## 2 Materials and Methods
### Modeling Details
#### 2.2.2 Model Parameterization and Statistical Analysis  
Harvested hay production was measured after each moving event for the mowed paddock and the amounts of biomass on the grazed paddock were measured just before and after each grazing events. These observations were used to constrain the grazing and harvesting procedures in CenW simulations and measured root biomass and soil water contents at different depth in the soil were used to constrain the soil water extraction of the CenW ecosystem model.  
Total SOC content was measured in early 2005 for different soil layers and for the two managed grasslands (mowed and grazed), and these values were used to initialize the CenW model independently for the two paddocks through the spin up of the model simulations until equilibrium conditions between measured and modeled initial SOC stocks were reached.  
Model simulations were optimized by selecting a set of parameter values that minimized the residual sums of squares across different EC measurements and ancillary observations. Measurements used for CenW parameterization were daily- and weekly-averaged estimates of evapotranspiration (ET) and net ecosystem exchange (NEE). We separated our five years of eddy covariance data into weekly sets, with one week of daily values used for parameter optimization and the other week for model validation. There are therefore two flux datasets for each paddock, one for model calibration, and one for model verification. CenW uses an automatic parameter optimization routine that worked by changing parameter values within specified boundaries to minimize the residual sums of squares. That was applied to both daily and weekly-averaged data within the data set selected for parameter optimization.  
Initial parameter values to run CenW for managed grasslands were retrieved from a previous study where the model was run for a grazed dairy farm of New Zealand [56]. Specific management practices from farm records were implemented in CenW and we used a spin up of the model to initialize soil carbon and nitrogen pools. Then, model simulations were optimized for these paddocks based on a selection of eddy covariance observations (NEE and ET) and ancillary data (amounts of vegetation mowed and grazed and soil water content) by the automatic parameter optimization procedure imbedded in the model that aim to maximize the agreement between model and observations.  
The overall goodness of fit was described by the Nash-Sutcliffe model efficiency (EF) [78]:  
\[EF=1-\frac{\sum(y_{o}-y_{m})^{2}}{\sum(y_{o}-\overline{y})^{2}}, \tag{1}\]  
where \(y_{o}\) represents the individual observations, \(y_{m}\) is the corresponding modeled values, and \(\overline{y}\) the mean of all observations. EF quantifies both the tightness of the relationship between measured and modeled data and assesses whether there is any consistent bias in the model. Model efficiency values range from minus infinity to 1. High model efficiency can only be achieved when there is a tight relationship with little unexplained random variation and little systematic bias. Negative values of model efficiencies indicate poor model fit and that the mean value of the observation is a better predictor than the model. EF = 0 implies that the mean of the observations is as good a predictor than the model, while positive values indicate that the model is a better predictor than the observed mean. The closer EF is to one, the stronger the agreement between observed and modeled data.  
The final sets of parameters values used for the simulations of the mown and grazed paddocks are given in Appendix B.