# [Proj] Pixel area errors

Micah Cochran mcochran at athensal.us
Mon Nov 20 14:28:19 EST 2017

```Hello Ken,

Just for completeness a projection is a flat representation of earth.  The
earth is usually represented as an oblate spheroid.  Any projection has
some level of approximation between distance, area, direction, and form
(does the landmass look like what it should look like).  Some projections
are good used for surveying application, others are better for representing
a really large area.

http://axismaps.github.io/thematic-cartography/articles/projections.html

If you limit the scope of area, you can very accurate measurements.

It depends upon what projection that you are using to what kinds of errors
you will get.  Mercator projection is very accurate at the 0 deg latitude.
Transverse Mercator project is very accurate at along a line of longitude.

Errors can be both latitude and longitude, depending on the projection.
For example, a polar projection will have distortion anywhere but the
center (the pole).

Tissot's indicatrix is used as a graphic illustration of a projection's
distortion.
https://en.wikipedia.org/wiki/Tissot%27s_indicatrix

You can calculate a grid distance, which can be very close or not close at
all based on the projection.    Geodetic/geodesic distance algorithms from
the GeographicLib::Geodesic libary (included with PROJ.4) has very accurate
distance calculations.
http://proj4.org/geodesic.html

I'm not to sure about keeping track of the errors of a particular
projection or how to exactly answer your specific questions.  I hope that
gives you some pointers.

In a slightly different tangent about using US Customary units for area and
exactitude, I was looking at the difference between calculating acres using
international feet (0.3048 m) and US Survey feet (0.3048006 m).  The size
of this City is about 1000 sq km.  When converting to acres (area) using
the two different feet as the basis of acres, I got a difference of 100
acres (40 hectares or 0.4 sq km) between the asnwers.  US Customary units
make me crazy.

Micah Cochran

On Mon, Nov 20, 2017 at 11:13 AM, Ken Mankoff <mankoff at gmail.com> wrote:

> Dear List,
>
> I've just learned that GRASS has a function to provide the true scale for
> a given cell. From this, I can determine the map projection error.
>
> My understanding is that for a given projection, the "lat_ts" term of the
> proj4 string describing the projection is where 1 m in GRASS is actually 1
> m. Elsewhere, errors grow. I'd like to track these.
>
> I asked the following on the GRASS list and was advised that this list
> might be a better place to ask:
>
> Is the scale error only in longitude and never in latitude? Or can it be
> in both? Is there a way to find the error for a length error rather than an
> area error? Specifically, for a vector line with an arbitrary heading?
>
> Thank you,
>
>   -k.
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