Table des matières
Les sédiments contaminés peuvent constituer une source de contaminants pour la colonne d’eau ainsi que pour la faune benthique qui vit et se nourrit des sédiments de surface. Ces organismes représentent un vecteur de contamination pour l’environnement puisqu’ils peuvent accumuler les composants toxiques contenus dans les sédiments et les transmettre aux organismes supérieurs à travers la chaîne alimentaire. La mise en place d’une couche de recouvrement composée de matériaux propres réduit et dans le meilleur des cas élimine le risque associé à la présence de contaminants dans les sédiments. Une couche de recouvrement constitue une barrière physique qui isole les contaminants de la colonne d’eau et de la faune. Le design d’une telle couche doit tenir compte des facteurs physiques, chimiques et biologiques qui affectent la migration de contaminant et qui déterminent son efficacité à long terme. Lorsque ces facteurs sont caractérisés par une variabilité ou une incertitude importante, la conception de la couche peut être faite à l'aide de l’analyse de décision. Cette méthode considère l’incertitude et compare les différentes alternatives de recouvrement sur la base des coûts et des risques ainsi que par rapport à l'objectif technique du projet. L'approche a été appliquée ici à un projet de réhabilitation hypothétique, afin de trouver l’épaisseur idéale pour une couche qui recouvrerait un secteur contaminé qui est fréquenté régulièrement par la population de bélugas de l’estuaire du Saint Laurent. Afin de déterminer la probabilité de succès des différentes options, nous avons réalisé des simulations Monte Carlo avec un modèle numérique représentant la migration de contaminants dissous à travers une couche de recouvrement et par la suite nous avons intégré l'aspect économique. Les résultats montrent que le coût total du projet dépend du coût d’échec, un paramètre difficile à évaluer. Néanmoins, l’analyse de décision s'est avéré une méthode efficace et utile pour identifier le design optimal.
Contaminated sediments represent a potential source of contaminants for the water column and for the benthic fauna. These sedimentfeeding organisms act as a contamination vector for the environment, because they accumulate toxic compounds and transmit them to higher level organisms through the food chain. Capping contaminated sediments with a clean layer can reduce or eliminate the risks of contaminant release to the environment. The cap represents a physical barrier that isolates the contaminants from the water column and from the fauna and its effectiveness depends upon its physical, chemical and biological characteristics, which are spatially variable and imperfectly known. Decision analysis is a method that accounts for uncertainty in engineering design to compare different alternatives considering the costs and risks associated to each management option. In this paper, we illustrate the application of the decision analysis approach for the design of a capping layer in a hypothetical remediation project, loosely based on a real situation. The decision analysis includes the risks related to the exposition of the St. Lawrence beluga population to contaminated sediments. In order to determine the probability of success of each management option, we performed Monte Carlo simulations using a numerical model that represents the migration of dissolved contaminants through a capping layer and thereafter we included the economical aspect. The result of the decision analysis shows that the total cost of the project depends on the cost of failure, a parameter that is difficult to estimate. Nevertheless, decision analysis has proven to be an effective and useful method to identify the optimal design.
Environmental engineers have to face uncertainty arising from the incomplete knowledge of natural environments when designing operational systems to prevent or reduce contamination. For example, the planning of wastecontainment facilities, remediation of contaminated soil or ground water and dewatering systems requires choosing the best option among a series of possible management alternatives. In this paper, we examine the design of a protective capping layer to isolate contaminated sediments from the water column. Given the complex geometry and interactions of natural systems, engineers have to rely on the results of numerical models to predict the effectiveness of management options. Unfortunately, due to the elevated costs associated with field investigation, the information concerning the input parameters and their spatial distribution is usually incomplete. The input values have therefore to be estimated and simulations are performed under conditions of uncertainty, implying that there is a probability, or risk, that the predicted value will not correspond to the true response of the system. If uncertainty is neglected and the management option is chosen uniquely from deterministic simulations, the reliability of the prediction remains unknown.
Decision analysis takes into account uncertainty when establishing the risk that a management option will fail to achieve the technical objective imposed by the project. The method calculates the total costs and benefits of each management option and transforms the results of the numerical model into an economic value. Thus, the decisionmaker can compare the design alternatives on an economical basis, and choose the design that meets the technical target, maximizing benefits and minimizing the costs of the project.
Freeze et al. (1990) clearly illustrated the advantages of the application of decision analysis to engineering design concerned with uncertainty in hydrogeological parameters. The authors developed a general framework that combines three types of models: a decision model, a numerical model and an uncertainty model (Figure 4.1). The decision model compares the costs, benefits and risks associated to each design alternative. The numerical model, for example a groundwater model, is utilized in a stochastic mode to calculate the expected performance of the system and particularly the probability of failure, which is a component of the risk factor used in the decision model. The uncertainty model describes the distribution of the system parameters, used as input values for the stochastic simulations, and is based on the data collected during field investigation. Freeze et al. (1990) illustrated the decision analysis framework by means of a hypothetical project involving the design of a containment facility at a new landfill. The usefulness and versatility of the methodology was further illustrated by applications to groundwater contamination (Massmann et al. 1991), open pit mine design (Sperling et al. 1992) and hydraulic leachate containment design (Lepage et al. 1999). The methodology was also applied to sediment remediation, for the design of the optimal sediment volume to be dredged in a contaminated area (Dakins et al. 1994).
