| To
Rucker or not to Rucker, what's in an index? |
Robert
Leverett |
| May
24, 2006 12:42 PDT |
ENTS,
In a "behind the list"
exchange of communications, several of us
are discussing the expansion of Rucker indexing in two distinct
ways.
Colby would be surprised and I hope proud.
We are looking at adopting a
compact system of notation to identify
the different kinds of indices we are now using, planning to
use, or
thinking about using. We are also looking at expanding the
number of
site indices that we typically post for a site on the ENTS
website. Some
of us compute several kinds of indices now, but usually don't
report
them in list communications. The kinds of indices that could be
computed
based on our collective interests include the following:
1. Regular 10-species height
index, [THIS IS THE STANDARD]
2. Regular height index, but based
on a different number of
species,
3. Iterated height index for
either of the above,
4. Regular 10-species
circumference index,
5. Regular circumference index,
but based on a different number of
species,
6. Iterated circumference index
for either of the above,
7. Regular 10-species crown spread
index,
8. Regular crown spread index, but
based on a different number of
species,
9. Iterated crown spread index for
either of the above,
10. Regular 10-species volume
index,
11. Regular volume index, but
based on a different number of
species,
12. Iterated volume index for
either of the above,
In all the above, a particular
species can contribute to an index
calculation only once. However, suppose we were to lift that
restriction
and compute a second family of indices where species repetition
is
allowed. In the case of 1. above, it would be just the 10
tallest trees
regardless of species. This is admittedly a less valuable kind
of index,
but it would add information about species and tree height
distribution
for a site. Under both systems, 24 different kinds of indices
arise.
Ouch!
We don't have to go all the way. A system of
regular reporting might
include 1and 4 from the above choices for both non-repetition of
species
and for repetition. That would be 4 indices per site. We could
add crown
spread, but I doubt that we'd ever keep up the crown index. So
the 4
could become our standard for site reporting.
A sample of a compact system of notation that
some of us are
experimenting with follows in the examples below, where RHI
stands for
Rucker Height Index, RCI for Rucker Circumference Index.
1. RHI-10-N indicates a height index
using 10 species (no species
repeats)
2. RHI-7-N would be a
7-species index with no repetition of
species.
3. RHI-10-N-3 would indicate the 3rd
iteration of a RHI-10-N type
index.
4. RCI-10-R would indicate a 10-tree
circumference index with
species repetition allowed.
5. RCI-8-N-2 would indicate the second
iteration of a 8-species
circumference index with no repetition allowed
A symbolic way of incorporating these index
attributes that utilizes
the power of mathematics and of computer meta-language
methodology
follows:
R{H,C,S}I-n-{N,R}
To use the above template, a selection is made
from the choices in
braces and the actual number of trees in the calculation is
substituted
for n. If iteration is allowed, the above form becomes:
R{H,C,S}I-n-{N,R}-j where j is the
number of the iteration.
This looks worse than it is. Using the
meta-language, we would
recognize RHI-10-N-4 as the 4th iteration of a non-repeating 10
species
height index. To simplify matters, we could agree by convention
that
RHI-10 will be shorthand for RHI-10-N. This is the form
recommended by
Ed Frank. In most list communications, there isn't a need to
utilize the
full notation, but it is there for more rigorous discussions of
indexing.
We are mercifully keeping most of these
technical discussions to
private e-mails among the few of us, with the intention of
periodically
reporting where we stand. If others among you want to
participate,
please let us know. If enough do, we'll discuss the topic on the
list,
but I suspect that most of you would vigorously exercise the
message
delete button.
Bob
|
| Re:
To Rucker or not to Rucker, what's in an index? |
Edward
Frank |
| May
24, 2006 15:08 PDT |
Bob,
With your broach of the nomenclature of the various indexes to
the ENTS
list, I thought I would make a post to the ENTS list rather than
to you
individually. I had hoped for more behind the scenes discussion
before
making a broader presentation.
Rucker Indexes strike me a special kind of index that includes a
composite
of measurements each from a different species. For example the
RI or RHI is
the average of the height of the tallest individual of each of
the ten
tallest species on the site. Similarly we can have a Rucker
Girth Index, Or
Rucker Volume Index, or any of a variety of indexes including
one
representative from each species. I would rather see Rucker
refer to just
this type of index as opposed to just any assortment of species.
