why variations in accuracy between R to ARCGIS for the same point reprojection?

Hi everyone,

I wonder if anyone knows the reason why the outputs of the same
reprojection in r and arcgis are different?. The magnitude of the change
can be up to 40 km in the poles.
Basically, I have a database of points equally separated by one degree
over the globe.
In ARCGIS,  I am projecting the data in GCS-WGS-1984 and then
reprojected it to Berhmann to ensure equal area distribution of the points.
In R, I am using:
spPoint <-
SpatialPoints(coords=coordinates(Data),proj4string=CRS("+proj=longlat
+datum=WGS84"))
and then reprojecting it to Berhmann with:
spPointReprj=spTransform(Data,CRS("+proj=cea +lon_0=0 +lat_ts=30 +x_0=0
+y_0=0 +ellps=WGS84"))

If I put the two outputs of the reprojections in the same map, they are
off by few meters in the tropics by up to 40km in the poles.

I decided to investigate how the reprojections are done and my
calculations are different from both R and ArcGis:

First, I calculated the radious of the Earth in two different ways:
=Re * (1 - e^2)/ (1 - e^2 *SIN(RADIANS(Latitude))^2)^(3/2)
=Re * SQRT(1 - e^2) / (1 - e^2 * (SIN(RADIANS(Latitude)))^2)

where Re is the radius of the Earth at the tropics(6378km) and e is the
eccentricity of the ellipsoid (0.081082).

According to several books I used, the position of a point in the Y-axis
in the Berhmann projection could be estimated as:
=Re*(SIN(RADIANS(Latitude))/COS(RADIANS(Spll)))
where Spll is the standard parallel, which in the Berhmann's projection
is 30.
Unfortunately, the resulting output, although similar in shape to the
outputs in R and Arcgis, is still not quite the same. Any thoughts why
these differences in supposedly the same calculations?

Any input will be greatly appreciated,

Thanks,

Camilo




Camilo Mora, Ph.D.
Department of Geography, University of Hawaii
Currently available in Colombia
Phone:   Country code: 57
          Provider code: 313
          Phone 776 2282
          From the USA or Canada you have to dial 011 57 313 776 2282
http://www.soc.hawaii.edu/mora/