Forestry Measurement Techniques

Measuring, quantifying, and displaying forestry data. Reference for: WILD2400, WILD3850, WILD4750, WILD5700 (updated September 2019)

Measuring trees to characterize stands or forests has its own unique set of tools and techniques. Because trees do not necessarily scale to forests to landscapes, etc., there are important considerations to make to accurately characterize trees and stands in the field. Generally, the data we collect have little meaning in and of themselves, they need to be tabulated, or displayed graphical to portray their meaning. These data are important if we want to make important silvicultural consideration with respect to characterizing, and/or treating the stand. This may be to portray wildlife habitat, quantify current volume, or to enhance future growth, among other things.

This handout is a review of some essential measurement and quantification skills requisite for forestry, and really any natural resource professional tasked with characterizing trees and forests. We will define some basic concepts, show you how to make some simple tree- and stand-level measurements. Then we will show you how to use the data collected for quantitative assessment of: stand stocking, determining site index (site quality), stand density, species composition, and diameter/age distributions.

I anticipate that you would keep this handout for future reference during your curriculum at USU, and that it might be a helpful reference in your future.

Tree Measurements (direct) Crown Base (CB): Height to the base of live branches. Used to calculate live crown ratio (LCR). Typically measured with a Biltmore stick, clinometer, or hypsometer.

Diameter at breast height (DBH): where breast height is 4.5 feet (or 1.3 m) off the ground. This international standard is important if one is going to use allometric equations for the subsequent prediction of other attributes (tree volume, biomass, or carbon being the most common). Tools used can be a diameter tape, caliper, or a Biltmore stick.

Height (HT): The total height of the tree typically measured with a Biltmore stick, clinometer, hypsometer, or laser. Depending on the tool you may need to know your pace, or use a tape or a range-finder for linear distance.

Age (years): The age of the tree typically determined at breast height as a standard. An increment bore is used to extract a core on which annual rings can be counted in the field for a quick assessment.

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Useful Definitions and Concepts

Concept of a Stand: In forestry, the most common delineation of a group of trees is called a stand, and is the typical scale at which vegetation is characterized. The stand is a useful way to think of a group of trees greater than an individual, but not so large that it contains too much heterogeneity (such as the entirety of Figure 1). Stands can range in size from ~ 1-10+ acres, and are identified silviculturally as having trees of a similar age class, composition, or structure. You can see in the image below the colored polygons have been drawn around some lodgepole pine stands that are similar in age, having been regenerated in the mid-1970s. The surrounding matrix with courser texture is lodgepole pine that regenerated after an 1840s fire. The green polygon to the right is composed mostly of aspen.

Figure 1. Air photo of a portion of the T.W. Daniel Experimental Forest showing different age classes, indicated by different spectral/textural signatures.

Allometry: The proportional relationship between various measurements of organisms. Practically speaking it allows us to measure things easily (e.g., DBH, and HT), and predict things that are more difficult to directly measure (tree volume). Allometry is common in all sciences, not just forestry.

Basal area (BA): The cross-sectional area (typically outside bark) of the tree at breast height, or the height where diameter is measured. Stand basal area is the total cross-sectional area of all trees measured at 4.5 feet above the ground, and is estimated from plot/point data.

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Cohort: A group of similarly aged trees in a given stand. Typically arising as a result of a previous harvest of natural disturbance.

Composition (stand): The make-up of the stand, typically defined in terms of the number and/or quantity of different species.

Crown length (CL): Length of the live crown. Typically measured at the same time as HT. Deciding on what constitutes the lower crown (i.e., structure of live branches) is subject to opinion.

Live crown ratio (LCR): Ratio of the live crown length to the total height of the tree.

Diameter cut-off, or break-point diameter: A predetermined value to indicate the overstory trees from the understory trees, commonly 5 inches. The cut-off differentiates the type of plot used to measure trees of different sizes.

Plot radius factor (PRF): The wedge prism-specific factor, associated with the angle of the prism. Needed to calculate the limiting distance.

