## Example

A waste site receives a contaminant in waste at a constant rate, M (kg yr). The contaminant inventory is reduced by two processes, degradation of the contaminant and leaching of the contaminant from the wastes. Degradation is first order with rate constant k (yr-1). Although leaching of the contaminant from the site depends on variables that include the infiltration rate of water, the physicochemical form of the waste, and contaminant sorption to backfill, among others, it is commonly...

## Irrigation Deposition

Deposition by irrigation can be calculated from where t is the irrigation rate L T and Cw is the contaminant concentration in the irrigation water. Irrigation rates vary depending on the water needs of the crop and can range from 0.23 to 1.4 m yr (Peterson 1983). The default agricultural irrigation 1 Equation 8.5 is obtained from the first two terms of the Taylor's series expansion of Eq. 8.3. That is, if ksts e < < 1, then exp(-ksts,e) 1 - kstse and C(t ) (1 - e-k-t) (1 -1 + kst) i- ts e...

## Example A1

This procedure can be illustrated for the first-order removal model (Eq. 2.8). The differential equation is with the starting value C (0+) C0. Taking the Laplace transform of both sides of the differential equation, we have Substituting the starting value and solving for C(s) gives us Taking the inverse transform, we obtain Applying Eq. A.17 from Table A.1 yields

## Atmospheric Deposition

Dry and wet surface deposition fluxes are calculated from where Ca is the contaminant concentration in air, fv the fraction of the contaminant intercepted by vegetation (taken as 0.25 in the absence of site-specific data), and vd the deposition velocity. The deposition velocity is an empirical quantity that varies widely depending on the physical and chemical form of the contaminant, the type of surface, and meteorological conditions, especially precipitation rate. Dry deposition velocities for...

## Units of Contaminant Concentration

Water For water, the preferred unit is mass per unit volume, or Occasionally, the concentration may be expressed as a mass ratio, typically parts per million by mass (ppm) or parts per trillion by mass (ppt). The mass ratio is converted to concentration by multiplying by the water density Cw mg(c) L ppm by mass g(c) 106 g(w) x pw g(w) m3 x 103 mg(c) g(c) x 10-3 m3 L Air For air, the preferred units are contaminant mass per unit volume of air at standard temperature and pressure C _ contaminant...

## A13 Error Function and Complementary Error Function

Mathematically, the error function is defined as erf (z) J J0Z exp (-z'2 )dz (A.7) and erf(-z) - erf(z). The integrand in Eq. A.7 is a Gaussian distribution with a V2 2, and the error function is one-half the area of the distribution between 0 and z or, equivalently, the area between -z and +z (Figure A.2). The complementary error function is defined as erfc(z) 1 - erf(z). The error function and the complementary error function are shown in Figure A.3.

## Descriptive Statistics

Frequently, a distribution is characterized by descriptive statistics derived from the underlying distribution. The most common and most important of these statistics, the arithmetic mean (also average or first moment of the distribution), is defined by where E(X) denotes the expected value of the random variable X. The variance, which is the second moment about the mean, is defined by g2 J+(xf (x )dx var (X) (12.16) where var(X) denotes the variance of the random variable X. In certain...

## CERCLA and SARA

The Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA) was enacted by Congress on December 11, 1980. CERCLA, commonly known as the Superfund Act, has been amended by the Superfund Amendments and Reauthorization Act (SARA), 1986. The main focus of CERCLA is the cleanup of hazardous waste sites however, some aspects of CERCLA require the federal government to respond to and effect the cleanup of any releases of hazardous substances. CERCLA may be described by four main...

## References

AAES American Association of Engineering Societies (1996). Risk Analysis The Process and Its Application, a Statement of the Engineer's Public Policy Council. Washington, DC AAES. ACS American Chemical Society (1998). Understanding Risk Analysis A Short Guide for Health, Safety and Environmental Policy Making. Washington, DC ACS and Resources for the Future. Also available at (accessed Jan 5, 2006) http www.rff.org ASME American Society of Mechanical Engineers (2002, Apr 15). The Role of Risk...

