Talk:Lapse rate/Archive 1

Low importance?
To quote from the article itself "The varying environmental lapse rates across the earth surface are of critical importance in meteorology." Why does the Met Project rate is as low? JMcC 14:56, 13 September 2006 (UTC)

Rename the article
Why isn't this article called Lapse rate? The adiabatic is just one of the lapse rates that the article describes. The environmental lapse rate in particular is not adiabatic. It is the actual change in temperature with height. JMcC 14:42, 13 September 2006 (UTC)
 * The simplest course was to copy this article to Lapse rate and to modify it so that it starts with lapse rates in general before getting specific. I suggest this article is now reduced to cover adiabatic lapse rates.  I would also suggest that the off-putting equation is moved to the end of the article. If there is no change in th next few days I will do this myself JMcC 11:38, 15 September 2006 (UTC)


 * Only Adiabatic lapse rate should be treated in this article, dry and moist, I agree. I just wonder why there is an article on Lapse rate in the first place as this should be a part of an article the atmosphere or the standard atmosphere. Lapse rate is just a term while Adiabatic Lapse Rate is a concept that needs to be explained? Pierre cb 11:56, 15 September 2006 (UTC)


 * Almost the other way round I think. The two adiabatic lapse rates are constants and are not as interesting as the environmental lapse rate.  They are just one of the physical properties of dry and moist air.  It is the variation in the environmental lapse rate that produces the weather.  This leads on the tephigrams and SkewTlogP (or is that Harry Potter? :-) ) and so needs separate explanation. JMcC 17:53, 18 September 2006 (UTC)


 * Well you have a point but one may think the other way around that all depends on the relation to the adiabatic lapse rates to be stable, neutral, or unstable. Thus explaining why it is so, is the important part for me. There is a proposition to merge the two articles. I was not for it but this could solve the problem with the proper redirections. Pierre cb 17:36, 19 September 2006 (UTC)

Merge
It seems to me that adiabatic lapse rate and lapse rate now strongly overlap. Should we merge them, or at least refactor them into 2 distinct articles? hike395 22:00, 16 September 2006 (UTC)


 * Yes they overlap but I don't think a merge is needed. Lapse rate should be trimmed to the minimum. It should ONLY mention that it is a change of temperature with altitude and refer to Adiabatic lapse rate for the rest. Pierre cb 01:32, 17 September 2006 (UTC)
 * I changed my mind on the subject and think that the merge might be the solution. Why not rename one of the articles Atmospheric Lapse Rates which is more accurate, put all the information from both articles and then make the redirect from the other to this new article. Pierre cb 17:32, 19 September 2006 (UTC)
 * I think the simplest title is the best --- I made Atmospheric lapse rate redirect to here. Completed the merge. hike395 11:15, 20 September 2006 (UTC)

Disambiguation
A lapse rate is also an important metric in various fields of insurance. Presently I'm not seeing anything about lapse rates on any of the insurance pages either, but maybe a link to the insurance category would be a good idea.


 * I would suggest starting an article on Lapse rate (insurance), and make that part of the insurance category, rather than having this non-insurance article be miscategorized. hike395 05:39, 20 October 2006 (UTC)

Inline references
I will give you all until June 20 to add inline references per the Wikipedia Guide of Style, at least one per paragraph. If not, I will downgrade the article to Start. Thegreatdr 20:45, 18 May 2007 (UTC)
 * Per a comment left on my talk page, I've decided to leave this article completely alone. If you all are happy with the current state of the article, that is definitely your call.  Just keep in mind that if a certain type of citation (like inline references) is needed for an article to become GA or FA class, why not do it early on in an article's life cycle to save a lot of work later in the article's life?  I can tell you that a lack on inline citations will generally keep me from updating an article because of all the extra work it would entail to upgrade its class.  The citations used in the article should all be of a similar type, however, which they currently are not.  Thegreatdr 03:26, 19 May 2007 (UTC)


 * Inline references are great --- we should definitely have them. I was just objecting to the multiple warning templates: it makes it seem that the article is dubious.


