spatial modelling projection question

so my question is: Wouldn't it make more sense to do spatial modeling with
a true distance projection, i.e. longlat, than an equal area projection for
which distances are skewed? What makes the variogram model potentially

I would say yes, but haven't given it much thought.

inappropriate on a sphere (overlooking the fact that the earth isn't really
a sphere)?

Some variogram models are not positive definite (or semi-negative
definite) in some spaces; linear-with-sill is only valid in 1 D,
circular only in 2D, spherical only in 3D. Spheres, or ellipsoides, are
another thing when measuring surface lines.

See also http://dx.doi.org/10.1007/s11004-011-9344-7

Edzer Pebesma
Institute for Geoinformatics (ifgi), University of M?nster
Heisenbergstra?e 2, 48149 M?nster, Germany. Phone: +49 251
83 33081 http://ifgi.uni-muenster.de GPG key ID 0xAC227795

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Most people suggest longlat is not  a proper 'projection' for
geostatistics ...

Dominik,

   longlat represent geographic coordinates, not a projection of
3-dimensional points on Earth to a 2-dimensional representation on paper or
a computer monitor.

The standard projection for a domain my size/geographic location seems to
be the conus albers from USGS (epsg:5070) which is an equal area
projection so my question is: Wouldn't it make more sense to do spatial
modeling with a true distance projection, i.e. longlat, than an equal area
projection for which distances are skewed?

What question(s) are you trying to answer with your data? Depending on the
size of the area analyzed you might find that UTM or State Plane Feet are
better projections for your use.

What makes the variogram model potentially inappropriate on a sphere
(overlooking the fact that the earth isn't really a sphere)? I appreciate
your help understanding this.

Every datum (e.g., NAD83 or NAD27; the North American Datums calculated in
the noted year) has errors because the Earth is neither a sphere or a
smooth ellipsoid.

   I highly recommend your studying Snyder, J.P. 1987. Map projections -- A
Working Manual. USGS Professional Paper 1395. It went out of print in the
early 1990s but is considered the benchmark for topographic map projections.
You can also read the documentation for Proj4, but John Snyder's monograph
will greatly increase your understanding.

   Understanding projections will help you select the most appropriate one
for each question you want to answer. You also need to be aware of what
happens when your analytical area is across two zones.

HTH,

Rich

Richard B. Shepard, Ph.D.        | Technically sound and legally defensible
Applied Ecosystem Services, Inc. | ... guaranteed.
www.appl-ecosys.com      Voice: 503-667-4517         Fax: 503-667-8863

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thanks for everyone's input. I have looked through the USGS publication but
will also check out those articles. I suppose, like with everything, some
sensitivity tests for the variogram models is in order.  My domain is the
Upper Colorado River basin and covers 4 UTM zones (12,13: S, T) which is why
I haven't used UTM. I am working with estimating a distributed snow surface
at 500m. Given the size of the domain, most geostats is fairly intensive so
moving to a cartesian projection like 5070 might speed things up which is
something I had not thought of and might be worth it alone.



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