Absolute measures of stand density include basal area per acre and ... expected TPA when QMD = 10 inches. Thus, the above equation can be rewritten as: 605.1. 10*. SDI ... does not vary much over a wide range of stand density. Foresters ...
Stocking and Stand Density Stocking refers to the amount of trees necessary to meet some management objective. The terms “fully stocked”, “adequately stocked”, and “under stocked” all refer to tree occupancy necessary to maximize timber production. Stand density is a quantitative measure of density that can be expressed in absolute or relative units. Absolute measures of stand density include basal area per acre and trees per acre, both of which you are already familiar. Relative measures of stand density express site occupancy as a percentage of a predetermined standard.
We will discuss stocking more fully when we talk about growth models. In these lecture notes, we will discuss several measures of relative stand density that you will encounter in forestry.
Stand Density Index This type of relative measure describes the relationship between basal area per acre (BA/A), trees per acre (TPA), and the quadratic mean diameter (QMD). Reineke (1933) first described this relationship for fully stocked stands. He developed an equation that predicted TPA as a function of QMD:
log TPA 1.605 * log QMD k or TPA * QMD1.605 where k and = constant that varies by species. Reineke defined Stand Density Index to be the expected TPA when QMD = 10 inches. Thus, the above equation can be rewritten as: SDI *101.605 ,
where SDI = Stand Density Index and the other variables as before. For any stand of known TPA and QMD, SDI can be found from the proportion:
1
TPA SDI 1.605 QMD 101.605 Solving for SDI gives:
TPA 101.605 10 SDI TPA 1.605 QMD 1 QMD
1.605
Often, SDI is expressed as a relative density (e.g., the relative density is 60 percent). Silviculturists commonly use relative density when applying stocking controls (i.e., thinnings) to stands. Relative Density can be calculated as a proportion of the SDI to the maximum SDI for a particular forest type: RD
SDI 100 , max SDI
where RD = Relative Density and max (SDI) = maximum SDI for a forest type (see table below). Forest Type Longleaf pine Loblolly pine Eucalyptus Douglas-fir White fir, Ponderosa pine Red fir, Redwood
Maximum SDI 400 450 495 595 830 1000
You should also know that relative density could be expressed as the ratio of TPA (or, alternatively, BA/A) to a maximum TPA (or, alternatively, a maximum BA/A).
EXAMPLE: Determine the SDI for a loblolly pine stand with 600 TPA and a QMD = 5.0 inches. 10 SDI 600 5
1.605
197
2
RD
197 *100 43 % 450
Crown Competition Factor Krajicek et al. developed the Crown Competition Factor (CCF) in 1961. CCF is another relative measure of stand density that represents the percent area covered by the vertical projections of tree crowns. There are three steps in determining CCF: 1. Calculate the open grown crown width for each tree from a its dbh (in inches):
CWi b0 b1 DBHi , where CW = open grown crown width in feet, b0 and b1 = parameters dependent on species i = ith tree. 2. Determine the maximum crown area for each tree: 2
CWi Max(CA) i , 2 where CA = crown area in square feet and other variables as before. 3. Sum the maximum crown areas for each tree to find CCF for the stand: n 100 CCF Max(CA) i , i 1 43560
where CCF = crown competition factor.
Stocking Guides Absolute measures of stand density have also been used in combination to describe stand stocking in the form of stocking guides. Stocking guides assume that gross volume increment
3
does not vary much over a wide range of stand density. Foresters commonly use stocking guides to prescribe thinnings.
Gingrich (1967) developed a stocking guide that describes the relationship between basal area per acre, trees per acre, and the quadratic mean diameter for upland hardwood forests in the midwest (see handout). The A line represents the upper-limit to stocking, above which the stand is over-stocked. The B line represents the minimum stocking necessary for full site utilization, below which the stand is under-stocked. The B line commonly corresponds to a relative density of 60 percent. The C line represents the lower limit for stocking necessary to reach the B line in 10 years. The region between the A and B lines (relative density between approximately 60 and 100 percent) represents the target stocking for optimal tree growth (optimal growth occurs when RD = 60 to 80 percent).
Silvicultural Prescriptions Silvicultural prescriptions (Rx) are short management recommendations for the stand over the next five years or so. Stand and stock tables and growth tree data provide the quantitative data necessary to make an Rx. Stand and stock tables provide the stand-level data such as basal area per acre and trees per acre that allow for the calculation of SDI and RD. This information also allows for the location of the stand structure in a stocking guide. Growth trees provide the data for percent basal area growth (%BAG) to determine the current growth rate of the stand. %BAG along with the stand and stock table can be used for stand table projection as well. All these tools allow the forester to make a decision about thinning or regenerating the stand.
4
Literature Cited Gingrich, S.F. 1967. Measuring and evaluating stocking and stand density in upland hardwood forests in the Central States. Forest Science 13:38 – 53. Krajicek, J.E., Brinkman, K.A., and Gingrich, S.F. 1961. Crown competition – A measure of density. Forest Science 7:35 – 42. Reineke, L.H. 1933. Perfecting a stand-density index for even-aged forests. Journal of Agricultural Research 46:627 – 638.
5
