How to know if two projections are the same?

Question

I am using R but also tried with QGIS, visually the two maps look the same but the projection info it's not. QGIS provides the same info.

first map

+proj=longlat +datum=WGS84 +ellps=WGS84 +towgs84=0,0,0 

second map

 +proj=cea +lon_0=0 +lat_ts=30 +x_0=0 +y_0=0 +datum=WGS84
    +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0

First I would like to know what these abbreviations mean, some are rather intuitive but not all of them. lat_ts? no_def? towgs?

How do I check with R that these two projections are the same?

Answer 1

You are looking at the PROJ representation of your two crs's. The high-level documentation for PROJ is here - https://proj4.org/usage/index.html, which describes what most of the +thing= parameters do.

PROJ crs definitions in common use have been mapped to EPSG codes, which may be what you're thinking of as CRS 'names'. You can try googling with the full string, looks like EPSG:6933 is a match for your second crs - http://epsg.io/6933.

Since PROJ strings are just that, plain text strings, a first pass check in R is as simple as reading it, or checking with identical(x, y). However, sometimes the component parameters for two crs's are all the same but in a different order, so you may wish to do some string manipulation before comparing like:

# split by spaces
a <- str_split('+proj=cea +lon_0=0 +lat_ts=30 +x_0=0 +y_0=0 +datum=WGS84 
                +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0', ' ')
b <- str_split('+proj=cea +lon_0=0 +lat_ts=30 +x_0=0 +y_0=0 +datum=WGS84 
                +units=m +no_defs +ellps=WGS84 +towgs84=0,0,0', ' ')
b[[1]] <- rev(b[[1]])
# a and b are now lists of proj params with a different ordering

# check equality with
identical(sort(unlist(a)), sort(unlist(b)))

# try tweaking a parameter and recheck
b[[1]][4] <- '+units=ft'

identical(sort(unlist(a)), sort(unlist(b)))

+proj=cea signifies the second crs you have is an equal area cylindrical, not equidistant (of which plate carrée is a special case). Its probably best suited for doing area calculations or raster plotting across the nothern mid-latitudes.