[GIS] How to calculate false easting/northing for Lambert Conformal Conic projection

coordinate systemparameters

I'm defining a new GRASS location using the Lambert Conformal Conic projection. My understanding is that the values for the standard parallels and central meridian are dependent on my area of interest; I'm mapping Canada, for which common values are:

1st parallel: 49
2nd parallel: 77
Central meridian: -91.86667 (ie, 91 52)

I'm not sure how to determine where to put the central parallel (or if it matters) and what values to use for false easting/northing.

I have found lots of definitions of these parameters online, but no explanation of how to calculate them. Usually this means it would be self-evident if I knew what I was doing!

How do I determine the false easting/northing values for a LCC projection?

UPDATE

After some experimentation, I realize that the false easting/northing values, and the central meridian/parallel, don't change the projection at all; rather, they just shift the location of the origin (i.e., the point considered (0, 0)) for the map. That being the case, is there any convention for setting the origin and/or false easting/northing, or do we just set them to any convenient values for our particular project?

Best Answer

As you've figured out, the false easting and false northing parameters don't affect the look of the coordinates or their distortion due to the map projection.

These parameters were used historically to make sure that all coordinates within a map / area of interest are positive. When you're calculating distances and areas by hand, you do not want to have to deal with both positive and negative values.

Some projections (Lambert conformal conic, Albers, transverse Mercator) have a latitude of origin that doesn't affect the projection distortion. It can also be used to make all northing values be positive. If you do that, you don't need to change the false northing from zero.

To calculate what the false easting or false northing values should be, either display the area of interest using the custom coordinate reference system (CRS) (leaving false easting/northing equal to zeroes) and visually check what the coordinate values are for the southern and western extents or project the limits of the area of interest into custom CRS. Now that you know the largest negative values, you can set the false easting or northing parameters to match.

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[GIS] Convert Lambert Conformal Conic to WGS84

GDAL runs on most platforms, including Windows, so I'm not sure where you get the idea it only runs on Macs! The easiest way of getting installed on your machine is to download OSGeo4W, which is an installer for all manner of desktop GIS goodness, from which you can just choose GDAL/OGR.

Once you've done that, you can use the command line tool gdalwarp to reproject the images:

gdalwarp -t_srs EPSG:3857 -s_srs EPSG:9802 -r cubic -co "TILED=YES" input1.tif input2.tif ... input30.tif output.tif

Where EPSG:3857 is shorthand for the "Web Mercator" projection (thanks Sean!), and EPSG:9802 is the shorthand for the Lambert projection. You may need to use a different sampling algorithm instead of cubic, it depends on the sort of data you've got, and how it looks when it is warped. Specifying all the source images in one command line will avoid unsightly seams between the original images. the "TILED=YES" is sensible for almost any geo rasters to speed up access and display. See here for explanation of the parameters.

To split the image into tiles, you can use gdal2tiles.py (which you'll need to install Python, but that can be done with the OSGeo4W installer).

Addendum

It ocurred to me last night that you would need to specify the two lines of parallel and the central meridian of your source images on the command line, just using EPSG:9802 won't cut the mustard if that metadata isn't already in the source images. If that is the case, you'll need to change the -s_srs parameter to something like this:

-s_srs "+proj=lcc +lon_0=110 +lat_1=25 +lat_2=47 +datum=WGS84"

Where +lon_0 is the longitude of the central meridian, +lat_1 is the upper standard parallel, and +lat_2 is the lower standard parallel. If the images you're warping are of the same series, these values are likely to be the same for each image, but it is worth checking them first.

If you're unsure about how these projections work, you could do worse than looking here for an explanation.

[GIS] Lambert projection with one or two standard parallels and proj4

A good point made by Rene W.

Here is the answer:

add +no_defs to your first example in order to avoid unwanted default values

about this part: +a=6367470 +b=6367470 +ellps=sphere +datum=WGS84 +datum=WGS84 is a shorthand for: +ellps=WGS84 +towgs84=0,0,0.

You already have +ellps=sphere. Your reference surface cannot be a shpere and the WGS84 ellipsoid at the same time. As you already have +a=6367470 and +b=6367470, you should drop both +ellps=sphere and +datum=WGS84`

in case of doubts, use cs2cs -v for more info about which parameters are actually takes, and which are ignored

Hermann

and

The default values of lat_1 and lat_2 are 33 and 45, so in your first example you had +lat_1=46.244 +lat_2=45 which is not what you intended. The second example does what you wanted.

Charles

Best Answer

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[GIS] Convert Lambert Conformal Conic to WGS84

[GIS] Lambert projection with one or two standard parallels and proj4

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