## AI-GEOSTATS: Risk Assessment with Gaussian Simulation?

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• Dear list, First, I would like to say thank you to Gregoire for keeping this list alive. I m trying to do risk assessment , and I have some questions about
Message 1 of 10 , Apr 27, 2002
Dear list,

First, I would like to say thank you to Gregoire for keeping this list alive.

I'm trying to do "risk assessment", and I have some questions about risk assessment with Gaussian Simulation:

(1) How to produce a probability map?

With Gaussian simulation, we can produce many maps/realisations, e.g., 100. Based on the 100 maps, a probability map of higher than a threshold can be produced. I wonder how to produce such a probability map? My understanding is that for each pixel, we just count how many values out of the 100 are >threshold, and the number is regarded as the "probability". Am I right? It seems that this is a time consuming procedure with GIS map algebra. Are there any suggestions for a quick calculation?

(2) Is a probability map better than a Kriging interpolated map for the purpose of risk assessment?

(3) Is "PCLASS" function in IDRISI 32 Release 2 better/easier than the probability map from Gaussian simulation?

From the online help of IDRISI 32 R2, Section "Kriging and Simulation Notes", it says "If the final goal of simulated surfaces will be to directly reclassify the surfaces by a threshold value, and calculate a probability of occurrence for a process based on that threshold, conditional simulation may be unnecessary. Instead kriging and variance images may be created and then used together with PCLASS." Any comments?

(4) How to carry out "PCLASS"?

Following the above question, I have a problem in doing PCLASS. I cannot input the file name of Kriging variance to the field of "Value error" of the documentation file. It seems that this field only accepts a "value", not an "image file name" or anything in text. Anyone has the experience?

Cheers,

Chaosheng Zhang
=================================================
Dr. Chaosheng Zhang
Lecturer in GIS
Department of Geography
National University of Ireland
Galway
IRELAND

Tel: +353-91-524411 ext. 2375
Fax: +353-91-525700
Email: Chaosheng.Zhang@...
ChaoshengZhang@...
Web: http://www.nuigalway.ie/geography/zhang.html
=================================================

[Non-text portions of this message have been removed]
• Hello, In the past few years stochastic simulation has been increasingly used to produce probability maps. To my opinion it s generally a waste of CPU time
Message 2 of 10 , Apr 27, 2002
Hello,

In the past few years stochastic simulation has
been increasingly used to produce probability maps.
To my opinion it's generally a waste of CPU time since
similar information can be retrieved using kriging,
either in a multiGaussian framework or applied to
indicator transforms.
The issue of when using simulation vs kriging
is further discussed in:
Goovaerts, P. 2001.
Geostatistical modelling of uncertainty in soil science.
Geoderma, 103: 3-26.

I take this opportunity to thank Gregoire
for a remarkable and often challenging job
of keeping this e-mail list alive through the years.

Pierre
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

________ ________
| \ / | Pierre Goovaerts
|_ \ / _| Assistant professor
__|________\/________|__ Dept of Civil & Environmental Engineering
| | The University of Michigan
| M I C H I G A N | EWRE Building, Room 117
|________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
_| |_\ /_| |_
| |\ /| | E-mail: goovaert@...
|________| \/ |________| Phone: (734) 936-0141
Fax: (734) 763-2275
http://www-personal.engin.umich.edu/~goovaert/

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

On Sat, 27 Apr 2002, Chaosheng Zhang wrote:

