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| Subject: | RE: GISList: interpolation question - chicken or the egg? |
| Date: |
05/12/2003 09:35:00 AM |
| From: |
Keith Miller |
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Rick,
My $0.02: If the model is linear, then there should be no difference between
the two methods. However, if the model is nonlinear, then they will be
different.
As an example, assume that you have two points of data, with values of X(1)
= 2 and X(2) = 10, and a farm half way in between. If your model is linear,
such as Y = 2X, then the two methods give the same results:
Method 1:
interpolate first: X(farm) = 6
then apply your model: Y(farm) = 12
Method 2:
model first: Y(1) = 4, Y(2) = 20
then interpolate: Y(farm) = 12
However, if your model is nonlinear, such as Y = X**2, then the two methods
give different results:
Method 1:
interpolate first: X(farm) = 6
then apply your model: Y(farm) = 36
Method 2:
model first: Y(1) = 4, Y(2) = 100
then interpolate: Y(farm) = 52
The wrinkle in this is that weather data are not necessarily distributed in
a spatially linear fashion (because of changes in topography, water bodies,
etc.). Therefore, the question is: Are the weather data more likely to be
spatially linear, or is the DSV more likely to be spatially linear? The
answer to this question will determine which method is give the "truer"
value of DSV for your farmers.
------------------------------------------------------------------------
Keith Miller
Principal Planner: GIS and Modeling
North Jersey Transportation Planning Authority, Inc.
One Newark Center, 17th floor
Newark, NJ 07102
973-639-8444 phone
973-639-1953 fax
kmiller@njtpa.org
-----Original Message-----
From: RICK GRAY [mailto:rgray@ridgetownc.uoguelph.ca]
Sent: Sunday, May 11, 2003 9:46 PM
To: gislist@geocomm.com
Subject: GISList: interpolation question - chicken or the egg?
Here's one for the GIS gurus on this wonderful list...
We collect weather data at a number of locations, run the data through
computer models to predict a Disease Severity Value (DSV) for various crops
based on temperature and hours that the leaves are wet (dew, rain, etc.),
then interpolate the DSVs to generate a map that farmers can use to
ascertain the best time to spray their crop. Farmers who subscribe to our
service are given the DSV for their farm, as it is extracted from the
interpolated map.
We have long pondered, but not had the time to experiment, as to whether
interpolating DSV's is actually better than interpolating the weather data,
THEN finding the DSV.
In other words, which way should generate the more reliable results? In the
first instance, all the modelling is done with known values, so on first
glance it would seem to provide truest values. On the other hand,
interpolating the weather parameters, then running the model at the farmer's
location, might be just as good - and offers some advantages as we attempt
to automate the process. We just don't know.
Has anybody looked into this? Know of any papers, etc. on the topic? Or even
have some strong intuitions? I'd love to hear your feedback.
Thanks,
Rick
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