Quadratic mean diameter (QMD, Dq): The diameter of the tree with average basal area, not to be confused with average or mean DBH. QMD is a geometric average, appropriate because the characterization of basal area over space (i.e., the plot) is inherently a two-dimensional metric.

Stand density index (SDI): A measure of stand stocking that simultaneously considers number of trees and average tree size (DBH). Important for characterizing relative density.

Structure (stand): The make-up of a stand in terms of QMD, BA, HT, canopy or other metrics.

Trees per acre (TPA): The number of trees, typically in the overstory (defined by the diameter cut-off), on a given unit area. A measure of absolute density.

Volume: The amount of board-foot or cubic meter of wood in a given section of the tree, typically defined as stump height to some top diameter (e.g., 5 inches). Rarely measured directly, most often predicted via allometric equations. The same is true for estimations of biomass and carbon.

Plot Sampling Why do we measure trees on plots? Because the space a tree occupies is related to its size, history of stand development, and the density of the stand in which it occurs. Measurements of trees in-and-of-themselves are useless for describing the stand or forest. Assessment of multiple trees over a given area (i.e., a plot) is necessary to appropriately characterize any forest or plant population. Typical characterizations of forest structure and composition are called density and stocking, and require the forester to estimate both the number of trees per acre and the stand basal area per acre. There is no “magic” sampling method that allows one to determine both basal area and trees per acre quickly and efficiently in the field. As a result, there are various types of plots we can deploy that will allow us to measure a relatively small number of trees and

Page 3 of 34 then ‘blow-up’ or expand that number to a per area basis (e.g., per acre). These are called expansion factors or blow-up factors. Plots are deployed within a given stand based on a sample design and desired level of accuracy and precision. These concepts are not covered here, but will be an integral part of your natural resource education.

Fixed-radius plot sampling Fixed-radius (e.g., one-fifth acre in area) plots make it easy to determine trees per acre – you just count the trees on the plot and multiply by the inverse of the plot size (the expansion factor, which is 5 in this case). Determining basal area on fixed-radius plots is more difficult, however, because it requires the forester to measure individual diameters for all trees on the plot, compute the basal area of each tree using the formula for the area of a circle, add them up for the entire plot, and multiplying by the expansion factor.

Because fixed-radius plots require the measurement of all trees of a given size, they can take more time. There are a number of good reasons to use fixed-radius plots, but saving time usually is not one of them. For long-term monitoring, that is, if you will be revisiting and re-measuring the same plot, fixed-radius plots are ideal. In the case of re-measurement, all the overstory trees on a fixed-area plot are typically ‘tagged’ with an aluminum tag, either at breast height or at the base, using an aluminum nail that hangs down from the tree. When fixed-radius plots are ‘mapped’ the distance and azimuth from the plot center, or some other fixed point, is measured to each tree.

Regeneration/Stocking sampling As mentioned above, a diameter cut-off is typically employed to reduce sampling effort for smaller trees. That means the size of the fixed-area plot for seedlings and/or saplings will be smaller. A common understory vegetation fixed-area plot is a 1/300th acre plot. That is a circle of 6.8 feet in radius. On this smaller plot trees are commonly tallied by species. A dot tally is sufficient here. Further delineation by height classes, measurement of diameter at root collar, etc. could also be done on the plot. The position of this plot is commonly at the center of the overstory plot, but can be offset.

A quick deployment of this type of plot can be done in recently cut or disturbed area to assess regeneration stocking. Stocking is typically some threshold of desired regeneration. Therefore, in addition to tallying the trees by species on a plot, multiple plots are employed in a sampling design, and the percentage of those plots with some predetermined number of the desired species on them is divided by the total number of plots.

Variable-radius (prism) plot sampling Basal area is a much more useful measure of stand density than trees per acre, and foresters have adopted variable-radius plot sampling (using a wedge prism) for rapid structural assessments. An important advantage of prism sampling is that it samples a higher proportion of bigger (and thus, more valuable) trees than it does small ones, giving it a big advantage over fixed-radius plots for conventional timber cruising.