> Dear list,
>
> First, I would like to say thank you to Gregoire for keeping this list alive.
>
> I'm trying to do "risk assessment", and I have some questions about risk assessment with Gaussian Simulation:
>
> (1) How to produce a probability map?
>
> With Gaussian simulation, we can produce many maps/realisations, e.g., 100. Based on the 100 maps, a probability map of higher than a threshold can be produced. I wonder how to produce such a probability map? My understanding is that for each pixel, we just count how many values out of the 100 are >threshold, and the number is regarded as the "probability". Am I right? It seems that this is a time consuming procedure with GIS map algebra. Are there any suggestions for a quick calculation?
>
> (2) Is a probability map better than a Kriging interpolated map for the purpose of risk assessment?
>
> (3) Is "PCLASS" function in IDRISI 32 Release 2 better/easier than the probability map from Gaussian simulation?
>
> >From the online help of IDRISI 32 R2, Section "Kriging and Simulation Notes", it says "If the final goal of simulated surfaces will be to directly reclassify the surfaces by a threshold value, and calculate a probability of occurrence for a process based on that threshold, conditional simulation may be unnecessary. Instead kriging and variance images may be created and then used together with PCLASS." Any comments?
>
> (4) How to carry out "PCLASS"?
>
> Following the above question, I have a problem in doing PCLASS. I cannot input the file name of Kriging variance to the field of "Value error" of the documentation file. It seems that this field only accepts a "value", not an "image file name" or anything in text. Anyone has the experience?
>
> Cheers,
>
> Chaosheng Zhang
> =================================================
> Dr. Chaosheng Zhang
> Lecturer in GIS
> Department of Geography
> National University of Ireland
> Galway
> IRELAND
>
> Tel: +353-91-524411 ext. 2375
> Fax: +353-91-525700
> Email: Chaosheng.Zhang@...
> ChaoshengZhang@...
> Web: http://www.nuigalway.ie/geography/zhang.html
> =================================================
>
>

--
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• Pierre, Thanks for the comments. It s my first time to use Gaussian simulation to do something possibly useful, and I have also found the calculation quite
Message 3 of 10 , Apr 29, 2002
Pierre,

Thanks for the comments. It's my first time to use Gaussian simulation to do
something possibly useful, and I have also found the calculation quite slow
even though the speed of my computer is not so bad. I'm using Idrisi 32
(with GStat), and the grid is about 500*500.

What I worry about is that how useful these realizations are? Obviously they
are not "realistic" even though some people say they want to produce a more
realistic map, instead of the smoothed Kriging map. Another concern is that
the probability map produced based on these realisations may not be so good
as the PCLASS (available in Idrisi), as PCLASS may have a better probability
background or clearer assumption. In PCLASS, the square root (not sure
yet???) of Kriging variances can be used as the RMS (root mean square) or
standard deviation of the pixel corresponding to the Kriging map, and the
probability > a threshold can be calculated based on the normal assumption.

More comments and suggestions will give me more confidence in doing the risk
assessment (heavy metal pollution in soils of a mine area).

Cheers,

Chaosheng

----- Original Message -----
From: "Pierre Goovaerts" <goovaert@...>
To: "Chaosheng Zhang" <Chaosheng.Zhang@...>
Cc: <ai-geostats@...>; "Dave McGrath" <dmcgrath@...>
Sent: Saturday, April 27, 2002 4:53 PM
Subject: Re: AI-GEOSTATS: Risk Assessment with Gaussian Simulation?

> Hello,
>
> In the past few years stochastic simulation has
> been increasingly used to produce probability maps.
> To my opinion it's generally a waste of CPU time since
> similar information can be retrieved using kriging,
> either in a multiGaussian framework or applied to
> indicator transforms.
> The issue of when using simulation vs kriging
> is further discussed in:
> Goovaerts, P. 2001.
> Geostatistical modelling of uncertainty in soil science.
> Geoderma, 103: 3-26.
>
> I take this opportunity to thank Gregoire
> for a remarkable and often challenging job
> of keeping this e-mail list alive through the years.
>
> Pierre
>
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
<><>
>
> ________ ________
> | \ / | Pierre Goovaerts
> |_ \ / _| Assistant professor
> __|________\/________|__ Dept of Civil & Environmental Engineering
> | | The University of Michigan
> | M I C H I G A N | EWRE Building, Room 117
> |________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
> _| |_\ /_| |_
> | |\ /| | E-mail: goovaert@...
> |________| \/ |________| Phone: (734) 936-0141
> Fax: (734) 763-2275
>
http://www-personal.engin.umich.edu/~goovaert/
>
>
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
<><>
>
>
> On Sat, 27 Apr 2002, Chaosheng Zhang wrote:
>
> > Dear list,
> >
> > First, I would like to say thank you to Gregoire for keeping this list
alive.
> >
> > I'm trying to do "risk assessment", and I have some questions about risk
assessment with Gaussian Simulation:
> >
> > (1) How to produce a probability map?
> >
> > With Gaussian simulation, we can produce many maps/realisations, e.g.,
100. Based on the 100 maps, a probability map of higher than a threshold can
be produced. I wonder how to produce such a probability map? My
understanding is that for each pixel, we just count how many values out of
the 100 are >threshold, and the number is regarded as the "probability". Am
I right? It seems that this is a time consuming procedure with GIS map
algebra. Are there any suggestions for a quick calculation?
> >
> > (2) Is a probability map better than a Kriging interpolated map for the
purpose of risk assessment?
> >
> > (3) Is "PCLASS" function in IDRISI 32 Release 2 better/easier than the
probability map from Gaussian simulation?
> >
> > >From the online help of IDRISI 32 R2, Section "Kriging and Simulation
Notes", it says "If the final goal of simulated surfaces will be to directly
reclassify the surfaces by a threshold value, and calculate a probability of
occurrence for a process based on that threshold, conditional simulation may
be unnecessary. Instead kriging and variance images may be created and then
used together with PCLASS." Any comments?
> >
> > (4) How to carry out "PCLASS"?
> >
> > Following the above question, I have a problem in doing PCLASS. I cannot
input the file name of Kriging variance to the field of "Value error" of the
documentation file. It seems that this field only accepts a "value", not an
"image file name" or anything in text. Anyone has the experience?
> >
> > Cheers,
> >
> > Chaosheng Zhang
> > =================================================
> > Dr. Chaosheng Zhang
> > Lecturer in GIS
> > Department of Geography
> > National University of Ireland
> > Galway
> > IRELAND
> >
> > Tel: +353-91-524411 ext. 2375
> > Fax: +353-91-525700
> > Email: Chaosheng.Zhang@...
> > ChaoshengZhang@...
> > Web: http://www.nuigalway.ie/geography/zhang.html
> > =================================================
> >
> >
>
>