 * Your user page states that you are an expert in meteorology --- are there specific dubious facts in this article? Anything you're uncertain about? Please feel free to mark them with fact. Thanks! hike395 04:45, 19 May 2007 (UTC)
 * Not offhand. Actually, considering the lack on inline references, I don't see any fact problems.  I've seen other articles with tags in each section without inline references before (October 2006 form of the tornado article, for instance).  It didn't appear right in this case to just tag the top, because it would imply there were no inline references at all in the article, when there are a couple in the last section. Thegreatdr 12:15, 19 May 2007 (UTC)


 * I found a more appropriate tag for the top: Refimprove. It still encourages people to improve the references, but doesn't imply that there are none. hike395 12:45, 19 May 2007 (UTC)
 * Good find. =)  Thegreatdr 13:36, 19 May 2007 (UTC)

mathematical definition
Is the lapse rate truly defined by professionals as the slope, -(T2-T1)/(z2-z1), rather than the derivative -dT/dz? 76.120.154.6 14:44, 30 September 2007 (UTC)

What matters? Altitude change or pressure change?
The lapse rates are always presented as some temperature change per altitude change. For example, 9.78 degrees per 1000 metres. Is this really constant? It would seem to me that it is the change of temperature with pressure change that would be constant and that since the pressure drop over a 1000 metre altitude change decreases with altitude, that the lapse rate with respect to altitude change would not be constant. Sancho McCann 05:15, 1 December 2006 (UTC)


 * Disregard... I see the discussion above. Sancho McCann 05:18, 1 December 2006 (UTC)

Actually, for completeness, would it be worth mentioning dry lapse rate as a function of pressure?? It isn't necessary for understanding of the term and a 9.78 per km is a really close approximation as mentioned above. There's a good description on a lecture slide here: http://www.sparc.sunysb.edu/atm205/fall2001/lecture7/sld004.htm. What do you think? Sancho McCann 19:40, 1 December 2006 (UTC)

Here is an alternative simpler way, the same as the German page uses, to calculate the lapse rate for rock in the earth interior. and it only depends on specific heat capacity which is almost the same for air and rock. Davidjonsson Davidjonsson 23:30, 1 December 2007 (UTC)

Mechanism
Can anyone comment on why the lapse rate has the value it does? The atmosphere is a complicated and dynamic system: There's convection, radiation, heating by the ground, etc. But it is universally true that higher altitudes are colder. My hunch is that gravity is the fundamental mechanism. I'm interested to know how an ideal gas behaves at equilibrium in a gravitational field. My guess is that it would end up with a temperature gradient equal to the adiabatic lapse rate 9.78 °C/km, otherwise parcels of air would generate energy by trading altitudes. I'll leave with the comment that 9.78°C/km is on the order of Mg/kB (34°C/km), where M is the mass of an air molecule (29 u). That is the lapse rate you'd get by making the naive assumption that kBT increases by the amount of energy gained as a molecule "falls" to lower altitude. I think the article would benefit from a statement about the fundamental reason it is colder up there. Spiel496 03:01, 20 July 2007 (UTC)


 * IIRC from my atmospheric physics lectures, then you're pretty much right - we ought to put something about the derivation of the adiabatic value on the page - this website offers quite a useful derivation of the constant, and shows how it would vary between different bodies. --Neo 10:18, 20 July 2007 (UTC)

I have just posted a revision about the changing temperature with height in the troposphere on [atmosphere] the explanation for the change is available at the end of this contribution [Talk: Earth's Atmosphere]. To sumarise: heated air expands and rises by convection (its density is reduced by expansion), it rises against the force of gravity, gaining gravitational potential energy as it does so. Thus some of its thermal (kinetic) energy is converted into gravitational potential energy - the gas cools.

As does this article, the NASA website of the link this website give this formula dP = -gρ dz as part of the calculation for the lapse rate: the density (ρ) is taken as a constant with height, this is selfevidently not the case, ρ is f(z), it results in a Lapse rate that is constant with height and far too high, 9.5K/km instead of 6.5K/km.

