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AI-GEOSTATS: Risk Assessment with Gaussian Simulation?

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  • 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
    Message 1 of 10 , Apr 27, 2002
    • 0 Attachment
      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]
    • Pierre Goovaerts
      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
      • 0 Attachment
        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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      • 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 3 of 10 , Apr 29, 2002
        • 0 Attachment
          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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        • 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 4 of 10 , Apr 29, 2002
          • 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
            =================================================




            --
            * 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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          • 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 5 of 10 , Apr 29, 2002
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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
              >


              --
              * 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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            • 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 6 of 10 , Apr 29, 2002
              • 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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              • 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 7 of 10 , Apr 29, 2002
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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

                  __________________________________________________
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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 8 of 10 , Apr 29, 2002
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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 9 of 10 , Apr 29, 2002
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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 10 of 10 , Apr 30, 2002
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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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