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

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  • Chaosheng Zhang
    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 1 of 10 , Apr 29 2:56 AM
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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 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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    • Brian R Gray
      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 2 of 10 , Apr 29 6:35 AM
      • 0 Attachment
        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
        Please respond to
        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
        =================================================




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      • Pierre Goovaerts
        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 3 of 10 , Apr 29 7:08 AM
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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 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
          your local probability distributions.
          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
          > Please respond to
          > 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
          >


          --
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        • McKenna, Sean A
          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 4 of 10 , Apr 29 8:04 AM
          • 0 Attachment
            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
            advantageous to use simulation for soil contamination studies, so I'll add
            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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            any useful responses to your questions.
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          • Isobel Clark
            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 5 of 10 , Apr 29 10:28 AM
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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 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
              Word format for download at my page
              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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            • Syed Abdul Rahman Shibli
              ... Taking this a step further, there was a paper in the AAPG Stochastic Modeling and Geostatistics Volume entitled The Visualization of Spatial Uncertainty
              Message 6 of 10 , Apr 29 12:34 PM
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                >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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              • Chuck Ehlschlaeger
                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 7 of 10 , Apr 29 10:29 PM
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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 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

                  The full paper is about to head out for peer review.

                  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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                • Chaosheng Zhang
                  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 8 of 10 , Apr 30 7:15 AM
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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 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
                    more comments.

                    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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