It isn't one equation, as far as I know. I'm sure that it has been backed out of global warming potentials as well as modeling. Obviously a big part of the debate over climate change is that you can't just go run a controlled experiment and get the number. The nature of it makes us rely on models, and as a modeler, I know that the only person who trusts the results of a model is the guy who made the model.
I suppose it depends on what you mean by alarming when you mention PPM levels. If alarming means we worry about the end of life on earth, then I completely agree. The earth's temperature, as you point out, is set by a few factors. The amount of solar 'heat' that gets to the earth is a celestial function. The amount of that heat that doesn't escape back out is an atmospheric effect. Water's properties are such that it will exist in fairly high concentrations in air. And, with water being a greenhouse gas, it traps a lot of the heat from getting back out to space and warms us. If it weren't for our atmosphere, we would be a very, very cold planet.
The reason that PPM levels of CO2 or other gases can matter is because these gases do a very good job of trapping in heat and a while they will not rival the warming of water because of its concentration, then can still certainly trap some additional heat it. They won't warm us up as much as water has warmed us up from a cold rock, but they can still warm. That warming would allow for more water to enter into the air, further warming the earth. This doesn't turn into a spiraling catastrophe because more water will also lead to more clouds, and eventually you reach a new balance at a higher temperature (where the clouds - and likely other negative feedbacks - are reflecting back enough heat to prevent the earth from spiraling up in temperature).
I don't buy into ideas of destroying the earth by emitting CO2. Very few reasonable people (or those who have taken the time to learn a bit about it) do think that. The concern is about stresses on people, animals, and plants that could be considerable and could be difficult to bear. Some areas may benefit, no doubt. But there are many areas that would not. If the warming is real, we could potentially choose to do nothing about it and just 'pay' our way out of it. We might have to deal with more world conflict as there are fights for land (as people move into new areas away from low-lying coastal areas) and fight for fresh water supplies as the volume of snow melt decreases.
I've gone on beyond the initial questions you raised and I'm sure I've given you some quotes that you'll want to key in on and address....but I was feeling verbose I guess.
Well I'm no climate scientist either but here are a few factoids that matter;
Never mind the verbosity, I can handle that, I'm no :cray: as some here are.
First let me state a few items that are scientific facts and which get lost or misrepresented in the global warming aka climate change so-called 'debate.'
Clouds have a net cooling effect on Earth.
The amount of clouds are determined by solar/celestial activity.
The mean temperature on Earth is mostly determined by sloar/celestial interaction.
The amount of clouds has no relationship with CO2 levels. The amount of CO2 has less than 2% of any warming/cooling of Earth's atmosphere.
CO2 is NOT a polutant. CO2 occurs naturally, human activity is also natural and CO2 output from human activity is nothing to be alarmed about.
Reasonable assesments of CO2 levels will in no way threaten life on Earth, that idea is bizarre!!
Earth has been in a warming trend for approximately four hundred years, warming causes the oceans to release CO2 into the atmosphere, not a bad thing as plants benefit from the higher levels of CO2, increasing crop yields etc etc etc.
You speak of stress which might bring about human conflict, well so far the solutions to the CO2 mental problem do far more to bring about real conflict than not acting at all would have.
Case in point, the ethanol mandate which is absolutely insane any way one looks at it.
Using ethanol for fuel does absolutely zero to lessen CO2 emissions, on the contrary using ethanol as fuel increases CO2 emissions while on the other hand it makes available food for those areas where people are litterally starving to death, harder to get!!!! That's insane. Not one good thing has been brought about by the ethanol mandate.
Trying to regulate CO2 IS the problem and NOT the solution to any problem.
This is being attempted under blatently false pretenses.