Decision analysis is usually preceded by sensitivity and uncertainty analyses (Figure 4.2). The sensitivity analysis compares the output of a numerical model for minimum and maximum values of input parameters. A limited number of simulations is performed to identify the input parameters that show the most important effect on the response of the model. The parameters are further investigated in the uncertainty analysis, which computes the effect of the global parameter uncertainty on the response of the model. The input values are represented by their probability density function PDF. A Monte Carlo analysis is then performed, where a large number of simulations are conducted with randomly sampled PDFs, to get a representative probability distribution of the response (an example of the output PDF for mass flux is shown in Figure 4.2). The resulting distribution is used for the decision analysis, which provides a link between uncertainty analysis and the economic framework of a management decision.
In this paper, we present the application of the decision analysis method to choose the optimal design of a hypothetical capping layer. The capping of contaminated sediments with clean material is a promising alternative for the isolation of contaminants from the water column and the prevention of the transfer of pollution through the ecosystem. This approach has the advantage of being effective and lowcost compared to other management options that require removal and exsitu treatment of sediments and it is applicable to large contaminated surfaces. A capping layer is designed to physically isolate the contaminants from the benthic fauna, stabilize the sediments and prevent or at least reduce the contaminant flux towards the new watersediment interface.
The objective of the study is to illustrate the advantages of combining the numerical model TRANSCAP1D with the decision analysis method. The numerical model simulates the migration of dissolved contaminants through a subaqueous capping layer, accounting for advection, diffusion and bioirrigation (Dueri et al. in press). The model was calibrated with concentration profiles of arsenic measured in the sediments of the Baie des Ha! Ha! and the Bras Nord, located in the upstream area of the Saguenay Fjord, where a major flood led to the deposition of a natural capping layer over contaminated sediments (Figure 4.3). Since the catastrophic flood, which occurred in 1996, the geotechnical and geochemical characteristics of the capping layer, as well as the recolonisation of the benthic fauna, have been extensively studied in the context of a multidisciplinary research project (Pelletier et al. 1999, Mucci et al. 2000a, Pelletier et al. 2003, Mucci et al. 2003). The collected information was used for a detailed sensitivity analysis, to assess the effect of variable input parameters on the mobility of dissolved contaminants that migrate through the capping layer (Dueri and Therrien 2003). The sensitivity analysis was performed for both nonreactive and reactive contaminants, where "reactive" means that in the anoxic sediment the compound is associated to sulfides and that it can be remobilized if exposed to oxygenated water. This mechanism was observed for arsenic, but it could affect other trace metals associated with sulfides, like Ni, Cu, Co, Hg, Pb. However, compared to As, these trace metals are probably less mobile than As, since they are more likely associated to less reactive phases (e.g. organic matter). The sensitivity analysis tested five factors: the depth of bioirrigated tubes, the quantity and dimensions of bioirrigated tubes per square meters, the bioirrigation velocity, the retardation factor and the dissolution coefficient. The results showed that the effect of each factor on the response of the model depends on the reactivity of the contaminant and on the considered response.
In the present study, we want to exploit the knowledge gained using the data collected at the Baie des Ha! Ha! and Bras Nord area, by applying it to another area of the Saguenay Fjord, near Baie SteCatherine (Figure 4.3), where similar grain size distribution and benthic fauna are found (Héroux 2000). The previous studies on the capping layer deposited in the Baie des Ha! Ha! and Bras Nord showed that the finegrained cap with an average thickness of 0.2 m is effective in isolating inorganic contaminants from the water column (Mucci et al. 2003). The deposition of that cap was the result of a natural event, therefore free of charge. Conversely, the design of a new capping layer for the remediation of a contaminated area requires consideration of costs and risks associated with the different options. Thus, it is useful to apply the decision analysis approach for the design.
The present decision analysis considers two capping materials: a finegrained cap (similar to the natural cap) and a more sandy cap. The analysis evaluates the total costs for different values of cap thickness. The hypothetical capping layer should cover an area that hosts the southernmost population of belugas. Since whale watching is an important tourist attraction of the region, the contamination of the beluga population could cause significant economical losses. The analysis presented here aims at illustrating the decision analysis with its advantages and limitations and should be considered with care for any actual decision on the remediation of contaminated sediments of the Saguenay Fjord or their impact on the beluga population.
