A global sensitivity analysis with regional properties is introduced. This method is demonstrated on two synthetic and one hydraulic example. It can be shown that an uncertainty analysis based on one-dimensional scatter plots and correlation analyses such as the Spearman Rank Correlation coefficient can lead to misinterpretations of any model results. The method which has been proposed in this paper is based on multiple regression trees (so called Random Forests). The splits at each node of the regression tree are sampled from a probability distribution. Several criteria are enforced at each level of splitting to ensure positive information gain and also to distinguish between behavioural and non-behavioural model representations. The latter distinction is applied in the generalized likelihood uncertainty estimation (GLUE) and regional sensitivity analysis (RSA) framework to analyse model results and is used here to derive regression tree (model) structures. Two methods of sensitivity analysis are used: in the first method the total information gain achieved by each parameter is evaluated. In the second method parameters and parameter sets are permuted and an error rate computed. This error rate is compared to values without permutation. This latter method allows the evaluation of the sensitivity of parameter combinations and thus gives an insight into the structure of the response surface. The examples demonstrate the capability of this methodology and stress the importance of the application of sensitivity analysis.