Forest Mensuration. Brack and Wood


Stand growth

Tree growth and increment ©

Growth is the biological phenomenon of increase in size with time. Growth involves the formation, differentiation and expansion of new cells, tissues or organs. The sudden increase in tree diameter often observed after rain is not due to growth but reflects the effects of bark swell.

Increment is the quantitative increase in size in a specified time interval due to growth. The terms growth and increment are not interchangeable.

Stages of tree growth

Basic to measuring trees and stands is an understanding of how individual trees develop in different situations. The relationships of tree size to age and increment to age are important to the forester particularly in predicting future growth. There are inter- and intra-seasonal trends to be considered.

Size / age relationship

The general size / age relationship is represented by the cumulative growth curve (CGC) which for biological organisms is sigmoidal.
Juvenile phase (youth) - accelerating rate of growth.
Full vigour phase (maturity) - constant rate of growth.
Senescent phase - decelerating rate of growth.
The pattern of the CGC is characteristic for the life span of an organism. This is often true also for the pattern of growth within a growing season.

Equations to predict size/age

Mathematical formulae can be fitted to the CGC, the general form of the equation being:
 ln Y = a +  b x (1 / A)

 where Y is a parameter of growth (dbh, height, volume), A is age
 and a and b denote coefficients.
The Chapman-Richards function is commonly used to describe the cumulative growth curve:
Y = k x (1 - e^(c x A))^m where Y is a parameter of growth (dbh, height, volume)
A is age
k, c, m denote constants and e = 2.71828
The Chapman-Richards function can be modified, by making c a function of site, to generate a series of growth curves:
Y = k x (1 - e^((a + b x S) x A))^m where Y, A, k, m and e are as above
a and b denote constants and
S denotes some index of site

Factors affecting growth

The following factors generally have important effects on growth in most plantations: Important factors in natural forests include:

Diameter/age relationship

The diameter of main interest is that at breast height. The main section of the general relationship varies from a linear to concave curve depending on species, environment and silvicultural treatment. If the relationship is linear, future diameter growth can be predicted with some certainty. However, if the relationship is concave, the equivalent basal area (G) /age graph may be linear or nearly so - this enables future diameter growth to be estimated from projection of G.

Height/age relationship

Example of height against age relationship for Pinus radiata in the ACT.

This relationship usually reflects clearly the inherent vigour of the tree and the environmental conditions under which it is growing. For this reason, the height/age relationship is a common basis of site classification.

There is no standard height/age relationship for trees because of the influence of both internal and external factors on height growth but the basic pattern is sigmoidal. Once again, projection from past growth to likely future growth is facilitated if the main section of the CGC is linear.

Volume/age relationship

This relationship, though basically sigmoidal, is likely to be somewhat erratic because of the effects of climatic changes and silvicultural treatment. The CGC usually shows a long early period of curvilinearity, a linear trend becoming evident much later than is found with the diameter/age and height/age relationships.

Increment/age relationship

This relationship is represented by the true growth curve (TGC) or increment curve.

The natural increment phases (juvenile, mature and senescent) are of extreme importance to the science of forest yield.

In light demanding species, culmination of the increment curve occurs early in life. In contrast, the rise of the curve in shade and semi-shade tolerant species is not so steep, the culmination point occurs later and the fall is more moderate.

The two conventional expressions of increment are current annual increment (CAI) and mean annual increment (MAI).

Current annual increment CAI:

the increment over a period of one year at any stage in the tree's history.
The period to which the CAI refers and the age and/or size of trees at that time must be defined (e.g. CAI 1969/70, age 25-26 years).

The CAI varies from year to year being affected by seasonal conditions and treatment. For this reason, it is common practice to express the increment as a mean over a period of years, termed the periodic mean annual increment (PMAI or PAI).

It is important to maintain the distinction between CAI and PAI. The PAI is a more realistic indicator of the capacity of a tree (or stand) of a certain age or size to grow.

Mean Annual Increment (MAI):

the mean annual increment over the whole period from origin to a specific age.
The specific age must be given when quoting MAI figures.

The interrelationships of the CAI and MAI curves of a tree (more particularly of a stand), their relative shape, and the position of their point of intersection, are of particular interest to management.

Conventionally, CAI and PAI data are plotted against the middle of the period to which they refer whereas MAI data are plotted against the specific year.

As long as the CAI exceeds the MAI, the MAI curve must rise since each added yearly increment improves the average. After the CAI culminates, the MAI curve begins to flatten, reaching a maximum at the point of intersection of the two curves. Beyond this, the MAI falls but at a slower rate than the CAI.

For sawlogs in particular, volume MAI is maximum at the time of intersection of the CAI and MAI curves but value increment may not maximize until many years later.

Factors affecting increment

The increment is determined by the pattern and rate of growth of the tree and varies with: Generally, increment is based on a period of one year. This smooths out the intra-seasonal variations in increment. In research projects, increment periods less than one year may be appropriate.

The adjacent figure shows an example of the seasonal variation in increment for Pinus radiata in the A.C.T.

Annual increment is often expressed as PAI over a number of years to smooth out the between year variation. Nevertheless, the average increment figure must still be related to the general weather conditions which prevailed during the period in question. If this is not done, a distorted idea of the capacity of a tree of a given age or size to grow may result.

Increment data must also be related to tree age or size. The data are meaningless otherwise. One can use the age or size at the beginning or end of the period. It doesn't matter which as long as it is specified.

Determining the age of a tree often presents problems. Age will be known for certain only when the year of sowing or planting is known, e.g. with plantation forests, age should be available from compartment history records.

Sometimes, the age of natural forests can be estimated from the date of some catastrophic event - fire, flood, cyclone, logging.

The age of some tree species can be estimated from:

True annual rings are very common in species of the northern hemisphere. They are the exception rather than the rule under Australian conditions. Where there are growth rings, stem analysis may be used to estimate growth.

Errors and their importance

Before leaving the subject of growth and increment, keep in mind that the forester, in managing a forest, manipulates the growth of its components, the trees. This manipulation is guided by the knowledge of tree and stand increment.

Estimates of height increment are usually satisfactory if height is measured by height sticks, but may be unsatisfactory if measured by hypsometer. Instruments such as the Haga, Blume Leiss, etc., are much less precise and more subject to bias in use than height sticks! Estimates of diameter increment are much more reliable particularly if the point of measurement on stems is marked permanently.

Better measurements of a tree are required when the interest is in growth over time rather than size at a particular time. A standard error (s.e.) of say 5% of the volume estimate at each of two measurements results in an 18% error in the estimated growth of the tree over the period between measurements, for example:
Volume (m^3)Standard error
Initial Volume 1.0 0.05 m^3 (5%)
Final Volume 1.5 0.075 m^3 (5%)
Increment 0.5 0.09 m^3 (18%)
Calculated as:
SQRT(0.05^2 + 0.075^2)
Some compensation of errors can be expected when working with stand data. Nevertheless, the standard error of the growth measurement will always exceed that of the volume estimate for the same standard of measurement.


As increment accumulates on a tree, it eventually becomes useful for some purpose, so we have a yield. Note that the purpose or product required must be specified when yield calculations are made.

Sun, 11 May 1997