Comparing tape drop height to that obtained with Nikon 440

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pdbrandt
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Comparing tape drop height to that obtained with Nikon 440

Post by pdbrandt » Mon Mar 31, 2014 2:47 pm

This post ended up being much longer than I imagined - my apologies to the casual reader!

Tape drop is considered the definitive measure of a tree's exact height, but climbing a tree to measure its height is usually not feasible. Don Bragg, Lee Frelich, Bob Leverett, Will Blozan and Dale Luthringer published a paper in 2011 (http://www.nativetreesociety.org/specia ... g2011D.pdf) wherein they measured 42 trees (mostly Tsuga conifers) via the NTS sine method with a TruPulse 200 hypsometer and compared the height to that obtained by tape drop. The trees were in the 150 foot range and they found that discrepancy for those 42 trees ranged from -1.9% to +1.4% with a standard deviation of 0.64%. In other words 68% of the time (definition of 1 standard deviation) one could expect that the sine-based measurement would be within 0.64% of the tape drop measurement. On a tree 150 feet tall, that equates to less than 12 inches. Or as the authors themselves put it,
  • "Hence, with the accurate laser rangefinders and electronic clinometers available today, instrument error when measuring total tree heights with the sine method can be expected to be consistently less than 1 percent for experienced users" (Bragg et al, 2011)

I was curious to know how accurate my Nikon 440 laser range finder and Suunto clinometer are when compared to a tape drop. To my knowledge there hasn't been a careful experiment done to answer that question for the Nikon 440. The manufacturer-stated accuracy of the TruPulse 200 is +/- 0.1 yards and for the Nikon it is +/- 0.5 yard. It is widely accepted that the accuracy of the Nikon 440 can be improved through instrument calibration. Even so, I embarked on this study with the expectation that the Nikon 440 might only be accurate to within 3% of tape drop accuracy. I'm happy to say that I had underestimated the Nikon's capabilities.

Study methods.

I measured the total height of 4 loblolly (Pinus taeda) conifers ranging in height from 126 feet tall to 141 feet tall. The pines were situated on 3 sites near Chapel Hill, NC that I located using LIDAR data obtained from Doug Newcomb, Cartographer at the Raleigh, NC Field Office of the US Fish and Wildlife Service. The first two pines are located in a stately grove of Loblolly pines along Morgan Creek near the NC Botanical Gardens. Here's a 360 panorama of that grove: http://photosynth.net/view/bbe1eb38-88f ... 51f3244b86. I used satellite imagery from Google and Bing to narrow the list of sites to those on publicly accessible land that were most likely to contain tall pine trees. Loblolly pines are common in the Piedmont of North Carolina and are ideal for this experiment because they have tall, straight boles and conical tops with easily identified height maxima.

I measured the trees from the ground first using the NTS sine method. Each tree was measured from at least three locations on different sides of the tree, often on 2 different days.

I had previously calibrated my Nikon 440 to determine the needed correction factor (see http://www.ents-bbs.org/viewtopic.php?f=235&t=4862). I recalibrated it in February 2014 with nearly the same results. I should point out that I have found it impractical in a woods setting to always step back or step forward to LRF "click over" in order to take a measurement -- usually there is only a small window through which to point the laser and often taking a step back or forward puts underbrush clutter in the way of a clear view to the tallest point of the tree. For this reason when I calibrate my LRF, I average the reading of 4 measurements for each reference point -- 2 readings walking backward to click over and 2 readings walking forward to click over.

