# Predicted Future Changes in the Mean Seasonal Carbon Cycle Due to Climate Change
## 2 Materials and Methods
### Model Runs, Validation, and Mean Seasonal Cycle Analyses under Climate Change  
The model simulations for model validation under measured forcing climate ran for CZ-Bk1 from 2000 to 2008, for IT-Col from 1997 to 2014, for FI-Hyv from 1996 to 2014, for FR-Lbr from 1996 to 2008, and for DK-Sor from 1996 to 2008 (see Table 1). For all sites model simulations under climate change scenarios began in 1997 and finished in December 2009. Model validation was performed by comparing modeled NEE, GPP, and Re\({}_{\text{co}}\) against measured eddy covariance estimates (for GPP and Re\({}_{\text{co}}\) using the night-time method with constant USTAR [67], as reported in the Fluxnet2015 Dataset [56]. To analyze 3D-CMCC-FEM's capabilities to simulate NEE, GPP, and Re\({}_{\text{co}}\) for daily and monthly time series, a set of commonly used statistical metrics have been applied to compare measured vs. modeled data (under observed climate forcing). To avoid considering bad quality data, a filtering procedure for quality-check has been applied; days with less than 60% of valid data were not considered and excluded both in the model and in the observed datasets. Therefore, daily NEE, GPP, and Re\({}_{\text{co}}\) eddy covariance data with low-quality values (i.e., less than 0.6; [68]) were removed. Consequently, the corresponding daily modeled data were removed too. The monthly NEE, GPP, and Re\({}_{\text{co}}\) values (both from eddy covariance and the model) were aggregated from the daily ones. The common statistic we applied includes Pearson's correlation coefficient (r), Relative Mean Bias (RMB), Normalized Root Mean Square Error (NRMSE), and Modeling Efficiency (ME)  
In climate change projections, we considered the potential modifications in the ability of forest stands to absorb or emit carbon throughout the season and across the years under two different locally bias-corrected climate change scenarios, each coming from three Earth System Models. This involves averaging the daily values of the MSC of the threefluxes considered. It is noteworthy that NEE represents the equilibrium between carbon absorption by vegetation during photosynthesis and carbon release through vegetation and microbial respiration. Not only the length of the growing season but also the balance between the yearly amount of photosynthesis and \(\mathrm{R_{eco}}\) has been shown to control much of the variability across the sites and the decades analyzed ([PERSON], 2014; [PERSON], 2015). This calculation is derived from the variance between GPP and \(\mathrm{R_{eco}}\) encompassing both autotrophic respiration (\(\mathrm{R_{A}}\), including ground components) and heterotrophic respiration (\(\mathrm{R_{H}}\)) ([PERSON], 2015). Under climate change scenarios, we account for potential changes in the sink/source capacity of the stands during the season by averaging NEE, GPP, and \(\mathrm{R_{eco}}\) values every ten years up to 2100 ([PERSON], 2015) and accounting for changes in the sink/source and source/sink length during the year, computed as the number of total days of the year (DoY) where a forest stand behaves as a C-sink (GPP \(>\)\(\mathrm{R_{eco}}\) with NEE \(<\) 0) or a C-source (GPP \(<\)\(\mathrm{R_{eco}}\) with NEE \(>\) 0), as described by the NEE. In addition, we also account for the changes in the DoY where NEE changes its sign at least for ten consecutive days to avoid artifact effects of pulsing, e.g., the 'Birch effect' on \(\mathrm{R_{eco}}\)([PERSON], 2015), and to account for unstable conditions and no clear source/sink and sink/source seasonal transition during the year. Therefore, we discuss changes in the MSC under the RCP 2.6 and RCP 6.0 for NEE, being the net result of opposite fluxes (i.e., GPP and \(\mathrm{R_{eco}}\)), through its changes in negative values, i.e., days in the year where NEE \(<\) 0 and describing \(\mathrm{CO_{2}}\) uptake from the atmosphere, and positive, i.e., days in the year where NEE \(>\) 0 and describing \(\mathrm{CO_{2}}\) release to the atmosphere.