How would you figure the rate of basal area increase?
A)You could do some destructive sampling, called stem analysis to measure increments of annual growth and calc the basal area increment from year to year. Of course keeping in mind the measurement of increment is at 4.5 feet. Basal area itself isn't really site specific like tree height is. It's increment is related to density, suppression, and other factors not unique to a specific site type.
B)If you were to take a modeling approach, you would have to do a cruise to determine crown class percentages and diameter distribution of dominant, intermediate, suppressed crown classes. You could use the first method to get a base line. Then, assume the percentages are constant without any management intervention. If you introduce management, then the junk disappears over time and the basal area rate of increment should increase.
I'm sure the universities have many such models and a lot more complicated which include harvest entry predictions.
C) If you construct a yield curve for a stand or site type, your one step ahead of basal area. A yield curve is just a volume equation. You've seen them for species like balsam fir, how it starts out at 4" dbh, inclines until maturity, levels off and then crashes.
If all you are asking for is the past rate of basal area increase at a specific point in time, then Swamp Donkey's answer A is the way when you don't have any past measurements. If you have past measurements for the specific piece of land, then annual rate of increase is simply the previous basal area subtracted from the present basal area, with the result divided by the number of years between measurements.
There are many publications (based on studies ) that give predicted basal area increase for individual species growing at specific densities, at specific age classes, on specific site classes, however most of these are from/for even-aged stands.
The problem is these stands are uneven aged, and multi size class. Plus I do not want it for one site type, but was hoping to be able to calculate it for any given stand.
The NF in this area has a general rate of increase, but again I was hoping something more specific.
I will have to mull over SD methods.
Do some Googling, try
"predicting basal area increment on uneven aged stand"
Another way might be to take some increment cores from representative diameter classes and calculate an average annual rate of diameter growth from the cores and convert that to a basal area basis by DBH class.
Alright, I am taking variable point samples with increment samples. I can calculate basal area /acre, trees/acre, volume /acre, basal area per tree and more. I can even calculate amount of incremental increase of the basal area /tree. I just can't figure the basal area per acre increase. Not without old data, which I don't have.
I am really scratching my head on this one.
It is starting to get more complicated then I can articulate on a post.
From the sample plots, calculate basal area per acre from some point in the past using the increment cores and determine the current basal area per acre from the same cores. Using the time interval from the cores, calculate the basal area growth per acre.
Yeah, like WDH said. Use those cores to establish a time line or a starting point in time. No reason not to assume the growth on that site wouldn't be the same as trees of similar dbh in the past.
How do you figure it per acre? Like I wrote, I can get current basal per acre and past and current basal area per tree. But from a variable plot each tree is worth 10 basal based on its diameter I have "in" trees that would not have been "in" the past, and future trees may be to small to be counted.
I'm thinking this through as I write...
So if I figure the Basal Area increase of a tree (based on growth rates) to figure per acre I would need to multiply it by that trees conversion factor (which is based on diameter) so would it be the current dbh or the dbh from the projected dbh.
Thanks
Establish what the dbh and basal area was in yesteryear from the cores and average it. I would look at every 10th year in the past from the current year or you could just go back say 40 years and average over the 40 years. Do you know the stand history of the site? I would limit myself to when there might have been a disturbance in there, like some partial cutting. It should show up in the core samples. You would get an average basal area per acre per year from disturbance to now. Then explain this is how I project it to grow for X number of years onward without further intervention. That's about the best you can do. I know from experience that precommercial thinning on even-aged stands is good for 25 years. You'll have to similarly draw from experiences to make your projection. At some point basal area increment slows and maybe that's another point in time to intervene. The numbers still have to make sense for the projection. And yes your Tree factors will come into play in your model. I think diameter distribution in the future should similar to now assuming no disturbances from now to that projected time ahead. Trees become "in" as they grow, they also exit as they die off.
Woodtroll,
Every tree in your variable plot sample represents a given # of trees per acre based on the diameter and critical distance of each sample tree. As long as the sample was random and you cored every tree in the plot, you could use each of the sample trees as the reference point to the past. They represent a given basal area growth per each tree. Then multiply that basal area growth by the # of trees/acre that each sample tree represents to blow up the value to a per acre basis. Easier said than done!! Keep us posted on what you are finding.
Here is what I came up with. There can be more data taken to be more precise, but the extra time did not seem warranted at this point. Plus I understand the limits of simple growth projection.
Objectives: To give a ball park estimate for-
• Volume/acre
• Basal area
• #trees/acre
All this data, past, present and future. Also separating my leave trees and cut trees.
Data collected was: dbh, merch height of each tree and if it was cut or leave tree in a variable plot. The first trees of each point was increment bored and the average rings per inch calculated. Basal area factor is 10.
Take DBH*2.75=plot radius of tree
(3.14159 *Plot radius of tree^2)/43560 = plot size per acre
1/plot size per acre= per acre conversion factor
Per acre conversion factor/# points sampled = trees/acre
.005454*dbh^2 = Basal area/ tree
To get the incremental growth in basal area I did all the same calculations based on a dbh less ten years of growth. Subtract the basal area per tree of the past from the current = BA incremental growth.
Here is where I get ify.
Take the past basal area /tree * present tree/acre = past basal area/acre.
(to get basal area of the stand, take the sum of basal area/ acre and divide by the number of points taken).
To this point the results pan out with what has happened on the stand. It just looks into the past. My stand is a currently at 140sqft BA, past BA 83sqft. It turns out the stand had been thinned to an 80-90 BA ten – twelve years past.
Now doing the same calculation but going forward, 60 BA of leave trees will be around 81 sqft of BA in ten years. Or 85 sqft will grow to 139 sqft of basal area.
