A Very Efficient Sampling Methods for Cruising Timber

by Doug Corrin, Malaspina University-College

This paper assumes the reader is familiar with the basic concepts of prism cruising; also values given are based on metric units (i.e. m3 and hectares (ha)). For the American readers, sorry about that, eh!

I once heard a seemingly lone, but determined voice say, "We measure too many trees in British Columbia." This simple statement is insightful and significant.

I am, of course, referring to cruising timber in BC. And yes, we do use a prism for point sampling. However, we are not being as efficient as we could be. Our measure of acceptability is:

  • a sampling error of less than 15% @ 95% confidence (for volume/ha), or
  • a sampling intensity of
  1. full measure plot/ha (with >=4 trees/plot) for cutting authorities >= 5.0 ha, or
  2. full measure plots/ha (with >=4 trees/plot) for cutting authorities < 5.0 ha.

When only full measure plots are used, sampling error is based on the variation (i.e. CV) of volume/ha between the plots. This CV is typically between 30-50%. Life is simple but not efficient. Given a CV of 40%, approximately 30 plots would have to be established to meet a 15% sampling error @ 95% confidence.

Now we do have the option of sampling with full measure plots (all trees fully measured) AND count plots (where simply a tree count is taken). This breaks the calculation of volume/ha into two parts: BA/ha (from tree counts) and VBAR (volume/BA ratio – based on measure trees). The CV’s for BA/ha and VBAR are approximately 45-55% and 15-20%, respectively. Given that we actually do know the typical CV’s for these two variables, we should optimize our sampling. Unfortunately, we do not.

A rough approximation indicates an optimal ratio of one measure tree for every 3 count plots. Under the current procedures, for every full measure plot a maximum of three count plots can be established. As there is a minimum of 4 trees/plot (on average), the best sampling ratio we can hope for is 4 measure trees for 4 prism sweeps (1 full measure + 3 count plots). Simplified this works out to 1:1 sampling ratio; a far cry from the optimal 1:3 ratio!

The following is a description of a project carried out by the second year class of the Forest Resources Technology Program at Malaspina University-College.

The Project
Various sampling methods other than "traditional" prism cruising are available. Some of these other methods offer greater sampling efficiencies. As a project during the regular school year, a "traditional" cruise was carried out on an 8-hectare block. As a special project at the end of the year this block was recruised using 3 different sampling methods:

  1. Point-3P – specifically Point-3P tree – (P-3Pt )
  2. 4P – more properly known as: Point-3P cluster (P-3Pc) or 3P-Point, (hence 4P)
  3. Big BAF – 2 prisms, one being a big fat one

This paper presents only method 3, Big BAF.

Eight full measure plots are required to fulfill Ministry of Forests sampling requirements (i.e. sampling intensity = 1 plot/ha). Note that a minimum of 32 measure trees is required, although more are likely to be measured. The objectives of this project were to:

  • test the mechanics of executing each sampling method,
  • discuss any accuracy issues, and
  • extrapolate the efficiencies of these methods to larger block sizes where reduction in work and/or increase in precision will occur.

What follows is a description of the Big BAF method followed by a summary of our findings.

Big BAF – Principle
This sampling method clearly separates the task of BA/ha determination from measure tree selection. At each sample point, 2 prism sweeps are made. The first is with a "regular" size prism, say a (metric) BAF of 11 (imperial: 11*4.356 = 48 BF/acre) for 2nd growth Douglas-fir. This provides the tree count to be used for BA/ha. Then, on that same point, a second sweep is made with a big fat prism, say with a (metric) BAF of 165 (imperial: 165*4.356 = 718 BF/acre). This second sweep takes in far fewer trees. Only the trees "in" the second sweep are measured.

Objective: take many sample points as BA/ha has a considerable CV (~55%) but measure relatively few trees as the CV for VBAR is small (~15%). A second advantage of this method is that the measure trees are not clumped in a few plots but are instead spread throughout the block. Volume/ha is calculated based on the following:

volume/ha = BA/ha * VBAR


  • average tree count (number of "in" trees) determines BA/ha, and
  • individual tree measures provide volume/BA ratio (VBAR).

