But how big --exactly-- are the pines in the Pine Orchard? I measured a few trees and the largest one I found has a diameter of 51 inches; just over four feet. I took this measurement by stretching a cord around the tree four and a half feet above the ground. The distance on the cord measured 161 inches and dividing that by 3.14 yields the diameter: 51 inches. That's not the six to seven feet that some have reported but I might not have measured the very largest trees. And while measuring the diameter at four and half feet is standard practice in forestry circles, others might have done it differently.
I'm interested in the history of the Adirondack forests and the large old trees have stories to tell. So I look for them when I hike. Over the past several years whenever I've spotted a large tree I've noted the location and estimated the size. Now that I've refined my measurement technique I see that my past estimates may have tended towards the high side (No, Dad, this does not apply to fish I've caught in the past). I carry an old ski pole as a walking stick and I've used the pole as a gauge for estimating tree diameters. I now see that this technique is insufficiently precise. In the Adirondacks, trees with diameters of 36-40 inches are found in many places. Trees of that size will typically be more than 125 years old and a stand containing many trees of that size may have been passed over, or selectively logged, in the first wave of industrial logging. That first wave took place after 1850 and continued into the early part of the 20th century. You can also find trees with diameters larger than 40 inches scattered about in the Adirondacks, but these are much less common. These trees were almost certainly standing before 1850. The really big and old trees, with diameters of 44 inches or larger, are rare. The Pine Orchard contains a number of trees in the 44-48 inch range and estimates that I've seen place the age of the stand at over 200 years. (Note: the correlation between tree size and age varies with species and growing conditions).
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The Pine Orchard: Old Growth Forest
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The Trail and the HikeThe route I followed leaves the Pumpkin Hollow road at the Murphy Lake trailhead. As with the the trail to Wilcox Lake this route is marked and maintained as a snowmobile trail. The 1994 ADK guide to Trails of the Southern Region described this trail as indistinct and hard to follow. That Guide advised that this route should be attempted only by hikers skilled with map and compass and it went so far as to say that the trail was not recommended for parties of fewer than three people. |
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There is also a meaningful discrepancy in the length of this route as stated on signs and as printed in various guides. As measured using GPS my hike covered a total of 11.8 miles. This included a bit of wandering around so the sign board at the road which states the distance to the Pine Orchard as 5.6 Miles is reasonably accurate. The 1994 ADK Guide lists the distance at 6.6 miles one way. And a third distance, derived by adding up distances seen on signs along the way, yields a total of 4.2 miles. Applied to the round trip, the difference between the shortest and longest mileage is over four miles. That's a serious lack of accuracy.
There are two apparent sources for the uncertainty. The first is that there is no distinct point or boundary to mark your arrival at the Pine Orchard. The lack of a clear "here it is" location accounts for a tenth mile or two of the discrepancy. This is a question of precision. Lacking a distinct end-point it's difficult to measure the distance to the tenth of a mile precision typically used on trail signs. The second consideration is that over the past 30-40 years the trail has been re-routed, probably more than once. The 1994 ADK Guide alludes to this noting that the trailhead had been moved to avoid a crossing of private land. This is also evident in an old sign seen at the junction with the Flatters trail. The sign says that it is 2.6 miles to the "Willis Lake Road" but the trail doesn't go to the Willis Lake Road. That was probably the original starting point. If the sign stated the distance as "a few miles" it would be more accurate but not very precise. As it sits, it is neither.
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Uncertainty, Accuracy and Precision
Measuring the diameter of a tree is pretty easy. And collecting measurements from many trees is a straightforward process:
- Measure the tree
- Record the location
- Record the species
- Note unusual or complicating factors
- Repeat
That sounds easy enough, and it is easy. Which is why I am continually surprised by all the different ways that uncertainty creeps into the data. Part of it comes from doing this work in the Adirondack Biting Insect Preserve. During the warm months you encounter many many small complications and distractions and for the rest of the year your fingers will be numb making it difficult to write out notes. But sometimes I run into more specific issues:
- Diameter: What about double-trunk trees? Or trees in difficult locations? What if there is a branch or some other oddity at the 4.5 foot height where I want to measure?
- Location: Assuming that the accuracy level of your GPS device is good enough, and assuming that you have a good signal from several satellites, and assuming that you correctly note which location goes with which tree, it nothing more than the push of a button.
- Species: I'm familiar with most tree species seen in the Adirondacks, especially the species that get to be big. Still, when I have gone back and looked at the same trees a second time I've found that I get some of the them wrong.
- Notes: Some days I do a good job of recording the unusual or complicating factors and some days not so good. And this information often turns out to be important when trying to draw conclusions from a body of data.
