## 1 Introduction  
Ecosystem models are valuable tools that describe and explain the processes and variable dynamics of photosynthesis and respiration in a forest ecosystem [1; 2]. They also play a key role in assessing the carbon equilibrium and the response of a forest ecosystem to global change at local and global scales [3; 4]. Existing ecosystem models integrate many ecosystem processes and are coupled into the earth system model (ESM) [5; 6; 7]. Terrestrial gross primary productivity (GPP) was the largest component flux of the global carbon cycles [8; 9]. There had uncertainty in the interannual variability of GPP simulation of the majority of ecosystem models [10]. The more complicated the models are, the more parameters they may have. This may introduce larger uncertainty caused by the parameter sensitivity, thus, it is indispensable to quantify the uncertainty and sensitivity of the parameters in forest ecosystem models. Under such background, various sensitivity analyses (SAs) were proposed and applied to ascertain the corresponding responses in the output variables when input parameters alter within their valid ranges [11; 12]. Indeed, various SA algorithms have been widely expanded to ecological models [13; 14], SCOPE model [15], hydrological models [16; 17], remote sensing models [18] and crop growth models [12]. Thus, performing an SA is a feasible way to characterize and reduce uncertainties in ecosystem models, and to improve their performance [19; 20]. The global and local SA algorithms can identify the influence of parameters on variations of the outputs in the model and are therefore key to understand the model performance in response to variations in environmental factors [12; 21]. Especially, global SA could be applied to non-linear models, but local SA could not [22; 23]. The global SA considers non-linear responses and parameter interactions [24], providing a comprehensive identification of parameter sensitivity on model outputs. For example, the Sobol' [25], Fourier amplitude sensitivity test (FAST), and extended FAST (EFAST) are variance-based SA methods, and they can quantify the sensitivities of model parameters, including first-order sensitivity index (or main sensitivity index, MSI), total sensitivity index (TSI) and interactions [26]. SA helps parameter uncertainty analysis (UA) and can identify the major uncertainties when combined with parameter optimization. Note that parameter optimization is an essential means of calibrating ecosystem models and increasing the accuracy of their predictions [27; 28]. However, the parameter calibration of complex process models is time-consuming and inaccurate owing to a lack of results in SA in general [29; 30; 31; 32; 33; 34; 35]. The flux-based ecosystem model (FBEM) was also widely used for parameter estimation or data assimilation studies [28; 36; 37; 38]. However, the model has as many as 16 parameters, and how these parameters govern the model behavior is still not clear. Thus, it is necessary to identify the sensitivities of the parameters, informing understanding of the uncertainties in the model. Specifically, we need to estimate the parameter sensitivities in FBEM and their variations in the growing season, as well as the relationship between parameters SI and environmental factors. In this study, the FBEM and EFAST algorithm were combined for parameters SA experiment. Three experiments were designed to systematically evaluate the parameters' sensitivities. Various parameter ranges, different model outputs and temporal variations of parameters SIs were carefully considered. The objective of this study is to evaluate the sensitivity index (SI) of all the parameters on the GPP of FBEM using the EFAST method and to improve the parameter estimation process based on the results of the SA for quantizing uncertainty. Four scientific questions are addressed: (1) how the parameter ranges influence their sensitivities on forest GPP simulation?