## 2 Materials and Methods
### The HJA-N Model
\begin{table}
\begin{tabular}{c c c} \hline
**Rate** & **Definition** & **Units** \\ \hline \(P_{{}_{c}}=P_{{}_{a}}\eta_{{}_{0}}\) & \(P_{{}_{n}}\) allocated to foliage(\(i=f\)), & kg C/m\({}^{2}\) \\  & wood (\(i=w\)) and fine roots (\(i=r\)) & kg C/m\({}^{2}\) \\ \(T_{{}_{c}}=B_{{}_{c}}\tau_{{}_{g}}\) & Turnover of C from foliage (\(i=f\)), & kg C/m\({}^{2}\) \\  & wood (\(i=w\)) and fine roots (\(i=r\)) & kg N/m\({}^{2}\) \\ \(U_{{}_{n}}=u_{{}_{\max}}\Bigg{(}\dfrac{W_{{}_{Nu,R}}}{u_{{}_{1/2}}+W_{{}_{Nu,R }}}\Bigg{)}\) & Uptake of N & kg N/m\({}^{2}\) \\ \(U_{{}_{Nu}}=U_{{}_{N}}\eta_{{}_{N}}\) & Uptake allocated to foliage (\(i=f\)), & kg N/m\({}^{2}\) \\  & wood (\(i=w\)) and fine roots (\(i=r\)) & kg N/m\({}^{2}\) \\ \(T_{{}_{Nu}}=B_{{}_{N}}\tau_{{}_{g}}\) & Turnover of N from foliage (\(i=f\)), & kg N/m\({}^{2}\) \\  & wood (\(i=w\)) and fine roots (\(i=r\)) & kg N/m\({}^{2}\) \\ \(FS_{{}_{N1}}=FS_{{}_{max}}\eta_{{}_{1}}\lambda\) & Symbiotic fixation allocated to foliage (\(i=f\)), & kg N/m\({}^{2}\) \\  & wood (\(i=w\)) and fine roots (\(i=r\)) & kg C/m\({}^{2}\) \\ \(D_{{}_{C1}}=B_{{}_{C1}}(1-f_{{}_{co_{2}}})d_{{}_{1}}\lambda\) & Decomposition to SOM from foliage (\(i=f\)), & kg C/m\({}^{2}\) \\  & wood (\(i=w\)) and fine roots (\(i=r\)) & kg C/m\({}^{2}\) \\ \(D_{{}_{Nu}}=B_{{}_{Nu}}e^{-(C_{{}_{Nu}}/C_{{}_{Nu}})^{{}^{\prime}}}d_{{}_{1}}\lambda\) & Decomposition of N from foliage (\(i=f\)), & kg N/m\({}^{2}\) \\  & wood (\(i=w\)) and fine roots (\(i=r\)) & kg N/m\({}^{2}\) \\ \(F\lambda_{{}_{u}}=F\lambda_{{}_{u}}\lambda\) & Asymbiotic fixation allocated to foliage (\(i=f\)), & kg N/m\({}^{2}\) \\  & wood (\(i=w\)) and fine roots (\(i=r\)) & kg N/m\({}^{2}\) \\ \(R_{{}_{C1,D}}=B_{{}_{C1}}f_{co_{2}}d_{{}_{1}}\lambda\) & Decomposition as resp from foliage (\(i=f\)), & kg C/m\({}^{2}\) \\  & wood (\(i=w\)) and fine roots (\(i=r\)) & kg C/m\({}^{2}\) \\ \hline \end{tabular}
\end{table} 
Table 4: Rate terms comprising vegetation mass balance equations. See Table 7 for definitions of parameter values. \begin{table}
\begin{tabular}{c c c} \hline
**Rate** & **Definition** & **Units** \\ \hline \(R_{{}_{C,i}}=S_{{}_{C,i}}f_{{}_{i}}\lambda\) & Respiration of C from root zone (\(i=R\)), below (\(i=B\)) & kg C/m\({}^{2}\) \\ \(T_{{}_{C,R}}=S_{{}_{C,R}}\tau_{{}_{t,R}}\) & Transfer of C from root zone to below & kg C/m\({}^{2}\) \\ \(M_{{}_{Nu,i}}=\dfrac{R_{{}_{C,i}}}{CN_{{}_{S,i}}}f_{{}_{Nu,R}}\lambda\) & Mobilization of unavailable N from RZ (\(i=R\)), & kg N/m\({}^{2}\) \\  & below (\(i=B\)) & kg N/m\({}^{2}\) \\ \(M_{{}_{Nu,i}}=\dfrac{R_{{}_{C,i}}}{CN_{{}_{S,i}}}(1-f_{{}_{Nu,R}})\lambda\) & Mobilization of available N from RZ (\(i=R\)), & kg N/m\({}^{2}\) \\  & below (\(i=B\)) & kg N/m\({}^{2}\) \\ \(T_{{}_{N,R}}=S_{{}_{Nu,R}}\tau_{{}_{t,R}}\) & Transfer of N out of root zone & kg N/m\({}^{2}\) \\ \(I_{{}_{Nu,j}}=i_{{}_{min}}\Bigg{(}\dfrac{W_{{}_{Nu,j}}}{i_{{}_{2/2}}+W_{{}_{Nu,j} }}\Bigg{)}\lambda\) & Immobilization of available N (\(j=R\)), below (\(j=B\)) & kg N/m\({}^{2}\) \\  & \(DP_{{}_{Na}}\) & Deposition of DIN & kg N/m\({}^{2}\) \\ \(D_{{}_{Na,i}}=W_{{}_{Na,j}}d_{{}_{Na,j}}\lambda\). & Breakdown of HMW DON from the root zone (\(i=R\)) & kg N/m\({}^{2}\) \\  & or below (\(i=B\)) & kg N/m\({}^{2}\) \\ \(DN_{{}_{Na,i}}=W_{{}_{Na,i}}dn_{{}_{i}}\lambda\) & Denitrification from RZ (\(i=R\)), below (\(i=B\)), & kg N/m\({}^{2}\) \\  & and instream (\(i=IS\)) & kg N/m\({}^{2}\) \\ \(Q_{{}_{i,R}}=\dfrac{W_{{}_{i,R}}}{W_{{}_{R}}}W_{{}_{R},{}_{R}}k_{{}_{R^{\prime},S _{i,R}}}\) & Hydroologic transfer of N from \(RZ\). & kg N/m\({}^{2}\) \\  & (\(i=Na\)—unavailable. \(i=Nu\)—available) & kg N/m\({}^{2}\) \\  & \(DP_{u}\) & Deposition of DIN & kg N/m\({}^{2}\) \\ \(Q_{{}_{i,R}}=\dfrac{W_{{}_{i,R}}}{W_{{}_{R},{}_{R}}}W_{{{}_{R},{}_{R}}(k_{{}_{R^{ \prime},S}}+k_{{}_{R^{\prime},S}})s_{{}_{i,R}}\) & Hydroologic transfer of N from brz. (\(i=Na\) represents unavailable, \(i=Nu\) represents available) & kg N/m\({}^{2}\) \\ \hline \end{tabular}
\end{table} 
Table 5: Rate terms comprising soil-processing mass balance equations.