How do coordinate reference systems and projections relate to each other?

Question

I would like to resolve some general confusion of mine concerning the terms (and concepts) of "coordinate reference system" and "projection". The way I initially understood these terms is that a CRS defines a set of properties, such as the spherical model used to approximate the shape of the earth and a datum that defines some fix point to which geographic latitudes and longitudes can relate to. A projection then is a mathematical function that is able to map these geographic 3D coordinates to a 2D plane. But after reading more about the topic my understanding gets more and more blurry.

Let's take for example the most common code EPSG 4326. My understanding was that this would be the part that defines the spherical model etc. in order to define lat/lon data points. This data could then be run through a projection such as a "Albers Equal Area" projection which would result in points on a 2D plane. So far I think my idea holds up to the test.

My understanding began to crumble when I started to work more with QGIS and looked more into EPSG codes. When I for example open a shapefile that was defined in EPSG 4326 in QGIS, it automatically displays the data on the 2D computerscreen without having to additionally specify how the data should be projected. Does QGIS just pick a default projection or does that mean that in EPSG 4326 there's a 2D projection defined as well? Similarly, when working with visualisation libraries such as D3, GeoPandas or Cartopy often times one only has to define a projection such as 'albersUsa' in order to draw a 2d map. Does this mean that these tools just assume as a default that the data was recorded using EPSG 4326 and we can then project them on a 2D plane using some other EPSG code that defines a projected coordinate system?

So to summarise my confusion and question: How do the terms "projected coordinate system", "geographic/geodetic coordinate system" and "coordinate reference system" relate and what of them is defined in an epsg code? Are they sometimes manually combined (EPSG 4326 + alberUsa projection) in order to create a 2D projected map and sometimes already combined within one single EPSG code such as for example EPSG 102008 (North America Albers Equal Area Conic)?

Answer 1

Does qgis just pick a default projection or does that mean that in epsg 4326 there's a 2d projection defined as well?

QGIS doesn't project the geographic coordinates to the map canvas. If the map has defined a geographic coordinate reference system, it gives to the X axis the angular coordinates of the Longitude axis, and to the Y axis the angular coordinates of the Latitude axis.

That process is not a projection and the map canvas with geographical units must not be confused with an equidistant cylindrical projection. Note than in an equidistant cylindrical projection of an ellipsoid, parallels are not equally spaced. Also its units are not angular.

The conversion method used is named Pseudo Plate Carrée and is coded EPSG:9825. Its formula is X = Longitude; Y = Latitude. It is not included in the geographic CRS, which can't have a conversion method associated itself.

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Does this mean that these [d3, geopandas or cartopy] tools just assume as a default that the data was recorded using epsg 4326 and we can then project them on a 2d plane using some other epsg code that defines a projected coordinate system?

I don't know those tools and my answer will no cover that question.

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How do the terms "projected coordinate system", "geographic/geodetic coordinate system" and "coordinate reference system" relate and what of them is defined in an epsg code?

A coordinate reference system may be a geodetic, a geographic or a projected one (there are also more types of CRS).

A projected CRS must be based on a geodetic or a geographic one. It is a special case of derived CRS, which have a special conversion method associated: a projection.

All geodetic and geographic CRSes must have a geodetic datum associated. The datum must contain the definition of the ellipsoid (a sphere is also an ellipsoid) and the prime meridian.

All of them, that are registered in the EPSG registry, have an EPSG code.

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Are they sometimes manually combined (epsg 4326 + alberUsa projection) in order to create a 2d projected map and sometimes already combined within one single epsg code such as for example epsg 102008 (North America Albers Equal Area Conic)?

North_America_Albers_Equal_Area_Conic CRS is not registered in the EPSG registry and its code is not EPSG:102008, but ESRI:102008.

It is a projected CRS and yes, may be registered and defined with an EPSG code.

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The last version of Coordinates Reference Systems standard is ISO 19111:2019.