## 2 Materials and Methods
### Global Sensitivity Analysis
To account for the influence of interactions, the variance of the output quantity \(\mathbb{V}(Y)\) is decomposed into the contributions of its inputs and their combinations:  
\[\mathbb{V}(Y)=\sum_{i}\mathbb{V}(X_{i})+\sum_{i}\sum_{j>i}\mathbb{V}(X_{i},X_ {j})+\ldots+\mathbb{V}(X_{123\ldots k}). \tag{5}\]  
Thus, the variance of the model is accounted for as the sum of the variance contributions of single inputs (main effects, first term in Equation (5)) and the variance cause by higher-order effects. The variance due to second-order effects \(\mathbb{V}\big{(}X_{i},X_{j}\big{)}\) then reads  
\[V_{ij}=\mathbb{V}\big{(}X_{i},X_{j}\big{)}=\mathbb{V}\big{(}\mathbb{E}\big{(} Y|X_{i},X_{j}\big{)}\big{)}-\mathbb{V}(\mathbb{E}(Y|X_{i}))-\mathbb{V}\big{(} \mathbb{E}\big{(}Y|X_{j}\big{)}\big{)}, \tag{6}\]  
and by dividing Equation (6) by the overall variance of the model \(\mathbb{V}(Y)\), the second-order effect \(S_{ij}=\frac{V_{ij}}{\mathbb{V}}\) can be computed:  
\[S_{ij}=\frac{\mathbb{V}\big{(}\mathbb{E}\big{(}Y|X_{i},X_{j}\big{)}\big{)}}{ \mathbb{V}(Y)}-S_{i}-S_{j}. \tag{7}\]  
Whereas Equation (4) holds only for purely additive models (i.e., those that have no interaction effects), a similar relation can be written for general models by dividing Equation (5) by the overall variance \(\mathbb{V}(Y)\):  
\[1=\sum_{i}S_{i}+\sum_{i}\sum_{j>i}S_{ij}+\ldots+S_{123\ldots k}, \tag{8}\]  
implying that for a general model, all main and interaction effects add up to one. Next to the main and interaction effects, the so-called total effects can be computed, which combine the main effect and all interaction effects for each input quantity \(X_{i}\). To compute the total effect for each input quantity, the idea is to compute the amount of variance in the model output that cannot be attributed to the input quantity under investigation and compared to the overall variance with all inputs. This yields the following form for the \(i\)-th total sensitivity index \(S_{T_{i}}\):  
\[S_{T_{i}}=1-\frac{\mathbb{V}(\mathbb{E}(Y|\mathbf{X}_{\sim i}))}{\mathbb{V}(Y)} \tag{9}\]  
with \(\mathbb{E}(Y|\mathbf{X}_{\sim i})\) denoting the conditional expectation of the output given all inputs except from the \(i\)-th input quantity. It should be noted that generally \(\sum_{i}S_{T_{i}}\geq 1\), since here, the interaction effects of all inputs are counted multiple times, i.e., in all corresponding interactions. An efficient method to compute the aforementioned sensitivity indices is presented e.g., in [56]. Within this study, the \(SALib\) implementation in python is used [57] for the necessary computations with respect to the GSA. The underlying Monte Carlo procedure employs a Quasi Monte Carlo approach with a Sobol sequence [58] for equal sampling of the parameter space. A total of \(1\cdot 10^{6}\) Monte Carlo runs is performed. Since the used python framework assumes a scalar valued model output, the analysis is performed for each output separately. However, since all inputs are processed in parallel, this is assumed to not limit the applied method. The parameter bounds for all inputs \(\mathbf{X}\) used according to Table 1 and scaled to a uniform distribution \(\mathbf{X}\sim\mathcal{U}(0,1)\).