Prisms

[Tom]

What is a Prism for and how do you use it when cruising tree plots?

[OneWithWood]

I knew!  I knew!  But I forgot :-[

I think Ron posted about prisms in the knowledge base - something about laying out an area and counting trees or dangling them from a string and watching all the cool colors - no, that was a different thread - go with the layout scenario.  I'm sure Ron will be along shortly with the tutorial.  ;)

[Dodgy Loner]

Actually, Tom, in a prism cruise, there are no "plots".  Rather, a prism cruise is deemed a "point sample", because unlike the more familiar (and easier-to-understand) plot cruise, there are no plots in a prism cruise.  It would take more time to write a thorough description of point sampling than I could possibly devote, so instead I will loosely quote a lesson plan from my undergradutate curriculum:

"Point sampling
Probability Proportional to Size (PPS) or point sampling has been widely used in forest inventory. It is the method of selection of trees based on their size rather than their frequency of occurrence. In point sampling, inclusion of a tree in a plot depends on the basal area (cross sectional area of a tree at breast height) of the tree and its proximity (distance) to the sample point. With point sampling, you are most likely to sample big trees. Thus, in other words it is called probability proportional to size (PPS). Point sampling is known with different names – angle count sampling, plotless cruise, prism cruising, variable-plot sampling, variable-radius plot and most commonly, point sampling.
The procedure to sample trees in the forest stand is simple and easy to use in the field, therefore it became popular among natural resource managers and ecologists. The instruments used in point sampling are wedge prisms and angle guages.

The basal area factor (BAF) is the number of units of basal area per acre (or per hectare) represented by each tree tallied in point sampling. In point sampling;
• Do not need direct measurement of either plot boundaries or tree diameters to figure out which trees are in and what basal area per acre is
• Use a fixed angle to determine which trees are in
• Each tree has it's own plot with a radius proportional to its diameter. It means the probability of tallying a tree depends on its cross-sectional area (diameter) and the sighting angle used
• The imaginary tree plots vary with tree size, such that big trees have big plots and small trees have small plots.
• Plot size is such that each "in" tree represents the same amount of basal area per acre.
• The smaller the sighting angle of prism or angle gauge, the more trees included in the sample.

Wedge prisms are used to determine whether or not to count a tree at a point sample. The prisms we have for class are 10 BAF prisms. Trees are counted as in, if the offset image at breast height viewed through the prism and the actual image of the tree have some overlap. If there is no overlap, the tree is not tallied.   With a prism the PRISM is the center of the point and must be held over your point center marker.



Borderline trees: For borderline trees, measure the dbh and the distance to the tree. The distance should be measured to the "center" of the tree, NOT THE FACE of the tree.   If the tree is equal to or closer than the limiting distance for its dbh, then it is tallied. Limiting distances for 10 BAF prisms and gauges are listed in the table below.  The table goes to 10ths of an inch. For an example, the limiting distance for a 15.4 in dbh tree is 42.35 feet . Any 15.4 in dbh tree 42.35 ft or closer to the sample point is counted.   If you forget your table, but have a calculator, you can determine the limiting distance in feet for a tree by multiplying the diameter (in inches) by 2.75 (for BAF 10 sampling only).  For instance, a 10.0" tree can be 27.5 feet away,

Common sources of error:

1. Not measuring borderline trees.  Do not count every other one.  Most people are biased one way or the other when they determine borderline trees, especially when they just start out.
2. Not holding the prism over plot center.
3. Missing "hidden" trees.  If a tree is behind another tree, carefully step to the side of your point center while keeping the same distance from the tree.  You should then be able to see if it's in, out or borderline.
4. Missing far away big trees.  It's important to look out in the distance for larger trees.  A 30.9" white pine can be 84.97 feet away and still be in!
5. Using a different prism or other measuring device than that which you normally work with."

Obviously, point sampling is a complicated procedure, and I'm sure that this description will probably lead to more questions than answers.  I would not recommend point sampling for anyone without hands-on experience and training.

