Most widely used projections

[Milo]

In the case of a temperature map, you might also want to know the rate of change of temperature with respect to latitude, which would be easier to visualize using a projection with equally spaced parallels than using an equal-area projection (except the sinusoidal, but then you might have other reasons for not using that). With a good compromise projection, areal distortion should still be low enough to tell that the Earth is mostly warm with some cold spots, although it could admittedly cause you to overestimate the size of those cold spots.

Incidentally, it occurred to me that insolation actually scales with the cosine of latitude (at least when axial tilt can be ignored, such as at an equinox), so it's actually the polar orthographic projection in which temperature would be expected to fall off linearly with distance-between-parallels-on-screen. Not quite the cylindrical equal-area projection (which scales with the sine instead of the cosine of latitude).

(As an aside, you've already seen it, but one of my posts on this subject got split into another thread.)

[PeteD]

Incidentally, it occurred to me that insolation actually scales with the cosine of latitude (at least when axial tilt can be ignored, such as at an equinox), so it's actually the polar orthographic projection in which temperature would be expected to fall off linearly with distance-between-parallels-on-screen.

Yes, this was actually how I got the idea for my open book novelty projection, when I realized that a projection where insolation varies linearly with the y coordinate in equatorial aspect wouldn't be useful for anything.

In any case, if you want to visualize the rate of change of temperature with respect to latitude, it's better for latitude rather than temperature to vary linearly with the y coordinate.

[Milo]

In any case, if you want to visualize the rate of change of temperature with respect to latitude, it's better for latitude rather than temperature to vary linearly with the y coordinate.

I suppose so. Having linear (idealized) temperature would be more useful when mapping something else that depends on temperature.

[PeteD]

Yes, this was actually how I got the idea for my open book novelty projection, when I realized that a projection where insolation varies linearly with the y coordinate in equatorial aspect wouldn't be useful for anything.

In case the link between a projection where insolation varies linearly with the y coordinate and my open book projection isn't obvious to everyone, this is what a cylindrical projection where insolation varies linearly with the y coordinate looks like:

linear insolation 1.png (80.88 KiB) Viewed 12837 times

In other words, like the equatorial regions have been lost in the fold of a book.

Of course, it doesn't have to be cylindrical. Here's a version with elliptical meridians:

linear insolation 2.png (152.31 KiB) Viewed 12837 times

[PeteD]

Having linear (idealized) temperature would be more useful when mapping something else that depends on temperature.

Yes, but if you want to show that something depends on temperature, it would be more intuitive in my opinion to show two maps side-by-side, one showing temperature and the other showing the thing that depends on temperature.

Either that or ditch the map completely and just plot a graph of the thing versus temperature.