With prism sampling, determining basal area is very simple. One sights at every candidate tree to determine whether it is “in” or “out” based on how much its image is offset. “In” trees are

Page 4 of 34 counted and measured/tallied; others are ignored. It is critical to hold the prism (not your eye!) exactly over the plot center, and to sight precisely at breast height (4.5 feet off the ground) where DBH is measured. Care must be taken to rotate the prism edge perpendicular to the tree for leaning trees. To compute basal area, one uses the simple formula:

[ ] (1) Stand BA = [ ] * BAF where BAF = the prism basal area factor, or how many square feet of BA each “in” tree represents. Common BAFs in the western US are 10, 15, and 20 using English units of square feet per acre. Metric prisms are available for assessment in square meters per hectare.

Figure 2. Examples of possible combinations of prism sampling.

In the borderline situation, you can simply tally every other one, or for more accurate work measure to the tree center and compare to its limiting distance.

Unlike fixed-radius plots where every tree, no matter what its size, represents the same number per acre, with prism sampling the actual “plot” size varies for each tree depending on its DBH. (Figure 3) The larger the tree’s DBH, the bigger the circular area around it in which it will be sampled if the plot center happens to fall there. The radius of this imaginary plot area is the tree’s DBH multiplied by a constant plot-radius factor (PRF), unique for each prism BAF (Table 1). For example, the PRF for a 20-BAF prism is 23 times the DBH (when both are in the same units of measure, e.g., inches) or 1.944 feet (23 inches) of plot radius for every inch of tree DBH. This is the ‘limiting distance’ and should be calculated for borderline trees for accurate inventories. Table 1 is a useful list of common BAF plot-radius factors, for calculating limiting distances.

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Sampling point

Figure 3. Visual representation of the ‘invisible’ circle around each tree, proportional to its DBH, and is equal to a constant multiplied by the tree DBH.

Table 1. Common basal area factors and their plot-radius factors Limiting distance = PRF * DBH

English Metric BAF PRF BAF PRF 10 2.75 2.5 0.3162 20 1.944 3.0 0.2887 30 1.588 4.0 0.25 40 1.375 5.0 0.2236 8.0 0.1768

In the situation where the plot center may be very close to the limiting distance (tree F in Figure 3), the observer can measure the distance from the plot center to the side of the tree. Although it is tempting to use your laser, hypsometer, or range-finder to site the tree face, the resulting limiting distance will be biased. It is best to measure to the tree side (Figure 4).

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Figure 4. Depiction of bias introduced be measuring distance to front versus side of tree.

Once the “in” trees have been determined for a given plot, subsequent measurements can be made. It is useful to temporarily “tag” the “in” trees using push-pins and numbered labels. The numbers can be used to individual identify each tree on your data sheet or data recorder.

To determine how many trees per acre a tallied tree on a prism plot represents, you must measure its DBH. Multiple the DBH by the PRF to determine the tree’s unique plot size (in square feet); this plot size is then divided into the area of one acre (43,560 square feet) to determine its expansion factor. Because larger trees have larger plots and a higher probability of being sampled, they represent fewer trees per acre than small trees. You can use this formula to compute trees per acre, but we find it is easier to remember the basic expansion formula that applies to all variable-radius plot sampling:

(2) (Individual tree basal area, in ft2) * (Trees per acre) = BAF, in ft2 / acre

Rearranging,

(3) Trees per acre = BAF / Tree BA

In other words, all you have to do is to divide the prism factor (a constant) by the BA of the sample tree. BA of a tree is calculated from the simple formula for the area of a circle, with a conversion from DBH measured in inches to BA in square feet:

2 Tree BA = p , or

p 2 (4) Tree BA = DBH

The constant p / 576 = 0.005454154, which is usually how equation 4 is defined.

In the lab, if you have a list of DBHs (in inches) in a spreadsheet, add a column with equation (4) and compute each tree’s BA, then add another column with the equation 3 that divides the tree BA into the BAF. Simply enter the BAF in a single cell at the top of the worksheet, and refer to it in the formula using a fixed reference (e.g., cell $A$1).