## Introduction

As described in Chapter 1, risk analysis is comprised of three components risk assessment, risk communication, and risk management (Figure 1.1 and Section 1.1). The role of risk management is to articulate alternative actions and select one for implementation. This requires a two-way flow of information with risk assessment and risk communication. Information flows into risk management from risk assessment activities (e.g., relative risks of various alternatives) and from risk communication...

## Problems

12.1 Classify the following examples in one or more of the following categories (1) parameter uncertainty (2) model uncertainty (3) scenario uncertainty. (a) It is not clear whether the dissolution of waste into groundwater at an abandoned waste site can be estimated by a single leaching coefficient or whether each species behaves differently. (b) Bioconcentration factors for radioactive 137Cs at the Savannah River Site, based on five fish muscle assays (piscivores), show a maximum value of...

## Contaminant Concentration and Contaminant Flux Formalized Treatment

Contaminant concentration and contaminant flux are defined in Section 2.3.1.3. More rigorous and formalized definitions are needed in deriving and developing a physical understanding of the contaminant continuity equation and the contami- 3 Logan uses the term general transport equation to refer to a generic continuity equation which can be applied to either the fluid medium or the contaminant contained within the fluid. 4 Rigorously, the dispersion coefficient is a tensor. However, in...

## Teratogenic Effects

Teratogenic effects are those induced between conception and birth. Although a teratogenic effect is defined rigorously as a birth defect (either a malformation or a retardation), embryonic or fetal death can occur from the same mechanisms that cause birth defects. Approximately 3 of live-born infants have major congenital malformations that are recognized in the first year of life (NCBDDD 2005). As is the case with other health effects, it is difficult to distinguish between the incidence of...

## Fraction Sorbed

It is useful to estimate the fraction of contaminant associated with the two phases. The fraction of contaminant associated with the solid phase, or the fraction sorbed, fs, can be approximated with the aid of Figure 5.3, which shows a volume of solution, V, containing a solid phase at a suspended solids concentration SS M(s) L3 . The fraction sorbed is the amount of contaminant associated with the solid phase divided by the amount associated with both the solid and aqueous phases where Ms and...

## Zero Dimensional Solutions of the Contaminant Transport Equation

Several zero-dimensional solutions of the contaminant transport equation are derived to illustrate how it can be used as the fundamental basis for most mathe- matical models of contaminant transport in risk assessment. In this section, the contaminant transport equation is used to derive the zero-dimensional (with respect to space) models that were developed in Sections 2.3.1 and 2.3.2 from a heuristic mass balance approach. In Chapter 4, the contaminant transport equation is used to derive the...

## Contaminant Emission Rate

In general, the spatial and temporal dependence of a contaminant release are quantified by the specific emission rate, S(r,i), which is mass emitted per unit volume per unit time. Since many of the closed-form analytical contaminant transport models are, by necessity, based on very simple spatial and temporal functions, Figure 3.7 Emission-rate approximations. Figure 3.7 Emission-rate approximations. actual emission rates are often replaced by simple approximations. Presented in Figure 3.7 are...

## SCx s Cx0 udCx sM kCx s

Applying the starting value C (x,0) 0 and rearranging yields a differential equation in x Since there is a bounding condition on C at x 0, the Laplace transform technique can be used for the x dimension just as it was for the t dimension. Taking the Laplace transform with respect to x and moving all quantities independent of x outside the Laplace operator gives us L x dC(x + l x C(x, s) A. L x S(x) dx u uAs Noting that Li d(x - a) exp(-ap) L d(x - 0) exp(0) 1, this becomes pC(p, s)- C(0, s) +...

## Carcinogenic Effects

In 2005, 22 of deaths in the United States were from cancer. Along with heart attacks and strokes, it is one of the three leading causes of death. Although life-style choices such as the use of tobacco products, alcohol consumption, and diet are thought to be responsible for a majority of cancers, it is also known that cancer can result from exposure to ionizing radiation and to some chemicals in the environment. In fact, cancer is often the primary stochastic effect analyzed in risk...

