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R: AI-GEOSTATS: Extreme values?

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  • claudio.cocheo
    Dear Chaosheng, ... Is it possible, in your opinion, to model your variogram excluding those few extremes data and after to krige all data, included the
    Message 1 of 10 , Dec 14, 2001
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      Dear Chaosheng,

      > Thanks. I think the sampling density is good enough to reveal the spatial
      > structure, and the extreme samples are located within the "hot spots". The
      > problem is that the few values are still extremely high within the "hot
      > spots". This may be what the "nugget effect" means.
      >
      > I'm just wondering if these few extreme values should really be
      > "discarded"/
      > "censored" or replaced. However, this could get some criticism as they may
      > be "real".

      Is it possible, in your opinion, to model your variogram excluding those few
      extremes data and after to krige all data, included the extremes values?
      In this way, probably, you loose some spatial information concerning the
      variability of your data but you could obtain a more reliable picture of the
      "background" values. It depends from what you are asking to your data.
      What you, or somebody else, think about?

      regards
      Claudio

      ----------------------------------------------------------------------------
      -----------------------------

      Claudio Cocheo
      Fondazione Salvatore Maugeri - IRCCS
      Centro di Ricerche Ambientali
      via Svizzera, 16
      I 35127 - Padova
      ph. (39) 0498064511
      fax (39) 0498064555
      mailto:ccocheo@...
      website: http://www.fsm.it


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    • Martin Roseveare
      Chaosheng Zhang said Another problem is when we carry out spatial interpolation, these values may produce artificial contour lines around these sampling
      Message 2 of 10 , Dec 14, 2001
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        Chaosheng Zhang said

        "Another problem is when we carry out spatial interpolation, these values
        may
        produce artificial contour lines around these sampling locations, even
        though they can be smoothed. I don't think this is the realistic situation
        in the field."

        This sounds like the crux of the problem. You sampled data and within it you
        have discrete large values. You have confidence in the integrity of the data
        but don't accept that for these values to be genuine you must have all these
        'artificial' contour lines. This suggests to me that you are expecting the
        data to behave so that these large values don't exist, yet you are saying
        they should be regarded as valid. Is your sampling at a high enough spatial
        resolution?

        If you were to sample another point right next to one of these large values
        would you expect another large value or a more 'normal' one? If you know the
        answer to that then you should be able to decide whether the large values
        are truly errors or simply unexpected but valid data. I would suggest the
        problem here lies with understanding the underlying spatial variation of the
        data set from which the samples were taken, rather than a problem of which
        process to apply to the sampled data.

        Just another way of looking at it!

        regards,

        Martin

        ______________________________________

        ArchaeoPhysica Ltd.
        Reconnaissance & Geophysics for Archaeology

        Telephone: +44 (0) 7050 369789
        E-mail: mail@...
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      • Pierre Goovaerts
        Hello, The crux of the problem is the smoothing effect of kriging. If you don t want to get artificial countour lines in your map, you have 2 choices: 1. use
        Message 3 of 10 , Dec 14, 2001
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          Hello,

          The crux of the problem is the smoothing effect of kriging.
          If you don't want to get artificial countour lines in your
          map, you have 2 choices:
          1. use stochastic simulation which generates maps that
          are consistent with (reproduce) the variability of your data.
          2. use a non-exact interpolator, that is filter the
          noise at data locations. An alternative is to slightly
          shift the interpolation grid so that no interpolation
          grid node coincides with a sampled location.