[Ron Wenrich]

I prefer the angle gauge over the prism.  They're cheaper and practically indestructible.  Anyone who is thinning down to a residual stocking level can use one.  They come in real handy. 

The angle gauge differs from the prism by using your eye as the center point as opposed to the prism.  Your not refracting light with the gauge.  There are still count, no count, and border trees.  But, instead of an offset, your tree will all be in a line.  If the tree is bigger than the gauge, its a count.  If it is smaller than the gauge, its a no count.  If the gauge and the sides of the tree match, its a borderline tree.

For the average landowner, he can go out and figure out which trees he wants to keep, and which should go.  Most people use a BAF (basal area factor) 10 gauge or prism.  That means each tree that counts represents 10 sq ft of basal area/acre.  If the actual basal area of the stand is something like 114 sq ft, then you're only going to have 11 or 12 count trees.  It isn't exact for each area, but gives a good idea.

So, you have a little basic knowledge of your current point.  You want to know if you should thin or let it alone.  If your optimum stocking is 70-90 (pretty much the case in many hardwood stands), then you should be trying to get 7-9 crop trees that count at your point.  Sometimes that's easy, sometimes its not. 

For the easy part, select the best 7, then try to thin from the others.  You want to thin those that are the poorest quality. 

For areas where it is hard to get 7, you can do other types of silvicultural work.  You could do a small clearcut, or a small seedtree or shelterwood cut.  You should have enough area that makes it effective.  You're looking at improving the regeneration in these areas, so you don't want to leave junk.  At your next thinning, you may want to remove the overstory to release your new regeneration.  It has all the makings of uneven aged management.

[SwampDonkey]

Remember this thread Tom?  ;D

https://forestryforum.com/board/index.php?topic=16165.msg231621#msg231621


Might want to scroll up a couple posts for more info in that thread.

[Tom]

So, in determining Basal area, out of 10 trees, 3 are 30 inch and are excluded by the prism and 3 are 5 in and excluded by the prism and 4 are "in" trees, this after examining all of the trees on the plot says that the plot holds 40 square feet of basal area?

How does this relate to number of trees?  Or, are the two not comparable?

Is the prism just a means for determining the size of the plot to be counted, or which trees get counted inside of a predetermined plot?

Hmm  MIght need someone to get a bunch more elemental here. 

[Ron Wenrich]

Your 40 square feet would be the correct assumption.   You're only counting the "in" trees and excluding all others.

You can figure out the number of trees per acre, but it is better to do this with more than one data point to have any significance. 

Here's how point sampling works.  Each tree has a plot radius where it can be measured.  Think of it as a circle around a tree.  If you happen to be standing inside that circle, then you'll count that tree.  For BAF of 10, the plot radius in feet computes out to the dbh in inches x 2.75. 

So, for your 5" tree, it would have a plot radius of 13.75'.  That means if you stand closer than 13.75', you'll count that tree.  Stand further away, then you won't.  Your 30" tree will have a plot radius of 82.5'. 

What happens when you take a reading is that you are measuring all those trees that you are standing in their plot radius.  There are a lot of overlapping circles.  Larger trees make larger circles.  As you move, those overlapping circles move.  Some go away and new ones come into play.

Now, if you have the plot radius, you can figure your plot size in acres.  Figure up the area of the circle, then divide by 43,560.  1/plot size will give you the number of trees of that size per acre that tree represents. 

[Tom]

Oh-h-h!   I've got lights coming on everywhere. :D    So, the context with which I should be considering prisms or angle gauges is How many trees on that plot are of that particular size.

Elementarily, If I wanted to include a different size tree, I would recount the plot for the basal area of that tree and add it to the first, continueing to do this until I had counted the basal area of the range of sizes in which I was concerned.

So, if I were counting 5" trees, I would use the prism to determine how many were within the 13.75' radius circle.  Then I would move, perhaps, 27.5' and count the "in" trees in that circle, with each new circle increasing my percentage of sampling.

