spatial modelling projection question

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spatial modelling projection question

dschneiderch
Hi -
I do some spatial modeling over the inter-mountain west of USA and am
wondering about projections.  Most people suggest longlat is not  a proper
'projection' for geostatistics and in fact some packages require a
projection with meters instead of degrees. I believe gstat will compute
great circle distances for longlat data. I have seen some caveats on this,
e.g. "there are no checks that the variogram model can be applied sanely on
a sphere"<http://r-sig-geo.2731867.n2.nabble.com/Kriging-and-datum-shifts-td7583666.html>
.
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 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.
Thanks
Dominik

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Re: spatial modelling projection question

edzer


On 05/13/2014 08:19 PM, Dominik Schneider wrote:
> 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 Münster
Heisenbergstraße 2, 48149 Münster, Germany. Phone: +49 251
83 33081 http://ifgi.uni-muenster.de GPG key ID 0xAC227795


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Re: spatial modelling projection question

Rich Shepard
In reply to this post by dschneiderch
On Tue, 13 May 2014, Dominik Schneider wrote:

> 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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Re: spatial modelling projection question

Michael Sumner-2
On Wed, May 14, 2014 at 4:53 AM, Rich Shepard <[hidden email]>wrote:

> On Tue, 13 May 2014, Dominik Schneider wrote:
>
>  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.
>
>

I believe that Dominik is referring to the fact that with longlat we can
use ellipsoid calculations for distance, which cover the most general
solution for "most accurate" across many situations. There are many map
projections that are more suitable for given applications, but then the
general confidence about Cartesian distances is gone: we need to be careful
that our distance calcs are appropriate within the constraints of that
projection. Any equi-distant projection can provide best accuracy only
within specific constraints.  (This is not true for area, those can be
always accurate in an equal-area projection albeit with loss of
conformality and usual numeric/topology constraints).

I think the only general solution is to back-transform and use the
ellipsoid for distance, unless you can be sure that the Cartesian methods
match your needs in the projection being used.  The only way to match
ellipsoid accuracy is to generate a local unique equi-distant projection
for each distance segment and measure from its centre to the other point.
(I think Manifold does this internally for the interactive
distance-measuring Tracker tool when you toggle the ellipsoid key. ).

I've been bothered by this for a while, especially with such a wide use of
UTM out there. I think you always need to be concerned about it, and do
some checks across your region/application to make sure Cartesian distance
is good enough when you have chosen a projection for other properties.  If
you can forget the need for expensive ellipsoid calculations or many local
equidistant projections it's obviously going to be more efficient.

Cheers, Mike.







>
>  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
>
>
> _______________________________________________
> R-sig-Geo mailing list
> [hidden email]
> https://stat.ethz.ch/mailman/listinfo/r-sig-geo
>



--
Michael Sumner
Software and Database Engineer
Australian Antarctic Division
Hobart, Australia
e-mail: [hidden email]

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Re: spatial modelling projection question

dschneiderch
In reply to this post by dschneiderch
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.