Elementary effects for models with dimensional inputs of arbitrary type and range: Scaling and trajectory generation

The Elementary Effects method is a global sensitivity analysis approach for identifying (un)important parameters in a model. However, it has almost exclusively been used where inputs are dimensionless and take values on [0, 1]. Here, we consider models with dimensional inputs, inputs taking values on arbitrary intervals or discrete inputs. In such cases scaling effects by a function of the input range is essential for correct ranking results. We propose two alternative dimensionless sensitivity indices by normalizing the scaled mean or median of absolute effects. Testing these indices with 9 trajectory generation methods on 4 test functions (including the Penman-Monteith equation for evapotranspiration) reveals that: i) scaled elementary effects are necessary to obtain correct parameter importance rankings; ii) small step-size methods typically produce more accurate rankings; iii) it is beneficial to compute and compare both sensitivity indices; and iv) spread and discrepancy of the simulation points are poor proxies for trajectory generation method performance.