Multivariate global sensitivity analysis for dynamic crop models

Abstract

Dynamic crop models are frequently used in ecology, agronomy and environmental sciences for simulating crop and environmental variables at a discrete time step. They often include a large number of parameters whose values are uncertain, and it is often impossible to estimate all these parameters accurately. A common practice consists in selecting a subset of parameters by global sensitivity analysis, estimating the selected parameters from data, and setting the others to some nominal values. For a discrete-time model, global sensitivity analyses can be applied sequentially at each simulation date. In the case of dynamic crop models, simulations are usually computed at a daily time step and the sequential implementation of global sensitivity analysis at each simulation date can result in several hundreds of sensitivity indices, with one index per parameter per simulation date. It is not easy to identify the most important parameters based on such a large number of values. In this paper, an alternative method called multivariate global sensitivity analysis was investigated. More precisely, the purposes of this paper are (i) to compare the sensitivity indices and associated parameter rankings computed by the sequential and the multivariate global sensitivity analyses, (ii) to assess the value of multivariate sensitivity analysis for selecting the model parameters to estimate from data. Sequential and multivariate sensitivity analyses were compared by using two dynamic models: a model simulating wheat biomass named WWDM and a model simulating N 2O gaseous emission in crop fields named CERES-EGC. N 2O measurements collected in several experimental plots were used to evaluate how parameter selection based on multivariate sensitivity analysis can improve the CERES-EGC predictions. The results showed that sequential and multivariate sensitivity analyses provide modellers with different types of information for models which exhibit a high variability of sensitivity index values over time. Conversely, when the parameter influence is quite constant over time, the two methods give more similar results. The results also showed that the estimation of the parameters with the highest sensitivity indices led to a strong reduction of the prediction errors of the model CERES-EGC.