There are other problems with this article, the mathematical convenience of using a constant density just happens to eliminate an important amospheric property, the expansion of the air with reduced pressure! --Damorbel (talk) 15:21, 3 July 2008 (UTC)

plain english
please can someone with expertise in this matter expand this article for the general reader. The concept of 'it gets colder as you go up because the pressure reduces and gas cools as it expands' is quite simple. Surely someone can work something like that into the article? Maybe you can add some examples of cirrus clouds forming as air cools due to lapse rate? Andrewjlockley (talk) 01:39, 1 July 2009 (UTC)

IR absorption
No one seems to mention that perhaps the driving force to many atmospheric events is the fact that moist air absorbs infrared energy from the sun while dry air transmits it.

Here are some links: John_Tyndall

http://www.emeraldinsight.com/fig/0870250407011.png

http://www.stormingmedia.us/93/9388/A938881.html

Arydberg (talk) 16:07, 22 August 2009 (UTC)

Lapse Rate Equation
My source for the wet adiabatic lapse rate equation is page 178 of An Introduction to Thermal Physics by Daniel V. Schroeder. Publisher: Addison Wesley Longman. Copyright 2000.

User:kloddant 9/5/09  —Preceding undated comment added 16:34, 5 September 2009 (UTC).

Examples exchanged?
Is it possible that the examples in the 'Significance in meteorology' section have been exchanged? There are three scenario's: the environmental lapse rate is either less than the moist rate, between moist and dry, or larger than dry. However, if the environmental lapse rate is small as in the first case (it is defined to be positive for a decrease, so small means close to zero and probably positive), that means that is cools little (or even heats) with increasing altitude. Now the example says 'rising air will cool faster than the surrounding air', but from what I understand the exact opposite happens? It would fit the description in the third scenario: 'a parcel of air will gain buoyancy as it rises both below and above the lifting condensation level or convective condensation level'. Please excuse me if I'm wrong, I'm not an atmosphere scientist or anything, it just confused me. Mverleg (talk) 21:23, 31 October 2010 (UTC)

Something wrong here
The erticle was edited on April 25th to include this:


 * The wet adiabatic lapse rate is given by the equation:


 * $$\color{blue}\frac{dT}{dz}=-(\frac{2Mg}{7R})(\frac{1+\frac{P_vL}{PRT}}{1+\frac{2P_vL^2}{7PR^2T^2}})$$


 * In this equation, M is the mass of a mole of air, which is about 0.018044454 kg.

It says that M is the mass of a mole of air but the number given is the mass of a mole of water. Would someone correct the Lapse rate accordingly? Thanks, mbeychok


 * I note that the above error has been corrected. Does anyone reading this know the source of the above equation? I have asked Kloddant who added the equation into this article, but have had no response. I would really appreciate knowing the source of the equation. mbeychok (talk) 18:25, 24 August 2009 (UTC)


 * Since neither Kloddant not anyone else has responded as to the source of the above equation, I propose it be replaced by the equation available from the American Meteorological Society Glossary here. Their equations is:


 * $$\Gamma_w = g\, \frac{1 + \dfrac{H_v\, r}{R_{sd}\, T}}{c_{p d} + \dfrac{H_v^2\, r\, \epsilon}{R_{sd}\, T^2}}$$


 * {|border="0" cellpadding="2"


