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 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 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

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Basic Examples(1)

Compute the geo grid unit area induced by the Mercator projection at the location of the Eiffel Tower:

A small square of side length 0.01 in projected coordinates has the following area:

Draw the square:

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:

Choose a spherical model of a specific radius:

UnitSystem(1)

Select the unit system used to return the distance scale:

They are the same value, but in different units:

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:

Possible Issues(1)

If a geo location cannot be projected, then the projected unit area cannot be computed for that location:

This location is not on the half-Earth covered by the "Orthographic" projection with a default center: