Topic 12.4: Measuring and Reporting Growth Rates

Given the wide range of natural products for which forests are managed, and the impacts on non-target species that need to be monitored, silviculturalists need to be aware of an equally wide range of mensurational techniques. Here we will focus on measuring plant growth rates, and focus even more closely in measuring trees.

Depending on the intended use of a forest product, many different dimensions of a plant might be relevant. The most common of these dimensions are the following:

1. Stem diameter: Generally measured at 1.3 m and referred to as “diameter at breast height” or “DBH.”  DBH can be read directly from a measuring tape made for this purpose, or converted from girth (=circumference) measurements. Some researchers measure and report GBH instead of DBH, but the latter is more common and easier to envision for most people.
2. Basal area: The cross-sectional area of the stem, generally at 1.3 m.
3. Stem volume: Volumes are generally calculated from measurements of stem diameter, height, and taper. Allometric conversion tables for converting diameter and height measurements into volume estimates have been published for many commercially valuable timbers, but caution should be used in using these tables because stem taper varies somewhat with growing conditions. Also note the minimum stem diameter included in these calculations.
4. Above-ground biomass: When whole plants are harvested, either total above-ground biomass or total above-ground woody biomass are often the relevant parameters. There are some published equations for converting stand table data (e.g, size-class frequency distributions) into estimates of above-ground biomass (virutually always given as oven-dry weight). For most applications, especially when growth forms other than canopy trees are of interest, estimating biomass requires the painstaking process of destructively harvesting, drying, and weighing plants representing the range of sizes of interest, and using the resulting data to calculate the allometric relationships.

One standard way of expressing growth rates of trees is as mean annual increment (MAI). To estimate MAIs, trees are measured over a period of at least several years, and the average annual increments are calculated.  MAIs are most useful when presented by size class and crown class.  Overall MAI is a good starting point for understanding how trees are growing, but the simple process of calculating a mean serves to obscure a great deal of interesting variation. For example, because the slowest growing trees in crowded stands may be unlikely to survive until they are of harvestable size, it might be better to present the mean growth rates of the fastest 25% of the trees.  Another problem with MAI in DBH as a measure of growth rate is that a 0.5 cm DBH increment on a 95 cm DBH tree represents a substantially greater absolute gain in volume than a similar DBH increment on a smaller tree.  Another less easily avoided complication is that equivalent increments on very different sized individuals represent substantial differences in growth as a proportion of initial size.

Where growth rates of individual plants are important and especially in experimental settings, relative growth rates (RGR) are generally preferable to absolute measures of growth. RGR is an expression of growth as a proportion of or relative to the initial size. RGR is often calculated as follows: RGR = loooog log log.

It may seem like a simple matter to measure DBH, but for many trees, this activity is less than straightforward. Fortunately, a number of conventions have developed over the past 100 plus years of mensuration. For example, to estimate the equivalent dbh of trees forked below 1.3 m, the standard method is to measure each of stems separately, convert each DBH to basal area, add the basal areas, and then back convert to total DBH.  This method may sound round-about, but some pencil-work will show its basic rationality. Other conventions for measuring trees are covered in detail in publications cited at the end of this chapter.

Of the utmost importance in monitoring growth rates in permanent plots is that the exact point of measurement is consistently used.  For measures of DBH increment, measuring a few centimeters above or below the initial measurement height can lead to great errors in estimating growth. The best way to avoid this problem is to paint mark a line around the tree at the height of measurement. Measuring close to the nail holding a numbered tag is generally not advisable because some trees respond to being wounded by producing abundant callous tissue that will bias growth estimates.

Dendrometer bands made from strips of metal are sometimes used for making more accurate estimates of diameter increments than are possible with a fiber-glass or metal tape.  For some research purposes, these devices are quite useful, but it is generally preferable to measure more trees over a longer period of time than to concentrate on the few trees that can be monitored with dendrometer bands.

Measuring the heights of forest trees is challenging, and measuring height increments is even more so.  The devices used to measure tree heights range from simple height poles to various sorts of angle gauges.  Use of a clinometer showing the trigonometric equation). The basic problem for measuring the heights of large trees is that it is generally impossible to determine where the very top is with more than +-2-4 m accuracy, which makes height growth measurements extremely questionable.

Although growth rate estimates from permanent plots represent the very most important data for setting sustainable harvesting rates, far too many management plans are written without good growth data. One of the reasons for this frequent deficiency is that permanent plots are expensive to establish and maintain over the years necessary to obtain reliable growth data.  There is no set formula for determining how many trees should be measured and for how long—answers to these questions need to be based on knowledge of variation in growth rates and the specific goals of management. Just to get some idea of how much work is needed to estimate how fast trees are growing, consider the hypothetical example of a forest with 50 tree species. If we are interested in the growth rates of trees 20-80 cm DBH, and want to have at least 20 trees in each 20 cm diameter class for each species, the minimum sample size would be 3000 trees. If there are 200 trees >20 cm DBH/ha, that means we would have to monitor the growth of all trees in a 15 ha area (but since there are likely many trees of other species, the minimum sampling area is likely to be much larger). And for how long do the trees need to be monitored?  If the mean annual increments (MAIs) in DBH in this hypothetical forest are 0.3 cm/yr, and we can measure to within +-0.2 cm accuracy (given bark sloughing and the other vagaries of even paint-marked tree stems, this seems reasonable), then we might want to measure for at least 3-5 years. Now if we want to consider differences in growth rates between wet and dry periods, or between vine-laden and vine-free trees, then the number of years and the number of trees we would need to sample would increase accordingly.  For good estimates of mortality rates, particularly of the large trees of which perhaps 1% die per year on average, quite a few years will need to pass before the estimates are reliable. And when all these data are eventually collected, the next big challenge is to analyze them.

When setting out to estimate growth and mortality rates of species that are rare (e.g., <5 individuals >20 cm DBH per hectare), alternatives to fixed area plots need to be considered.  For rare species, in particular, it might be preferable to search out, mark, map, and measure all individuals in a large area, without reference to a sample plot. The data cannot then be used to estimate densities, but can provide cost-effective growth rate estimates.

Filing cabinets, stacks of punch cards, floppy disks, and hard drives full of growth data from permanent sample plots are collecting dust in forest research institute all over the world because the data are cumbersome and complicated to analyze. Too many foresters are enthusiastic field workers, but are not enthusiastic about spending months working through large data sets in the office. High-speed computers and somewhat user-friendly software (some of which is cited at the end of this module) make plot data analysis easier, but the task is still substantial.

When setting out to estimate growth rates, alternatives to fixed area plots need to be considered.  For rare species, in particular, it might be preferable to search out, mark, map, and measure all individuals in a large area, without reference to a sample plot. The data cannot then be used to estimate densities, but can provide cost-effective growth rate estimates.