Here are the details of my calibration protocol: I calibrate the LRF by measuring the distance to the side of a brick shed at the end of a long, level parking lot. I stake the end of a 300 foot tape measure at the base of the shed and extended it past 80 yards (240 feet). I record the actual distance (tape measure reading) at 10 yard intervals between 20 yards (60 feet) and 80 yards (240 feet) as measured on the LRF. For example, I step backward until the LRF says 20 yards and then record the actual distance from the tape measure. Then I step forward until the LRF reads 20 yards and record the actual distance at that point. I repeat both measurements once more and then average all 4 measurements for the 20 yard distance. Then I repeat that process for the 30, 40, 50 , 60 , 70 and 80 yard reference points. At each point the standard deviation of the 4 averaged measurements was between 0.4 and 0.5 feet meaning that most any measurement returned by the LRF can be trusted within an accuracy of 6 inches or less. Comparing the LRF reading at each 10 yard reference point to the average of the 4 measurements from the tape measure allows me to determine a correction factor for each range distance:
  • subtract 0.8 feet for measurements between 0 and 59 feet (0 and 19.9 yards)
    subtract 0.9 feet for measurements between 60 and 89 feet (20 and 29.9 yards)
    subtract 1.0 feet for measurements between 90 and 119 feet (30 and 39.9 yards)
    subtract 1.1 feet for measurements between 120 and 149 feet (40 and 49.9 yards)
    subtract 1.1 feet for measurements between 150 and 179 feet (50 and 59.9 yards)
    subtract 1.2 feet for measurements between 180 and 209 feet (60 and 69.9 yards)
    subtract 1.2 feet for measurements between 210 and 239 feet (70 and 79.9 yards)
    subtract 1.25 feet for measurements over 240 feet (over 80 yards)
I use a spreadsheet program on my iPad to calculate the total height in the field based on the equation:
  • Height(feet) = [[[LRF(top) * 3] + CF] * sine of angle(top)] + [[[LRF(base) * 3] + CF] * sine of angle(base)]

    LRF is the reading from the Nikon 440 in yards
    CF is a correction factor determined from the calibration process
I did not calibrate my Suunto clinometer since extensive conversations between Karl Heinz, Bob Leverett and others in this thread (http://www.ents-bbs.org/viewtopic.php?f=235&t=4876 and math I don't completely follow) indicates that clinometer error is essentially negated when combining crown and base angle measures.

Results.

Angle, distance and resulting sine-based height calculations are listed in Table 1 along with the CBH, date of measurement, and rough GPS coordinates of each tree.

Within a few weeks of the ground based measurements I climbed each tree and measured the trees by tape drop. It is best to have a ground helper when performing a tape drop, but I couldn't convince anyone to come out to the woods with me for a few hours at a time in February/March. The person on the ground is helpful because they can position the tape at the correct point at the base of the tree and provide tension while the climber reads off the measurement. A ground person with the right perspective can also let the climber know when a telescoping measuring pole is at the same height as the tallest twig of the tree.

Since I was performing the tape drops myself, I carried a 200 foot construction tape measure into the canopy and lowered the end directly to the ground using a brightly colored, 1 pound throw bag as weight. In each case it was easy to tell when the bag hit the ground both by visual confirmation and because the tension on the tape relaxed. In each tree I could climb safely to within 10 feet of the highest point. When I reached that point I used a metal tape measure to record the remaining distance to the top of the tree. Then I added the numbers from the upward measurement to the tape drop measurement to obtain the total height. Although I did not have a ground helper, I have no reason to believe that my tape drop measurements are off by more than 2 inches. Tape drop measurements, dates, and comparison to sine-based ground measurements are listed in Table 1.

Table 1(click on the table for a larger view)
loblolly height data.jpg
Conclusions.

1). The average % divergence was 0.49%, but that value is misleading because some LRF values are high (positive % divergence values) and some are low (negative % divergence values) so the average looks artificially low. For that reason it is more informative to look at the absolute value of the % divergences. The average of the absolute values of all the divergences was 0.88% with standard deviation = 0.57%. The range of the divergences was -1.83% to +1.59%. These numbers are almost exactly what Don Bragg and his coauthors reported for the TruPulse in the paper mentioned in the first paragraph above.

2). I have heard some NTSers state that when taking multiple sine based measurements on the same tree they will throw out all but the highest measurement assuming that in that attempt they found the true highest point in a nested crown and in the others they were not measuring the highest sprig in the crown. Interestingly, I noticed that in 2 out of 4 trees in this small study, the highest LRF measurement I recorded was actually the most accurate measurement (lowest % divergence from tape drop). (The highest LRF measure for each tree is colored red in Table 1 above.) This observation lends some credibility to the practice of throwing out all but the highest sine-based height value. However, even though the tallest measurement was the most accurate in half the cases, it was also an overestimate of the true height in 4 out 4 cases.

3). In 3 out of 4 cases (Loblolly #4 being the only exception), averaging the LRF measures from different sides of the tree resulted in a height value that was closer to the tape drop measure. That leads me to conclude that when possible it is better to average multiple measurements from different locations around the tree.

Overall, I'm happy to learn that the Nikon 440/Suunto clinometer pairing is very good at estimating the height of woods grown trees up to 140 feet tall. I think it is safe to reaffirm that the Nikon 440 is an excellent low-cost alternative to the TruPulse brand hypsometers and that % divergence from tape drop measurements is comparable between the two instruments.

