Good projection for N/S America?

On Mon, 9 Apr 2007 White.Denis at epamail.epa.gov wrote:

For preview graphics and for large areas such as continents, large
countries, hemispheres, or the whole earth, spherical projections are
often adequate.  I can provide some of the ones I have used.  For
detailed work at sites and small areas, ellipsoidal projections such as
UTM are usually used, and then the coding gets more complicated with
choices of datums and so forth.

The attached script shows how to do the interrupted sinusoidal projection
using spTransform in rgdal, for the whemi.lin data posted with the
free-standing functions by Denis White a couple of days ago. Once the
lines are converted into SpatialLines objects, the rest is robust and
simple, as is the use of gridlines() in sp. The one catch is calculating
the offset, here in an x_0= offset along the Equator in metres between the
two central longitude values. The output is attached as a PNG image. The
point about the sp objects is that they contain enough metadata (here a
PROJ.4 projection description) to let them be moved to other R packages or
external software.

The half-dozen basic projections are easy to specify in PROJ.4, for
example from the geotiff list:

http://www.remotesensing.org/geotiff/proj_list/

which is what I used here. The other projections mentioned are:

Lambert Cylindrical Equal Area "+proj=cea +lon_0=-80"

Lambert Azimuthal Equal Area "+proj=laea +lat_0=0 +lon_0=-80"

while the Northern hemisphere sinusoidal is:

Sinusoidal "+proj=sinu +lon_0=-100"

So I'd argue that PROJ.4 projection descriptions are not difficult to use,
and with sp objects, do stay stuck to the data (has anyone else ever
forgotten what projection was used when revisiting data, not just me?).

Using the maptools map2SpatialLines() interface function, or the Rgshhs()
interface to GSHHS shorelines, even getting the lines is quite easy,
qualified by clipping and bounding box issues in extremities for
projection from geographical coordinates.

Of course, it would help to have MacOS X and selected Linux binaries of
rgdal, we're very lucky that Uwe Ligges is so helpful with the Windows
binaries.

Roger

r-sig-geo-bounces at stat.math.ethz.ch wrote on 2007-04-08 07:56:03:

Denis,

That's really useful. It occurs to me that we only really need a
half-dozen basic projections to cover 90% of user cases. Perhaps these
could be incorporated into the 'sp' group somewhere and relieve the
dependence on proj4. (It could be packaged separately for R  for the
other 10% of cases where its needed.)

THK

On 4/6/07, White.Denis at epamail.epa.gov <White.Denis at epamail.epa.gov>

wrote:

Thanks, Roger.  There was a request to see the R code for these

figures.

Attached is the script for the second PDF file plus the input

boundary

file I used for the hemisphere.  The three projection functions are

for

simple spherical, rather than ellipsoidal, models of the earth.  The
graticule generating function could be more elegant.  I'm not yet up

to

speed with sp and the many new spatial capabilities in R so please
excuse the old style "lines()" format encoding and graphics.

Tim, I don't know whether proj4 could do the interrupted sinusoidal.

(See attached file: whemi.projs.r)(See attached file: whemi.lin)

r-sig-geo-bounces at stat.math.ethz.ch wrote on 2007-04-06 04:51:53:

Since this topic is of general interest, I've made an exception

and

allowed (this once!) a posting of more than 200K. In general, if

graphics

are big, please consider either an alternative device (png is

often

OK),

or posting just a URL to the real file.

With apologies to list members on dial-up connections in the

field,

Roger


On Thu, 5 Apr 2007 White.Denis at epamail.epa.gov wrote:

Yes, for many uses that is my choice also.  For the conterminous

US

for

example, the Lambert azimuthal has lower mean distortion than

the

commonly used standard projection, the Albers conical equal

area,

although Albers was chosen by USGS as a standard because of

lower

extreme distortion than many other possible projections.

For our hemispherical application, because we were gridding the

data, we

wanted parallels of latitude to be parallel in the projected

coordinate

space, which we wouldn't get with the Lambert azimuthal.

(See attached file: whemi.projs.pdf)

Tim Keitt <tkeitt at gmail.com> wrote on 2007-04-05 10:56:09:

Thanks. My application is not that demanding. Really, I just

want

it

to look reasonable. My plan is to lay out the postings in the
projected coordinates and then back transform into geographic
coordinates for analysis. I tried lots of projections and

found

Lamberts Azimuthal Equal Area to be quite good. I like the

look of

the

Azimuthal Equidistant better, but figured equal area was a

good

choice.

THK

On 4/4/07, White.Denis at epamail.epa.gov

<White.Denis at epamail.epa.gov>

wrote:

Tim,

It depends on which kind of distortion is of most concern.

For

many

types of extensive data, especially counts, for example, the

equal

area

property is desirable.  We used the Lambert cylindrical

equal

area

projection with standard parallels of +/- 30 degrees for

some

western

hemispherical work, see reference below.  (The center

longitude

could be

-80 west, but that is less important than the choice of

parallels.)

Before falling back on the Lambert as an easy to use

projection,

I

tried

to get several ESRI products to implement an interrupted

projection

using the sinusoidal projection, in part for reasons given

in

the

second

reference.  I used a separate center longitude for north and

south

of

the equator and the appearance is certainly more

satisfactory

than

the

Lambert in my opinion.  I'll attach a PDF of an illustration

of

this

approach generated in R that I hope you will get but not the

rest of

the

list unfortunately.  I can send PDFs of the references also

if

needed.

Denis

Lawler JJ, White D, Neilson RP, Blaustein AR.  2006.

Predicting

climate-induced range shifts: model differences and model

reliability.

Global Change Biology 12:1568-1584.

White D.  2006.  Display of pixel loss and replication in

reprojecting

raster data from the sinusoidal projection.  Geocarto

International

21(2):19-22.

(See attached file: whemi.sinus.pdf)

r-sig-geo-bounces at stat.math.ethz.ch wrote on 2007-04-04

12:17:39:

Anyone know of a particularly good map projection for

showing

all

of

North and South America without too much distortion?

THK

--
Timothy H. Keitt, University of Texas at Austin
Contact info and schedule at

http://www.keittlab.org/tkeitt/

Reprints at http://www.keittlab.org/tkeitt/papers/
ODF attachment? See http://www.openoffice.org/

--
Timothy H. Keitt, University of Texas at Austin
Contact info and schedule at http://www.keittlab.org/tkeitt/
Reprints at http://www.keittlab.org/tkeitt/papers/
ODF attachment? See http://www.openoffice.org/

--
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian

School

of

Economics and Business Administration, Helleveien 30, N-5045

Bergen,

Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no

--
Timothy H. Keitt, University of Texas at Austin
Contact info and schedule at http://www.keittlab.org/tkeitt/
Reprints at http://www.keittlab.org/tkeitt/papers/
ODF attachment? See http://www.openoffice.org/

--
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no