Statistical Characterization of Hazards and Risk in Coastal Areas

Abstract

We examine the foundation for hazard/risk assessment and its application to coastal problems. Historically, emphasis was on specifying expected values of wind waves and storm surges; however, as shown by the recent tsunamis in Southeast Asia in 2004 and in Japan in 2011, there are critical parts of the world where tsunamis represent the dominant threat to coastal communities. Recently, there has been an increased awareness of the combined effects of heavy rainfall and/or river discharge with surge levels and strong winds. This forcing combination played an important role in the flooding in southern Louisiana during Hurricane Isaac in 2012, where water levels exceeded the 500-year return interval levels. Such forcing combinations complicate both the modeling systems required for their simulation and the treatment of the multivariate probabilities that define the relative importance of their impacts.

We begin with a set of consistent hazards and risk definitions, along with comparative definitions from other fields. This should help readers who have focused primarily on traditional coastal hazards and risks understand the broader context of risk assessment and also allow readers with a broader perspective gain insight into the specific nature of coastal hazards and risk. Following this, we introduce the basic concepts used in estimating coastal hazards and risks. We then examine the historical perspective for the evolution of coastal risk assessment, beginning with early deterministic methods and culminating in a recent transition to probabilistic methods. The steady increase in the ability of probabilistic methods to deal with persistent problems such as the lack of data and uncertainty is documented as a part of this transition.

Appendix: Glossary of Probability and Risk Terms

• Confidence intervals: A confidence interval is a statistical representation of how certain one is that a given variable will lie within a given range. A confidence interval includes two components – the interval (the value will be between x and y) and the level of certainty (a 90 % confidence interval indicates one can say that there is a 90 % probability the value will fall between the cited interval. As the interval gets smaller, the certainty that the values will fall within the interval goes down. Confidence intervals are related to uncertainty in that they are a statistical method of measuring uncertainty of a predicted value based on past data that provides the probability distribution and variance of the specific parameter of interest.

• Error: Error itself has multiple meanings. In the modeling/predictive sense, the concept of error requires that there be a correct answer against which to compare a predicted answer (modeling context) or sample result (statistical context). Error is then defined as the difference between the actual and predicted answer or measured sample. Therefore, in the sense of predictive risk assessment (looking forward in time), error is not a useful concept, as there is not yet any actual or true value against which to measure or compare. Error should not be confused with mistake, which is the result of an incorrect assumption, calculation or model formulation. The hallmark of a mistake is that it is avoidable.

• Error (Types I and II): Type I error and Type II error are technical terms used in statistics to describe particular types of erroneous results in a testing process. The terms relate to the acceptance or rejection of the hypothesis being tested (the null hypothesis). If the null hypothesis was rejected (found to be false) when it actually is true, then a Type I error occurred. Conversely, if the null hypothesis is not rejected (found to be true) when it actually is not true, a Type II error has occurred. These definitions correlate to the concepts of false positives (Type 1 error) and false negatives (Type II error) in testing. For a good technical tutorial on Type I and Type II errors [26.87].

• Exposure: The process of the receptor coming into contact with the hazard.

• Exposure pathway: The route by which the receptor is exposed. For animals, this is either by ingestion, inhalation, or dermal absorption.

• Exposure assessment: Quantitative analysis of how much (concentration, duration) of the hazard reaches the receptor.

• Hazard/stressor: An event (storm, accident), agent (chemical, radiation), situation or action with a potential for an undesirable consequence, such as harm to property, the environment, and human health or life. This term is often used synonymously with threat.

• Probability: In its most basic sense, probability is the chance or likelihood that something will happen. Qualitatively, the more likely an event is to happen, the more probable the event is. Quantitatively, probability is a value between 0 and 1, with 1 representing absolute certainty of the event occurring. The probability of an event is typically measured as the ratio of the number of times an event occurred over the total number of times the event could have occurred. For example, if we consider the event to be the occurrence of precipitation on any given day, we would collect information on whether it rained on a given day for a period of time (say 1 year). The probability of rain would then be

  $$\text{probability of precipitation}=\frac{\text{number of days with precipitation}}{\text{total number of days}}.$$

• Probability distribution: The basic definition of probability works for discrete events, but when the event or parameter being evaluated is continuous in nature (the maximum temperature on any given day, the stage of a river on any given day), then a single probability is not sufficient. Instead, possible values are grouped into discrete ranges, and the number of occurrences in that range are counted then divided by the total number of measurements.