          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 Fri, 14 Dec 2001, Martin Roseveare wrote:

          > Chaosheng Zhang said
          >
          > "Another problem is when we carry out spatial interpolation, these values
          > may
          > produce artificial contour lines around these sampling locations, even
          > though they can be smoothed. I don't think this is the realistic situation
          > in the field."
          >
          > This sounds like the crux of the problem. You sampled data and within it you
          > have discrete large values. You have confidence in the integrity of the data
          > but don't accept that for these values to be genuine you must have all these
          > 'artificial' contour lines. This suggests to me that you are expecting the
          > data to behave so that these large values don't exist, yet you are saying
          > they should be regarded as valid. Is your sampling at a high enough spatial
          > resolution?
          >
          > If you were to sample another point right next to one of these large values
          > would you expect another large value or a more 'normal' one? If you know the
          > answer to that then you should be able to decide whether the large values
          > are truly errors or simply unexpected but valid data. I would suggest the
          > problem here lies with understanding the underlying spatial variation of the
          > data set from which the samples were taken, rather than a problem of which
          > process to apply to the sampled data.
          >
          > Just another way of looking at it!
          >
          > regards,
          >
          > Martin
          >
          > ______________________________________
          >
          > ArchaeoPhysica Ltd.
          > Reconnaissance & Geophysics for Archaeology
          >
          > Telephone: +44 (0) 7050 369789
          > E-mail: mail@...
          > Website: http://www.archaeophysica.co.uk
          > ______________________________________
          >
          > This e-mail is intended only for the addressee
          > named above and may contain confidential or
          > privileged information. If you receive this e-mail
          > by mistake please advise the sender and destroy
          > it without further disclosure of its content.
          >
          > Unless otherwise stated no opinions expressed in
          > this e-mail should be regarded as representative of
          > any policy of ArchaeoPhysica Ltd.
          >
          >
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          >


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        • Marcel Vallée
          Dear Chaosheng Zhang This problem can be looked in various perspectives. You have to fit the data in the broader picture and objectives. First, what do your
          Message 4 of 10 , Dec 14, 2001
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            Dear Chaosheng Zhang

            This problem can be looked in various perspectives. You have to fit the data in the broader
            picture and objectives.

            First, what do your soil samples represent? How were they collected, what was their size? Are
            they spot samples, multiple takes in a cross pattern with x metres between takes up to y
            meters away from the centre? Etc.?

            A significant part of nuggets effects when dealing with rock or soil materials may be sampling
            and sample preparation generated. If these samples were assayed by AA, what was the size
            of the portion used? If one gram, it is much more liable to generating a nugget effect than with 5
            or 10 grams whenever pulverisation size was not fine enough and uniform.

            Second, what is the purpose of your study. Academic work? Detection, remediation-
            restoration, etc.? The high values might have physical significance in the later perspective
            and smothing them may not be the ideal solution. Lead and Arsenic contamination cannot be
            neglected or minimized.

            In an industry or regulation perspective, the recommendation in that case might be to to carry
            out additional sampling around the hot spots to delineate them better, say samples at 100 m
            spacing, as well as checking the original hot spots, with a sampling method designed to be
            representative. I am afraid I may not be easing you out of your problem, but such is physical
            reality.

            Chapter 8 in Jeff Myer's book "Geostatistical Error Management," deals with sampling and
            Chapter 16 with sampling strategy. I published a text on "Sampling Quality Control" in a
            mineral exploration and development perspective in Exploration and Mining Geology, Vol 7,
            No 1-2, p. 107-116 (1998). This issue has several other papers on sampling. If it is not
            available to you, I could send you a file copy of my paper.

            Cheers

            Marcel Vallée

            Geoconseil Marcel Vallée Inc.
            706 Routhier Ave
            Québec, Québec G1X 3J9
            Canada
            Tel: (1) 418 652 3497
            Fax: (1) 418 652 9148
            Email: vallee.marcel@...