Because decision analysis compares a finite number of different design alternatives defined by the project managers, it does not apply to cases where a possibly infinite number of designs are to be evaluated. The different options are compared using a riskcostbenefit objective function (Freeze et al. 1990), which is expressed in monetary value and incorporates the technical and the economical objective of the project. The technical objective of a remediation project is to meet the regulatory standard imposed by environmental laws, whereas the economical objective is to minimize the costs and maximize the benefits of the project. The objective function includes the costs, benefits and risk of failure for a given management option j, over a specified time horizon and accounting for the interest rate. The objective function is represented by the equation:
(4.1)
where Φj is the objective function for management option j [$], T is the time horizon [a], i is the discount rate [decimal fraction], Bj(t) is the benefit of option j in year t [$], Cj(t) is the cost of option j in year t [$] and Rj(t) is the risk of option j in year t [$].
The costs associated to the risk factor are calculated by multiplying the cost of failure with the probability that the management option does not meet the technical objective and are described by the following equation:
(4.2)
where Pf(t) is the probability of failure in year t [decimal fraction] and Cf(t) is the cost associated with failure in year t [$].
In the case studied here, the probability of failure associated with different values of capping thickness can be calculated from the output distributions of stochastic simulations, provided by the uncertainty analysis. Given a normal distribution, the probability of failure can be graphically represented as the part of the distribution exceeding a specific limit, defined as the nonattainment of the technical objective of the project (Figure 4.4).
In our example, we simulate the contaminant migration over a time limited to 10 years and the time dependencies of the equation (4.2) are therefore assumed to be negligible. Moreover, we assume that there are no direct benefits associated with the remediation of the contaminated sediments of the study site. The example assumes that the government would accept to meet the cost for remediation to preserve this very sensitive and particular ecosystem and to prevent economical losses associated to the persistence of diseases in the beluga population. Combining equation (4.1) and (4.2), the objective function becomes:
(4.3)
Several studies have documented the distribution of contaminants in water (Gobeil and Cossa 1984, Tremblay et Gobeil 1990) and in sediments (Barbeau and al. 1981, Pelletier and Canuel 1988, Gagnon and al. 1993, Cossa 1990, Coakley and Poulton 1993, Muris 2001) of the Saguenay Fjord and the St. Lawrence Estuary. The presence of trace metals (Hg, Pb, Zn, Cd) and organic compounds (PAH, DDT, PCB) are related to the industrial and agricultural activities located in the region. At the beginning of the 20th century, the tributaries of the Saguenay Fjord and the St. Lawrence Estuary started to carry the effluents from a highly industrialized area. However, after the introduction of environmental regulations in the 1970s, the industrial discharge of pollutants was markedly reduced. Although regulations lead to an improvement of water quality, the sediments of the Saguenay fjord and the St Lawrence estuary still store large amounts of contaminants and represent a risk for the environment.
The Saguenay Fjord and the St. Lawrence Estuary represent a very sensitive ecosystem, because they are inhabited by the world's southernmost population of belugas. This population is isolated from other beluga populations, located in the Arctic, and is exceptional for its accessibility for public viewing and research. Unfortunately, due to the past hunting activity, the beluga population is now only 500600 individuals and is classified as an endangered species by the Committee on the Status of Endangered Wildlife in Canada. Despite hunting prohibition since the end of the 1970’s, the population has not recovered. The main causes of this failure are the deterioration of their habitat caused by contamination, the disturbance by recreational and commercial traffic and the low genetic variability (Lesage and Kingsley 1998). A large whale watching industry has developed at the confluence of the Saguenay fjord and the St. Lawrence estuary. Thus, contamination not only represents a risk for the preservation of this particular ecosystem, but could eventually compromise the income related to the whale watching business.
A comparative study of Wagemann et al. (1990) reports that belugas of the St. Lawrence Estuary have significantly higher levels of lead, mercury and selenium, than most Arctic whales. Moreover, the St. Lawrence population has higher levels of PCB, DDT and mirex (Muir et al. 1990) compared to Arctic populations. The presence of toxic compounds in their environment surely affects these mammals, but the exact longterm consequences of the exposure to contaminants are difficult to evaluate. Nevertheless, the results of Martineau et al. (2002) indicate that the population living in the Saguenay Fjord and the St. Lawrence Estuary has an annual rate of cancer much higher than that reported for any other population of cetaceans.
Belugas are exposed to contaminants through their consumption of contaminated fish and benthic organisms as well as through accidentally ingestion of polluted sediments (Vladykov 1946). Since the benthic fauna lives inside the sediments and is at the lower level of the food chain, these organisms are an important vector for the diffusion of contaminants from the sediments towards higher level organisms (e.g. fishes and marine mammals). The bioaccumulation of toxic compounds in the benthic fauna occurs either by direct ingestion of sediment particles containing insoluble contaminants, like PAH, PCB or DDT, or by adsorption of soluble compounds from the solute phase (Otero et al. 2000, Yan and Wang 2002).
Belugas move in groups and exhibit a tendency to fidelity to some areas. The distribution of the population depends on the season, but specific zones are preferred for feeding, calving or resting (Pippard and Malcolm 1978). A list of sites representing a risk of contamination for the belugas has been published, considering the seasonal distribution of belugas and the concentration of toxic compounds (Comité multipartite sur les sites contaminés pouvant affecter le béluga du SaintLaurent 1998).