Please let me know what you think...

Lastly, here are some pictures of the trees from the ground and from the crown. Enjoy!

Loblolly #1

Click on image to see its original size
view form top of Loblolly #1

Click on image to see its original size

Loblolly #2

Click on image to see its original size
view from top of Loblolly #2

Click on image to see its original size

Loblolly #3

Click on image to see its original size
view from top of Loblolly #3

Click on image to see its original size

Loblolly #4

Click on image to see its original size
View from top of Loblolly #4

Click on image to see its original size
Last edited by pdbrandt on Tue Apr 01, 2014 10:38 am, edited 1 time in total.
Patrick

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Will Blozan
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Re: Comparing tape drop height to that obtained with Nikon 4

Post by Will Blozan » Mon Mar 31, 2014 4:38 pm

Patrick,

Excellent! I'm pretty darn sure all those hemlocks were from the Tsuga Search project and measured via Nikon 440. When Jess and I found a superlative hemlock we would monument mid slope with a thumbtack and then use it for the tape drop. This way the same base is used.

Will

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pdbrandt
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Re: Comparing tape drop height to that obtained with Nikon 4

Post by pdbrandt » Tue Apr 01, 2014 6:58 am

Will Blozan wrote: Excellent! I'm pretty darn sure all those hemlocks were from the Tsuga Search project and measured via Nikon 440. When Jess and I found a superlative hemlock we would monument mid slope with a thumbtack and then use it for the tape drop. This way the same base is used.
Will,

That would explain why the % divergence numbers are essentially the same! From the paper it sounded like most of the hemlock measurments were taken with a TruPulse. It was still good for me to convince myself of the accuracy of my own Nikon 440 -- and I'm always looking for an excuse to get into the woods to find, measure, climb, and appreciate impressive trees like these.
Patrick

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dbhguru
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Re: Comparing tape drop height to that obtained with Nikon 4

Post by dbhguru » Tue Apr 01, 2014 9:40 am

Patrick,

We congratulate you. Your report bolsters other research that supports the use of the sine method, but you go farther by illustrating laser calibration and its inclusion in the actual measuring. I encourage you to send a Word version of your post to Dr. Don Bragg for inclusion in a future edition of the Bulletin of the Eastern Native Tree Society. But now I'd like to deal with one point in your post. First a quote.

I did not calibrate my Suunto clinometer since extensive conversations between Karl Heinz, Bob Leverett and others in this thread (viewtopic.php?f=235&t=4876 and math I don't completely follow) indicates that clinometer error is essentially negated when combining crown and base angle measures.

Here is an Excel example illustrating what we're talking about. I'll first present the diagram and then make comments.
Screen shot 2014-04-01 at 10.24.56 AM.png
When a mechanical clinometer is out of calibration, it is often off either on the high or low side by some amount such as a quarter or half a degree, i.e. the direction of the error stays the same whether pointing the instrument up or down. If a clinometer reads high, it means that the clinometer's role in the calculations will be to add an erroneous height component for heights above eye level and subtract it for heights below eye level. If the clinometer error is under, them the impact in total height will be the opposite of the above - of course. But our point is that the errors often almost cancel one another for mechanical clinometers. This is an observation that Ed Frank made and stressed long ago.

In the diagram, I added a quick way of evaluating the impact of angle and/or distance errors using differential calculus. The formula for dH gives the height error associated with an angle error dA and/or distance error dL when using the sine method. Note that dA, dL, and dH are just variables in the equation, but the value of dA and dL must be small relative to A and L for differentials to work. There is an equivalent formula for the tangent method, but I won't complicate the discussion by including it here. Oh yes, dA must be in radians in the formula, so that if your clinometer is off a half degree, the equivalent radian measure is 0.5(π/180). There is an Excel function named RADIANS that converts degrees to radians. So 0.5(π/180) and RADIANS(0.5) return the same value, i.e. 0.0087. Angles feed to trigonometric functions in Excel must be in radians. I expect that degrees versus radians causes lots of headaches for people who do not think in mathematical terms. Just remember, you can use the Excel function to RADIANS to convert degrees to radians. Conversely, you can convert radians to degrees using the Excel function DEGREES. RADIANS AND DEGREES are inverse functions of one another.

