Categoría: Descripción e interpretación de los dilemas sociales que se presentan en el

Analysis in the probabilistic approach involves describing load and resistance as belonging to respective possible probability distributions. Uncertainty in both load and resistance is introduced through the use of random variables. Therefore, the system reliability is realistically measured in terms of probability. The principal objective of the probabilistic reliability analysis is to ensure, in terms of probability, that load does not exceed resistance throughout a specified time horizon in terms of probability.

Ganoulis (1994) states that by considering the system variables as random, uncertainties can be quantified on a probabilistic framework. Load, l, and resistance, r, are taken as random variables L and R, with the following probability distribution and probability density distribution functions:

FL(l), fL(l) : load

FR(r), fR(r) : resistance

In the probabilistic framework, the simple definition of failure is when the load exceeds the resistance. Thus probability of failure or risk is defined by the following relation:

PF = P(R<L) (2.1)

The quantity PF is obtained by the joint probability density function fLR(l,r) of the random variables R and L. Figure 2.2 shows the risk PF above the bisectrice line L=R that can be calculated by integrating the following equation.

PF = P(L>R) = ∫ ∫ α 0 0 ) ) , ( (l f_LR l r dr dl (2.2) Equation (2.2) is a general expression to quantify the risk in a probabilistic framework.

Figure 2.2: Definition of probabilistic risk (after Ganoulis 1994)

The intensive calculations involved in this approach require prior knowledge of the probability density functions of both load and resistance and/or their joint probability distribution functions. The amount of data required to perform such calculations is usually insufficient and even if data are available to estimate these distributions, approximations are almost always necessary to calculate system reliability, (Ang and

r = 0 L = R r = l L > R L < R FLR(l.r) l r

Tang, 1984).

In flood risk analysis the probabilistic (stochastic) risk analysis approach has been extensively used. Normally, expected annual flood loss computation (HEC, 1989) is used to address the hydrologic (flood-frequency analysis), hydraulic (rating curve development) and economic uncertainties (stage damage analysis) in flood risk analysis. Quite often this analysis is subject to data insufficiency and inaccuracy; knowledge uncertainty in selecting an appropriate modeling tool and model parameters; and complete ignorance of subjective and perceived aspects of flood risk.

There are several approximate methods available to overcome the problem of data insufficiency and consideration of objective and subjective uncertainties at the same time. For example, researchers (Tung and Yen, 2005) have suggested that in some cases it is possible to use the normal representation of non-normal distributions as a practical alternative that is based on the central limit theory. In this case, data requirements for estimating the first two moments of the assumed normal distribution are very high. Another approach to avoid the problem of data insufficiency is the use of subjective judgment of the decision-maker to estimate the probability distribution of a random event, i.e. subjective probability (Vick, 2002). The third approach is the integration of judgment with the observed information using Baye’s theory (Ang and Tang, 1984). The problem with Bayesian reliability analysis is that the selection of prior distribution does not often reflect the true uncertainty inherent to the system. The choice of subjective probability distribution, in these two approaches, presents difficulties in the translation of

prior knowledge into meaningful probability distribution, especially for multi-parameter problems (Press, 2003). Therefore, accuracy of the derived distributions is strongly dependent on the realistic estimation of the decision-maker’s judgment (El-Baroudy and Simonovic, 2004).

The probabilistic approach usually fails to address subjective and perceived risks. People utilize the concept of risk to increase their understanding of various uncertainties and to develop their capacity to cope with the negative impacts of disasters. The concepts of failure and risk imply different meanings for different people. Slovic (2000) stresses the difference in risk perception, i.e. acceptance of failure, or judgmental and heuristics beliefs. Studies of the probabilistic information processing show that people do not use the proper probabilistic principles in judging the likelihood of a certain event. However, subjective probability is used to quantify engineering judgment about the likelihood of the occurrence of an uncertain event, the existence of an unknown condition, or the confidence in the truth of a proposition, (Vick, 2002).

An innovative framework is proposed in this work for: (a) integrating different perspectives of flood risk; (b) performing flood risk assessments; and (c) developing flood risk management strategies for an entire river basin. It is typically the case that the public awareness of flood disasters is generally quite low, owing largely to the fact that people tend to underestimate or ignore entirely the extent to which they are financially and personally vulnerable to the effects of flooding. This phenomenon can be explained by pointing to the common tendency to assess flood risk on the basis of past experiences

of damage. If, for instance, a previous flood did not cause significant damage to a community and its population, we can reasonably assume that the flood prevention measures in place will not have adequately taken into account the likelihood and risk of a more severe flood event in the future. Progress in flood risk prevention and flood disaster mitigation is thus contingent on the likely harm experienced by the people affected. This directly affects investments in flood risk prevention and mitigation measures as well as the development of legislation, standardization and governmental regulations and control. The framework developed in this research provides support for the broad range of decision-making processes related to flood management.