Probabilistic Spill Occurrence Simulations and Quantitative Water Quality Risk Analysis for Chemical Spill Management

................................................................................................................................... ii ACKNOWLEDGEMENTS ........................................................................................................... iv DEDICATION ................................................................................................................................ v TABLE OF CONTENTS ............................................................................................................... vi LIST OF TABLES ......................................................................................................................... xi LIST OF FIGURES ..................................................................................................................... xiv LIST OF APPENDICES ............................................................................................................. xvii CHAPTER


LIST OF TABLES
and average monthly temperature in Canada (1901Canada ( -2009

Background
Thousands of oil and chemical spills occur each year worldwide through accidents or natural disasters and bring a great potential to harm human health and impact water, air and land and their associated terrestrial and aquatic species, which has been well documented by Tagatz (1961), Hutchinson et al. (1974), McKinley et al. (1982) and Shales et al. (1989). As defined by several environmental legislation, a spill is a form of ‗discharge' (Ontario Water Resources Act s. effects (Canadian Fisheries Act s. 34 1985), ‗impairment' to water quality (Ontario Water Resources Act s. 1(3) 1990), and ‗adverse effects' (Ontario Environmental Protection Act s. 1 (1) 1990; Environmental Protection Act, Ontario Regulation 675/98 Part I). A spill occurrence is ‗abnormal in quality or quantity in light of all the circumstances' (Ontario Environmental Protection Act s. 91(1)(c) 1990) and represents a failure in system, education, engineering, regulation, enforcement or packaging (Castle 1999).
Inland spills have been identified as one of the major sources of pollution of the Great Lakes (Cheng 2010) and pose great threats to water quality there. Unlike tanker spills in oceans, inland spills originate from industrial and municipal lands (Li 2005), including production sites, local product stores and transportation corridors and can be transported by groundwater and surface water, and air to another location. They can occur for a number of reasons and situations, such as equipment failure or human error, and may cause impairment of drinking water quality, contamination of surface water and groundwater, destruction of freshwater invertebrates and vertebrates, and disturbance of fish habitats and wildlife populations, especially in spawning areas (Li & McAteer 2000). The types of spill that are of most concern are those of toxic substances which can directly or indirectly be deposited into watercourses through several different routes, such as airborne dispersal, leaking (e.g. ground/underground tank and landfills), discharge, overflow, and so on (Environment Canada 1997). Spills in large quantity could acutely elevate certain toxic chemicals at water intakes (Cheng 2010). Even in small quantities spills could affect the long-term toxicity levels in ambient waters.
Federal facilities, agencies, boards and crown corporations are involved in a wide variety of activities that may result in the use or production of any of the following materials containing potentially deleterious substances: biomedical and other hazardous wastes, food and food processing wastes, sewage and water treatment facility effluent, laboratory chemicals, garage and machine shop fuels, oils and lubricants, paint and printing shop solvents, paints, dyes, and deicing chemicals for aircraft and airport grounds, and hydrocarbons from aircraft fueling operations (Environment Canada, 1997). All activities using or producing these materials anywhere may cause inland spills and discharges into the environment. Therefore, multijurisdictional responsibilities for inland spill management are shared by all levels of government 3 (federal, provincial, and municipal), industries, and individual Canadians (Environment Canada, 1998).

Relevant Legislation
Federal, provincial, and municipal governments have enacted relevant legislation for water resource protection. The regulations prescribed by these acts mainly focus on maintaining the integrity of the natural environment and preventing any adverse effects to the natural environment by spills (Li, 2002d (1) and (3)).  (1)). The Ontario Municipal-Industrial Strategy of Abatement (Ontario MOE, 2007c) regulations require industries that are prone to toxic releases to report spills, and implement spills prevention and contingency plans as well. Municipal sewer by-laws restrict the quantity and quality of the disposal of hazardous spills into the sewer system, which travel through the infrastructure as runoff into the catch basins and sewers.
There have been some initiatives targeting spill prevention, preparedness, and management in Canada. For instance, the Environmental Emergencies Branch of Environment Canada has developed the Priority List for chemical spills to focus on research and development efforts for the most frequently spilled and harmful chemicals (Fingas et al., 2000).

Research Needs
As discussed in Section 1.2, the federal, provincial and municipal acts, regulations and initiatives have targeted industrial spill prevention and management. Threrefore, it is hypothesized that spill events will be decreased with time. However, hundreds of chemical spills still occur every year in Southern Ontario and present an increasing tendency for the period of 2003-2007, resulting in surface water pollution and other negative environmental impacts (Cao et al., 2012), implying that industries may not well prevent, control, and management spill occurrences. For instance, benzene spills generated by various facilities in the St. Clair River Area of Concern (AOC, a site where environmental quality is significantly degraded and beneficial uses are impaired) have been reported to enter directly or indirectly into the river leading to violations of water quality at water treatment plant (WTP) intakes and justifying plant shutdowns (Cheng, 2010). Therefore, a new research is acutely needed to address the issue of effective measures on spill occurrecence prevention and management in order to protect source waters and human health.
Additionally, most current spill-related research is focused on oil spills. A Tactical Decision Problem (TDP) associated with oil spill cleanup operations was formulated as a general integer 7 program to optimize total response time to the spill over a planning horizon with an assumption of known oil type, quantity and occurrence location ). An optimization procedure for this TDP model was developed based on an aggregation scheme and strong cutting plane methods . A multiperiod mixed-integer linear programming model was developed under economic and responsive criteria and coupled with oil transport and weathering model to simultaneously predict the optimal time trajectories of oil slick's volume and area, transportation profile, response resource utilization levels, cleanup schedule, and coastal protection plan with various specifications of the response time span (Zhong and You, 2011;You and Leyffer, 2011). However, although many researchers engage in developing water quality models for the investigation of the fate and transport of contaminants in source water, not enough studies on the effect of inland chemical spills on fresh water has been justified and there is a lack of models for forecasting the probabilistic quantifiable occurrences of inland spills and analyzing their risks of water quality impairments at downstream locations along receiving waters that can be used to aid decision making. Without spill occurrence prediction and risk analysis models, all decisions on spill management are lack of technical support and will lead to high costs on spill prevention and control. For instance, the lack of information of potential spill occurrence time, magnitude and location would mislead to spill management resources allocation (e.g. finance and human resources) which may cause a long response time for an emergent spill event and impairments of the environment and/or human health if the spill could not be controlled and cleaned up promptly. Therefore, it is indicated again that a new research is needed to address the origins and management of inland spills in order to protect source waters. 8

Research Scope and Objectives
Since the SAC spill database records the spills that occur in Southern Ontario, the research scope focuses on this area. The main objective is to develop a framework for a comprehensive inland chemical spill management strategy, which can be used to assist a municipality or a conservation authority for preventing, controlling and responding to an inland spill and protecting water resources. In order to achieve this objective, a planning tool was to be considered which includes the following components: (1)

Expected Outcome
The outcome of the research is expected to be as follows: (1) A framework for a comprehensive inland chemical spill management plan for source water quality protection and management, which will require the models as outlined in (2) and (3); These models are not only the main components but also the technical support of the spill management plan and associated risk-informed decision making.
(2) a quantifiable probabilistic model for simulating inland chemical spill occurrences by time, magnitude and location, and quantifying expected spill occurrence time and mass for a location, based on categories of business establishments according to type of economic 9 activity (process of production) defined by North America Industry Classification System codes; and (3) a quantitative risk analysis model for downstream water quality impairment due to inland chemical spills along a receiving water, which involves water quality modelling.
These outcomes can fill in the current research gaps mentioned in the Section 1.3. The approach of this research not only can be used by water quality practitioners to develop spill occurrence prediction models and estimate the associated risks of water quality violations along waterways, but also can be used by regulatory agencies and municipalities to make decisions on spill management in order to minimize the spills' potential that threatens source water quality and/or human health. The approach is also appropriate to assist an industry to develop spill prevention, control and management plan according to its own historical spill characteristics and regulatory requirements.

Organization
This dissertation comprises seven chapters. Chapter 1 is the introduction and overview of the

CHAPTER 2 LITERATURE REVIEW
This chapter reviews literature related to the fate and transport of contaminants in receiving waters (especially in river systems), water quality models, risk analysis, common probability distributions (PD), and some applications.

Previous Work
Inland chemical spills are considered emergent non-point water pollution sources generally not related to storm events (Li and McAteer, 2000) and pose threats to the Great Lakes basin and everywhere. Unfortunately, most spill research activities concentrate on marine spills rather than the more frequent inland spills. Recognizing the importance of inland spills in the Great Lakes, Li et al. (2002aLi et al. ( , 2002bLi et al. ( , 2002cLi et al. ( , 2002dLi et al. ( , 2002e, 2003  respectively. The media that received spills from highest to lowest number was air, water courses and surface water, soil and vegetation, multiple media and human health and safety, while the chemical sector (47%) was responsible for most chemical spills followed by the petroleum (20%) and general manufacturing (19%) sectors. Cheng's results also showed that discharge/bypass to water courses accounts for 97% of benzene mass spilled to air, water, and soil. The log-normal probability distribution was used to describe the spill events' mass. The risk of water treatment plant shutdowns due to benzene spills over a two-year period was found to be 41% and 19% for 1988respectively. Finally, Cheng (2010 suggested risk-based spill 13 management criteria to evaluate the effectiveness of spill prevention and control programs.

