<p>For dry adiabatic, you simply ignore the greenhouse gas.   This might sound like a cheat, but it's not.   The dry adiabatic lapse rate doesn't change with temperature or latitude. </p>

<p>For a physical explanation, if you consider what the greenhouse gas does, it captures heat and raises the temperature near the Earth's surface, which expands the troposphere and raises the tropopause.   In other words, the troposphere grows taller, so the lapse rate can remain the same and the tropopause moves a little higher up.   This can also be seen in higher and lower latitudes on Earth in that the tropopause is about 5 miles closer to the Earth at the poles than over the equator.   </p>

<p>The adiabatic lapse rate is a property of the ideal gas law.  Heat trapping greenhouse gas doesn't affect it because the gas expands accordingly with trapped heat.  </p>

<p>The true environmental lapse rate is a bit more complicated as that fluctuates with humidity.   As the Earth warms, absolute humidity should increase but relative humidity should slightly decrease.   A lower relative humidity, on average, should raise the lapse rate slightly (I think), as the dry adiabatic rate is greater than the moist rate.    But this last paragraph take with a grain of salt.   The environmental lapse rate is more complicated.  </p>

<hr>

<blockquote>
  <p>2 identical planets, with 2 identically thick atmospheres, same c,
  same g, same lapse rate but one is a pure CO2 atmosphere and the other
  is a non greenhouse gas with the same c (fictional gas, we will call
  it CO2U)</p>
</blockquote>

<p>I'm not an expert in lapse rate, so my answer is a little bit of a cheat, but I'll take the thought experiment as best I can.</p>

<p>Fictional gas - same density as CO2 (at standard temperature &amp; Pressure "STP").   Both atmospheres are on planets of identical surface area, with identical gravity and both atmospheres have identical mass and (just to clarify) Identical density at STP.</p>

<p>The atmosphere that traps heat will expand, so it will have a higher troposphere.   Hot gas expands.   Cold gas contracts.</p>

<p>So the planet without the greenhouse gas will have a troposphere that's 6 miles high, the one with the greenhouse gas and a higher surface temperature will have a troposphere 10 miles high.   The rate of temperature drop can remain consistent at (-g/c) but the hotter planet will have a higher troposphere and a more expanded atmosphere.   That's for the theoretical model anyway.   I don't do real world models.  Those are much harder.</p>

<blockquote>
  <p>So the planet with the GHE atmosphere will be hotter at the surface,
  hotter at any given height in the atmosphere and hotter as a complete
  body/system (atmosphere+solid planet). Everything is hotter. Errr...
  what happened to the supposed radiative S-B balance as viewed from
  space then ?? Radiative input from sun the same, radiative output from
  the GHE planet now higher</p>
</blockquote>

<p>The energy balance question is a fun one, especially when climate change "skeptics" use it to say "climate change can't possibly be right" - look at the chart they use, more heat leaves the Earth's surface than comes from the sun.   </p>

<p><a href="https://i.sstatic.net/KHETu.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/KHETu.png" alt="https://earthobservatory.nasa.gov/Features/EnergyBalance/images/global_energy_budget_components.png"></a></p>

<p><a href="https://earthobservatory.nasa.gov/Features/EnergyBalance/page6.php" rel="nofollow noreferrer">Source</a>.</p>

<p>Lets ignore that debate for brevity and look at the overall theory of increasing greenhouse gas driven climate change.   The Energy from the sun is same, so, why does Earth get warmer?  The answer is trapped heat.   So, what does this look like from space?   Counter intuitively, from space the Earth looks colder than it did 30/40/50 years ago.  It's giving less thermal radiation into space.   This is because heat is being trapped in the lower atmosphere and oceans.  The upper atmosphere on Earth is actually cooling and contracting and less thermal radiation is leaving the Earth, not more, even with the warming surface temperature.  Measuring the decrease in heat that leaves the Earth is one way to measure the total amount of heat being trapped by climate change.   </p>

<p>In time, a new equilibrium will eventually be reached and heat in will equal heat out again but for now on Earth, Heat in is greater than heat out.  The difference is heat added, which does things like warm the air, the oceans and melts the ice.   In your scenario, there's no change, it's already warmer, but it's warmer in equilibrium, so heat in = heat out.</p>

