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| GeoCommunity Mailing List |
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| Subject: | Re: [gislist] calculate change in cropland for Missouri |
| Date: |
02/12/2004 02:00:01 PM |
| From: |
Quantitative Decisions |
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At 11:39 AM 2/12/2004 -0600, Diane True wrote:
>We would very much like to calculate change in cropland ... Right now all
>we have is the county summaries ...
The natural and most accurate way to _map_ the change is with a choropleth
map. Going beyond this--showing a smooth surface, for
instance--unnecessarily introduces assumptions, arbitrary distortions, and
possible errors.
Where is there a calculation involved? Are you trying to estimate change
within regions that are independent of the counties?
>How does this sound:
>
>- calculate total acres lost or gained in cropland,
>- assign that value to the centroid of each county, and rank 1 to 5 in
>terms of acres lost to cropland
>- create a surface from the centroids, thus getting rid of the county
>boundaries -- this will give the surface a smooth look, at least
Yes, but you can also create a smooth surface by manufacturing any kind of
data you like and interpolating it: it would be hardly less arbitrary than
this method. Time does not permit a full discussion of all the problems
with this approach, but let me list just a few:
* The ranking is arbitrary.
* Even with a rigorous ranking, such as into quintiles, the ranking
transforms the data most likely in a nonlinear way. This will have a
strong effect on the interpolation and visual impression.
* The surface's appearance will also depend strongly on what interpolation
method is used.
* The method will bias the visual impression low for small counties, high
for large counties. (You should be mapping crop change density, not crop
change itself: see below.)
* Choosing the centroids for the point locations is arbitrary and can
strongly influence the surface.
* There probably _should_ be breaks at county boundaries: why should this
surface be smooth across administrative areas?
* Displaying a smooth surface hides the fact that cropland loss is (a) a
discrete phenomenon, (b) actually balances gains versus losses, and (c) is
known in toto only at the county level.
If you really, really, need to generate a smooth surface for creating a
nice visual impression, then consider forming a crop change density map
using a smooth kernel, such as a Gaussian. This at least will preserve the
total amount of crop change throughout the surface. It's also fairly easy
to do. Using a kernel width approximately one-half the thickness of a
typical county will almost completely eradicate any impression of county
outlines in the surface.
(By "crop change density," I mean that you should re-express crop change in
each county as net crop change divided by the total county area, depending
on your needs. Thus, if one looks at a particular point on the resulting
surface and it corresponds to a value of 'x', it could be interpreted as
meaning that "within the immediately surrounding area, roughly a fraction
'x' of all land was put to use for crops ['x' is positive] or taken out of
use ['x' is negative].")
>Is this any worse than assigning one value for the whole county when it
>obviously varies depending on where you are in the county?
Yes, because it is deceptive: besides distorting the results, perhaps
grossly, such a surface will make it look like you have a lot more data
than you really do. In effect, you are replacing a small table of 115
numbers by a map of, say, a million pixels. That is a huge
over-representation of what you really know.
For creative yet simple ways to present such a dataset, see John Tukey's
book, "Exploratory Data Analysis" (Addison Wesley, 1977). For an criticism
of maps like the one proposed above, read Ed Tufte's "The Visual Display of
Quantitative Information" (Cheshire Press, 1983) and its sequelae, as well
as Mark Monmonier's "How to Lie With Maps" (U. Chicago Press,
1991). Tufte's ideas of evaluating the "Lie Factor" and maximizing the
"Data-to-ink ratio" are particularly apt.
You might also consider simulating what the change looks like, provided you
have an accurate map of land use made at some time just before the period
of change. This is much easier to do than it sounds: at the simplest
level, it can be executed as a dot density map of a croplands layer
organized by county, using total crop change as the attribute and choosing
the dot size appropriately. More realistic simulations can be executed
using fairly simple raster operations. You just have to be very clear in
any publication that such a map is a simulation, not reality.
Indeed, you could go so far as to generate a raster rendition of such a
simulation, then smooth it with a moving neighborhood. That would achieve
your aims without being too deceptive, especially if you make it clear that
the detailed undulations in such a map are indeed simulate
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