If I'm getting close, I need cogitate on this a bit and get it to sink in.  If I'm off base i'll go back and read a little slower.  ;D   :P 8)

[SwampDonkey]

Ron's 2.75 is what is called the limiting distance factor (LDF).

LD = diameter at breast height/(12 in_/foot x K)

where: K=sqroot(BAF/10890ft²_/acre) = 0.0303, where BAF is basal area factor, in this case 10 ft²/acre.

LD = Diameter/(12 in_/foot x 0.0303) equivalent to Diameter x 2.75  just a little math juggling. ;)

We were doing point centres at 25 meter intervals and 50 meters between strip lines and a huge old western red cedar fell in 4 plots.  And we were using a 12.25 m²/ha prism, actually a reloscope. ;D

For density, all you need is a spread sheet or Tree Factor tables for that prism BAF.

TF=BAF/(0.005454 X Diameter Class^2)

ooops another constant, 0.005454 comes from pi/(4 x 144 in²/ft²) area of a circle converted to ft² from in², since you measure diameter in inches. Just another constant to remember without going through all the math. ;D

Now take your calculated TF for that diameter 'class' and multiply by trees tallied for that diameter 'class' and divide by number of plots sampled to calculate the density. Now add them all up for total density. That's why it's nice to use a spread sheet. ;)

[WDH]

You are pretty close, Tom.  Imagine that you are sampling a tree with a limiting distance of 37.2 feet.  That is equivalent to a plot of 1/10th acre (a circle with raduis of 37.2 feets is 1/10th acre in size).  If there is one tree that is counted "in" at that sample point of that DBH (13.5") then that is one tree per 1/10th acre which is the same as 10 trees in 1 acre.  If there are three trees of that size that are 37.2 feet or less from your sample point, that is equivalent to 30 trees pere acre.

So at a sample point, the area represented by each tree is different depending on its size.  So, you figure each sampled tree separately to determine the area it represents and convert that to a per acre basis.  Say there are two trees counted "in" by the prism at the first sample point.  One is 13.5" DBH, and one is 16.0" in DBH.  The limiting distance on the 13.5" tree is 37.2 feet which is equivalent to a circle with an area of 1/10th acre.  So finding one in 1/10th acre is like finding 10 in one acre.  The 16" tree has a limiting distance of 44 feet.  A circle of 44 feet represents 1/7 acre (rounded).  So 1 tree in 1/7 acre is the same proportion as 7 trees on one acre.  So adding the two together, there are 10 trees per acre represented by the 13.5" DBH tree and 7 trees per acre represented by the 16" tree, so the total trees per acre represented at the sample point with 2 trees counted "in" relates to 17 trees per acre.   

The number of trees/acre represented by each tree counted "in" is a function of the size of each tree counted "in", so the total trees/acre is the sum of the total represented by each tree in the sample.  Got it ???.

[Texas Ranger]

DanG, all them numbers make my head ache.  I built a spread sheet that takes all the math out of the calculations, and gives me the number of trees, sizes, volume, value, trees per acre, etc.  And built it for a  bunch of form classes, took a while, but cut down on time later.

Simply put, Tom, you take a talley book, establish a variable plot with a prism, count the  "in" trees and record diameter and height for each "in".  If your doing a plantation, your plot distance of 27.5 feet would be way to much.  While cruising for Champion and their eventual sale, we put one plot per 35 acres on plantations that had not been thinned.  thinned plantations and natural stands required more points, generally controlled by aerial photography and standard deviations.  You do enough standard deviation calculations until they show uniformity.  You then throw all your plots into the spread sheet and push the button.  For non-spread sheet users, a lot of calculations later, and there it is.  While your at it you bore a few trees and do a site index, unless it is already available.  So you end up with site index, basal area, form class, stand information, and your ready to write a plan, management or harvest.

That is a quick and dirty way to do, and it does not always work, have gone back and re-cruised stands when I was not comfortable with the data.  More points the merrier.

And WDH beat me to the punch.

[WDH]

And WDH beat me to the punch.

That means that you have to buy breakfast next :D.

