29 th International Geographical Congress A Comparison of Equal-Area Map Projections for Regional and Global Raster Data E. Lynn Usery and Jeong-Chang

29th International Geographical Congress

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



Results

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


60

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Per

cent

of

area

rep

rese

nte

d

0.5 1 4 8 16 25 50Spatial Resolution (km)

Goode

Mollweide

Equal-Area

Robinson


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Per

cent

of

area

rep

rese

nte

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0 25 50 75Latitude (degree)

Goode

Mollweide

Equal-Area

Robinson


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)



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 Equal Area CylindricalProjection (8 km Pixels)


Asia Land Cover inMollweide Projection (8 km Pixels)


Asia Land Cover inRobinson Projection (8 km Pixels)


Asia Land Cover Percentages by Projection 16-km Pixels 50-km Pixels

Land Cover Categories Lam Goode Eq-Cyl Mw Rob Lam Goode Eq-Cyl Mw Rob Urban & Built-Up Land 0.16 0.17 0.16 0.16 0.15 0.14 0.17 0.21 0.15 0.09 Dryland Cropland & Pasture 12.36 12.70 12.13 12.47 11.97 12.24 13.16 12.48 12.57 11.76 Irrigated Cropland & Pasture 11.26 12.24 11.20 11.06 10.33 11.60 12.38 11.59 11.07 10.70 Cropland/Grassland Mosaic 5.89 5.78 5.91 5.79 5.83 5.95 5.81 5.66 5.78 5.84 Cropland/Woodland Mosaic 4.24 3.96 4.33 4.32 4.28 3.85 3.79 4.15 4.37 3.97 Grassland 17.12 14.82 17.05 17.00 17.65 17.14 14.55 16.61 16.96 17.57 Shrubland 14.27 11.69 14.45 14.25 14.31 13.94 11.96 14.19 14.44 14.62 Mixed Shrubland/Grassland 2.05 2.39 2.07 2.10 1.96 2.05 2.42 2.24 2.05 2.03 Savanna 4.49 5.23 4.39 4.55 4.58 4.54 4.96 4.64 4.65 5.03 Deciduous Broadleaf Forest 3.20 3.67 3.23 3.16 3.14 3.44 3.44 3.41 2.93 3.02 Deciduous Needleleaf Forest 1.87 2.86 1.92 1.89 2.23 1.88 2.94 1.86 2.04 2.08 Evergreen Broadleaf Forest 2.70 3.09 2.79 2.73 2.40 2.60 3.19 2.72 2.60 2.57 Evergreen Needleleaf Forest 0.83 0.94 0.86 0.85 0.81 0.85 0.76 0.86 0.96 0.85 Mixed Forest 8.56 9.46 8.52 8.64 9.25 8.63 9.53 8.25 8.45 9.01 Herbaceous Wetland 0.14 0.19 0.16 0.14 0.15 0.12 0.18 0.16 0.12 0.11 Wooded Wetland 0.11 0.13 0.11 0.09 0.14 0.17 0.10 0.12 0.11 0.11 Barrenor Sparsely Vegetated 9.20 8.66 9.19 9.24 9.19 9.28 8.65 9.38 9.12 9.02 Herbaceous Tundra 0.16 0.06 0.17 0.16 0.17 0.17 0.07 0.12 0.21 0.17 Wooded Tundra 1.11 1.56 1.07 1.12 1.16 1.23 1.54 1.07 1.10 1.19 Mixed Tundra 0.04 0.11 0.05 0.05 0.07 0.03 0.11 0.04 0.04 0.02 Snow or Ice 0.25 0.28 0.24 0.25 0.25 0.15 0.30 0.24 0.28 0.25


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Lam Goode Eq Cy Mw Rob

Asia Land Cover by Projection, 1 km Pixels


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Lam Goode Eq Cyl Mw Rob



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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

Documents

29 th International Geographical Congress A Comparison of Equal-Area Map Projections for Regional and Global Raster Data E. Lynn Usery and Jeong-Chang