--
* To post a message to the list, send it to ai-geostats@...
* As a general service to the users, please remember to post a summary of any useful responses to your questions.
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• I am curious about the use of 100 realizations to generate a probability map. is this a standard approach? if so, is a small p-value (such as .05) used?
Message 4 of 10 , Apr 29, 2002
I am curious about the use of 100 realizations to generate a probability
map. is this a standard approach? if so, is a "small" p-value (such as
.05) used? if so, it would seem like 100 iterations might be a smallish
sample size for distinguishing, say, .05 (ie 5 outcomes out of 100) from,
say, .01. is 100 used because it seems like it is a reasonable number or
because of the computer time restrictions?

do geostat folks treat these as realizations or as pseudo-realizations?

brian

****************************************************************
Brian Gray
USGS Upper Midwest Environmental Sciences Center
575 Lester Avenue, Onalaska, WI 54650
ph 608-783-7550 ext 19, FAX 608-783-8058
brgray@...
*****************************************************************

Chaosheng Zhang
<Chaosheng.Zhang@nui To: ai-geostats@...
galway.ie> cc: Dave McGrath <dmcgrath@...>
Sent by: Subject: AI-GEOSTATS: Risk Assessment with Gaussian Simulation?
ai-geostats-list@uni
l.ch

04/27/2002 10:25 AM
Chaosheng Zhang

Dear list,

First, I would like to say thank you to Gregoire for keeping this list
alive.

I'm trying to do "risk assessment", and I have some questions about risk
assessment with Gaussian Simulation:

(1) How to produce a probability map?

With Gaussian simulation, we can produce many maps/realisations, e.g., 100.
Based on the 100 maps, a probability map of higher than a threshold can be
produced. I wonder how to produce such a probability map? My understanding
is that for each pixel, we just count how many values out of the 100 are
>threshold, and the number is regarded as the "probability". Am I right? It
seems that this is a time consuming procedure with GIS map algebra. Are
there any suggestions for a quick calculation?

(2) Is a probability map better than a Kriging interpolated map for the
purpose of risk assessment?

(3) Is "PCLASS" function in IDRISI 32 Release 2 better/easier than the
probability map from Gaussian simulation?

From the online help of IDRISI 32 R2, Section "Kriging and Simulation
Notes", it says "If the final goal of simulated surfaces will be to
directly reclassify the surfaces by a threshold value, and calculate a
probability of occurrence for a process based on that threshold,
conditional simulation may be unnecessary. Instead kriging and variance
images may be created and then used together with PCLASS." Any comments?

(4) How to carry out "PCLASS"?

Following the above question, I have a problem in doing PCLASS. I cannot
input the file name of Kriging variance to the field of "Value error" of
the documentation file. It seems that this field only accepts a "value",
not an "image file name" or anything in text. Anyone has the experience?