## Factors Affecting Toxicity Pharmacokinetics and Pharmacodynamics

Quantitative dose-response analysis requires a quantitative understanding of how the response is related to the dose. There are three assumptions required to establish a dose-response relationship (Klaassen and Eaton 1991) There is a molecular site within the target tissue with which the contaminant interacts to produce a biological response, the production and degree of the response are related to the concentration of the contaminant at these molecular sites, and the concentration of the...

## One Dimensional Advection

The simplest one-dimensional problems are those for which dispersion can be neglected and advection is the only conservative transport process of importance. The first problem to be considered is a semi-infinite emission rate with firstorder contaminant degradation between the source and the receptor. The solution (Eq. 4.3 in Table 4.1) is C(x, t ) Q h t - U j exp f-fcU (4.10) Graphical depictions of one-dimensional time-dependent solutions such as Eq. 4.10 are in two forms, concentration vs....

## Release with Inversion Aloft

As noted in Section 7.2 and illustrated in Figure 7.3d, an inversion aloft (i.e., above the effective release height) can result in high contaminant concentrations for receptors at ground level. At a sufFcient downwind distance, it can be assumed that the concentration in the region between the ground and the inversion layer is uniform (Turner 1994). The concentration is then given by where L is the mixing height. This equation is applicable for x > 2XL, where XL is the downwind distance at...

## Example 124

An abandoned industrial site is contaminated by beryllium and carbon tetrachloride. If the site were used for a residential farm, the point estimates of doses to a resident from these two contaminants are 2.2 x 10-3 and 2.3 x 10-3 mg kg d, respectively. The EPA reference doses for these contaminants are 0.005 and 0.007 mg kg d, respectively. (a) What are the hazard quotients for Be and CCl4 (b) What is the hazard index for the site (c) Would this site be a candidate for immediate release based...

## Methods for Decision Analysis Under Certainty

The extensive literature on decision analysis methods cannot be incorporated here. Instead, examples of five different utility-based decision-making approaches are illustrated. The five approaches are dimension reduction, dominance, sequential decision making, attitude-based, and dimensional scoring. Dimension reduction simplifies the selection process by expressing all attributes in terms of one common measure, such as monetary value. Dominance is a screening method used to reduce the number...

## Atmospheric Transport Models

Presented in this section are four models for estimating contaminant concentrations in the atmosphere. Two of the models apply to point sources with constant emission rate (Gaussian plume and sector averaged), one applies to a point, instantaneous emission (Gaussian puff model), and one applies to a linear source with constant emission rate. The theoretical basis for each of these is the contaminant transport equation (Eq. 4.14). In the atmosphere, turbulent diffusion is quantised by the eddy...

## Dermal Absorption

Although the skin is an effective barrier to the entry of contaminants, it is possible for small amounts to penetrate and enter the body. The two approaches for estimating contaminant absorption through the skin recommended by the EPA for Superfund sites (EPA 1989) are adopted here. One applies to contact with contaminated water and the other to contact with contaminated soil. For both scenarios, the contact rate does not have an easily described, intuitive physical meaning as it did for...

## Example 114

Presented in Table 11.3 are data on the incidence of leukemia and other forms of cancer among survivors of the atomic bombings in Japan. Presented in the table TABLE 11.3 Incidence of Leukemia and Other Forms of Cancer Among the Survivors of the Atomic Bombings in Japan TABLE 11.3 Incidence of Leukemia and Other Forms of Cancer Among the Survivors of the Atomic Bombings in Japan are six discrete dose ranges, the number of people in each dose range, the expected number of leukemias or other...

## Physical And Mathematical Basis For Risk Assessment Models

This section is organized around three important points regarding most of the models encountered in environmental risk assessment that they are based on mass TABLE 2.1 Characteristics of Various Phases in a Tiered Approach to Environmental TABLE 2.1 Characteristics of Various Phases in a Tiered Approach to Environmental Source Data from NCRP 1996 EPA 2001 IAEA 2001. a In general, as the level of the assessment advances, the models and parameter choices move from conservative and generic toward...

