An efficient computational method for global sensitivity analysis and its application to tree growth modelling

Global sensitivity analysis has a key role to play in the design and parameterisation of functional–structural plant growth models which combine the description of plant structural development (organogenesis and geometry) and functional growth (biomass accumulation and allocation). We are particularly interested in this study in Sobol's method which decomposes the variance of the output of interest into terms due to individual parameters but also to interactions between parameters. Such information is crucial for systems with potentially high levels of non-linearity and interactions between processes, like plant growth. However, the computation of Sobol's indices relies on Monte Carlo sampling and re-sampling, whose costs can be very high, especially when model evaluation is also expensive, as for tree models. In this paper, we thus propose a new method to compute Sobol's indices inspired by Homma–Saltelli, which improves slightly their use of model evaluations, and then derive for this generic type of computational methods an estimator of the error estimation of sensitivity indices with respect to the sampling size. It allows the detailed control of the balance between accuracy and computing time. Numerical tests on a simple non-linear model are convincing and the method is finally applied to a functional–structural model of tree growth, GreenLab, whose particularity is the strong level of interaction between plant functioning and organogenesis.