Imaginary Heights in Variable Plot Cruising
by Kim Iles

When fixed plots were used, they measured (or estimated) all the tree heights.  Not a smart idea, just a habit formed over years.  As we moved to Variable Plot sampling, the computer programmers tried to shove the VP sampling system into the old computer routines.  Having a height was expected, even though VP volume calculations did not require heights on all the trees.  People did not think this through very well. 

The VBAR of measured trees was all that was needed.  Multiply that by the basal area of the stand and you had volume.  The VBAR trees also provided grade percent and other measurements per square foot of basal area.  If you only used count/measure plots, computer routines still worked because all the trees heights were available.

The "need" for tree heights (a convenience for programmers) made us want heights of all trees on all plots.  The current use of taper equations – a good idea and clearly the modern trend, also wanted heights for any extra diameters on trees that were usually only counted.  This allows better log distributions, and should make things better.  We just wanted heights without the effort of measuring them.  Then the trouble started, and it has become increasingly nasty over the years.

Soon, people had to search out lots of tree heights to produce a curve, and they had elaborate rules for choosing what they "needed" – particularly for  trees of rare species (with virtually no volume in some cases).  The statisticians got involved with technical problems of fitting lines to the data.  Things got worse and worse … expensive too.

Unbelievably, nobody knew if the process actually worked.  Nobody checked.  Let's imagine that we let the office janitor assign heights for the DBH's on the count trees and get on with it.  This allows us to imagine that we could fail and that no complex rules, statistics or suffering in the woods will save us.  We would ask two questions.

1)       Does the process work, or do the assigned heights lead us astray ?

2)      If it does not work (or we don't want to trust it), how can we eliminate any bias in this process of assigning heights?

It is amazing that that these questions are not asked and answered.  The practical work of forestry is full of these simple and important issues that researchers never examine.  You can be sure that Forest Science would never publish it.  The common belief was that anything complex, expensive and with lots of rules should give us good results.  Nuts.

There is a long and ugly history of the problems involved in Diameter/Height curves.  In short, the process is almost impossible to get right.  Let me ask a simple question.  Where is the data to show that assigning imaginary heights works?  Try to find it. "Well, it just feels OK" does not count as data.

Here is one suggestion. 

The assignment of heights will not change stand basal area, so all that can go wrong is the VBAR.  The average VBAR of the measured sample trees should be easy to find, even if you have to do it by hand.  Better yet, just eliminate the non-measured trees and run a computer compilation with only sample trees.  The average VBAR is simple to get from those results (the basal area will change, but that does not matter).  Stand Volume, divided by Basal Area is the average VBAR with the real sample trees and measured heights.  That is what we get without assigning any imaginary heights to other trees and it is normally an unbiased process (at least any problems do not involve imaginary janitor heights).  I would suggest that competent compiler programs ought to give you the simple average of sample tree VBARs, and their statistics, on every printout.

Now let's find the average VBAR for the cruise using the heights assigned by our janitor.  The usual compilation with only imaginary heights will give us that.  Again, it is just the total volume divided by the total basal area. 

Do they match?  If not, the assignment of imaginary heights can be seen to cause that much difference.  If the assigned heights give you a difference in VBAR of +4%, change all the heights by -4% and try it again.  Rounding can be a problem here in some cases, but somehow you are trying to drop heights to cause the volume to come out correctly. 

There might be some differences on individual cruises, but do they balance out?  If you do that on many cruises, you might expect the ratio to vary around zero.  When combining lots of stands, the total stand VBARs can indicate the overall bias inserted into the process by the phoney heights.  You do not need to understand anything about the sampling process for height data, regressions, factors and all the rest.  You just look at the results – as is so often the case if we just step back for a moment and think about it. 

In Big BAF sampling it is a bit like computing the basal area for the larger BAF, as well as the basal area for the smaller BAF.  You just like to see that in the long run, they are about the same.  A few people still cling to count/measure plots (vs. Big BAF) and some of them check to see if the long run basal area on the count plots is equal to the basal area on the measures.  Are they getting sloppy on the counts because they are too easy? 

Mind you, I like the idea of using cheaply and easily obtained diameters (even estimated ones) in VP cruising and assigning them heights.  What I find hard to understand is why people would so uncritically use imaginary measurements without finding out how much difference they cause.  The mistakes will not go away. 

If you have a problem here, there are several ways to solve it.  Finding out if there is a problem, however, is the first step.

As in all things, if you prove that your procedure is working fine then continue without worrying about it.  Smart inventory people monitor lots of things on a regular basis, just to verify that things are on track.  Perhaps you are wondering if it also works for large and small trees, or do they just luckily cancel out?  Break the data up, and check them individually.  By species? – same answer.  It's way too simple to publish in Forest Science, but your boss might appreciate you being on top of this issue.