<p>In other words:  A warmer atmosphere at equal heights doesn't mean more heat leaves the planet, because the CO2 rich atmosphere makes it harder for the thermal radiation from the warm surface to reach space.   The greater heat is balanced out by a greater percentage being reflected back to the surface.   The amount that goes into space is equal on the 2 planets.   </p>

CC BY-SA 3.0
2017-04-13T23:19:19.897Z
If your answer is correct then I conclude the following:So when considering the dry adiabatic lapse rate the formulae is the same (-g/c) irrespective of whether the gas has any greenhouse effect at all. This implies that two gases with the same specific heat capacity will have the same lapse rate even if one is a greenhouse gas and the other is not.
user7733
CC BY-SA 3.0
2017-04-13T23:32:42.750Z
(continued) Now we know the lapse rate independent of the surface temperature, there is no temperature term in -g/c and you stated "The dry adiabatic lapse rate doesn't change with temperature or latitude". We also know the lapse rate is the same with a thin atmosphere or a thick one. So lets construct a thought experiment. 2 identical planets, with 2 identically thick atmospheres, same c, same g, same lapse rate but one is a pure CO2 atmosphere and the other is a non greenhouse gas with the same c (fictional gas, we will call it CO2U). Place each planet in identical solar orbit. Observe.
user7733
CC BY-SA 3.0
2017-04-13T23:33:53.897Z
(continued). What is different ?
user7733
CC BY-SA 3.0
2017-04-14T17:42:32.880Z
@user7733  Added to answer above.
userLTK
CC BY-SA 3.0
2017-04-14T18:57:54.577Z
Right. I sort of expected that answer (modified/added to your previous). I don't think either of us need to be experts in lapse rate BTw, as I think the physics and the formulae are pretty basic/quite simple. Anyway back to your answer.  So the planet with a GHE atmosphere will have a higher surface temperature. Well that only follows as you have defined what a GHE atmosphere does, but lets say its true. We therefore have 1) a higher surface temperature 2) An atmosphere that is on average hotter and contains more heat 3) an atmosphere that is less dense at the surface, heated up and expanded.
user7733
CC BY-SA 3.0
2017-04-14T19:02:13.233Z
So the planet with the GHE atmosphere will be hotter at the surface, hotter at any given height in the atmosphere and hotter as a complete body/system (atmosphere+solid planet). Everything is hotter. Errr... what happened to the supposed radiative S-B balance as viewed from space then ?? Radiative input from sun the same, radiative output from the GHE planet now higher as both planet surface AND atmosphere hotter.
user7733
CC BY-SA 3.0
2017-04-14T20:58:18.117Z
@user7733  Updated.
userLTK
CC BY-SA 3.0
2017-04-15T22:20:45.310Z
@user7733 here's a really simplified analogy.  Light and Heat are comparable in this circumstance because all the heat that escapes a planet into space is in the form of thermal radiation.   Imagine a lamp with a 100 watt bulb and a thick shade and a lamp with a 60 watt bulb and a thin shade.   From outside they might emit the same brightness if the thicker shade blocks 40 watts more light than the thin one.   Same principal.
userLTK
CC BY-SA 3.0
2017-04-16T23:25:17.493Z
Your light bulb analogy is inappropriate as we are considering a heat source (the sun) external to the planet (the bulb) and an atmosphere (the shade) which has a 2 way flow of different frequency band radiations. I therefore reject it as unhelpful and an over simplification which does nothing to assist the understanding of the real world scenario. Back to the 2 planets and your added comment(s). For the moment forget transient effects or adjustments. I will just consider the steady state equilibrium reached after however many decades or centuries it takes ! (continued below).
user7733
CC BY-SA 3.0
2017-04-16T23:31:22.453Z
In the final equilibrium state we have agreed we have 2 planets with differing surface temperatures. The GHE planet being hotter on the surface. You also agree with my conclusion (based on your reasoning) that at any given height the GHE planet has a hotter atmospheric temperature. We know that any planet will radiate to space and by measuring that radiation you can determine the planets effective temperature. So looking outside from space since the radiation is the same you presumably agree that the effective temperature is the same on the GHE planet as the other one ?
user7733
CC BY-SA 3.0
2017-04-16T23:38:24.880Z
So if effective temperature is the same, looking from outside in space, and after equilibrium, there is no way to determine which planet is which, they look the same. Radiation out = Radiation in (on average of course, it is rotating and one side always dark). The only way you can see which is the GHE planet is to get some measurement of the inside of the "system" e.g. surface temperature measurement or atmospheric measurement. The GHE planet being hotter than the other in both surface and atmosphere (at same height). But suppose we can only measure one planet.
user7733
CC BY-SA 3.0
2017-04-16T23:44:46.457Z
If we can only measure one planet what would we choose to determine if it is the GHE one or not ? We need some parameter which changes in relation to another parameter ON THE SAME PLANET as opposed to comparison between GHE and a non-GHE atmosphere. So what is it we can measure to see that ? Lets get back to the real world (at last !). What can we measure on earth in the atmosphere right now, not by comparing it with something in the past but current state only, that confirms we do indeed have a GHE atmosphere on earth ? Open to answer from anyone.
user7733
CC BY-SA 3.0
2017-04-16T23:50:41.417Z
BTW @LTK I forgot to comment on your Trenberth style diagram. You made a comment about "more heat leaving the earth.." . Can we be absolutely clear please - ALL these diagrams which show radiative flux in W/m^2 are NOT heat transfer diagrams, they are Radiative Flux diagrams.
user7733
CC BY-SA 3.0
2017-04-17T04:17:31.193Z
@user7733 please put these comments into a separate question.  I think you've gone outside the scope lapse rate.
userLTK
CC BY-SA 3.0
2017-04-08T02:03:16.810Z
2017-04-14T20:57:50.683Z
2017-04-14T20:57:50.683Z
userLTK
<p>I am restricting my consideration, for the moment, to just the troposphere. With regard to our understanding of the GHE do we predict that an increased GHE due to increasing CO2/Water/Methane will change the lapse rate postively or negatively? The dry adiabatic lapse rate (DALR), according to my old text books, is easily calculated from the formulae -g/c, where g is the acceleration due to gravity and c is the specific heat capacity of the atmosphere. This is supposed to be a general formulae that can be applied to any planet with a solid surface and a gaseous atmosphere. So for earth is the formulae now -g/c + (GHE) or is it -g/c - (GHE)? The bracketed GHE term being specific to the atmosphere of a specific composition, e.g. including 400ppm CO2. 
The second part of the question then , after we have the correct sign, is how is the term (GHE) expected to vary as the CO2 (or other greenhouse gas) concentrations vary? </p>

