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Re: AI-GEOSTATS: Sampling on v-bladed land

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  • Nicholas Lewin-Koh
    Hi, Even though your goal is to compare overall means in the plots, it seems that especially in the 1st rotation plots (and possibly the second) you may have a
    Message 1 of 3 , Mar 20, 2001
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      Hi,
      Even though your goal is to compare overall means in the plots, it seems
      that especially in the 1st rotation plots (and possibly the second) you
      may have a problem of non-stationary mean, in the sense that there may be
      two processes in soil phosphate. The high points on the mounds may have
      very different characteristics than the troughs. Maybe you might want to
      think about comparing the spatial processes across plots rather than
      aggregated values.

      Nicholas


      CH3
      |
      N Nicholas Lewin-Koh
      / \ Dept of Statistics
      N----C C==O Program in Ecology and Evolutionary Biology
      || || | Iowa State University
      || || | Ames, IA 50011
      CH C N--CH3 http://www.public.iastate.edu/~nlewin
      \ / \ / nlewin@...
      N C
      | || Currently
      CH3 O Graphics Lab
      School of Computing
      National University of Singapore
      The Real Part of Coffee kohnicho@...

      On Wed, 21 Mar 2001 Barbara.Hock@... wrote:

      > Hallo,
      >
      > An M.Sc. student is look at soil phosphate issues in a plantation forest.
      > He needs
      > to sample for phosphate in areas some of which have been v-bladed (details
      > below) - a group of us came up with a sampling schema which we'd be
      > interest to
      > have the list comment on.
      >
      > The aim of the work is to compare three sites representing
      > pre-plantation/undisturbed
      > conditions, 1st rotation plantation trees (Pinus radiata), and 2nd rotation
      > trees. An
      > area has been found where examples of these sites occur close to one
      > another on
      > the same soil type, elevation and slope. The confounding factor is the site
      > preparation
      > that was used: for a number of reasons, the topsoil gets pushed together
      > into long
      > mounds about 2 metres apart. These mounds are obvious in the 1st rotation
      > site, but
      > less so in the 2nd rotation site. Sample sites of approx 5ha have been
      > located, and
      > an unbalanced hierachical sampling schema was decided on (from Webster and
      > Olivier, if I recall correctly):
      > 24 primary centres are located at the nodes of a 40m grid of random origin
      > all other plots are at random orientation from each other according to the
      > following
      > schema:
      > - from the primary centre, locate a 2nd plot site at 13.5m (random
      > orientation)
      > - from each of these plot sites, locate a 3rd set of sites at 4.5m
      > - and from each of the above, locate a 4th set at 1.5m
      > This gives a total of 144 plots per study site.
      >
      > The distance of 1.5m was selected as it was less than the mounding
      > spacings. The
      > other distances proceed by approximately trebbling the previous one. The
      > total size
      > of the grid starts being constrained by the overall sizes of the study
      > sites and
      > somewhat by the number of samples that can be processed.
      >
      > The intent is to aggregate individual plot values into a single value
      > (average) for each
      > site and to compare the latter. Mapping within each site is of secondary
      > interest.
      >
      > Your comments will be appreciated.
      > Barbara
      >
      >
      >
      > Barbara Hock
      > Forest Research
      > Private Bag 3020
      > Sala Stree
      > Rotorua
      > New Zealand
      >
      >
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    • Ruben Roa
      ... [snip] ... in the 2nd rotation site. Sample sites of approx 5ha have been located, and an unbalanced hierachical sampling schema was decided on (from
      Message 2 of 3 , Mar 21, 2001
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        >===== Original Message From Barbara.Hock@... =====
        [snip]
        >The aim of the work is to compare three sites representing
        >pre-plantation/undisturbed conditions, 1st rotation plantation trees (Pinus
        >radiata), and 2nd rotation trees. An area has been found where examples of
        >these sites occur close to one another on the same soil type, elevation and
        >slope. The confounding factor is the site preparation that was used: for a
        >number of reasons, the topsoil gets pushed together into long mounds about 2
        >metres apart. These mounds are obvious in the 1st rotation site, but less so
        in >the 2nd rotation site. Sample sites of approx 5ha have been located, and
        an >unbalanced hierachical sampling schema was decided on (from Webster and
        >Olivier, if I recall correctly):
        >24 primary centres are located at the nodes of a 40m grid of random origin
        >all other plots are at random orientation from each other according to the
        >following schema:
        >- from the primary centre, locate a 2nd plot site at 13.5m (random
        >orientation)
        >- from each of these plot sites, locate a 3rd set of sites at 4.5m
        >- and from each of the above, locate a 4th set at 1.5m
        >This gives a total of 144 plots per study site.

        Since the origin of the grid is chosen at random, you may use standard
        estimators from sampling theory (no need for spatial modelling). The chosen
        design is rather complex, with 4 stages as i can see from your description.
        Perhaps it can be simplified to a 2-stage random systematic design and then
        use well known estimators found in, for example Cochran 1977 Sampling
        Techniques, page 279.
        On the other hand, spatial modelling can be undertaken under the transitive
        method, in which the structural tool is the transitive covariogram, where the
        estimation variance of the zonal mean is computed by considering all estimates
        which can be obtained by shifting the grid rigidly across the region (Petitgas
        1993 Ices J Mar Sci 50:285-298, Petitgas and Lafont 1997 EVA2: Estimation
        Variance version 2, this is the manual of the EVA software, widely used to
        estimate the geoestatical zonal mean and its variance in the fisheries
        community).
        Since the purpose is hypothesis testing (the comparison of the 3 situations
        with regard to pine forest disturbance) you will need to obtain interval
        estimates for the zonal mean, and see if those intervals overlap, and
        therefore assume a distribution for the estimator. I think the normal
        distribution can be assumed in both the spatial transitive framework and the
        standard sampling theory.

        Ruben


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