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I am working on a personal 3D project which combines metadata from shapefiles, and rasters for topography, true color, bathymetry, etc...

I am using the Blue marble images (which I understand are using the WSG Datum WGS84 and the Plate Carrée projection) with shapefiles from natural-earth (which also use the WSG Datum WGS84).

It was my understanding that both are using the same projection (which could be referenced with epsg:4326) and indeed they seem to match to a point.

However when looking at lands near the the poles, some inconsistencies are very apparent (see screenshot of Greenland below)

Blue Marble + Natural Earth Coastlines

Looking at the Blue Marble Navigator (blue-marble.de) which offers an interface to navigate through the Blue Marble images, I noticed the exact same discrepancy (see screenshot below, with the mismatched black zones)

Blue Marble Navigator Screenshot: Greenland

Should I re-project the raster/shapefiles with a different projection, or are the Blue Marble images altogether unfit to be correctly matched to epsg:4326 shapefiles?

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This could very well be an issue with when the imagery was taken. Along the coast, high vs low tide can greatly affect the imagery collection.

NOAA Tidal Facts talks about some of the greater differences between high and low tide:

The highest tides in the world can be found in Canada at the Bay of Fundy, which separates New Brunswick from Nova Scotia. At some times of the year the difference between high and low tide in this Bay is 16.3 meters, taller than a three-story building.

The highest tides in the United States can be found near Anchorage, Alaska, with tidal ranges up to 12.2 meters.

A 10 meter or so difference would definitely show some low lying land during low tide that wouldn't be detected in imagery taken during high.

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