Even if our example is based on a real situation, we have to make a few assumptions and approximations in order to perform the decision analysis. The proposed strategy usually assumes that in a previous stage remediation has been judged necessary. In the case of the Saguenay Fjord, even if the observations suggest that the contaminated sediments contribute to the deterioration of the beluga population (Martineau et al. 2002), no environmental agency assessed the necessity to cover the contaminated sediments with a capping layer. In fact, the problem has complex interactions and other sources of contamination have been identified for the beluga population, like the American eels migrating from Lake Ontario (Hickie et al. 2000). Moreover the beluga population is mobile, lives and feeds on a large surface extending over the Saguenay Fjord and the St Lawrence Estuary and several sectors present contaminated sediments. Nevertheless, the dock of BaieSainteCatherine has been identified as a site at risk, where further characterization is highly requested, since it is highly contaminated and intensively frequented by belugas (Comité multipartite sur les sites contaminés pouvant affecter le béluga du SaintLaurent, 1998).
The cost for in situ capping of contaminated sediments are derived from the cost estimates of the Palos Verdes Shelf capping project, off the coast of Los Angeles, California (Palermo et al. 1999). The cap placement costs are divided in three components: the costs for the mobilization/demobilization of the dredging equipment CM, the costs to dredge, transport and dispose the material CDTD and the engineering and design costs CE. Thus, the construction cost of the project is described by the following equation:
(4.4)
The cost for the mobilization CM and the engineering costs CE are fixed and do not depend on the cap thickness, whereas the dredging/transportation/disposal cost CDTD are a function of the volume of sediments required for the capping project. The value of the construction cost components are based on values reported for the Palos Verdes Project and are described in Table 4.1.
Table 4.1: Costs of components used for the capping management options (in $ CAD).
Components 
Symbol 
Cost 
Mobilization/Demobilization 
CM 
$750 000 
Engineering 
CE 
$250 000 
Dredging/Transportation/Disposal 
CDTD 
$5 m3 
Cost of failure 
Cf 
$3 000 000 year1 
Estimating the cost of failure of the capping layer is associated here with the impact of belugas on the economy. Whale watching is a worldwide fast growing industry that stimulates tourism, contributes to the economic development of coastal communities and encourages regional business. Recent studies report that throughout the St. Lawrence Estuary there are 75 operators offering whalewatching tours. About 300 000 people participated in 1995 to these tours spending $7 million CAD on tickets, $44 million CAD on travel, meals and accommodation and $17 million CAD on additional direct economic spinoffs for a total of $68 million CAD (Hoyt 2000, Le Groupe Type 1996).
Local and international newspapers reported the results presented by Martineau et al. (2002) relating the cancer rates of belugas with the degradation and contamination of their habitat. The economical consequences of the diffusion of this information on the whale watching industry are difficult to evaluate. Belugas represent a patrimony with a high recreational, commercial and scientific value. In order to quantify the cost of failure Cf, we have to estimate the regional economic loss associated to the bad publicity due to the persistence of the health problems of the beluga population. We considered that bad publicity could slightly reduce the attractiveness of the whale watching tours and affect the incomes associated with tourism. Thus we approximate the cost of failure to the conservative value of $3 million CAD per year, which represents less than 5% of the total economic spinoff of the whale watching industry (Table 4.1).
In our example, we consider six capping options with different values of cap thickness, varying between 0.1 and 0.34 m (Table 4.2). The cost of a capping layer depends upon the area to be covered and thus upon the extension of the contamination. At the dock of BaieSainteCatherine the contaminant distribution is poorly documented, but in order to perform the decision analysis we had to estimate this parameter and based on the morphology of the dock we assumed a contaminated area of about 4 km2. Thus the sediment volume necessary for the capping options varies between 0.4 million m3 and 1.36 million m3 and construction costs fluctuate between $3 million CAD and $7.8 million CAD (Table 4.2).
Table 4.2: Capping options and construction cost to cap an area of 4 km2.
Capping option 
Thickness [m] 
Volume [106 m3] 
Total Cost [106 $] 
1 
0.10 
0.40 
3.0 
2 
0.14 
0.56 
3.8 
3 
0.20 
0.80 
5.0 
4 
0.24 
0.96 
5.8 
5 
0.30 
1.20 
7.0 
6 
0.34 
1.36 
7.8 
The numerical model used for contaminant transport in capped sediments (TRANSCAP1D) simulates advection, diffusion and bioirrigation . The sediments are represented as a dual porosity medium composed of microscopic sediment pores and macroscopic tubes and burrows (Dueri et al. in press). The benthic fauna, and particularly polychaete worms, dig and live in these mainly vertical tubes and burrows. Bioirrigation results from the pumping of overlying water into the tubes and burrows to provide oxygen for respiration and prevents the accumulation of potentially noxious chemical compounds.