Cheers,

Chaosheng Zhang
=================================================
Dr. Chaosheng Zhang
Lecturer in GIS
Department of Geography
National University of Ireland
Galway
IRELAND

Tel: +353-91-524411 ext. 2375
Fax: +353-91-525700
Email: Chaosheng.Zhang@...
ChaoshengZhang@...
Web: http://www.nuigalway.ie/geography/zhang.html
=================================================

--
* To post a message to the list, send it to ai-geostats@...
* As a general service to the users, please remember to post a summary of any useful responses to your questions.
* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
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• Hi Brian, One hundred realizations are typically generated mainly for CPU reasons. You are perfectly right that this number is too small when looking at small
Message 5 of 10 , Apr 29, 2002
Hi Brian,

One hundred realizations are typically generated
mainly for CPU reasons.
You are perfectly right that this number is
too small when looking at small probabilities
like 0.05 or 0.01. It's why I wouldn't recommend
using stochastic simulation to derive probability of occurrence
of events at pixel locations. Just use kriging to build
Use simulation if you have a transfer function, such as flow
simulator, that requires a model of spatial uncertainty,
or if you need to derive block probability distributions
(upscaling or aggregation problems).

More generally, there is more research to be done on the
use of stochastic simulation for probabilistic assessment,
including the question of equally-probability of realizatiuons
being generated.

Pierre
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

________ ________
| \ / | Pierre Goovaerts
|_ \ / _| Assistant professor
__|________\/________|__ Dept of Civil & Environmental Engineering
| | The University of Michigan
| M I C H I G A N | EWRE Building, Room 117
|________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
_| |_\ /_| |_
| |\ /| | E-mail: goovaert@...
|________| \/ |________| Phone: (734) 936-0141
Fax: (734) 763-2275
http://www-personal.engin.umich.edu/~goovaert/

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

On Mon, 29 Apr 2002, Brian R Gray wrote:

>
> I am curious about the use of 100 realizations to generate a probability
> map. is this a standard approach? if so, is a "small" p-value (such as
> .05) used? if so, it would seem like 100 iterations might be a smallish
> sample size for distinguishing, say, .05 (ie 5 outcomes out of 100) from,
> say, .01. is 100 used because it seems like it is a reasonable number or
> because of the computer time restrictions?
>
> do geostat folks treat these as realizations or as pseudo-realizations?
>
> brian
>
> ****************************************************************
> Brian Gray
> USGS Upper Midwest Environmental Sciences Center
> 575 Lester Avenue, Onalaska, WI 54650
> ph 608-783-7550 ext 19, FAX 608-783-8058
> brgray@...
> *****************************************************************
>
>
>
> Chaosheng Zhang
> <Chaosheng.Zhang@nui To: ai-geostats@...
> galway.ie> cc: Dave McGrath <dmcgrath@...>
> Sent by: Subject: AI-GEOSTATS: Risk Assessment with Gaussian Simulation?
> ai-geostats-list@uni
> l.ch
>
>
> 04/27/2002 10:25 AM
> Chaosheng Zhang
>
>
>
>
>
> Dear list,
>
> First, I would like to say thank you to Gregoire for keeping this list
> alive.
>
> I'm trying to do "risk assessment", and I have some questions about risk
> assessment with Gaussian Simulation:
>
> (1) How to produce a probability map?
>
> With Gaussian simulation, we can produce many maps/realisations, e.g., 100.
> Based on the 100 maps, a probability map of higher than a threshold can be
> produced. I wonder how to produce such a probability map? My understanding
> is that for each pixel, we just count how many values out of the 100 are
> >threshold, and the number is regarded as the "probability". Am I right? It
> seems that this is a time consuming procedure with GIS map algebra. Are
> there any suggestions for a quick calculation?
>
> (2) Is a probability map better than a Kriging interpolated map for the
> purpose of risk assessment?
>
> (3) Is "PCLASS" function in IDRISI 32 Release 2 better/easier than the
> probability map from Gaussian simulation?
>
> >From the online help of IDRISI 32 R2, Section "Kriging and Simulation
> Notes", it says "If the final goal of simulated surfaces will be to
> directly reclassify the surfaces by a threshold value, and calculate a
> probability of occurrence for a process based on that threshold,
> conditional simulation may be unnecessary. Instead kriging and variance
> images may be created and then used together with PCLASS." Any comments?
>
> (4) How to carry out "PCLASS"?
>
> Following the above question, I have a problem in doing PCLASS. I cannot
> input the file name of Kriging variance to the field of "Value error" of
> the documentation file. It seems that this field only accepts a "value",
> not an "image file name" or anything in text. Anyone has the experience?
>
> Cheers,
>
> Chaosheng Zhang
> =================================================
> Dr. Chaosheng Zhang
> Lecturer in GIS
> Department of Geography
> National University of Ireland
> Galway
> IRELAND
>
> Tel: +353-91-524411 ext. 2375
> Fax: +353-91-525700
> Email: Chaosheng.Zhang@...
> ChaoshengZhang@...
> Web: http://www.nuigalway.ie/geography/zhang.html
> =================================================
>
>
>
>
> --
> * To post a message to the list, send it to ai-geostats@...
> * As a general service to the users, please remember to post a summary of any useful responses to your questions.
> * To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
> * Support to the list is provided at http://www.ai-geostats.org
>

