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The estimation of variance-based importance measures (called Sobol' indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for high-dimensional model involving a large number of input variables (typically more than ten). Recently, Sobol and Kucherenko have proposed the Derivative-based Global Sensitivity Measures (DGSM), defined as the integral of the squared derivatives of the model output, showing that it can help to solve the problem of dimensionality in some cases. We provide a general inequality link between DGSM and total Sobol' indices for input variables belonging to the class of Boltzmann probability measures, thus extending the previous results of Sobol and Kucherenko for uniform and normal measures. The special case of log-concave measures is also described. This link provides a DGSM-based maximal bound for the total Sobol indices. Numerical tests show the performance of the bound and its usefulness in practice.

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 N2O gaseous emission in crop fields named CERES-EGC. N2O 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

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In the context of managed herds, epidemiological models usually take into account relatively complex interactions involving a high number of parameters. Some parameters may be uncertain and/or highly variable, especially epidemiological parameters. Their impact on the model outputs must then be assessed by a sensitivity analysis, allowing to identify key parameters. The prevalence over time is an output of particular interest in epidemiological models, so sensitivity analysis methods adapted to such dynamic output are needed. In this paper, such a sensitivity analysis method, based on a principal component analysis and on analysis of variance, is presented. It allows to compute a generalised sensitivity index for each parameter of a model representing Salmonella spread within a pig batch. The model is a stochastic discrete-time model describing the batch dynamics and movements between rearing rooms, from birth to slaughterhouse delivery. Four health states were introduced: Salmonella-free, seronegative shedder, seropositive shedder and seropositive carrier. The indirect transmission was modelled via an infection probability function depending on the quantity of Salmonella in the rearing room. Simulations were run according to a fractional factorial design enabling the estimation of main effects and two-factor interactions. For each of the 18 epidemiological parameters, four values were chosen, leading to 4096 scenarios. For each scenario, 15 replications were performed, leading to 61440 simulations. The sensitivity analysis was then conducted on the seroprevalence output. The parameters governing the infection probability function and residual room contaminations were identified as key parameters. To control the Salmonella seroprevalence, efficient measures should therefore aim at these parameters. Moreover, the shedding rate and maternal protective factor also had a major impact. Therefore, further investigation on the protective effect of maternal or post-infection antibodies would be needed.

Nitrous oxide, carbon dioxide and methane are the main biogenic greenhouse gases (GHG) contributing to net greenhouse gas balance of agro-ecosystems. Evaluating the impact of agriculture on climate thus requires capacity to predict the net exchanges of these gases in a systemic approach, as related to environmental conditions and crop management. Here, we used experimental data sets from intensively-monitored cropping systems in France and Germany to calibrate and evaluate the ability of the biophysical crop model CERES-EGC to simulate GHG exchanges at the plot-scale. The experiments involved major crop types (maize-wheat-barley-rapeseed) on loam and rendzina soils. The model was subsequently extrapolated to predict CO 2 and N 2 O fluxes over entire crop rotations. Indirect emissions (IE) arising from the production of agricultural inputs and from use of farm machinery were also added to the final greenhouse gas balance.One experimental site (involving a maize-wheat-barley-mustard rotation on a loamy soil) was a net source of GHG with a net GHG balance of 670 kg CO 2 -C eq ha −1 yr −1 , of which half were due to IE and half to direct N 2 O emissions. The other site (involving a rapeseed-wheat-barley rotation on a rendzina) was a net sink of GHG for -650 kg CO 2 -C eq ha −1 yr −1 , mainly due to high C returns to soil from crop residues. A selection of mitigation options were tested at one experimental site, of which straw return to soils emerged as the most efficient to reduce the net GHG balance of the crop rotation, with a 35% abatement. Halving the rate of N inputs only allowed a 27% reduction in net GHG balance. Removing the organic fertilizer application led to a substantial loss of C for the entire crop rotation that was not compensated by a significant decrease of N 2 O emissions due to a lower N supply in the system. Agro-ecosystem modeling and scenario analysis may therefore contribute to design productive cropping systems with low GHG emissions.1

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