Global sensitivity analysis and Bayesian inference framework
Our framework was based on Bayes' theorem: Pr(θ|V) Pr(V|θ) Pr(θ) where Pr(θ|V) is the posterior after Bayesian inference conditioned on available observations V (hereafter the bold letter indicates a matrix). θis the matrix of parameters and TEM outputs (e.g., GPP) and V is the matrix of observation or the matrix of the differences between prior simulations and the corresponding observations, whose element Vij denotes the type j data V(·)j at time step i. Pr(V|θ) is the likelihood function, which will be calculated as a function of TEM Monte Carlo simulations and the available eddy flux data. Pr(θ) is the prior of the TEM parameters and our estimated C fluxes (e.g., GPP, RESP and NEP) and EET. To address our research questions, we first conducted TEMensemble simulations with parameter priors. Second, the likelihood function Pr(V|θ) was calculated based on model simulations and observations. Third, the global sensitivity analysis was applied, and fourth, the Bayesian inference was conducted.