The mathematical formulation in the model consists of two partial differential equations, corresponding to the contaminant transport in the bioirrigated tubes and in the sediment pores. These equations are coupled via a nonlocal exchange term that represents the mass transfer of contaminant between the sediments and the tubes . The formulation is mathematically similar to the one describing solute transport in a dualporosity medium, in the context of groundwater flow (for example, Zheng and Bennett 2002). The consolidation of the sediments and associated fluid advection are not included in the model, because for the studied cap thickness the full consolidation is usually achieved relatively rapidly compared to the lifetime of a capping layer.
The model was calibrated with profiles of dissolved arsenic because its chemistry has been extensively studied in the sediments of the Saguenay Fjord (Saulnier and Mucci 2000, Mucci et al. 2000a, 2000b). For the simulation presented here, the sediment column represented in the model has a constant thickness of 0.6 m. The column is equally subdivided in 30 cells, each having a height of 0.02 m (Figure 4.5). The contaminated layer has a total thickness of 0.14 m and its position in the column varies with the thickness of the cap. The simulation time varies between of 2.5 years (912 d) and 10 years (3650 d) and the time increment is set at 0.02 d .
The input parameters of the model are presented in Table 4.3. The values of the sediment porosity ns and of the inner radius of the tubes r1 reflect the values observed in the sediments of the Bras Nord and the Baie des Ha! Ha! (Dueri et al. in press). Two values were used to represent the porosity of the capping layer nscap, one corresponding to a finegrained cap composed of silt and clay (nscap = 0.7) and the other representing a sandy cap (nscap = 0.4). Advection velocity in the sediments and dispersivity are set to zero, because we assume that there is no advection in the sediments of the Saguenay Fjord. The molecular diffusion coefficient Dm corresponds to the range of values presented in Vanysek (2000) and Domenico and Schwartz (1998) for cations having a charge of 3+. This value was chosen because it represents the As3+ cation, which was used for model calibration (Dueri et al. in press). The effective diffusion coefficient Dd is calculated by multiplication of the molecular diffusion coefficient Dm with a mean tortuosity value of 0.64.
Table 4.3: Input parameters of the numerical model.
Parameter 
Name 
Units 
Value 
Sediment porosity 
nS 
[] 
0.7 
Cap porosity 
nScap 
[] 
0.4 and 0.7 
Advection velocity 
vS 
[m d1] 
0 
Dispersivity 
αL 
[m] 
0 
Effective diffusion coeff. 
Dd 
[m2 d1] 
1.6 * 105 
Molecular diffusion coeff. 
Dm 
[m2 d1] 
2.5 * 105 
Inner radius of tubes 
r1 
[m] 
0.001 
Initial and boundary conditions are required to solve the coupled system of equations. To impose the initial conditions one specifies the initial solute concentration in the two domains, sediments and tubes. Boundary conditions are required at the top and bottom of the domain and can be either a prescribed concentration or prescribed mass flux for both domains. We assume that solutes leaving the sediments from the upper boundary do not accumulate in water but are promptly carried away by the bottom currents. On the other hand, the solute mass reaching the lower control volume by diffusion leaves the system by the same rate. Since sediments underlying the modeled system are assumed to be clean, we set the advective flux entering the sediment column from the lower boundary to zero. Thus, the concentration at the lower limit stays at a constant value of zero.
The governing equations are discretized with the finite volume method (Versteeg and Malalasekera 1995). The equations are coupled through a mass exchange term and a simultaneous solution for the concentration in the sediments and tubes is obtained for each finite volume. The system of equations is thus solved in a fullycoupled fashion, avoiding the use of iteration that is necessary when the equations are decoupled. The block tridiagonal matrix resulting from the discretization and assembly of the terms is solved with the Thomas algorithm adapted to block matrices. The numerical solution was tested by comparing to the semianalytical solution of Neville et al. (2000), which has been developed for onedimensional solute transport in a dualporosity medium with multiple nonequilibrium processes (Dueri et al. in press).
The objective of the uncertainty analysis presented in this section is to define the distribution of the model response for conditions similar to those observed in the Saguenay Fjord. The uncertainty analysis considers the results of the previously performed sensitivity analysis (Dueri and Therrien 2003), which tested five factors: the depth of bioirrigated tubes, the number of bioirrigated tubes per square meters and their dimension, the bioirrigation velocity, the retardation factor and the dissolution coefficient. In the Saguenay Fjord, the depth and number of tubes are characterized by spatial variability, whereas the value of the bioirrigation velocity, the retardation factor and the dissolution coefficient are poorly documented and have to be estimated. Only the first four of those factors are varied in the uncertainty analysis. The dissolution coefficient is kept constant, because we do not have enough information to justify upper and lower limits for this parameter.
