Forest measurement: measuring one tree
To manage a forest we first need numbers. Measuring trees and forests is called forest measurement (or mensuration).
Diameter. We measure the trunk thickness at breast height, which is 1.3 m above the ground. This is the DBH. We use the same height every time so the numbers can be compared. A tape round the trunk gives the circumference; diameter = circumference / 3.14.
Height. Tall trees are hard to measure with a tape. The simple way is by shadows: a stick and a tree at the same time of day have the same ratio of height to shadow. Foresters also use a clinometer (it measures the angle to the treetop) or a laser.
Volume: how much wood is in a tree
Volume tells how much wood a tree holds. Steps:
- Basal area = 0.785 x d x d (the area of the trunk circle, d in metres).
- Cylinder volume = basal area x height.
- A trunk is thinner at the top, so multiply by a form factor of about 0.5.
For d = 0.30 m and h = 12 m: 0.785 x 0.09 = 0.071 m2; x 12 = 0.85 m3; x 0.5 = 0.42 m3. Because d is squared, a trunk twice as thick holds four times the wood.
Measuring a whole forest: sample plots
We cannot measure millions of trees. So we choose small sample plots (for example 20 m x 20 m), spread over the forest. In each plot we measure every tree. Then we scale up: if a plot is 1/10 of the area and holds 6 trees, the forest holds about 60. The more plots, and the better spread, the closer our estimate. The total wood in a forest is called its growing stock, often given in m3 per hectare (1 hectare = 10 000 m2).
Using remote sensing
Remote sensing gets information about a forest without touching it. A camera or sensor on a satellite, aircraft or drone records light from the ground. Healthy leaves look different from bare soil, so colours show where the forest is thick, thin or cut. A laser scanner (LiDAR) sends light pulses down and times the return to find tree heights. Good: it covers huge or hard places fast, and it can be repeated every year to see change. Limits: clouds, cost, and we still need a few field plots to check the picture is right.
Forest evaluation
Evaluation means judging what the numbers tell us. We ask: how much wood is there and what is it worth? Is the stock growing or shrinking each year? How is the forest doing for the other jobs: clean water, soil, wildlife, stored carbon, a place for people? Then we compare with our goal (see the lesson on forest management goals) and decide: cut more, cut less, thin, or replant. We repeat the measurement every few years, so we can see if our choices work.
Try it: measure a tree at home
Find a tree. Ask a friend to stand beside it. Measure your friend's height and shadow length with a tape. Measure the tree shadow at the same moment. Tree height = tree shadow x (friend height / friend shadow). Then wrap a string round the trunk at your chest height, measure it, and divide by 3.14 to get the diameter.
Key formulas and definitions
- DBH is measured at 1.3 m above the ground
- Diameter = circumference / 3.14
- Tree height = tree shadow x (stick height / stick shadow)
- Basal area = 0.785 x d x d (d in m)
- Tree volume = 0.785 x d x d x h x form factor (about 0.5)
- Forest estimate = plot count x (forest area / plot area)
- Net change = growth - cutting
Worked examples
1. A stick 1.5 m tall has a 1 m shadow. A tree casts an 8 m shadow at the same time. How tall is the tree?
Height / shadow is the same: 1.5 / 1 = 1.5. Tree height = 8 x 1.5 = 12 m.
2. A tape round a trunk reads 94.2 cm. Find the DBH.
Diameter = circumference / 3.14 = 94.2 / 3.14 = 30 cm.
3. Find the wood volume of a tree with d = 40 cm, h = 20 m and form factor 0.5.
d = 0.40 m. Basal area = 0.785 x 0.16 = 0.1256 m2. Cylinder = 0.1256 x 20 = 2.512 m3. Volume = 2.512 x 0.5 = 1.256 m3, about 1.26 m3.
4. A sample plot of 400 m2 holds 10 trees of average volume 0.5 m3. Find the wood per hectare.
10 trees x 0.5 = 5 m3 in 400 m2. 1 ha = 10 000 m2 = 25 plots. 5 x 25 = 125 m3 per hectare.
5. The forest in the last example has 50 ha. Find its growing stock.
125 m3/ha x 50 ha = 6250 m3.
6. The forest grows 125 m3 a year and the owner cuts 150 m3. Is this sustainable? What is the net change?
Net change = 125 - 150 = -25 m3. It is negative, so the stock shrinks. Not sustainable. Cutting must come down to 125 m3 or less.
Common mistakes
- Measuring the diameter at a different height each time. Always use 1.3 m.
- Forgetting to change cm to m before using the volume formula: 30 cm is 0.30 m.
- Forgetting the form factor. Without it, the volume is about double the real wood.
- Trusting one plot. A single plot may be unusually thick or thin; use several plots spread over the forest.