Mollweide Projection

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Introduction

Mollweide Projection is an equal-area pseudocylindrical projection proposed by German mathematician Karl Brandan Mollweide in 1805. The projection maps the earth’s surface onto a flat surface through mathematical transformation, aiming to maintain the accuracy of area ratio while minimizing the distortion of shape and direction. The central meridian of the Mollweide projection is a straight line, the other meridians are symmetrical elliptical arcs, the parallels are parallel straight lines, and the length of the equator is twice the length of the central meridian.

Projection Method

The projection method of the Mollweide projection is to map the earth’s surface to a plane through mathematical transformation, using an equal-area pseudo-cylindrical projection method. Its core features are that the equator and the central meridian are both straight lines with equal spacing, the meridians are projected into elliptical curves, and the latitudes are straight lines parallel to the equator. The details are as follows:

**Meridian projection: **The meridians are projected into elliptical curves. Except for the central meridian, which is a straight line, the other meridians are projected into symmetrical elliptical arcs. The two meridians 90° east and 90° west of the central meridian will be projected into circles, and the other meridians are regularly distributed semi-ellipses, and these meridians are concave to both sides with the central meridian as the center.
**Latitude projection: **The latitudes are straight lines parallel to the equator, and all latitudes are straight lines perpendicular to the central meridian and unevenly distributed. The farther away from the equator, the smaller the spacing.
**Projection outline: **The projection outline forms an elliptical shape. The meridians ±90° from the central meridian are projected to form a circle. The horizontal diameter of the circle and its extension are used as the projection of the equator, and the vertical diameter of the circle is used as the projection of the central meridian. The radius of the circle is determined based on the area of the circle being equal to half the area of the earth.

Pros

**Equal-area properties: **The Molweide projection is an equal-area projection that maintains the accuracy of global area proportions, which is important for applications that require comparisons of different regions.
**Global coverage: **This projection is suitable for data presentation on a global scale and can clearly present global geographic features.
**Evenly distributed deformation: **Compared with some other projections, the Molweide projection has a relatively even distribution of deformation, without extreme localized deformation.

Cons

Shape and direction distortion: Although the Mollweide projection maintains area proportions, there is still some distortion in shape and direction, especially in high latitudes.
Meridian curvature: Except for the central meridian, all other meridians are elliptical arcs, which may cause some errors when measuring distances and directions on the map.
**Visual effects: **For some users, the Mollweide projection may not be as visually intuitive as other projections (such as the Mercator projection), especially when showing high latitudes.

Application Scenario

The Mollweide projection is suitable for global geographic data presentation that needs to maintain the accuracy of area ratio, such as global climate distribution maps, global population density maps, global vegetation distribution maps, etc. In these applications, the accuracy of area ratio is crucial for data analysis and decision-making. At the same time, since the deformation distribution of the Molwede projection is relatively uniform, it is also suitable for applications that need to display the overall geographical features of the world. However, for applications that require accurate measurement of distance and direction, or applications that have high requirements for visual effects, other projection methods may need to be considered.

Example

The Moorweide projection centered on Greenwich.

Sea-surface freon levels measured by the Global Ocean Data Analysis Project. Projected using the Mollweide projection.

Mercator Projection

Transverse Mercator Projection

Wagner Projection

Longitude / Latitude Projection