*2.1. Study Area*

The State of Michigan has a large biomass resource base that could be used as feedstock for biofuel facilities. In 2009, more than half (54%) of Michigan's land area was covered by forests [28]. The map of Michigan (Figure 1) shows the forest distribution on region basis in Michigan. A description of the study theme in this study is presented in Figure 2.

**Figure 1.** Michigan regions and forest (Based on study of [29]).

**Figure 2.** A description of the study theme.

### *2.2. Timber Volume Assessment and Prediction*

Timber volume serves as a reasonable, though incomplete, measure of biomass [30]. Time trend analyses were employed by the U.S. Department of Agriculture (USDA) Forest Service timber assessments to understand how the timber supply today as it relates to the previous 50 years. The timber harvest trends were predicted by the functional form [31]:

$$\ln\left(HARNEST\right)\_t = a\_0 + a\_1 TIME\tag{1}$$

where the dependent variable is the natural log of total harvest at time *t*, *a*0 is a constant, *a*1 is the slope of the trend line (rate of change of harvest divided by rate of change of time), and *TIME* is the number of years since the start of the sample (current year less *t*0 the date of the initial year) [31].

To use the above formula for long-term timber harvest estimates and forecasts, 26 years (1990–2015, fiscal year (1 October–30 September) annual timber sales data (in cords) were collected from literature. Cord is a volume unit commonly used in North-America. The Statewide Forest Resource Plan of 1983 promoted "stabilized timber supplies from public land", resulting in a stabilized forest products industry in Michigan [32]. This plan supports the suitability of using Equation (1) to estimate Michigan's timber harvest trend. As shown in Figure 3, a probability distribution describing the likely future timber harvests in Michigan by 2065 (over the 50-year time period) was created using the historic data collected. The calculated coefficients *a*0 = 13.428 and *a*1 = 0.0077. Thus, the Equation (1) can be rewritten as:

$$Q\_{timbr}^T = e^{13.428 + 0.0077TIME} \tag{2}$$

where *QTtimber*(cords) is the annual timber harvest in year *T* and *TIME* is the number of years since 1990.

**Figure 3.** Graph showing the harvest trend developed from historic data for creating a probability distribution describing likely future harvests in Michigan.