Transport and Fate of Contaminants in Receiving Waters
Contaminants travel down slopes over land, and most often end up in surface water bodies such as a stream, river, lake, or sea. During their travel, a part of the total amount might be depleted due to evaporation or loss by adhering to surface vegetation, rocks, and soils, and deposition in surface puddles and pools (Farrar, et al., 2005). The overland flow of spilled contaminants is governed by the properties of the contaminant, physical nature of the land surface and the degree of slope. Once they reach and enter surface water, such as a river or a lake, their transport and fate are affected by physical, chemical, and biological processes (Al-Rabeh et al., 1989), and a number of environmental conditions (e.g. winds, waves, current, water depths, temperatures, salinities, organisms, nutrients, and chemical type). Therefore, it is very important to account for the characteristics of receiving waters. This research mainly focuses on river systems.
The most distinct characteristic of a river is its natural downstream flow. The health of a river is directly linked to the health of its surrounding watershed. The water quality in a river will deteriorate if the watershed condition deteriorates. River characteristics can change significantly over time in response to human activities and changing climate and hydrologic conditions. Rivers vary widely by morphological, hydraulic, and ecological characteristics, including slope, width, depth, flow rate, flow velocity, water temperature, sediment transport, contaminants deposition, nutrient inflows and eutrophication processes (Ji, 2008). Point and nonpoint pollution sources have caused a wide range of water quality problems and the deterioration of the ecological state in rivers. According to the U.S. EPA (2000), the kdy pollutants and stressors in 14 rivers are pathogens/bacteria, siltation, habitat alterations, oxygen-depleting substances, nutrients, thermal modifications, toxic metals, and flow alterations.
When a pollutant is discharged into a waterbody, it is subject to fate and transport processes that modify the concentration of the pollutant downstream (Ji, 2008). Advection, dispersion, and convection are three hydrodynamic transport processes. Substances in water systems can be transported by one or all of these processes. Advection refers to horizontal transport by flows, resulting in the movement of a substance downstream; dispersion is the horizontal spreading and mixing of water caused by turbulent mixing and molecular diffusion, resulting in the reduction of the substance concentration and the net transportation of the dissolved substance from the areas of high concentration to those of low concentration; and convection refers to vertical transport of water and very small pollutants in rivers and lakes. In addition, turbulent mixing that combines advection and convection mechanisms is the dominant component of dispersion in a river; longitudinal mixing leads to the substance spreading in the same dimension; and lateral and vertical mixing determines the complete mixing time of the substance across the river (Ji, 2008).
Transport currents and horizontal shears in the currents contribute to dispersion of contaminants in water column (Reed et al., 1995). The advective velocity is a significant factor in the transport of the pollutant, while the flow velocity controls the travel time of the contaminant in the river.
Rapid transport of the pollutant by high flow results in a short residence time and has minimal water quality problems. Conversely, slow transport of pollutants by low flow results in a long residence time and can lead to water quality problems such as oxygen depletion and drinking water impairments.
Over the past decades, mathematical models to describe the fate of contaminants have been investigated by many researchers. Al-Rabeh et al. (1989) discussed the transport and fate of spilled oil in surface water, which is being affected by physical, chemical, and biological processes including advection, turbulent diffusion, surface spreading, evaporation, dissolution, emulsification, vertical mechanical dispersion, photo-oxidation, biodegradation, and sinking and sedimentation, and proposed a comprehensive stochastic model, which consisted of a set of algorithms to describe these processes, to simulate the fate and transport of oil spills in surface water. Al-Rabeh et al. (1989) concluded that dissolution was the most active process shortly after a spill entering into a river, while photo-oxidation and biodegradation were both unimportant over the first few days. These processes also apply to the transport and fate of chemical spills in rivers.
In rivers, mass balance is a fundamantal to describe the changes of a conservative substance with time, as given by Eq. (2.1). Based on this equation, Chapra (2008) proposed a water quality model to estimate the concentration of a conservative substance at various times, as shown in Eq.
(2.2), whose numerator represents an Euler-method prediction of the mass in segment i of the river at a time step and whose denominator is an Euler prediction of its volume. Where: A is the cross-sectional area of river, m 2 ; C is the concentration of a substance, kg/m 3 ; Q is the flow rate of river, m 3 /s; t is time and ∆t represents a time interval, per second; x is a location in river or stream, m; V is the volume of water, m 3 ; l represents a time point.
Contaminants in a water column are carried to the water floor primarily by adsorption to suspended particulates and subsequent settling. Reed et al. (1995)  Contaminants which sank directly to the sediments might be returned to the water column by the process of dissolution (Reed, et al., 1995). The contaminants concentrations in sediment were suggested to be distributed between adsorbed and dissolved states by linear partitioning, as in the water column. The ratio of adsorbed to dissolved contaminant was also determined by Eq. (2.3).
Thibodeaux (1977)  where Re is Reynolds number; Sc is Schmidt number; C is bulk concentration, kg/m 3 ; V ∞ is the velocity far removed from interface, D AB is molecular diffusivity of A in B, m 2 /s; and L is length of pool, m.
A c is the interfacial area for mass transfer at concentration C s , m 2 ; C s is the minimum contaminant concentration at the sediment/water interface and the saturation concentration; and C w is ambient concentration of the contaminant in water.
The transport of contaminants from injection at a riverbank to a point downstream in the river is estimated using the distribution of the chemicals in the flow direction of the river and the distribution of the flow rate of the river. After an instantaneous contaminant enters a river, its concentration at any time and any distance downstream could be estimated by a one-dimensional equation (Hemond and Fechner-Levy, 2000), as shown in Eq. (2.8). where: C is the concentration of conservative chemical, kg/m 3 ; M is the mass of chemical entered per cross-sectional area of river, kg/m 2 ; x is the distance downstream of entrance, m; V is the average river velocity, m/s; t is the time elapsed since entrance, s; and D L is the longitudional dispersion coefficient, m 2 /s, which can be estimated by Eqs. (2.9) and (2.10) (Fischer et al., 1979). w is the width of the river, m; d is the depth of the river, m; u* is the shear velocity, m/s g is the acceleration of gravity, m/s 2; , and S is the slope of the river (dimensionless).
Typical values of D L range from 0.05 to 0.3 m 2 /s for small streams (Genereux, 1991) to greater than 1000 m 2 /s for large rivers (Wanner et al., 1989). Rutherford (1994) (Hemond and Fechner-Levy, 2000). At any given time t, the maximum concentration of the chemical (C max ) is found at a distance downstream of the entrance point (x) equal to the product of the time elapsed (t) since entrance and the average river velocity (V). At this location, the C max can be determined by Eq. (2.12). where k is a first-order rate constant (in per second) for chemical transformation and removal processes.
Eqs. (2.8), (2.11) and (2.12) are used under the assumption that a chemical enters a river uniformly across a river cross section. In fact, after entering a river, the chemical must travel a certain distance before its concentration becomes uniform. For a chemical released at a river bank, the length of the transverse mixing zone can be roughly estimated by Eq. (2.13) (Hemond and Fechner-Levy, 2000).
where L is the length of transverse mixing zone (m), D t is the transverse Fickian mixing coefficient (m 2 /s), and others are the same as discussed above. For typical natural channels, the coefficient D t can be roughly estimated by t w D t 2 2 , where t is the time since the chemical was released (s). Rutherford (1994) reported some D t coefficients in several rivers, such as 0.12, 0.038, and 3.1 m 2 /s in Missouri, Danube, and Orinoco, respectively. Chan (1980) (Chan, 1980 Where: C is the peak concentration of a spill, kg/m 3 ; x and y are alongshore and cross-stream coordinates, m; x * is a distance upstream and used to determine the position of the virtual source used for the prediction for extended sources, where Q is the spill discharge and T is spill M is the amount of spilled mass, kg; d is the mean depth of River, m; t is the time after the spill release, s; u is the longshore current, m/s; K x and K y are the dispersion coefficients, m 2 /s.

Probabilistic Distributions and Occurrences
To investigate probabilistic events of a stochastic process (e.g. spill occurrences), it is important to analyze available historical data and determine the probability distribution (PD) of observations. Many researchers have discussed the applications of linear least square, maximum likelihood, moments, and order statistics for estimating the PD parameters of a stochastic process (see e.g., Bhattacharya and Bhattacharjee, 2010;Mijić et al., 2009;Izsák, 2008;Wu, 2002;Holland and Fitz-Simons, 1982). The most common applied probability distributions in general are listed below.

Normal
Normal distributions are extremely important in statistics and have been often used in the natural and social sciences for real-valued random variables whose distributions are unknown (Casella and Berger, 2001). Its probability distribution function (PDF) and cumulative distribution function (CDF) are given by Eqs. (2.23) and (2.24).
where μ and σ are two parameters of the distribution, which are the mean and standard deviation of random variable, respectively. Johnson and Kotz (1970) discussed the methods of linear least square, maximum likelihood, moments, and order statistics for estimating the parameters μ and σ. Mage and Ott (1984) evaluated the methods of fractiles, moments and maximum likelihood for estimating parameters μ and σ when sampling air quality data and demonstrated that the maximum likelihood was preferred.

Lognormal
The lognormal distribution has been used by researchers for decades to model many kinds of environmental contaminant data. For instances, the concentrations of pH, alkalinity, chlorides, ammonia, iron, and aluminum in river water (Dolgonosov and Korchagin, 2011), the concentrations of PM10 -particulate matter with an aerodynamic diameter lower than 10 μm -in the City of Volos, Greece (Papanastasiou and Melas, 2010), benzene and vinyl chloride spill mass in the St. Clair River AOC (Cheng, 2010), the concentrations of volatile organic compounds (Jia et al., 2008), and total petroleum-hydrocarbon concentrations in soil (Salmeen et al.,1995), air quality data (Mage, 1981;Georgopoulos and Seinfeld, 1982), trace metals in fish (Giesy and Weiner, 1997), radionuclide data sets (Pinder and Smith, 1975;McLendon, 1975;and Horton et al., 1980), strontium-90 and other fission-product concentrations in human tissues (Schubert et al., 1967). Air pollution data are more often lognormal due to atmospheric dynamics and concentration levels that are never less than zero (Goldman et al., 2011 x represents one datum of the data set (X) of the benzene spilled mass.
μ y (= μ ln(x) ) and σ y (= σ ln(x) ) are the two parameters of the lognormal distribution, which are true mean and variance of transformed random variable Y = ln X, respectively.
Through some software such as MATLAB built-in function, the mean and variance of a twoparameter normal or lognormal distribution can be estimated easily, but the user is required to purchase a software license.

Weibull Distribution
A Weibull distribution has been widely used to describe environmental contaminant data, such as the waiting time of metal cutting acoustic emissions (Polito et al., 2010), air pollution concentration (Georgopoulos and Seinfeld, 1982), radionuclides (Pinder and Smith, 1975), spatial and temporal distribution of atmospheric radioactivity (Apt, 1976), and ambient ozone data (Johnson, 1979). Its PDF and CDF are expressed by Eqs. (2.27) and (2.28).
Where t represents one datum of the data set (T) of the benzene spill inter-event time.
λ and β represent scale and shape parameters of the Weibull distribution, respectively.
The scale parameter determines the range of the distribution, while the shape parameter gives the distribution its flexibility. If = 1, the Weibull distribution is identical to the exponential distribution.

Exponential Distribution
As a special case of the Weibull distribution, an exponential distribution has been widely used to describe inter-event time in engineering evaluation, such as rainfall events, floods, droughts, time to failure for certain engineering systems, and so on (Singh et al., 2007). where:λ is a parameter of the distribution, often called the rate parameter.