 * align=right|where:
 * align=right|$$\Gamma_w$$
 * align=left|= Wet adiabatic lapse rate, K/m
 * align=right|$$g$$
 * align=left|= Earth's gravitational acceleration = 9.8076 m/s2
 * align=right|$$H_v$$
 * align=left|= Heat of vaporization of water, J/kg
 * align=right|$$r$$
 * align=left|= The ratio of the mass of water vapor to the mass of dry air, kg/kg
 * align=right|$$R$$
 * align=left|= The universal gas constant = 8,314 J kmol-1 K-1
 * align=right|$$M$$
 * align=left|= The molecular weight of any specific gas, kg/kmol = 28.964 for dry air and 18.015 for water vapor
 * align=right|$$R/M$$
 * align=left|= The specific gas constant of a gas, denoted as $$R_s$$
 * align=right|$$R_{sd}$$
 * align=left|= Specific gas constant of dry air = 287 J kg-1 K-1
 * align=right|$$R_{sw}$$
 * align=left|= Specific gas constant of water vapor = 462 J kg-1 K-1
 * align=right|$$\epsilon$$
 * align=left|=The dimensionless ratio of the specific gas constant of dry air to the specific gas constant for water vapor = 0.6220
 * align=right|$$T$$
 * align=left|= Temperature of the saturated air, K
 * align=right|$$c_{pd}$$
 * align=left|= The specific heat of dry air at constant pressure, J kg-1 K-1
 * }
 * align=right|$$R_{sw}$$
 * align=left|= Specific gas constant of water vapor = 462 J kg-1 K-1
 * align=right|$$\epsilon$$
 * align=left|=The dimensionless ratio of the specific gas constant of dry air to the specific gas constant for water vapor = 0.6220
 * align=right|$$T$$
 * align=left|= Temperature of the saturated air, K
 * align=right|$$c_{pd}$$
 * align=left|= The specific heat of dry air at constant pressure, J kg-1 K-1
 * }
 * align=right|$$c_{pd}$$
 * align=left|= The specific heat of dry air at constant pressure, J kg-1 K-1
 * }
 * }


 * Are there any objections to my replacing Kloddant's unsourced equation with the above equation from the American Meteorological Society? mbeychok (talk) 22:26, 29 August 2009 (UTC)


 * OK, but Hv should be Lv as in the AMS Glossary. Also it should be noted that the equation is only an approximation (for example it neglects the variation of Lv with temperature). Overall this article is pretty bad so anything that can be done to improve it would be helpful. Short Brigade Harvester Boris (talk) 22:39, 29 August 2009 (UTC)


 * Boris, thanks for your support. Meteorologists may prefer Lv but, in my experience, most engineers and others use Hv ... that was my reason for changing it from the AMS glossary. In any event, whether we use Hv or Lv does not change the equation. mbeychok (talk) 04:45, 30 August 2009 (UTC)


 * Is there a reason so many unused variables are defined below the equation? $$ R_{sw}$$ for example? It would also be useful to include units.  If I can find a good source I'll update and cite. Clegett (talk) 20:33, 17 April 2011 (UTC)

Understandability
The derivation of the dry adiabatic lapse rate is  not understandable since not all symbols are defined.I think that for an average reader the names of all symbols should be given. — Preceding unsigned comment added by FrankBerninger (talk • contribs) 07:04, 19 October 2011 (UTC)

Repetition
There are several paragraphs repeated under "Mathematical definition" that are already under "Definition".Jon Stephen Horridge (talk) 12:08, 4 April 2012 (UTC)
 * I don't really think there should be separate sections; there is one definition William M. Connolley (talk) 12:34, 4 April 2012 (UTC)

Units
Conversions should be provided for non-metric users. Aviation users in particular need to know feet/F rather than km/C for the dry adiabatic lapse rate.


 * The article has been changed, but I actually find the change less satisfactory. American aviation uses F/1000ft, and european aviation uses C/m (I think). In Canada, we use C/1000ft &mdash; do we just get screwed? (I actually can't see a reasonable way to prevent Canadian pilots from getting screwed, especially as I do not support the numbers being expressed in three different units). -Lommer | talk 23:24, 26 July 2005 (UTC)


 * How about a little table with three columns? -- hike395 03:33, July 27, 2005 (UTC)


 * Actually, that's not a bad suggestion... -Lommer | talk 04:31, 27 July 2005 (UTC)


 * The US FAA converted from Fahrenheit to Celsius in 1996. American aviators have been using Celsius for the last ten years. Bobblewik 03:37, 23 September 2005 (UTC)