The uncertainty analysis is performed using the TRANSCAP1D numerical model and applying the Monte Carlo method (Morgan and Herion 1990). A Monte Carlo realization is a simulation with input values, which are randomly sampled within their specific PDFs and for which the numerical model calculates the corresponding output. A series of Monte Carlo realizations forms a Monte Carlo simulation and produces a finite range of independent output values that corresponds to the probability distribution of the inputs (see graph illustrating the output of uncertainty analysis presented in Figure 4.2). The Monte Carlo method allows estimating the output distribution from the sample of calculated output values, but the accuracy and stability of the distribution depends on the number of performed realizations. For a larger number of realizations we expect a better accuracy and stability of the Monte Carlo simulation.
The present uncertainty analysis is used to design the optimal Monte Carlo simulation for the decision analysis, minimizing the number of realizations and thus the time required for each simulation, and maximizing the accuracy and stability of the output distribution. Moreover, we use this analysis to verify whether the output distribution is normal or lognormal and to test the effect of the shape of the input distribution.
Two types of PDFs are used for the input of the uncertainty analysis: uniform distribution and normal distribution. The number of tubes per square meter and the irrigation depth are defined by both distribution types, in order to investigate the impact of the distribution type on the response. The normal distribution is defined so that the upper and lower limits of the uniform distribution correspond to the 5% and 95% limit of the normal distribution. The minimum and maximum values of each tested parameter were determined from the available information, which includes data measured at the Saguenay Fjord and data derived from the literature. The values of the parameters are discussed in the following paragraphs and are presented in Table 4.4.
The values for the bioirrigation velocity were derived from data measured during laboratory tests carried out on polychaete families living in shallow water (Riisgard 1989, Riisgard 1991). In the calibrated model, the irrigation velocity is equal to 1 m d1. The minimum and maximum values of this parameter were estimated by modifying the calibrated value by a factor of five. Thus, we obtain a range of values going from a minimum bioirrigation velocity of 0.2 m d1 to a maximum value of 5 m d1, which represents a reasonable approximation of the variation of this parameter for the studied site.
Table 4.4: Definition of uniform and normal PDFs describing the variable parameters.
Parameter 
Uniform Distribution 
Normal Distribution 

Minimum 
Maximum 
Mean 
Variance 

Irrigation Velocity [m d1] 
0.2 
5 

Retardation Factor 
5 
45 

Number of Tubes [m2] 
500 
1500 
1000 
62,500 
Irrigation Depth [m] 
0.06 
0.26 
0.16 
0.0025 
The minimum and maximum values for the retardation factor have been estimated from the calibration of the model on two measured arsenic concentration profiles (Dueri et al. in press), from the values presented by Fuller (1978) for different metals, as well as from the values determined by Bourg (2002) for the transport of Zn and Cu in the Saguenay sediments. The range of retardation factors is very wide and depends on the element and on the sediment composition. For our uncertainty analysis we chose the range of values with the smallest retardation, therefore assuming that the contaminant has a good mobility and taking the “worst case” for contaminant migration. The minimum and maximum values of Rt have thus been set to 5 and 45, respectively.
The values of the number of tubes per square meter were visually determined from photographs of the undisturbed bottom sediments taken in the Saguenay Fjord during the summer 2001. The minimum and maximum values of this parameter are 500 and 1500 tubes per square meter, respectively. The number and the dimension of the tubes in the upper sediment layer are an indicator of the intensity of bioirrigation in this zone. Two input values of the model are directly calculated from the number of tubes: the tube porosity at the surface and the mass transfer coefficient.
The depth of bioirrigation is represented in the model by the maximum depth attained by the tubes. The value of this parameter has direct consequences on the mass transfer coefficient between tubes and sediments as well as the value of the tube porosity. The three parameters are related since the maximum bioirrigation depth corresponds to the location where mass transfer and tube porosity exponentially tend to zero. According to field observations and measured bioturbation intensities (De Montety et al. 2000), the minimum value of the bioirrigation depth was set to 0.06 m and the maximum value to 0.26 m.
In order to test the stability and accuracy of the output distributions for a wide range of possible scenarios, we performed several Monte Carlo simulations considering different values of maximal simulation times, cap thickness and maximal concentration of contaminant. For the maximal simulation time, values of 2.5, 5, 7.5 and 10 years were chosen, whereas the ranges of cap thickness varied between 0.04, 0.10, 0.14, 0.20, 0.24 and 0.30 m. Two values were chosen for the maximal concentration of contaminant, which was set at 25 000 μg m3 and at 100 000 μg m3. The distribution of contaminant is represented by a symmetrical peak (Figure 4.5) with a limited thickness of 0.14 m. This representation was chosen for practical reason and is not based on observation since, to the authors' knowledge, the contaminant distribution in the sediment column of Baie Ste Catherine has not been reported so far. The response that was considered for the uncertainty analysis is the released mass and the concentration at the surface of the sediment. The maximal number of realizations was determined considering the time required to perform the Monte Carlo simulation. For a prediction of contaminant migration over 5 years and 4000 realizations, the Monte Carlo simulations required 28 hours on a Pentium III computer, 450 MHz.