Gamma Distribution
The PDF and CDF of a Gamma distribution are expressed by Eqs. (2.31) to (2.34). They have been used to describe many stochastic processes, such as rainfall (Aksoy, 2000).
where: k and α are scale and shape parameters of the distribution, respectively.

Risk and Risk Analysis
Risk is calculated as the joint probabilities of an occurrence of an event and its consequences and risk analysis refers to a process of the estimation of the frequency and physical consequences of undesirable events (Ricci et al., 1981). It is characterized by two quantities: the magnitude of possible adverse consequence(s) and the probability of the occurrence of each consequence (Stamatelatos, 2000). Usually, risk is taken as the mean or expected value of consequences or damages expressed by the product of probability and its consequences (Ganoulis, 2009) where P i is probability of event i, and D i is the consequence of event i, such as a damage.
According to Ganoulis (2009), mathematical estimations for the risks to surface water quality are intended to estimate the expected deviation from defined quality standards and possible consequences. In terms of source water quality, the magnitude of adverse consequence is treated as 1 because of the violoation of water quality caused by a pollutant and therefore its risk becomes the probability of exceeding the acceptable concentration set by regulation or environmental quality standards, which is given by Eq. (2.37). Considering the concept of risk, p F is the asymptotic limit of the ratio of number of times system fails and total number, as shown in Eq. (2.38).
where p F is the probability of failure of the pollutant in a steady-state system, C is the concentration of the pollutant in surface water, C s is the standard concentration for the pollutant in surface water, N F is number of times the system fails where C > C s , N S is number of times the system succeeds, and N is total number which is N F + N S .
It is necessary to analyze the risk of chemical spills for water quality due to their toxicity. To estimate the risk of the contamination of a river, variabilities in time and space of water quality 29 characteristics should be taken into consideration (Ganoulis, 2009

Model Uncertainty, Sensitivity, Calibration, and Verification
Both mechanistic models and empirical models involve physical or empirical parameters that cannot be quantified accurately and have predictive uncertainty (Tung and Yen, 2005). When a model involves parameters whose values cannot be certain, the traditional approach is to conduct sensitivity analysis by changing a parameter's value, such as ± 10 or ± 20%, from each input; this helps with an understanding of the model and avoids a mistaken impression. However, it is fundamentally meaningless to run this analysis to determine the uncertainties in the final point estimates (Thompson et al., 1992). Sensitivity analysis only provides partial information needed for conducting an uncertainty analysis (Tung and Yen, 2005). Therefore, performing an uncertainty analysis could encompass sensitivity analysis. Uncertainty is a situation where an observed or calculated value may differ from the true value due to the lack of perfect information on processes, which results in risks for decision making. Mays and Tung (1992) simply defined uncertainty as the occurrence of events that are beyond control. Although uncertainty is undesirable and unavoidable, manageable uncertainty provides the freedom to make creative decisions.
Generally, the sources of uncertainty in evaluating the reliability of environmental and water resources systems or in designing the systems baased on reliability include the uncertainties of nature, model structure, model parameter, data, computation, and operation (Singh et al., 2007;Tung and Yen, 2005). Natural uncertainties are associated with the inherent randomness of natural geophysical processes (Tung and Yen, 2005). Since model formulation varies over a wide spectrum, ranging from simple empirical equations to sophisticated partial differential equations with computer simulations, their uncertainties reflect the inability of model or design 31 procedures to represent precisely a system's true physical behaviour. Parameter uncertainties could be caused by the inherent variability of inputs and parameters in time and space and the lack of sufficient data. For instance, the parameters of a PD model cannot be estimated accurately due to limited numbers of observations; an empirical equation's coefficients are developed through calibrating or fitting a model to a limited amount of sample data. Data uncertainties arise from measurement errors, inconsistency and non-homogeneity of data, data handling and transcription errors, and inadequate representation of data samples due to time and space limitations (Singh et al., 2007;Tung and Yen, 2005). Operational uncertainties are associated with construction, manufacture, deterioration, maintenance, and other human factors that are not accounted for in the modeling or design precedure (Singh et al., 2007). Model prediction errors can be classified into systematic and random errors (Ang and Tang, 1984).
Measurement errors can also be categorized into systematic and random errors (British Standard Institution, 1998;Rabinovich 2000). Systematic errors may arise from factors that are not accounted for in the model, while random errors may be associated with the range of possible errors primarily due to sampling errors. In general, systematic errors associated with model prediction could be removed by multiplying a several bias-correction factors to or by subtracting the bias from the model output.
In order to improve the accuracy and usefulness of models, the following four problem areas that are affected by uncertainties must be addressed (Beck, 1987): (1) uncertainty about model structure or formulation, i.e., what are the basic processes involved, how are their interactions be mathematically characterized in an efficient and parsimonious manner; (2) uncertainty in the model parameters, i.e., parameter identification and calibration problems; (3) uncertainty associated with estimates of the future behaviour of the system, i.e., aggregation of uncertainties in model structure or formulation, model parameters, and in the definition of design or decision scenario into overall estimation uncertainty; and (4) reduction of critical modelling uncertainties through carefully designed experiments and monitoring programs. Uncertainties can be categorized as either aleatory or epistemic. If the uncertainties are caused by randomness in nature, it is characterized as aleatory, while those characterized as epistemic arise from the lack of the knowledge of systems or paucity of data. It is imposible to reduce aleatory uncertainties but epistemic uncertainties could be reduced through increasing the knowledge and a longer history of quality data (Singh et al., 2007;Kiureghian and Ditlevsen, 2009).
Uncertainties can be measured in terms of the probability density function (PDF), confidence interval, or statistical moments of random variables (e.g., standard deviation or coefficient of variation) of stochastic parameters (Tung and Yen, 1993). The PDF can provide the most complete and ideal description of the uncertainty features of a quantity (Tung and Yen, 2005).
Confidence interval is a measure of the uncertainty over the range of a variable and can be used to express the uncertainty in terms of a reliability domain. Using statistical moments associated with a quantity subject to uncertainty is a practical way to quantify the level of uncertainty for a parameter. In particular, the second order moment (i.e., variance) is a measure of the dispersion of a random variable. Either the variance or standard deviation can be used.
Model calibration is also necessary due to the semi-empirical nature of water quality models.
However, a calibrated model does not mean that it has predictive capability. It may contain incorrect mechanisms, and the consistency between model simulation results and measured data could be the result of unrealistic parameter values (Ji, 2008). Calibration is the first stage testing or tuning of a model to a set of data, preferably not used in the original model construction (Thomann, 1982). Calibration or tuning should include consideration of a consistent set of theoretically defensible parameters and inputs.
Model verification is important and can confirm that a calibrated model is useful over an extensive range of conditions in a water body (Ji, 2008). To verify a model, the conditions, such as the range of applicability (physically, chemically, or biologically), should be specified (Thomann, 1982). Any mechanisms, which were identified as a part of the initial construct but not incorporated in the verified model or vice versa, should be summarized. A verified model provides more confidence to predict future conditions of a system (Ji, 2008). However, the verified model is still limited to the range of conditions defined by the data sets used in calibration and verification procedures except if they are extrapolated. Any model prediction outside this range remains uncertain. A good verified model does not imply the ability to accurately predict future or distant water quality (Thomann, 1982).
Calibration and verification of a water quality model are not simply curve-fitting exercises but wherever possible should reflect more fundamental theoretical constructs and parameters (Thomann, 1982). James and Bierman (1995) suggested three ways of model calibration and validation: (i) graphing model output and observed data over time, (ii) Student's t-test between mean of model output and mean of field data for a time period (e.g. a year), and (iii) regression analysis of averaged model output (independent variable) with averaged observed data (dependant variable) for a time period (e.g. day or month).
With high performance computers, studies on stochastic processes and uncertainty analysis can be achieved, such as through Monte Carlo simulation (MCS), which is a powerful tool in many fields of mathematics, physics, and engineering (Dimov and McKee, 2007). MCS is a technique that generates random values of stochastic input parameters according to their respective probabilistic characteristics (Tung and Yen, 1993). In MCS the system response of interest is repeatedly measured under various sets of system parameter that were generated from unknown or assumed probabilistic laws (Tung and Yen, 2005). It offers a practical approach to uncertainty analysis because the random behaviour of the system response can be probabilistically duplicated.
The general procedure of MCS are: (1) to generate a large number of random sets to compute corresponding model sets, and (2) to analyze simulated model output to determine the statistical characteristics of model output such as the mean, variance, and PDF.
Particularly, the bootstrap resampling method, which is a form of MCS first proposed by Efron (1982) to deal with the variance estimation of sample statistics based on observations, has been applied for uncertainty analysis for several decades (see e.g., Pandey et al., 2003;Tung, 1993;Tung andMays, 1981 and. Efron (1982) and Efron and Tibshirani (1993) (Tung and Mays, 1981) and assessing the uncertainty associated with optimal risk-based hydraulic design of bridges (Tung and Mays, 1982). Tung (1993) also discussed its application for the assessment of the confidence interval of optimal risk-based design parameters. In the bootstrap procedure, a synthetic data set is generated by randomly selecting N observations from an original data set, which is the same size as the original data set (Richardson and Hollinger, 2005). Each synthetic data set will have different elements from the original one. The method assumes that the synthetic data set has a similar PD to that of the original data set. Tung and Yen (2005) presented a basic algorithm of bootstrap technique in estimating the standard deviation associated with any statistic of interest from a set of sample observations that involves the following steps: Step1: For a set of sample observations of size n, that is x = {x 1 , x 2 ,…, x n }, assign a probability mass 1/n to each observation as Eq. (2.39) Where fˆ is the non-parametric maximum likelihood estimator of the unknown probability mass function f x (x) for each individual observation.
Step 2: Randomly drawn observations from the original sample set using fˆto form a bootstrap sample, x * = {x 1* , x 2* ,…, x n* }. Note that the bootstrap sample x * is a subset of the original samples x Step 3

Remarks
Previous studies examined inland spills in different areas in Southern Ontario from various perspectives. They started with spill database analysis to point out the problem of inland spills and then raised their research interests and purpose. However, each study only focused on one Given n independent observations

Select a distribution function for generating bootstrap random
Calculate the value of the sample statistic of interest i * based on the bootstrap Calculate the properties of ˆ, such as the mean, standard deviation, sampling distribution, and confidence intervals, based on 38 aspect of inland spills -economic damage of oil spills (Tang, 2005), a web-based GIS for inland spill management (Han, 2007), and risk-based spill management criteria (Cheng, 2010). This research is comprehensive in that it includes probabilistic occurrences, fate of spills along rivers, risk analysis of water quality violation in compliance with associated standards at downstream locations along rivers, and management planning framework of inland chemical spills. The following are remarks based on literature review: The data analysis results, including spilled time, mass, and NAICS-based location, are used for the development of associated PD models to achieve one of the research objectivespredicting inland chemical spill probabilistic occurrences.
MCS is applied for simulating the probabilistic occurrences by time, magnitude, and location in a certain area. MATLAB software is used to develop the associated MCS program.
One thousand times of nonparametric unbalanced bootstrapping is employed to analyze the uncertainties of the PD's parameters and inadequate representation of inland spills data.
Benzene spills in the St. Clair River AOC are used as case study and their characteristics are further transferred to the Mimico Creek watersheda hypothetical case study.
The water quality models SpillMan for the St Clair River and Neely et al.'s model (1976) for small rivers will be applied for the case studies to demonstrate the developed MATLABbased MCS models associated with inland benzene spills, which can achieve another research objectivequantitative risk analysis of water quality impairment at downstream locations along rivers.