 * As an American aviator who made the initial comment, temperature is reported in C but all vertical distances are, and will for a very long time, be in feet. In aviation publications, the formula for lapse rate is almost -always- given as degF/ft or degC (degF) / ft. However, the important part here (And perhaps it wasn't strongly enough emphasized)is that we need the 'feet' part, not so much that we need the temperature part in F.Kysh 22:14, 20 October 2005 (UTC)


 * What you say is reasonable. Just add the feet equivalents. Bobblewik 20:08, 8 October 2005 (UTC)


 * P.S. please use the autosignature function by adding 4 tildes ~.


 * Didn't have an account at the time, but I now do. Thanks. Kysh 22:14, 20 October 2005 (UTC)

UPDATE FOR PILOTS. In Europe we use the JAA as the aviation authority, and they state and test that the SALR is 0.6C/100m for the purpose of the ATPL exams. Very seldom do instructors and very seldom in the exams now will you see the SALR as c/ft. (1.8C/1000ft).--Pugzi 08:29, 15 May 2006 (UTC) (Steve Francis)
 * What's for sure is what was there was not suitable for those that use the metric system. I converted from this form...  5.5°F (3.05°C) per 1,000 feet (304 m)... to this form...5.5°F/1,000 ft (10°C/km)... using the formula °C/km=(°F/1,000ft)/1.8/(12*2.54/100). I rounded off... 6.38 to 6.4...10.02 to 10...5.47 to 5.5 Dave3457 (talk) 18:04, 31 May 2012 (UTC)

Title
British english calls this a slew rate rather than lapse rate. I found this article a little difficult to find due to different terminology. Are we able to put in a redirection?

Tony Wallace — Preceding unsigned comment added by 122.58.21.179 (talk) 07:04, 22 June 2013 (UTC)

Problem with Saturated Adiabatic Lapse Rate Formula
The formula given in the article is:

$$\Gamma_w = g\, \frac{1 + \dfrac{H_v\, r}{R_{sd}\, T}}{c_{p d} + \dfrac{H_v^2\, r}{R_{sw}\, T^2}}= g\, \frac{1 + \dfrac{H_v\, r}{R_{sd}\, T}}{c_{p d} + \dfrac{H_v^2\, r\, \epsilon}{R_{sd}\, T^2}} $$

Substituting numerical values, this expands to:

$$\Gamma_w \approx 9.8 \frac{ {}^\circ \text{C}}{\text{km}}\, \frac{1+\dfrac{4897.8 \text{ K}}{T}}{1+\left ( \dfrac{2619.7 \text{ K}}{T} \right )^2}$$

The prefactor looks good since this is the same as the dry adiabatic lapse rate. However, when I run some numbers, the results don't look reasonable:


 * T = 250 K => 1.8 C/km
 * T = 270 K => 2.0 C/km
 * T = 300 K => 2.2 C/km
 * T = 320 K => 2.3 C/km

The article says that the moist adiabiatic lapse rate is typically around 5 °C/km, and many other sites on the internet seem to support that.

If I had to guess the problem is actually with that second dimensionless r, and the formula should be:

$$\Gamma_w = g\, \frac{1 + \dfrac{H_v\, r}{R_{sd}\, T}}{c_{p d} + \dfrac{H_v^2\, r^2}{R_{sw}\, T^2}}= g\, \frac{1 + \dfrac{H_v\, r}{R_{sd}\, T}}{c_{p d} + \dfrac{H_v^2\, r^2\, \epsilon}{R_{sd}\, T^2}} $$

So that $$H_v\, r$$ are squared together in the denominator. In that case, the numerical expansion is:

$$\Gamma_w \approx 9.8 \frac{ {}^\circ \text{C}}{\text{km}}\, \frac{1+\dfrac{4897.8 \text{ K}}{T}}{1+\left ( \dfrac{1571.8 \text{ K}}{T} \right )^2}$$

Which then gives:


