From logy
Jump to navigation Jump to search

Earth2014 provides five different layers of height data, comprising Earth’s surface (lower interface of the atmosphere), topography and bathymetry of the oceans and major lakes, topography, bathymetry and bedrock, ice-sheet thicknesses and rock-equivalent topography. The Earth2014 global grids are provided as heights relative to the mean sea level

The Earth2014 global topography and relief model provides layered topography grids at 1 arc-minute resolution. Other than SRTM30plus, Earth2014 provides information on ice-sheet heights and bedrock (that is, topography below the ice) over Antarctica and Greenland

SRTM30_PLUS v9 (Becker et al. 2009) bathymetry over the oceans and major inland lakes, and over land in high northern latitudes (except for Greenland)... The RET-layer (also denoted RET2014) models ice, water and rock masses based on a uniform mass-density of 2670 kg/m3... a constant value of 6,371,000 m has been subtracted from all shape models... land types as follows: 0 - land topography above mean sea level (MSL), 1 - land topography below MSL, 2 - ocean bathymetry, 3 - inland lake, bedrock above MSL, 4 - inland lake, bedrock below MSL, 5 - ice cover, bedrock above MSL, 6 - ice cover, bedrock below MSL, 7 - ice shelf, 8 - ice covered lake (Vostok)... For use of Earth2014 in #spectral modelling, sets of fully-normalized (4pi) SHCs complete to degree and order 10,800 were derived from the 1 arc-min grids... SHCs are stored in Curtin University's binary SHC (bshc)-format in "double precision". The bshc-format holds the data as follows: n_min n_max C-coefficients ascending in degree, followed by the order, S-coefficients ascending in degree, followed by the order


Producing a precise model of the geoid has proven to be a challenge. Until recently, there was no single source for producing a geoid map. Data from several dozen satellites, along with surface measurements over land and from ships at sea, had to be combined to produce a model of the gravitational field... GRACE provides, for the first time, global coverage of the Earth’s gravity field every 30 days from a single source. GRACE is already able to measure the gravity field with a level of precision that is at least 100 times greater than any existing measurement

geoid undulations[edit]

Calculating the undulation factor is mathematically challenging. This is why many handheld GPS receivers have built-in undulation lookup tables to determine the height above sea level.

Geoid undulations N were obtained from the EGM96 geopotential model (Lemoine et al. 1998)... We note that the choice of the geoid model is not too much a concern for global relief modelling, given the differences between present geoid models are mostly at or less the 1m‐level

geoid undulations in units of gravity[edit]

geoid undulations, using units of gravity Geoids_sm.jpg Spherical harmonics are often used to approximate the shape of the geoid. The current best such set of spherical harmonic coefficients is EGM96... equation describes the Earth's gravitational potential V, not the geoid itself







there are places where #MASK points on land topography below MSL but #SUR is greater than 0


Map may be built with help of the Earth2014Correction.cs script

#1 arc-min is more correct

shape model[edit]

While the previously described relief models provide elevations of the topography or bedrock with respect to the mean sea level, shape models represent the geometry of the planet via the planetary radius (i.e., distances Rp between the geocenter and the surface points). As such, relief and shape models differ by the sum of (a) the ellipsoidal radius, and (b) the geoid height, with the latter being an approximation of the separation between the mean sea level and the ellipsoid surface. Following this definition, radii Rp of the Earth2014 shape models were constructed as sum of ellipsoidal radii Re, geoid undulations N and relief heights Hp... Rp = Re + N + Hp... Geoid undulations N were obtained from the EGM96 geopotential model (Lemoine et al. 1998)... We note that the choice of the geoid model is not too much a concern for global relief modelling, given the differences between present geoid models are mostly at or less the 1m‐level... Earth2014 is formally independent from ETOPO1... Given that ETOPO1 is based on a 2008 measured/estimated 2 arc‐min bathymetry grid by Scripps Institution of Oceanography... RET represents ice and water masses as mass‐equivalent layers of rock, based on the mass compression procedure

shape models represent the geometry of the planet via the planetary radius... These were obtained as sum of ellipsoidal radii of the the GRS80 ellipsoid, EGM96 geoid undulations, and the elevations

ellipsoidal radii EllipsFormula.png

geoid undulations in HEALPix resolution k=10 (12,6 millions of cells) are limited from -108.1 m to +85 m Earth2014 1min lines2048.jpg


5 arc min Earth shapes in HEALPix projection are visually distorted Earth2014 5 shapeError.jpg,

but in native Latitude-Longitude are visually normal Earth2014 5.jpg.

If to look on 1 arc min shapes then situation is opposite

- picture is visually correct in HEALPix projection Earth2014 1.jpg

but in native Latitude-Longitude is distorted Earth2014 1 shapeError.jpg.


5 arc-min[edit]

1 arc-min[edit]

spectral modelling[edit]

Earth2014 sphere H.png with the fully normalized SHCs Tnm of degree n and order m (m<0: sine associated; m≥0: cosine associated), the elevation H of the topography model can be retrieved at any point on Earth, given by geocentric latitude  and longitude  . Ynm denote the spherical harmonic functions that evaluate the associated Legendre functions (ALFs) depending on the co‐latitude, and sine / cosine arguments depending on longitude... If full topographic information is sought, the data grids should be used instead of the spherical harmonic representations.

The spherical harmonic coefficients (SHCs) are stored in binary format as double and big endian. The file structure is: n_min n_max (minimum and maximum harmonic degree) C-coefficients ascending in degree, followed by the order S-coefficients ascending in degree, followed by the order Example for a degree-10800 file: 0 10800 C(0,0), C(1,0), C(1,1), C(2,0), C(2,1), ... C(10800,10799), C(10800,10800), S(0,0), S(1,0), S(1,1), S(2,0), S(2,1), ... S(10800,10799), S(10800,10800)... into a matrix with triangle form

gravitational potential[edit]

Potential models for each layer (crust, ocean, ice,lakes) and for their combined effect (=Earth) are available explicitly as a series of spherical harmonic coefficients of the spherical topographic potential (STP) and the ellipsoidal topographic potential (ETP), relying on spherical and ellipsoidal approximation, respectively.... Due to the ellipsoidal-appoximation (ETP) in the spherical harmonic model, the model may not be truncated at degrees below the maximum degree nmax without suffering of severe errors at high latitutes. Therefore it is recommended to use the models only up to their maximum degree.