--
* To post a message to the list, send it to ai-geostats@...
* As a general service to the users, please remember to post a summary of any useful responses to your questions.
* To unsubscribe, send an email to majordomo@... with no subject and "unsubscribe ai-geostats" followed by "end" on the next line in the message body. DO NOT SEND Subscribe/Unsubscribe requests to the list
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• Chaosheng, I agree with Pierre that if your only goal is to generate a probability map, then IK is faster and more straightforward than simulation and that MG
Message 6 of 10 , Apr 29, 2002
Chaosheng, I agree with Pierre that if your only goal is to generate a
probability map, then IK is faster and more straightforward than simulation
and that MG kriging will give the same results, faster, than MG simulation.

However, we have found a couple of practical reasons where it may be
my two cents worth to this discussion:

1) When trying to explain the concepts of spatial variability and
uncertainty, we have found that showing example realizations of what the
possible distribution of contaminants could look like provides the groups
involved to get a more intuitive understanding of these ideas. People
understand the idea of flipping a coin 100 times to get the probability of
heads or tails, but have a hard time visualizing in their mind what a "coin
flip" looks like in a 2-D soil contamination problem. Showing some example
conditional realizations gives them a stronger feel for the nature of the
answers geostats is providing to their questions.

2) A number of sites are in the process of designing chemical and/or
mechanical treatment systems for the soil that will be removed from the site
while the remediation map is being determined. One set of design parameters
for these treatment systems is the best and worst case estimates of the
total amount of contamination (curies, grams, etc.) contained in the soil at
the site. These best/worst case estimates depend on the joint estimate of
the contamination at all locations across the site. This is something
simulation provides, but kriging doesn't.

3) For soils with radioactive contaminants, there are a number of different
sensors (e.g., a gamma detector mounted several meters off the ground) being
deployed at field sites that integrate the activity of the contaminant over
a larger area/volume. Simulation of the fine scale distribution of the
activity can be useful in looking at how these sensors scale up the activity
values to the integrated measurement.

Also when looking at IK vs MG kriging (or simulation) keep in mind that
rarely do the client, stakeholder(s) and regulator(s) have a single action
level or threshold that they have all agreed to for application at the site.
There are usually multiple thresholds corresponding to different future-land
use scenarios and different health risk models. If creating the probabilty
maps through IK then each different threshold requires a new set of
indicator variograms. If you use MG kriging or simulation, you only need do
the variography once-keep in mind that the MG assumption does have other
problems with connectivity of extreme values that may or may not be
important in your application (this is generally a bigger concern in fluid
flow problems than in soil contamination problems).

I'll add my thanks to Gregoire for 7 years of superb work!

Sean

Sean A. McKenna Ph.D.
Geohydrology Department
Sandia National Laboratories
PO Box 5800 MS 0735
Albuquerque, NM 87185-0735
ph: 505 844-2450

-----Original Message-----
From: Chaosheng Zhang [mailto:Chaosheng.Zhang@...]
Sent: Monday, April 29, 2002 3:57 AM
To: Pierre Goovaerts
Cc: ai-geostats@...; Dave McGrath
Subject: Re: AI-GEOSTATS: Risk Assessment with Gaussian Simulation?

Pierre,

Thanks for the comments. It's my first time to use Gaussian simulation to do
something possibly useful, and I have also found the calculation quite slow
even though the speed of my computer is not so bad. I'm using Idrisi 32
(with GStat), and the grid is about 500*500.