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Slope Correction Any time the sample point is on relatively flat ground the plot is a circle. As slope increases the plot increasingly becomes and oval. The long axis of this oval is the “slope fall line”, and we can correct for it using trigonometry. In practice though, we put the trigonometric output in a handy table to keep with us in the field. The table below is an example of this.

1. Using a clinometer, or your compass find the slope of the plot.

2. Find the slope correction from the adjacent table.

3. Multiply the correction factor by the plot radius (or the linear distance). The result is the corrected radius (or distance for determining “in” trees).

4. Use this method to get the corrected radius for a fixed-radius plot AND to determine the limiting distance for a given tree on a variable-radius (prism) plot.

Measuring Tree Height Accurate height measurement is essential to determining site index, getting accurate tree volume estimates, and assessing tree crowns. Lasers, hypsometers, Biltmore sticks, and clinometers are the main height measurement tools. The most common way to measure heights is with a clinometer that has a percent scale. These can be used to measure the tree height at any distance but, assuming the tree is growing at a right angle from the ground, the ideal situation is that one would stand roughly the same distance from the tree as the tree is tall, so that the view angle to the top is about 45 degrees. Sight at the base of the tree and record the percent reading (A), then sight on the top and record this percent (B). Add these readings, and multiply by the horizontal distance (D) to get total height (Figure 5).

If you are reading over 110-120% when looking at the treetop, then you are probably too close to the tree. Move farther away, as long as you can still see the tree. If you are on steep terrain, you may encounter a situation where your eye is actually below the base of the tree. In this case, subtract the readings before multiplying by the horizontal distance (see Figure 6A & 6B below).

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Commonly, we are interested in the amount of live foliage, and one way to measure this is by determining the live crown ratio (LCR). It is convenient to measure height to crown base (CB) at the same time you measure height. Site to the lowest living foliage (or group of foliage) and add this reading to the base sighting to determine CB. Then you can calculate LCR by subtracting the crown base from the total height to determine the crown length (CL). Then express the crown length as a percentage of the total height. In the field we often measure height and crown base, then calculate LCR when we get back to the lab.

Figure 5. Height Example 1.

Height Example 2.

1. First, you measure with a 66’, 75’, or 100’ tape (or use your pace), this will depend on the type of clinometer, from the tree to a % of slope viewpoint where you can clearly see the top of the tree. Measure or pace the necessary distance from the tree and make sure you have a clear view of the top, and also the crown base. Have your field Degrees partner stamp their heel against the tree if you are not sure which or tree top you are measuring. height

2. Keeping both eyes open, direct the black crosshair in the clinometer level with the base of the tree at ground level. Using the left-hand scale (the right scale is in percent) you will read a negative number if looking down (level ground, or downhill). You will read a positive number if the slope is up.

3. Keeping both eyes open, direct the black crosshair in the clinometer to the top of the tree. Your view may be obscured by other trees, shrubs, etc. Make sure you are sighting on the top of the tree—easy to see with conifers, much more difficult to ascertain with hardwoods.

4. Add or subtract the numbers you just read in 2 and 3.

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A. If your eye is at a level between the base of the tree and the top, the numbers are added together for the total tree height. The same base number (#2 above) can be used to then measure crown base.

B. If your eye is below the level of the base of the tree (tree is upslope from you), the base reading (2) must be subtracted from the top reading (3) to determine height.

Figure 6A. Figure 6B.

Measuring Tree Age The age of a tree is an important variable for determining the site potential productivity (site index, in combination with tree height), and also for determining age structure of your stand (even-aged, uneven-aged, multiple cohort). Diameter increment measured from an increment core can also be used for assessment of recent growth. Increment cores are collected for a huge number of other research-related questions.

