Sensitivity analysis in Earth and environmental systems modelling typically demands an onerous computational cost. This issue coexists with the reliance of these algorithms on ad-hoc designs of experiments, which hampers making the most out of the existing datasets. We tackle this problem by introducing a method for sensitivity analysis, based on the theory of variogram analysis of response surfaces (VARS), that works on any sample of input-output data or pre-computed model evaluations. Called data-driven VARS(D-VARS), this method characterizes the relationship strength between inputs and outputs by investigating their covariograms. We also propose a method to assess ‘robustness’ of the results against sampling variability and numerical methods’ imperfectness. Using two hydrologic modelling case studies, we show that D-VARS is highly efficient and statistically robust, even when the sample size is small. Therefore, D-VARS can provide unique opportunities to investigate geophysical systems whose models are computationally expensive or available data is scarce.