CC BY-SA 3.0
2017-04-05T11:59:34.260Z
Lapse rate feedback, see also: https://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch8s8-6-3-1.html
gerrit
<climate><climate-change>
How does the existence of a Greenhouse Gas Effect (GHE) in the atmosphere affect the tropospheric lapse rate?
user7733
# How does the existence of a Greenhouse Gas Effect (GHE) in the atmosphere affect the tropospheric lapse rate?

(Asked by: username_0 on 2017-04-05)

I am restricting my consideration, for the moment, to just the troposphere. With regard to our understanding of the GHE do we predict that an increased GHE due to increasing CO2/Water/Methane will change the lapse rate postively or negatively? The dry adiabatic lapse rate (DALR), according to my old text books, is easily calculated from the formulae -g/c, where g is the acceleration due to gravity and c is the specific heat capacity of the atmosphere. This is supposed to be a general formulae that can be applied to any planet with a solid surface and a gaseous atmosphere. So for earth is the formulae now -g/c + (GHE) or is it -g/c - (GHE)? The bracketed GHE term being specific to the atmosphere of a specific composition, e.g. including 400ppm CO2.
The second part of the question then , after we have the correct sign, is how is the term (GHE) expected to vary as the CO2 (or other greenhouse gas) concentrations vary?

**Tags:** climate, climate-change

> **Comments:**
> **username_1**: Lapse rate feedback, see also: https://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch8s8-6-3-1.html  

---

## 1 answers

### Answer by username_2 on 2017-04-08. Score: 1

For dry adiabatic, you simply ignore the greenhouse gas. This might sound like a cheat, but it's not. The dry adiabatic lapse rate doesn't change with temperature or latitude.

