Comparison of FOSS4G Supported Equal-Area Projections Using Discrete Distortion Indicatrices

Luís Moreira De Sousa,Laura Poggio,Bas Kempen

doi:10.3390/ijgi8080351

Luís Moreira De Sousa, Laura Poggio + Show 1 more

Open Access

https://doi.org/10.3390/ijgi8080351

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Abstract

This study compares the performance of five popular equal-area projections supported by Free and Open Source Software for Geo-spatial (FOSS4G)—Sinusoidal, Mollweide, Hammer, Eckert IV and Homolosine. A set of 21,872 discrete distortion vindicatrices were positioned on the ellipsoid surface, centred on the cells of a Snyder icosahedral equal-area grid. These indicatrices were projected on the plane and the resulting angular and distance distortions computed, all using FOSS4G. The Homolosine is the only projection that manages to minimise angular and distance distortions simultaneously. It yields the lowest distortions among this set of projections and clearly outclasses when only land masses are considered. These results also indicate the Sinusoidal and Hammer projections to be largely outdated, imposing too large distortions to be useful. In contrast, the Mollweide and Eckert IV projections present trade-offs between visual expression and accuracy that are worth considering. However, for the purposes of storing and analysing big spatial data with FOSS4G the superior performance of the Homolosine projection makes its choice difficult to avoid.

Highlights

In a relatively short span of time, the field of Geographic Information Systems (GIS) went from data wanton to data galore
Another relevant projection found to be fully usable is the one proposed by Hammer [15], which was developed in an attempt to address the extreme distortions at the edges of elliptical equal-area projections
This study clearly indicates the Homolosine as the most performant of the equal-area projections analysed

Summary

Introduction

In a relatively short span of time, the field of Geographic Information Systems (GIS) went from data wanton to data galore. In the particular case of global rasters, analysts of big spatial data are often confronted with datasets provided in awkward map projections, that greatly increase demands on storage and computation. These areas equate to the number of cells in a global raster with a cell side of 1 km. The Marinus of Tyre and Mercator projections, even though arguably the most popular projections in Earth Sciences today, impose massive overheads in storage space and computation time with the number of extra raster cells they require to discretise the surface of the globe. In order to minimise the size of the datasets and render them spatially representative of the surface of the Earth, big spatial data researchers often undertake as first task a re-projection with an equal-area projection

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