As a side issue, part of training for the National Cadre for support of American Forest(likely an NTS role) is doing just what you did. Each member must develop an understanding of what causes errors and sense of where the errors are significant and where they are not. Your actual climbing the trees and documenting what you measured is immensely important. Also, it is critically important to know what point in the crown or at the base is being measured, and as we all know that requires practice, practice, practice. Identifying the tips and developing better field methods to do so is where those of you who climb can really contribute.

Again, thanks for the post, and all the work that went behind it. You make us proud.

Bob
Robert T. Leverett
Co-founder, Native Native Tree Society
Co-founder and President
Friends of Mohawk Trail State Forest
Co-founder, National Cadre

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Matt Markworth
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Re: Comparing tape drop height to that obtained with Nikon 4

Post by Matt Markworth » Tue Apr 01, 2014 8:27 pm

Patrick,

Cool study! I've thought of doing something similar using a pedestrian bridge or a fire tower, but haven't found anything quite tall enough, so it's really cool to see these results.

I know what you mean about not always being able to utilize click-over when only small windows to shoot through are present. If I'm understanding your method correctly, you used click-over points as a way to establish correction factors, but didn't utilize click-over when measuring the trees. Utilizing click-over (when possible) would probably result in heights even closer to the tape drop. Another technique that I find helpful is leaving the tape wrapped around the tree at 4.5' while I'm searching for the top, especially on uneven terrain. I can shoot to the tape from any side and don't have to worry about slight differences in the mid-slopes being selected. Of course, then I just have to remember to add 4.5' to my final height.

Again, nice work!

Matt

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pdbrandt
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Re: Comparing tape drop height to that obtained with Nikon 4

Post by pdbrandt » Wed Apr 02, 2014 7:02 am

dbhguru wrote: When a mechanical clinometer is out of calibration, it is often off either on the high or low side by some amount such as a quarter or half a degree, i.e. the direction of the error stays the same whether pointing the instrument up or down. If a clinometer reads high, it means that the clinometer's role in the calculations will be to add an erroneous height component for heights above eye level and subtract it for heights below eye level. If the clinometer error is under, them the impact in total height will be the opposite of the above - of course. But our point is that the errors often almost cancel one another for mechanical clinometers. This is an observation that Ed Frank made and stressed long ago.

Bob
Thanks for the encouragement, Bob, and thank you for showing the calculations to prove clinometer error can be neglected in most cases. Your table helps me see why. What I take from your explanation is that it is advisable to avoid measuring a tree from below the level of the base of the trunk, as you might be tempted to for a tree on a steep hillside. If you measured up to the crown AND the base of the tree the clinometer error would be compounded. In contrast if you measure up to the crown and down to the base of the tree the clinometer error negates itself. Thanks!
Patrick

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edfrank
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Re: Comparing tape drop height to that obtained with Nikon 4

Post by edfrank » Wed Apr 02, 2014 7:22 am

Patrick,

I talk about clinometer error here: http://www.nativetreesociety.org/measur ... sic_3a.pdf
Is my 0 degree reading really level?

These are precision instruments and if they are not reading exactly
level, they should be really close. You can test to see if the instrument is reading exactly level with the
help of another person or some creativity on your part.

Sight with the clinometer from a marked point on a tree or pole toward another distant object. Have an
assistant mark the point on that distant object that the clinometer or instrument says is level. Move to
that spot and sight back to your original position. If it is perfectly accurate the back-sight will be right on
the point you shot from originally. If it is reading high, then the angle it is off will be under-reading by
arc tan [(0.5 x error)/distance] = reading error in degrees,

where distance in the above formula is the distance between the two targets and error is the
distance on the original pole or tree between the original mark and where the sighting from the
second target falls on the original pole or tree.

If it is pointing lower than the starting point, then it is reading high. The calculations are the same. In
this way you can tell at least if the original level line is actually level or not (Frank 2005). In trigonometry
arc tan is the inverse of the tangent function. On most calculators it is a second level function marked as
tan-1 on the keypad. What this means is that instead of using the tangent function to calculate a height
from and angle and distance, the height and distance are being used to calculate an angle. Stated
another way, the tangent returns the ratio of the opposite side to the adjacent side for the included
angle, and the arc tangent returns the included angle from the ratio.