The proper use and care of an increment borer is paramount for getting good quality cores, and therefore good estimates of age and increment. The borer consists of three parts, the handle, the spoon, and the bit. The sharp end of the bit is the most important part of the borer, and care should be made never to touch it to anything but the tree sampled, EVER! Once the bit has been inserted into the handle, set the spoon aside being careful not to let the tip touch the ground. Align the bit perpendicular to the tree bole and aim the tip preferably into a bark crevice. Once the appropriate spot has been determined, a firm thrust of the tip into the bark should push the bit through to phloem. With care not to change the angle of the borer, carefully begin to turn the borer until the threads of the bit have made a purchase into the tree. This will be clear as they disappear into the stem. Now using even pressure with both hands continue to turn the borer.

It’s at this point in boring a tree that considerable experience is helpful. Consistent backpressure should be felt while driving the bit. If it suddenly becomes much easier or harder to turn the bit, stop immediately, and reassess the situation using the spoon and judgement.

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Figure 7. Point of view and side view of appropriate technique when boring a tree.

Assuming no issues with rot or compressed wood, once the bit has been sunk sufficiently deep to be near the pith of the tree, slowly slide the spoon into the bit using consistent pressure. Give the spoon handle a final push so it’s full hilt, taking care not to bend the spoon. Back the handle off one full turn, which will break the last connection of the core from the inside of the tree. Then some care is required to remove the spoon. This part takes some practice. Using the thumb and index finger of your dominant hand, grip the spoon handle. Using your other hand, grab your dominant hand and pull back. Use your arm strength and not your body to pull. The spoon will break free and then the core can be carefully removed. If collecting the core, carefully insert the core into the straw just as it came out of the tree. If not collecting the core, carefully set it aside, or hand it to your field partner, and remove the bit from the tree. Then you can sit down and count the rings and/or measure the diameter increment with a ruler.

Height-age Relationships and Site Index Curves Height growth of dominant and codominant trees is not affected by stand density (except perhaps at extremely high or low densities), but is strongly influenced by soil or site productivity. As a result, a dominant tree growing on a good site will be taller at a given age than the same species growing on a poor site, regardless of how stand density has been regulated. Site index is defined as the total tree height at a predetermined index age (usually 50 or 100 years). A site index chart is a family of height-over-age curves that pass through increasingly taller heights at the index age. By convention, the site index (= the height at the index age) usually increases in increments of 10 feet; the curves range from the poorest to the best sites found in the forest.

Because each species has its own unique height growth pattern over time, separate site index curves have been developed for most important western species. Beware: some curves were developed using total age (measured at stump height); while others use age at breast height since it is a more convenient measurement point. Often, the captions of the curve will give the

Page 11 of 34 number of years it takes for the species to grow to breast height (4.5 feet above the ground), so one can convert from one kind of data to the other.

To determine the site index of a stand, one selects the tallest, most dominant trees in a stand, measures their total heights, and takes an increment core to determine their age if the stand age is not already known from records. This height-age pair for each tree is plotted on the site index curve, and the site index is estimated by visually interpolating between the two surrounding curves. For example, a red pine tree 100 years old and 100 feet tall would correspond to a site index of about 65 (Figure 8). If possible, one should take several of the tallest trees in the stand, determine their site index separately, and then compute the average of these site indexes for the stand. Trees with a history of growth suppression (as evidenced by many narrow rings near the pith) should not be used.

For most site index curves, two equations are given that permit site index (SI) to be predicted from height and age, or height (HT) to be predicted if site and age are known. The Table 2 below from Milner (1992) has the equations and coefficients for four western species.

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Figure 8. Height-age relationship for red pine with site index curves. Base age 50 years.

Characterizing the Stand – Diameter Distributions A distribution is a graphical representation of how some individuals are grouped according to one (or more) of their attributes. One widely used example in forest ecology is the diameter (or DBH) distribution. A diameter distribution is a graph of the stand table, or the number of trees in each diameter class present in the stand. In forestry, the DBH distribution is often referred to as the stand structure, although “structure” can have a broader meaning, including within-stand variation in tree heights and canopy layers. Several stands with the same density can have very different structures, depending on how the total number of trees is distributed among the different DBH classes. Diameter distributions are widely used to depict and control various cutting prescriptions in both even- and uneven-aged silviculture. The simplest method of representing a distribution is by a bar graph; the height of the bar shows either the number or percentage (of the total) in that class. When we graph diameter distributions, however, we usually just plot the points and "connect the dots", forming a continuous distribution.