• Receptor: A receptor is the specific thing or entity being affected by the hazard/stressor. In a human health risk assessment  – the receptor is a person.

• Risk: The potential for realization of unwanted, adverse consequences to human life, health, property, or the environment. The estimation of risk is usually quantified using the expected value of the conditional probability of the event occurring times the consequence of the event given that it has occurred. This definition is currently used by the Society of Risk Analysis. Mathematically, this is expressed as

  $$R=P\left(A\right)*P\left(B\right|A),$$

  (26.23)

  where $R=$ risk (a probability from 0 to 1), $P\left(A\right)=$ probability of event (A) occurring, and $P\left(B\right|A)=$ probability of a consequence (B) occurring given that event A occurred.

  This technical definition is what will be used through this handbook. However, there are other definitions in other fields of which the knowledgeable practitioner should be aware. Table 26.2 presents a summary of other definitions used in various fields and a list of citations to which one may refer for more information. In each case, the same mathematical representation can be used, but there are assumptions made that result in the definition being slightly different. This is also presented in Table 26.2.

  Table 26.2 Risk definitions in different applications

  Besides having multiple potential definitions, risk can also be differentiated by types. Different types of risk, even if they are of the same quantitative value, are often managed differently or even ignored. Some of the common risk types that greatly influence both how these risks are assessed, managed and communicated are defined below.

  • Actual risk: A scientifically verifiable risk. For example, it is well researched and documented that smoking places you at-risk for cancer [26.3, 26.4, 26.5, 26.6]. Actual risk is sometimes referred to as objective risk, but whether risk is subjective or objective is related more to its ability to be measured than it is to its actual verifiability.

  • Perceived risk: Risk that is thought to exist by an individual or group that is non-existent or exaggerated. This often occurs in situations where the public is misinformed or in which media reports instill unnecessary panic. Food safety concerns often top the list of such events and lead to the significant public policy debates, see, for example, [26.7].

  • Assumed risk: Risk that is taken by choice. Assumed risk can be quantifiably large or small, and actual or perceived. For example, individuals who choose to partake in risky activities (skydiving, mountain climbing) choose to assume the relatively large risks associated with these activities, but choosing to drive a car, take medicines or be involved in day-to-day activities all involve some assumed risk.

  • Comparative risk: Risk placed in context through comparison with another, perhaps better known risk. For example, stating that one is more likely to be hit by a meteor than to be injured in a plane crash compares a risk that people perceive as low (being hit by a meteor) with one they perceive as high but which actually is not. This helps place the risk in a conceptual framework.

  • Imposed risk: Risk that is forced upon an individual, either without the knowledge of the individual or if known, without consent. For example, second-hand smoke exposure is seen as an imposed risk [26.10, 26.8, 26.9]. Natural events such as earthquakes, hurricanes. and extreme weather events are, to a large extent, imposed risks, but to some extent individuals assume that risk based on where they choose to live. For an interesting approach to this, the reader is referred to the work of Parsad [26.11].

  • Relative risk: Risk of a particular outcome compared between two different groups or conditions. The relative risk is calculated as

    $$\text{relative risk}=\frac{\text{risk under condition 1}}{\text{risk under condition 2}}.$$

    Thus relative risk proved a value of the risk for Condition 1 as a multiple of the risk for Condition 2. For example: suppose property bordering a coastline (Condition 1) has a 30 % probability of being inundated during a storm surge, while properties over 100 m away from the coastline (Condition 2) have a 25 % probability of inundation. The relative risk of inundation is, therefore, 1.2 times higher along the coastline (Condition 1).

    It is imperative that the underlying information about the actual baseline risk be given (i. e., 30 % and 25 % probability of inundation). Relative risk statistics where no baseline information is given can be very misleading. For example, if there is a 1 in 1000000 (10${}^{-6}$) chance of an event at location A, and a 1 in 10000000 chance of the same event at location B, saying that location A has a 10 times greater risk than B belies the fact that the risk is still exceedingly small at location A.