            ================================================

            14/12/01 06:33:35, Chaosheng Zhang <Chaosheng.Zhang@...> wrote:

            >Dear Marcel Vallée,
            >
            >Thanks. I think the sampling density is good enough to reveal the spatial
            >structure, and the extreme samples are located within the "hot spots". The
            >problem is that the few values are still extremely high within the "hot
            >spots". This may be what the "nugget effect" means.
            >
            >I'm just wondering if these few extreme values should really be "discarded"/
            >"censored" or replaced. However, this could get some criticism as they may
            >be "real".
            >
            >If it is hard to find the best way, I will have to "replace" all the extreme
            >values with 99% or 98% percentiles. But I'm not sure if it is appropriate to
            >do so.
            >
            >Cheers,
            >
            >Chaosheng Zhang
            >
            >
            >----- Original Message -----
            >From: "Marcel Vallée" <vallee.marcel@...>
            >To: <ai-geostats@...>; "Chaosheng Zhang" <Chaosheng.Zhang@...>
            >Sent: Thursday, December 13, 2001 10:40 PM
            >Subject: Re: AI-GEOSTATS: Extreme values?
            >
            >
            >>
            >> Dear Chaosheng Zang
            >>
            >> The sampling interval is so wide that the high values could easily be
            >>related to "hot spots" of
            >> higher grade contamination, i..e dumping areas for particular kinds of
            >>slags, mineralized waste, etc. A property map might help.
            >>
            >> Have you contoured the data? If so, the sampling interval is so wide that
            >>real hot spots of
            >> environmental significance might not show 2D distribution on such a wide
            >sampling grid, however.
            >>
            >> Regards
            >>
            >> Marcel Vallée, Eng,, Geo.
            >> Geoconseil Marcel Vallée Inc.
            >> 706 Routhier Ave
            >> Québec, Québec G1X 3J9
            >> Canada
            >> Tel: (1) 418 652 3497
            >> Fax: (1) 418 652 9148
            >> Email: vallee.marcel@...
            >>
            >> ==============================================
            >> 13/12/01 08:01:48, Chaosheng Zhang <Chaosheng.Zhang@...> wrote:
            >> >
            >> > Date: Thu, 13 Dec 2001 13:01:48 +0000
            >> >
            >> > From: Chaosheng Zhang <Chaosheng.Zhang@...>
            >> > Subject:AI-GEOSTATS: Extreme values?
            >> > To: ai-geostats@...
            >> >
            >> > Dear all,
            >> >
            >> > My question is: How to deal with the extreme/outlying values in a data
            >>>set?
            >>>
            >> > I am dealing with heavy metal concentrations in soils from a mine area.
            >>>The sample number is 223, and the samples are spatially evenly distributed
            >>>with the sampling interval of 400 metres. There are several samples with
            >>>extremely high values, which makes me feel uncomfortable. The
            >>>percentiles of the dataset are listed as follows (in mg/kg):
            >> >
            >> >
            >> > Zn Cu Pb Cd As
            >> > Min 4 1 25 0.0 2
            >> > 5% 35 6 35 0.1 6
            >> > 10% 40 7 41 0.2 7
            >> >
            >> > 25% 65 13 62 0.3 9
            >> > 50% 122 18 168 0.6 15
            >> > 75% 338 27 821 1.5 28
            >> > 90% 907 56 2799 2.8 58
            >> >
            >> > 95% 1986 116 4490 4.2 80
            >> > 96% 2462 151 4698 4.9 82
            >> > 97% 3493 178 5413 6.2 91
            >> > 98% 4697 207 7609 8.3 111
            >> >
            >> > 99% 6712 247 11750 12.4 184
            >> > Max 11473 1293 16305 48.5 1060

            >> > When doing geostatistical and statistical analyses, we need some confidence
            >> > in dealing with the these very high extreme values which account for less
            >> > than 2% of the total sample number.
            >> >
            >> > Any suggestions?
            >> >
            >> > Cheers,
            >> >
            >> > Chaosheng Zhang
            >> > ===================================
            >> > Dr. Chaosheng Zhang
            >> > Department of Geography
            >> > National University of Ireland
            >> > Galway
            >> > IRELAND
            >> >
            >> > Tel: +353-91-524411 ext. 2375
            >> > Fax: +353-91-525700
            >> > Email: Chaosheng.Zhang@...
            >> > ===================================
            >>
            >>
            >>
            >>
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            >any useful responses to your questions.
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            >
            >
            >




