calculating+volume

The information contained here is obtained from the NorthPro forest harvest model, which we have adapted for use in Trails Forward. It is the same source for the growth model.

The amount of the wood resource on any given tile is determined by calculating the volume of the two different potential products produced from the trees. The type of product is determined by the forest type and size class of the individual trees. In our model, the first two sizeclasses (2 and 4) are assumed to be of no monetary value. The larger trees are divided into **poletimber**, a product that has a number of applications (ie. pulp for paper, telephone poles, engineered wood products), but is generally too small to be sawn into usable lumber, and **sawtimber**, which are large enough to be taken to a mill and sawn into lumber (generally, material for construction). In reality, there are a number of specialty products in various markets, such as flooring, veneer, and even popsicle sticks, but for simplicity we will stick to the two different types. Because of the growth form of the different species, coniferous trees are able to produce lumber (and therefore considered sawtimber) at a smaller diameter. Therefore, in our coniferous stands, the 6 and 8 inch diameter classes are considered poletimber, while the larger classes are sawtimber. In the other forest types, poletimber is produced in the 6, 8, and 10 inch size classes; sawtimber is produced by the 12 inch and greater size classes.

More explicitly:

media type="custom" key="12916168"

We start by calculating the volume of contained within each size class in terms of cubic feet per acre. Later we will convert the volume into product-specific units, and then product-specific monetary values, but to start the volume of wood in each size class from 6 to 24 is calculated in the same way. The size class information will still be relevant in the future in order to determine the specific product, so be sure to retain that information. You could, for example, create a vector that represents the volume present in each size class. While we currently have the diameter based on the size class, in order to calculate the volume we need to approximate the height of the tree. To do this we have three different height equations, specific to each forest type (just as with the growth equations). Again, the mixed forest and forested wetland habitat types share the same algorithms. Height of trees in each diameter class are calculated using the equations

math H = 4.5 +6.43 (1-exp(-0.24D))^{1.34} S^{0.47} T^{0.73} BA^{0.08} math math H = 4.5 +7.19 (1-exp(-0.28D))^{1.44} S^{0.39} T^{0.83} BA^{0.11} math math H = 4.5 +5.34 (1-exp(-0.23D))^{1.15} S^{0.54} T^{0.83} BA^{0.06} math where
 * coniferous**
 * mixed and forested wetland**
 * hardwoods**

H = the height of the tree D = the diameter S = site index (typically reflective of the productivity of the location, but for our purposes assumed to be a constant value of 80) T = 1.00001 - d/D d = top diameter of cylinder, assumed to be 4 for poletimber and 9 for sawtimber. BA = total basal area of current tile

Once the height data is calculated, the volume of each tree (in cubic feet) can be calculated. Again, these are habitat-specific equations:

math V = 1.375 + 0.002 * D^2 * H math math V = 0.002 * D^2 * H math math V = 2.706 + 0.002 * D^2 * H math
 * coniferous**
 * mixed and forested wetland**
 * hardwoods**

Summing the volume of the trees within a size class, we should now have the volume of wood in each size class calculated in terms of cubic feet. We can now calculate the product-specific volumes by converting the volume of poletimber to a traditionally used unit of measurement, cords. A cord is simply a stacked unit of wood, measuring 4 x 4 x 8 feet, and is equal to 128 cubic feet. Ergo, you can just take your total volume of poletimber in cubic feet (across all of the poletimber size classes) and divide by 128 to obtain the number of cords. This will provide one estimate of cordwood volume per patch/tile/acre.

The volume of sawtimber is approximated by using the Scribner rule to approximate the proportion of the volume of wood that will eventually be turned into lumber. The table below provides a conversion factor for each size class, which is multiplied by the volume in cubic feet to get an estimate of the industry standard thousand board feet (Mbf). For reference, a board-foot is a 12" x 12" x 1" piece of wood. This should be calculated individually for each sawtimber size class (so that the appropriate conversion factor is used), and can then be summed to get one sawtimber volume estimate for the patch.

Finally, implement a monetary valuation of timber products from each tile using the following values: media type="custom" key="12916984" Once the volume calculation is completed, we can move on to implementing some harvest strategies.