Even if the instrument is off by a few tenths of a degree, this does not substantially affect the accuracy
of the readings when employing the sine method that will be described later in detail. John Eicholz
wrote (Nov 10, 2003):

“I think I can prove mathematically that the error in tree height that results from each degree of
clinometer error is approximately between 1.75% and 1.9% of the horizontal distance to the
trunk... Because the factor: (1/cos(@))*(Sin(@)-sin(@+e)) is nearly a constant! Its range is a
smooth progression from 1.74% at 0 degrees to 1.9% at 80 degrees. I think I'm always within +/-
0.4 degrees with my Suunto. This translates to +/-0.8 feet per segment on a 100 foot baseline,
or +/-1.6 feet overall.”

Basically what that means is that the error added or subtracted by a misreading clinometer is essentially
cancelled out by an error in the same direction at the base of the tree, when using the sine method.
When using the tangent method any errors in the calibration of the clinometer do not cancel out and
are incorporated as an error in the final height calculation.
So this shows how you can measure the amount your mechanical clinometer is off from true. If you measure this value and you do happen to measure a tree whose top and bottom are both above the eye level of the surveyor, you can correct for any angle error that is introduced. The amount of angle error is the same at both the top and bottom, and will not change over time - so you only need to make this measurement once.

Edward Frank
"I love science and it pains me to think that so many are terrified of the subject or feel that choosing science means you cannot also choose compassion, or the arts, or be awe by nature. Science is not meant to cure us of mystery, but to reinvent and revigorate it." by Robert M. Sapolsky

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mdvaden
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Re: Comparing tape drop height to that obtained with Nikon 4

Post by mdvaden » Wed Apr 02, 2014 7:52 am

Just got up, so it's way to early to read a lot of your post, but I read the first part.

Now, it's not the NIkon, but Taylor and I used the Impulse 200 LR for the world's tallest pine that's close to 268' tall, and I recall the tape drop differing from our laser measurement by 1 or 2 millimeters.
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pdbrandt
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Re: Comparing tape drop height to that obtained with Nikon 4

Post by pdbrandt » Wed Apr 02, 2014 7:56 am

Matt Markworth wrote:Patrick,

Cool study! I've thought of doing something similar using a pedestrian bridge or a fire tower, but haven't found anything quite tall enough, so it's really cool to see these results.

I know what you mean about not always being able to utilize click-over when only small windows to shoot through are present. If I'm understanding your method correctly, you used click-over points as a way to establish correction factors, but didn't utilize click-over when measuring the trees. Utilizing click-over (when possible) would probably result in heights even closer to the tape drop. Another technique that I find helpful is leaving the tape wrapped around the tree at 4.5' while I'm searching for the top, especially on uneven terrain. I can shoot to the tape from any side and don't have to worry about slight differences in the mid-slopes being selected. Of course, then I just have to remember to add 4.5' to my final height.

Again, nice work!

Matt
Thanks, Matt. I thought of doing a simpler study from the top of a building on UNC campus where I work, but getting access to the roof is not easy and the spectacle that would likely occur as I dropped a tape measure off the side of the building is a little more attention than I am comfortable with! The ideal "building" on campus would be our ~170 foot tall bell tower with an open cupola at the top, but it is closed to the public except one day per year when they do tours for the Rich and Famous. My guess is the folks in charge wouldn't be too keen on me dropping a tape from the cupola with all the potential donors down below. Your idea to use a bridge over a deep gorge would be perfect if you can locate bridges between 100-200 feet tall.

You're right about how I use the click back and click forward values for LRF calibration. At each reference point I looked at, the difference between the click back point and click forward point was 5 inches at the least and 10 inches at the most. By taking the average of the click back and click forward points during calibration, and then concerning myself primarily with finding the best sight line to the crown in the field (ignoring click over), I'm assuming that in the field I will never be off by more than 10 inches and usually I will be off be no more than 5 inches. Whatever absolute error there is in the distance measurement to the crown and base will be reduced when taking the sine of that value, too. I do like your idea of keeping the D tape around the trunk to aid in taking the base reading, but am I correct in thinking that you would still have to stand at the same elevation compared to where you took the crown measurement in order to not introduce error from moving between crown and base measurements?

Thanks again, Matt and everyone! I find this topic fascinating!
Patrick

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pdbrandt
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Re: Comparing tape drop height to that obtained with Nikon 4

Post by pdbrandt » Wed Apr 02, 2014 8:01 am

mdvaden wrote:
Now, it's not the NIkon, but Taylor and I used the Impulse 200 LR for the world's tallest pine that's close to 268' tall, and I recall the tape drop differing from our laser measurement by 1 or 2 millimeters.
Wow! That is impressive for a ground based measurement!
Patrick

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