External Spoke Method for Measuring Crown Spread

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#1)  External Spoke Method for Measuring Crown Spread

Postby dbhguru » Sat Feb 27, 2016 1:42 pm

NTS,

   Of the three dimensions we measure for champion tree competitions, the weak link in the chain is average crown spread. The traditional way of determining that dimension is to find the absolute longest spread and the longest spread at right angles to the absolute and average the two values. This method works for some shapes, but not very well for others, so we developed the spoke method. The two approaches are illustrated below.


               
                       
TradAndSpoke.png
                                       
               


   Both these methods involve locating the drip line of the crown and following it around - more or less. However, many trees do not allow access to part or all of the drip line. So, the External Spoke Method was developed. See the attachment. This method frees us from the sometimes insurmountable obstacles that plague the two methods mentioned above. With an LTI TruPulse 360, using its missing line (ML) routine, determining average crown spread becomes doable in the vast majority of cases.

  The new method will be included in future releases of the AF Tree-Measuring Guidelines Handbook. Actually several of us in the National Cadre have been using variations of this method for a long time.

Bob
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AdvancedExternalSpokeMethod.xlsx
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Robert T. Leverett
Co-founder and Executive Director
Native Native Tree Society
Co-founder and President
Friends of Mohawk Trail State Forest

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#2)  Re: External Spoke Method for Measuring Crown Spread

Postby Larry Tucei » Tue Mar 01, 2016 1:41 pm

Bob-  Great Illustration of the old vrs the new Crown Measuring Method. I use the spoke method but only 4 measurements not 8 but in the case of Champion Trees I would use 8.  Larry
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#3)  Re: External Spoke Method for Measuring Crown Spread

Postby dbhguru » Tue Mar 01, 2016 2:48 pm

Larry,

 I'll key off your comments to make some points for other members.

 The key to the new crown spread method is picking out measurable limbs that appear to be the longest from different vantage points. Here is a graphic depicting a hypothetical situation.

               
                       
Screen shot 2016-03-01 at 1.49.25 PM.png
                                               
Screen shot 2016-03-01 at 1.49.25 PM.png (39.58 KiB) Viewed 1106 times
               
               


 The operative assumption is that the limb extensions being measured are the ones visible from the indicated locations (the orange circles). The red spokes are measured using the ML routine of the TP360. A further assumption is that the locations of the orange circles represent the best vantage points that the measurer can find to see crown extensions. This frees the measurer to circle the tree and pick convenient locations to take measurements as opposed to trying to get positioned beneath the tips of the crown extensions along the drip line - which may be only partially accessible at best.

 The two questions are how accurate is the ML routine and how well can the measurer hit the tip of a limb? Where the measurer cannot get positioned beneath the tip of a limb, it doesn't matter. In that case, the regular Spoke Method cannot be employed. For urban trees where limbs often extend over the roofs of buildings, busy streets, and inaccessible private properties, following drip lines isn't even an option. What were measurers doing in these situations? Estimating by the method of Kentucky windage. The new method (which has no doubt been in use in various forms for those owning 360s) frees measurers from the drip line protocol that simply can't be applied to many trees.

Bob
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#4)  Re: External Spoke Method for Measuring Crown Spread

Postby DougBidlack » Tue Mar 01, 2016 4:04 pm

Bob,

I have a problem with your methodology in measuring and calculating the average crown spread.  If you only measure the longest limbs your crown spread measurement will be significantly greater than 'average'.  It would be the equivalent of measuring the top of each wave crest and saying that this is the level of the surface of the lake, ocean etc.  You need to measure just as many troughs as crests or the spokes must be placed such that they are as likely to fall at a trough, crest or intermediate area in order to get a true mean.

Doug
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#5)  Re: External Spoke Method for Measuring Crown Spread

Postby Will Blozan » Tue Mar 01, 2016 4:40 pm

DougBidlack wrote:Bob,

I have a problem with your methodology in measuring and calculating the average crown spread.  If you only measure the longest limbs your crown spread measurement will be significantly greater than 'average'.  It would be the equivalent of measuring the top of each wave crest and saying that this is the level of the surface of the lake, ocean etc.  You need to measure just as many troughs as crests or the spokes must be placed such that they are as likely to fall at a trough, crest or intermediate area in order to get a true mean.

