# Environmental risk analysis : probability distribution calculations

We conclude with an example illustrating how the method can be used to analyse how environmental change may alter risks posed by environmental change to carbon fluxes in ecosystems. The specific goal of the analysis is to quantify how drought risks to carbon sinks in coniferous forest may change across Europe, and whether the underlying causes will mainly be changes in drought frequency or changes in forest vulnerability. We refer to the environmental variables which may or may not attain hazardous conditions as ' env ', and to the ecosystem variables at risk as ' sys '.

Our risk analysis is based on the probability distributions for these variables, denoted as P env and P sys. The degree to which the environment accounts for the state of the system is represented by the conditional probability distribution P sys env.

The three distributions are linked through the law of total probability:. Average environmental conditions and ecosystem behaviour are given by the expectations E env and E sys. Our aim is to use the three probability distributions to define 'hazards', 'vulnerabilities' and 'risks' such that risk equals the product of hazard probability and vulnerability.

We define hazard as a factor that can cause damage. Because any environmental variable can, on occasion, be too low or too high for optimal ecosystem performance, each constitutes a hazard. We shall say that an environmental variable is hazardous if it is in the range of values whose negative impacts we want to study.

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Vulnerability is defined here as a property of the conditional response distribution P sys env. It is the difference in expected system performance between hazardous and non-hazardous environmental conditions:. Finally, risk is defined as the product of the probability of hazardous conditions and the ecosystem's vulnerability to such conditions:. This alternative formula emphasizes that risk can be seen as the average loss that a system experiences due to occasional hazardous conditions. We propose the following six-step procedure for implementation of the risk analysis:.

In step 1, we may decide to use more than one ecosystem model, which would make the analysis more comprehensive by taking into account uncertainty about model structure. In step 2, the easiest choice would be to focus on individual input variables such as precipitation or temperature.

Alternatively, we may decide to use composite environmental variables, such as weather indices which combine the values of multiple input variables, e.

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Blanchard W Select emergency management-related terms and definitions, vulnerability assessment techniques and applications VATA. Even were the science to be perfect and all scientists and stakeholders agree that the outcomes associated with each decision option are known with certainty, the different stakeholders to the problem are likely to value these outcomes differently, due to real or perceived differences in allocation of the benefits, costs, and risks associated with them. The hazard-forming environment can therefore be used to identify which natural hazards influence a given area. For the Truncated Normal distribution, the standard deviation was set to a value similar to that one used for Triangular distribution. Out of stock. Williams, T. References in periodicals archive?

The analysis can also be performed using combinations of environmental variables without formally combining them in one index. The env -variable would then be multidimensional and P env would be a multivariate probability distribution. In step 3, we may select criteria for hazardousness from the literature, e. We can also base our criterion on the frequency distribution of the env -variable. We may however vary the reference climatic conditions across space. Amounts of rain that constitute a drought in wet regions may be above average elsewhere, but we can define as hazardous those weather conditions that are locally extreme.

In step 5, we define the region, spatial resolution and time period for which we carry out model simulations underpinning the risk analysis. We may be interested in the spatial distribution of hazards, vulnerabilities and risks, how they change over time, and how they differ between ecosystem types. In such cases, the ecosystem-specific environment and system distributions P env and P sys can be determined separately for individual spatial grid cells and by inspection of model outputs over limited periods of time, e.

Compared to P env and P sys , the response distributions P sys env will differ less between grid cells—because they are primarily determined by underlying universal mechanisms as represented in the models. If so, and if the selected env -variables cover the key sensitivities of the system, P sys env can be derived from modelling results across larger regions or strata consisting of multiple similar grid cells. In step 6, we use the modelling results to calculate risk and its components. This is done by interpreting the frequencies of input and output values as approximations of their probabilities.

We suggest carrying out the calculations in the following order:.

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The following is a simple example using virtual data. Example of model input—output pairs. In bold : results for hazardous conditions. In this example, we have just one env -variable rainfall and one sys -variable NPP. We assume here that P env and P sys can be approximated by the frequency distributions of the values in the table.

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For a serious analysis, we would need more than ten simulation results. So the risk analysis has the following results:. The vulnerability of this system is high, with drought reducing NPP by two-thirds on average. We now give a more complex example. Because we focus on presenting the method for probabilistic risk assessment, rather than on the properties of any single model, we keep the following model description brief. BASFOR is a forest model that requires as input meteorological variables radiation, temperature, precipitation, wind speed, atmospheric humidity , atmospheric CO 2 concentration and N-deposition rate.

The model runs on a daily time step and simulates the dynamics of pools of carbon, nitrogen and water in tree organs and soil. The model is applied on a latitude-longitude grid of 0.

## On Risk and Reliability Studies of Climate-Related Building Performance

For the first period, CO 2 concentrations and daily weather data were based on observations as assembled by the WATCH project and downscaled from 0. The absolute threshold for 'hazardousness' will thus be lowest in the driest regions. The probability of bad conditions is everywhere 0. Risk analysis for NPP in — as affected by precipitation. Note that in this example, risk E is a rescaling of vulnerability C because of the constant probability of hazardousness D.

Note that 'hazardousness' is unchanged: Q25 still refers to — Many theoretical expositions and applications of risk analysis can be found in the literature e. Can you calculate with uncertain numbers?

## Environmental Risk Analysis : Probability Distribution Calculations - backhowcime.tk

Sure, you just need the right methods. Risk Calc supports both traditional interval analysis and classical probabilistic arithmetic. It also provides comprehensive implementations of fuzzy arithmetic and probability bounds analysis. These methods are especially useful when empirical data are of mixed quality and when uncertainty encompasses both variability and incertitude. How is uncertainty defined? Risk Calc allows you to specify uncertainty in several ways. What can Risk Calc do? Risk Calc computes with scalars, intervals, fuzzy numbers, probability distributions, and interval bounds on probability distributions.

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Summary. A Training Tool for the Environmental Risk Professional. Environmental Risk Analysis: Probability Distribution Calculations defines the role that. A Training Tool for the Environmental Risk Professional. Environmental Risk Analysis: Probability Distribution Calculations defines the role that probability.

Risk Calc also has many functions to characterize the features of uncertain numbers. Probability distributions. Probability bounds in calculations. Risk Calc also accepts units that accompany numbers, checks that units entered balance dimensionally, and automatically handles unit conversions when necessary. In Risk Calc you can define variables, and you can automate complex expressions using loops, conditional statements, user-defined functions and procedures and other programming constructs.

Risk Calc can also import and export data to disk files and Excel spreadsheets. What is probability bounds analysis?

## Environmental Risk Analysis

Probability bounds analysis is a marriage of probability theory and interval analysis that handles uncertainty and variability more comprehensively than either one can alone. Risk Calc supports over 30 named distributions normal, lognormal, binomial, Poisson, Weibull, Pareto, etc. Risk Calc lets you do calculations with these probability bounds without making any assumption about the shape of the distribution. What is probabilistic arithmetic?