# 3. How to measure: Special techniques for trees

Vegetation scientists have developed some special techniques for trees, the dominant growth form in many vegetation types. Whereas cover within quadrats is the most common way to measured abundance of herbaceous plants, the most common way to measure the abundance of trees is the "diameter at breast height" of individual trees. The diameter at breast height, or DBH, is just what it sounds like: the diameter of the tree's trunk at the height of the archetypal forester's chest (4.5 feet, or 1.37 m). It is lucky for vegetation science that the most accessible part of the tree—the trunk—is also the best general indicator of tree size! Diameter is difficult to measure directly, because the trunk gets in the way. Because tree trunks are usually almost circular in cross-section (lucky again!), vegetation scientists can calculate diameter indirectly by measuring circumference.

 Special measuring tapes are available that do the geometry for you. These "diameter tapes" are marked on one side in centimeters, on the other the diameter of a circle with a given circumference. The first step in using these diameter tapes is to calibrate "breast height" on your body. This will save you gobs of time in the field trying to measure 1.37 m from the ground.
 Start using the tape to measure DBH by attaching its end at the proper breast-height, then stretching the tape around the trunk at breast height. You read diameter from the point that the tape overlaps zero on the tape. The photographs show the process, which is really very simple. The diameter of this tree is 55.6 cm. A common mistake is using the wrong side of the tape. Remember, one side measures distance, just like any other tape.  Don't use that side! Use the other side, which reads diameter when the tape is wrapped around a circular trunk.

Even better than DBH is basal area. Tree basal area is the cross-sectional area of a tree's trunk at breast height (not at the base of the trunk, despite its name). Again assuming a circular trunk, basal area (BA) is a simple function of diameter:

 A related vegetation characteristic is stand basal area. One way to think of stand basal area is as simply the sum of all individual tree basal areas of all the trees in the sampling universe. But stand basal area is usually expressed on a per area basis, such as m2/ha. So where BAi is the basal area of the ith tree and A is the area of the stand (or individual quadrats, if stand basal area is measured by sampling within quadrats). Stand basal area is a very robust way to compare the stature and biomass of different forests.

But wait, there is an even easier way to measure stand basal area. This magical technique is variously called the prism or angle gauge method, after the tools used in the measurement, or the Bitterlich method, after the discoverer. Bitterlich realized that one technique could combine tree size and tree density, the two components of stand basal area. Picture yourself standing in the middle of a forest for which you are trying to estimate stand basal area. If the trees were larger, the stand would have more basal area. But if trees were closer together (more dense), the stand basal area would be higher, even if the trees were the same size as before.

The technique works by using angles of sight to determine contributions to stand basal area. Trees whose breast height diameters appear larger than the fixed angle subtended by the angle gauge are included in the sample as "hits;" trees that are narrower than the angle are "misses." The process is to scan the stand by rotating around the sample location point, counting hits (and ignoring misses). Notice that a tree can be a hit by being very large or, if small, very close to the measurement point.

 The angle gauge is the simplest tool for creating the fixed angle. The line of sight from your eye to the left edge of one of the openings establishes one line. The line of sight from your eye to the right edge of the same opening establishes the second line. The two lines define the fixed angle. (The other openings can also be used, but have different conversion factors; see below.) Of course, the angle is fixed only if the angle gauge is a set distance from your eyes. That is what the chain from head to gauge is for. Keep your eye over the sampling point because your eye is where the angle starts. (Photograph courtesy of Ben Meadows Company)
 The Cruiser's Crutch™ provides another way to get a fixed angle.  Trees that appear wider than the width of the plastic are big enough or close enough to be counted.  The length of the chain away from your eyes determines the basal area factor. An advantage of this particular tool is its ability to correct for slope. (Photograph courtesy of Southwestern Environmental Consultants, Inc.)
 Prisms are another tool for creating the fixed angle. Hold the prism with the flat edge at the bottom. (Thanks to physics, upside-down also works, but sideways doesn't.) Put the prism (not your eye) at the sampling point because the prism is where the angle starts. (Photograph course of Forestry Suppliers, Inc.) Check to see if a tree is a hit by looking at its trunk both through the prism and just over the prism. The image through the prism will appear offset from the image over the prism. If the two images of the tree trunk overlap, the tree is so big or so close that it is a hit. If the tree trunks do not overlap, the tree is too small or too far away--it's a miss. Be sure you're determining all this at "breast height" on the tree.