CHAPTER 3 INLAND SPILLS IN SOUTH ONTARIO
Chemical spills have been of great concern by the public and politics over the past decades due to extraordinary spill events in southern Ontario. This chapter mainly focuses on the inland chemical spill characteristics in Southern Ontario and their significance. In particular, benzene spills in the St Clair River AOC are analyzed because benzene is toxic and carcinogenic contaminant and was among the top 20 chemical pollutants in the Environment Canada's Priority List for the period of 1987-1997 (Fingas et al., 2000).

Spill Database
The inland chemical spill records for Southern Ontario were originally provided by the SAC and updated by Ryerson University (e.g. assignment of longitude and latitude of spills, spill locations, etc. While some spill events are recorded in both databases, there are discrepancies between the two recording systems. This may be attributed to the definition of spill events and differences in the use of spill information between the SAC and the SLEA. The SAC is a provincial agency which collects and coordinates spill response. Its mandate addresses provincial priorities and fulfills the requirements of reporting and cleaning up spills immediately and restoring the environment promptly by the owner of the spilled material, the person causing/permitting the spill, and the person controlling a material when it was spilled under the Environmental Protection Act (Ontario MOE 2007a. The spill data are analyzed annually to identify spill occurrences and types in various regional municipalities and industries. The SLEA is an industrial association which focuses on local industrial cooperation and sharing of technical information. It is understandable that the data collected by these organizations are not consistent.

Statistical Characteristics of Chemical Spills in Southern Ontario
As The volume of Ontario imports grew from 1997 to 2007 (Ontario MOF 1995. In particular, the top three international imports, motor vehicles and parts, mechanical equipment and electrical machinery, were related to industries and accounted for over 50% of the total international imports in this period. Moreover, the rapid development the average monthly spill occurrences and average monthly temperature appear to be correlated. This may be attributed to an increase in transportation activities during summer months (Environment Canada, 2006). Researchers said that -actual changes in temperature, rainfall, and other weather variables have direct effects on various economic series, such as those concerned with agricultural production, construction, and transportation, and consequent indirect effects on other series‖ (Granger 1978); -weather is a powerful force affecting the economy‖ (Niemira 2005); and -seasonal fluctuations are an important source of variation in all macroeconomic quantity variables, including consumption, investment, government purchases, employment and the money stock‖ (Barsky & Miron 1989). Niemira (2005) also raised three basic aspects in assessing weather effects on consumer and business activity: the role of weather as noise in temporarily shifting the timing of purchases or production; the role of weather as a seasonal shock in possibly permanently impacting demand and output; and the potentially casual relationship between weather cycles and macroeconomic activity. He concluded that -weather impacts economic activity‖. Consequently, the winter months may result in a total loss of demand and a decrease of production resulting in a small number of spills.

Statistical Characteristics
The chemical spills which impact surface water (surface-water-impact spills) were compiled from the SAC spill database. As indicated in Table 3 3.4 (b), which accounted for about 63% of the surface-water-impact spills reported. Compared with Fig. 3.3 (b), this observation is similar to that for the total spills, implying that chemical spills may also significantly impact other environmental media such as soil and air in these municipalities.

Spatial Characteristics
The ArcGIS-based spatial distribution of the surface-water-impact spills in all reported municipalities is presented in Fig. 3.5. It is observed that the cities that have higher densities of industries (small dots shown in the figure) have the larger number of surface-water-impact spills in cities, such as Toronto, Hamilton, Mississauga, Sarnia, and Brampton. This might explain the higher proportion (63%) of all recorded surface-water-impact spills in these five cities as mentioned above. It is also noted that the St Clair River and the Humber River are the two major rivers which have received the most spills (i.e. Sarnia and Toronto) and may potentially suffer local water quality impairments, which may be attributed to the fact that 450 petrochemical facilities are located within a 30 km stretch of the St Clair River (Ontario MOE 2005) and 5.6% (5,760 hectares) of the total area of the Humber River watershed has industrial land use (TRCA 2008).   59

52
In terms of the causes of surface-water-impact spills, 23 causes including unknown were specified. Some of them had estimated reported volume, others had reported mass, while a majority had no reported volume or mass. Other than the chemical spills with unknown causes, the cause ‗discharge/bypass to watercourse' is the most frequent followed by causes such as ‗other discharges', ‗container/tank/lagoon overflow' and ‗pipe/hose leak'. The total occurrences, total volume and mass of chemical spills are presented in Table 3.2. It is observed that the occurrences of these five causes account for 80% of the total but occupy about 96 and 85% of the total volume and mass, respectively. This result may be able to guide not only municipalities but also industries on reporting procedure and the identification of priorities for chemical spill prevention, control and emergency response. 60

Benzene Spill in the St Clair River AOC
Benzene is a colorless, sweet smelling, flammable organic chemical liquid with the molecular formula C 6 H 6 (Benzene MSDS). Its density varies with temperature (0.8787 kg L -1 at 15 o C (Benzene MSDS) and 0.8765 kg L -1 at 20 o C (Lide, 2007)). The solubility in water is 1.8 g L -1 at 15 o C (Arnold et al., 1958). Benzene is also a confirmed carcinogen for humans (Benzene MSDS). It is toxic to blood, bone marrow, the central nervous system, and the haematopoietic system (at low concentration); it may also damage the liver and urinary system and cause a continuum of haematological changes such as leukaemia (Benzene MSDS;WHO, 2003).
Benzene can be used in a number of products such as paint, rubber, detergents, tires, shoes, drugs, plastics, synthetic rubber, phenol, nylon, aniline, polyester resins, dyes, and insecticides (U.S. EPA, 2009a), which implies that a number of industries related to the production and use of benzene could be potential spill sources that may consequently have an adverse affect on human health. Therefore, benzene spills have been of great concern for the local government of the River AOC (Cheng, 2010). In addition, Environment Canada's top Priority List, based on chemical spill data over a 10-year period from 1987 to 1997, show that benzene was among the top 20 chemical pollutants (Fingas et al., 2000).
This research used benzene spills in the St Clair River AOC as a case study to demonstrate the models that were developed for its probabilistic occurrences and risk analysis for water quality violation at the water treatment plant intakes along the river. Therefore, the statistical and spatial characteristics of benzene spills in the St Clair River AOC are mainly focused on in the following sections.

Statistical Characteristics
The statistical characteristics of benzene spills in the River AOC were analyzed based on the spill data collected by the SAC and the SLEA between 1988 and 2007. From the 64 benzene spills whose occurrence was recorded in the River AOC, only two occurred in the same day at different workshops of the same industry, and 39 had reported the magnitude of the spill by mass or volume. Industrial plants and pipeline systems in the chemical, general manufacturing, and petroleum refinery sector were the sources of the benzene spills, in addition to unknown/unspecified sectors. In order to determine the probability distribution of benzene spills in the NAICS based group, the spill inter-event time and the spilled mass, as well as simulate the probabilistic spill occurrences in the St Claire River AOC, the two spills which occurred in the same day were treated as one spill. Since temperature was unavailable for correction, spills with magnitudes quantified spills were compiled and the relevant volumes were converted into masses using a density of 0.8765 kg L -1 at 20 o C (Lide, 2007).
After conversion, the total amount of benzene spills from 1988-2007 is estimated to be approximately 2218 kg (average 111 kg yr -1 ). The frequency of benzene spills per year quantifiable or not in the River AOC is compared in Fig. 3.8. It is observed that the annual number of benzene spills in the River AOC fluctuated from 0 to 17. Fig. 3.9 presents the environmental impacts (a) and the causes (b) of all benzene spills in the River AOC. It was found that 38% of spills resulted in surface water pollution directly and 38% of them were not identified. Thirty-eight percent of spills were caused by various leaks, such as container leaks, pipe line leaks, and valve/fitting leaks, 24% of them were caused by discharge/bypass to watercourses, and 20% were of unknown causes. About 39% of recorded spills had no accurate 63 quantities, which may be attributed to the difficulty in estimating the amount of spilled benzene discharging into a watercourse or leaking into the ground. It is executed that some of these frequencies may provide information for associated industries to develop effective spill prevention and control plans at source (e.g. staff training, equipment replacement, operation and maintenance, implemented to prevent and control spills over a realistic period of time).  1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Spatial Characteristics
Under the NAICS, three types of industries, cosed as NAICSs 325210, 325110, and 324110, which represent resin and synthetic rubber manufacturing, petrochemical manufacturing, and petroleum refineries are identified to have produced benzene spills in the River AOC, in addition to unknown sources (with the representation of NAICS Unknown). Therefore, a spill's source (a location) can be represented by a NAICS code. The statistics of 38 benzene spills that had magnitudes and formed 3 NAICS based industrial groups (hereafter referred as NAICS groups) along with an unknown NAICS group are shown in Table 3.3. According to the SAC and SLEA databases in the St Clair River AOC, the annual spilled mass varies between 0 to 769 kg, and the mass of the most benzene spills is less than 120 kg, with the exception of two large spills that

Summary of Findings
According to the above statistical and spatial characteristics analysis of the SAC and the SLEA spill databases, inland chemical spills in Southern Ontario from 1988-2007 were continuous nonpoint pollutants, which had caused impacts on the environment and human health. The other findings are concluded as below: Many of inland chemical spills which caused surface water pollution originated from industrial plants. The top four sectors having the most frequent spills include the sectors metallurgy, chemical, general manufacturing, and transportation.
Major causes of inland chemical spills are pipe/hose leak, fuel tanks/barrels leak, process upset, and discharge/bypass to watercourse, resulting in surface water pollution, soil contamination, air pollution, and other impacts.
The St. Clair River and the Humber River are the two major rivers which have been exposed to frequent chemical spills resulting in high potential impairments of water/drinking water quality.
Discharge/bypass to watercourses, other discharges, container/tank/lagoon overflow, pipe/hose leakage, and fuel tanks/barrel leakage are the major causes of chemical spills.
The majority of spilled chemicals were not cleaned up and their fates in the environment may impact on air, water, and soil quality and human health.

