# Research Trends and Future Direction for Utilization of Woody Biomass in Japan
## 3 Supply Potential and Availability of Woody Biomass
### Methods and Results of Supply Potential Estimation
#### 3.1.1 Methods
The estimation method can be summarized using the following equation:  
\[SP=\sum_{i=1}^{n}S_{i}\cdot Cr_{i}\cdot Er\cdot Br \tag{1}\]  
where \(SP\) is the supply potential of woody biomass, \(i\) is the sub-compartment targeted for harvesting, \(n\) is the number of sub-compartments, \(S\) is the forest stock, \(Cr\) is the cutting rate, \(Er\) is the extraction rate, and \(Br\) is the biomass rate. The interpretation of the variables in the above equation occurs as follows:  
1. Forest stock  
Forest stock is the sum of the stem volumes of living trees in a sub-compartment and is usually recorded in forest registers for each region of Japan. While many studies directly utilize these data, some focus on long-term estimates and choose not to rely directly on them. Instead, they utilize tools such as yield tables [20; 21], empirical growth curves [29], or other projection methods to estimate future forest stock considering tree growth [18]. 2. Cutting rate  
The cutting rate indicates how much of the tree will be harvested during harvesting activities such as thinning and final felling. The value of this variable was always set to \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{Results of Supply Potential} & \multicolumn{3}{c}{Result of Availability} & \\ \cline{2-7} Case & \multicolumn{1}{c}{Supply potential [m\({}^{3}\)/year]} & \multicolumn{1}{c}{Supply potential per} & No & \multicolumn{1}{c}{Availability} & Maximum availability & Availability & Reference \\ No. & \multicolumn{1}{c}{Supply potential [m\({}^{3}\)/year]} & \multicolumn{1}{c}{unit area} & \multicolumn{1}{c}{subsidy} & \multicolumn{1}{c}{rate [\%]} & \multicolumn{1}{c}{[m\({}^{3}\)/year]} & \multicolumn{1}{c}{rate [\%]} & \\  & & [m\({}^{3}\)/year/ha] & \multicolumn{1}{c}{[m\({}^{3}\)/year]} & & & & & \\ \hline
1 & 990,113 & 5.50 & N.A. & N.A. & N.A. & N.A. & [18] \\  
\hline \hline \end{tabular} N.A.: Not applicable.  
\end{table} 
Table 1: _Cont._100% in the final felling, representing complete harvesting of the targeted forest. Thinning is often determined according to the regional forest management plan and ranges from 10% to 40%, depending on forestry conditions such as tree species, age, and harvesting method. The biomass rate is a variable indicating the number of harvested trees that can be used as woody biomass, with its counterpart being the timber rate. Woody biomass mainly refers to unused wood, such as forest residues, which distinguishes it from traditional lumber used in construction or furniture. In the case of final felling, the biomass rate is often based on the actual harvesting activity in the study area, and typically ranges from 15% to 28%. However, in the case of thinning, the biomass rate varied widely, ranging from 15% to 100%. This variability is attributed to the lack of economies of scale, which stem from thinning yields being lower than those of final felling. In Japan, many forests are not well-maintained and require a certain scale of harvesting to be profitable. During thinning, when the scale of harvesting is typically small, harvested trees are often left unutilized in a forest. Cases 1 and 30 to 32 have considered this situation and set the biomass rate of thinning to a high value, assuming that the remaining wood can be fully utilized [18; 27; 28]. Incidentally, Cases 2 to 5 and 25 to 32 considered pre-commercial thinning separately and set the biomass rate of pre-commercial thinning to be higher than that of commercial thinning, ranging between 70% and 100%. Pre-commercial thinning is the initial thinning of relatively young stands for density control purposes and has a high probability of being left on forest land because the trees are small and have little or no utility value as timber at the time of harvest. Regionality  
In addition to the four variables mentioned above, the age of the tree at the time of thinning and final felling, the number of thinnings, the tree species, and the site indexes also have a direct impact on the supply of woody biomass.