# Presentation: 262505

## A Comparison of Equal-Area Map Projections for Regional and Global Raster Data 

- E. Lynn Usery
- and
- Jeong-Chang Seong

## Outline

- Objectives
- Hypotheses
- Approach
- Theoretical Results
- Empirical Results with Land Cover
- Conclusions

## Objectives

- Determine effects of various map projections on regional and global raster data
- Assess problem mathematically
- Test empirically
- Long-term goal -- develop specialized projection, if necessary, to optimize projection of raster data

## Hypotheses

- Projection of raster data will produce variable results dependent on three factors:
- Projection type and specific projection
- Raster resolution
- Latitude

## Approach

- Theoretical
- Use vector representation of 1x1 degree squares at various latitudes to determine actual areas
- Convert squares to raster and transform using exact projection equations (rigorous transformation) to various projections
- Tabulate resulting areas of cells and compare to the vector “truth”

## Projections Used

- Equal Area
- Goode Homolosine (Goode)
- Equal Area Cylindrical (Eq-Cyl)
- Mollweide (Mw)
- Pseudocylindircal -- compromise
- Robinson (Rob)

## Resolutions Examined

- 500 m – MODIS sensor IFOV
- 1 km – AVHRR IFOV, NDVI base
- 4 km – LAC, GAC temporal composites
- 8 km – LAC, GAC temporal composites
- 16 km, 25 km – Extent of largest features
- 50 km – Larger than most geographic features used in modeling applications

## Slide 8

## Results

- Areas of 1x1 degree squares vary according to:
- Projection
- Resolution
- Latitude

## Slide 10

## Slide 11

## Approach

- Empirical
- Transform land cover of 1 km raster pixels of Asia to various projections with resampling to different pixel sizes
- Tabulate land cover percentages and compare among projections and among raster resolutions of the same projection

## Asia Landcover

- Downloaded from EDC
- Lambert Azimuthal Equal Area Projection
- Goode Homolosine Projection
- USGS Land Cover Classes (24 categories)

## Slide 14

## Asia Land Cover in Lambert Azimuthal Equal Area  Projection

-                                    (8 km Pixels)

## Asia Land Cover in Goode Projection

-                     (8 km Pixels)

##     Asia Land Cover in

-     Asia Land Cover in
-  Equal Area Cylindrical
- Projection (8 km Pixels)

##  Asia Land Cover in

-  Asia Land Cover in
- Mollweide Projection
-        (8 km Pixels)

## Asia Land Cover in

- Robinson Projection
-        (8 km Pixels)

## Slide 20

## Asia Land Cover by Projection, 1 km Pixels

## Asia Land Cover by Projection, 4 km Pixels

## Asia Land Cover by Projection, 8 km Pixels

## Asia Land Cover by Projection, 16 km Pixels

## Asia Land Cover by Projection, 25 km Pixels

## Asia Land Cover by Projection, 50 km Pixels

## Asia Land Cover by Projection

- Verifies theoretical analysis
- Robinson overestimates except at 50 km
- 16 km
- Lam, Mw, Eq-Cyl retain almost identical %
- Mw same at 50 km
- Goode doesn’t maintain between 16 and 50 km

## Asia Land Cover by Projection

- Latitudinal results verified by examining specific land covers which occur at unique latitudes
- Deciduous needleleaf forests occur in high latitudes
- Order of areas lowest to highest
- Mw, Eq-Cyl, Robinson
- Goode anomaly because different source

## Summary

- Empirical results at 1, 4, 8, 16, 25, and 50 km verify the theoretical results shown in the graphics.
- Visually which is most pleasing?

## Conclusions

- Regional and global raster data yield varying areas when projected in different equal area projections.
- Variance is by projection, resolution, latitude
- 1 km or less, any equal area is okay
- 1 to 8 km, Mw shows best accuracy
- 16 to 25 km, Eq-Cyl and Goode better
- 50 km, Mw best
- Overall, Mw a good alternative

## Current Work

- Global datasets
- Land Cover (1 km)
- Elevation (30 arc-sec and 5 min)
- Vegetation (1 degree)
- Precipitation (30 min)
- Temperature (30 min)

- Projections
- Equal Area Cylindrical
- Eckert IV
- Hammer
- Mollweide
- Quartic Authalic
- Sinusoidal
- Robinson
- Van der Grinten

## Future Work

- Correct problems with raster projection
- DSS for use with current software based on empirical base developed
- Develop dynamic projection for raster data
- Implement error correction procedures
- Prefect resampling from one projection to another