Methodology for Probabilistic Simulation of Inland Chemical Spill Occurrences
In designing a stochastic process, inter-event time is a very significant parameter. The cumulative effects of consecutive spills in a short time period are of high concern. After examining the updated SAC and SLEA databases, it was observed that similar chemical spills 71 rarely occurred more than once on any given day between 1988 and 2007. However, there were close occurrences which might lead to cumulative effects on surface water quality. Additional research on cumulative impact assessment is required but is beyond the scope of this study. The MATLAB-based Monte Carlo Simulation (MMCS) model was developed by assuming that spill occurrence is a homogenous stochastic process and no occurrences happen simultaneously on the same day.   (1) determination of the PD and parameters (inter-event time and spilled mass) for each NAICS code, and (2) spill database limitations, including the estimated errors of spill quantity, inconsistency and non-homogeneity of spill data, errors of spill data handling and transcription, and inadequate representation of data due to time and space limitations. This study addresses uncertainties related to model selection and relevant parameters. Other uncertainties, such as spill data uncertainty and human error, are outside the area of this study and have not been analyzed.
The nonparametric unbalanced bootstrapping technique is used in this study to analyze the uncertainties of the PD parameters and inadequate number of spill events. It can substitute sensitivity analysis to investigate parameter uncertainties in the MMCS model. The resampling is done by randomly selecting a synthetic data set following the bootstrap procedure discussed in the Sectin 2.5. The synthetic data is assumed to have the same PD as the original data set and its PD parameters are then estimated using the maximum likelihood method. This procedure is repeated 1000 resamples to estimate a confidence interval and to achieve uncertainty analysis.   Canada, 1996 andOntario MOE, 2002;Ontario MOEE, 1994). The implication is that drinking water quality and human health would be harmed by benzene if its concentration exceeds these regulations/standards.

Correlations of Benzene Spill Data in the St. Clair River
Correlation is one of the most common and useful statistical methods that measures the relation between two or more random variables or two or more sets of data. Since the MMCS model contains 3 variables (i.e. NAICS code, spill inter-event time, and spilled mass) and spill interevent time comes from spill occurrence time, it is necessary to examine their correlations before applying the model to predict spill probabilistic occurrences. This chapter investigates the correlations between benzene spill inter-event time and spilled mass, and between spill occurrence time and spilled mass. Using regression analysis, very low coefficients of determination (R 2 ) of 0.014 and 0.025 are obtained for these two cases respectively. Therefore, the investigation concludes in both cases that the investigated variables are virtually independent.
It could be assumed that there is no relationship among the industries for benzene spills. The 75 frequency of NAICS code, spill inter-event time, and spilled mass are also assumed to be independent of each other.

Probability Distributions of Benzene Spill Variables
To simulate the probabilistic occurrences of benzene spills in the River AOC, the probability distributions of spill variables (i.e. NAICS code, spill inter-event time, and spilled mass) were investigated. Using data presented in Table 3.3, the frequencies of spill variables for the 4 NAICS groups were determined. The histogram of NAICS codes is shown in Fig. 4.3 (a). Each NAICS group consists of various industries which are assumed to be equally likely to produce a benzene spill. The frequencies of NAICS groups are assumed to be their probabilities. Therefore, the probability distribution of NAICS groups is treated as a discrete uniform distribution.
The study tested various common used distributions, including normal, lognormal, Weibull, exponential, and Gamma, using the method of maximum likelihood in MATLAB software, to investigate the PDs of the benzene spill inter-event time and spilled mass. The fitted cumulative distribution functions (CDF) using these distributions for benzene spill inter-event time and spilled mass are shown in Fig. 4.4 (a) and (b) respectively. According to the maximum likelihood method, benzene spill inter-event time and spilled mass were better fitted with Weibull and lognormal distributions (solid red lines in the figure), so were those for each NAICS code.
Through MATLAB functions -WBLFIT‖ and -LOGNFIT‖, which also apply the maximum likelihood method, the parameters of Weibull (λ and β) and lognormal (μ y and σ y ) distributions of benzene spill inter-event time and spilled mass respectively, were determined for each NAICS code as summarized in Table 4

Simulation of Probabilistic Occurrences of Benzene Spills in the St
Clair River AOC

Selection of Simulation Runs and Time Period
The simulation of probabilistic benzene spill occurrences in the River AOC was conducted following the procedure shown in Fig. 4.1. The MATLAB functions -RAND‖, -RANDINT‖, and -LOGNRND‖ were used to generate random variables of NAICS code, an industry from NAICS group, and spilled mass, respectively. The variable inter-event time is determined by -λ *((log(1/U))^(1/β))‖ through a generated random number -U‖. The purpose of the randomly generations is to simulate the spill occurrences by time, mass, and NAICS-based location. The MATLAB codes for generating the random variables are summarized in Fig. 4.5.
Generally, the numbers of simulation runs have a direct effect on the accuracy of the simulation 79 results. Increasing the numbers of runs will reduce the standard error (E μ ) of the mean of a distribution and no effort is made to harness the distribution (Anonym, unknown date). The accuracy only improves as the square root of the ratio of the number of additional runs, which means 100,000 runs instead of 1,000 are needed to achieve an improvement of ten. Through specifying a maximum acceptable percentage error E μ for the mean, the minimum numbers of simulation runs, n, can be determined by Eq.
Where: σ is the true output standard deviation and z is confidence coefficients for different confidence interval (e.g., for 95 and 99% of confidence of normal distribution, and z is 1.96 and 2.58). Since σ is not known, various numbers of n can be performed to find appropriate numbers of simulation runs.
The bigger numbers of simulation runs with longer simulation time period (TP) leads to the longer time simulations. Therefore, it is important to determine the appropriate TP and simulation runs for simulating probabilistic spill occurrences. Ten, twenty, and fifty-year TPs with 10 5 runs were first used in the MMCS model to select the simulation TP. It was found that the benzene spill occurrences over 20 and 50 years were approximately 2 and 5 times respectively, of those occurring over 10 years, which implies that the system of probabilistic spill occurrences could be considered as a steady-state system. Therefore, a 10-year simulation TP is selected for the MMCS model of benzene spill occurrences in the St Clair River AOC, which is also corresponding to the 10-year period of the re-evaluation of Environment Canada's Priority List.

80
Subsequently, 10 4 , 10 5 , and 10 6 runs with a 10-year TP were input into the MMCS model to select the appropriate simulation runs. It was found that the numbers of benzene spill occurrences with 10 5 , and 10 6 runs were almost the same, while those with the 10 4 runs were slightly different from other two results, which implies that 10 5 or more runs may be big enough for the simulation. Therefore, 10 5 runs were selected for the simulation of benzene spill occurrences in the River AOC. The MCS running ended when occurrence time was outside of 10 years (3650 days) and this loop repeated 10 5 times. The results of the selection of simulation TP and runs are summarized in Table 4.2.

Simulation Results and Discussion
The simulated benzene spill time series including expected spill occurrences, occurrence time, and spilled mass in the St Clair River AOC for the next 10 years are summarized in Table 4.3.  Table 4.3. After examining the distribution of simulated spill occurrences using the maximum likelihood method, the four simulated NAICS groups were found to be properly described by normal distributions.
Their probability distribution functions (PDF) with their parameters (μ and σ) are illustrated in Fig. 4.6 (d). Therefore, the NAICS-based probabilities of having specific number of inland occurrences could be determined through their normal PDFs. Furthermore, it is observed that more than 90% of simulated masses of all NAICS groups have relatively small values, which 83 may be attributed to the factor that most of historical spilled masses are relatively small (see the medians and 90 th percentiles in Table 3.3).

Uncertainty Analysis
In terms of the occurrences of inland chemical spills, they exhibit both aleatory uncertainties in time and space due to their feature of randomness and epistemic uncertainties due to the    clues to industries that involved in spills on how frequency potential spills will occur, whether they need to be treated as severe events based on the simulated masses, and when measures (e.g. technologies on site, equipment, and finance, and human resources) need to be ready to deal with them. Moreover, the simulation results also provide support for the next stage of the quantitative risk-based analysis of drinking water quality impairments in the WTP intakes along the St Clair River, which will discuss in Chapter 5.

Simulation of Probabilistic Occurrences of Benzene Spills in the Mimico
Creek

Model Description
As discussed in Chapter 3, although there were thousands of spills occurred in Southern Onteriao for the past two decades, 90% of chemical types happened less than 10 times. This brings difficulties for investigating the probability distributions of model variables (i.e., spill occurrences, inter-event time, spilled mass) and probabilistic spill occurrences to assist decision making. Therefore, this hypothetical case study is presented to investigate the possibility of the transferrable characteristics of a historical database from one area to another area. The Mimico Creek

Simulation Results and Discussion
The simulated benzene spill time series, including expected spill occurrences, spill occurrence time, and spilled mass, in the Mimico Creek watershed for a 10-year time period are summarized in Moreover, if a spill's initial concentration C o at the outlet to Mimico Creek is estimated by Eq.
(4.2), where the volume of benzene spill is negligible compared to the creek's volume.
where M is simulated spilled mass, in kg; Q is the creek's flow rate at the outlet, in m 3 /s; and SDT is spill duration time, in s. It is noticed that the most spill occurrences will cause violation of the maximum acceptable concentration of benzene in drinking water at the outlets to Mimico Creek, indicating that to prevent and control benzene spills at source is highly required regarding water quality protection.
95 The histograms of simulated spill occurrences, violation-causing occurrences, occurrence time and spilled mass for potential individual industries are illustrated in Fig. 4.9. The label of a is found that normal distributions could be used to describe them properly, as illustrated in Fig.   4.10. The associated PDF parameters (μ and σ) are shown in Table 4.8. Therefore, the probabilities to have a specific number of inland occurrences casued by industries could be determined through these PDFs.  Table 4.7). This significance depends on the magnitude of spill, flow rate and geographical characteristics of waterways, water quality model applied, and weather condition. The implications of simulated spills for the water quality of Mimico Creek are discussed in Chapter 5. Similarly, NAICS-based and City-based simulated spill occurrences and violation-causing occurrences are also found to be normally distributed, as shown in Fig 4.13. The associated PDF parameters (μ and σ) are presented in Table 4.8. The simulation results indicate that most simulated spill occurrences by potential industries would cause water quality violation at the outlets to Mimico Creek, which may provide clues to the attitude of industries and/or municipalities with respect to the priority of benzene spill prevention and management.     Clair River AOC and the Mimico Creek watershed (hypothetical case), along with their fates along these waterways, are used as case studies to demonstrate the EMMCS model.

