27

This summarizes my understanding of some of the basic ideas. Because it is hard to find all of them clearly described and summarized in one place, I could be wrong or misleading about some of them: comments and corrections are welcome. "Geoids" are approximations to a surface of gravitational equipotential. The geoid is a hypothetical Earth surface ...


20

The elevation above the ellipsoid (ellipsoidal height) is the elevation above a mathematical model that approximates the shape of the earth. The current most common one is WGS84. These are the elevations that you'd get from a GPS. Orthometric heights are measured above the geoid or equipotential surface, that is, the surface of equal gravity. MSL is "mean ...


17

Ian's answer is incorrect. WGS84 approximates Earth by an elipsoid, which is basically a deformed sphere. EGM96 is a more complex model based on the gravitational force of the Earth (which is not constant) that defines what "sea level" or "up/down" mean, a smooth but irregular shape called "geoid". WGS84 is the elipsoid that best fits that geoid, and this ...


15

No, a datum and ellipsoid are not equivalent. For a loose definition, think of the ellipsoid as defining size and shape. The datum then fixes that ellipsoid to the earth. NAD83 (various realizations) and WGS (another set of realizations) use almost the same ellipsoid GRS80/WGS84, and were originally designed in the 1980s to be equivalent. Since then, NAD83 ...


10

I am not a Geodesy expert, but far as I understand it, the geoid, is the shape that the surface of the oceans would take under the influence of gravity alone. It is the surface at which the intensity of gravity is the same. The Problem isn't that it is difficult to describe mathematically, but it might be impossible to predict correctly and accurately. ...


8

Mean Highest High Water is a reference surface corresponding to the height of high tides, averaged over a certain period of time (usually 19 years, a value close to a Metonic Cycle and a Lunar Node cycle). Data from tidal gauges, satellites, etc. are usually processed and stored in grid files, which contain the difference in elevation between different ...


7

The heights on google earth refer to EGM96 and are, therefore, Geoidal heights. The lat/long are referred to the WGS 84 ellipsoid.


7

Convert from (EGM96) geoid vertical datum to (WGS84) ellipsoid vertical datum: gdalwarp -s_srs "+proj=longlat +datum=WGS84 +no_defs +geoidgrids=egm96_15.gtx" -t_srs "+proj=longlat +datum=WGS84 +no_def" dem_in_egm96_geoid.tif dem_in_wgs84_ellipsoid.tif You will need the gtx file containing vertical datum shifts from here: http://download....


7

Following on Ian Turton's comment... Prior to performing ANY geometry calculations or analysis on a layer(s), the layer(s) MUST be 1) projected to the desired CRS, and 2) that CRS must be the same for all layers. (Sidenote #1: in QGIS, projecting a layer to a different CRS is typically accomplished using Save As...) Your analysis will always fail if the ...


5

An ellispoid is a mathematical model of the earth that approximates its three dimensional shape. See this definition. Elevation on top of the ellipsoid is 0, but since it's just an approximation one can be above or below the ellipsoid at any given point. "Elevation above the surface of the ellipsoid" is the distance between the measurement and the 0 value of ...


5

Esri first proposed the WKT format for OGC around (estimating) 1998 using what we'd already developed in-house. The SPHEROID format has to support both ellipsoids and spheres. It is easier to allow the second numerical value to be a numerical value rather than have it sometimes be a string (yes, I know it's always a string when parsing it) and sometimes a ...


5

I have done this before using forward azimuths, here is a link that has descriptions and algorithms that may be helpful: Inverse/Forward Utilities A forward azimuth calculates a new point that is a specified distance and compass bearing from a starting point. The basic idea is that you have a point in Lat/Lon and you calculate a series of forward azimuths ...


5

With these sorts of questions, the issue isn't so much with the earth or the reference system, but with the definition of "real." Angular coordinates only make sense in an axiomatic framework, with reference to an origin and an axis. There are no straight lines or points in nature, of course. These are things that are only defined in the mind. In the case ...


4

This answer isn't a single command, but I'll put it in to get the ball rolling. Use gdalwarp to resample the geoid grid, then gdal_calc.py to shift the original raster. gdalwarp -s_srs epsg:4326 -t_srs epsg:26910 -r cubic -tr 10 10 -tap HT2_0.gtx HT2_0_resampled.tif gdal_calc.py -A original.tif -B HT2_0_resampled.tif --calc="A+B" --outfile=shifted.tif If ...


4

Summary The short answer is that you take a weighted average of the coordinates to combine independent unbiased measurements of a given location. The weights are proportional to a particular quantitative expression of the precision of each measurement. The weights further determine confidence intervals for the coordinates. Those intervals can themselves ...