Doug


Doug,

Crown spread measurement has never measured troughs. Limb extensions measured will represent the longest and the shortest tips that reach dripline. Indeed, the dripline is in the troughs but these do not represent the crown spread of the tree in a maximal way. Similarly, we don't measure the height of subordinate leaders and average for height.

Will
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#6)  Re: External Spoke Method for Measuring Crown Spread

Postby dbhguru » Tue Mar 01, 2016 6:37 pm

Doug,

  As Will says, traditionally, we haven’t measured troughs, at least that has been the intention. However, the way I described the External Spoke Method is admittedly not the external equivalent of the regular Spoke Method, which follows the drip line and has the objective of determining the average distance from the drip line to the trunk and then doubling that distance. You are always at a maximum crown extension from the trunk in the direction of the trunk, but following the drip line as it juts out and dips in.

   As you know, the traditional method takes only two measurements of crown spread: one at right angles to the other: the absolute longest and the longest at right angle to the absolute. Some descriptions called the second measurement a minimum, but the AF rule is the minimum of the two - not an absolute minimum. When state rules are examined, it gets more complicated. Some state rules tried to implement a minimum wherever it occurred at right angles to the longest extension. Rules may state or imply that the two extensions go through the trunk, with one being the longest spread across the crown through the trunk.

 Traditional method may work for circular crowns (more or less) and oval-shaped ones, but highly irregular shaped crowns are another matter. The Spoke Method was introduced to take into consideration all crown shapes. In that method, we go along the drip line shooting back to the trunk to approximate the crown shape, tak the average spoke length and double it. The Spoke Method is the AF gold standard, but it depends on continuous access to the drip line. The External Spoke Method frees is meant to free the measurer from needing to access the drip line. However, the way I described it, we would get something between the traditional method(s) and the Spoke method. A more appropriate implementation of the latest method would be to select points along what would be the drip line and measure them externally. Identifying those points from a distance is no mean feat. However, how would they be determined in absence of access to the drip line. The solution I presented is a compromise and may be the most practical one. We can discuss it further.

  To extend the discussion, we can approach crown spread and its measurement in other ways. One is to see crown spread from a distance approximating a silhouette and measure the maximum extension of the two-dimensional image. The process would be repeated from a 90-degree rotation and the two extensions averaged. An improvement on this approach would be to use the TP360 and get the actual horizontal separation of the limb ends. The Guidelines present this solution.

 BTW, the AF Measuring Guidelines Working Group (Will, Don, Don, and me) are always willing to entertain improvements two existing methods and explore new ones. For example, we've toyed with the idea of crown area projected onto either a horizontal plane or a vertical one. The horizontal plane makes the most sense. There would be potentially many vertical planes. We've also discussed crown volume - the ultimate solution. As I'm sure you recognize, the problem with the advanced methods is complexity.

Bob
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#7)  Re: External Spoke Method for Measuring Crown Spread

Postby DougBidlack » Tue Mar 01, 2016 11:54 pm

Will, Bob,

wow, I can now see why I have never fully understood the crown spread measurement.  From my perspective average crown spread was always just that...an average measurement of the crown diameter.  I mainly thought in terms of area of ground that would be shaded rather than dripline but it's the same thing.  I believe Ed also made a similar argument to the way I think of average crown spread.  Can't think much right now because I need to get to bed, but I now understand why my crown spread measurements always seem so small and yours always seem unusually large to me.

Doug
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#8)  Re: External Spoke Method for Measuring Crown Spread

Postby dbhguru » Wed Mar 02, 2016 8:07 pm

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
                                               
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 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
                                               
Screen shot 2016-03-02 at 4.04.43 PM.png (25.27 KiB) Viewed 1011 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
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