[Tom]

I think so.

The number of trees per acre is derived by counting the number of trees in the examining plot(limiting distance) relative to the sampling point.

The Sampling point is relative to the DBH.  The number of trees in the sampling point with the same DBH (in) Determines the density of that size tree based on the extrapolation of that Sampling point to reflect an acre Which is determined by learning what part of an acre the Sampling point represents.

Once the DBH can be assigned a Limiting Distance then the Sampling area can be defined to encompass all sizes of trees.  By knowing the Limiting Distance and the number of trees in the sampling area you can determine the number of trees per acre.

So, the purpose of the prism is to determine whether the tree is within the sampling area and has no relation to the size of the tree.  It is just an aid to tell you what to count.  If I understand this right, you could use a piece of string and draw a circle to accomplish the same thing.  

How far am I getting off base now?
Texas Ranger, If I were to take one of Grandmom's spread sheets to the woods, she'd kill me.  :-\  I might best stick with this prism thingy.

[WDH]

You have it, Tom. 

Also,definitely stick with the prism thingy in the woods and spread the sheets on the bed .

[Texas Ranger]

The piece of string and the circle is a fixed point.  Prisms are variable points, or am I beating a dead horse?

the prism has a  relation to the size of the tree, Dodgy Loaners post with pictures indicates how you count the trees by the refraction of the image, how big the tree is in diameter is what allows the prism to work its magic.

then again, we may be going in circles here, shoot, I'll just come to Florida and bring my prism, no, on second thought, WDH, you do that. ;D

[Ron Wenrich]

From a landowner standpoint, I wouldn't worry too much about the number of trees.  The prism captures the stand density at any given point.  It shows if your stand is too thick, too thin, or just right.  With that information, you can decide if you want to thin, what you want to thin, or to do nothing. 

You can also see if the stand has enough of good quality trees to take forward.  Or if it is mainly stocked with poor quality trees.  It works real good for doing on the ground thinning and checking to see if you are getting the results that you want. 

Foresters use them to conduct inventories.  That's where you take down all the pertinent data, such as species, dbh, and height.  From there, you can get number of trees, average diameter, suggested stocking level, and a whole lot more.  But, that's for doing number crunching.  Its not normally done on the spot.

[SwampDonkey]

So, the purpose of the prism is to determine whether the tree is within the sampling area and has no relation to the size of the tree.  It is just an aid to tell you what to count.  If I understand this right, you could use a piece of string and draw a circle to accomplish the same thing.   

Tom, only use the string of fixed length for trees of the same diameter. Won't work for other sized trees. The string is different length for them. You have to calculate a new length (limiting distance) for each unique tree diameter. ;D

Here is how it works:

The prism is ground to a fixed angle, in this case a 10ft²/acre prism has an angle of refraction of 104.14 minutes expressed in decimal degrees (divide that by 60 to get degrees =1.7357 degrees ). In other words, light bends as it passes through the wedge of glass. Remember it's a wedge, thicker on one end than the other. ;) To calibrate the prism, or in other words to find that refracted angle of your wedge prism, use trig.

tan θ = width of tree/distance to tree  , express the tree width in feet. Do this for a tree that is just 'in' on the borderline. ;)

thus,

θ = arc tan (width of tree/distance to tree)

Ex: a 16" tree is 1.33 '

tan θ = 1.33 feet/44 feet
        = 0.030303  ooops, there's that constant k again. ;)

equivalent to k= 2 sin (θ/2)  remember them trig equivalents. ;)

so,
θ = arc tan (1.33/44)
   = 1.7357 degrees or (104.14 minutes)  How did they grind it to such a tiny angle?

for us metric dudes this works out to k=0.02828 because our prism of 2 m²/ha has a refracted angle of 97.22 minutes. ;D

[Texas Ranger]

Yup on that Swamp, and I use this wonderful little device that measures that distance electronically.  Makes it easy, all you have to do is estimate the center of the stem, and look at the tables.  Quick cruise.

[SwampDonkey]

And now for something totally different.............