 * T = 250 K => 5.0 C/km
 * T = 270 K => 5.4 C/km
 * T = 300 K => 6.0 C/km
 * T = 320 K => 6.4 C/km

However, guessing is not really a good solution. So could someone please try to verify / derive the formula to figure out what the correct expression is. Dragons flight (talk) 20:21, 13 September 2013 (UTC)


 * Dragons flight, I trust the AMetSoc formula. However, in the description of terms, it was incorrectly stated that r (mass mixing ratio) is a constant value ~= 0.622. I've fixed up the formula to match the AMetSoc glossary. At 10 deg C, with a vapor pressure of 9.21 mm Hg and air pressure of 760 mm Hg, I get a saturated lapse rate of 5.28 K/km. LijeBailey (talk) 02:54, 20 March 2014 (UTC)

Proposed notational reversion
The notation °C was recently (Nov. 16) changed to C° throughout. If this is standard for relative temperatures I'm happy to leave it as is, if not I'll either revert it or change it to K as people prefer. Vaughan Pratt (talk) 23:33, 1 March 2015 (UTC)

Fundamentally flawed
It starts well enough - A formal definition from the Glossary of Meteorology is:
 * The decrease of an atmospheric variable with height, the variable being temperature unless otherwise specified.

.... and then immediately degrades into fantasy
 * In the lower regions of the atmosphere (up to altitudes of approximately 40,000 feet [12 km]), :temperature decreases with altitude at a fairly uniform rate. Because the atmosphere is :warmed by conduction from Earth's surface, this lapse or reduction in temperature is normal with increasing distance from the conductive source.

The atmosphere isn't "warmed by conduction..."; if it was, the temperature at a few metres above the surface would be very low. Air is a good insulator. Neither has lapse rate anything to do with "parcels of air".

The discussion for Dry adiabatic lapse rate contradicts itself immediately. After stating that
 * The term adiabatic means that no heat transfer occurs into or out of the parcel.

which is of course correct, and
 * Air has low thermal conductivity, and the bodies of air involved are very large, so transfer of :heat by conduction is negligibly small.

which also is correct and contradicts the earlier "warmed by conduction...". it goes on to state
 * As the air parcel expands, it pushes on the air around it, doing work (thermodynamics). Since :the parcel does work but gains no heat, it loses internal energy so that its temperature :decreases.

"loses internal energy" must mean loss of kinetic energy, which means that the process as described in this article is not adiabatic.

I've found similar descriptions on many (most?) university websites, all discussing "rising parcels of air", occasionally envisaging an "invisible container" which has "work done on it" by the "expanding air".

The lapse rate is a characteristic of Earth's atmosphere whether "parcels of air" rise, fall or dance a jig. Those imaginary "parcels" are expanding into an atmosphere whose temperature (in the troposphere) and pressure decrease with height; in other words, an existing set of conditions. This article doesn't address the reason(s) for those conditions, and so is fundamentally flawed.Rambler24 (talk) 18:32, 1 March 2013 (UTC)


 * Are you sure that cooling of a rising air parcel is "not adiabatic"? A Google search on the phrase "cooled by adiabatic expansion" yields over 30,000 hits. Is each one of those web pages wrong?  Spiel496 (talk) 20:47, 1 March 2013 (UTC)
 * I should have made it more clear - "which means that the process as described is not adiabatic." I've edited my comment. Rambler24 (talk) 20:59, 1 March 2013 (UTC)


 * I mean why does "loss of kinetic energy" mean "not adiabatic"? I thought adiabatic requires only that there be no heat transfer.  The air gets colder because it did work, rather than because of heat being conducted away.  Spiel496 (talk) 23:55, 1 March 2013 (UTC)
 * Ahem! What do you think heat content wrt a gas is, if not the total kinetic energy of the molecules? The "parcels of air" while irrelevant to the derivation of lapse rate, do no work at all while rising (convection). They rise because they're hotter and the air therein is less dense than the surrounding air, and so are buoyant. They are acted upon by a net force equal to the difference in weight of the "parcel" and the weight of the equivalent volume of denser gas which surrounds them. The rate at which they drop in temperature with height owes more to the starting conditions than to the lapse rate they encounter on ascending. They will stop ascending when they reach a level where the external density matches that of their own (by then) decreased density, whatever their heat content and temperature may be at that time. Rambler24 (talk) 22:42, 2 March 2013 (UTC)


