[seek-kr] ontology figure from abq
Rich Williams
rwilliams at nceas.ucsb.edu
Wed Sep 3 09:40:34 PDT 2003
There is a widely-used extension of dimensional analysis beyond simply
making sure that the units of terms match up. It is based on Buckingham's
Pi-theorem, is used extensively in fluid dynamics (that's where I've run
into it) but I haven't seen it used in ecology. It involves taking a set of
governing equations (the Navier-Stokes eqns in fluid dynamics),
non-dimensionalizing each variable and re-expressing the governing equations
in terms of the non-dimensional variables and various dimensionless
parameters. The canonical example of a dimensionless parameter in fluid
dynamics is the Reynolds number, which is essentially the ratio of the
inertial forces to the viscous forces in the problem at hand. By plugging
in estimates for the length scale, time scale, fluid density and viscosity
you can check which forces are likely dominant in the flow regime of
interest, and therefore which terms it's probably safe to toss out of the
governing equations in an attempt to produce a more tractable system.
I've never seen this technique applied in ecological models, but I can't
claim to have great breadth of knowledge in the area. I think one reason it
hasn't been applied is that the basic approach used in ecological modeling
is very different than that used in physical modeling. For example, in
fluid dynamics, you start with a very complex set of equations that very
precisely express the physics of the system (f=ma and equations of state).
The basic problem is to figure out how to throw stuff out so you can have
some chance of solving the system analytically or numerically. In the
ecological models I've looked at, the model is built up from a researcher's
interest in understanding the effects of various interacting processes -
there is no 'f=ma' for ecology. Since the model was developed with the a
priori assumption that a certain set of processes are important, there's
typically no attempt to do a non-dimensionalization and scaling analysis to
make sure that all the terms in the model are important.
Rich
-----Original Message-----
From: seek-kr-admin at ecoinformatics.org
[mailto:seek-kr-admin at ecoinformatics.org]On Behalf Of Matt Jones
Sent: Wednesday, September 03, 2003 9:04 AM
To: Bertram Ludaescher
Cc: seek-kr at ecoinformatics.org
Subject: Re: [seek-kr] ontology figure from abq
Bertram,
Yes, dimensional analysis is the correct term for the manipulation of
unit types from STMML. Its all simple algebra, and is generally taught
early on (I think I first learned it in high school in chemistry). I
don't understand how you plan on 'extending' what Shawn did because what
he did is already dimensional analysis. What am I missing here?
One important area that we have only superficialy considered is the area
of 'dimensionless' numbers. I think this exposes a lot of the
distinction between 'UnitType' and 'SemanticType', but its pretty muddy
for me. The problem boils down to this: dimensionless numbers are
often ratios of two quantities that are measured in the same units. For
example, grams of Carbon per grams of Nitrogen (the C/N ratio) is
dimensionless because the unit grams cancel. However, there is
important information that still needs to be captured (e.g., that we are
measuring Carbon and Nitrogen, not Carbon and Oxygen). This part, the
'what' that is being measured, is somehow part of the semantic type -- I
think it fits nicely into the diagram I posted to CVS yesterday. The
problem really crops up when considering 'counts' of things, which is
incredibly common in ecology. I wrote a bit of a treatise on this topic
with respect to its impact on EML [1], and several people followed up
with some excellent commentary [2] [3] [4]. In [4] Tim Bergsma presents
some interesting ideas about just what a "dimension" is and how it
relates to counts. In [3] Peter McCartney follows up with ideas about
what might be in a semantic type in EML. You might find those to be
interesting reading, as I stated that SEEK would be dealing with these
issues head on in that email ;-)
Matt
[1]http://www.ecoinformatics.org/pipermail/eml-dev/2003-March/000738.html
[2]http://www.ecoinformatics.org/pipermail/eml-dev/2003-March/000744.html
[3]http://www.ecoinformatics.org/pipermail/eml-dev/2003-March/000745.html
[4]http://www.ecoinformatics.org/pipermail/eml-dev/2003-March/000747.html
Bertram Ludaescher wrote:
>
> Hi Matt:
>
> Thanks!
>
> Shawn and I had discussed units, unit types, quantities, dimensions
> and the likes today.
>
> I found some interesting papers on "dimensional analysis" and was
> wondering whether that could be a natural extension to the simple
> "reasoning with units" that Shawn has implemented in Prolog.
>
> I found this simple intro quite readable:
> http://www.physics.uoguelph.ca/tutorials/dimanaly/index.html
>
> The next level seems this:
> http://www.wikipedia.org/wiki/Dimensional_analysis
>
> which also has a pointer to Buckingham's \pi-theorem
>
> This guy seems to be really ino dim.-analysis:
> http://www.isd.uni-stuttgart.de/~rudolph/
>
> Also: this book includes a chapter on applying dimensional analysis to
> ecology:
>
http://www.amazon.com/exec/obidos/tg/detail/-/0444892508/104-2454972-2037526
?v=glance
>
> What do the Eco-folks say? Is this worth investigating further for
> adding not only unit conversion but more general reasoning and in
> particular dimensional analysis to SMS?
>
> Bertram
>
>
>
>
>>>>>>"MJ" == Matt Jones <jones at nceas.ucsb.edu> writes:
>
> MJ>
> MJ> Mark, Bertram, Shawn, and Rich,
> MJ> I checked in the diagram that we made in ABQ regarding the carbon flow
> MJ> ontology. It is in CVS:
> MJ> seek/docs/figures/seek-cf-measure-ontology.ai
> MJ> and in case you don't have Adobe Illustrator:
> MJ> seek/docs/figures/seek-cf-measure-ontology.png
> MJ>
> MJ>
> MJ> The major change is the addition of "UnitType" to the properties of
> MJ> MeasurementType. I was thinking where "unit" went (as opposed to
> MJ> UnitType) and decided it was a property of a particular attribute
rather
> MJ> than a MeasurementType.
> MJ>
> MJ> This whole thing doesn't really consider nominal and ordinal scale
> MJ> things, so we need to determine how MeasurementScale fits in to the
> MJ> picture. But I thought my updated version would be of use to you.
> MJ>
> MJ>
> MJ> Matt
> MJ>
> MJ> --
> MJ> -------------------------------------------------------------------
> MJ> Matt Jones jones at nceas.ucsb.edu
> MJ> http://www.nceas.ucsb.edu/ Fax: 425-920-2439 Ph: 907-789-0496
> MJ> National Center for Ecological Analysis and Synthesis (NCEAS)
> MJ> University of California Santa Barbara
> MJ> Interested in ecological informatics? http://www.ecoinformatics.org
> MJ> -------------------------------------------------------------------
> MJ>
> MJ> _______________________________________________
> MJ> seek-kr mailing list
> MJ> seek-kr at ecoinformatics.org
> MJ> http://www.ecoinformatics.org/mailman/listinfo/seek-kr
--
-------------------------------------------------------------------
Matt Jones jones at nceas.ucsb.edu
http://www.nceas.ucsb.edu/ Fax: 425-920-2439 Ph: 907-789-0496
National Center for Ecological Analysis and Synthesis (NCEAS)
University of California Santa Barbara
Interested in ecological informatics? http://www.ecoinformatics.org
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