All three shapes have a perimeter of 12 inches. All three could be stand perimeters drawn on a map.  ;D

[Tom]

I know y'all know what you are talking about, but it isn't coming across.  Don't these prisms have a label on them so that you don't have to do all that trig?

I started off thinking that the prism would mysteriously identify the size of tree to be counted.  Then I saw that it seemed to be used to identify the sampling area.
Then I thought it identified the sampling area, but also the relative LD to an acre.

Now, and it might make more sense, I'm back to Basal Area and a sampling area defined by the Limiting distance ...relative to the gauge or prism.

I need to study this a bunch more.  I guess, if anything, I see that I won't be utilizing one of these tools.  But it it sticks in my craw that I can't understand how they work.

[SwampDonkey]

Simple? Why didn't ya ask? ;D

Usually on the prism there is an inscribed number, such as '2'  or '2 m' for metric 2 m²/ha prism or a '10' or '10 f' for a 10 ft²/acre prism. So, forget plot size and concentrate on sample size. Depending on the local standard, you may be required to put in 1 plot per ha or 1 plot per 5 acres or some other number. The more the variablity you encounter in your woods, the more samples you need. To start with, you have to group similar sites together and come up with the area of each. Then take your dandy prism, stand at point centre and use a stick, planted firmly in the ground and fixed vertically, to rotate about that point and tally trees by species and diameter class. A diameter class in usually a spread of 2 cm or an inch between one class and another. List species in a column on the left of the page and diameter classes along the top of the page.

Each tree that is 'in' represents 10 ft²/acre regardless of size. And as you know, there is likely to be more 4 inch trees than 50 inch trees in your woods. ;) That's why TF (tree factor) tables, or the equation, is used to determine density from your samples. Your sampling predicts how many trees of each diameter class is expected to be growing in your woods. So the higher the frequency you encounter a particular sized tree in your samples the greater the density of the diameter class.


Beyond that,
In my area when I have a stand with 26 m²/ha, it is handy to 25 cords/acre. Some sites will be lower, some higher. Remember the site influences heights, regardless of species or density.  You have to have a feel for your local situation to make shortcuts if accuracy is not paramount. Sometimes close is good enough. ;D

[WDH]

Stick to the prism for basal area and growing density like Ron said.  If you want trees per acre, do a simple count on a 1/10th acre plot and multiple by 10.  99.9% of people and 98% of foresters don't truly understand why a prism works, only that it does ;D.

[SwampDonkey]

Yup, I agree with WDH and Ron. I like to go over this stuff once in awhile to jog my noodles. About the only place I know that requires you to know the theory is in BC when you write your Timber Cruiser/Evaluator exam. I think starting next year it's going to be mandatory to document seminars and write refresher exams periodically to maintain your registration as a timber cruiser/evaluator. Up to this point it has been voluntary. There is even a provincial standard cruising manual for BC and cruise cards used on crown lands. Been there done that. I believe member Tillaway worked the same forest up there I did in BC for a short stint.

[SwampDonkey]

Well Tom, I can say with a high degree of certainty that there have been a few folks print this topic off. I've even got it bookmarked along with similar threads.  I'm also quite certain some of the printers are also foresters. ;D  8)

[beenthere]

I appreciate this thread. I have 8 prisms, that came from the estate of one of the Forest Service Statisticians/Mensurationists. I've been trying to decipher the pencil marks on the paper wrappers, and have such hierogliphics as
3 delta     BAF 9.33
3 delta  BAF 9.76
3 delta  BAF 9.70
4 delta BAF 16.31
6.00 delta BAF 39.6
7.00 delta 38.0 (looks like Sq)
7      delta  38.0 (looks like Sq)
8.00 delta  BAF 64.80

I'm trying to fit these numbers into what y'all have been saying. Have found it interesting.
Do these numbers correspond to the percent sample? The 3 delta prisms have the least taper. 
None have any etching or numbers/letters on the prisms themselves, only the wrapper.

When the Forum auction fires up next, I will put some of these up for bidding.