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GEOSTATS: interpolating pH values

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  • Kim Bryceson
    We are creating interpolated regional scale maps of various soil characteristics One of which is pH as measured in CaCl2. Given that pH is measured on a
    Message 1 of 6 , Feb 4, 1998
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      We are creating interpolated regional scale maps of various soil
      characteristics One of which is pH as measured in CaCl2. Given that pH is
      measured on a logarithmic scale in the "vertical" plane so-to-speak...do we
      have a theoretical problem in interpolating it in the "horizontal" plane using
      ordinary kriging where the estimates for non-sampled regions are made on a
      non-log basis?

      >From a management map perspective classified to pH ranges of interest, I am
      thinking there is no problem - but from a theoretical accuracy perspective
      there is debate in the Lab and we would appreciate comments

      regards
      kim

      --
      **************************************************************************

      Kim Bryceson BSc(Hons) METM, PhD
      Program Leader, Land Assessment & Policy Unit / Senior Research Fellow (GIS)
      CRC Soils & Land Management / Dept Agron & Farm Systems
      Hannaford Building, Waite Campus / Adelaide University
      University of Adelaide, SA 5064.
      Tel: (08) 83036522 Fax: (08) 83036711
      Email: kbryceso@...
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    • Jeffrey White
      IMHO, yes there is a problem in interpolating pH values directly using most interpolations methods, including kriging. Such methods tend to be based on
      Message 2 of 6 , Feb 4, 1998
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        IMHO, yes there is a problem in interpolating pH values directly using
        most interpolations methods, including kriging. Such methods tend to be
        based on averaging, the validity of which depends on the parameter of
        interest being additive, which pH is not. Additivity is also a basic
        assumption of the theory of regionalized variables on which kriging is
        based. IMHO pH estimation via kriging should be based on the antilog of
        the (negative) pH (i.e., the hydrogen ion concentration that the pH
        represents, a parameter which is additive, with subsequent
        transformation back to pH as the final step.

        Jeffrey G. White, Ph.D.
        Assistant Agronomist - MAFES
        Pontotoc Experiment Station
        8320 Hwy 15 South
        Pontotoc, MS 38863

        Tel: 601-489-4621; FAX: 601-489-6011
        email: jgwhite@...

        On Wed, 4 Feb 1998, Kim Bryceson wrote:

        > We are creating interpolated regional scale maps of various soil
        > characteristics One of which is pH as measured in CaCl2. Given that pH is
        > measured on a logarithmic scale in the "vertical" plane so-to-speak...do we
        > have a theoretical problem in interpolating it in the "horizontal" plane using
        > ordinary kriging where the estimates for non-sampled regions are made on a
        > non-log basis?
        >
        > >From a management map perspective classified to pH ranges of interest, I am
        > thinking there is no problem - but from a theoretical accuracy perspective
        > there is debate in the Lab and we would appreciate comments
        >
        > regards
        > kim
        >
        > --
        > **************************************************************************
        >
        > Kim Bryceson BSc(Hons) METM, PhD
        > Program Leader, Land Assessment & Policy Unit / Senior Research Fellow (GIS)
        > CRC Soils & Land Management / Dept Agron & Farm Systems
        > Hannaford Building, Waite Campus / Adelaide University
        > University of Adelaide, SA 5064.
        > Tel: (08) 83036522 Fax: (08) 83036711
        > Email: kbryceso@...
        > --
        > *To post a message to the list, send it to ai-geostats@....
        > *As a general service to list users, please remember to post a summary
        > of any useful responses to your questions.
        > *To unsubscribe, send email to majordomo@... with no subject and
        > "unsubscribe ai-geostats" in the message body.
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        >

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      • Jeffrey White
        ... Log transformations are commonly used to provide a more normal population, although many have expressed their view that normality is not a necessary nor
        Message 3 of 6 , Feb 5, 1998
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          On Thu, 5 Feb 1998, Syed Abdul Rahman wrote:

          > One has to reason why logarithmic transforms are used, a common
          > reason is to work with a manageable range of values, and another
          > is to get a stable variogram. Nevertheless, krigings become extremely
          > sensitive to changes in sill values, once the results are transformed
          > to their raw values. Another problem is that such results are
          > biased, what you expect to be the expectation (assuming this is what
          > you're after) would be the median after backtransformation. Therein
          > lies the bias. To be theoretically more "rigorous", go for log-normal
          > kriging.

          Log transformations are commonly used to provide a more normal population,
          although many have expressed their view that normality is not a necessary
          nor inherent assumption in the theory of regionalized variables, but MAY
          be a condition for unbiased estimation. With respect to pH, it is the
          transformation bias of which Syed wrote that is the problem when pH units
          are used directly in any additive process (such as averaging or
          semivariography and kriging), rather than the actual concentrations that
          they represent.

          An illustation: A simple example is mixing equal volumes
          of two solutions of different pH, say pH 6 and pH 8. Simple (and
          erroneous!) averaging of the pH's indicates that the resulting solution
          would have pH 7, while the true pH is about pH 6.3 : pH 6 => hydrogen
          ion concentration of 0.000001 M; pH 8 => hydrogen ion concentration of
          0.00000001 M. Equivolume mixture has hydrogen ion concentration of
          (0.000001 + 0.00000001)/2 = 0.000000505 M, negative log (or pH) of which
          is 6.296.


