<p>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.</p>

<p>The earth is not as linear as people would like.</p>

CC BY-SA 3.0
2018-02-27T03:55:47.270Z
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?
f.thorpe
CC BY-SA 3.0
2018-02-27T14:51:43.020Z
@gansub I interpreted OP as asking if $\bar{T}=f([GHG])$ (linear) or if $\bar{T}=f([GHG],T) $ (nonlinear)?.
BarocliniCplusplus
CC BY-SA 3.0
2018-02-27T15:12:09.300Z
@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
CC BY-SA 3.0
2018-02-26T18:49:52.483Z
2018-02-26T18:49:52.483Z
BarocliniCplusplus
<p>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. <a href="https://en.wikipedia.org/wiki/Climate_sensitivity#Equilibrium_and_transient_climate_sensitivity" rel="nofollow noreferrer">Wikipedia</a>.</p>

CC BY-SA 3.0
2018-02-27T03:54:36.613Z
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.
f.thorpe
CC BY-SA 3.0
2018-02-27T05:47:42.097Z
@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
CC BY-SA 3.0
2018-02-27T08:59:43.337Z
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: https://skeptics.stackexchange.com/questions/40636/does-each-doubling-of-co2-cause-a-2-4c-increase/40653#40653
Communisty
CC BY-SA 3.0
2018-02-27T18:21:25.730Z
@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’ "](http://www.realclimate.org/index.php/archives/2007/08/the-co2-problem-in-6-easy-steps/).
Keith McClary
CC BY-SA 3.0
2018-02-27T20:17:05.210Z
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
CC BY-SA 3.0
2018-02-28T00:28:49.180Z
@Communisty Some sources say "for each doubling" or "per doubling". The termionology seems to vary.
Keith McClary
CC BY-SA 3.0
2018-02-28T08:16:24.610Z
If there are any notable sources (like the IPCC assessment reports), could you link them? I believe that the definition of ECS is precisely for the first doubling of CO2 because climate has different feedbacks that vary depending on the absolute amount of warming.
Communisty
CC BY-SA 3.0
2018-02-28T18:27:13.220Z
@Communisty I found: ["In IPCC reports, equilibrium climate sensitivity (units: °C) refers to the equilibrium (steady state) change in the annual global mean surface temperature following a doubling of the atmospheric equivalent carbon dioxide (CO2 ) concentration."](https://www.ipcc.ch/pdf/assessment-report/ar5/syr/AR5_SYR_FINAL_Glossary.pdf#page=5) They don't specifically say "pre-industrial". Seems to suggest a slightly different meaning in the context of modelling. Googling for  [ECS "per doubling"] and [ECS "each doubling"] turns up quite a few hits, it depends which you consider notable.
Keith McClary
CC BY-SA 3.0
2018-02-27T03:21:02.983Z
2018-02-27T03:21:02.983Z
Keith McClary
<p>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? </p>

CC BY-SA 3.0
2018-02-27T03:56:05.477Z
Definitely not linear.  You should take a look at section 7.3 here: http://acmg.seas.harvard.edu/people/faculty/djj/book/bookchap7.html
f.thorpe
CC BY-SA 3.0
2018-02-27T08:45:59.223Z
Your definition of linear is wrong. In linear system y = kx and you propose it to be y = x.
Communisty
CC BY-SA 3.0
2018-02-27T08:49:07.783Z
@Communisty No, I don't
Mark
CC BY-SA 3.0
2018-02-27T09:03:39.907Z
Well if doubling emissions leads to tripling warming, the system is still linear. At least you seem to imply a linear relationship with a factor of 1.
Communisty
CC BY-SA 3.0
2018-02-27T12:35:54.720Z
@Communisty That's not true. If you have y = kx and you double x you still get double y, no matter what the value of k is.
bon
CC BY-SA 3.0
2018-02-27T12:54:08.387Z
Um, I'll just crawl under a rock if thats ok with you.
Communisty
CC BY-SA 3.0
2018-02-27T12:58:36.350Z
@Communisty Yes, that's perfectly fine :)
Mark
CC BY-SA 3.0
2018-02-27T18:00:21.563Z
By "doubling the emission" do you mean the rate of emission or the cumulative amount in the atmosphere? Also, I assumed you were referring to the persistent GHGs (predominantly CO2) - is that correct?
Keith McClary
CC BY-SA 3.0
2018-02-27T19:38:55.623Z
@Keith McClary I mean doubling the amount of GHG emission from mankind e.g. in a year: will that rise the the global temperature x2 in comparison to the "normal"  emission
Mark
CC BY-SA 3.0
2018-02-28T00:55:34.597Z
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
CC BY-SA 3.0
2018-02-28T19:02:38.427Z
My other question was, are you asking about persistent GHGs (predominantly CO2) that accumulate in the atmosphere over decades, or water vapor, which is not cumulative, but fluctuates in the short term depending on temperature?
Keith McClary
<climate-change>
Is global warming a linear process?
Mark
# Is global warming a linear process?