## Regulatory Implementation

The preceding discussions were generic in nature. Because of the many uncertainties and judgments required in carrying out risk assessments, many of the judgments have been standardized in various regulatory programs. In the following section we deal with some of the methods that are currently being used to implement the concepts discussed previously. 11.6.1 Deterministic (Noncancer) Endpoints The acceptable daily intake concept was modified and adopted by the EPA, which has traditionally...

## Example 1110

A home garden is used for raising vegetables on a plot of land contaminated with aldrin and heptachlor epoxide. Doses from the consumption of produce from the garden are calculated to be 2.3 x 10-5 and 6.4 x 10-6 mg (kg d), respectively. From Table 11.9, the RfDs for aldrin and heptachlor epoxide are 3 x 10-5 and 1.3 x 10-5 mg (kg d), respectively. The hazard index for this scenario is found by the addition of the separate hazard quotients HI 2.3 x 10-5mg (kg d) + 6.4 x 1Q-6mg (kg d) 0 + 049 3...

## A21 Definitions and Notation

Laplace transforms are a powerful mathematical tool that can be used to solve solve initial value problems (i.e., differential equations for which the initial conditions are specified). Laplace techniques are of particular utility in environmental transport because many environmental transport problems are of the initial value type (i.e., given concentration or emission rate at some initial time and or some initial location, the problem is to predict concentration at elapsed times and distant...

## Fractional Response

For contaminants that are assumed not to exhibit a threshold, an MOS approach is not possible, since any dose could result in some increased level of adverse effects. These contaminants are typically characterized by a fractional response obtained by estimating the dose and then determining, from the appropriate dose-response model, the fraction of the population that could be affected. This was illustrated in Figure 11.5, in which a dose of 1 mg (kg d) resulted in a response being observed in...

## Example 117

The one-hit model can be fit to the data in Table 11.2 by estimating the parameter p for each of the data points and then averaging. The equation for the one-hit model is where p is the cancer slope factor. This equation can be rearranged to yield The daily average value of p for the data in Table 11.2 is 0.015 (mg kg) 1. Using this value in the one-hit model yields the fitted curve in Figure 11.9. Another approach is based on the observation that age-specific incidence rates vary proportional...

## Constant Source First Order Removal The constantsource firstorder

Removal model is used for systems in which the contaminant is either being produced in, or is entering, an environmental compartment at a constant rate and the removal rate is first order. Examples include buildings (constant generation rate inside with venting to the exterior), well-mixed ponds or lakes (constant emission rate into the pond from either a stream or an end-of-pipe source, and first-order removal by sedimentation, degradation, etc.), vegetation (constant deposition on foliage and...

## Risk

Defining risk is a challenging problem. Physical scientists may tend to prefer a quantitative view of risk, and social scientists may favor inclusion of qualitative social and psychological elements in defining risk. Psychological and sociological studies have shown that a person's perception of risk can be affected by a myriad of objective and subjective factors. A quantitative approach to defining risk as appropriate for quantitative analysis has been adopted. However, as discussed in...

## Saturated Zone Transport Solutions

6.5.2.1 One-Dimensional Solutions Solving Eq. 6.17 can be complex. As discussed in Chapter 2, there are two general approaches for solving the contaminant transport equation numerical and analytical. Numerical solutions typically involve the use of finite-element or finite-difference techniques. Analytical solutions provide fundamental insights into the transport behavior of contaminants. Analyti cal solutions to Eq. 6.17 for a wide variety of initial conditions and boundary conditions are...

## Risk Calculation

When applied to human health effects, the objective of the risk calculation component of the risk assessment process is to produce a quantitative estimate of human health risk due to the release of a contaminant to the environment. The process for making this estimate of health effects can be formulated in different ways. In this book it is presented as four sequential steps (Figure 1.6) release Figure 1.6 Risk calculation component of the risk assessment process. Figure 1.6 Risk calculation...

