## 1 Introduction  
Global concerns over increasing levels of greenhouse gas concentrations, particularly carbon dioxide (CO\({}_{2}\)), have pushed research efforts to better investigate biogeochemical carbon (C) flux dynamics and patterns between atmosphere and biosphere, and to upscale C flux estimates from site-specific to regional, continental and global scales. Increased atmospheric concentration of CO\({}_{2}\), combined with increasing temperatures and size variations of ecosystem C pools, are responsible for year-to-year terrestrial ecosystem carbon flux perturbations, through the variation of both photosynthetic and respiration rates [1]. In the last decades, the eddy covariance (EC) technique has provided long-term continuous measurements of net carbon ecosystem exchange (NEE), water vapor and energy, within the global network of EC flux towers (FLUXNET) distributed over major terrestrial ecosystems. The availability of EC measure of NEE contributed to quantify and to determine seasonal and inter-annual variability of ecosystem C budgets at EC tower site-specific scale [2; 3; 4]. Observed NEE does not directly quantify the two major components of ecosystem C flux balance represented by ecosystem respiration (R\({}_{\text{eco}}\)) and gross primary productivity (GPP). Thus, flux partitioning algorithms have been developed to partition eddy covariance NEE into photosynthetic uptake and respiratory release [5; 6]. At the same time, EC flux measurements provide key information for the parameterization, calibration and validation of process-based forest ecosystem models (FEMs) contributing to large-scale estimates of main ecosystem C pools. The implementation of both forest process-based models (PBMs) [7; 8; 9; 10; 11; 12] and functional-structural tree models (FSTMs) [13; 14; 15; 16], based on the widely used light use efficiency (LUE) approach [17], has contributed to understanding and upscaling the main physiological processes supporting ecosystem C uptake. Although most of forest ecosystem models provide reliable estimates of forest growth, limitations for NEE estimates are related to the uncertainty in R\({}_{\text{eco}}\) estimation [18; 19]. Hence, the implementation of biogeochemical models integrating soil respiration models and FSTMs is a great opportunity to reliably estimate NEE [20; 21; 22]. Although soil respiration and soil organic matter (SOM) decomposition depend mainly on abiotic factors, such as temperature and soil moisture [23; 24; 25], a key role is played by soil organic carbon (SOC) stock size, microbial pools [26; 27], and dynamics of SOC supply to soil with littering [28]. Leaf and fine root senescence is of primary importance in determining dynamics in heterotrophic respiration [29; 30], and exhibits seasonal patterns and intra-seasonal pulses [31; 32]. These pulses are mostly driven by phenological transitions through stages of dormancy, active growth, and senescence. For example, supply of dead leaves in soil is strongly dependent on a tree's leaffal strategy. This is also true when predicting tree respiration, which is directly related to their growth and nitrogen content, which depends on spring phenology. Unfortunately, processes involving budburst and senescence are still partly obscure. PBMs usually represent these processes simplistically; these simplifications may lead some terrestrial ecosystem models to result in biased predictions [33; 34; 35]. For these reasons, we developed the 3D-CMCC-PSM (3D-CMCC-Phenology and soil Model), a new version of the hybrid process-based model 3D-CMCC FEM proposed by [PERSON] et al.