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        • Syed Abdul Rahman
          One has to reason why logarithmic transforms are used, a common reason is to work with a manageable range of values, and another is to get a stable variogram.
          Message 4 of 6 , Feb 5, 1998
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            One has to reason why logarithmic transforms are used, a common
            reason is to work with a manageable range of values, and another
            is to get a stable variogram. Nevertheless, krigings become extremely
            sensitive to changes in sill values, once the results are transformed
            to their raw values. Another problem is that such results are
            biased, what you expect to be the expectation (assuming this is what
            you're after) would be the median after backtransformation. Therein
            lies the bias. To be theoretically more "rigorous", go for log-normal
            kriging.

            Syed


            From: Jeffrey White <jgwhite@...>


            >IMHO, yes there is a problem in interpolating pH values directly using
            >most interpolations methods, including kriging. Such methods tend to be
            >based on averaging, the validity of which depends on the parameter of
            >interest being additive, which pH is not. Additivity is also a basic
            >assumption of the theory of regionalized variables on which kriging is
            >based. IMHO pH estimation via kriging should be based on the antilog of
            >the (negative) pH (i.e., the hydrogen ion concentration that the pH
            >represents, a parameter which is additive, with subsequent
            >transformation back to pH as the final step.
            >
            >Jeffrey G. White, Ph.D.
            >Assistant Agronomist - MAFES
            >Pontotoc Experiment Station
            >8320 Hwy 15 South
            >Pontotoc, MS 38863
            >
            >Tel: 601-489-4621; FAX: 601-489-6011
            >email: jgwhite@...
            >
            >On Wed, 4 Feb 1998, Kim Bryceson wrote:
            >
            >> We are creating interpolated regional scale maps of various soil
            >> characteristics One of which is pH as measured in CaCl2. Given that pH is
            >> measured on a logarithmic scale in the "vertical" plane so-to-speak...do
            we
            >> have a theoretical problem in interpolating it in the "horizontal" plane
            using
            >> ordinary kriging where the estimates for non-sampled regions are made on
            a
            >> non-log basis?
            >>
            >> >From a management map perspective classified to pH ranges of interest, I
            am
            >> thinking there is no problem - but from a theoretical accuracy
            perspective
            >> there is debate in the Lab and we would appreciate comments
            >>
            >> regards
            >> kim

            >

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          • Rane Curl
            ... I am responding to this as a chemist, and not as expert in kriging. I am also sure that others have dealt with pH values in this context in one way or
            Message 5 of 6 , Feb 5, 1998
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              On Fri, 6 Feb 1998, Inakwu Ominyi Odeh wrote:

              > The transformation bias of pH values as negative log of H+ concentrations being
              > referred to here is important iff the pH range within the immediate domain used
              > for kriging is large. If the range is within a unity, then there is probably
              > not much to be gained by transforming back to H+ concentration before kriging.
              > If, however, the pH range is 2 or more, then theoretically, additivity bias may
              > be introduced as a result of any quantitative interpolation. One should judge
              > each case carefully before embarking on kriging of pH values or their H+ conc.
              > But then other problems may arise as the H+ concentration (in soil) is
              > generally very low and may vary (spatially) exponentially.

              I am responding to this as a chemist, and not as expert in kriging. I am
              also sure that others have dealt with pH values in this context in one way
              or another, but I would raise questions about the procedures being
              recommended and the theoretical foundation for them.

              While [H+] is "additive" as a strong acid with nothing else present, in an
              real environment there are many other solutes present as well as reactive
              minerals. Natural solutions are usually buffered, so mixing two solutions
              of different pH does *not* average the [H+]. I would suggest that the
              objective be looked at more deeply and a transformation of pH for the
              purposes of kriging be chosen on a more realistic basis than additivity of
              [H+].

              There may even be justification for using pH. After all, the *solutions*
              do not get mixed when kriging - just the numbers. pH does represent a real
              thermodynamic quantity, which is the Gibbs Free Energy of formation of
              [H+] in solution and, under some conditions, free energies are additive.
              Other reactions also respond in a multiplicative manner to [H+] (via
              mass-action equilibria), so the pA of (the activities) of those other
              species respond in a generally additive manner to changes in pH.

              I presume that someone, somewhere, has done a much more thorough
              investigation of the meaning of kriging in pH, but I would not dismiss it
              out of hand unless some more fundamental objections can be put forward
              that the "additivity of [H+]" (sometimes, but rarely).

              --Rane L. Curl
              Prof. of Chemical Engineering


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            • Inakwu Ominyi Odeh
              The transformation bias of pH values as negative log of H+ concentrations being referred to here is important iff the pH range within the immediate domain used
              Message 6 of 6 , Feb 6, 1998
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                The transformation bias of pH values as negative log of H+ concentrations being
                referred to here is important iff the pH range within the immediate domain used
                for kriging is large. If the range is within a unity, then there is probably
                not much to be gained by transforming back to H+ concentration before kriging.
                If, however, the pH range is 2 or more, then theoretically, additivity bias may
                be introduced as a result of any quantitative interpolation. One should judge
                each case carefully before embarking on kriging of pH values or their H+ conc.
                But then other problems may arise as the H+ concentration (in soil) is
                generally very low and may vary (spatially) exponentially.

                --
                Dr Inakwu Ominyi Odeh, |
                Dept. of Agric. Chem. & Soil Science |
                The University of Sydney |
                Ross Street A03 NSW 2006 AUSTRALIA |
                Phone +61 (02) 9351 4178 |
                Fax: +61 (02) 9351 5108 |
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