The topographic Earth

By Phil Plait | October 18, 2011 1:30 pm

This is pretty nifty: a new elevation map of the Earth has just been released by NASA and Japan. It’s a "significantly improved" version of one that came out in 2009.

It uses Japan’s ASTER, the Advanced Spaceborne Thermal Emission and Reflection Radiometer, an instrument on board NASA’s Terra satellite. Terra is an Earth-observer, with detectors on board used to study various properties of our planet. ASTER looks both straight down and slightly behind the satellite’s track on the Earth is it passes. Over time stereo image pairs are created, and these can be used to create very high-resolution elevation maps (called topographic maps) of the surface of the Earth.

The new images are higher-res than before, and cover the Earth better to the tune of 260,000 more images. As an example of what can be done, they used it to make this map of the Grand Canyon:

[Click to enmesanate.]

One thing that struck me as funny when I read it: the coverage of ASTER’s observations goes from the Equator to as far north and south as 83° latitude… and they say that this is 99% of the Earth! That sounds odd, doesn’t it? You’d think the north and south poles of the Earth from 90° to 83° would be more than that, but in fact it’s true.

The portion of a sphere above a certain latitude line is called a cap, and the area of that cap depends on the latitude in question, and the radius of the sphere. I drew myself a diagram, fiddled with the numbers a bit, and found that the area of the Earth north of 83° compared to the surface area of the northern hemisphere is about 0.75%! So in fact, ASTER covered a bit more than 99% of the Earth’s surface, even if it never got past that 83°latitude.

Math! Surprising people since the time of Pythagoras.

Anyway, if you want to download the ASTER data yourself, you can: it’s public. Japan has a copy, and so does the USGS. I imagine it won’t be long before it’s integrated into Google Earth and all that too. Living in the future is pretty cool.

Image credit: NASA/GSFC/METI/ERSDAC/JAROS, and U.S./Japan ASTER Science Team


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CATEGORIZED UNDER: Cool stuff, NASA, Pretty pictures

Comments (22)

  1. Argus

    Anyone who has seen a certain diagram for the surface area of a sphere (or is familiar with the Lambert or Gall-Peters map projection) should quickly understand why the sine function will work for this.

    sin 83˚ = 0.992546

    (The 99% threshold is passed just before 82˚.)

  2. Yeah, it’s an awesome fact that the surface area of the sphere is the same as the cylinder (thank you Archimedes!) so you only need to know how far up along the axis you are to know what fraction of the surface area you’ve covered.

    Does anyone know how big a correction to this we might need because the Earth isn’t actually a sphere? I mean, are we talking 0.75% vs 0.74% or is it a bigger error?

  3. Pete Jackson

    The latitude limit just about matches the most northerly point of land which is in Greenland at 83 degrees 40 minutes north. There is a bit of ‘land’ missing near the South Pole, but that is just a flat glaciated plateau.

  4. Justin
  5. Wayne Robinson

    The cap also means that with global warming, the farm land lost in midlatitudes won’t be compensated by the farm land gained in higher latitudes. If only the Earth were like its Mercator projection.

  6. Kurt Kohler

    “ASTER looks both straight both and slightly behind the satellite’s track on the Earth is it passes.”

    There’s something wrong with this sentence. ;-)

    Should it be “both straight down and slightly behind”?

  7. Come on, Phil. Clearly the best pun there is engorge.

  8. Joe Alvord

    Darn! I just got back from a backpacking trio in the Grand Canyon and the area I hiked was JUST off the bottom of the picture.

  9. Infinite123Lifer

    I don’t see any Sasquatch but I certainly see an insanely detailed image of an insanely beautiful geological location!

    There must surely be infinite wonderful relationships throughout geometry and all of mathematics for that matter. But perhaps the sphere/ball(?) is capable of giving us the most . . . easily seeable (?) relationships of space to points to lines.

    The equality of the ‘derivative of the area of circle’ and ‘the circumference of that circle’ is just one I learned and remember!

    For me it is difficult to understand the concepts and the level of deduction which can be shown on paper of how and why measurements evolve with respect to other elements of equations but it is always a moment of awe when relationships are discovered.

    sin 83˚ = 0.992546 from comment #1.

    I don’t have my scientific calculator to check if his math is correct.

    I know I know:
    1. Argus is probably right and undoubtedly yields vastly superior mathematical skills
    2. Don’t ever not check the math
    3. This IS actually one calculation I Could check :)
    4. I am still struggling with the concept behind what Argus has mentioned and Phil’s explanation and what is really going on . . . oh wait I think I got what Phil is saying……..ASTER covered the region from the equator to the regions at approx 83 degrees latitude both north and south which equals 99% of the Earth’s total surface area (if it were a perfect ball) and that might seem odd (i know its right there but sometimes you have to read things a couple times to get it). Yes I would think that there might be more surface area proportional to the whole than 1% from 83 – 90 degrees especially if you include both hemisphere’s but understanding the math behind it kinda makes that thought go away :) or drawing lines on a ball and visualizing it :) but the math sure makes you sleep better.

    Phil said: Math! Surprising people since the time of Pythagoras.

    Whether math was “knowingly” sewn into the fabric of our existence or not is not a question which is answerable to me. The fact that man has discovered some amazing equalities and relationships about that existence within our time is though. Whether philosophy or physical understanding of the world is more important, well, I argue they are one in the same.

    It is sometimes better to be a dreamer than a technical genius and vice versa; though I suspect I would gladly have my rates of change in the understanding of philosophy and mathematics gradually increase to infinity together as one. I even suspect perhaps one cannot exist without the other. For the base philosophy behind even being able to count to ten by ones could be considered a magical understanding perceived through mathematical reasoning.

