How can satellites measure the Earth’s surface temperature when higher layers of the atmosphere are hotter?

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How can satellites measure the Earth’s surface temperature when higher layers of the atmosphere are hotter?

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They measure infrared radiation, warmer things glow more.

Air is transparent to infrared, much like it is to visible light. Clouds block it only a little bit, and you can compensate for that if you know how thick are the clouds.

PS higher layers of atmosphere are colder. Sun does not warm the air (air is transparent to infrared), sun warms the ground, then ground warms the air. If you are high up, there is less ground to warm the air, and less air to insulate you from the eternal chill of space.

I’d compare it to watching a distant object through fog:

The fog will block some of the light coming from the object. It will also send some light your way, making it even harder for you to get a clear picture.
But depending on the opacity of the fog and your distance to the object, you can identify it perfectly fine. You automatically sort the information hitting your eye to be either relevant to your question (what’s that object?) or just some noise from the fog.

In a very similar way, the sattelite will see the infrared radiation (IR) from the ground slightly reduced, beause greenhouse gases absorb a part of it. It will also see some IR emitted from the higher layers of the atmosphere.
But both effects are predictable or pretty small (because of low air density especially at high altitudes), so they can be filtered out, leaving you with a signal that reflects actual ground temperature fairly well.