3

The term horizontal datum is used because it is more easily flattened into 2 dimensions and more useful for finding locations on a flat plane (compared to a vertical datum). As in the ESRI post you referenced (image below), the Earth's surface is very uneven, so modeling this very difficult. The "ellipsoid" used in horizontal datums is close approximation ...


3

The answer is ~10001.966km (see Wolfram and sigurdhu) The fixed JavaScript Implementation gives me 10001.959km. Close enough. JavaScript was introducing errors at a precision bigger than 16 digits at Math.pow(0.5, digits)


3

GeographicLib includes classes to compute the geoid height via interpolation on a grid of values (the Geoid class) and via summing the spherical harmonic sum (the GravityModel class). The interpolation method is pretty straightforward; see the associated documentation, Geoid height. I agree that the NGA programs for computing the geoid height via spherical ...


3

PDAL can do this with its filters.reprojection capability, which is based on the vertical datum transformation capabilities of Proj.4. pdal translate input.las output.las reprojection --filters.reprojection.in_srs="EPSG:4326+4326" --filters.reprojection.out_srs="EPSG:4326+3855" Make sure that egm08_25.gtx, defined in GDAL_DATA's vertcs.csv file ...


3

I recommend you to read this article. An extract: Height can be measured in two ways. The GPS uses height (h) above the reference ellipsoid that approximates the earth's surface. The traditional, orthometric height (H) is the height above an imaginary surface called the geoid, which is determined by the earth's gravity and approximated by MSL. ...


3

The mathematical solution belongs rather to https://math.stackexchange.com/ but a simple image is challenging your intuition. Look at the ellipsoid and lines at angles of 0, 45, and 90 degrees. What you say would mean that the red segment is as long as the olive green one but obviously it isn't.


3

If I´m not mistaken, you will need to provide a transformation context and set the layers source CRS to the QgsDistanceArea() object accordingly. Try: ... def calculate_area(in_lyr_name, ellipsoid, units): input_layer = QgsProject.instance().mapLayersByName(input_lyr_name)[0] lyr_crs = input_layer.crs() elps_crs = QgsCoordinateReferenceSystem()...


3

The Cartesian area is dependant on the layer's CRS. It's a "raw" value, testing the coordinates as 2d numbers only. So for geographic coordinates systems with coordinates as degree values, it's impossible to convert these to a planar meters/hectares/etc value.


2

The python code for EllipseCircumference given on wikipedia is right. Your translation into Javascript, however, is wrong. The python statement x, y = 0.5 * (x + y), math.sqrt(x * y) does the assignments in parallel and so it is not equivalent to x = 0.5 * (x + y); y = math.sqrt(x * y) but to t = x; x = 0.5 * (t + y); y = math.sqrt(t * y) Make this ...


2

Yes, you must use an ellipsoid (or other mathematical surfaces). the reason is that the Geoid is a Physical surface (defined as the equipotential surface of gravity strength field). Simple meaning - it has no mathematical formula (another simple meaning - it is a surface at the height of the mean sea level that if you put a drop of water on it it wont move)....


2

The answer depends on what you are interested in and therefore what you mean by 'earth's surface'. The Geoid is the equipotential surface (in terms of gravitational potential). The ellipsoid is a geometric approximation of the irregular land-sea (physical) surface. Given the irregularities even in the physical surface, no ellipsoid can ever do a perfect job. ...


2

An "ellipsoid" is a mathematical approximation of the shape of the Earth. Many different ellipsoids exist, but the two most widely used today are the GRS80 and the WGS84, which attempt to provide a best-fit across the globe. Heights were traditionally referenced to MSL, but with satellite and other technologies, we can often do better in terms of accuracy. ...


2

You need to define exactly what you mean by "move due east"! If you follow a rhumb line (aka a loxodrome) you will always be travelling east be following a parallel of latitude not be going in a straight line (ie, not the shortest path) stay at the same latitude If you follow a great circle (aka a geodesic or orthodrome), one that is initially heading ...


2

You have to create your own custom CRS using the correct ellipsoid. DHDN projections use +ellps=bessel +towgs84=598.1,73.7,418.2,0.202,0.045,-2.455,6.7. ETRS89 projections use +ellps=GRS80 +towgs84=0,0,0,0,0,0,0. The full proj string for EPSG:31467 is: +proj=tmerc +lat_0=0 +lon_0=9 +k=1 +x_0=3500000 +y_0=0 +ellps=bessel +towgs84=598.1,73.7,418.2,0.202,0....


2

If two ellipsoids share the same origin and axes (both use Greenwich and the same North pole), but have different axes lengths, only the geodetic latitude will change between the two. This is true because geodetic latitude is defined as a line perpendicular to the ellipsoid surface. However, you shouldn't normally think in terms of the ellipsoids, but of ...


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