Stand basal area

Stand basal area
Forest Measurement and Modelling.

Stand basal area, denoted by the symbol G, is a very useful parameter for quantifying a forest stand. It may be seen as a summary of the number and the size of trees in a stand. As individual tree basal area is related to tree volume, biomass, crown parameters, etc., so too stand basal area is related to stand volume, biomass, etc. G is also correlated with competition or the density of a stand.

In Australian forests, stand basal area of fully stocked stands frequently lies in the range 20-50 m^2/ha. For heavily thinned stands and young poorly stocked crops, basal areas of 10-20 m^2/ha are common. In rare cases, on exceptionally good sites, G may reach 150 m^2/ha!

G is the sum of the basal area of all (living) trees in a stand, expressed in m^2/ha. It can be calculated from measurements of the diameter (dbh in cm) of all trees in a known area (a in ha) (e.g. a plot of fixed dimensions):

Alternatively, G can be estimated using a variable probability sampling approach called angle count sampling, point sampling, variable radius plot sampling (VRP sampling), plotless cruising, angle counting, probability proportional to size (PPS) sampling or horizontal point sampling. This sampling approach allows unbiased estimates of G to be made very quickly without the need to measure the dbh of each tree. The speed and efficiency of angle count sampling, in conjunction with the correlation of G with so many stand parameters of interest has meant that G is almost always measured in any stand inventory or assessment, and measured using angle count samping.

Angle count sampling Inclusion of a tree in an angle count depends on the basal area of the tree and its proximity to the sampling point. Small trees are not included if they are some distance from the sampling point, while larger trees will be included at even greater distances.

A simple "mind experiment" might help explain the principle of the angle count method:

Imagine that there exists a forest with only small and large diameter trees (e.g. 10 cm and 50 cm dbh respectively) for which we want to determine stand basal area. A single 10 cm dbh tree only has a basal area of 0.00785 m^2 while each 50 cm tree is 0.196 m^2. We do not want to waste time measuring too many small trees, but do not want to miss the big values contributed by the large trees, so we use 2 circular plots of 5 m and 25 m radius and measure only small and large trees respectively within each plot.

Now imagine that we established our plots and found that there were three small trees within the 5 m radius plot and four large trees within the 25 m radius plot. Noting that the radius of a 10 cm and 50 cm dbh tree is 5 cm and 25 cm respectively, the stand basal area would be calculated as the sum of the two plots:

But of course a real forest would have trees of a range of DBH values. We could therefore establish a range of plots for all the different DBH classes. For example, our imaginary forest above might also have trees of 20, 30 and 40 cm DBH that we could sample in circular plots of 10, 15 and 20 m radius respectively. Using the same calculations as above therefore, we would find that each 20, 30 or 40 cm DBH tree that is within its 10, 15 or 20 m radius plot adds 1 m^2/ha to the overall stand basal area. Now that is the important part of the matter! We have set up our plot dimensions so that each tree of X cm dbh adds 1 m^2/ha to the stand basal area if it is within a radius X/2 m of the plot centre - where X is any number. In fact, we no longer even need to know what is the value of X. All we need to know is whether the ratio of dbh to distance from the plot centre is greater than 2 cm : 1 m. If the ratio of dbh : distance is greater than 2 cm : 1 m (i.e. 1 : 500), then the tree of whatever dbh is within its respective plot and that tree adds another 1 m^2/ha to the estimate of the total stand basal area. An optical wedge, Dendrometer II, Spiegal Relakop or similar instrument simply helps determine if the ratio of dbh : distance away exceeds the critical ratio and therefore whether the tree is within the plot and adds to the estimate of stand basal area.

Note that a tree of X cm dbh is within its respective plot when the ratio of dbh : distance from centre exceeds 2 * X cm : X m. Thus a tree of 20 cm dbh is counted if it is anywhere from 10 m away right up to the exact plot centre! A tree is either IN or OUT of the plot - a 20 cm dbh tree right at the centre is no more or less within the plot than a similar tree that is 3, 6 or 9 m away from the centre.

Basal Area Factor
In the above example, G was determined by counting the number of trees that were IN (i.e. ratio of dbh : distance was greater than 1:500) and multiplying by 1. The value 1 is determined by the ratio of dbh to distance from the plot centre and is called the basal area factor (BAF). Different BAFs can be chosen in different circumstances.

For example, if we decide that too many trees are IN with a ratio of 1:500, we might decide to count trees when the ratio of 1:250 is exceeded. That is, instead of a 10 or 50 cm dbh tree being IN when it is within 5 or 25 m of the plot centre respectively, it is now only counted as IN when it is within 2.5 or 12.5 m respectively. If you repeat the equations given above, you will see that G is estimated as the number of IN trees times 4. That is, the BAF is 4 when the ratio of dbh : distance from the plot centre is 1:250. On average, you would expect to count only one-quarter as many IN trees with a BAF of 4 as you would in an angle count sample with a BAF of 1. In our example, only 2 trees are IN with a ratio of 1:250 - therefore G = 2*BAF = 8 m^2/ha.

Any instrument that allows a fixed angle to be subtended can be used this sampling technique once its BAF has been calibrated. To calibrate an instrument, move back from a target tree of known dbh until the tree appears to be exactly the same angle (or size) as your instrument. For example, you can calibrate your thumb by holding it straight out and walking away from the tree until the dbh appears to be the same size as your thumb. Measure the distance (D) from the centre of the tree to your eye (for Relakop, thumb, etc) or to the instrument (wedge) and apply the following formula:

  • BAF denotes the basal area factor of the instrument
  • dbh denotes diameter breast height (m)
  • D denotes distance from eye (relaskop and thumb) or prism to centre of tree (m)
  • Lprism denotes limiting distance for a borderline tree when using a prism (m)
  • LRela denotes limiting distance for a borderline tree when using a Relaskop (m)
  • Q denotes angle of slope (degrees) eye to breast height position on target

[s_ba.htm] Revision: 6/1999