What I worry about is that how useful these realizations are? Obviously they
are not "realistic" even though some people say they want to produce a more
realistic map, instead of the smoothed Kriging map. Another concern is that
the probability map produced based on these realisations may not be so good
as the PCLASS (available in Idrisi), as PCLASS may have a better probability
background or clearer assumption. In PCLASS, the square root (not sure
yet???) of Kriging variances can be used as the RMS (root mean square) or
standard deviation of the pixel corresponding to the Kriging map, and the
probability > a threshold can be calculated based on the normal assumption.

More comments and suggestions will give me more confidence in doing the risk
assessment (heavy metal pollution in soils of a mine area).

Cheers,

Chaosheng

----- Original Message -----
From: "Pierre Goovaerts" <goovaert@...>
To: "Chaosheng Zhang" <Chaosheng.Zhang@...>
Cc: <ai-geostats@...>; "Dave McGrath" <dmcgrath@...>
Sent: Saturday, April 27, 2002 4:53 PM
Subject: Re: AI-GEOSTATS: Risk Assessment with Gaussian Simulation?

> Hello,
>
> In the past few years stochastic simulation has
> been increasingly used to produce probability maps.
> To my opinion it's generally a waste of CPU time since
> similar information can be retrieved using kriging,
> either in a multiGaussian framework or applied to
> indicator transforms.
> The issue of when using simulation vs kriging
> is further discussed in:
> Goovaerts, P. 2001.
> Geostatistical modelling of uncertainty in soil science.
> Geoderma, 103: 3-26.
>
> I take this opportunity to thank Gregoire
> for a remarkable and often challenging job
> of keeping this e-mail list alive through the years.
>
> Pierre
>
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
<><>
>
> ________ ________
> | \ / | Pierre Goovaerts
> |_ \ / _| Assistant professor
> __|________\/________|__ Dept of Civil & Environmental Engineering
> | | The University of Michigan
> | M I C H I G A N | EWRE Building, Room 117
> |________________________| Ann Arbor, Michigan, 48109-2125, U.S.A
> _| |_\ /_| |_
> | |\ /| | E-mail: goovaert@...
> |________| \/ |________| Phone: (734) 936-0141
> Fax: (734) 763-2275
>
http://www-personal.engin.umich.edu/~goovaert/
>
>
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
<><>
>
>
> On Sat, 27 Apr 2002, Chaosheng Zhang wrote:
>
> > Dear list,
> >
> > First, I would like to say thank you to Gregoire for keeping this list
alive.
> >
> > I'm trying to do "risk assessment", and I have some questions about risk
assessment with Gaussian Simulation:
> >
> > (1) How to produce a probability map?
> >
> > With Gaussian simulation, we can produce many maps/realisations, e.g.,
100. Based on the 100 maps, a probability map of higher than a threshold can
be produced. I wonder how to produce such a probability map? My
understanding is that for each pixel, we just count how many values out of
the 100 are >threshold, and the number is regarded as the "probability". Am
I right? It seems that this is a time consuming procedure with GIS map
algebra. Are there any suggestions for a quick calculation?
> >
> > (2) Is a probability map better than a Kriging interpolated map for the
purpose of risk assessment?
> >
> > (3) Is "PCLASS" function in IDRISI 32 Release 2 better/easier than the
probability map from Gaussian simulation?
> >
> > >From the online help of IDRISI 32 R2, Section "Kriging and Simulation
Notes", it says "If the final goal of simulated surfaces will be to directly
reclassify the surfaces by a threshold value, and calculate a probability of
occurrence for a process based on that threshold, conditional simulation may
be unnecessary. Instead kriging and variance images may be created and then
used together with PCLASS." Any comments?
> >
> > (4) How to carry out "PCLASS"?
> >
> > Following the above question, I have a problem in doing PCLASS. I cannot
input the file name of Kriging variance to the field of "Value error" of the
documentation file. It seems that this field only accepts a "value", not an
"image file name" or anything in text. Anyone has the experience?
> >
> > Cheers,
> >
> > Chaosheng Zhang
> > =================================================
> > Dr. Chaosheng Zhang
> > Lecturer in GIS
> > Department of Geography
> > National University of Ireland
> > Galway
> > IRELAND
> >
> > Tel: +353-91-524411 ext. 2375
> > Fax: +353-91-525700
> > Email: Chaosheng.Zhang@...
> > ChaoshengZhang@...
> > Web: http://www.nuigalway.ie/geography/zhang.html
> > =================================================
> >
> >
>
>

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• My tuppence worth. The major advantages of simulation as a risk assessment tool lie in the cases where you are trying to derive some conclusion from the data
Message 7 of 10 , Apr 29, 2002
My tuppence worth.

