# Is global warming a linear process?

Is global warming linear in the sense that doubling the emission of Greenhouse gases will result in a doubling of global warming. Is there a threshold, i.e. is there are certain concentration of GHG where global warming is triggered and additional gases do not lead to a faster global warming?

• Definitely not linear. You should take a look at section 7.3 here: acmg.seas.harvard.edu/people/faculty/djj/book/bookchap7.html – farrenthorpe Feb 27 '18 at 3:56
• Your definition of linear is wrong. In linear system y = kx and you propose it to be y = x. – Communisty Feb 27 '18 at 8:45
• @Communisty No, I don't – Mark Feb 27 '18 at 8:49
• @Communisty Yes, that's perfectly fine :) – Mark Feb 27 '18 at 12:58
• If we held CO2 emissions constant then the CO2 concentration (and temperature) would continue to rise for a long time until an equilibrium is reached. Is it that equilibrium temperature you mean? I think we would run out of fossil fuels before that, though. – Keith McClary Feb 28 '18 at 0:55

No. Consider water vapor. Water vapor is a greenhouse gas. As the temperature increases, more water is evaporated. Since water vapor is a greenhouse gas, the temperature will increase. Clouds, however, form from water vapor, reflect sunlight.

The earth is not as linear as people would like.

• @BaroclinicCplusplus - Can you add a description in terms of the Math i.e. what is linear and non linear ? – gansub Feb 27 '18 at 2:58
• You've described a feedback loop, which is not really what the question is about. Perhaps you could try to answer the question in terms of a long-lived GHG? – farrenthorpe Feb 27 '18 at 3:55
• @gansub I interpreted OP as asking if $\bar{T}=f([GHG])$ (linear) or if $\bar{T}=f([GHG],T)$ (nonlinear)?. – BarocliniCplusplus Feb 27 '18 at 14:51
• @BarocliniCplusplus - That makes sense to us but I am not sure of OP's background. If you could add an English version of that mathematical relation maybe that would help – gansub Feb 27 '18 at 14:56
• @farrenthorpe The equations governing the evaporation, condensation and precipitation of water are nonlinear, therefore it answers OP's question. Even neglecting the feedback loop, or even GHGs altogether, the primitive equations are nonlinear, due to advection, But to address longer lived GHGs consider this loop- GHGs increase the temperature. In response, humans consume more electricity on air conditioning, which increases the $\ce{CO_2}$ concentration.... – BarocliniCplusplus Feb 27 '18 at 15:12

No, it is logarithmic. Each doubling of CO2 concentration will result in a constant increase in temperature which is called the equilibrium climate sensitivity, estimated to be 1.5C to 4.5C. Wikipedia.

• Climate sensitivity values are only valid within certain temperature/climate regimes. So, while response to CO2 is logarithmic and estimated at a certain value for our present temperature... that value changes if the temperature of Earth is much colder or hotter than it is now. – farrenthorpe Feb 27 '18 at 3:54
• @farrenthorpe As I understand it, the log behaviour is generally accepted to (approximately) hold over the range of CO2 concentrations from pre-industrial to burning all fossil fuels. If the ECS changes with temperature then, by definition, the function is not logarithmic. – Keith McClary Feb 27 '18 at 5:47
• The ECS is defined to be for the first doubling of CO2 from pre-industrial times by climate models and most probably does change with temperature. Related: skeptics.stackexchange.com/questions/40636/… – Communisty Feb 27 '18 at 8:59
• @Communisty You don't give a source for this. There are theoretical reasons that it should: "The logarithmic form comes from the fact that some particular lines are already saturated and that the increase in forcing depends on the ‘wings’ ". – Keith McClary Feb 27 '18 at 18:21
• The first sentence of AR5 10.8.2 is: 'The equilibrium climate sensitivity (ECS) is defined as the warming in response to a sustained doubling of carbon dioxide in the atmosphere relative to pre-industrial levels (see AR4).' – Communisty Feb 27 '18 at 20:17