Diameter distributions can be approximated by mathematical relationships but opinion varies over whether there is any biological significance implied in the equations. There is no doubt, however, that distributions develop characteristic shapes that change over time as the stand develops. The negative-exponential (or "reverse-J-shaped") distribution [the second and fourth examples in Fig. 2.2 from Smith et al. (1997)] can describe several different types of stands, all of which have relatively few large-diameter trees and many smaller ones. This

Page 13 of 34 distribution form tends to fit very young and very old stands, truly balanced uneven-aged stands, as well as even-aged stratified species mixtures of almost any age. Middle-aged stands tend to exhibit a more normal (bell-shaped) distribution (the first example in Fig. 2.2 from Smith et al. (1997) that may be skewed towards the small diameters.

Unimodal

“Reverse-J”

“Reverse-J”

Bimodal

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Diameter distributions can be used to display the effects of different thinning methods (e.g., low, crown, dominant, geometric) on stand structure. Figure 5.12 (reproduced below from Smith et al. 1997) illustrates how the trees designated for removal in thinning (cross-hatched area) differ among the several thinning methods, and consequently produce different residual stand structures.

In addition to simply describing the structure of many different types of stands, the reverse-J distribution is also a very important concept for controlling the structure of balanced, uneven- aged stands managed under the selection system. Important parameters are (1) the maximum diameter (where the distribution is truncated on the right); (2) the total basal area (which can be thought of as the area under the entire curve; and (3) the so-called “q-factor”, or the (constant) ratio of the number of trees in successive, adjacent diameter classes.

Figures 15-6 and 15-7 in Smith et al. (1997) (reproduced below) illustrate this distribution as well as some of the alternative structures exhibited by unbalanced uneven-aged stands. We will learn in lecture and future labs how to manipulate these distributions to accomplish various silvicultural ends.

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Characterizing the Stand – Stocking The concepts of Density and Stocking are often (erroneously) used interchangeably, but there is an important difference. Stand Density is an absolute measure of growing-space occupancy expressed in terms of basal area or number of trees per unit of area (or occasionally, other units). Stocking is a relative measure of growing-space occupancy expressed as a percentage of some predetermined standard (Figure 9). The main function of an assessment of stocking is to provide objective standards based on decades of research that reveals how much growth and yield to expect at various densities. They are intended for use mainly in even-aged stands and probably work reasonably well in two-aged stands. However, the theoretical basis for their construction does not necessarily apply to stands with several age classes; such stands require different methods. We will cover the basics of the two types of stocking you are most likely to encounter in the western U.S., Density Management Diagrams and Stocking Guides. Stocking assessment and density management in the west has been greatly facilitated by the development of DMD, and associated maximum stand density indexes for most commercially and ecologically important species (see Appendix 1). Given their clear and strong basis in biological growth, the use of DMDs in forest management is a great way to link silviculture and ecology (see Jack and Long 1996).

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Figure 9. Example stocking guide showing the relationship between basal area and trees per acre and their influence on stand development and/or management.

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Characterizing the Stand – Density Management Diagrams An important graphical format for depicting stocking is the density management diagram (DMD, Figure 10). DMDs are widely used in the western U.S. and Canada, but are available just about everywhere. The biological basis of the DMD is the -3/2 “self-thinning law” that defines the maximum possible density a stand can achieve at a particular stage of development. DMDs typically show average tree diameter (and sometimes volume) on the y-axis, with density (trees per acre) on the x-axis. The DMD can be used to estimate relative density, or stocking (in percent), by expressing the actual density as a proportion of the maximum, holding mean tree size constant (i.e., moving horizontally to the right on the diagram). With the addition of volume curves and height curves to the DMD, stand development can be simulated (Long and Smith 1984). Relative densities above 0.5 to 0.6 will experience mortality from thinning (the so-called “zone of imminent competition mortality”). Relative densities of 0.3 to 0.5 are regarded as optimum for stand growth (but not individual tree growth), and the lower limit of crown closure occurs at lower relative densities of <0.3 (Long 1985).