The major advantages of simulation as a risk
assessment tool lie in the cases where you are trying
to derive some conclusion from the data rather than
just look at the values themselves.

For example, see Bill and my papers at Battelle
Conference 1987 or the paper at the Geostat Avignon in
1988. There are oters. All of these are available in
http://uk.geocities.com/drisobelclark/resume/Publications.html

We were trying to derive the travel path of a particle
given the pressure of fluid in an aquifer. Not a
linear transform by anyone's standards.

Isobel Clark

__________________________________________________
Do You Yahoo!?
Everything you'll ever need on one web page
from News and Sport to Email and Music Charts
http://uk.my.yahoo.com

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• ... Taking this a step further, there was a paper in the AAPG Stochastic Modeling and Geostatistics Volume entitled The Visualization of Spatial Uncertainty
Message 8 of 10 , Apr 29, 2002
>From: "McKenna, Sean A" <samcken@...>
>
>1) When trying to explain the concepts of spatial variability and
>uncertainty, we have found that showing example realizations of what the
>possible distribution of contaminants could look like provides the groups
>involved to get a more intuitive understanding of these ideas.

Taking this a step further, there was a paper in the AAPG Stochastic
Modeling and Geostatistics Volume entitled "The Visualization
of Spatial Uncertainty" (R Mohan Srivastava) which proposes the use
of probability field simulation to generate dynamic animations
of different realizations. I have yet to see it being implemented in
commercial software, although in concept I can see the benefit
of having something like this to illustrate the "equiprobable"
realizations. The idea was to generate smooth transitions of
successive "frames" by sampling from adjacent columns of a set of
probability values, for a movie-like effect.

Syed

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• Dear Syed, et al., I did much of what you described in the GRASS GIS a while back. (GRASS is public domain, not commercial, but it is a very good GIS.) The
Message 9 of 10 , Apr 29, 2002
Dear Syed, et al.,

I did much of what you described in the GRASS GIS a while back. (GRASS
is public domain, not commercial, but it is a very good GIS.) The title
of the paper is "Visualizing Spatial Data Uncertainty Using Animation"
and a copy of it is located at:

http://www.geo.hunter.cuny.edu/~chuck/CGFinal/paper.htm

The special issue of Computers & Geosciences (Vol. 23, No. 4, pp.
387-395, 1997) included a CD-ROM that contained some of the animations
in MPEG form. My web site includes the animations and instructions on
how to construct them.

I used spherical interpolation to generate smooth transitions between
realizations in order to keep the interpolations valid statistically.

I have a more recent work that studies user perception of animated maps
representing data and application uncertainty. An outline of that work
from a conference presentation (with all equations and animations) is
available at:

http://www.geo.hunter.cuny.edu/~chuck/GIScience2000/paper.html

sincerely, chuck

Syed Abdul Rahman Shibli wrote:
>
> >From: "McKenna, Sean A" <samcken@...>
> >
> >1) When trying to explain the concepts of spatial variability and
> >uncertainty, we have found that showing example realizations of what the
> >possible distribution of contaminants could look like provides the groups
> >involved to get a more intuitive understanding of these ideas.
>
> Taking this a step further, there was a paper in the AAPG Stochastic
> Modeling and Geostatistics Volume entitled "The Visualization
> of Spatial Uncertainty" (R Mohan Srivastava) which proposes the use
> of probability field simulation to generate dynamic animations
> of different realizations. I have yet to see it being implemented in
> commercial software, although in concept I can see the benefit
> of having something like this to illustrate the "equiprobable"
> realizations. The idea was to generate smooth transitions of
> successive "frames" by sampling from adjacent columns of a set of
> probability values, for a movie-like effect.

