# Equal-Area Projections: An Overview And Comparison For Marine Applications

## Purpose of Equal-Area Projections

Equal-area projections aim to accurately represent the proportional areas of features on the Earth’s surface. By preserving the relative sizes of countries, lakes, and other geographical entities, equal-area projections facilitate analysis related to size and scale.

Two key applications where preserving accurate areas is critical are **oceanography** and **marine biology**. In oceanography, equal-area projections allow for assessing ocean currents, sea ice coverage, and other phenomena based on total surface areas. In marine biology, the range or extent of species habitats can be quantified and compared using an equal-area projection.

### Preserving area proportions

On any map projection, some level of distortion is inevitable when portraying the three-dimensional Earth on a two-dimensional surface. However, equal-area projections are designed to specifically maintain the correct proportional areas of features. This property of equal-area projections makes them invaluable for particular types of spatial analysis and data visualization.

By correctly representing the **relative sizes** of geographical entities, equal-area projections allow for accurate calculations and comparisons based on total area. The typical trade-off is increased distortion in shapes and distances in order to preserve true areas. Thus applications where the total spatial extent or coverage of features takes precedence can benefit greatly from using an equal-area projection.

### Applications in oceanography and marine biology

In the context of **oceanography**, equal-area projections enable important analyses such as:

- Assessing the total coverage of sea ice year-to-year
- Quantifying the aerial extent of a current system or gyre
- Identifying shifts or changes in marine ecosystems based on geographical range

For **marine biologists**, equal-area projections allow for critical tasks including:

- Mapping species ranges and habitats
- Modeling distributions and spread of invasive species
- Analyzing impacts related to loss of habitat area

By facilitating quantitative area-based analysis, equal-area projections thus provide vital tools for both ocean science and conservation. Key disciplines that utilize such projections include physical oceanography, marine geosciences, population dynamics modeling, and species distribution mapping.

## Common Equal-Area Map Projections

Many different map projections exist to represent the spherical Earth on a 2D plane. Only certain projections exhibit the equal-area property, with some designed specifically to optimize area fidelity. Four common categories of equal-area projections are outlined below.

### Albers equal-area conic

The Albers projection is an **equal-area conic** projection, meaning it is constructed by projecting the Earth’s surface onto a cone which is then unrolled into a plane. By using multiple reference parallels where the cone intersects the globe, distortion is minimized between those latitudes.

Advantages of Albers equal-area conic include:

- Very low distortion in mid-latitude regions like the continents
- Can customize for any region by adjusting standard parallels
- Conforms well to an ellipse representing the Earth

### Lambert cylindrical equal-area

As its name suggests, this projection portrays the world on a cylinder wrapped around the Earth east-west. This cylindrical projection preserves area proportions by having variable spacing between pole-to-pole parallels.

Benefits of the Lambert cylindrical include:

- No distortion along the equator, useful for global views
- Simple cylindrical form
- Low distortion near equatorial regions

### Mollweide

The Mollweide projection depicts the globe on an ellipse, offering an aesthetically pleasing oval layout. It is essentially a sinusoidal equal-area projection bounded north-south.

Favorable attributes are:

- Pseudocylindrical: relatively low distortion overall
- Aesthetic oval shape
- Equal-area and conformal along lat 40°N/S

### Eckert IV and VI

The Eckert family of projections use ellipses placed around the globe to construct the map. Eckert IV and VI variants exhibit the equal-area property while reducing some forms of distortion.

Notable pros for Eckert IV/VI:

- Minimized distortion in polar regions
- Distributed distortions more evenly
- Visually appealing and symmetric

## Comparing Distortion Patterns

While equal-area projections maintain accurate proportions for area, they still exhibit forms of spatial distortion. Understanding how distortion manifests in an equal-area projection assists with selecting the optimal one.

### Meridional distortion

Meridional distortion refers to the north-south stretching or compression of shapes. At high latitudes near poles, meridians of longitude converge rapidly. Certain projections handle this convergence better. Visual scrutiny can reveal unacceptable elongation or squashing along a north-south axis.

### Latitudinal distortion

Analogous to meridional distortion, latitudinal distortion constitutes improper east-west stretching or compression of features. Some equal-area projections control latitudinal distortion via careful mathematical representation of parallels. Excessive widening or slimming along an east-west axis signifies high latitudinal distortion.

### Areal distortion

Lastly, areal distortion describes the distortion of relative spatial areas and proportions. Even though equal-area projections define areas correctly, individual shapes can still exhibit distortion leading to inaccurate representations of terrain. The distribution and magnitude of local areal distortions should be minimized.

## Choosing a Projection

Several factors guide the choice of which equal-area projection to apply for a particular region or analytical purpose.

### Intended use and region of interest

First and foremost, the intended use and location of study dictate projection needs. Global views favor cyclindrical or pseudocylindrical types, while regional analyses benefit from conic projections tailored to that latitude span. Oceanographic basins and poleward realms require controlling meridional distortion as well.

### Minimizing key distortions

Additionally, spatial distortions should be checked to ensure acceptable limits for the intended use. Conic and pseudocylindrical projections often balance distortions adequately, whereas cylinders maintain truer meridians and parallels. For country or continent scales, conic Albers or sinusoidal types excel by distributing distortion evenly across middle latitudes.

## Example Usage in Python

Modern GIS packages facilitate generating equal-area projections. Python in particular, leveraged for geospatial data science, provides built-in functionality for some of the most common variants. Its cartographic plotting libraries like Cartopy and Pyproj enable both projecting geo-referenced data as well as visualizing aspect of projection distortions through graticules.

### Sample code for Albers, Lambert, Mollweide

A simple script in Python can create instances of Albers, Lambert cylindrical, and Mollweide projections based on coordinate reference system specifications and parameters. GeoPandas further allows quick plotting of coastlines and graticule lattices on these projections for fast visualization.

### Visualizing distortion patterns

By generating multiple plots with varying projection aspects, Cartopy permits visually inspecting distortion signatures across latitudes/longitudes. Graticules illustrating the translation of meridians and parallels from globe to projection facilitates comparing spatial warpings to select optimal parameters or entire projection class.

## Recommendations for Marine Applications

For oceanographic and biological use cases covering sea surface phenomena or marine ecosystems, certain equal-area projections confer advantages.

### Emphasize low areal distortion

Minimizing areal distortion preserves regional surface areas for calculations. Conic Albers or sinusoidal Mollweide achieve smooth area representation without irregular shapes.

### Lambert cylindrical near equator

The latitude bands near the equator exhibit the least distortion in Lambert cylindrical equal-area projections, ideal for analyses centered on tropical/equatorial waters.

### Albers for mid-latitude regions

For studies focused on the open ocean gyres, robust western boundary currents, or poleward biomes in mid-latitudes, Albers equal-area conics offer a very distortions-conscious perspective.