## 4 Discussion  
First, it is important to clarify some terms used in this analysis. Gross primary production (GPP) is the net rate of carboxylation and oxygenation by RuBisCO and is calculated as \(\text{GPP}=P_{g}-R_{p}\), where \(P_{g}\) is gross photosynthesis and \(R_{p}\) is photorespiration. In EC flux data analyses, GPP is also known as gross ecosystem exchange (GEE) or gross ecosystem production (GEP) and is often estimated inversely from NEE or NEP flux tower retrievals as \(\text{GPP}=\text{NEE}-R_{e}\), where \(R_{e}\) is ecosystem respiration or the sum of auto- and heterotrophic respiration components. Thus, \(R_{e}=R_{m}+R_{g}+R_{h}\) where \(R_{m}\) is maintenance respiration, \(R_{g}\) is autotrophic growth respiration, and \(R_{h}\) is heterotrophic respiration. While GPP is the total amount of C fixed by plants in photosynthesis, NPP subtracts autotrophic respiration (\(R_{a}\)) as \(\text{NPP}=\text{GPP}-R_{a}\) where \(R_{a}=R_{g}+R_{m}\). NEE or net ecosystem production (NEP) is then calculated as NPP minus heterotrophic respiration, or \(\text{NEE}=\text{NPP}-R_{h}\), which is equivalent \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Site** & **Model** & **Duration (years)** & **Elapsed (s)** \\ \hline HF-EMS & PPA-SiBGC & 11 & 8.51 \\ HF-EMS & LANDIS-II NECN & 11 & 101.15 \\ JERC-RD & PPA-SiBGC & 5 & 2.25 \\ JERC-RD & LANDIS-II NECN & 5 & 61.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Simulation timing results. to \(\text{NEE}=\text{GPP}-R_{e}\). During the day, \(\text{NEE}=P_{g}+R_{p}+R_{m}+R_{g}+R_{h}\) while during the night, \(P_{g}\) and \(R_{p}\) are absent, making NEE approximate to ecosystem respiration, or \(R_{e}\). Traditionally, gross or net exchange of CO\({}_{2}\) into the forest is negative and fluxes into the atmosphere are positive, while each constituent process is discussed with a positive sign. Thus, NEE is often calculated as \(\text{NEE}=R_{e}-\text{GPP}\) where each constituent flux term is always positive [133; 134; 135; 136; 137]. All this is to say that there exists much difficulty in relating NPP from field inventories and soil respiration samples directly to NEE from EC flux towers, integrated over the year. In our analyses, we assume that the observed annual biomass growth increment is equivalent to ANPP and that soil respiration (\(r_{soil}\)) is equivalent to ecosystem respiration (\(R_{e}\)), or \(\text{NEE}=\text{NPP}-r_{soil}\). Yet, there are known error contributions at multiple conversion points, making the comparison of models based on field data and EC flux tower measurements difficult. For example, field inventory estimates of ANPP contain known sources of error in converting DBH to biomass, both above- and belowground [115], and there are additional errors in converting biomass to C based on a fixed fraction for each biomass compartment. Meanwhile, unlike \(R_{e}\), \(r_{soil}\) does not account for \(R_{g}\) or \(R_{m}\), only \(R_{h}\). Even if these fluxes were approximately similar, spatial biases in the EC flux tower footprint or contributing area [138; 139; 140; 141; 142] may make field inventory and tower measurements difficult to harmonize. As others have noted [118; 119], including a previous study on flux measurements at the HF-EMS site [88], it is evident that treating ANPP as the C fraction of woody biomass increment per allometric relations from field data is a loose proxy for ecosystem ANPP, given its visible disconnection from observed NEE and \(r_{\text{soil}}\) fluxes. Given the definition of NEE, the relation between these variables should be approximately linear. While others have reported hysteresis between peaks in NEE and growth increment at the HF-EMS site [88], we did not see evidence of this dynamic. Instead, flux tower NEE appears to have little to no connection to field data ANPP and observed \(r_{\text{soil}}\) fluxes at both sites in this analysis. Nevertheless, both models showed good agreement with net changes to C and N pools.