The nomenclature for these types of lists needs to be clearly
stated
initially and follow a logical pattern, to keep from needing to
revise it in
the future. I would like to suggest the following naming
protocols, instead
of the structure you have cited below and in the MTSF 2006
report.
Rucker Index
The Rucker index was initially devised to characterize the
maximum heights
found in a particular area or plot. It is essentially a
foreshortened
version of a tree height profile listing in order the maximum
heights of all
the species found there. The Rucker Index in its basic form
consists of the
numeric average of the ten tallest individuals of the ten
tallest species on
the site. It can be used to compare sites in different areas
that include
different assortments of species. Other measurements can used to
generate
Rucker Indexes following the same format. A Rucker Girth Index
would be the
numeric average of the ten fattest individuals in each of the
ten fattest
species in the site or area. I can envision Rucker Indexes from
a variety of
measurements that may be devised in the future with more data:
Rucker
Volume Index, Rucker Canopy Index, Rucker Age Index, Rucker
Anything Index.
I would use Girth rather than Circumference. The terms are
synonymous and
can be used interchangeably. Why I want to use girth is because
G is a
distinctive letter that is not used by any of the other
hypothetical indexes
I can think of. The next most common measurement after height
and girth is
some for of crown spread or canopy. I can't think of another
initial to use
for crown spread or canopy other than C, so I would like to
reserve the RCI
for crown spread, and call the circumference or girth measure
the Rucker
Girth Index or RGI
Format:
RI or RHI: Rucker Height Index Either form is fine, if more than
1 type of
index is being presented then the expanded RHI form should be
used
RGI: Rucker Girth Index
In some cases it may be useful to derive a Rucker Index using
some number of
species greater or less than 10. Whenever possible a ten species
Rucker
should be calculated. Some reasons for using a smaller number of
species in
a Rucker Index might include: 1) A limited number of
measurements in one or
more sample sets, 2) a strongly bimodal distribution of heights
(or other
measured value) among the species in the population, 3) a
limited number of
species present in the population in the sample area. Where
possible I
would suggest using a five species Rucker index. Fewer numbers
than this
would limit the probative value of the index. In addition a
mixture of 5,
6, 7, and 8 species numbers would be hard to compare and
contrast between
sites. Using a single number, 5 is my suggestion, would
facilitate these
comparisons. In other cases a more in depth analysis of a
particular site
might be warranted and a larger number of species included in
the index. A
Rucker index of twenty species would be an example. Again twenty
would be a
good number because it could be standardized to facilitate
comparisons
between different areas with more in depth measurements, and it
is different
enough from the basic ten species index to give a broader
picture of values
in the area under consideration. These numbers would be used as
a modifying
suffix to the basic Rucker Initials. For example a Rucker Height
index
using 5 species would be RI5 or RHI5. A Rucker girth index of 20
species
would be listed as RGI20
Format:
RH5 or RI5: Five species Rucker Height Index
RGI20: Twenty Species Rucker Girth Index
In Bob's recent report he used an average of the heights of the
ten tallest
trees in the plot and called it a Rucker Height Index-2. This
nomenclature
conflicts with the above protocol for indicating the number of
species in
the index. In addition, I do not believe these should be called
Rucker
Indexes. And third, I do not believe Bob's proposed nomenclature
is
distinctive or can clearly be understood based upon the letters
and number
combinations alone. These values may be of importance is some
situations
and I am not opposed to gathering them. In general an index of
these
measurements should include ten specimens to make it comparable
to standard
Rucker Indexes. Fewer than ten values for a numerical average
suggests that
there is not enough data for the average to even be meaningful.
I would
suggest the numerical average of the ten tallest trees on the
site simply be
called a Height Index: or HI, the numerical average of the ten
fattest trees
be called a Girth Index or GI. Again if fewer or more than the
standard
number of ten specimens were included in the index it could be
modified as
noted above for the Rucker Indexes, but I do not think this is
something
that should be done except under extraordinary circumstances.
Format:
HI: Height Index - numerical average of the heights of the ten
tallest
trees in a plot
GI: Girth Index - numerical average of the girths of the ten
fattest trees
in a plot.
