Measuring a little to learn about a lot
A forest of a few thousand hectares may hold millions of trees. Measuring each one would take far more time than anyone has, and the answer would be out of date before it was finished. A forest inventory solves this by sampling. Crews measure everything in a number of small plots, then use statistics to estimate what the whole forest looks like, together with a measure of how uncertain the estimate is.
The idea is the same as an opinion poll. A well-chosen sample of a few thousand people can describe a country, but only if the sample is chosen carefully and is not biased toward one kind of person.
What a plot is
A plot is a small defined piece of ground in which trees are measured. Common designs include:
- Fixed-area plots. A circle (set by a radius from a center point) or a rectangle. Every tree inside the boundary above a minimum size is measured. Circles are popular because they only need one point and a measuring cord.
- Nested plots. Large trees are measured in a larger circle, while smaller trees and saplings are measured in a smaller one inside it. This avoids wasting time on a big area for lots of tiny stems.
- Point sampling. Instead of a fixed boundary, the observer uses an angle gauge or prism from the plot center and counts trees that look wide enough from that spot. Larger trees are more likely to be counted. This approach is efficient for estimating basal area, though it is less intuitive.
- Strips and transects. A long, narrow band is measured, which can be easier to lay out in dense terrain.
In each plot crews typically record species, trunk diameter, tree status (alive, dead, standing, fallen) and often height and health signs. Methods for measuring individual trees are covered in the article on measuring tree height and diameter.
Where plots go
The location of plots is the most important design choice, because it controls bias. Several layouts are common.
Simple random sampling. Points are placed at random across the forest. It is statistically straightforward, but random points can clump by chance and leave gaps.
Systematic sampling. Plots are set on a regular grid, perhaps with a random starting point. This spreads coverage evenly, is easy to navigate and is widely used in national inventories.
Stratified sampling. The forest is first split into groups that are internally similar, such as conifer stands and broadleaf stands, using maps or satellite imagery. More plots go into groups that vary more, or that matter most. This can give better precision for the same effort.
Cluster sampling. Several small plots are grouped together at each location, which reduces travel time between plots.
Convenience is the enemy. Placing plots only near roads or in nice-looking stands makes the estimate unrepresentative. Crews are normally told to measure the plot where the grid or the random draw says, even if it is steep, swampy or awkward.
Scaling up
Once the plots are measured, the numbers are scaled to the full area. A hypothetical example, with all figures invented for illustration:
- A forest block covers 100 hectares.
- Crews measure 20 circular plots, each 0.05 hectare, so 20 × 0.05 = 1 hectare is sampled, or 1 percent of the block.
- Each plot is scaled up by an expansion factor: 1 ÷ 0.05 = 20, since one plot represents 20 times its own area on a per-hectare basis.
- Suppose one plot holds 10 trees of 30 centimeters diameter. The cross-sectional area of a 30 centimeter trunk is about 0.0707 square meters (using π × 0.15² ≈ 0.0707). Ten trees give 0.707 square meters, and multiplying by 20 gives about 14.1 square meters of basal area per hectare.
Averaging the per-hectare values across all 20 plots and multiplying by 100 hectares would give an estimate for the block. Basal area is a standard measure of how crowded a stand is, and it is a common starting point for estimating wood volume, and, via the steps in the article on estimating biomass and carbon in standing trees, tree biomass.
Sampling error
Because only part of the forest is measured, the result has uncertainty. If the trees vary a lot from place to place, the estimate has a wider margin; if they are quite uniform, a few plots will suffice. Statisticians calculate a standard error or confidence interval to express this. More plots narrow the margin, though with diminishing returns: doubling the number of plots does not halve the error.
An inventory report that gives only a single figure without a margin of error should be read with caution. A difference between two surveys is also only meaningful if it is larger than the combined uncertainty.
Permanent versus temporary plots
Permanent plots are marked so they can be found and remeasured, often every five to ten years. They show growth, mortality and recruitment directly, because the same trees are followed. Temporary plots are measured once, which is cheaper but gives only a snapshot. Many programs use a mix. Remeasured plots are also valuable as ground truth for remote sensing, such as forest lidar and satellite imagery.
What inventories feed
Inventory data support forest management plans, timber supply forecasts, forest certification audits, national reporting and carbon accounting. They also help set the baseline for monitoring forest health indicators and for comparing against remote sensing maps.
Strengths and limits
Plot sampling gives rich, trustworthy detail about tree size, species and condition, and it is relatively cheap per hectare compared with measuring everything. But it says little about places between plots, and small or patchy features such as a single clearing may be missed entirely. For that reason, plot data are frequently combined with maps made from aircraft and satellites, with plots providing the details and remote sensing providing full coverage.