Impairments by Inland Chemical Spills
As discussed in the Section 4.2.3.1, the system of probabilistic spill occurrences could be a steady-state system. So the risks due to the spill occurrences were also in the steady-state system.

Risks of Drinking Water Quality Violation due to Benzene Spills along the St. Clair River
According to SLEA database, benzene spills generated by various facilities in the St Clair River AOC have been reported to enter directly or indirectly to the river leading to 6 shutdowns of WTPs during the period of 1990-2004. With respect to unknown or expected risk to public health, 0.005 mg/L of MAC is set out for benzene in drinking water (Ontario MOE, 2002), which is used as a standard concentration (C s ), as presented in Eq. River (Ontario MOE, 2005), which become the sources of potential spills bringing potential threats to water quality.

Variables
Chapter 3 presents statistical analysis and spatial characteristics of benzene spills in the St Clair River AOC. Three known NAICS-based industrial groups, NAICS 325210, 325110, and 324110, which involved in the production of benzene spills, in addition to unknown sources had been used in Chapter 4 to demonstrate the MMCS model. Fig. 3. Canada. Using the maximum likelihood method, various probability distributions, including normal, lognormal, Weibull, exponential, and Gamma, were tested for the goodness-of-fit for the PDs of monthly flow rates, and the minimum and maximum monthly based daily flow rates of the River. It was found that the PDs of the monthly flow rates could be properly described by the lognormal distribution. Fig. 5.2 shows the fitted monthly flow rates, and their parameters are summarized in Table 5.1. The PDs of both the minimum and the maximum monthly based daily 114 flow rates were found to be better fitted with the Weibull distributions.

Water Quality Models
The calibrated SpillMan model (Nettleton and Hamdy, 1988)  Critical spill duration time (TC, in hr), which was used to determine a spill typeshortduration spill or long-duration spill at an outfall; Time between arrival and peak or peak and departure (TAPD, in hr); General decay factors (DF, in s -1 ), which was used in correcting the predicted concentrations for decay loss at various TT; No-decay peak concentration for a loading rate of 1 kg/s (PC, in ug/L), which was applied to determine predicted peak concentrations at an intake, as shown in Eq. Where: CPC is predicted peak concentration at an intake for a short-duration spill, in ug/L; and NUMDF is the fraction of the conservation contaminant's concentration remaining at the water intake, based on the loss rate as provided by general decay factor and mean travel time from associated outfall to the intake.
No-decay peak equilibrium concentration for a loading rate of 1 kg/s (EC, in ug/L), which was applied to calculate predicted peak concentrations at an intake, as shown in Eqs.

EMMCS Model Simulations
The risks of drinking water quality violations due to simulated benzene spills at the 11 WTP intakes along the River are determined using the EMMCS model (see Fig. 5.1). Since the spill database has no information on SDT, a range from 0.01 to 24 hours was selected for the SpillMan model. If a spill were released for more than one day, it is assumed that measures must be implemented to stop the spill. This also corresponds to the EPCRA (1986) guide: a facility emergency plan must have a 24-hour emergency coordinator and an alternate 24-hour emergency coordinator. This also implies that a spill reporting system should include the collection of SDT information. Therefore, in order to investigate the implications of river flow conditions on the risks of water quality violations due to spills along the River, the following five flow scenarios are applied for the EMMCS simulations for the period 1988-2007: (1)  In order to increase the accuracy of simulation results, the following two conditions were used in the case of daily flow rate to analyze the risk of violating drinking water quality requirements: (1) a river flow rate of 6,050 m/s that is the average of 6,800 and 5,300 m 3 /s assumed in the SpillMan model and (2)

Simulation Results and Discussion
For the regular case, the simulation spill time series that were obtained in Chapter 4 are summarized in Table 5 year period are between 0.3 and 1.4, while the overall probabilities (i.e. risk) of drinking water quality violation due to the simulated benzene spills are between 9 and 37%, as also indicated in presents expected arrival and departure times of peak concentration and expected arrival and departure times of the spill plume at the Ontario WTP intakes, which could provide assistance to downstream WTP operators' for water quality control.  As discussed in Chapter 4, the NAICS-based probabilities of having a specific number of inland occurrences can be determined by normal distribution function. After examining the simulated violation-causing occurrences at the WTP intakes, it is found that they could be described by exponential distributions. Their distribution parameters (μ, σ) or λ are presented in Table 5.3.
Therefore, the probability of having a specific violation-causing occurrence can be estimated. As  Michigan side except the intake at Old Club, which may be attributed to the same reasons as those of the intakes at Ontario's three islands. At the intake at Old Club, the NAICSs 325210 and 324110 caused water quality violation with the probabilities of 0.7 and 4.6% and expected peak concentrations of 0.01 and 0.07 mg/L over a 10-year period. This may be attributed to the fact that the mean spilled masses of NAICSs 325210 and 324110 were much high (due to a spill event with much high mass in each of them) and the Old Club intake is located at a branch of the St Clair River where flow rate was lower than main stream resulting water quality violation.
However, the violation-causing occurrences at the Old Club intakes were found to be lower than other intakes. Therefore, it could be concluded that the simulated benzene spills would not impair the drinking water quality at the Michigan intakes but further research on extreme spill events should be conducted to investigate water quality violation at all intakes.

Uncertainty Analysis
Uncertainty analysis was conducted under the flow condition of month-based daily flow. A bootstrap resample using EMMCS was repeated one thousand times to determine the uncertainty of the spill related distributional parameters. The uncertainty of river flowrate related distributional parameters was not analyzed due to sufficient flow data of the river provided by Environment Canada. For each simulation of the EMMCSs, a subset of benzene spill inter-event time and spilled mass was first generated using the nonparametric unbalanced bootstrapping technique for each NAICS code. Similar to the PDs of the original NAICS codes, the PDs of these bootstrap subsets (i.e. inter-event time and spilled mass) followed Weibull and lognormal distributions. The PDs' parameters were then estimated using the maximum likelihood method.
After performing 1000 simulations of EMMCS, the spill occurrence, the mean spill occurrence time, the mean spilled mass in the River AOC, and the violation-causing occurrences at the WTP intakes over the next 10 years were determined. It was found that the lognormal distribution could properly describe the PDs of NAICS-based simulated spill occurrences, the mean spill occurrence, and the mean spilled mass of each NAICS code.

131
The sample mean, standard deviation, and 95% confidence interval of NAICS-based and overall probabilities of drinking water quality violation at the WTP intakes on the Ontario side are presented in Table 5.5 presents. In addition, the NAICS-based probabilities of drinking water quality violation are observed to be Weibull distributed. Fig. 5.6 illustrates their histograms and Weibull distributions.

Background of Mimico Creek
Mimico

Correlations and Probability Distributions of EMMCS Model Variables
The potential spill inter-event time, occurrence times, spilled mass, and daily river flowrates were assumed to be statistically independent of each other according to the case study of benzene it is found that they could be properly described by lognormal distributions. Fig. 5.7 illustrates their fitted CDFs and Table 5.5 summarizes their parameters. As shown in Table 5.6, all parameter μ y values are negative because of the negative skewness of the distributions.

Water Quality Model
As introduced above, Mimico Creek is a long and narrow creek with low flow rate and relatively steep watershed. Therefore, the creek can be considered as a small river differening from a large river because the former together with streams becomes the latter. According to Neely et al.'s (1976) I is mass rate entering into the nth compartment, kg/s, which is calculated as QC n-1 , where Q is river flowrate (m 3 /s) and C n-1 is concentration in the (n-1)th compartment; O is mass rate leaving the nth compartment, kg/s, which is calculated as QC n ; G is mass loss rate due to water-to-air exchange, kg/s, which is determined by k e AC n (Wick et al., 2000), where k e is the exchange rate of water-to-air that is 0.5 m/d (Schwarzenbach et al., 1993) and A is surface area of the compartment (m 2 ); B is mass loss rate due to biodegradation, kg/s, which is considered as the pseudo-firstorder decay and so can be determined by k b VC n , where k b is decay rate that is between 1 and 2.5 per day (Wick et al., 2000) and 1.5 per day is used in this study; F is mass loss rate due to episodic flushing events, kg/s, which can be negligible because only large rain events will affect this loss and it is difficult to quantify it in these event (Wick et al., 2000); P is mass loss rate due to photolysis, kg/s, which can be negligible since benzene does not undergo a significant direct photolysis in sunlight (Wick et al., 2000).
S is the mass loss rate due to settlement, kg/s, which can be negligible due to a very low loss of benzene to the sediment bed (Wick et al., 2000).
Therefore, the mass balance Eq. (5.13) can be simplified to Eq. (5.14) by using the expressions of I, Q, G, and B and neglecting F, P and S. initially is set to be C n (0) = 0. Solving the differential Eq. (5.14), the concentration in the nth

EMMCS Model Simulations
If continuous data on river width and depth are lacking on a global scale (Schulze et al., 2005), the river width and depth can be estimated as a function of channel discharge, as expressed in Eqs. (5.18) and (5.19) introduced by Leopold and Maddock (1953). Their applications can be found in hydrology textbooks (e.g. Mosley and McKerchar, 1993;Dunne and Leopold, 1978). In order to quantify the best-fit coefficients (a and b) and exponents (c and f) Table 5.7 presents the information on inland travel distances and travel times and distances between selected locations along Mimico Creek and the mouth of Lake Ontario. As shown in the table, most travel times are shorter than 3.1 minutes except for one industry with 10 minutes. Therefore, the inland decay of benzene is assumed to be neglected, resulting in all simulated benzene masses entering into Mimico Creek.
Similar to the inland benzene spill simulations in the Mimico Creek watershed in Chapter 4, the uncertainty analysis for the parameters of the PDs of inter-event times and spilled masses are not conducted.

