Why Are All Maps Inaccurate?
Most of us know the Earth is spherical, or more accurately an ellipsoid. The fact that we have to represent a curved 3-dimensional surface to a 2-dimensional flat piece of paper or screen means that some distortions are involved. This method of "projecting" the Earth's surface to a 2D image is called a map projection.
There are hundreds of map projections, and each of them minimises distortion in the shape, distance, area and direction in various degrees. However, no map projection can eliminate them all, hence understanding the pros and cons of each projection is essential to determine what to use for your project.
Table of Contents
Orthographic Projection Mercator Projection Transverse Mercator Projection Lambert Conformal Conic Projection Robinson Projection Summary
Source Code
To visualise the various projections, we can use the Python libraries matplotlib and cartopy.
pip install matplotlib cartopyThe code source for most of the world maps created in this article is provided below.
import matplotlib.pyplot as plt
import cartopy.crs as ccrs
import cartopy.feature as feature
# fix maplotlib params
plt.rcParams['figure.dpi'] = 175
# projections & borders
CRSs = [ccrs.Orthographic(),
ccrs.Orthographic(central_longitude=0, central_latitude=-90),
ccrs.Mercator(),
ccrs.UTM(zone=29),
ccrs.Robinson(),
ccrs.LambertConformal()]
borders = [(0, 1, 1, 0.05),
(0, 1, 1, 0.05),
(0, 1, 1, 0.05),
(0, 1, 1, 0.05),
(0.05, 1, 1, 0),
(0, 1, 1, 0)]
names = ["ortho", "ortho_southpole", "merca",
"utm", "robin", "lambertc"]
dir = "/Users/jake/Desktop/GIS"
for crs, br, name in zip(CRSs, borders, names):
fig, ax = plt.subplots(subplot_kw={'projection': crs})
projection_name = str(crs).split(" ")[0]
# Draw countries and coastlines
ax.coastlines(linewidth=0.5)
ax.add_feature(feature.BORDERS, linestyle=':', linewidth=1)
# Draw parallels and meridians
gridlines = ax.gridlines(draw_labels=True, linewidth=0.25, color='gray', linestyle='--')
gridlines.top_labels = False
gridlines.right_labels = False
gridlines.xlabel_style = {'size': 7}
gridlines.ylabel_style = {'size': 7}
# spacing
plt.subplots_adjust(left=br[0], right=br[1], top=br[2], bottom=br[3])
# border
for spine in ax.spines.values():
spine.set_linewidth(0.5)
# save the map
plt.savefig(f"{dir}/{name}.png")Orthographic Projection
The Orthographic projection represents the most accurate depiction of the Earth when viewed from space. This type of projection is known as a planar projection, where the Earth's surface is projected on a flat, imaginary plane.
However, we can only view one hemisphere in this flat plane, and distortions of all forms occur when we move from the centre of the map and are especially pronounced towards the edges. We seldom see this projection used, except for aesthetic purposes or any cases when we want to inject some realism into our map.
That being said, when we shift the focus to the South Pole, the shape of Antarctica is more accurate compared to the other Maps after this. An even more accurate type of planar projection for mapping polar regions is the Stereographic projection.
Mercator Projection
The Mercator projection, created by Gerardus Mercator in 1569, is undoubtedly the most recognisable of all projections. Google Maps uses a variant of this called the Pseudo Mercator or Web Mercator.
The reason for its popularity is that it preserves shapes and angles very well, which is essential for the navigation of ships in the past and our current use of digital map applications to view the shapes of the territorial borders and then zoom in while keeping the shapes intact.
The Mercator is a type of cylindrical projection with the equator touching the cylinder, hence only the stripe along the equator is not distorted in terms of its area. The distortion becomes more significant and exaggerated the further we move to the poles.
A good example is that in the Mercator projected world map above, you can see that Greenland is about the same size as the continent of Africa. But in reality, Greenland is 14 times smaller than Africa, or just 7% of Africa's area!
Transverse Mercator Projection
The main takeaway from the earlier Mercator projection is that there is the least distortion at the equator because it is touching the imaginary cylinder. This knowledge is used to make another very popular projection called the Transverse Mercator.
Instead of the cylinder being upright, and touching the equator, it is "traversed" so that a particular length of longitude touches the cylinder. Only this narrow stripe is used since it has the least distortions. There are many variants of transverse Mercator, but the logic of projection is similar. The difference is where the central meridian (the longitudinal line which touches the cylinder) is and the width of the stripe.
This unique, narrow zone or stripe of projection is used widely for land surveys with a North-South extent because of its accuracy. For the same reason, meters (or feet in the United States) are used instead of latitude and longitude as units of the coordinates.
Universal Transverse Mercator
Known commonly as UTM, the Universal Transverse Mercator is the most known and used among the Transverse Mercator projections. It projects along each stripe of longitude and hence divides the Earth equally into 60 longitudinal stripes or zones, with each of these zones being 6 degrees latitude-wide.
Since each zone is a unique projection on its own, we can't display them together on the world map but have to use another projection to display it as above. As you realise, due to the narrow width, many countries and states have their territorial areas overlapping multiple UTM zones.
Singapore Transverse Mercator
Some countries use variants of the Transverse Mercator. For example, Singapore has its national projection, called SVY21 (Singapore Vertical Datum 2021). This makes sense as Singapore is a tiny country. While it is located within the UTM zone of 48, it will still experience distortions since it is not at the central meridian of that zone.
For SVY21, the central meridian is situated at the centre of Singapore, giving it the highest possible accuracy.
Lambert Conformal Conic Projection
The world map view looks peculiar using the Lambert Conformal Conic Projection as it looks like it is being projected on a 3/4 circle.
This is because it is a conic projection type, whereby a cone, like a party hat is placed on top of the Earth, and the surface is projected onto the insides, and then unrolled.
You can imagine that there will be a circumference of the cone that will touch the Earth at a point. This line called a standard parallel, is the line where the area projected has the least distortion.
The strength of conic projections occurs when we want to project countries located at mid-latitudes and with an east-west mass spread where the standard parallel is placed. This cannot be achieved accurately from the previously stated planar and cylindrical projections.
In addition, the Lambert Conformal Conic Projection can preserve angles, shapes and direction along the standard parallel, hence it is used widely for creating maps for the United States, Australia and China.
Robinson Projection
All the previous projections are excellent at minimising only one or two types of distortions or excel only in limited ranges. The Robinson projection is good at minimising all distortions of the world to an extent. Hence, it is often considered a compromise between different types of distortions.
This projection was created by Arthur H. Robinson in 1963 and was used by National Geographic as their world map for a decade.
This is also known as a pseudo-cylindrical type of projection since the longitudes are curved to minimise distortions. Another similar projection is the Winkel Tripel projection which the United Nations uses for its world map at this point of writing.
Summary
I have shown some popular projections used in maps today. They can be broadly classified into three families of projection surfaces and hopefully, the reasons why they are used are obvious to you now. Of course, this is a much more complicated topic if we go even deeper, but the fundamentals shown here should suffice to explore on your own.
Further Readings
8. Coordinate Reference Systems – QGIS Documentation documentation
