Indexes and units

[Tim Bergsma]

I would hesitate to call an index dimensionless, but it very well could
be unitless.  

For example, the shannon-wiener index is clearly a one-dimensional
concept, whereas there might be some other index that rates diversity
along two abstract "dimensions", e.g. separate values for richness and
eveness.  So dimensionality applies (if you can count them, they must
exist).  However, to make units apply, I find myself starting to say
things like "plot x has a diversity of 1.2 shannon-wieners", which is
simply not how ecologists talk.  So it is quite possible for a quantity
to have dimension but not units.  

For better or for worse, metadata about dimensions is relegated to
attribute descriptions; a rather informal solution relative to EML's
precision-handling of units, but appropriate nonetheless.  To recap my
theory on this:  units are a formal subset of dimensions.  This becomes
particularly relevant for attributes that have mixed models, such as
feeding habits for gazelle.  Consider "Grams per day per animal".  Grams
and day are units, since they meet the NIST test:  "A unit is a
particular physical quantity, defined and adopted by convention, with
which other particular quantities of the same kind are compared to
express their value."
(http://physics.nist.gov/cuu/Units/introduction.html).  The concept
"animal" is only a dimension, not a unit, since it does not meet the
NIST test.  In this case, I would make "per animal" part of the
attribute definition, and register grams per day as "the units".

The problem with indexes is that they are highly formal (unlike "per
animal") and yet (potentially) dimensionless.  So I'm not able to
express with precision the manner in which units are a subset of
dimensions:  a simple appeal to formality doesn't do it.  Nevertheless,
the shannon-wiener index is not expressed in terms of something that
passes the NIST test, so I'm advocating the postion that it is unitless.

Tim.

> Peter McCartney wrote:
> 
> How are we currently recording indexes (for example, a vegetation
> density index derived by a ratio of the values of two or more bands
> within a RS image; or a diversity index such as shannon wiener where
> the value of H' is an abstract measure with little relation to a
> measurable quantity)? Are these dimensionless?
> 
> Peter McCartney (peter.mccartney at asu.edu)
> Center for Environmental-Studies
> Arizona State University
> 
> 

-- 
Tim Bergsma
LTER Information Manager
W.K. Kellogg Biological Station
Michigan State University
Hickory Corners, MI   49060
269/671-2337
tbergsma at kbs.msu.edu
http://lter.kbs.msu.edu