Simulation Results and Discussion
Under simulation conditions (i.e., [0.01, 24] hours of SDT, 10 years of TP, and 10 5 simulation runs), the scenarios of 0.1, 1, 5, and 10 m length of each compartment were conducted. The industries' concentration profiles related to distance and associated arriving time along Mimico Creek are shown in Fig 5.8 (a) and (b), while their probabilities (i.e. risks) of drinking water quality violation caused by each industry at the downstream location are illustrated in Fig. 5.9.
As observed in these figures, the peak concentrations and violation probabilities reduced quickly to much lower values after travelling a few kilometers from outfall to downstream. The shorter the length of each compartment leading to a smaller volume, the lower the downstream peak concentrations and violation probabilities, as revealed by Eq. (5.17) having been applied to this case (i.e. treating a small river as a series of compartments and the concentration in each compartment assumed to be same).
In addition, in order to investigate the effect of benzene decay rate k b on the annual occurrences and risks of water quality violation at the downstream locations, the simulations are also conducted respectively using 1 (minimum rate by Wick et al., 2000) and 2.5 (maximum rate Wick et al., 2000) day -1 of biodegradable rates with 10 m length of each compartment. It is found that most annual occurrences and risks of water quality violation at the same location from the same industry are same under the decay rates of 1, 1.5, and 2.5 day -1 . The maximum differences of annual occurrence and risk are 0.003 and 0.015 respectively. It can be concluded that the change of benzene decay rate has very small effect on the risks of water quality violation and can be neglected. Therefore, the length of each compartment becomes a control factor for the decay of spill concentration. Although there are no direct field data available for calibrating the water quality model, it would be reasonable to apply the simulation results of the EMMCS model for the purpose of spill prevention and management.
The NAICS-based and City-based expected annual benzene spill occurrences and violationcausing occurrences (including those at the entrances of Mimico Creek and some selected downstream locations along its length) in compliance with 0.005 mg/L of benzene's MAC in drinking water are summarized in Tables 5.8 and 5.9. As shown in Table 5.8, the City of Mississauga may experience the highest potential benzene spills occurrences followed by the Cities of Brampton and Toronto. For all simulation scenarios, violation-causing occurrences present very small numbers at main stream's downstream locations. It is observed that the simulated spills in the City of Brampton do not violate the benzene MAC at downstream locations close to the mouth of Lake Ontario, which may be attributed to the long distance between the outfall and the mouth. Table 5.9 suggests that the NAICS 325210 will have the highest inland potential spill occurrences and violation-causing occurrences. Similarly, very low violation-causing occurrences are seen at downstream locations. The potential spills from the NAICS 324110 industry will not violate the benzene MAC at the outlet to the creek as well at the downstream locations. Both figures present very low probabilities to have one violation-causing occurrence close to the mouth of Lake Ontario.

Summary of Findings Regarding EMMCS Simulations
Based on the above simulation results, the following findings are summarized: The proposed EMMCS can simulate spill time series, including the probabilistic spill occurrences by time, magnitude, and NAICS-based location, and determine the associated quantitative risks of water quality impairments at any location downstream of receiving waters.
The model can provide information on prior industries that could need to reduce spill frequency and magnitude by implementing spill prevention and control. Regulatory The simulation results of benzene spills in Mimico Creek show that 99% of spilled masses have relatively small values leading to very low probabilities of having one violationcausing occurrence at the locations that are close to the mouth of Lake Ontario (about 14 km). When historical spill data are unavailable, the method of transferring available historical spill data from one area to another one with reasonable adjustments would help to provide valuable information to industries or municipalities with respect to benzene spill prevention and management.

MANAGEMENT PLANNING FRAMWORK
Inland chemical spills can be significant environmental events that potentially impair receiving water quality and damage human health. Spills in large quantity could acutely elevate certain toxic chemicals at water intakes (Cheng, 2010). Even small quantity spills could increase chronic toxicity levels in receiving waters. As discussed in Chapter 3, hundreds of chemical spills occur every year in Southern Ontario, resulting in surface water impact and other multiple environmental implications. Additionally, receiving waters have experienced continuous impairments by thousands of spilled chemicals (Cao et al., 2012). According to Fig. 3.1, for the 5-year period of 2003-2007, the numbers of chemical spill events have an increasing tendency, implying that industries may not well prevent, control, and manage their spill problems.
Therefore, a comprehensive inland chemical spill management framework is acutely needed to assist industries and governmental organizations to allocate considerable resources to conduct analyses and preparedness tests (Kenar et al., 2007) to protect source water quality, human health and ecosystem health. CCME (2008) published a -Canada-wide strategy for the management of municipal wastewater effluent environmental risk management framework and guidance‖, whose recommendations are very practical and helpful for spill prevention, control and management and are presented in the following sections.
However, no such framework can be found in most municipalities across Canada. A survey of municipal preparedness for spills in major cities in Canada between 2006 and 2007 indicated that only Toronto and Edmonton had a sewer use bylaw, a spill management plan, and an emergency spill response team simultaneously (Han, 2007). Spill management plans have been reported to exist for cities such as Toronto, Edmonton and Victoria, while most cities have a sewer use bylaw and some have a spill response team. Responding to this challenge, a comprehensive chemical spill management framework is developed, which consists of a spill pollution prevention plan, a spill control plan, and an emergency response plan, as shown in Fig. 6.1 (Cao et al., 2012). Through effective technical planning tools, such as the MMCS and EMMCS models proposed in Chapters 4 and 5, it would be appropriate for a municipality to prepare a spill management plan by identifying the key chemicals, industries, and areas of concern from historical spill data analysis and stochastic model simulations. This chapter discusses the spill management framework.

Spill Pollution Prevention Plan
Pollution Prevention (P2) is -the use of processes, practices, materials, products, substances or energy that avoid or minimize the creation of pollutants and waste, and reduce overall risk to human health or the environment‖ (Canadian Environmental Protection Act, 1999). It is at the top of a hierarchy of environmental protection methods that include reuse and recycling, pollution control or treatment, disposal and destruction, and remediation and clean-up due to the most cost-effective opportunities for reducing environmental and health risk. Spill P2 plans (P2P) can eliminate, minimize or reduce the probability of occurrences spill occurrences at source, identify specific spill prevention and management measures to be implemented within the operation over a realistic period of time. The goal of P2P is to protect human health and the environment, specifically protect source water quality in this research.

Education Programs
An education program is an essential component of a spill P2P. One impetus of this program is to increase public awareness of the occurrences of spill events and encourage them to promptly report the occurrence to regulatory authorities with as much information as they can. Another impetus of this program is to train workers in the relevant industries on preventative maintenance 155 and operating procedures in order to prevent and reduce spill occurrences. An education program can include employee training, rehearsals, public education, and media response, and can be carried out by governments and industries. The priority industries obtained through MMCS and EMMCS model simulations especially need an education program.
1. Employee training includes preventive maintenance and operation procedures. Maintenance is a key to prevent and reduce spill occurrence on site. Therefore, it is necessary to train employees to be aware of the regular maintenance of equipment and relevant operation procedures. An effective tool is to prepare an operation and maintenance (O&M) schedule.
If an O&M schedule exists, it should be reviewed and updated to increase its efficiency and reduce the probability of spill occurrences. This can be achieved by -changing production schedules to minimize equipment and feedstock changeovers, improving maintenance scheduling, segregating by-products at source, training and encouraging staff to improve materials handling and to recognize pollution prevention opportunities, and implementing relatively easily through the introduction of work procedures that target process control systems‖ (CCME, 2008).
2. Rehearsals are staff training for spill occurrence response and clean-up practices. For instance, emergency response rehearsals could be practiced for evacuating staff from the site, closure of operations, sector, and even the facility if necessary.
3. Public education can be provided through workshops, and seminars. Public education needs to be directed at industries that have spilled in the past or will potentially produce spills in the future (CCME, 2008). A potential spill industry can be identified by model simulations in which the risks of water quality violation at downstream locations are over a specific threshold of probalility.
4. Media programs can target audiences through radio, television, newspapers and magazines, internet, flyers, posters, brochures, fact sheets, newsletters, environmental and community groups, and schools and universities (CCME, 2008).

Collaboration and Cooperation Program
Collaboration and cooperation among various facilities or municipalities can enhance spill prevention and reduce spill control costs (e.g. inspection, monitoring, and spill clean-up).
Municipalities should also collaborate and cooperate with provincial and federal agencies and industrial associations to promote spill education and training for spill-prone industries (e.g., NAICS 325210). Employee training and preventive maintenance should be emphasized in training programs for spill-prone sectors. For instance, those which have high spill potential should find valuable information through spill data analysis such as spill causes and impacts.
An information sharing platform could be created to provide industries and municipalities information on occurred and potential spill events that are generated through MMCS model, consequences, control measures, clean-up technologies, technologies onsite, etc. Sometimes, information on clean-up technologies specific to industrial sectors can be cost shared and/or specifically developed for the particular spill reduction requirements (CCME, 2008). A waste exchange platform could be helpful for some industries that have opposite chemical properties.
For instance, manufacturers of acid and those of bases can exchange their wastes to neutralize their wastewater before discharge. Additionally, information sharing may be needed between countries. For instance, there is a joint committee of Canadian and U.S. municipal people for spill notification.

Inspection and Monitoring Program
An inspection and monitoring program is usually industry-based and should include an inspection and monitoring schedule, maintenance procedures, and a repair and replacement plan if applicable, listing concerned chemicals, probabilistic occurrence time series, physical conditions (e.g., workplace environment and machinery condition), and monitored processes that will potentially produce spill occurrences (e.g., material shipping and storage, manufacturing and operating). An inspection and monitoring schedule should include persons who perform inspection/monitoring, the exact place to be inspected/monitored, the lists of potential or existing hazardous or dangerous materials (e.g. benzene), frequency of inspection and monitoring during a specific period (e.g. quarterly, monthly, etc.), suggested techniques or methods and equipment, and health and safety issues. Maintenance procedures (if non-exist) for the whole industrial processes should be prepared (including pipe systems and equipment) to reduce the possibility of system leakage. Environmental sensitivity is defined as a place, a location, or an area that is sensitive to spills and should be emphasized in an inspection and monitoring program. Important spill information can be derived from analysis of historical data and the risk analysis of spill occurrences using the methods presented in previous chapters.

