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

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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 1 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
      > =================================================
      >
      >
      >
      >
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      >


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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 2 of 10 , Apr 29 8:04 AM
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        Chaosheng, I agree with Pierre that if your only goal is to generate a
        probability map, then IK is faster and more straightforward than simulation
        and that MG 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 3 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 4 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 5 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 6 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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