    I must contend though that our grand understanding of mathematics cannot reach infinity faster than our grand understanding of philosophy can ;) reach infinity ha; but then again perhaps mathematics and philosophy share a relation which cannot be expressed without using the other. Perhaps one effects the other on opposite sides of the equal sign. Perhaps there is an equation for the grand types of understanding in men.

    Until then,
    Great Job Humanity

    Whether the Evolutionary Creation of the Universe employed mathematics to develop itself with itself or if it just sprung up as a resultant of all the hustle and bustle between matter and elements and space and time . . . I don’t think it matters folks. It is a beautiful reality to wonder is what does matter.

    p.s. Iama get a Life soon :)

  10. flip

    Math! Surprising people since the time of Pythagoras.

    That made me smile. What a great phrase!

  11. Infinite123Lifer

    Yeah its funny how less can be more sometimes.
    Made me smile as well, and got me ol’ brain a ramblin . . .
    Here is a bit more:

    Besides what Wikipedia says about John Wesley Powell being a U.S soldier, geologist, explorer of the American West, and director of the major scientific and cultural institutions including the first known passage through the grand canyon and serving as second director of the US Geological Survey (1881-1894) and being director of the Bureau of Ethnology at the Smithsonian Institution for a period of time I don’t know what type of man John Wesley Powell was but he’s recorded as saying the following regarding this puzzle piece within the Earth known as the Grand Canyon.

    “The wonders of the Grand Canyon cannot be adequately represented in symbols of speech, nor by speech itself. The resources of the graphic art are taxed beyond their powers in attempting to portray its features. Language and illustration combined must fail.”

    &

    “You cannot see the Grand Canyon in one view, as if it were a changeless spectacle from which a curtain might be lifted, but to see it you have to toil from month to month through its labyrinths.”

    John Wesley Powell 1834-1902

    It is amazing to actually imagine how powerful an image like this could be to a man living at that time period. I wonder what John Wesley Powell would have thought about ASTAR :)

    I mean I know google earth has been around for awhile. . . but really. Who cares.
    The Earth Never Gets Too Old To See! :)

  12. Fleegman

    Seeing the Grand Canyon like this, makes it even more amazing that it was created in just a year. Those were some seriously choppy seas.

  13. Ray Bellis

    The release actually says it covers 99% of the _landmass_, not the Earth.

    There’s barely any land in the Arctic above 83ºN, but in the Antarctic below 83ºS it’s 100% land (with maybe the odd frozen lake below the ice cap). I’ll net those out and assume that half of the total area missed is land (i.e. 0.375% of the globe).

    Hence the coverage figure needs to account for that missing chunk. A quick search reveals that land covers 29.22% of the globe, but ASTER has missed that 0.375% of the global land coverage at the poles, so by my rough calculation they’ve actually only covered 98.71% of the _landmass_, compared to 99.25% of the planet.

    i.e. 100 * (29.22 – 0.375) / 29.22

  14. Infinite123Lifer

    @13
    I should have actually drawn lines on the ball :) always thanks for the FYI’s ;)

  15. Blargh

    Anyway, if you want to download the ASTER data yourself, you can: it’s public.

    … but it’ll take you hours to figure out how, and you’ll have to create a bunch of thoroughly unnecessary accounts to do so.

    I can’t for the life of me imagine why they’re making it this difficult. The Blue Marble images, by comparison, are easily accessible and directly downloadable over HTTP, FTP, and bittorrent.

  16. Ray Bellis

    Following up my own post.

    A possibly simpler way of saying it is that at the poles, the land:sea ratio is disproportionately high (at ~1:1) than the planet as a whole (~29:71).

  17. Don Bunnell

    Just curious about the word “enmesanate” as in “click to enmesanate” I couldn’t find any reference to a definition for this word anywhere. While is is an interesting construction, it was hard to determine its meaning from context. I could only assume that it meant to raise and flatten as in a mesa. I was disappointed to find the map was just enlarged.

  18. lunchstealer

    That will definitely be useful north of 60%, where the SRTM (Shuttle Radar Topography Mission) data cuts off. I fiddled around with some of this data in Florida (admittedly a very difficult place for stereo-derived topography), and it’s pretty noisy, compared to USGS 1:24k DEMs. I think it will also be useful in areas of high topography where the side-looking radar of the SRTM missions had large gaps. Also, the SRTM dataset is intentionally degraded from 30m resolution to 90m resolution outside the US, for reasons that have never really been clear to me.

    Also, Don, Mr. Phil likes to coin his own neologisms for ‘embiggenate’. So if you’re expanding an image that includes mesas, you are ‘enmesanating’ the image.

  19. Oscar

    @lunchstealer

    I work somewhat in the field and one important reason that the SRTM dataset is 90 meters is that the data volume is lower. In fact the SRTM global mosaic at 90m is still about 120 gigabytes of data.

    Its actually quite a bit of a problem that this new GDEM v2 is at 30m since that means that its size would be 9 times larger if it covered the same area but as you mention this dataset covers up to 83 latitude which in the WGS84 coordinate system means quite a bit more map space.

    Additionally I have heard from other people who have read the validation report that the real resolution is quite a bit less than 30 meters and that the choice of 30m pixels is based on the ASTER sensor not on the meaningful resolution for the dataset.

    All that said, that this dataset covers more than the widely used SRTM is important since the 60 latitude limitation on that excludes many northern areas of the world.

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