## 2 Materials and Methods
### The HJA-N Model
#### 2.3.6 Control Capacity  
To facilitate a discussion of the seasonal variation in the features controlling nitrogen cycling, we propose the nitrogen control capacity as a set of normalized rate terms which can be derived from the temporally varying model results to provide insights into these features. Hydrology controls nitrogen dynamics through export of dissolved nitrogen compounds. To capture this flushing behavior, we define the term transport control as:  
\[\text{Hydroologic Flushing}=Q_{\text{DIN,IS}}+Q_{\text{DON,IS}}+Q_{\text{DIN, RZ}}+Q_{\text{DIN,BRZ}}+Q_{\text{DON,RZ}}+Q_{\text{DON,BRZ}} \tag{1}\]  
where \(Q_{\text{DIN,IS and }}Q_{\text{DON,IS}}\) are the simulated export rates of DON and DIN from the stream and \(Q_{\text{DIN,RZ}}\), \(Q_{\text{DIN,BRZ}}\), \(Q_{\text{DON,RZ}}\) and \(Q_{\text{DON,BRZ}}\) are the rates of movement of dissolved N through the watershed. Hydrologists tend to view nitrogen dynamics through the lens of the flushing hypothesis and this term is designed to capture the contribution of flushing to the movement of N in the system. The contributions of simulated DIN and DON to the flushing index were normalized by the area of the stream, rather than the area of the watershed. We used an area of 767 m\({}^{2}\), following from [30].  
The vegetation controls N cycling through nitrogen mobilization, which we define as the difference between litter decomposition rates and uptake. We have elected to group litter and vegetation together, though clearly they could also be treated independently. Under this definition, the above ground control term is defined as:  
\[\text{Vegetation Processes}=D_{\text{N,f}}+D_{\text{N,w}}+D_{\text{N,r}}-U_{ \text{DIN,RZ}} \tag{2}\]  
where \(U_{\text{DIN,RZ}}\) is the uptake rate into vegetation and \(D_{\text{N,f}}\), \(D_{\text{N,w}}\), \(D_{\text{N,r}}\), are the decomposition rates contributing nitrogen from foliar, woody, and root litter respectively.  
Soil control is defined analogously as the of the net mobilization rate, in this case:  
\[\text{Soil Processes}=M_{\text{DIN,RZ}}+M_{\text{DON,RZ}}+M_{\text{DIN,BRZ}}+M_ {\text{DON,BRZ}}-\left(I_{\text{DIN,RZ}}+I_{\text{DIN,BRZ}}\right) \tag{3}\]where \(M_{\rm DIN,RZ}\) and \(M_{\rm DON,RZ}\) are the mobilization rates of DIN and DON within the root zone, respectively, \(M_{\rm DIN,BRZ}\) and \(M_{\rm DON,BRZ}\) are the mobilization rates of DIN and DON below the root zone, respectively, and \(I_{\rm DIN,RZ}\) and \(I_{\rm DIN,BRZ}\) are the immobilization rate of DIN in the root zone and below the root zone, respectively. Note that DON is assumed to be unavailable to plants or the microbial complex, and as such has no immobilization rate.  
We then define the aquatic control in a somewhat different fashion, including the net mobilization of nitrogen, but also the simulated rate of particulate export.  
\[\rm{Instram\ Processes}=M_{\rm DIN,IS}+M_{\rm DON,IS}-I_{\rm DIN,IS}+P_{\rm N,IS} \tag{4}\]  
where \(M_{\rm DIN,IS}\) and \(M_{\rm DON,IS}\) are the mobilization rates of DIN and DON from the aquatic biomass, \(I_{\rm DIN,IS}\) is the immobilization rate of DIN from the aquatic biomass, and \(P_{\rm N,IS}\) is the export rate of particulate N, which again originates from the aquatic biomass. Similar to the simulated values of stream DIN and DON, the instream process control was normalized by stream area, rather than the full watershed area.  
For comparative purposes, the four values are then normalized by the overall sum of the included rate terms to produce a ratio of control for each term, which varies throughout the model timeframe, given the system dynamics.