Forest mensuration: diameter, basal area, volume
Forest mensuration basics: DBH rules, girth and diameter tools, measuring height, basal area, form factor, log volume formulas, and worked examples.
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Forest mensuration is the measurement of trees, logs and forest stands. A forester has to answer questions such as how much timber stands in a compartment, how fast it is growing, and how much carbon it holds. Every one of these answers starts with a few simple field measurements: diameter, height and the volume that follows from them. The methods are standardised so that measurements made by different people, in different years, can be compared.
Diameter at breast height
Diameter is the easiest and most accurate tree measurement. It is taken at breast height, which is 1.37 m (4 ft 6 in) above ground in India, the USA and much of the Commonwealth, and 1.3 m in Europe and in most international inventories. This is diameter at breast height (DBH). Indian practice often records girth at breast height (GBH) instead, where girth = π × diameter.
Standard rules apply:
- On a slope, measure from the uphill side.
- On a leaning tree, measure along the stem on the side of the lean, not vertically.
- If a tree forks below breast height, measure each stem as a separate tree. If it forks above, measure it as one.
- If a swelling or branch is at breast height, measure just above or below it.
- On buttressed trees, measure just above the buttress, recording the height.
Instruments
- Tree calipers have two arms on a graduated beam. Take two readings at right angles and average them, because stems are rarely perfectly round.
- A diameter tape (π tape) is wrapped around the stem. It is marked in units of π cm, so it reads diameter directly.
- Other tools include the Biltmore stick, a quick visual estimate, and electronic calipers that log the data.
Height
Total height runs from ground to the tip of the tree. Merchantable height runs to a top diameter or defect limit. Small trees are measured with height rods. Tall trees are measured with hypsometers, which use either trigonometry or similar triangles:
- trigonometric instruments include the Abney level, Haga, Blume-Leiss, Suunto clinometer and laser hypsometers;
- geometric instruments include the Christen hypsometer and the Indian Ravi multimeter.
Measuring a teak
A forester stands 20 m from a teak and reads 50° to the top and 5° below horizontal to the base. h = 20 × (tan 50° + tan 5°) = 20 × (1.192 + 0.087) = 25.6 m. To keep errors small, choose a distance roughly equal to the tree's height, so the angle to the top is near 45°, and check that the top you sight really is the leader.
Basal area
Basal area (g) is the cross-sectional area of a stem at breast height:
A tree 40 cm in DBH has g = 3.1416 × 0.402 ⁄ 4 = 0.126 m2. Stand basal area per hectare is one of the most useful forest statistics. It measures stocking density, guides thinning, and is closely related to stand volume. Basal area can be estimated quickly without measuring every tree, using point sampling with a wedge prism or Bitterlich's relascope.
Volume of standing trees
A tree is neither a cylinder nor a cone, so its volume is estimated with a form factor (f): the ratio of the tree's volume to the volume of a cylinder with the same basal area and height.
The 40 cm, 25 m tree above, with f = 0.5, has V = 0.126 × 25 × 0.5 = 1.57 m3.
In practice, foresters use volume tables and volume equations. These are developed by felling sample trees, measuring their volume section by section, and fitting regressions such as V = a + b d2h. A local volume table uses diameter only. A general volume table uses diameter and height. The Forest Survey of India and state forest departments publish such equations for teak, sal, chir pine, eucalyptus and other species.
Volume of logs
Felled logs are measured with length and end or middle diameters:
| Formula | Expression | Notes |
|---|---|---|
| Huber | V = gm × L | Uses the cross-section at mid-length |
| Smalian | V = (g1 + g2) ⁄ 2 × L | Uses both end sections; easy to measure, tends to overestimate |
| Newton | V = (g1 + 4gm + g2) ⁄ 6 × L | Most accurate; needs three measurements |
| Quarter girth (Hoppus) | V = (cm ⁄ 4)2 × L | Timber trade measure; gives about 78.5% of true volume, allowing for squaring losses |
Here gm, g1 and g2 are the cross-sectional areas at the middle and the two ends, cm is mid-girth, and L is length.
Stand description
A stand is summarised by:
- number of stems per hectare;
- basal area per hectare;
- quadratic mean diameter, the diameter of the tree of mean basal area: dq = √(4G ⁄ πN);
- top height or dominant height, the mean height of the largest trees, often the 100 thickest per hectare. Top height at a reference age gives the site index, which measures site quality;
- volume per hectare, often divided into total and merchantable volume.
These figures feed yield tables, working plans and carbon inventories.
Key points
- DBH is measured at 1.37 m in India (1.3 m internationally), on the uphill side, and below forks and swellings. GBH = π × DBH.
- Calipers, diameter tapes and Biltmore sticks measure diameter; hypsometers measure height, and h = D(tan α + tan β).
- Basal area g = π d2 ⁄ 4. Stand basal area per hectare measures stocking.
- Tree volume V = g h f; form factors of about 0.5 are common. Volume tables and equations are used in practice.
- Log volume formulas are Huber, Smalian, Newton, and quarter girth (Hoppus) in the timber trade.
- Top height at a reference age gives site index.
What the exams ask
- State the breast height convention and DBH rules for sloping, leaning, forked and buttressed trees.
- Calculate basal area from diameter or girth.
- Calculate tree height from angles and distance.
- Compare the Huber, Smalian and Newton formulas.
- Define form factor and site index.
Described in general terms: the kind of examination, not a past paper. Laisha never reproduces exam questions.
Questions people ask
Why 1.37 m?
It is 4.5 feet, roughly the chest height of a standing adult. That makes it convenient to measure, and high enough to avoid the swollen stem base (butt swell). The metric countries rounded it to 1.3 m. Both are fine, as long as the same standard is used throughout a dataset.
Is girth or diameter better?
They measure the same thing. Girth is easier to measure with an ordinary tape on large trees, while diameter is more natural in formulas. Indian working plans and timber markets have traditionally used girth; scientific inventories increasingly use diameter.
How accurate is a volume estimate?
For a single standing tree, errors of 10–20% are common, because form varies. Stand-level estimates based on good volume equations and enough sample plots can be accurate to within a few per cent.
Sources
- Husch, B., Beers, T. W. and Kershaw, J. A. Forest Mensuration, 4th edition. Wiley, 2003.
- Chaturvedi, A. N. and Khanna, L. S. Forest Mensuration and Biometry. International Book Distributors, Dehradun, revised edition 2011.
- West, P. W. Tree and Forest Measurement, 3rd edition. Springer, 2015.
- Forest Survey of India. Volume Equations for Forests of India, Nepal and Bhutan. FSI, Dehradun, 1996.
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