## 3 Materials and Methods
### Parameterization for Deciduous Broadleaf Forests  
#### 3.3.1 Biomass Partitioning  
Tree canopy properties were measured in a 100 m \(\times\) 100 m permanent plot near the flux tower at Takayama [19]. Within the plot, 24 trees (comprising several species) were selected to measure DBH, height, and tree density. Trees with DBH from 1.7 to 29.0 cm were selected to represent the different stand ages, because the actual stand age was not identified. Nine of the 24 sampled trees were _B. platyphylla_, with a range of small to large DBH. The different DBHs can be used to predict forest growth. The trees were harvested for biomass calculation using the dry mass of the stem and the foliage. Data for _B. platyphylla_ were used for parameterization in biomass partitioning. Figure 2a shows the allometric relationship between DBH and stem biomass. Figure 2b shows the allometric relationship between DBH and foliage biomass. The allometric parameters gave an excellent fit to the trend lines, with r\({}^{2}\) = 0.97 and 0.98 for stem and foliage biomass, respectively. The equations in Figure 2 were used to re-estimate stem and foliage biomass at Hitsujigaoka for validation. The results are shown in Figure 3, where the plots of estimated _versus_ observed stem and foliage biomass were  
\begin{table}
\begin{tabular}{l c c} \hline  & **Takayama** & **Hitsujigaoka** \\ \hline Latitude & 36 8\({}^{\circ}\)46\({}^{\prime\prime}\) N & 42 59\({}^{\prime}\)13\({}^{\prime\prime}\) N \\ Longitude & 137 25\({}^{\prime}\)23\({}^{\prime\prime}\) E & 141 237\({}^{\prime\prime}\) E \\ Maximum Temperature ( \({}^{\circ}\)C) & 22.4 & 24.9 \\ Minimum Temperature ( \({}^{\circ}\)C) & \(-\)11.7 & \(-\)12.4 \\ Precipitation (mm) & 2,275 & 1,047 \\ Solar Radiation (MJ m\({}^{-2}\) day\({}^{-1}\)) & 12.43 & 12.25 \\ Dominant Species & _Betula platyphylla_ & _Betula platyphylla_ \\ Average Canopy Age (year) & 50 & 100 \\ Mean DBH (cm) & 11.4 & 23 \\ Mean Tree Height (m) & 22 & 24 \\ \hline \end{tabular}
\end{table}
Table 2: Summary of the site description at Takayama and Hitsujigaoka.  
close to one-to-one linear relationships. Stem biomass was underestimated by around 3%, whereas foliage biomass was overestimated by about 15%.  
From those relationships, \(a_{s}\), \(n_{s}\), \(a_{F}\), and \(n_{F}\) were calculated as 0.049, 2.64, 0.002, and 2.56, respectively (r\({}^{2}\) = 0.97 for stem biomass and 0.98 for foliage biomass). Based on the allometric relationships, \(a_{P}\) and \(n_{P}\) were computed by substituting \(a_{s}\), \(n_{s}\), \(a_{F}\), and \(n_{F}\), to retrieve \(a_{P}\) and \(n_{P}\). _pFS2_ and _pFS20_ were 0.03 and 0.02, respectively, in these deciduous broadleaf forests of _B. platyphylla_.  
Figure 3: The estimated biomass _versus_ the observed biomass at Hitsuijigaoka for validation, the estimated values equal the observed values, **(a)** stem biomass (open circle); and **(b)** foliage biomass (open triangle). The linear regression showed \(\mathrm{y}=0.98\mathrm{x}-1.60\) for stem biomass, and \(\mathrm{y}=1.15\mathrm{x}-0.04\) for foliage biomass, respectively.  
Figure 2: Allometric relationship between **(a)** stem biomass and DBH (open circle); and **(b)** foliage biomass and DBH (solid rectangular) at Takayama. The allometric equation of stem biomass and DBH is \(\mathrm{y}=0.049\mathrm{x}^{2.64}\), while foliage biomass and DBH is \(\mathrm{y}=0.002\mathrm{x}^{2.56}\). The values from the allometric equation were used to calculate the parameter values in the biomass partitioning.