Figure 10. Hypothetical description of stand dynamics on a density management diagram.

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Direct Effect of Thinning on the DMD: Initial vs. Residual Structure (“chainsaw effect”) On the ponderosa pine DMD (Long and Shaw 2005) below, the black line indicates one trajectory of stand development. The stand starts with 1000 TPA, is pre-commercially thinned to ~275 TPA (lower red star). Notice the immediate effect on DBH (x-axis) due to the choice of superior trees during the thinning. This is called the “chainsaw effect.” The stand then continues development until it reaches the threshold of 10 inches QMD, when a commercial thinning is possible (upper red star). The thinning reduces the TPA further to ~100 TPA, setting up the stand for an end-of-rotation mean diameter of ~18 inches. With the inclusion of height, based on height-age relationships, on the DMD we can estimate the time frame for such a regime. Similarly, with the inclusion of volume on the DMD, based on localized volume equations, we can estimate the amount of material removed, and therefore have a basis for the commercial value of the thinning.

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Stand Growth and Development on the DMD Using the same ponderosa pine stand with ~1000 TPA, instead of conducting any sort of treatment this stand is left to grow and undergoes natural stand development. The red line indicates that as the stand approaches 60% of maximum stand density it will begin to exhibit self-thinning mortality, i.e., that is the reduction of TPA over time as DBH increases. In the absence of any sort of density reduction one can expect this stand to reach 18 inches in substantially more time than the previous example.

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Characterizing the Stand – Stocking Guides Stocking guides are important and widely used graphical tools that provide foresters with an objective method for determining the stocking level of a particular stand relative to certain guidelines. Stocking guides have been developed for many species and are widely used in conjunction with silvicultural handbooks that give prescription options for typical conditions. Stocking guides show various combinations of basal area (on the vertical axis) and trees per acre (horizontal axis) that correspond to three different stocking levels: the maximum biologically attainable density (A Line); the lower limit of full crown closure (B Line); and a level (C Line) that is expected to reach full crown closure within 10 years.

Once the BA and TPA are known (as a result of cruising the stand), the average stand diameter (D) can also be calculated by dividing the total stand BA by the TPA:

Average Basal Area Per Tree = (Stand BA / TPA)

The equivalent DBH of this tree, based on equation (4):

7)

Where: BA = stand basal area, in square feet per acre; TPA = total number of trees per acre; and DBH of tree of average basal area, in inches.

This diameter of the tree of average BA is usually called the quadratic mean diameter (QMD), and is different from the simple arithmetic average of all DBHs. When foresters talk about the "average" or "mean" stand diameter, we usually are talking about the QMD, not the simple mean. QMDs are shown on a stocking guide by lines radiating outward from the origin (see figure below).

To apply stocking guides, one measures several plots in the stand, and calculates the BA and TPA. If only BA is needed, it is not necessary to measure DBHs of the "in" trees. However, plotting a stand on the stocking guide also requires TPA, which requires individual DBHs to be recorded.

Even though stocking guides have a traditional "X-Y format", there is no causal relationship implied between BA and TPA. Nor is there any suggested relationship to age or time, which is a weakness of this approach. Rather, stocking guides merely provide a convenient way to display and communicate to other foresters the two-dimensional response of both BA and TPA to various silvicultural treatments that manipulate stocking.

It is important to understand how stand development is displayed on stocking guides. Since age or time is not one of the variables, one must use supplementary information such as a density management diagram, or a computer simulation model such as the Forest Vegetation Simulator to predict changes in BA and TPA. In general, there are two types of "movements" on a stocking guide: the direct effect of thinning, and stand growth.

