The Sobol analysis works by evaluating the variance of the model output that can be attributed to each individual input variable and their interactions with other input variables. This is done by generating a set of samples based on a specified probability distribution for each input variable and calculating the resulting model output.

The method evaluates two measures of sensitivity, the main effect and the total effect. The main effect is the impact of a single input variable on the model output, while the total effect measures the combined impact of an input variable and its interactions with other input variables.

The results of the Sobol analysis are often presented in a graphical format, such as a bar chart or a scatter plot. These graphs show the relative importance of each input variable in influencing the model output.

By using Sobol sensitivity analysis, researchers can identify the most influential input variables and focus their efforts on refining and improving the accuracy of those variables. This can lead to better model predictions and more informed decision-making in a wide range of fields, including engineering, environmental science, and economics.