# [Proj] Bad Mercator Projection string?

Mikael Rittri Mikael.Rittri at carmenta.com
Fri Jul 20 04:42:23 EST 2012

```> ... how you arrived at the scaling factor?

You know how a Mercator map enlarges stuff at high latitudes. This enlargement is known as
the local scale factor, k, and for Mercator, it depends only on the latitude, phi. An "ordinary" instance
of Mercator has k = 1 on the equator by definition, and the k at latitude phi is then 1/cos(phi) if you use
spherical formulas, or slightly different in your case since you use ellipsoid formulas for WGS84.

Anyway, to make your Mercator instance with latitude of true scale at 41.5 degrees, I computed k
at 41.5 degs for the corresponding ordinary instance, and then used k_0 = 1/k for your instance.

With ellipsoid formulas for Mercator, the formula for k at latitude phi is

k = sqrt(1 - e2 * sin2(phi)) / cos(phi)

where e2 is the ellipsoid's first eccentricity squared, defined as 1 - (b/a)2 where a is the
equatorial radius and b is the polar radius, or as (2-f)*f where f is the flattening.

(Every 2 above - except the last - should really be a superscript.)

The formula for k can be found as Eq. (7-8) at page 44 of

John  P. Snyder.
Map Projections: A Working Manual, 1987.
http://pubs.er.usgs.gov/pubs/pp/pp1395

And you can find e2 and other properties of WGS84 at

http://home.online.no/~sigurdhu/WGS84_Eng.html

Best regards,

Mikael Rittri
Carmenta
Sweden
http://www.carmenta.com

20 jul 2012 kl. 01:15 skrev "Geoff Shipton" <geoff at tritonimaginginc.com<mailto:geoff at tritonimaginginc.com>>:

Hello again Mikael,

Many thanks!

That seems to have fixed the problem.  As I said I am not a geodesist, can you give me a clue as to how you arrived at the scaling factor?  I suppose its some function of the Latitude of true scale?

Geoff

From: Mikael Rittri [mailto:Mikael.Rittri at carmenta.com]
Sent: Thursday, July 19, 2012 10:41 AM
To: <geoff at tritonimaginginc.com<mailto:geoff at tritonimaginginc.com>>; PROJ.4 and general ProjectionsDiscussions
Cc: proj at lists.maptools.org<mailto:proj at lists.maptools.org>; Howard Unkeles
Subject: Re: [Proj] Bad Mercator Projection string?

I don't know what the trouble is, but maybe GeoTIFF doesn't support Mercator with
a lat_ts parameter (latitude of true scale). If so, you can try to use a scale factor instead.

That is, replace your

+lat_ts=41.5

by

+k_0=0.750058844766239

This will give you an equivalent definition, and maybe it will work better.

Best regards,

Mikael Rittri
Carmenta
Sweden
<http://www.carmenta.com>http://www.carmenta.com

18 jul 2012 kl. 19:16 skrev "Geoff Shipton" <<mailto:geoff at tritonimaginginc.com>geoff at tritonimaginginc.com<mailto:geoff at tritonimaginginc.com>>:
Hello everyone,

We “inherited” this Proj4 string from a previous product – it has always seemed to work but we are having problems using it with gdalwarp, the warped .tif image looks valid but has errors in the TIF tags.  If anybody has any idea what’s wrong I would be grateful.  Comparing it with other Mercator Proj4 strings it looks a bit simple…

Here’s the string:

+proj=merc +datum=WGS84 +lon_0=0 +lat_ts=41.5 +x_0=0 +y_0=2000000

I am not a geodesist, be gentle.

Many thanks,
Geoff Shipton,
Triton Imaging Inc.
Customer Support.
Capitola CA.
<mailto:geoff at tritonimaginginc.com>geoff at tritonimaginginc.com<mailto:geoff at tritonimaginginc.com>

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