## 2 Materials and Methods
### Model Initialisation Calibration and Evaluation  
The model was calibrated using data in 2017 and 2018 and then ran continuously from 2017 to 2019, with 2019 used to evaluate the model. The calibration process included optimisation of crop phenological parameters (thermal days to maturity, biomass fraction, root: shoot ratios, stem: leaf: grain fraction, water demand, N fixation index, and optimum temperature, Table 2). For modelling purposes, a 16-year spin-up period was introduced to allow time for simulated soil carbon stocks to stabilise. The crop setup consisted of two systems, the first consisted of a perennial grass ley (land put down to grass and/or clover for a limited period) calibrated to simulate a grass/legume mixture. The second system simulated the same, with the addition of a barley cover crop, though no cuts were carried out in 2020 (Table 3). Input parameters for soil and management are as described in Section 2.1, though fertiliser applied (106 kg N/ha/year) was divided equally among the number of fertilisation events for that year. Both calibration and evaluation were conducted using base R and the package 'Hydro-GOF' [46]. Four evaluation metrics were used to evaluate model performance against measured GHG fluxes. These were [PERSON]'s rho (\(\rho\), Equation (1)), where \(\rho\) is the [PERSON]'s rank correlation coefficient, \(d_{i}\) is the difference between the two ranks of individual measured and corresponding simulated data pairs, and \(n\) is the number of observations. Mean absolute error (MAE, Equation (2)) which assesses the size of prediction errors at the individual level, but does not allow comparison between positive and negative predictors. Root mean square error (RMSE, Equation (3)) measures absolute quadratic prediction error. \(S_{i}\) is the simulated, and \(M_{i}\) are the measured variables. Percent bias (\(pBIAS\), Equation (4)) gives a relative bias estimation to determine over or underestimation in the simulation. \[\rho=\mathbf{1}-\frac{6\sum d_{i}^{2}}{n(n^{2}-\mathbf{1})} \tag{1}\]  
\[MAE=\frac{\sum_{i=1}^{n}\left|S_{i}-M_{i}\right|}{n} \tag{2}\]  
\[RMSE=\sqrt{\frac{\sum_{i=1}^{n}\left(S_{i}-M_{i}\right)^{2}}{(n)}} \tag{3}\]  
\[pBIAS=\mathbf{100}\ \frac{\sum_{i=1}^{n}(S_{i}-M_{i})}{\sum_{i=1}^{n}M_{i}} \tag{4}\]  
Following setup and calibration we again ran the model continuously from 2000 to 2020 and used 2019 for model evaluation against gross primary production (GPP kg C ha\({}^{-1}\)), net ecosystem exchange (NEE kg C ha\({}^{-1}\)) and ecosystem respiration (Reco kg C ha\({}^{-1}\)), soil temperature (\({}^{\circ}\)C) at 5 cm, and soil moisture (WFPS cm\({}^{3}\)/cm\({}^{3}\)) at 5 cm and 20 cm according to a pre-determined criteria (Table 4). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Perennial Grass** & **Grain** & **Leaf** & **Stem** & **Root** \\ \hline Max. biomass production (kg C/ha/yr) & 400 & & & & \\ Biomass fraction & 0.04 & 0.28 & 0.28 & 0.4 \\ Biomass C/N ratio & 35 & & & & \\ Annual N demand (kg N/ha/yr) & 143 & & & & \\ Thermal degree days to maturity & 1500 & & & & \\ Water demand (g water/g dry matter (DM)) & 150 & & & & \\ N fixation index (crop N/N from soil) & 1.5 & & & & \\ Optimum temperature (\({}^{\circ}\)C) & 18 & & & & \\ \hline
**Barley** & & & & & \\ \hline Max. biomass production (kg C/ha/yr) & 2496 & & & & \\ Biomass fraction & 0.3 & 0.23 & 0.23 & 0.23 \\ Biomass C/N ratio & 45 & 75 & 75 & 85 \\ Annual N demand (kg N/ha/yr) & 129 & & & & \\ Thermal degree days to maturity & 1500 & & & & \\ Water demand (g water/g DM) & 150 & & & & \\ N fixation index (crop N/N from soil) & 1 & & & & \\ Optimum temperature for crop growth (\({}^{\circ}\)C) & 18 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Crop calibration parameters used in this study. Figures in grey are automatically produced model outputs in response to calibration, and not directly subject to manipulation.