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          • Myers, Jeff
            Chaosheng Zhang - I think Marcel Vallee is headed in the right direction on your problem. There is a good chance that the problem is one of sample and or
            Message 5 of 10 , Dec 14, 2001
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              Chaosheng Zhang -

              I think Marcel Vallee is headed in the right direction on your problem.
              There is a good chance that the problem is one of sample and or subsample
              support. As mentioned, if you sampled within a foot or tow of a location
              that displays an extreme or "outlier" value, you may find values an order of
              magnitude or more below the outlier. Similarly, you may also have
              "inliers", where a sample nearby a location with a low concentration may
              contain a significantly higher value. Of course, no one gets excited about
              the inliers that may be unrepresentative, but we get very excited about the
              outliers!

              The possibility of extreme values should be planned for in the initial stage
              of the sampling program. Pierre Gy's work has revealed that the physical
              size, volume, and orientation of a sample and subsample (i.e. the support)
              are crucial to the concentration estimate obtained. You are asking a lot to
              have a 10-g sample represent 400 meters between sample locations in any
              case. Unless the support of the original sample and all subsampling stages
              was sufficient, there is little chance that the samples are highly
              representative of the true concentration. Mine areas typically are very
              heterogeneous and proper sampling support when sampling is essential.
              Perhaps you can provide some details. If the underlying data are not
              representative due to improper suppoort, you are trying to "contour an
              illusion", and typically the results are not pleasing.

              The way in which the data are used in decision-making is also important.
              For instance, if your purpose is to delineate hot spots for risk assessment,
              extreme values do not pose a problem as they will be addressed. You may,
              however, be very interested in getting your best information at an economic
              cutoff value or risk threshold, since the decision for treatment of values
              high above or way below the action level is easy.

              Jeff Myers
              Westinghouse Safety Management Solutions
              2131 S. Centennial Ave., SE
              Aiken, SC 29803
              803.502.9747 (direct)
              803.502.9767 (main)
              803.502.2747 (fax)
              jeff.myers@... <mailto:jeff.myers@...>
              http://www.gemdqos.com <http://www.gemdqos.com>


              -----Original Message-----
              From: Chaosheng Zhang [mailto:Chaosheng.Zhang@...]
              Sent: Thursday, December 13, 2001 8:02 AM
              To: ai-geostats@...
              Subject: AI-GEOSTATS: Extreme values?


              Dear all,

              My question is: How to deal with the extreme/outlying values in a data set?

              I am dealing with heavy metal concentrations in soils from a mine area. The
              sample number is 223, and the samples are spatially evenly distributed with
              the sampling interval of 400 metres. There are several samples with
              extremely high values, which makes me feel uncomfortable. The percentiles of
              the dataset are listed as follows (in mg/kg):

              Zn Cu Pb Cd As
              Min 4 1 25 0.0 2
              5% 35 6 35 0.1 6
              10% 40 7 41 0.2 7
              25% 65 13 62 0.3 9
              50% 122 18 168 0.6 15
              75% 338 27 821 1.5 28
              90% 907 56 2799 2.8 58
              95% 1986 116 4490 4.2 80
              96% 2462 151 4698 4.9 82
              97% 3493 178 5413 6.2 91
              98% 4697 207 7609 8.3 111
              99% 6712 247 11750 12.4 184
              Max 11473 1293 16305 48.5 1060

              When doing geostatistical and statistical analyses, we need some confidence
              in dealing with the these very high extreme values which account for less
              than 2% of the total sample number.

              Any suggestions?


              Cheers,

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

              Tel: +353-91-524411 ext. 2375
              Fax: +353-91-525700
              Email: Chaosheng.Zhang@...
              ===================================




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