary. It should

be noted that during the period of high water discharge, this longitudinal gradient of saline intrusion

(dotted line: 13 May 1969) is transferred downstream (until PK90) and during the period of low fresh water discharge, this gradient (solid line with three points: 15 September 196 1) is shifted to the

river-end at Bet d’Amb& (PK20) (Allen, 1973).

This phenomenon is clearly reproduced by the model (Fig. 3) which corresponds to low and high river

discharge, respectively. It reproduces the drastic changes in the salinity gradient along the estuary and

COIN. Salinity(C) COW. Salinity(%)

t.0 - l.O-

X 5.EtOl x 5.EtOl

0 50 100 km 0 50 PK 100km

Fig. 3. Simulated axial distribution of salinity for different tidal ranges (solid line: spring tide, dotted line: neap tide) and for different

seasons (on the left: low river discharge, on the right: high river discharge) in the Gironde estuary.

168 M.K. Pham eral./Marine Chemistry 58 (1997) 163-172

Bee d’Ambcs PdllSX Lameno Mortagne TYlm0d

---27June ,968 - 8 Jomta,y~ 1969 Begin ol/IOod

Begin ebb- end offlood -----2~.-lprd1968 ..‘..... ,3.Wa,‘l969 Flood

-. I . ISSeprember 1961 Ebbpnrod F b<,m,m s wfoer

Fig. 4. Evolution of the average surface and bottom salinity of the Gironde estuary for different river discharges (by average tide) (reprint

from Allen, 1973). (F) bottom, (S) surface. (a), (b), (c) stand for ebb period, flood period and intermediate flow discharge, respectively.

the transfer of the saline intrusion corresponding to different regimes of river water discharge. When the

river discharge reaches its maximum (about 2200 m3/s> the saline intrusion is flushed towards the

mouth (PK90). Conversely, during the season of

minimum fresh water discharge (about 200 m3/s> the saline water invades the estuary until PK20. We

have also compared the values of salinity at several

points obtained from the ECoS model with the measured data for different hydrodynamical conditions

(at PK20 and PK70 for low river discharge and at PK45 for high river discharge). This comparison shows a good agreement (Table 1).

Table 1

The comparison of salinity values given by the model and ob-

served data for different hydrodynamical conditions

Kilometer

point

(km)

20

45

70

Salinity

given by

model (%o)

2.27

0.1

1.57-7.7

Observed

salinity (%o)

2.0 a

0.2 a

1.6-7 a

a Bout& et al. (1989).

4.2. Turbidity

As for salinity, the turbidity maximum formation

of an estuary depends also on three parameters: tidal

cycle, tidal range and river discharge.

4.2.1. Turbidity variation during one tidal cycle

The Gironde estuary is strongly characterized by

asymmetrical tidal currents in which flood currents exceed ebb currents. The stronger flood current ve-

locity enhances the resuspension of bottom sediment which is subsequently transported into the estuary. Ebb currents produce less resuspension and less transported sediment. The residual transport is then

directed landwards (Dyer, 1978). This process pro- vokes a temporal increase of turbidity during spring

tides. In the short term, this phenomenon seems to play an important role in the variation of turbidity. Unfortunately, the structure of ECoS cannot repro-

duce these variations.

4.2.2. Erosion and resuspension processes associ-

ated with the tidal range Fig. 5 shows the profiles of turbidity obtained

from the model for different tidal coefficients. The

M.K. Pham et al./Marine Chemistry 58 (19971 163-172

Cone. Turbidity (g/l) Cone. Turbidity (g/l)

1OOkm o PK 100

Fig. 5. Simulated turbidity profile for different tidal ranges (dotted line: spring tide, solid line: neap tide) and for different seasons (on the

left: low river discharge, on the right: high river discharge) in the Gironde estuary.

169

dotted line corresponds to the maximum tidal range (4.9 m) and the solid line corresponds to the mini-

mum tidal range (2.5 m). When simulating a sinu-

soidal cycle between spring and neap tides and as- suming a 29.52 day lunar month, we observe that

when the tide reaches its maximum, the erosion and resuspension of sediments reach their maximum value (dotted line) and the maximum of turbidity shifts

landwards. This is in good agreement with observa-

tion. The resuspension phenomenon called ‘tidal pumping’ of sediment occurring during spring tides

would provide a mechanism for the production or

enhancement of the turbidity maximum in the upper estuary (Uncles et al., 1985). Conversely, during

neap tides, there is a deposition of sediment and the

smaller maximum of turbidity moves seawards (solid

line).

4.2.3. Variation of turbidity due to river water dis-

charge

The model has also been used to investigate the possible effects of a river flood upon the formation

of the turbidity maximum and on the sediment fluxes.

Erosion is primarily the result of large currents pro-

duced by the river water discharge. For a river water discharge of 700 m3/s or more (Fig. 6b), the resid-

ual fluxes of suspended sediment are directed sea-

wards throughout the whole estuary. A turbidity maximum persists in the lower estuary because of

currents and therefore, resuspension is maximal in

2Okm Bordeaux 4Okm I 8Okm I

I I I I I I I

Fig. 6. Synthetical diagram showing the evolution of the turbidity, salt intrusion and residual circulation in the navigation channel of the

Gironde estuary (reprint from Allen, 1973).

