GeoGridUnitArea
GeoGridUnitArea[proj,loc]
gives the actual geo area corresponding to a unit area on the geo grid obtained with projection proj, evaluated in the limit of small geo regions around location loc.
Details and Options
- GeoGridUnitArea describes the local distortion of area induced by a geo projection around a given location.
- GeoGridUnitArea combines the global nominal scale (the shrinking factor of the geo model to the reference model of the map, traditionally denoted as 1:125000 and similar) and the local distortion of area induced by the geo projection.
- The result of GeoGridUnitArea[…] corresponds to a ratio of Quantity geo areas on the geo model (of Earth or any other body) and dimensionless areas of the projected geo grid.
- A geo projection can be given as a named projection "proj" with default parameters or as {"proj",params}, where "proj" is any of the entities of GeoProjectionData and params are parameter rules like "StandardParallels"->{33,60}. GeoProjectionData["proj"] gives the default values of the parameters for the projection "proj".
- The location loc can be given as a coordinate pair {lat,lon} in degrees, a geo position object like GeoPosition[…] or GeoGridPosition[…] or as a geo entity Entity[…].
- GeoGridUnitArea threads over its location and direction arguments.
- Possible options of GeoGridUnitArea include:
-
GeoModel Automatic model of Earth or a celestial body UnitSystem $UnitSystem unit system to use in the result
Examples
open allclose allBasic Examples (1)
Scope (5)
Compute the geo grid unit area at your geo location for the "VanDerGrinten" projection:
These are the default values of the parameters of the "VanDerGrinten" projection:
Specify other values for the parameters of the projection:
Specify a location using a pair {lat,lon} in degrees:
Use locations with geo position heads:
Specify a location using a geo Entity object:
Compute the geo grid unit area for a list of locations:
Convert the QuantityArray output into its normal form:
GeoGridUnitArea can efficiently process values for large numbers of locations:
Options (2)
GeoModel (1)
By default, GeoGridUnitArea returns values for Earth:
Performing the same computation on the corresponding point of the Moon returns smaller scales:
Applications (3)
For a cylindrical projection, the projected unit area only depends on latitude:
Use GeoGridUnitArea to approximate the geo area of a small region using the projected area in a map:
Project with the Albers projection and compute the flat map area:
Multiply the result with the geo grid unit area at some central location of the region:
Compare with the correct value of the geo area:
Compute the geo area of a region defined on the projected map:
Compare with a computation based on a polygonal approximation of the disk:
Properties & Relations (3)
Take a location and a projection:
Construct a family of projected squares of decreasing size, converging to that location:
Compute the ratios of an unprojected area over a projected area for those squares:
The values converge to the value given by GeoGridUnitArea for that projection at that location:
The projected unit area varies with the square of the geo model size:
The projected unit area varies with the inverse square of the reference model or the central scale factor:
Equal-area projections have constant geo grid unit area over the globe:
For a random set of locations across the world, check that ranges of projected unit area have zero width:
Text
Wolfram Research (2019), GeoGridUnitArea, Wolfram Language function, https://reference.wolfram.com/language/ref/GeoGridUnitArea.html.
CMS
Wolfram Language. 2019. "GeoGridUnitArea." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeoGridUnitArea.html.
APA
Wolfram Language. (2019). GeoGridUnitArea. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeoGridUnitArea.html