## Sampling Based SA Methods

Before sampling-based SA methods can be applied, suitable ranges over which the model inputs of interest are likely to vary need to be defined. Historical data and experience can be used to define appropriate ranges for model forcings and boundary conditions. Experience can also be used to define the range over which the model parameters are likely to vary. Consequently, the choice of appropriate ranges of model inputs can have a significant impact on the results of SAs - particularly if the ranges that have been selected are too narrow.

Once appropriate ranges for all model inputs of interest have been defined, various sampling strategies can be employed to obtain the desired sensitivity outputs (Figure 2). Different sampling strategies provide tradeoffs between functionality (e.g., the ability to deal with higherorder interactions and the usefulness of the information provided) and computational efficiency (Table 3). As one-at-a-time sampling strategies, such as that employed as part of the Morris method, consider variation in one model input at a time, they are relatively computationally efficient.

Table 3 Degree to which different sampling-based SA methods satisfy desirable criteria

Joint variation

Desirable SA method characteristics

One-at-a-time variation (e.g., No transformation (e.g., Monte Morris method) Carlo, Latin hypercube)

Transformation (e.g., Sobol', FAST, Extended FAST)

Model nonlinearity ✓

Parameter interaction x

Comprehensiveness of Low output

Computational High efficiency

High Low

Medium Medium

However, they do not consider interactions between parameters and therefore provide limited sensitivity information. Sampling strategies that consider joint model input variations are more computationally expensive, but are able to provide more comprehensive SA outputs. The most common sampling strategies that fall into this category include Monte Carlo and Latin hypercube sampling approaches, for example. While such approaches provide the most comprehensive SA information, they are also the most computationally expensive. As a compromise between computational efficiency and the amount of information provided, a number of approaches, such as the Sobol', Fourier amplitude sensitivity testing (FAST), and extended FAST methods, use transformation functions to make the joint sampling process more efficient, but only provide aggregated SA information in the form of sensitivity indices.

1. description of input uncertainties, which involves quantification of the uncertainty in all model inputs/ parameters;

2. uncertainty propagation, which entails the propagation of the input uncertainties through the model to predict the resulting output uncertainty;

3. uncertainty importance analysis, which involves assessment of the importance of each uncertain model input with respect to its relative impact on output uncertainty.

It should be noted that it is not uncommon to refer to steps (2) and (3) jointly as UA. Some of the common approaches for conducting each of the above steps are shown in Figure 3 and discussed below. It should be noted that model uncertainty, although not discussed here, can also have a significant impact.

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