# Improving a Process-Based Model to Simulate Forest Carbon Allocation under Varied Stand Density
## 3 Results
### Carbon Allocation and Growth Change with Stand Density  
Overall, _EtaS_ was higher than _EtaFR_ and _EtaF_ (Figure 3). Stands with a high density generally allocated more carbon to the stem for the tree architecture, while stands with a low density allocated more carbon to the nutrient organs, such as the foliage and fine roots, for the improved allocation method (Figures 3 and 4). The effect of density on _EtaS_ and _EtaF_ was obvious, especially at the late growth stage of the stand, while the effect on _EtaFR_ was not large (Figure 3).  
Figure 2: Comparisons between simulations for the original model (**a**) and modified model (**b**), and the estimated aboveground biomass (t ha\({}^{-1}\)), respectively, for 10 poplar stands with different stand densities in northern Jiangsu Province. The solid line represents the fitting line, and the diagonal line represents the 1:1 line.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & _MAE_ & _NRMSE_ & \(d\) \\ \hline
**Original model** & & & \\ Mean DBH (cm) & 24.8 & 0.3 & 0.6 \\ Mean height (m) & 24.4 & 0.4 & 0.7 \\ Aboveground biomass (t ha\({}^{-1}\)) & 60.5 & 0.6 & 0.5 \\
**Modified model** & & & \\ Mean DBH (cm) & 18.7 & 0.2 & 0.7 \\ Mean height (m) & 15.4 & 0.2 & 0.8 \\ Aboveground biomass (t ha\({}^{-1}\)) & 26.6 & 0.3 & 0.8 \\ \hline \hline \end{tabular} _MAE_ is the mean absolute error, _NRMSE_ is the normalized root mean square error, and \(d\) is the refined Willmott index.  
\end{table}
Table 3: Performance of the original and modified TRIPLEX-Management model.  
Figure 3: Changes in the annual carbon allocation ratios to the stem (**a**), foliage (**b**), and fine root (**c**) with age under different stand densities (200, 400, 800, 1000, and 1200 stems ha\({}^{-1}\)) using the modified model.  
The average DBH decreased from 31.7 to 21.5 cm and the average tree height decreased from 26.9 to 21.9 m with the increasing stand density for the improved method (Table 4). The aboveground biomass increased with density until 400 stems ha\({}^{-1}\), and then became relatively stable thereafter.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Poplar**} & \multicolumn{6}{c}{**Density (Stems ha\({}^{-1}\))**} \\ \cline{2-7}  & **200** & **400** & **600** & **800** & **1000** & **1200** \\ \hline \multicolumn{7}{c}{Site 9 (Age = 20 years)} \\ \(\overline{D}\) & 31.7 & 26.6 & 24 & 22.7 & 22 & 21.5 \\ \(\overline{H}\) & 26.9 & 25.3 & 23.6 & 22.7 & 22.3 & 21.9 \\ AGB & 246.9 & 261.2 & 252.9 & 231.9 & 221.9 & 217.1 \\ SC & 124.5 & 124.7 & 124.8 & 126.4 & 127.3 & 127.5 \\ \hline \hline \end{tabular} \(\overline{D}\) is the mean diameter at breast height (cm), \(\overline{H}\) is the mean tree height (m), AGB is the aboveground biomass (t ha\({}^{-1}\)), and SC is soil carbon (t C ha\({}^{-1}\)).  
\end{table}
Table 4: Simulated effects of the planting density on the stand characteristics at a stand age of 20 years old using the modified model.  
Figure 4: Simulated seasonal dynamics of the carbon allocation ratio to stems (**a,b**), foliage (**c,d**), and fine roots (**e,f**) for the 6-year-old (**a,c,e**) and 13-year-old (**b,d,f**) stands with different densities (200 vs. 1200 stems ha\({}^{-1}\)) using the modified model.