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Hi Syed,
Maribeth actually presented an example of a
lognormal functional relationship between two parameters and not an example
of a lognormally distributed random variable (saturated hydraulic
conductivity). So I am not sure what statement of hers you consider to
be 'probably accurate.' So...
With regard to the saturated
hydraulic conductivity (K)--well, I note the inclusion of adverb
"empirically' in your statement. That is my point regarding saturated hydraulic
conductivity. Lognormality is a widely accepted and used rule of thumb
backed by observation). However, I do not believe it is in general established
from first principles, i.e., with no attendant assumptions. If I am wrong,
and that has been known to occur, someone please point me in the right
direction.
I have merely posited that
the assertion of lognormality has a strong historical/cultural
influence--at least for K. I interpreted Gregoire's question question as
why would one chose lognormality? and not when should one choose
lognormality? For some individuals the
choice of lognormality is more a deliberate selection of a model than
applying a transformation to facilitate calculations.* That would even
seem to be implied by the discussion in the thread where the lognormality of K
is 'defended'. For better or worse, it is second nature in many people and
people do like work with something they think they understand or think they have
seen.
A final observation: "petroleum engineers have been
struggling with these issues for a long while", but the resulting effort, the
use of empiricism--must be 'economically' viable because it has been used a
"long while" :O)
To my mind the viability of empirical models is an open question in
environmental work. Litigation.
Best
Regards,
Mike
* I hope that it is obvious that my remarks pertain
to the use of both geostatistics and classical
statistics.
----- Original Message -----
Sent: Friday, August 11, 2006 4:43
AM
Subject: Re: AI-GEOSTATS: Log versus
nscore transform
Michael,
Looking at the plots you mentioned, I doubt
that you'd ever get a straight line at high saturations purely because of the
presence of the capillary transition. I am thiking that straight line
(relative) conductivities will only be discernable at 100% saturation of any
one phase, and with no transition zone, denoting a clean break between two
phases. For instance, segregated flow of gas and water.
Absolute,
rather than relative, conductivities should empirically be close to log
normal, and Maribeth's statement is probably accurate.
Us hapless
petroleum engineers have been struggling with these issues for a long while,
and even worst, for multiphase flow at that (oil/gas/water simultaneously both
steady and unsteady state).
Regards,
Syed
On Thursday,
August 10, 2006, at 06:20PM, Michael Grant <[EMAIL PROTECTED]>
wrote:
>
><<Original Attached>>
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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