Conducting Environmental Impact Assessment in Developing Countries (UNU, 1999, 375 pages)
 5. EIA tools
 5.1 Impact prediction
 (introduction...) 5.1.1 Application of methods to different levels of prediction 5.1.2 Informal modelling 5.1.3 Physical models 5.1.4 Mathematical models 5.1.5 Modelling procedure 5.1.6 Sensitivity analysis 5.1.7 Probabilistic modelling 5.1.8 Points to be considered when selecting a prediction model 5.1.9 Difficulties in prediction 5.1.10 Auditing of EIAs 5.1.11 Precision in prediction and decision resolution

### 5.1.6 Sensitivity analysis

Any analysis of an environmental model, a cost/benefit study, or other investigation, will involve a number of input factors which have different degrees of uncertainty. These will influence the outcomes of the study to varying extents. The process can be considered as an input/output process, as shown earlier in Box 5.1. Usually we select the inputs as "most likely'' values. The relative response of outputs to changes in inputs, is their sensitivity.

As an example, consider the model shown in Box 5.1. The factors in the analysis can be seen as inputs (A, B), and the outcomes as outputs (D, E). If the parameters were set at X = 1.1 and Y = 1.9, and the most likely inputs were A = 75 and B = 102, the outputs will be D = 27.1 and E = 12.2.

Now suppose that input A is considered to be accurate to ± 40% and input B to be accurate to ± 25%. The limits for A might therefore be from 45 to 105, and B from 76.5 to 127.5. Taking the highest and lowest sets of values, we can repeat the calculations. The low values of A and B lead to outputs of D = 22.3 (-18%) and E = 11.4 (-7%). The high values of inputs (with A truncated from 105 to 100) will give D = 30.8 (+ 14%) and E = 12.7 (+4%). The percentage figures show that the outputs are relatively insensitive to the 25% changes in inputs; this is due to the square root and log functions in the equations for D and E. Other relationships might amplify changes in inputs, and give sensitive responses.

Sensitivity analysis is a powerful, yet simple, technique for determining the effects of individual factors and their variations on the overall results of an analysis. By changing the value of an input variable in an equation, the response of a system to new external influences can be tested.

Taking the plume dispersion equation above, the concentration of an air pollutant can be calculated (i) at different distances from the source by changing x (and therefore changing y and z), (ii) resulting from different chimney heights can be calculated by changing h, and (iii) for different emission rates by changing Q.