The magic of the method is that a very good estimate of stand basal area is simply the number of "hits" multiplied by a coefficient. This coefficient is called the basal area factor, and is larger for wider angles and smaller for narrower angles. (Do you see why?)  The formula is

Stand basal area = (number of hits) × (basal area factor).

The basal area factor is shown on the angle gauge, Cruiser's Crutch, or prism that you happen to be using.  (But watch out!  Often the basal area factor is written with just the number and not the units, like "20."  In general, the the basal area factor is reported in English units, ft2/ac, unless it has a special code, like "4M."  In that case, the units are metric, m2/ha.)

 Let's see how the technique works, using a very hypothetical forest. The brownish disks represent tree trunks. The sample location is marked by an asterisk near the middle. Tree #1 is a "hit," but tree #4 (exactly the same size as tree #1) is a "miss." Altogether 7 trees are hits (1, 3, 5, 8, 9, 10, and 11). Trees 2, 4, 6, and 7 are too small and/or too far away to be counted as hits.

The basal area factor (BAF) for this fixed angle is 52 m2/ha. So the stand basal area in the diagram is calculated as: SBA = (7 hits) × (52 m2/ha per hit) = 364 m2/ha.

(By the way, 52 m2/ha is a whoppingly big BAF. Most angles used in the field have BAFs of 2-10 m2/ha. But it is easier to illustrate the technique with an artificially high BAF in a forest unreasonably thick with big trees. A good practice is to select a BAF so you get 8-12 hits.)

Notice two things about this method. First, it is very fast because you don't have to move from the sample location point. No setting quadrats or picking trees at random. Second, there are no definite borders to the sample; big trees far away can be hits, but small trees can be misses even if they are close.

Of course, just like all the other sampling methods, you need to repeat the Bitterlich method for several locations within the vegetation you are sampling. I promise you'll soon learn how to pick these locations.

 You might be wondering why measure at breast height and not at the tree's true base. There are two reasons. The bad, but understandable, reason is that it is a lot more convenient to look at arm height rather than foot height. The good reason is that some tree trunks flare outwards towards the base. Trees of about the same biomass could have quite different diameters at true base if one tree's trunk is flared and another's is not. Most flaring, at least in temperate zones, occurs below breast height. In other words, diameter and cross-sectional area are more reliable measures of a tree's abundance when measured at breast height, above any flaring. Mountain hemlock (Tsuga mertensiana)

Sometimes tree canopy cover is more important to measure than DBH. For example, if you want to characterize shading of the understory by trees, it makes sense to measured tree cover directly. Using quadrat frames doesn't work, because it is nearly impossible to visually extend the quadrat boundaries from the ground to the canopy.

 You have already read in the course about using the line intercept method for estimating tree cover. The point intercept method can also be adapted to tree cover, by using a specialized tool called the spherical densiometer. The spherical densiometer is a convex mirror with lines etched on it. The lines intersect to form a grid of 24 points. Because the mirror is convex, it reflects most of the canopy over your location. The proportion of the 24 points intercepted by tree canopy is your estimate of tree cover for that sample location. (Photographs courtesy of Roland Gesthuizen)

A non-standard use of the spherical densiometer is to use the lines on the mirror as a virtual quadrat frame, and visually estimating cover within the frame. This is the way I do it.

The principles of the spherical densiometer method have been extended by combining fish-eye photography and digital scanning technology. In this method, a fisheye (wide-angle) photograph is taken of the tree canopy from each sample location. The photograph is then digitally scanned, with each of the thousands of resulting pixels in essence acting like a point. A computer program then counts the number of pixels filled with tree canopy. New generation sensors and programs can also estimate stand leaf area index For details of some of these approach, see articles by Frazer et al. (2000) and Coops et al. (2004) and products by Dynamax and Licor.

© 2007 Mark V. Wilson and Oregon State University