Loading ...
Sorry, an error occurred while loading the content.

Re: GEOSTATS: interpolating pH values

Expand Messages
  • 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 1 of 6 , Feb 5, 1998
    • 0 Attachment
      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.


      --
      *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.
      DO NOT SEND Subscribe/Unsubscribe requests to the list!
    • 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 2 of 6 , Feb 5, 1998
      • 0 Attachment
        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

        >

        --
        *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.
        DO NOT SEND Subscribe/Unsubscribe requests to the list!
      • 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 3 of 6 , Feb 5, 1998
        • 0 Attachment
          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


          --
          *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.
          DO NOT SEND Subscribe/Unsubscribe requests to the list!
        • 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 4 of 6 , Feb 6, 1998
          • 0 Attachment
            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 |
            --
            *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.
            DO NOT SEND Subscribe/Unsubscribe requests to the list!
          Your message has been successfully submitted and would be delivered to recipients shortly.