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

Question

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?

Answer 1

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.