Doug,

I believe that I speak for a group of us. You are not alone in feeling confused. Most of us have vacillated between competing definitions and methods of measuring crown spread.

There has long been is a disconnect between the rules given for measuring crown spread and the geometrical features of a tree's crown. The clash has not been adequately understood let alone resolved. So, let me review the concepts, heretofore presented measurement solutions, and open the matter up for further discussion.

The simplest depictions of the shape of a crown projected onto a horizontal plane is that of a sloppy circle or ellipse with the trunk at the center. These shapes supports the two axis method of measuring average crown spread where each axis goes through the center and the two axes are perpendicular to one another. One axis is as long as it can be, which corresponds to the major axis of the ellipse. By default, the other axis is the minor axis since both go through the trunk. This approach makes intuitive sense for such simple shapes, but falls immediately into conflict with the definition of average spread as

the average of the maximum spread and the minimum at right angles to the maximum for two possibilities: (1) axes going through the center, and (2) no requirement to go through the center.

Definitions calling for an absolute maximum spread and a minimum at right angles to the maximum run into difficulty with crown models approximating circles and ellipses. For these simple forms, where is the minimum spread? They occur at either end of the major axis, and are therefore equal to 0. This obviously makes no sense at all. The problem is eliminated if we define average crown spread as the

average of the absolute maximum spread and the maximum at right angles to the absolute. This is the old American Forests method - despite confusion on the website from the use of the word minimum.

When we introduce significant perturbations in crown shape, we encounter challenges if we try to reintroduce the original absolute maximum-absolute minimum definition. In fact, this version and others of the two axis method falls short all the way around. Consider the following diagram. In the top figure, the two axis method is implemented in 3 ways: (1) absolute max and absolute min at right angles, (2) absolute max and max at right angles to the absolute, and (3) absolute max and a compromise location at right angles. The compromise presumably is to get a better average.

- LotsOfSpokes.png (40.39 KiB) Viewed 1014 times

I think we would all agree that none of these axis pairs captures the average spread that the eye beholds in the diagram. In the Guidelines, we allow for the absolute maximum and maximum to it at right angles (orange and blue spreads) so as not to totally upset the apple cart. We gave this wiggle room in the Guidelines because we knew that the State Coordinators and their field forces would still be doing the lion's share of the measuring, but our preferred method is the

Spoke Method shown in the lower figure. Shooting horizontal distances from the drip line to the trunk all the way around the crown, averaging the spokes, and doubling the average captures average crown spread better than the arbitrary two-axis method. Our clear preference for use by the Cadre is the Spoke Method.

Now to introduce a new consideration, namely accessibility to the drip line. If we can't access the drip line, what can we do to come as close to implementing the Spoke Method as possible? This is where the

External Spoke Method comes in. In the diagram I presented in the prior post, I visualized the problem as one in which the measurer sees a limb sticking out over a roof, road, water, etc. and measures it using the ML routine of the TP360. Other limb extensions become most visible when you can see them fairly isolated which occurs when their tips appear at the greatest horizontal angles from measurer's vantage point. This can occur by the measurer repositioning himself/herself so that the limb's tip appears at the greatest horizontal angle from the eye. Limbs defining an inward part of the drip line will be less visible and apt to be less frequently measured by the External Spoke Method. I think this is basically what you were referring to, Doug, and you were right.

When we wrote the AF Guidelines, we tried to allow for situations where all you could see was the outline of the crown from a distance. Here is a diagram of what can be done with a TP360. The operative measurement to take is D, which is the horizontal distance between the apparent greatest limb extensions on the left and right sides of the crown. The TP360's Missing Line (ML) routine is what does the job.

- Screen shot 2016-03-02 at 4.04.43 PM.png (25.27 KiB) Viewed 1014 times

From other locations, we could take additional measurements of the greatest apparent crown spread. If we can get close to the tree, we can mix the External Spoke Method and the regular Spoke Method.

The competing concepts of crown measurement can be summarized as follows (more or less):

1. Measure and average maximum crown extension with the minimum taken from 90 degrees to the max - a method used by some states

2. Measure and average maximum crown extensions taken from two directions 90 degrees apart - one of the AF methods. See the

Guidelines at

http://www.americanforests.org/wp-conte ... nes_LR.pdf. Crown spread starts on

page 59

3. Measure limb extensions from around the drip line, average them and double the average - the primary AF method

4. Measure apparent maximum limb extensions from a distance, average them and double the average - one version of the External Spoke

Method

5. Combination of 3 and 4

6. Measure the apparent maximum spread from a distance, i.e. the actual horizontal distance across a basically silhouetted image. Pick up

several of these measurements as access allows and average them - an advanced method explained in the Guidelines.

The MGWG is looking at projected crown area as a future method for handling the crown measurement. We already have a method of measuring crown area based on following the drip line and modeling the enclosed region using an irregular polygon. The TP360 offers a method for implementing this method. However, drip line access would limit this method just as it limits the Spoke Method.

Bob

Robert T. Leverett

Co-founder and Executive Director

Native Native Tree Society

Co-founder and President

Friends of Mohawk Trail State Forest