--
Chuck Ehlschlaeger N 40 46' 07.7", W 73 57' 54.4"
Dep. of Geography 212-772-5321, fax: 212-772-5268
Hunter College chuck@...
695 Park Ave. http://www.geo.hunter.cuny.edu/~chuck/
New York, NY 10021
"We should not be ashamed to acknowledge truth from whatever
source it comes to us, even if it is brought to us by former
generations and foreign people. For whoever seeks the truth
there is nothing of higher value than truth itself" - al-Kindi

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• Dear all, Thanks for so many interesting replies and thoughtful discussion. This is not a summary yet, as I am expecting more to come. Just to express my
Message 10 of 10 , Apr 30, 2002
Dear all,

Thanks for so many interesting replies and thoughtful discussion. This is
not a summary yet, as I am expecting more to come.

Just to express my feeling about Indicator Kriging. To produce a probability
map, IK might be one of the choices. However, I always feel that too much
information is lost when doing the indicator transformation. When I see so
many "0"s in a dataset, I just feel the data quality is too poor.

Well, the other method of combination of Kriging and Kriging variance for
risk assessment has not been well discussed yet, and I would like to read

My last question "(4) how to carry out "PCLASS" " is now answered by the
developer of Idrisi. The fact that the file name of Kriging variance cannot
be entered (with Metadata command) is a bug of the program, which will be
corrected soon. At present time, a text editor may be used to modify the
image documentation file.

Now, let me discuss how I would like to make a probability map based on
Kriging and Kriging variance. For each pixel of the Kriging interpolated
map, there is a value of Kriging variance. The Kriging variance is a measure
of uncertainty (which is related to sampling density and spatial variation,
etc.???). If we assume that the value of the Kriging pixel follow a normal
distribution and the standard deviation is equal to the SQRT of Kriging
variance, the probability of any threshold can be calculated. Furthermore,
to make the risk assessment more realistic, I would like to include other
errors, such as sampling error and laboratory analysis error into risk
assessment. These errors can hardly be quantified, but if we say 10% or 20%
of the pixel value (for soil samples), perhaps there is no objection.
Therefore, the standard deviation of the pixel is increased by adding this
kind of errors.

I am not clear how to calculate the total standard deviation of the two
sources, is it:
Total standard deviation =
SQRT (Kriging Variance + SQUARE (Sampling Errors) ) ?

Any ideas and comments on this method?

Chaosheng Zhang

> On Sat, 27 Apr 2002, Chaosheng Zhang wrote:
>
> Dear list,
>
> First, I would like to say thank you to Gregoire for keeping this list
alive.
>
> I'm trying to do "risk assessment", and I have some questions about risk
assessment with Gaussian Simulation:
>
> (1) How to produce a probability map?
>
> With Gaussian simulation, we can produce many maps/realisations, e.g.,
> 100. Based on the 100 maps, a probability map of higher than a threshold
can
> be produced. I wonder how to produce such a probability map? My
> understanding is that for each pixel, we just count how many values out of
> the 100 are >threshold, and the number is regarded as the "probability".
Am
> I right? It seems that this is a time consuming procedure with GIS map
> algebra. Are there any suggestions for a quick calculation?
>
> (2) Is a probability map better than a Kriging interpolated map for the
> purpose of risk assessment?
>
> (3) Is "PCLASS" function in IDRISI 32 Release 2 better/easier than the
> probability map from Gaussian simulation?
>
>From the online help of IDRISI 32 R2, Section "Kriging and Simulation
> Notes", it says "If the final goal of simulated surfaces will be to
directly
> reclassify the surfaces by a threshold value, and calculate a probability
of
> occurrence for a process based on that threshold, conditional simulation
may
> be unnecessary. Instead kriging and variance images may be created and
then
> used together with PCLASS." Any comments?
>
> (4) How to carry out "PCLASS"?
>
> Following the above question, I have a problem in doing PCLASS. I cannot
> input the file name of Kriging variance to the field of "Value error" of
the
> documentation file. It seems that this field only accepts a "value", not
an
> "image file name" or anything in text. Anyone has the experience?
>
> Cheers,
>
> Chaosheng Zhang
> =================================================
> Dr. Chaosheng Zhang
> Lecturer in GIS
> Department of Geography
> National University of Ireland
> Galway
> IRELAND
>
> Tel: +353-91-524411 ext. 2375
> Fax: +353-91-525700
> Email: Chaosheng.Zhang@...
> ChaoshengZhang@...
> Web: http://www.nuigalway.ie/geography/zhang.html
> =================================================
>

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