[GRASSLIST:1589] Re: interpolate nominal values

[Rich Shepard]

On Fri, 9 Mar 2001, Edzer J. Pebesma wrote:

> I disagree here. It depends on how the data were obtained: were they
> mapped in the field as polygons (in which case vector seems most appropriate)
> or were they interpolated (estimated) from point samples (e.g. in the case
> of chemical composition)? In the latter case, raster representation seems
> the obvious way to go -- most interpolation programs output raster maps.

Edzer,

  Actually, I think that we agree. I've no idea how soil taxonomists do
their field mapping in any other country, but in this one they take samples
and extrapolate from those. The presumed boundaries (often inferred from
vegetation, topography and other indicators) are drawn as vectors on
georeferenced aerial photographs (the forerunners of today's digital
orthophoto quad, or DOQ). There is no other way the old Soil Conservation
Service (now with the snappy new name of Natural Resource Conservation
Service) could map soils for agricultural and other purposes
county-by-county in all the states. It is a very coarse estimate, and the
descriptive text notes the assumed percentages of different types within a
map unit.

> Like the confusion about "nominal" vs. "interval/ratio" data, you're mixing
> two spatial data types here -- geostatistical data vs. point pattern data
> (using Cressie's "Statistics for spatial data" terminology). Geostatistical
> data are obtained (measured) at a limited number of locations, but takes on
> a value (could be measured) at any location in the region of interest. Point
> pattern data are patterns of occurences of specific items (cities, fast food
> stores, trees,...) in a region. The latter can be "transformed" to the former
> by using the concept of local density.

  Now here we disagree. Perhaps in some limited cases this may work, but not
in many real world sitiations. Consider this: you have recorded the
locations of bunny rabbits (using a GPS receiver) throughout a large area
(say, for example, 200 hectares). Can you use spatial statistics to
determine the home range of each bunny? I suggest that you cannot validly do
this.

> One typical problem for geostatistical data is interpolation. E.g., soil type
> is measured at a limited number of sites, and now we want to make a soil map
> from it. For nominal data, the way to go is define an indicator variable
> for each soil type, give it a 1 if the soil type is present and else a 0.
> Interpolated values may be interpreted as _estimated_ probabilities of
> occurence for that soil type. (Note that they are not real probabilities).

  If you take into account factors such as topography and vegetation, you
can estimate the bounds of a specific soil type by kreiging or drawing
Veronoi polygons. But, ... that's not the implications of the original
question nor the first batch of responses.

  The assumption of the initial responders was that a 3D surface could be
generated from the point data. My response was that you cannot interpolate
nominal data (whether '1'/'0' or a textual name) into a meaningful surface.
I still stick with this opinion.

Rich

Dr. Richard B. Shepard, President

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