Multivariate global sensitivity analysis for discrete-time models
Résumé
Discrete-time models are frequently used in ecology and agronomy. These models can be used for the management of endangered species, for understanding intraspecific and interspecific competitions, for pest management, or for predicting plant growth. Their outputs can be expressed as time series. It is often impossible to estimate all the parameters of a discrete-time model due to their large number. A common practice consists in selecting a subset of parameters by sensitivity analysis, in estimating the selected parameters from data, and in fixing the others to some nominal values. For a discrete-time model, global sensitivity analysis can be applied separately on each output, but there is a high level of redundancy between close dates and, on the other hand, interesting features of the dynamic may be missed out. In this paper, a method based on principal component analysis and on analysis of variance is presented to compute a generalized sensitivity index for each model parameter. The proposed index synthesizes the influence of the parameter on the whole time series output. It may be used to select a subset of parameters to be calibrated. In addition a quality criterion is proposed for any approximation associated with the ANOVA decomposition on the principal components. The method was applied to a winter wheat dynamic model including seven parameters with few observations for estimating all the parameters. The results showed that two parameters had a strong influence on the wheat biomass simulated by the model at a daily time step: the radiation use efficiency and a parameter of the mathematical function describing the kinetic of the leaf area index. We also showed that the generalized index can be accurately computed by using only the first three principal components. The proposed approach is quite general and can be applied to any dynamic model predicting one or several output variables at a discrete time step.