Species Index: In past analysis Bob has used a species height
index which
consisted of the numerical average of the ten tallest
individuals of a
particular species on a site. This can be expanded to include
other
parameters than just height. The nomenclature should be straight
forward.
A Species Height Index would be designated SHI, As noted above
some
situations may require that fewer than 10 or more than 10
individuals be
used when calculating the species index, this can be noted as
explained
above for the Rucker Index. One example of why a lower number
might be
used, would be if a series of species indexes were calculated
for multiple
species at a site. For common species ten individuals would be
easy to
include. For other less common species ten mature individuals
might not be
present . I can only think of the locations of three Sassafras
Trees at Cook
Forest, while Dale has dozens of white pines over 150 feet tall.
Format:
SHI: Species Height Index - numerical average of the ten tallest
individuals of a particular species in a population
SGI: Species Girth Index
There are a number of other indexes being used by ENTS. One is
the Tree
Dimension Index which has been described elsewhere. It is in two
forms.
One form includes Height, Girth, and Maximum Crown Spread. The
other form,
like the one used by Bob in his most recent MTSF Forest Research
Report,
consists of just Height and Girth. Each value is expressed as a
percentage
of the maximum dimension of the parameter know for that species.
These
percentages are then summed to calculate the TDI. The TDI with
height and
girth has a maximum value of 200% for a tree that is both the
tallest and
fattest of the species.
Another measure that has been discussed are multiple iterations
of various
indexes. ...I will suggest a format for nomenclature. For
example the
10th iteration of a 10 species Rucker Height Index would be
listed as
RHI10-IT10. Other indexes for which multiple iterations are
calculated
could use a similar naming format.
These are suggestions for general discussion. I believe they are
reasonable, more straight forward to interpret, and simpler to
implement
than the nomenclature suggested by Bob L. below.
Ed Frank
|
| RE:
To Rucker or not to Rucker, what's in an index? |
Robert
Leverett |
| May
25, 2006 06:27 PDT |
Ed,
You've done your customary thorough job of
presenting the
alternatives. Thanks as always. I decided to post the discussion
to the
list to test the level of interest on the topic and to insure
that folks
like Anthony Kelly, Carl Harting, Darian Copiz, Michael Davie,
etc.
aren't left out. The limited list of addressees in the off-list
communications was growing quite long.
Actually, I can live with any of these forms:
RHI, RI, RHI10, RI10,
RHI-10, or RI-10. G for girth as opposed to C for circumference
is fine.
I prefer girth to circumference since the latter implies a
circle and
misleads people into thinking that circumference and diameter
really do
apply to the shapes of tree trunks.
In terms of HI or HI10 for overall 10
tallest tree height index,
that's fine. In terms of my original definitions, this implies
that
species repetition is allowed, i.e. the 10 tallest. GI or GI10
for the
10 fattest, is fine.
Ed, what I'm really arguing for in all
this is for us to move toward
the use of multiple indices so that we get a clearer idea about
the
maximums achieved by a site's trees. That is what Rucker
indexing is all
about. What are the best ways to profile a site from the top
down. Thus,
when I presented a combination of indices for MTSF, the choices
looked
as follows:
Site RHI10-N RHI10-R RCI10-N RCI10-R
MTSF 136.0 161.0 12.4 13.7
Simplifying the above notation, per your
recommendations, we get:
Site RHI HI RGI GI
MTSF 136.0 161.0 12.4 13.7
The second notation is simpler
(obviously). The simpler the better.
Bob
|
| RE:
To Rucker or not to Rucker, what's in an index? |
John
Knuerr |
| May
25, 2006 17:06 PDT |
I'd like to throw in my two cents on this one from the
perspective of not
forgetting who came up with the Rucker Index. Colby saw this as
a way to
profile the forest canopy champions and through iterations of
the index to
get a sense of the "height robustness". When comparing
different sites, the
value of the multiple iterations become clearly evident.
Another point to keep in mind is that the Rucker Index caught on
amongst
many of us and generated lot's of energy and friendly
competition among our
ENTS colleagues and continues to do so.
I would like to see us honor the memory of Colby and only use
the "Rucker"
label in its original formulation.
|
| Re:
To Rucker or not to Rucker, what's in an index? |
Edward
Frank |
| May
26, 2006 17:13 PDT |
|