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Hi Maribeth,
Sorry, I was not more clear. I was referring to
saturated hydraulic conductivities at different locations on a site (and of
course in the same hydrogeological unit). In so far as retention
curves...do you perhaps mean logK vs. water content. Very often
portions of those curves are nicely(?) fit to, say, Brooks-Corey parameters (
the simplest expontial relationship used). Things break down in that regard near
saturation--the extent depending of your soil. BTW, consider the curves (both K and h) shown in http://math.lanl.gov/~dmt/papers/shmuel.pdf .
Clearly these do not have lognormal behavior.
Then there is hysteresis.... Also, how tame are artificial soils compared to
soils taken in the wild? Glass beads are nice:O)
A more fundamental point here,
however, is that you are noting FUNCTIONAL RELATIONSHIPs that are
exponential or often sufficiently so. However, I am referring to a random
variable. So we have apples and oranges.
Finally, I would
venture, that your response does support my view of an earth
science culture still stuck on the lognormal. BTW I think that often
lognormal works fine...but sometimes it doesn't so we just need to justify--in a
given context--that which we do or that which we choose not to do.
Unfortunately it is too often my experience that if I try too hard to justify
something, I seem to raise more issues than I resolve. C'est la
vie.
Best regards,
Mike
----- Original Message -----
Sent: Thursday, August 10, 2006 11:37
AM
Subject: Re: AI-GEOSTATS: Log versus
nscore transform
Mike,
I can't speak to EPA UCLs, and I'm
too far removed from the literature at this point to make a cogent argument...
but I do remember my work characterizing the hydraulic properties of
artificial soils and there was no doubt that the soil water retention curves
(tension vs water content) were log normal. I also remember Wilford
Gardner (UW-Madison) commenting on how often that function form appeared in
soil water physics.
While digging through an old folder I
found a classic reference ...
Spatial Variability of Field-Measured
Soil-Water Properties
DR Nielsen, JW Biggar and KT Erh
Hillgardia Vol
42, Number 7, pp 215-260, Nov 1973
Maribeth
At 08:50 AM
8/10/2006 -0400, Michael Grant wrote:
My apologies. The email below accidentally
only went to Gregoire only. It turns out that I haven't quite reconnected to
the list correctly.. So...
------- Original Message -----
From: Michael Grant
To: Gregoire Dubois
Sent:
Wednesday, August 09, 2006 8:48 AM
Subject: Re: AI-GEOSTATS: Log
versus nscore transform
Hi
Gregoire,
Please forgive
the rambling philosophical response but I find your question interestingly
provocative.
Is a preference of
lognormality mathematical elegance or is it tradition? I remember an era of
virtually automatic assumption of lognormality for two key classes of
variables in our business (nuclear/environmental): contaminant
concentrations and hydraulic conductivity. That practice
lingers.
By
the early and mid 1990's many human and ecological risk assessors assumed
lognormality of contaminant concentrations in environmental media as an
article of faith. 'The data are skewed and hence lognormal.' In the US, I
suspect that this state of affairs reflected in part the issuance of a
single document--the USEPA's approachable supplemental guidance on
calculating UCL for human health risk assessment (May 1992). While the EPA
clearly evolved beyond that point, e.g., the agency's work on bootstrapping
UCLs, numerical/computational savvy of many but not all 'street' assessors
probably lagged.
This lag was due in part to a mix of
professional focus (toxicology versus numbers), availability of tools, and
convenience. Also the commercial environmental business has significantly
matured as a class of business and we all know that it is crowded.
Competitive pressures are significant, and thorough data analysis--an
expensive endeavor--is often a loser. The convenience and economy of
sanctioned lognormality (no-one reads the fine print) beckons. For me going
beyond nominal practice(?) almost always as been on my time. However, that
is the nature of things and as long as we learn...:O) I think that the
wider development, elucidation, and/or implementation of computationally
intensive techniques, e.g., bootstrap, Monte Carlo, is changing at a
fundamental level how we formulate our approaches to many problems,
vis-a-vis simulation. (Consider the transparency in the formulation of
resampling methods relative to the 'obscurity' of traditional parametric
statistics.)
Now regarding hydraulic conductivity. Again lognormality is a long-standing
tradition of nominal practice. Certainly the last 25 years have witnessed a
real evolution of concepts and understanding with respect to hydraulic
conductivity. And that evolution certainly continues. But again, a mature,
over-crowded environmental business dictates nominal practice. Not everyone
is a numbers-oriented (hydro)geologist, and many who compile/interprets
conductivity data have other duties/interest. The convenience of
long-standing tradition--all theory aside--is powerful when faced with a
need of a 'quick' characterization. BTW is there a hydraulic conductivity
analogy to the 92 EPA supplemental guidance for concentrations UCLs? Sort
of. I suspect that early co-kriging of water levels (H) and K (T) has
had a cementing impact on perception of K as lognormal.
Is this
pessimistic? Well, not really. There are both academic and business
opportunities here, and some individuals will recognize those opportunities.
'Justification' is the sort of issue that lead to progress both in the
advance of theory and the application of theory (technology). Also I do not
mean for any of my remarks to be judgemental or disparaging as to how others
approach their work. I am just trying to communicate what I perceive as
(commercial and government sector) participant in the environmental business
for over 25 years.
In closing, some related scrap thoughts: We
operate (or should operate) in the context decision or decisions being
made and sometimes 'nominal' practice may suffice--although that has to be
reasonably demonstrated. I never have understood why decision analysis has
not had a better reception over the years. Also how are things going to play
out as some attempt to weave equifinality more into our consciousness?
Finally, all work has a finite shelf-life.
Best regards,
Mike
----- Original Message
-----
- From: Gregoire
Dubois
- To: [email protected]
- Sent: Wednesday, August 09, 2006 4:15 AM
- Subject: AI-GEOSTATS: Log versus nscore transform
- Dear list,
- I am puzzled about the use of logarithmic and nscore transforms in
geostatistics.
- Given the apparent advantages in using nscore transforms over the
logarithmic transform (nscore has no problem when dealing with 0 values
and is "managing" the tails of the distribution very (more?)
efficiently), why would one still want to use log-normal kriging?
Because of the mathematical elegance of using a model only?
- Moreover, one can frequently not be "sure" about the lognormality of
the analysed dataset, so why would one still take the risk of using
log-normal kriging?
- Thank you in advance for any feedback on this issue.
- Best regards,
- Gregoire
- __________________________________________
- Gregoire Dubois (Ph.D.)
- European Commission (EC)
- Joint Research Centre Directorate (DG JRC)
- Institute for Environment and Sustainability (IES)
- TP 441, Via Fermi 1
- 21020 Ispra (VA)
- ITALY
-
- Tel. +39 (0)332 78 6360
- Fax. +39 (0)332 78 5466
- Email: [EMAIL PROTECTED]
- WWW:
http://www.ai-geostats.org
- WWW:
http://rem.jrc.cec.eu.int
-
- "The views expressed are purely those of the writer and may not in
any circumstances be regarded as stating an official position of the
European Commission."
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