Forest-Based Biomass Basic Computations - Mathematics and Statistics for the Environment - page 324

13.1.1 F orestry s erviCe and m athematiCs : t he i nterFaCe
As mentioned throughout this text, environmental practitioners must be well versed in mathemati-
cal operations. There is no clearer or more fundamental need for mathematical skills than that of
the professional forester who must perform all the duties listed to this point plus surveying and
sampling forest biomass, especially with regard to wood-to-energy processes. Why do we sample
forest biomass instead of just counting the trees, adding them up, and computing the total woody
biomass contained? Freese (1976) observed that partial knowledge is a normal state of doing busi-
ness in many professions; the same can be said for the practice of forestry. The complete census is
rare, and the sample is commonplace. A forester must advertise timber sales with estimated vol-
ume, estimated grade yield and value, estimated cost, and estimated risk. The nurseryperson sows
seed whose germination is estimated from a tiny fraction of the seedlot, and at harvest he or she
estimates the seedling crop with sample counts in the nursery beds. Enterprising pulp companies,
seeking a source of raw material in sawmill residue, may estimate the potential tonnage of chip-
pable material by multiplying reported production by a set of conversion factors obtained at a few
representative sawmills.
On the surface, and in many cases, it would seem better to measure and not to sample; however,
there are several good reasons why sampling is often preferred. In the first place, complete measure-
ment or enumeration may be impossible. That is, not all units in the population can be identified. For
example, how does one accurately count each branch or twig on a tree? How do we test the quality
of every drop of water in a reservoir? How do we weigh every fish in a stream or count all seedlings
in a 1000-bed nursery, enumerate all the egg masses in a turpentine beetle infestation, or measure
the diameter and height all merchantable trees in a 20,000-acre forest? Moreover, the nurseryperson
might be somewhat better informed if he or she knew the germinative capacity of all the seed to be
sown, but the destructive nature of the germination test precludes testing every seed. For identical
reasons, it is impossible to conduct tests that are destructive on every chainsaw without destroying
every chainsaw. Likewise, it is impossible to measure the bending strength of all the timbers to be
used in a bridge, the tearing strength of all the paper to be put into a topic, or the grade of all the
boards to be produced for a timber sale. If the tests were permitted, no seedlings would be pro-
duced, no bridges would be built, no topics printed, and no stumpage sold. Clearly, where testing is
destructive, some sort of sampling is inescapable. Obviously, the enormity of the counting task or
the destructive effects of testing demand some sort of sampling procedure.
Sampling will frequently provide the essential information at a far lower cost and in less time
than a complete enumeration. Surveying 100% of the lumber market is not going to provide infor-
mation that is very useful to a seller if it takes 11 months to complete the job. In addition, it is often
the case that sampling information may at times be more reliable than that obtained by a 100%
inventory. There are several reasons why this might be true. With fewer observations to be made,
measurement of the units in the sample can be and is more likely to be made with greater care.
Moreover, a portion of the savings resulting from sampling could be used to buy better instruments
and to employ or train higher caliber personnel. It is not difficult to see that good measurements on
5% of the units in a population could provide more reliable information than sloppy measurements
on 100% of the units.
The bottom line to making sampling effective and accurate is obtaining reliable data from the
population sampled and making correct inferences about that population. The quality of the sam-
pling depends on such factors as the rule by which the sample was drawn, the care exercised in
measurement, and the degree to which bias was avoided (Avery and Burkhart, 2002). The triple
bottom line in sampling forest biomass comes down to how the data are drawn and measured and
made bias free, thus leading us to the final step of performing mathematical operations to produce
representative results that can be analyzed to obtain the ultimate bottom line: the object of our work.