170 M.K. Pham et al./Marine Chemistry 58 (1997) 163-172

this area. For these hydrodynamical conditions, the

ECoS model gives a turbidity of 700 mg/l located at PK70 which is in reasonable agreement with a mea-

sured average of 500 mg/l located at the same PK.

Finally, if the model is run for neap tides during low river water discharge, the ECoS model gives a turbidity of 1470 mg/l located at PK25 which is in

good agreement with a measured average of 1400

mg/l located at the same PK (Fig. 6a). This maximum results from the maximum velocity of neap

tidal currents in this area.

Furthermore, the movement of the turbidity maximum for different seasons is especially well repro-

duced as shown Fig. 5. In winter, when the total river water discharge <Q> is about 2000 m3/s, the

turbidity maximum is lower and is flushed to the ocean. In the summer, when Q is about 200 m3/s, it becomes stronger and extends riverwards. When we

simulate the turbidity profile from the beginning of

winter to the beginning of summer we observed a

deplacement of the turbidity maximum along the estuary as shown Fig. 2. Finally, the model has

computed a year averaged solid mass of suspended matter (1.67 X lo6 ton), a value in agreement with

the observation (2 X lo6 ton) (Allen, 1973).

4.3. Simulation of the Cd distribution

ECoS has been shown to describe well the distri-

bution and the evolution of salinity and turbidity

transport in the Gironde estuary. We further attempted to use this model to simulate the distribution

of Cd which has long been known to represent one

of the critical contaminants in this region (Boutier et

al., 1989). In winter, when the fresh water runoff is maxi-

mum, the Cd coming from the river in the particulate

form is transported by water current towards the sea.

In the mixing region, desorption of Cd*+ to the solution phase occurs. This mechanism will generate one maximum of dissolved Cd wherever the axial saline gradient is the strongest. Fig. 7a and c shows the dissolved Cd distribution versus salinity obtained from the model (solid line) as compared to the actual data (dots). The model reproduces fairly well the actual distribution of actual dissolved Cd in winter in different years.

Fig. 7. Distribution of dissolved Cd (a) in winter 1989, (b) in

summer 1991, (c) in winter 1994. Solid line: simulated profile.

Dots: 1989 data (from Boutier et al., 19891, 1991 data (Boutier

pers. corn. in 1993) and our data in 1994.

During the summer, when the river discharge is minimum, the estuary is invaded by salt water. The axial salt gradient is shifted upstream. The region of desorption of Cd*+ is thus transfered upstream. Fig. 7b shows the Cd distribution simulation (solid line) as compared with observation (dots). The maximum of dissolved Cd is obtained for a salinity range of 15-20%0 and then decreases by dilution of Cd with sea water.

We have also compared the actual Cd concentration in suspended matter and sediment phases with

M.K. Pham et al. /Marine Chemistry 58 (1997) 163-172 171

Table 2

The comparison of Cd concentration given by the model and data

Form Salinity Cd given Measured

of Cd (%a) by model Cd

Dissolved 17.2 3.24 nM 3.62 nM a

In suspended matter 29.05 2 cLg/g 1.6 cLg/g a In sediment 35 0.2 I.Lg/g 0.2 pg/g b

a Boutier et al. (19891.

’ Salomons and Fdrstner (1984).

the results obtained from the ECoS simulation (Table 2). Both suspended matter and sediment calculated

Cd concentration are similar to actual data. We attempted to use this model in a predictive

way. For example, for an instantaneous input of 10

kg of Cd at Bordeaux, what would be the concentration of dissolved Cd after its release into the Gironde

estuary? For a winter river flow rate of 2000 m3/s,

180 days after input (i.e. the following summer) the model computes a maximum of dissolved Cd equal

to 460 mM at PK60. Two years later, the level of Cd

contaminant in this estuary returns to normal i.e. of the order of 2.84-3.21 nM in the salinity range of 1520%0. This simulation gives one estimate of the ‘residence time’ of Cd contaminant in this estuary.

This value is in agreement with the renewal time of suspended matter (l-2 years) in the Gironde estuary

(Martin et al., 1986).

5. Conclusion

5.1. Advantages of the model

ECoS is a practical model which is able to recon-

struct the distribution of salinity, turbidity and their evolution as a function of river water discharge and

tidal range, as well as the deposition and the resuspension of sediment in the mobile sediment layer.

As for contaminants, the distribution of Cd con-

centration between different phases is well described by the model. The coupling of hydro-dynamical data with the chemical behaviour of Cd simulates the actual mobilization process of this element and the local concentrations according to the season in the Gironde estuary. The model allows also to estimate

the “residence” time of trace metal after an acciden-

tal input in the estuary. The time for a single simulation of one seasonal

cycle (from the beginning of winter to the beginning

of summer) is approximately 8 min on a PC 486.

The variation of these parameters for different seasons in this estuary can thus be quickly visualized

with this model.

5.2. Limitations of the model

Shape of estuary: ECoS requires an ideal rectan-

gular shape of estuary. The tidal cycle: the variation of salinity and tur-

bidity with the tidal cycle was not taken into account

in the model. K, problem: the K, required for simulation as

measured includes both residual and labile particulate fractions of trace metals. The ‘true’ K, should

only take into account the labile fraction. Good results are obtained if the labile fraction predomi-

nates (as in the case for Cd). The application to other

trace metals with a small labile fraction remains questionable.

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on the possibility of using the commercially available ecos model to simulate cd distribution in the...

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