Forest Mensuration. Brack and Wood
Tree growth and increment ©
Increment is the quantitative increase in size in a specified time interval due to growth. The terms growth and increment are not interchangeable.
|Juvenile phase (youth) - accelerating rate of growth.|
|Full vigour phase (maturity) - constant rate of growth.|
|Senescent phase - decelerating rate of growth.|
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
|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
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.
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.
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:
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%)|
SQRT(0.05^2 + 0.075^2)
Sun, 11 May 1997