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Direct Effect of Thinning on Stocking Guide: Initial vs. Residual Stand Structure (the “chainsaw effect”) Stocking guides are a useful way of depicting various thinning options and methods that are classified according to their effect on the average DBH. Reductions in both BA and TPA caused By the removal of a portion of the stand in thinning are plotted by a line having a downward and leftward direction (shown as “southwesterly” arrows in the example below). This line originates at the stand density before thinning, and ends at the residual density after thinning. Average diameter may increase of decrease as a result of thinning: in a low thinning that removes many small trees below the average diameter, TPA will take a big drop to the left without reducing BA nearly as much, thereby increasing the average stand diameter. Conversely, in a dominant thinning that removes just a few big trees, BA will drop substantially with relatively less reduction in TPA, and average DBH of the residual stand will be reduced. A geometric thinning that removes trees uniformly without regard to size will have no effect on the average diameter.

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Stand Growth and Development on the Stocking Guide Growth after thinning, or natural stand development, is the net result of two processes: (1) mortality of trees in the lower crown classes (intermediate, overtopped) that drop behind in the competitive struggle for crown expansion; and (2) growth in diameter and height of surviving trees. Growth is plotted as an upward, leftward movement on the stocking guide, as TPA declines (mortality) and BA increases (shown as dashed lines below). The "steepness" of this response depends on many factors: a stand receiving a heavy low-thinning that removes all of the lower crown classes may experience very little subsequent mortality, resulting in an almost- vertical growth trajectory. Very dense stands near the A level are probably experiencing intense self-thinning without much increase in BA; this would show as an almost-flat trajectory with a slight upward direction to the left. In even-aged stands, one would rarely encounter a situation where stand development produced a line moving to the right. This would represent the process of ingrowth, or stems reaching measurable size for the first time.

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References

Alexander, R.R., 1967. Site indexes for Engelmann Spruce in the central Rocky Mountains. (No. RM-32). USDA Forest Service Research Paper.

Alexander, R.R., Edminster, C.B., 1981. Management of lodgepole pine in even-aged stands in the central Rocky Mountains. Res. Pap. RM-229. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Forest and Range Experiment Station. 11.

Jack, S.B., Long, J.N., 1996. Linkages between silviculture and ecology: an analysis of density management diagrams. Forest Ecology and Management 86, 205–220.

Long, J.N., 1985. A practical approach to density management. Forestry Chronicle 61, 23–27.

Long, J.N., Smith, F.W., 1984. Relation between size and density in developing stands: a description and possible mechanisms. Forest Ecology and Management 7, 191–206.

Long, J.N., Shaw, J.D., 2005. A density management diagram for even-aged ponderosa pine stands. Western Journal of Applied Forestry 20, 1–11.

Long, J.N., McCarter, J.B., Jack, S.B., 1988. A modified density management diagram for coastal Douglas-fir. Western Journal of Applied Forestry 3, 88–89.

McCarter, J.B., Long, J.N., 1986. A lodgepole pine density management diagram. Western Journal of Applied Forestry 1, 6–11.

Milner, K.S., 1992. Site Index and Height Growth Curves for Ponderosa Pine, Western Larch, Lodgepole Pine, and Douglas-Fir in Western Montana. Western Journal of Applied Forestry 7, 9–14.

Smith, D.M., Larson, B.C., Kelty, M.J., Ashton, P.M.S., 1997. The practice of silviculture: applied forest ecology, 9th ed. John Wiley and Sons, New York.

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Appendix 1 – Regional Density Management Diagrams

Douglas-fir (Long et al. 1988)

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Lodgepole pine (McCarter and Long 1986)

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Ponderosa pine (Long and Shaw 2005)

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Quaking aspen (unpublished)

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Whitebark pine (unpublished)

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Appendix 2 – Regional Site Index Curves Douglas-fir

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Engelmann spruce

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Lodgepole pine (Alexander and Edminster 1981)

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Ponderosa pine Over a dozen site index curves have been created for ponderosa pine (see Long and Shaw 2005 for a list). Depicted below is Milner (1992), height-age relationships at a base age of 50 years. Note: a vertical line drawn at 50 would intercept each Site Index curve at its respective height.

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Appendix 3 – Regional Stocking Guides Ponderosa pine (Gingrich 1967 style)

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