usage - What's the difference between [上]{あ}がる and [上]{のぼ}る?

The textbook I'm studying from lists [上]{あ}がる as "to go up", but I've previously learnt that [上]{のぼ}る also means "to go up".

Jisho.org only lists "to go up" and any derivations of that as a single definition out of its 23 definitions for 上がる. I'm currently only wondering about when it means "to go up", but explaining the other definitions would be good too.

Also, what are the differences between 上がる and the other kanji, 挙がる and 揚がる? From my Chinese background, the other two seems to mean about the same, "to raise up something", but I want to confirm this for Japanese too. Jisho.org doesn't help much here either since it lists the same 23 definitions for all three, and doesn't provide any examples for the latter two.

Answer

のぼる means "to climb" and あがる means "to rise".

I find it an interesting observation that both are used when describing a weather event:

太陽が[昇]{のぼ}る

The sun rises.

雨が上がる
The rain stops.

As Jesse Good explains in his answer, のぼる and あがる are different in that the former means that something/someone is climbing by his own strength, whereas the latter means that something simply rises with no own input.

The above examples are interesting in the sense that お日様/太陽 is often assigned a personality in Japanese and therefore can climb out of its own accord. The rain is usually not personified and thus just "rises", as a natural phenomenon.

Here のぼる was written 昇る, which is usually only used for the "climbing" sun. Other 漢字 are 登る for "hiking" and 上る for climbing stairs or "climbing" numbers (e.g. 2倍に上る "to double").