The output distribution resulting from the uncertainty analysis was tested for normality with the KolmogorovSmirnov test. The test was used to assess if the distribution is normal or lognormal and to investigate the effect of increasing the number of simulations. A distribution is considered normal if the calculated KolmogorovSmirnovcoefficient is smaller than the critical value of the test, for a given confidence level. The results of the test are presented in Figure 4.6. Both responses, concentration at the top of the sediment column and mass flux, diverge from normality for almost every Monte Carlo simulation. On the opposite, the KolmogorovSmirnovcoefficients calculated from the natural logarithm of the output values (filled symbols) fall near the critical value for a confidence level of 95%. Therefore, the lognormal distribution seems to better represent the distribution of the output values.
The coefficient of skewness, which determines the asymmetry of the distribution, and the coefficient of kurtosis, a measure of the sharpness of the data peak, were calculated for the model output and for its logarithm. The coefficients calculated with the logarithm of the response were generally nearer zero, which corresponds to the value for a normal distribution (results not presented). Therefore, we validate the assumption that the lognormal distribution better approximates the output than the normal distribution.
Several series of Monte Carlo simulations were performed in order to evaluate the stability of the response as a function of the number of realizations. The simulations consider two types of responses: the cumulative sum of the released mass and the concentration in the top layer of the sediments. Since the lognormal PDF describes reasonably well the distribution of the model response, the logarithm of the output values can be represented by a normal distribution, characterized by a mean and a standard deviation. As the number of realizations increases, these parameters should converge towards a stable value. In order to verify this hypothesis and to determine the number of realizations that is required to get a stable response we performed a series of 48 Monte Carlo simulations, gradually increasing the number of realizations, from 100 to 4000. The simulation time was set to 5 years and the series include Monte Carlo simulations with a cap thickness of 0.1 m or 0.2 m and normal or uniform distribution of the input variables. The mean and the standard deviation of the result of each Monte Carlo simulation were calculated and thereafter compared to the mean and standard deviation of the Monte Carlo simulation composed of 4000 realization, which is supposed to present the best convergence towards the true distribution of the model response. The mean deviation of the mean MDμ [%] and the mean deviation of the standard deviation MDσ [%] and are obtained with equation (4.5) and (4.6) and presented in Figure 4.7. A mean deviation of 0% means that the result perfectly overlaps the 4000realizations output.
(4.5)
(4.6)
The results show that for a number of realizations greater than 1000 both responses present a good stability and that the mean and the standard deviation fluctuate around the 4000realizations value with a deviation of ± 2%. The response was similar for uniform or normal distribution of the input value.
Sediment contamination at the dock of BaieSainteCatherine is poorly documented, but since the municipal effluents represent the main source of pollution, the sediments are expected to contain both metals and organic contaminants (Gagnon 1995). TRANSCAP1D represents only the migration of dissolved compounds, thus the model is well suited to simulate the fate of inorganic contaminants (metals). The organic compounds commonly found in the Saguenay sediments (PAH, PCB, DDT) have a very low solubility and are associated with sediment particles. Therefore they cannot be represented by the numerical model. In order to include these contaminants in the decision and calculate the probability that they reach the surface of the capping layer another method has to be used.
Since the organic compounds are bound to the solid particles, their migration is related to the mixing of sediments caused by the activity of the benthic organisms. This process is called bioturbation. The representation of the bioturbation depth is based on the observation of sediments collected with a boxcorer in the Bras Nord and Baie des Ha!Ha! during summer 2000 and 2001 and we assume that the bioturbation profile is similar in BaieSainteCatherine. Since the bioturbation depth shows a very strong spatial variability, this parameter is represented with a normal distribution, having a mean value of 0.1 m and a standard deviation of 0.05 m. The probability that a sediment particle located under the cap reaches the top of the sediment layer is set equivalent to the probability that the bioturbation depth reaches the contaminated layer. This simple method gives an approximation of the probability that the cap thickness is effective in isolating organic contaminants from the sedimentwater interface.
The decision analysis is performed for both, soluble and low solubility contaminants, in order to account for trace metals and organic compounds. The probability that trace metals migrate as a solute through the capping layer is obtained from Monte Carlo simulations using the TRANSCAP1D model with uniform input distributions. The mobility of the organic compounds is evaluated by accounting for the bioturbating activity of the benthic fauna.
The decision analysis strategy requires the definition of a criterion for the failure of the cap. Since we do not dispose of exact information about the concentration of contaminants in the sediments of the studied site, we cannot define the criterion for failure from toxicological thresholds. Thus, we have to define the limit between success and failure from the improvement comparatively to the situation before capping. The objective of a capping layer is to reduce significantly the contaminant concentration in the upper layer of the sediments. Therefore, we assess that the cap fails if 10 years after capping, the contaminant concentration at the surface of the sediments exceeds 10% of the concentration before capping.
In order to obtain stable and accurate output distributions for the decision analysis, we performed Monte Carlo simulations composed of 1000 realizations and the simulation time was set to 10 years. Since the contamination level at the studied site is poorly documented, two values were chosen for the maximal concentration of contaminant in the sediment column: 25 000 μg m3 and 100 000 μg m3. Both simulations gave very similar output distributions, thus we only present the results obtained with the peak value of 100 000 μg m3.