For a physical explanation, if you consider what the greenhouse gas does, it captures heat and raises the temperature near the Earth's surface, which expands the troposphere and raises the tropopause. In other words, the troposphere grows taller, so the lapse rate can remain the same and the tropopause moves a little higher up. This can also be seen in higher and lower latitudes on Earth in that the tropopause is about 5 miles closer to the Earth at the poles than over the equator.

The adiabatic lapse rate is a property of the ideal gas law. Heat trapping greenhouse gas doesn't affect it because the gas expands accordingly with trapped heat.

The true environmental lapse rate is a bit more complicated as that fluctuates with humidity. As the Earth warms, absolute humidity should increase but relative humidity should slightly decrease. A lower relative humidity, on average, should raise the lapse rate slightly (I think), as the dry adiabatic rate is greater than the moist rate. But this last paragraph take with a grain of salt. The environmental lapse rate is more complicated.

---

> 2 identical planets, with 2 identically thick atmospheres, same c,
> same g, same lapse rate but one is a pure CO2 atmosphere and the other
> is a non greenhouse gas with the same c (fictional gas, we will call
> it CO2U)

I'm not an expert in lapse rate, so my answer is a little bit of a cheat, but I'll take the thought experiment as best I can.

Fictional gas - same density as CO2 (at standard temperature & Pressure "STP"). Both atmospheres are on planets of identical surface area, with identical gravity and both atmospheres have identical mass and (just to clarify) Identical density at STP.

The atmosphere that traps heat will expand, so it will have a higher troposphere. Hot gas expands. Cold gas contracts.

So the planet without the greenhouse gas will have a troposphere that's 6 miles high, the one with the greenhouse gas and a higher surface temperature will have a troposphere 10 miles high. The rate of temperature drop can remain consistent at (-g/c) but the hotter planet will have a higher troposphere and a more expanded atmosphere. That's for the theoretical model anyway. I don't do real world models. Those are much harder.

> So the planet with the GHE atmosphere will be hotter at the surface,
> hotter at any given height in the atmosphere and hotter as a complete
> body/system (atmosphere+solid planet). Everything is hotter. Errr...
> what happened to the supposed radiative S-B balance as viewed from
> space then ?? Radiative input from sun the same, radiative output from
> the GHE planet now higher

The energy balance question is a fun one, especially when climate change "skeptics" use it to say "climate change can't possibly be right" - look at the chart they use, more heat leaves the Earth's surface than comes from the sun.

[![https://earthobservatory.nasa.gov/Features/EnergyBalance/images/global_energy_budget_components.png](https://i.sstatic.net/KHETu.png)](https://i.sstatic.net/KHETu.png)

[Source](https://earthobservatory.nasa.gov/Features/EnergyBalance/page6.php).

Lets ignore that debate for brevity and look at the overall theory of increasing greenhouse gas driven climate change. The Energy from the sun is same, so, why does Earth get warmer? The answer is trapped heat. So, what does this look like from space? Counter intuitively, from space the Earth looks colder than it did 30/40/50 years ago. It's giving less thermal radiation into space. This is because heat is being trapped in the lower atmosphere and oceans. The upper atmosphere on Earth is actually cooling and contracting and less thermal radiation is leaving the Earth, not more, even with the warming surface temperature. Measuring the decrease in heat that leaves the Earth is one way to measure the total amount of heat being trapped by climate change.

In time, a new equilibrium will eventually be reached and heat in will equal heat out again but for now on Earth, Heat in is greater than heat out. The difference is heat added, which does things like warm the air, the oceans and melts the ice. In your scenario, there's no change, it's already warmer, but it's warmer in equilibrium, so heat in = heat out.

In other words: A warmer atmosphere at equal heights doesn't mean more heat leaves the planet, because the CO2 rich atmosphere makes it harder for the thermal radiation from the warm surface to reach space. The greater heat is balanced out by a greater percentage being reflected back to the surface. The amount that goes into space is equal on the 2 planets.

