Line Intersect Sampling:
An example of computations other than volume.
sampling is widely used to estimate down wood. It was developed to
efficiently estimate volume (or weight) of coarse woody debris after
logging and is almost always presented this way in textbooks and articles.
Past articles in the Newsletter have presented the theory behind transect
sampling (issue 21, page 1) and a simple example (issue 25, page 3).
however, we are interested in things other than the volume of logs per
acre in a unit. We may want to know the number of logs, the average size of logs,
or the volume of logs in a particular decay class. In this article we
demonstrate how to use data from a
transect sample to estimate values other than volume.
sampling, like Variable Plot sampling (also “angle count”, “prism”
or “Bitterlich” sampling) is a probability sample. In Variable Plot sampling, trees are selected with probability
proportional to basal area so that smaller trees represent more trees per
area than larger trees. With transect sampling logs are selected with a probability
proportional to their length so that shorter pieces represent more pieces
per area than longer pieces. Knowing this we can compute an expansion factor (the number of
pieces per acre a specific log represents) for logs using transect
sampling just as we would for other kinds of sampling (number of trees per
acre a sample tree represents, also called a stand table factor). For transect sampling this expansion factor is:
where 43,560 is the square feet in an acre, p is 3.14159, L is the length of the transect in feet and li is the length of a specific log in feet. For example, if we had a transect of 120 feet and a piece that intersected along a transect that was 15 feet long, then that piece would represent 38.0 pieces per acre. If one was doing this in metric, L and li would be in meters and 43,560 would be replaced with 10,000 m2/ha. The nice thing about this expansion factor is that it expands everything about the log. The problem with it is that you have to know the length of the log (Before you give up, remember in angle count sampling you have to know tree diameter to get trees per acre).
Using this idea of an expansion factor we can now compute any per acre estimate by multiplying that attribute by the expansion factor per acre (or hectare) for each log. If we designate something we want to know about the logs in a stand as x, we can compute the per acre estimate
are the attribute of interest on the log and length of each of the (i)
intersected pieces on a transect. The
value of xi/ li
is summed for all logs crossed by the transect. If multiple transects were measured in an area, one would have to
divide the answer from above by the number of transects to get the
Now you might remember from the previous articles
or from doing transect sampling that you did not need the log length to
get volume. This is true
because if xi were log volume it would be estimated from di2*
li or diameter squared (cross-section area of the
log) and log length. When we combine terms, note that the log lengths
cancel (and we convert diameters to a radius to compute area in square
feet) and we have:
which is the
formula most often seen in textbooks and articles on transect sampling.
Note that in this case, di (in feet) is
the minimum diameter of the log as you cross the centerline (at right
angles to the centerline). The
article in issue 21 discusses this measurement short cut in more detail.
the example used in issue 25 with a 120-foot transect and 5 logs
intersected by the transect:
How many logs
per acre are there? In this case xi is 1.0 so we just have to sum up 1.0/li for all the logs (i.e. sum up the
You could compute the average log size by dividing the volume per acre by the
number of logs or the average log length by dividing the total length by
the number of pieces. In this
example from issue 25, the total volume was calculated as 4,507 ft3/ac
so our estimate of average log volume would be 4,507/472 = 9.55 ft3
or 2850/472 = 6.0 ft.
you had classified the logs by decay class or whether they were
merchantable or not, one could find the number of logs in each class by
doing the above calculations for only those logs which intersected the
transect and were in the class of interest (just like creating a stand
table in angle count sampling).
If you were interested in estimating how many logs met a certain
merchantability standard based a minimum piece diameter and length, you would have to measure the lengths of the logs that were intersected and
had diameters at the small end of the log greater than the minimum
interesting question that will comes up when one begins collecting data in
the field to compute expansion factors for transects is, what is the
length of the log? Length is obvious for nice straight logs, but is not so
obvious for logs that are forked or other strange shapes. Our advice on
this is to measure piece length as the straight line distance along the
piece you measured where it would have been included on the transect
hope with this example it is clear that with a transect sample, estimates
can be computed for any attribute on logs that are crossed
by a transect.
In preparing this article we ran across an error in the example of line
intersect sampling presented in issue 25. The example begins with a
transect with a length of 30 feet but the numbers in the example are
worked out for a transect of length 120 feet. The 120 foot transect is the
Originally published January 2002
Regular Article Index