Figure 4.8 shows the graphical result of decision analysis presenting the trend of the objective function for the six capping options and a cap porosity of 0.7. The analysis uses the values of the construction cost C presented in Table 4.1. The cost associated with the risk of failure R is calculated multiplying the probability of failure Pf (schematically represented in Figure 4.4) with the cost of failure Cf that is conservatively assumed to attain $3 million CAD per year (Table 4.1). As presented in equation (4.3), the objective function is the total cost of the project corresponding to the sum of the cost of construction and the cost associated with the risk of failure. Figure 4.8 shows that, due to the reduction of the cost associated with the risk of failure, the total cost of restoration decreases rapidly from 32 million CAD to 7 million CAD corresponding to increasing thickness from 0.1 m to 0.2 m and seems to attain a minimum between 0.2 m and 0.24 m. The true leastcost option is the 0.24 m option, because this alternative has a total cost of $6.98 million CAD whereas the 0.2 m options has a total cost of $7.02 million CAD. The two options are considered equivalent.
Figure 4.9 shows the graphical result of decision analysis for the same values of capping thickness, but with a cap porosity of 0.4, thus representing a more sandy cap. This time the leastcost option is the 0.3 m option with a total cost of $7.84 million CAD, but we note that this option is almost equivalent to the 0.24 m option, which has a total cost of $7.92 million CAD. Once more we observe the very rapid decrease of the objective function from 33 million CAD to 9.4 million CAD between 0.1 m and 0.2 m.
The strategy used in this example to represent the migration of the organic contaminants is very simplified. Low solubility contaminants are transported with sediment particles by bioturbation and the probability that the contaminant reaches the surface of the cap is equivalent to the probability that the bioturbation depth reaches the contaminated layer under the cap. The results illustrated in Figure 4.10 show that for an organic contaminant the objective function decreases rapidly from 0.1 m to 0.2 m and thereafter increases again. The cap thickness of 0.2 m represents the least cost option with a total cost of $5.68 million CAD and a probability of failure of 2%.
The representation of the results of the decision analysis is straightforward and shows clearly that if the capping layer is too thin, the risk of failure is high, affecting the total cost of the project. Since the cost associated to the risk of failure depends on the cost of failure Cf, which is difficult to estimate, we investigated the influence of different costs of failure on the result of the decision analysis. Figure 4.11 represents the variation of the objective function for different costs of failure considering a soluble contaminant. For Cf values of $ 0.75 and $ 1.5 million CAD, the least cost option is the 0.2 m cap thickness, while for a Cf of $ 3 million CAD, the optimal alternative is the 0.24 m option. Finally for a Cf of $ 6 million CAD the least cost alternative is the 0.3 m cap thickness. We observe that between 0.1 m and 0.2 m cap thickness, for increasing values of cost of failure we obtain steeper decreases in the total cost of the capping project. On the other hand, between 0.2 m and 0.34 m cap thickness, the total cost function seems to attain a plateau. Thus, even if the optimal option is affected by the variation of the cost of failure, the general trend of the total cost function does not change.
The decision analysis method was applied to the design of a hypothetical capping project, loosely based on a real situation (concern for belugas health in the St. Lawrence Estuary). The main advantage of this strategy is that it allows for systematic comparison of different capping alternatives, accounting for uncertainty and for the costs associated with the construction and the risks of failure of the project. The design alternatives are evaluated by comparing the total cost associated to construction and risk of failure of the project. The representation of the results is straightforward and suitable for communication with decisionmakers.
The presented decision analysis is based on several hypotheses. The PDFs of the input parameters are estimated from the limited available data. Since we disposed of very few informations on the Baie SteCatherine area, we had to extrapolate the necessary parameters from the studied sites located in the Bras Nord and the Baie des Ha! Ha! and we used the numerical model that was calibrated at those sites. These hypotheses were necessary to carry out the decision analysis but they limit the reliability of the results. A better characterization of the study site is recommended in order to confirm the results of the decision analysis.
The current knowledge about the ecosystem does not allow linking the contamination of the study site with the health problems observed in belugas. Nevertheless, environmental reports already assessed the need to collect more information at the site in order to produce a more accurate description of the contamination and its extension. Furthermore, a better knowledge of the site characteristics would also reduce the uncertainty in the decision analysis. If the link between the contamination of this area and the health problems of belugas was provided, the decision analysis method could be used under the condition that more accurate information on the contaminant types and the characteristics of the area be included.
The cost of failure is often difficult to evaluate. However, the evaluation of the cost of failure is required not only for the presented decision analysis method, but also for decision techniques, which do not include variability. In our example, we approximated the cost of failure with a value equivalent to about 5% of the total economic benefits of whale watching industry. This estimation does not consider the uniqueness of the beluga population of the St. Lawrence Estuary. A more detailed analysis of the economic value of belugas could be performed to better estimate the cost of failure.
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