The volume/ha determination is essentially the same as prism cruising with count plots, except two different prisms are used: one for tree count (i.e. BA/ha) and a second for measure tree selection.

In the end, more sample points are established than "traditional cruising" but fewer trees are measured. In addition to sampling efficiency and better dispersal of measure trees, a third advantage of this method is a superior estimation of species composition. This is because the BA is more intensively sampled.


Sampling error is based on the variation of BA/ha among the count plots and of VBAR among the measure trees. To get the combined SE%, determine each SE% on it’s own and then combine with

Combined SE% Equation

It is important to note that, unlike prism cruising with count plots, BA/ha is based solely on the count plots (i.e. the tree counts from the "Big BAF" plots are not used). This is because there will be great variation in BA/ha based on the big BAF – typically no trees in many plots and few plots with one or two trees (with each tree representing a substantial basal area).

Mechanics of the Cruise

  • Office planning:
    Little BAF
    (for count plots): Given that the estimated BA/ha of our block is 55 m2/ha and we are targeting an average of 5 trees/count plot, we would want a BAF of 11 (55 m2/ha 5 trees/plot = 11 BAF). (Remember the American version is BAF = 48 BF/acre)
  • Big BAF (for measure trees): If we want to measure only 12 trees over 36 sample points, we would on average measure a tree every 3rd plot. This gives us a target of 0.333 trees/plot, therefore, 55 m2/ha 0.333 trees/plot = a BAF of 165. (American BAF = 718). An alternate way to calculate this would be if you want to measure every 15th tree, use a BAF 15 times the size of the "count BAF."

Field procedure:
At each sample point:

  1. Take a sweep with a "regular" size prism, e.g. for 2nd growth BAF = 11 (or BAF=48 BF/acre), and tally the "in" trees.
  2. Take a second sweep with a much bigger prism, e.g. BAF = 165 (or BAF=718 BF/acre) to select any measure trees. Fully cruise any trees in the second sweep.

Note: it is important to establish the sample point without bias. Specifically to ensure that if the sample point lands inside a tree, THAT is where the sample point is. There is often a bias to establish the sample point where we can physically stand. As the plot radius factor is very small for a BAF of 165 (or 718 BF/acre), it is important to establish plot centers properly. The prime reason is not for BA determination, as it is less affected by a bias of a few centimeters (or inches) in plot location. Instead, if there were an unconscious bias to move the plot centers from the inside of trees, it could result in selecting too few measure trees.

Also, note as few trees are measured, it is important to not miss measuring less common species. This is easily handled by measuring the first tree of a "new" species when it occurs in a count plot, i.e., it becomes an enhanced count plot. If you are a purist, trees selected this way could later be dropped from the compilation if additional trees of that species are selected by the big BAF as measure trees.

Volume per hectare could not be compiled solely with a ‘regular’ cruise compilation program. This is because the program we used wanted to use the tree counts from the Big BAF sweeps to determine BA/ha. Although the mean of all the Big BAF sweeps would yield a proper estimation of BA/ha, the CV of this mean would be very high. This is because, as stated before, you will get many zero sweeps with only a few sweeps with one, or possibly two, trees. In our case, each tree represented 165 m2/ha (718 BF/acre).

The proper way to compile this cruise is to determine BA/ha solely from the sweeps using the "regular" BAF (in our case BAF = 11, or BAF = 48 BF/acre) and to determine VBAR solely from the sweeps using the big, fat prism (in our case BAF = 165, or BAF = 718 BF/acre).

Determination of sampling error was already described under "Statistics."

Quick Summary of Results
Bottom line: The traditional cruise included 42 measure trees over 8 sample points (i.e. averaging just over 5 trees per plot) and yielded a sampling error of 45% @ 95% confidence. Big BAF included 14 measure trees over 40 sample points and yielded a sampling error of 13.5% @ 95% confidence. Thus, life is simple and efficient! Need I say more?

Credit Where Credit is Due!
I’d like to acknowledge the Malaspina Forestry Grad Class of ‘98 for the enthusiasm and effort they afforded this project. Also, credit for the ingenuity of the sample method rests solely with Kim Iles; any errors in its description or execution are mine. Kim, thanks for your patience and generosity of time.

Originally published July 1998

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