At this point I need to repeat this on different stands to compare results. I take it with a great big grain of salt. What is that old saying? "liars always figure and figures always lie"?
If your looking at the ring data, it's far better than a guess. ;D
Quote from: woodtroll on November 03, 2009, 02:40:22 PM
Take DBH*2.75=plot radius of tree
Known as Limiting Distance from point centre to tree centre, yes
Quote
(3.14159 *Plot radius of tree^2)/43560 = plot size per acre
1/plot size per acre= per acre conversion factor
Per acre conversion factor/# points sampled = trees/acre
Known as Tree Factor, which gives density by diameter. Short cut method is:
TF = BAF/(0.005454 x Diameter
2)
Quote
.005454*dbh^2 = Basal area/ tree
Multiply by TF and get Basal Area per acre by diameter.
Looks good so far. ;D
To project future growth, you will have to make an assumption about the future diameter growth in the stand. If you thin again, that should increase the diameter growth versus what it has been over the last 5 years or so.
This rate of increase would be conservative. Mainly to compensate for the stands that do not release, or still grow at their average slow rate.
In my way of thinking the stand takes a year or to kick it in gear, then will slow done again once a full stocking is reached.
Have you heard of the FVS modeling software? You can plug in your cruise data and "grow" the stand forward in time. If you get fancy and read the literature it will let you simulate stem mortality, various harvest styles, fire, etc. Just a thought.
What?
actually use someone else's program!?
That would be much to simple.
I will look it up.
Just so you know, I do this because I am questioning some of the current numbers.
I'm getting into this a little late, so there is probably some overlap here.
I've done some things like you're talking about in hardwood forests. When I take variable plots, I like to take them at 1/acre, but have done some with fewer. This gives me a chance to map out the area, and to show changes in timber type. I number the plots for reference.
At each plot I collect the dbh, species, tree height, dominance in stand, and cut or leave. Core samples can be taken of representative trees in different categories. I only use 10 years worth of past growth to project 10 years into the future.
When I crunch the numbers, I put all the plots that represent the same timber type together and average out my numbers per acre. I'll get an average volume, BA, number of trees, etc on a per acre basis. I can also graph out the diameters by # of trees. It should be a J shaped graph if you're shooting for an uneven-aged stand. Most of the stands I worked in were J shaped, but they had bumps at certain diameters. I interpreted that as being disturbances of cutting or disease. Common cutting style for the area is to cut sawtimber out of the higher dbh classes.
Since I have data for growth, I can throw that on the existing stand to see what how my diameters increase. You can add diameters onto the standing timber and come up with estimated volume and BA out 10 years. Since you have cut or leave trees, you can project the forest with or without your prescription. But, as the stand becomes overstocked, growth will slow. And, you have no way of knowing whether future growing conditions will be the same as in the past. The 10 year window seems to be a nice solution, at least in our hardwood stands.
I'm like woodtroll, I like doing it myself. But, not only that I know how the calculations are made instead of feeding a calculator. That way your brain doesn't get lazy and someone can ask how this is calculated and you can recall the math with some confidence. ;)
Growth and yield models based on site quality are available for southern pine. I am sure that there are similar models for hardwoods.
Quote from: SwampDonkey on November 04, 2009, 03:21:34 AM
I'm like woodtroll, I like doing it myself. But, not only that I know how the calculations are made instead of feeding a calculator. That way your brain doesn't get lazy and someone can ask how this is calculated and you can recall the math with some confidence. ;)
But using a forest modeling program allows you to do things that are next to impossible on paper. And with FVS if your really interested the equations are available so you could stare at them with a blank look for a while ???.
I prefer the forest models for the areas involved. ;)Much research has gone into developing them.
I don't think he's doing thousands of acres. I get the feeling Woodtroll is looking to get a feel of things on a small scale. Otherwise, I'm sure he could look at the models. Most states or USDA region would have them. I'm not sure how accessible they are. I know I would have to buy such models here, I couldn't go into DNR and ask for it for free. Most of the time they are written by Universities on contract or even a professor with a side business for such things, such as REMSOFT.
Actually, I want to look at forest on a stand basis. That may be a hundred acres or as small as 10.
The local forest service uses a general 10sqft of basal area growth/ten years. The stand I used for my cruise is 25-30.
Plus if I make this my self, I know how to run the program, instead of learning a new one. Plus it is a review of the formulas.
How did you make out with all of this. I am interested to see how you dealt with some of the issues you presented in earlier posts.
The first stand I looked at with these formulas showed the growth to be consistent with the samples taken. What I mean is the... were thinning it right now. I a can see rings on many more samples and my average is staying the same as the cruise. (That is good to know). It also showed that around 15 years ago it was thinned. That is good because it was. And the math works out that it grew from a basal area of around 80 to its current (pre cut) of 140. The BA level of 80 is the likely stocking it was thinned to, sadly no written record. So I am hoping that I will get at minimum the same growth over the next 10 years. It would be growing at 2.4 sqft BA/year. That is not counting on any boost in the growth rates.
So does this help me? That is what my boss wanted to know. Yes it reassures me of my prescription. I will not know on the projections till ten years have passed, but this is a starting point.
I know that my current practices have lowered the stocking to below my fully stocked target range, but in 10 years it will start being overstocked. Fifteen years it will be ready for a harvest to drop the stocking again.
Now it it needs to be repeated a few times to check it on other stands.
Of course this is all just numbers, we need the markets to come back.
What you did for sampling and math at that stand may only hold for that stand or similar site and cover type. As you do a few more and keep good accounts of the site you get better confidence of the outcomes. It's a whole lot better than a guess or fly by the seat. 8)
That is why I want an easy way of doing this. Take quick data for a specific stand and have the info I need for that spot. Not a generalization over a large expanse of ground with different growing conditions.