Hypsographic Curve of Earth's Surface from ETOPO1
Overview.
NGDC has calculated a histogram (distribution of elevations) and hypsographic curve (cumulative elevations) of Earth's surface (Figure 1) using the ETOPO1 Ice Surface global relief model [Amante and Eakins, 2009]. ETOPO1 is a 1 arcminute digital representation of Earth's solid surface that integrates land topography and ocean bathymetry from numerous global and regional data sets.
The histogram reveals two primary elevation groupings: the continents, several hundred meters above sea level, and the oceanic abyssal plains, roughly 4,300 meters below sea level. This distribution indicates that the crust of the ocean floor is fundamentally different from the continents, which has been confirmed by countless research studies. The dramatic steepening of the hypsographic curve at mountains and oceanic trenches can only be maintained by a dynamic Earth. On geologic timescales, such features would quickly erode or fill in with sediments.

Figure 1: Global histogram and hypsographic curve of Earth's surface.

Coastal Hypsographic Curve.
Figure 2 shows an enlarged hypsographic curve spanning the coastal zone (100 to 100 m elevation). While ETOPO1 does not resolve meterlevel variations, the curve nevertheless reveals three distinct trends between 112 and 51 meters of elevation.

Figure 2: Coastal hypsographic curve.

Histogram Calculation.
The histogram was determined using Equation 1 to calculate the area of each cell, which were grouped by elevation and summed (Table 1). ETOPO1 elevation values are to the nearest meter, with an accuracy no better than ten meters. In deep ocean areas, depths are accurate to tens of meters at best. The hypsographic curves (Figs. 1 and 2) were smoothed to remove anomalies, and show the proportion of Earth's land and sea floor areas.
dA = a^{2} cos[ø (1e^{2})] dø dl / (1e^{2} sin^{2}ø)^{2} Equation 1
where:
Latitude (ø) = latitude of cell's center (in radians)
Unit of Latitude (dø) = 1 arcminute (0.0166667 degrees)
Unit of Longitude (dl) = 1 arcminute (0.0166667 degrees)
The WGS84 spheroid was used for values of Earth's radius and eccentricity:
Equatorial radius (a) = 6378.137 km
Eccentricity (e) = 0.08181919

How to Cite These Data:
Eakins, B.W. and G.F. Sharman. Hypsographic Curve of Earth's Surface from ETOPO1, NOAA National Geophysical Data Center, Boulder, CO, 2012
References:
Amante, C. and B. W. Eakins, ETOPO1 1 ArcMinute Global Relief Model: Procedures, Data Sources and Analysis. NOAA Technical Memorandum NESDIS NGDC24, 19 pp, March 2009. [http://www.ngdc.noaa.gov/mgg/global/relief/ETOPO1/docs/ETOPO1.pdf]
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