DS differs from current methodologies by utilizing the climate information in the latter stages of the process within a decision space to guide preferences among choices. Thus, in the first step of the analysis vulnerabilities are identified. These vulnerabilities can be defined in terms of those external factors and the thresholds at which they become problematic.

The purpose is to identify the scenarios that are relevant to the considered decision which serve as the basis for any necessary scientific investigation. In the second step of the decision making process, future projections of climate are then used to characterise the relative likelihood or plausibility of those conditions occurring. By using climate projections only in the second step of the analysis, the initial findings are not diluted by the uncertainties inherent in the projections.

In the third step of the analysis strategies can be planned to minimize the risk of the system. This setup marks DS primarily as a risk assessment tool with limited features developed for overall risk management. The workflow of DS is compared with the one of RDM in Figure 2, where the workflow of the traditional top-down approach is also depicted. Figure 2. Multi-Criteria Decision Analysis is a mathematical optimization procedure involving more than one objective function to be optimized simultaneously.

It is useful when decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. MCDA solutions are evaluated against the given criteria and assigned scores according to each criterion performance. The target may be to produce an overall aggregated score, by weighing criteria into one criterion or utility function.

An alternative is to identify non dominated solutions or Pareto efficient solutions.

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As this usually implies a deterministic approach, accounting for multi-objectives is the way to way to seek robustness rather than accounting for uncertainty Ranger et al. If uncertainty is accounted for, it is usually done so by performing a sensitivity analysis on each criterion to uncertainty Hyde and Maier, ; Hyde et al.

While it is herein presented as an approach on its own, MCDA can be also used within the previously reviewed methods as a means to assess the outcome of a policy with respect to alternatives and assigned scenarios. When combining the several criteria into one final score weights need to be assigned to each criterion. Analytic hierarchy process AHP is a structured technique for handling complex decisions. It was developed by Thomas L. Saaty in the s and has been extensively studied and refined since then.

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The AHP supports decision makers by first decomposing their decision problem into a hierarchy of more easily comprehended sub-problems, each of which can be analyzed independently. Once the hierarchy is structured, the decision makers evaluate its various elements by comparing them to each other two at a time, by using Pairwise comparison.

The AHP converts preferences to numerical values that can be processed and compared over the entire range of the problem. A numerical weight or priority is derived for each alternative and element of the hierarchy, allowing diverse and often incommensurable elements to be compared to one another in a rational and consistent way. This capability distinguishes the AHP from other decision making techniques. In the final step of the process, numerical priorities are calculated for each of the decision alternatives.

These numbers represent the alternatives' relative ability to achieve the decision goal, so they allow a straightforward consideration of the various courses of action. AHP can account for uncertainty for instance by evaluating alternatives with respect to several future scenarios. Therefore, if conveniently applied it may be considered a robust approach. The first step in the analytic hierarchy process is to model the problem as a hierarchy.

A hierarchy is a stratified system of ranking and organizing people, things, ideas, and so forth, where each element of the system, except for the top one, is subordinate to one or more other elements.

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Diagrams of hierarchies are often shaped roughly like pyramids, but other than having a single element at the top, there is nothing necessarily pyramid-shaped about a hierarchy. An AHP hierarchy is a structured means of modeling the decision at hand. It consists of an overall goal, a group of options or alternatives for reaching the goal, and a group of factors or criteria that relate the alternatives to the goal. The criteria can be further broken down into subcriteria, sub-subcriteria, and so on, in as many levels as the problem requires.

The design of any AHP hierarchy will depend not only on the nature of the problem at hand, but also on the knowledge, judgments, values, opinions, needs, wants, and so forth, of the participants in the decision-making process. Constructing a hierarchy typically involves significant discussion, research, and discovery by those involved. Once the hierarchy has been constructed, the participants analyze it through a series of pairwise comparisons that derive numerical scales of measurement for the nodes.

The criteria are pairwise compared against the goal for importance. The alternatives are pairwise compared against each of the criteria for preference. The comparisons are processed mathematically, and priorities are derived for each node. Figure 3 reports an example of application of AHP to a water resources management problem. In this case the decision is taken according to 4 criteria:. Net benefit is evaluated along the lifetime of the alternative, by assessing the cost of the intervention and the benefit gained through, for instance, increased crop productivity, hydropower production and so forth.

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Environmental impact needs to be evaluated through a proper index, as well as the impact on flow regime. CO 2 emissions can be quantitatively evaluated as those due to construction works, use of electrivity and so forth.

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Measures of each criteria need to be rescaled in the same range of variability, to allow values to be combined. Assessment and rescaling of criteria can be carried out through utility functions assigning a real number in range [0,1] to each alternative, in such a way that alternative a is assigned a utility greater than alternative b if, and only if, the individual prefers alternative a to alternative b.

Finally, the overall score utility of each alternative is computed by averaging the score corresponding to each criteria by using the weights W 1 , W 2 , W 3 and W 4. Those can be computed through Pairwise comparison. Figure 3. When there are N alternatives in the above case they are 3 the decision makers will need to make N pairwise comparisons with respect to each criterion.

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In the above case we need to compare dam versus reduction of losses, dam versus precise irrigation, and reduction of losses versus precise irrigation. For each comparison, one forst need to judge which member of the pair is weaker with respect to the criterion under consideration. Then a relative weight is to be assigned to the other member. The scale given in Figure 4 can be used to quantify preference. Figure 4. Preference scale used in pairwise comparison. The next step is to transfer the measures of preference to a matrix. For each pairwise comparison, the number representing the preference is positioned into the matrix in the corresponding position; the reciprocal of that number is put into the matrix in its symmetric position.

For instance, for the above example the matrix resulting from pairwise comparison of the three alternatives with respect to net benefit may be:.

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By processing the above matrix mathematically, weights for the alternatives with respect to the considered criteria can be derived. Mathematically speaking, weights are the values in the matrix's principal right eigenvector rescaled to give a sum of 1. They can be easily computed by using R, for instance.

It is important to check that the decision is consistent, which implies that preferences expressed in each pairwise comparison are not contradicted by subsequent comparisons. A consistent matrix implies, e. Unfortunately, the decision maker is often not able to express consistent preferences in case of several alternatives. Then, a formal test of consistency is required. If the matrix is not fully consistent, a consistency index CI can be computed as:. Then, a consistence ratio CR can be computed as the ratio of the CI for the considered matrix and a random consistency index RI, which corresponds to the consistency of a randomly generated pairwise comparison matrix:.

The same procedure needs to be repeated for the other criteria.