 * The article clearly states that a rising parcel of air does do work, and it clearly explains why: "it expands, because the pressure is lower at higher altitudes. As the air parcel expands, it pushes on the air around it, doing work". If you have a force (atmospheric pressure) and motion in the direction of that force (expansion) you have work. In my opinion, the wording of the article on this point is fine the way it is.
 * Regarding your "Ahem!" question, I am not familiar with the term "heat content". Heat is the transfer of energy from a warmer system to a cooler system. It is not something a system "contains" . The total kinetic energy of the molecules is called the internal energy, which can change either due to heat or work. Spiel496 (talk) 15:19, 3 March 2013 (UTC)
 * I agree - "heat" is the amount of energy transferred to a body by the process of heating, not the increase in the "heat content" of the body. A body does not contain "heat", or, if you insist that it does (properly called the thermal component of the internal energy), then there is no way of knowing how much the heat content will increase when the body is heated. The added energy may manifest itself as work. Also, for a given amount of heat content, you cannot tell whether that heat came from the heating process or from work. "heat content" is not a conserved quantity, which is the mistake here. Please see discussion at Talk:Adiabatic process
 * I agree that the article is fundamentally flawed. The explanation of the temperature gradient (which does not need a special misleading name "lapse rate") should be carried out using the Kinetic Theory of Gases.  That theory can be used to understand the Ideal Gas Law used here.  However, it is unnecessary to introduce that law (with the implication that pressure is involved) because, as we see later in the derivation of the dry rate, pressure cancels out.  All we need to do is to understand that the temperature gradient evolves as the state of thermodynamic equilibrium with maximum entropy and thus no unbalanced energy potentials. When that state evolves at the molecular level in an isolated system (even in a sealed insulated cylinder) we must have a homogeneous sum of micro (molecular) mean kinetic energy and gravitational potential energy per molecule, assuming no other internal energy changes.  Hence we can deduce that there is a temperature gradient, because molecules exchange kinetic energy (KE) and gravitational potential energy (PE) when in flight between collisions, and temperature is determined only by the mean kinetic energy of the molecules.  For a downward moving molecule, for example, we only need to equate potential energy loss with kinetic energy gain.  That KE gain is equivalent to the energy needed to raise mass m by a temperature change dT.  The potential energy loss over height dH is -m*g*dH and so we equate this to KE gain of m*cp*dT (where cp is the specific heat at constant pressure)and we get the temperature gradient dT/dH = -g/cp.  The main fallacy in the article's roundabout derivation is the assumption that a parcel of air somehow clings together as an entity which does work "pushing out" the air above. Only wind and weather conditions could hold some air molecules together to some extent, but we are excluding such wind (and forced convection) in this consideration of an isolated system.  The assumption begs the question because it assumes that the density gradient has already formed.  What if a horizontal sealed insulated cylinder were rotated to a vertical position.  Which comes first, the density gradient or the temperature gradient?  In fact they both evolve simultaneously as entropy increases towards the state of maximum entropy when both the density and temperature gradient become stabilized. The molecules do not "do work" against the other molecules in air above that is already less dense.  Instead they do work against gravity as they rise at about 1,700Km/hr in their normal inter-molecular flight between collisions.  Thus they lose kinetic energy as they gain potential energy.  At thermodynamic equilibrium molecules that are about to collide have, on average, the same kinetic energy, and so there is no further net transfer of energy across any internal boundary.  Likewise there is no net transfer of mass, and so we have equal numbers of molecules with the same mean kinetic energy passing up and down through any horizontal plane.  Since pressure is proportional to the product of temperature and density, we have equal pressure from above and below at that horizontal plane. We can understand the density gradient on the basis that gravity causes a slightly greater propensity for molecules to move downwards rather than upwards, and so, with equal numbers crossing a horizontal plane, there must have been greater density below and less density above.  We understand the temperature gradient because, when the cylinder was rotated from horizontal to vertical, there was some net movement of molecules downwards to form the density gradient and, at the same time, gaining kinetic energy that makes the lower regions warmer.  Finally, we understand natural convection as occurring whenever there is a new source of thermal energy which disturbs a previous state of thermodynamic equilibrium, because then there will be a propensity for that new thermal energy to spread out in all accessible directions away from the source of new energy.  Douglas Cotton 110.146.150.203 (talk) 14:09, 8 April 2015 (UTC)