Spill Control Plan
A spill control plan involves industry control at source, technology onsite, cost analysis, and relevant downstream control if applicable. Associated regulations, guidelines, acts or by-laws must be emphasized in the spill control plan. All measures used in controlling a spill at source must be cost-effective. If a spill accidently discharges into receiving waters, downstream water treatment plants must take action immediately to protect source water quality, human health and ecology health. Downstream governments must announce the situation immediately to the public and report real time treatment progress until the spill is completely controlled.

Technology Onsite
Technology onsite is a highly effective tool for cleaning up and removing spilled chemicals at

Industrial Control Plan
An industrial control plan targets specific sectors that produced spills in the past or have the potential for spills in the future. The two major components are system update and new materials.
System update could include equipment modifications and process changes, such as introducing new technologies or approaches to existing operating systems, processes and practices (CCME, 2008). System update provides opportunities to improve the facility's operation.

Emergency Response Plan
An emergency and response plan could consist of a Response Centre, a Spill Clean-up Plan, and a Potential Spill Plan. Response Centre can be set up in an area that has high frequency of existing or potential spill occurrences or high spilled masses. These information can be obtained through spill database analysis and MMCS model simulations. Under an emergency response plan, a response team could be formed in advance to act promptly when a spill event occurs.
Typical response teams are oriented around three entities: Regional Response Team (RRT), Municipal Response Team (MRT), and On-Site Response Team (SRT). Contact information, such as telephone number and person's name, in the case of an emergency should be provided in an emergency and response plan. Since some municipalities share water resources, such as St Clair River and Lake Ontario with the U.S, emergency response preparedness should consider international cooperation to ensure appropriate and effective preparedness, reporting, and response measures between the two countries when a spill enters the shared water resources.
RRT is a team consisting of representatives from various municipalities within one or more region. The reason to form a RRT is to recognize the water quality impacts of multiple jurisdictions along the receiving water. The case studies of benzene spills in the St Clair River AOC and the Mimico Creek watershed show that multiple municipalities along the receiving water are affected by the spills. A RRT coordinates planning, preparedness, training and response support on a regional basis and provides support to a MRT.
MRT is necessary for a municipality that has a high frequency of spill occurrences. A MRT focuses on planning and preparing activities in the event of spill occurrences and obtaining technical and financial support from all possible sources.
SRT is a response team formed by industries that have a high risk of spill occurrences within a certain time period (e.g. 10 years). The responsibilities of SRT are to prepare emergency response plans for potential spill occurrences, provide activities in the event of spills, and cooperate with and obtain support from MRT and RRT.

Response Centre
A response center will be necessary for emergent spill events within high frequent spill occurrence areas. For a strategic decision making, available components (i.e., equipment, materials, and human resources) must be prepositioned to assure a promptly response to spill events (Wilbelm and Srinivasa and Wilhelm, 1997). Spill databases should be 162 created to record all possible spill information. The written report or a notification after a spill has occurred should include the industrial NAICS code (that is used for spill location PD), the concentration of spill with volume or estimate mass (that is used for spilled mass probability distribution), media into which the spill occurred and associated impacts (i.e. air, surface water, ground water, land, human health, or all of the above), and known or anticipated acute or chronic health risks associated with the spill and advice regarding treatment for exposed individuals and media. Since the current spill database has no information of spill duration time, the model applies a randomly select one within a specific time period. If spill duration time can be recorded or estimated properly, it is very helpful for its probability distribution's determination. The additional information will help to reduce model's epistemic uncertainties.
A map for the recommended positions and industrial locations of spill occurrences can be created by using ArcGIS or other tools and distributed to involved industries and local governments.
ArcGIS software can also help to find the shortest distance from response center to occurrence position, so that response teams can reach the spill location at the best time to clean up and control spilled chemicals. For instance, according to the spatial distribution of inland chemical spills in Fig. 3.5, it is clear that these cities should establish spill response centers in order to prepare for spill events and protect source water. By applying ArcGIS tools, the locations of the centers could be considered to be closed to the area with higher spill densities. This arrangement will shorten the travel distance to reach spill locations by the centers' staff.

Clean-up Plan
If a spill has occurred and has been transported into a water body, such as a river or a lake, downstream water quality impairments in compliance with associated water quality standards (e.g. maximum acceptable concentration of a chemical in drinking water) must be investigated to ensure a healthy water resource for the ecological environment and human beings. Once the downstream concentrations exceed the limit, actions must be taken and risk-informed decisions must be made to minimize impairments. The first action should be to clean-up at the occurrence site to reduce the continuous discharge of spilled chemicals at source. Therefore, a clean-up plan should be prepared, such as human resources (assigned persons who are responsible for quickly responding to spill events), feasible technologies (e.g., physical/chemical removal or spilled chemical disposal), supported materials and equipment, funding, and so on. Appropriate professional contractors could be available to quickly control emergencies. The technologies onsite as discussed above could be used for cleaning up spilled chemicals.

Spill Potential Plan
If an industry had a high frequency (e.g. twice a year) of predictive spill occurrences or high risk of impaired water quality in the receiving water from MMCS and EMMCS model simulations, a potential spill plan should be included under an ERP so that we can be well prepared for a potential spill event. A PSP should have information on possible industry that can be represented by a NAICS code, location, possible occurrence time, and magnitude. The MMCS model simulation can be used to provide the necessary spill information given enough historical spill data are available. Consequently, it is important to maintain a well-designed and managed spill reporting system.

Finance Plan
A finance plan in terms of spill management may include government subsidy and industry budget if applicable. Government finance plan should provide information on who needs a subsidy and how much to allocate. An industry finance plan should include the information on why needs governmental finance supports, how to obtain them, and where and how to spend them on spill management. Historical spill analysis and model simulations can provide clues as to which kind(s) of industries should have priority to receive government investment.
An industry is required to provide written proposal that includes all necessary plans discussed in above sections and its own budget to the governments in order to get their supports. After the governments approve and release the subsidy to the industry, the industry is required to report the progress of spill management to the government periodically (e.g., semi-yearly or yearly). If spill events still occur in the industry, the government can punish it (e.g., penalties) and require a written report to explain its situations and how to improve. It is necessary for the governments to supervise industries on their implementation of spill management, especially those subsidized.

Conclusions
Inland chemical spills have been identified as one of the major water pollution sources in the Great Lakes basin and have a deleterious effect on the aquatic, terrestrial, and air environment.
Every Based on the study findings, the following conclusions can be drawn: The literature review showed that not enough research has been conducted on the effect of chemical spills on fresh inland water and there is a lack of models for predicting the probabilistic quantifiable occurrences of inland spills that can be used to aid decision making.
River water quality models have been investigated by many researchers. Appropriate models have been chosen for studying the fate of inland spilled chemicals in receiving rivers of Southern Ontario.
Inland chemical spills in Southern Ontario from 1988 and potential non-point pollutants, which had various impacts on the environment and human health.
Inland spills are significantly hazardous to receiving water quality according to the analysis of frequency, volumes, and masses, especially as almost half of the spills were not cleaned up.
The independent spill event characteristics (e.g. inter-event time, mass, etc.) enable stochastic spill models such as MMCS to be developed easily to simulate the probabilistic occurrences of inland spills by time, magnitude, and NAICS-based location. If these event characteristics are inter-dependent, joint distributed spill models must be developed.
The MMCS model can be easily extended to the EMMCS model for quantifying the risks of water quality impairments due to inland chemical spills. The two models serve to provide technical support for a comprehensive spill management framework.
The industry's probability of having a specific number of spill occurrences can be determined through the PDF obtained from simulated spill occurrences. With the assistance of spill simulations, the priority of spill prevention and management can be obtained.
Both MMCS and EMMCS models can be easily re-developed for various characteristics and conditions. For instance, replacing the probabilistic distributions of spill event's variables (i.e. spill inter-event time, spilled mass, and spill NAICS-based location) can switch the models from a large industrial operation (e.g. in the St. Clair River AOC) to a small one (e.g. in Mimico Creek); and applying PDs of river flow rates based on river's characteristics and environmental conditions (no matter how big or small of the river) and appropriate water quality models (e.g. models for big river or small river) can achieve the associated risk analysis of water quality violation due to the spills.
Both MMCS and EMMCS models are able to characterize temporal and spatial randomness of any type of chemical/oil spill inland or in water and to quantify aleatory and epistemic uncertainties in face of very limited spill data through integrating the bootstrap resampling technique.
Two case studies, benzene spills in the St Clair River AOC (real case) and the Mimico Creek watershed (hypothetical case) have been used to demonstrate the MMCS and EMMCS models. The former is conducted for big sizes of industrial operations along a big river with high flow rates, while the latter demonstrates the models for small sizes of industrial operations along a small river with low flow rates.
As demonstrated by the Mimico case, simulated spill characteristics can be transferred from one area to another area for simulating potential spill probabilistic occurrences and analyzing risks of water quality violation if there are no historical spill records available; in order to have reasonable simulation results to support spill management decision making, industries' operation information (e.g., manufacturing capability, the amount of materials used in the manufacturing processes, and the yield of production) in various areas could be compared to adjust historical spilled mass data. If there is a lack of the information, the spilled mass data can be adjusted through applying the ratio of employee between two industries. The model simulation results could still be used as preliminary clues with respect to the development of a spill prevention and management plan.
The developed EMMCS model not only can be used by water quality practitioners to predict the probabilistic quantifiable occurrence of inland chemical spills and estimate the associated risks of water quality violations at downstream locations along a river, but also can be used by regulatory agencies and municipalities to determine the priority industries for spill prevention, control and emergency response, to evaluate the effectiveness of actions against the spills, and to make decisions on where to implement management measures and allocate resources.
A comprehensive chemical spill management framework, consisting of a spill pollution prevention plan, a spill control plan, and an emergency response plan, can effectively assist a municipality or an industry for inland spill management in order to minimize the spills' potential that threatens human health and/or water quality.

Recommendation
The MMCS and EMMCS models require known probability distributions of spill inter-event time, spilled mass, industrial NAICS code, and river flows in order to simulate the probabilistic spill occurrences and quantify risks of water quality violation. Also, the reduction of the model's epistemic uncertainty demands a longer history of sufficient spill data and the information on spill duration time. Therefore, it is recommended to improve spill reporting systems, such as reporting or estimating spill duration time, identifying spill industrial NAICS code and geocoding (i.e. geographic location).