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by wickedwillie on April 16th, 2005

wickedwillie

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How far would the sea level have to drop for the Earth's surface to have more land than sea?

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  • by zeropointburn on April 21st, 2005

    zeropointburn

    Let's consider points on land to have a positive height, and points on the seafloor to have a negative height. Assuming we have accurate maps for both (and the number of points per unit area are the same), we can add up the height of every point, then divide by the number of points to get the average height. Since there is more ocean than land, this should be a negative number. This will also be approximately the required level drop to make land and ocean area equal.
    To obtain a more accurate answer, using the same data, one would use the previous average height as an arbitrary sea level, and repeat the process using the new values for each point's height. This will account for inaccuracies due to the difference in depth and area of continental shelves, midoceanic rifts, seamounts, etc.
    Incidentally, high-quality "bump" maps are available from the USGS website. It should be possible to compare these to depth soundings using the above methods. This will result in a realistic answer as accurate as the data's precision allows. That is, if one could get complete data for the whole surface of the earth...
    Similar methods are used to produce flood maps and hurricane surge maps, among other things.

    Resources:
    United States Geological Survey
    http://www.usgs.gov
    US geospatial one-stop site
    http://www.geodata.gov/gos

    Response (21/4/05):
    Granted, average height alone will not produce an accurate value for the required drop in sea level, as I mentioned. This value (first approximation) is used in the first iteration of an algorithm applied to the unified dataset which will provide sucessively more accurate values. The volume of either land or water is irrelevant. The 'depth below sea level' value is linear. More importantly, the surface area of earth's landmass is essentially infinite; it is a fractal function highly dependant on the resolution of measurement. For instance, if you were to measure the shoreline of an island using a meter stick and a 12" ruler, the figure derived using the 12" ruler will be larger. Which one is accurate?
    For this discussion, the length of the stick is the point resolution of the dataset. We are dealing with area (not surface area), which is a 2D approximation of 3D reality. The current figure for land/water ratio is based on this simplification, so there should be no problem answering the question with similar simplification.
    The reason for finding the sum of heights is to see which way the value needs to go. The first approximation will not be very accurate. Using the first value, every point on the map has its height recalculated. A new average value is derived from the new heights, and each point is modified to reflect it, then checked. If the sum of heights ever equals zero, you've found the answer which is as precise as the data allows.
    Perhaps there is a one-step method for finding this value, but I don't know what it is offhand. As it is, this answer is far more complex than the question demanded, and still offers no actual value. (mainly because the data is simply unavailable for global, high-resolution altitude/depth maps) Still, the question implies a linear value, and a simplified definition of 'area' to mean the percentage of the surface of a sphere representing the Earth. The critical point occurs when land area and sea area are equal, and the above method is the only one which takes into account both the irregularities of the seafloor and the minimization of inherent accuracy restrictions.

    Furthermore, were the question regarding displacement of a volume of water, then the same set of data will reveal the volume of water present for each step in height, to the limits of the data's accuracy. The question conceivably could be construed to mean, "At what level will the volume of water in the oceans equal the volume of land above that level?", in which case a slightly different manipulation of the same dataset will provide an answer to the best accuracy available. Questions regarding surface areas, land or sea, are murky at best unless they include the desired resolution of measurement. Even then, the whole concept of the surface area of a complex, three-dimensional body subject to tidal strains, erosion, and chemical alteration is so obscure as to be practically undefinable, let alone measureable.

    Comments

    • average height can't be used to calculate the difference in sea level needed to get more land than water (volume vs. surface)

      Lucas_

      by Lucas_ on April 21st, 2005

    • You're wrong about the landmass area being infinite .. the boundary is essentially infinite but the area is finite.

      Quirkie

      by Quirkie on October 24th, 2005

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