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I hope this is right here in Earth Science, it's a bit of a Computer Science-y problem, too:

I want draw (or really just calculate the total area) of a boundary of X miles (with X varying between around 200-400) around all of Earth's landmass. It would be very much like the problem of drawing Territorial waters, only that I don't care about countries and nations at all. I just want a line around all landmass, including islands etc and then calculate the area of that.

Anyone knows a good way how to go about this?

PolyGeo
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user160531
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    Look at GIS packages and buffer options. You will also need vector data. Buffering that many polygons can cause problems, you may have to chop up the data, buffer than merge the buffered polygons. – mkennedy Jul 21 '18 at 20:57
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    You also will run into the coastline paradox, so you need to decide your scale of measurement. –  Jul 22 '18 at 06:24
  • It's an interesting beginner GIS question which I certainly would like to see a nice simple explanation given for! After all, I bet quite a few folks who haven't come across GIS would wonder how to do it. user160531, your question may be better suited for the GIS Stack Exchange... though please wait to see if anyone answers it here. If not, you can ask for a moderator to move it over there, and hopefully you'll get a good answer. Welcome to the site! – JeopardyTempest Jul 22 '18 at 08:33
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    http://resources.esri.com/help/9.3/arcgisengine/java/gp_toolref/geoprocessing/proximity_analysis.htm doesn't answer your question, but may be helpful. The general field here is "proximity analysis" –  Jul 22 '18 at 23:18
  • I've become obsessed w/ this question. My latest find: https://www.arcgis.com/home/item.html?id=d742a2904d864517870a9baa4016d394 -- you can view this using a free account, but you can't download the data as nearly as I can tell. Additionally, the starting contour is 250km, not very useful to you. There's also https://s3-us-west-1.amazonaws.com/www.moyhu.org/2017/04/n4.png -- if you search images.google.com for "distance from shore" map you get a few results, including https://commons.wikimedia.org/wiki/File:Distancia_a_la_costa.png but nothing really great. –  Aug 07 '18 at 16:19
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    OK, I'm working on a "final answer" using the signed file on https://oceancolor.gsfc.nasa.gov/docs/distfromcoast/ –  Aug 07 '18 at 17:39
  • Still working on answer, but here's a neat map: http://test.bcinfo3.barrycarter.info/bc-image-overlay-nokml.pl?e=180&w=-180&n=90&s=-90¢er=0,0&url=map3.png&zoom=3&maptypeid=ROADMAP –  Sep 07 '18 at 03:25

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To expand on what people have already written in comments:

You need, (a) a GIS package, such as QGIS; (b) A vector coastline for the world, such as GSHHG. If you're looking at the whole world, don't choose the highest resolution version.

Then, look up "Buffer" commands for the GIS system you are using. This will help you to define a zone reaching a certain distance off the coast.

Flyto
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I'd go simply with google maps if you don't want to "dig deeper" on software. Note that it will take you quite some time to draw the coastal outlines.

However, the tricky part is that - even if you would be so folish to take the better part of your lifetime drawing lines on a computer screen - the drawing will not lead you to an excact answer, due to the coastline paradox: The more accurate you draw the coastline the longer it will appear to be. The ratio of accuracy to length is the starting point to understand fractal dimensions. This is well explained HERE or HERE.

So what is the length of all coastlines combined? Depending on accuracy (scale of measurement), you can sum-up this list: List of countries by length of coastline

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    Question: will the coastline paradox affect area that much? I know it affects length, but I think area remains relatively constant. As a note, I'm working on this question here: https://github.com/barrycarter/bcapps/blob/master/STACK/bc-buffer-land.m –  Jul 23 '18 at 16:08
  • @BarryCarter If you have a simple-ish polygon, I'd agree with you, but you're talking about really big areas. Densifying the coastline at different levels can cause relatively large changes to the area. – mkennedy Jul 23 '18 at 23:19
  • My instinct is that the effect of changes in length scale will be much proportionately less for area, although still extant. The reason for this is that so long as the measurement scale is much less than the distance offshore that the line is being drawn, the majority of the area comes from points far from the line that are not affected by adding more detail. – Flyto Jul 24 '18 at 15:02
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    I was thinking of the https://en.wikipedia.org/wiki/Weierstrass_function -- as you build it up, the length grows without bound; the area also grows, but is bounded. The https://en.wikipedia.org/wiki/Koch_snowflake is perhaps a better example. https://en.wikipedia.org/wiki/Coastline_paradox itself mentions the https://en.wikipedia.org/wiki/Sierpi%C5%84ski_curve which has a similar property (converges to finite area, infinite length) –  Jul 24 '18 at 17:27
  • @mkennedy, not necessarily. Consider the following example: take a circle with a radius of exactly 10 centimeters. It's trivial to calculate the area (to two decimal places) as 314.16 cm^2. Now draw another circle 9.95 cm in radius: area 311.03 cm^2. If you draw a line in the gap between those two circles, you can make it arbitrarily long by drawing the line at different densities of fractal complexity, but the area it encloses by definition cannot exceed 314.16, nor be less than 311.03. "Densifying" rapidly starts producing diminishing returns when it comes to altering the overall area. –  Jul 27 '18 at 20:57