*2.3. Harvest Residues Estimation*

Harvest residues are those associated with growing stock volume cut or knocked down during harvest (including branches and tops) [12]. In most cases, harvest residues are left at the harvest site, while only a limited quantity is collected from the landing point for energy purposes [33]. As a result, harvest residues are among the largest unused feedstock [19] with annual growth far exceeding removals [3], which presents an opportunity to increase harvest rates for strategic, economic, and forest health reasons [34]. The study [35] estimated logging residues by determining the proportional volume of tops and limbs in growing stock trees, which is approximately 17% of growing stock merchantable bole volume (tops/bole) for softwoods and 29% for hardwoods. In this study, the estimate method can be revised as the corresponding proportional volume of tops and limbs in timber harvest volume. Hardwoods and softwoods ratio was estimated to be 3:1 in Michigan based on the statistical information from [36].

Further, to estimate the quantity of logging residues for new biofuel facilities, it is critical to differentiate harvest types of all merchantable timber, since it is not a practical option by assuming clearcut treatment of all removals [37]. The main harvest types characterizing the logging industry in Michigan include [37,38]: (1) clearcutting all merchantable timber; and, (2) partial removal treatments (including 70% shelterwood and 30% selective cut). On the other hand, managemen<sup>t</sup> of logging residue is also an important part of timber sale planning, which involves controlling the amount of residue remaining on the ground [39]. The residue managemen<sup>t</sup> options (%) by harvest types were collected, as shown in Table 1. To explore use of residue in biofuel production and GHG reduction potential in Michigan, a residue collection rate of 65% (onsite retention of 35%) was assumed for the removing residue managemen<sup>t</sup> options in Table 1.


**Table 1.** Residue managemen<sup>t</sup> options (%) by harvest types in Michigan (Based on study of [37]).

Based on above assumptions, the quantity of logging residues can be estimated using the formula:

$$\mathbf{Q}\_{residuc}^{T} = \mathbf{Q}\_{timber}^{T} (H\_{cr} + H\_{pr}) (\mathbf{P}\_{timber}^{hard} p\_{hard}^{residuc} + \mathbf{P}\_{timber}^{soft} p\_{soft}^{residuc}) \theta \tag{3}$$

where *QTresidue* is the annual collectable residue volume (cords) in year *T*. *Phard timber* is the proportion of hardwoods in Michigan's timber harvest and *Pso f t timber* is the corresponding percent for softwoods.*presidue hard* is the proportion of hardwoods in timber harvest, and *presidue so f t* is the corresponding percent for softwoods. *θ* is the residue collection rate.

For Michigan's case, the Equation (3) is simplified as:

$$\mathbf{Q}\_{\rm residue}^{T,MI} = \mathbf{Q}\_{\rm timber}^{T} \left( 9.9\% + 9.7\% \right) \times \left( 7\\$ \% \times 29\% + 25\% \times 17\% \right) \times 65\% = 0.033 \mathbf{Q}\_{\rm timber}^{T} \tag{4}$$

The Equation (4) shows that harvest residue collectable is only 3.3% of timber harvest. This is due to the low percent of removing residue options (9.9 + 9.7% = 19.6%) in Table 1. Most of the cases, logging residues are left onsite for retention.

### *2.4. Implications of Use for Ethanol Production and GHG Savings*
