Natural Earth 1: properties, uses, and limitations
A compromise projection tuned by hand rather than derived: neither conformal nor equal-area, and severe at neither. It turns out to have one true-shape parallel, at 36.2 degrees, that appears in no definition of it.
Description
Tom Patterson released the Natural Earth projection in 2008. It was not derived from a condition to preserve something; it was adjusted parallel by parallel in Flex Projector, and its original definition is a table giving the length and spacing of every fifth degree of latitude. In 2011 Savric and colleagues fitted a polynomial to that table, and the polynomial is what software uses today - d3-geo included.
It is a compromise projection: neither conformal nor equal-area. The design goal was that a world map should simply look right.
Projection properties
- Family
- Compromise pseudocylindrical
- Frame ratio
- 1.923:1
- Latitudes drawn
- The whole world
- Pole line
- 55% of the equator
- True-shape parallel
- 36.2°
- Area distortion doubles
- 72.5°
- Shape distortion doubles
- 67.2°
- Held at 1.00 by definition
- Neither
Parallels are straight horizontal lines, meridians curve, and the corners are rounded. Each pole is drawn as a line 55 percent the length of the equator - measured here, and much shorter than the 0.87 often quoted, which is a different quantity.
The frame is 1.923:1. Area distortion runs 1.11 at 30 degrees, 1.49 at 60, 3.47 at 84, and does not double until 72.5. Shape distortion is already 1.16 at the equator - it is not conformal there - then 1.55 at 60, doubling at 67.2, and 9.24 at 84.
It has exactly one parallel along which shapes are undistorted, measured here at 36.2 degrees. That line appears in no definition and no documentation lists it as a standard parallel; it is a by-product of the polynomial fit.
One implementation detail: it squeezes low latitudes to fit its canvas, and its area scale at the equator is 0.877 of the nominal scale. Readings on this site are normalised to each projection's own measured equator, which is why this page shows 1.00 rather than 0.88.
Measured distortion
| Latitude | 0° | 30° | 45° | 60° | 72° | 84° |
|---|---|---|---|---|---|---|
| Area distortion | 1.00 | 1.11 | 1.26 | 1.49 | 1.97 | 3.47 |
| Shape distortion | 1.16 | 1.05 | 1.12 | 1.55 | 2.51 | 9.24 |
Both rows are measured against this projection's own equator, taken as 1. They compare with each other and with nothing on another projection's page - every projection is normalised to itself.
Uses
World maps in atlases, teaching maps, and anywhere nobody intends to measure anything off the picture.
That is the case for compromise projections generally: if you are neither doing area statistics nor navigating, keeping both distortions mild usually beats zeroing one and letting the other run. For contrast, Mercator's area at 84 degrees is 91.5 and Gall-Peters' shape at the same latitude is 45.8, against this map's 3.47 and 9.24.
Limitations
It preserves nothing, so areas and angles taken off it have no standing. An area-based thematic map needs an equal-area projection instead.
The poles are lines rather than points, and high-latitude features are flattened east-west, so it is a poor place to discuss polar geography.
There is also a Natural Earth II, from 2012, with tighter corners. It is a different map; this page is about the first.
Parameters
How this site builds it (w and h are the canvas; sphere is the whole globe):
geoNaturalEarth1().fitExtent([[0, 0], [w, h]], sphere)geoNaturalEarth1 exposes no standard parallel and no adjustable pole-line length: the polynomial coefficients are fixed. Only the central meridian moves.
That is typical of compromise projections. They are defined by looking right rather than by a condition that can be solved for a parameter, so there is usually nothing to tune.