## Random Variables and Distribution Functions

Fundamental to probability and statistics is the concept of a random variable,1 which is a real-valued function defined over a sample space with a probability measure. Random variables may be either continuous or discrete. An example of a continuous variable is the flow rate of a river over an extended period of time such as a year. Most parameters in risk assessments are treated as continuous variables. An example of a discrete variable is the final system state shown in the example of an...

## Major Organ Systems

There are 12 major organ systems in the human body. The digestive and urinary systems process food for energy and eliminate waste products the respiratory system provides the source of oxygen necessary for oxidative energy production the cardiovascular, lymphatic, and immune systems circulate oxygen, nutrients, and other compounds within the body and provide a communication network to regulate the function of the various specialized cells and to ward off disease the nervous and endocrine...

## Effective Release Height and Plume Rise

Because ground-level concentration is proportional to exp(-h2), it is particularly sensitive to the height of a release. However, the physical height of a release is often not the appropriate height to use in calculations. For example, in Figure 7.9 buoyancy and momentum of the exhaust gases (termed plume rise) cause the effective height of the release to differ from the physical height of the stack. Effective release height, he, is given by where hs is physical release height and hpr is plume...

## Atmospheric Dispersion

As noted above, the focus here is on localized effects close to the release point (up to about 50 km). Localized transport occurs in the part of the atmosphere adjacent to the surface of the Earth known as the planetary boundary layer, which can vary in thickness between approximately 100 and 3000 m. The dispersion of contaminants in the planetary boundary layer depends on the stability of the atmosphere. Atmospheric stability depends largely on the vertical temperature gradient, or...

## Keith L Compton

A JOHN WILEY & SONS, INC., PUBLICATION Copyright 2007 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without...

## Example 111

Dosimetric models to evaluate the effects of radionuclide intake are examples of pharmacokinetic models applied in a radiological health setting. A very simple model is the ICRP model of radionuclide uptake through the gastrointestinal (GI) tract (ICRP 1978) shown previously in Figure 10.2. The model consists of four compartments the stomach, the small intestine, the upper large intestine, and the lower large intestine. Clearance from one compartment to the next is based on fixed rate constants...

## Preface

Environmental risk analysis for human health is the systematic analytical process of assessing, managing, and communicating the risk to human health from contaminants released to or contained in the environment in which humans live. It is a discipline central to the development of environmental regulations and the demonstration of compliance with those regulations. The goal of the book is to provide both the methods that are commonly used in environmental risk analysis and the underlying...

## Contaminants In The Environment

In the context of environmental risk assessment, a contaminant can be defined as a substance in the environment that is capable of causing adverse human health, ecological, or aesthetic effects. Recognizing that virtually any element or compound in sufficient quantity is capable of causing harm, identification of specific substances as contaminants requires the exercise of judgment. The Environmental Protection Agency EPA defines a contaminant as any physical, chemical, biological, or...

## Porosity and Hydraulic Conductivity

The values of parameters such as hydraulic conductivity and effective porosity are strongly dependent on the type of material comprising the subsurface. Presented in Tables 6.1 and 6.2 are results of an analysis of measurements of porosity and hydraulic conductivity for various aquifer materials. Since porosity and hydraulic conductivity both show considerable variability, they usually are determined on a site-specific basis. Porosity can be measured by weighing a sample of the aquifer material...

## Remedial Actions Under CERCLA

The remedial process under CERCLA consists of 13 steps EPA 2002 2. Preliminary assessment site investigation 3. Proposed listing on the National Priorities List NPL 5. Remedial investigation feasibility study RI FS begins 6. FS completion and proposed plan 7. Notice and comment on consent decree if needed 8. Pre-record of decision ROD significant changes if needed 10. Post-ROD significant changes if needed 11. Remedial design remedial action 13. Proposed NPL deletion and final NPL deletion in...