Dry adiabatic lapse rate cannot be a constant
The relationship between temperature and pressure is nearly fixed (it'll vary as the composition of the atmosphere changes, but presumably not by much). However, the relationship between pressure and altitude is not so nearly fixed, since it depends on the density profile over altitude, which depends on temperature over altitude (and also on humidity over altitude, to some extent).

The relationship of temperature and pressure is

$${T_2 \over T_1} = \left({P_2 \over P_1}\right)^{{\gamma-1} \over \gamma}$$


 * This is only true if T1,P1 and T2,P2 have the same entropy, i.e. if state 2 can be reached from state 1 by an adiabatic process.

The $$\gamma$$ here is not the same as the gamma used in the article body to denote lapse rate. The usage in the article is unfortunate, since $$\gamma$$ is usually used to denote the specific heat ratio, see adiabatic. Is the article's usage standard?


 * Actually, the $$\gamma$$ in the adiabatic equation is precisely the specific heat ratio. Same letter, same meaning.

The pressure in the atmosphere drops off approximately exponentially with altitude. This means a 1000m increase in elevation typically produces a 12.6% drop in pressure. That drop in pressure would cause a 3.45% drop in temperature, which is about 10 C.

In any case, my point is that pressure at altitude varies, and varies with some independence from the pressure at sea level directly below, and as a result the dry adiabatic lapse rate is not a constant.

Iain McClatchie 18:34, 1 October 2005 (UTC)

Ok, it's not strictly constant, but it does turn out to be vary remarkably little if you do the numerical integration.


 * The dependence of pressure on altitude is only exponential if the temperature is constant. The dry adiabatic lapse rate is how the temperature varies with altitude if the atmosphere is adiabatic, i.e., if the entropy is constant.  It turns out that in this case, dT/dz is in fact exactly constant.  Of course, the atmosphere is neither precisely isothermal nor adiabatic; the troposphere is approximately adiabatic, and the stratosphere is approximately isothermal. 67.186.28.212 11:44, 2 September 2007 (UTC)

Customarily, undergraduates are shown the simple derivation giving the dry lapse rate of -g K/km, or -9.86K/km. This at ground/sea level. Once water vapour is present the figure is 6.5K/km. The potential temp greatly increases with altitude, of course.27.33.81.127 (talk) 06:20, 1 February 2016 (UTC)

Inversion?
"For example, there can be an inversion layer in which the temperature increases with altitude." I think I am correct in saying that the temperature does not necessarily need to increase in temperature to be described as an "inversion." If the lapse rate drop below the standard lapse rate this is also called an inversion because this is the boundary where major meterological behavior ceases because the air has no excess temperature derived kinetic energy and stops rising. (It may still have horizontal kinetic energy - wind.) Most atmospheric inversions are not strict inversions and this can be very confusing nomenclature for people when they see a measured lapse rate chart on a day "with an inversion" and there is no temperature reversal illustrated. I've done no editing but feel free to do so. Anyone who rewrites relevant sections should incorporate some of the above using filled in lapse rate charts as an illustrative tool. Ecstatist (talk) 04:17, 2 December 2016 (UTC)

Potential Temperature
Please relate this to the article.Biggerj1 (talk) 08:27, 26 June 2018 (UTC)