On one point I have no doubt. All non-trival data contains errors and considerations of precision and accuracy are relative to the intended use. These are the sources of uncertainty.
A Couple of Miles: I was just being accurate
As often happens, the use of a tool under less than ideal conditions leads to a deeper understanding how the tool works. Using GPS to record locations and to record the tracks I've follow has given me a deeper understanding of how the system works. I'm going to return to this topic in the future but a few key points go right along with the theme of this post. First, take a look at image five. The lines show a short section of the track captured by my GPS receiver on the hike to the Pine Orchard and back. The line on the left was from the inbound leg of the trip and the line on the right is from the return trip. I walked the same path both ways so it's odd that the the lines are so far apart. To get to the bottom of this you need to know something about how I hike.
I took much longer to complete the trip to the Pine Orchard then I did on the return and this is typical for me. And this was not because of the terrain. The route crosses a couple of small ridges but there is very little difference between the elevation at the turn around point. It's counter intuitive, but I typically travel at a slower pace on the way in because I'm fresher. On the way in I stop to record measurements, I take photos and I generally take more time to enjoy the forest the scenery. On a hike of this distance by the time I'm half way back to the car I'm starting to get tired. And this is the counter-intuitive part, I tend to walk faster and I move along without stopping. On this particular day, it was hot and by the time I reached the area shown in image five I'd been hiking for over five hours. It was also into the early afternoon and I was I not hiking alone. I was traveling with dozens of new (and now really annoying) friends that I'd made along the way. Deer flies, midges, mosquitoes and a few too-stupid-to-just-give-up-and-die black flies. The bug spray that had been mostly effective earlier in the day was no longer working.
A GPS track like the one shown in the image is recorded as a series of points. Every second or so (this will vary based on the device) the GPS receiver calculates your location and stores the coordinate pair representing that location. When you stop the receiver gets extra time to correct for errors so stopping periodically improves the accuracy of the track overall. This is especially true when walking through a dense forest where the strength of the signals is reduced by foliage. In image five I added a note to a place where it looks like I took a short side trip off the trail. But I know that that never happened. What did happen is that the GPS recorded a couple of points with much lower accuracy and those points became part of my route. If I was planning to use this track as data I would need a method to clean up these kinds of errors.
There are many factors that limit the best case accuracy of GPS. A GPS receiver captures signals sent by satellites orbiting the earth and when the receiver has signals from at least three of these satellites it can calculate your location. The U.S. GPS system uses a constellation of 32 satellites positioned so that there should always be at least three satellites above the horizon and "visible" to a GPS receiver located anywhere on the earth. Under good conditions a typical consumer GPS receiver can fix your location to within about 10 yards -30 feet- using signals from three satellites (four are required to also calculate your elevation). At that accuracy level you use the coordinates calculated by the receiver and place a point on a map. Then you draw a circle with a diameter of 30 feet around the point. Your actual location lies somewhere in that circle.
Depending on what you are trying to do that may or may not be accurate enough and it's usually possible to get much more accurate data. For instance, it's common for there to be more than the minimum of three satellites available to your receiver. Modern GPS receivers including the ones found in most smart phones, use the "extra" satellites to average out some of the errors that otherwise limit GPS accuracy. For example, when I save a waypoint (the coordinates for a single location) using my Garmin GPS it tells me how accurate the fix will be based on the set of satellites available to it. The use of additional satellites and averaging commonly improves accuracy into the ten to twenty foot range. On the other hand, dense foliage, cliffs, mountains and other obstructions reduce accuracy or prevent the receiver from getting any fix at all.
The point is that data taken from measurements is always uncertain to some degree and the level of uncertainty varies based on the specifics of how you gather the data and your intended use. You have to ensure that your data is accurate enough for the intended use and you have to avoid mis-representation by overstating the level of precision. When I use a cord to measure the circumference of a tree, if my measurement is accurate to within one inch then I can state the diameter in inches. Dividing the circumference by Pi to get the diameter will almost always yield an answer with a remainder, something like 45.3. But the .3 must be thrown away. The accuracy level of my measurement does not support that level of precision. If a trail sign states a distance as 2.6 miles, then assuming typical rounding to the nearest tenth we can say that it's accurate if the actual distance is between 2.55 and 2.65 miles. Assuming, of course, that it's the correct sign for the trail you are on. My GPS gives me coordinates with 6 decimal places of precision. That's precise enough to separate locations that are just inches apart. But the device is not nearly that accurate and the last digit (and maybe the last two) should be discarded. The extra precision is meaningless at best and misleading at worst. Whenever we take measurements there is uncertainty and the level of precision we use should not overstate the accuracy of our technique.
You see kids, when I said it was a "couple miles" I was giving you the most accurate answer that I could.