> **Comments:**
> **username_0**: If your answer is correct then I conclude the following:So when considering the dry adiabatic lapse rate the formulae is the same (-g/c) irrespective of whether the gas has any greenhouse effect at all. This implies that two gases with the same specific heat capacity will have the same lapse rate even if one is a greenhouse gas and the other is not.  
> **username_0**: (continued) Now we know the lapse rate independent of the surface temperature, there is no temperature term in -g/c and you stated "The dry adiabatic lapse rate doesn't change with temperature or latitude". We also know the lapse rate is the same with a thin atmosphere or a thick one. So lets construct a thought experiment. 2 identical planets, with 2 identically thick atmospheres, same c, same g, same lapse rate but one is a pure CO2 atmosphere and the other is a non greenhouse gas with the same c (fictional gas, we will call it CO2U). Place each planet in identical solar orbit. Observe.  
> **username_0**: (continued). What is different ?  
> **username_2**: @username_0  Added to answer above.  
> **username_0**: Right. I sort of expected that answer (modified/added to your previous). I don't think either of us need to be experts in lapse rate BTw, as I think the physics and the formulae are pretty basic/quite simple. Anyway back to your answer.  So the planet with a GHE atmosphere will have a higher surface temperature. Well that only follows as you have defined what a GHE atmosphere does, but lets say its true. We therefore have 1) a higher surface temperature 2) An atmosphere that is on average hotter and contains more heat 3) an atmosphere that is less dense at the surface, heated up and expanded.  
> **username_0**: So the planet with the GHE atmosphere will be hotter at the surface, hotter at any given height in the atmosphere and hotter as a complete body/system (atmosphere+solid planet). Everything is hotter. Errr... what happened to the supposed radiative S-B balance as viewed from space then ?? Radiative input from sun the same, radiative output from the GHE planet now higher as both planet surface AND atmosphere hotter.  
> **username_2**: @username_0  Updated.  
> **username_2**: @username_0 here's a really simplified analogy.  Light and Heat are comparable in this circumstance because all the heat that escapes a planet into space is in the form of thermal radiation.   Imagine a lamp with a 100 watt bulb and a thick shade and a lamp with a 60 watt bulb and a thin shade.   From outside they might emit the same brightness if the thicker shade blocks 40 watts more light than the thin one.   Same principal.  
> **username_0**: Your light bulb analogy is inappropriate as we are considering a heat source (the sun) external to the planet (the bulb) and an atmosphere (the shade) which has a 2 way flow of different frequency band radiations. I therefore reject it as unhelpful and an over simplification which does nothing to assist the understanding of the real world scenario. Back to the 2 planets and your added comment(s). For the moment forget transient effects or adjustments. I will just consider the steady state equilibrium reached after however many decades or centuries it takes ! (continued below).  
> **username_0**: In the final equilibrium state we have agreed we have 2 planets with differing surface temperatures. The GHE planet being hotter on the surface. You also agree with my conclusion (based on your reasoning) that at any given height the GHE planet has a hotter atmospheric temperature. We know that any planet will radiate to space and by measuring that radiation you can determine the planets effective temperature. So looking outside from space since the radiation is the same you presumably agree that the effective temperature is the same on the GHE planet as the other one ?  
> **username_0**: So if effective temperature is the same, looking from outside in space, and after equilibrium, there is no way to determine which planet is which, they look the same. Radiation out = Radiation in (on average of course, it is rotating and one side always dark). The only way you can see which is the GHE planet is to get some measurement of the inside of the "system" e.g. surface temperature measurement or atmospheric measurement. The GHE planet being hotter than the other in both surface and atmosphere (at same height). But suppose we can only measure one planet.  
> **username_0**: If we can only measure one planet what would we choose to determine if it is the GHE one or not ? We need some parameter which changes in relation to another parameter ON THE SAME PLANET as opposed to comparison between GHE and a non-GHE atmosphere. So what is it we can measure to see that ? Lets get back to the real world (at last !). What can we measure on earth in the atmosphere right now, not by comparing it with something in the past but current state only, that confirms we do indeed have a GHE atmosphere on earth ? Open to answer from anyone.  
> **username_0**: BTW @LTK I forgot to comment on your Trenberth style diagram. You made a comment about "more heat leaving the earth.." . Can we be absolutely clear please - ALL these diagrams which show radiative flux in W/m^2 are NOT heat transfer diagrams, they are Radiative Flux diagrams.  
> **username_2**: @username_0 please put these comments into a separate question.  I think you've gone outside the scope lapse rate.  

---