(Asked by: username_0 on 2018-02-26)

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?

**Tags:** climate-change

> **Comments:**
> **username_1**: Definitely not linear.  You should take a look at section 7.3 here: http://acmg.seas.harvard.edu/people/faculty/djj/book/bookchap7.html  
> **username_2**: Your definition of linear is wrong. In linear system y = kx and you propose it to be y = x.  
> **username_0**: @username_2 No, I don't  
> **username_2**: Well if doubling emissions leads to tripling warming, the system is still linear. At least you seem to imply a linear relationship with a factor of 1.  
> **username_3**: @username_2 That's not true. If you have y = kx and you double x you still get double y, no matter what the value of k is.  
> **username_2**: Um, I'll just crawl under a rock if thats ok with you.  
> **username_0**: @username_2 Yes, that's perfectly fine :)  
> **username_4**: By "doubling the emission" do you mean the rate of emission or the cumulative amount in the atmosphere? Also, I assumed you were referring to the persistent GHGs (predominantly CO2) - is that correct?  
> **username_0**: @username_4 I mean doubling the amount of GHG emission from mankind e.g. in a year: will that rise the the global temperature x2 in comparison to the "normal"  emission  
> **username_4**: 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.  
> **username_4**: My other question was, are you asking about persistent GHGs (predominantly CO2) that accumulate in the atmosphere over decades, or water vapor, which is not cumulative, but fluctuates in the short term depending on temperature?  

---

## 2 answers

### Answer by username_5 on 2018-02-26. Score: 6

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.

> **Comments:**
> **username_1**: 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?  
> **username_5**: @gansub I interpreted OP as asking if $\bar{T}=f([GHG])$ (linear) or if $\bar{T}=f([GHG],T) $ (nonlinear)?.  
> **username_5**: @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....  

---

### Answer by username_4 on 2018-02-27. Score: 0

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](https://en.wikipedia.org/wiki/Climate_sensitivity#Equilibrium_and_transient_climate_sensitivity).

> **Comments:**
> **username_1**: 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.  
> **username_4**: @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.  
> **username_2**: 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: https://skeptics.stackexchange.com/questions/40636/does-each-doubling-of-co2-cause-a-2-4c-increase/40653#40653  
> **username_4**: @username_2 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’ "](http://www.realclimate.org/index.php/archives/2007/08/the-co2-problem-in-6-easy-steps/).  
> **username_2**: 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).'  
> **username_4**: @username_2 Some sources say "for each doubling" or "per doubling". The termionology seems to vary.  
> **username_2**: If there are any notable sources (like the IPCC assessment reports), could you link them? I believe that the definition of ECS is precisely for the first doubling of CO2 because climate has different feedbacks that vary depending on the absolute amount of warming.  
> **username_4**: @username_2 I found: ["In IPCC reports, equilibrium climate sensitivity (units: °C) refers to the equilibrium (steady state) change in the annual global mean surface temperature following a doubling of the atmospheric equivalent carbon dioxide (CO2 ) concentration."](https://www.ipcc.ch/pdf/assessment-report/ar5/syr/AR5_SYR_FINAL_Glossary.pdf#page=5) They don't specifically say "pre-industrial". Seems to suggest a slightly different meaning in the context of modelling. Googling for  [ECS "per doubling"] and [ECS "each doubling"] turns up quite a few hits, it depends which you consider notable.  

---