  • Percent increased risk: Risk of a particular outcome compared between two different groups or conditions measured as a relative difference of the two risks related to a base risk. Percent increases risk is calculated as

    $$\text{percent increased risk}=\frac{\begin{array}{c}\text{risk under}\\ \text{Condition 1}\end{array}-\begin{array}{c}\text{risk under}\\ \text{Condition 2}\end{array}}{\text{risk under Condition 2}}\times \mathrm{100\hspace{0.33em}.}$$

    Using our example from conditional risk, the percent risk increase for inundation by living on the coast would be

    $$\text{percent increased risk }=\frac{30-25}{25}\times 100=20\%\text{ increase }.$$

    Just as with relative risk, it is imperative that the underlying information about the actual baseline risk be given (i. e., 30 % and 25 % probability of inundation). Percentage increased risk can be even more misleading than relative risk, especially where small risks are involved. For example, if there is a 1 in 1000000 (10${}^{-6}$) chance of an event at location A, and a 1 in 10000000 chance of the same event at location B, the percent increased risk at location A would be 900 %, which clearly presents a very different picture than saying that location A has a one in a million chance of the event.

• Risk analysis: The overall name given to the application of risk concepts to decision making. It involves detailed examinations performed to understand the nature of unwanted, negative consequences to human life, health, property, or the environment. The process includes identification of potential events (scenarios), quantitative and/or qualitative assessment of risk, analysis of risk management alternatives, and communication of that risk to the necessary stakeholders; an analytical process to provide information regarding undesirable events; and the process of quantification of the probabilities and expected consequences for identified risks. Figure 26.11 gives a graphical representation of the iterative and highly interactive relationship of the various aspects of risk analysis.

  Fig. 26.11

  

  Graphical representation of relationship of the elements of risk analysis

• Risk assessment: The use of scientifically supported relationships to evaluate the magnitude and probability of adverse impacts on selected endpoints of specific actions, events or hazards/stressors. The assessment may be either qualitative or quantitative. An example of a qualitative risk assessment is the prediction of cancer based on decreased ozone in the atmosphere conducted by the World Meteorological Organization. The risk assessment predicted that if conditions did not change, there would be 50 million additional skin cancer cases due to sunburn by the year 2000 [26.116]. An example of a qualitative risk assessment concerning the same topic (cancer from sunburn) is that a person’s risk for melanoma – the most serious form of skin cancer–doubles if he or she has had five or more sunburns [26.117].

• Risk estimation: The scientific determination of the characteristics of hazards/threats, usually in as quantitative a way as possible. This includes the magnitude, spatial scale, duration, and intensity of adverse consequences and their associated probabilities, as well as a description of the cause and effect links.

• Risk evaluation: A component of risk assessment in which judgments are made about the significance and acceptability of risk.

• Risk identification: Recognizing that a hazard exists and trying to define its characteristics. Often risks exist and are even measured for some time before their adverse consequences are recognized. In other cases, risk identification is a deliberate procedure to review, and it is hoped, to anticipate possible hazards.

• Stochastic: The property of having inherent random variation. The variation in a stochastic process, while random, is describable through probability theory (see uncertainty and variability below).

• Threat: See hazard/stressor above.

• Uncertainty: Uncertainty is a widely used term that is unfortunately often misused as a catchall term. In some instances, it is erroneously applied to the concept of confidence interval, which is actually a method of quantifying uncertainty. For the purpose of risk assessment, modeling, and/or prediction, uncertainty arises from three main components: error, variation, and lack of knowledge (see definitions herein and in the chapter text).

• Variability (alleatory uncertainty): Variability is a range of potential values for a given parameter. Variability is a natural characteristic of natural processes (also called natural variation). It is describable using probability distributions. The result of natural variation is sometimes called alleatory uncertainty. Variability in natural processes (and the resulting alleatory uncertainty ) cannot be reduced, as it is an inherent property of the process itself.

• Lack of knowledge (epistemic uncertainty): The result of a lack of knowledge in risk assessments is also sometimes called epistemic uncertainty. A lack of knowledge can arise because the knowledge is not yet scientifically available – and as such, it can be reduced (along with the resulting epistemic uncertainty) going forward through additional data, experimentation, theoretical development, and scientific inquiry. However, lack of knowledge also includes things that we do not even know we do not know. This area of lack of knowledge is more difficult, because it is not easily identifiable and as such, becomes included in variability, or is called error when comparing model results to reality.