Kevin Kilty
In my effort to produce the series called “Earth’s Energy Imbalance, parts 1-3” I left open a couple of ideas that simply became loose threads for another time. That time has arrived, partially because of a recent publication that caught my attention.
Background
As summarized in Earth’s Energy Imbalance part II the theory of response to radiative forcing from CO2 is most simply explained using an idealized, 1-D atmospheric profile. This explanation is shown in Figure 1, and for purposes of background its explanation is this:
With a fixed Te and fixed gradient (Lapse rate Γ) surface temperature then becomes; Ts = Te + ΓZe. In this simple model only changes in Ze matter. Now the argument takes the following path.
An increased concentration of CO2 in the atmosphere makes the atmosphere more opaque to outgoing infrared radiation from the surface. Thus, to have a CO2-doubled atmosphere equally transparent above Ze to enable escape of the average photon, Ze must reside higher in the atmosphere. A doubling of CO2 makes the more opaque atmosphere equally transparent above at Ze+150m. However, the invariant gradient of 6.5K/km means the temperature at Ze+150m is lower by about 1K, and according to the Stefan-Boltzmann law this amounts to a reduction in outgoing radiation by about 4W/m2 (236.3 = σ 2544). There is an energy imbalance that warms the entire atmosphere and surface.
This is an analysis dependent entirely on a temperature profile with an invariant temperature gradient. Let me just say as an aside, that sometimes a very simple and valid explanation is pertinent to an imagined problem; but the imagined problem is different than the problem of pertinence. I think we are facing such a situation here.
Nonetheless, elements of this same 1-D thinking are pervasive in the climate debate.[1] I don’t want to speak for Dr. Spencer, and perhaps he’d elaborate on this topic, but in a comment I made in “Earth’s Energy Imbalance, part II an Addendum” I mentioned something he’d written on a listserve elsewhere:
“…Roy Spencer has said that when it comes to climate change, the problem doesn’t realy [sic] involve “weather” but is largely a matter of radiative transport surface to space, which is why 1-d models work about as well as global climate models. I agree, but only to a point. I think convection, and advection from tropics to poles are also important, but not even included on the list of feedbacks. Lindzen has lately been emphasizing that poleward transport processes are very important. The whole question is so complicated that it is bound to generate strong disagreement ….”
Because of the focus on 1-D geometry, an important question to explore is “What does an atmospheric profile, a 1-D column, tell us about heat transport surface to space?”
The short answer is that it tells us nothing definitive until it is augmented with other information. The reason for this is that any number of processes can arrive at the same atmospheric profile. The forward problem, going from processes to profile, arrives at a unique answer. The inverse problem, going from an observed profile back to the processes producing it is not unique, but rather infinitely degenerate. This is the same problem I identified as fatal to a published paper arguing for CO2 having no effect on atmospheric temperature.
Each small parcel, let’s say each kilogram, of the atmosphere has a current temperature. This temperature is a reflection of its specific internal energy.[2] Taking a Lagrangian point of view, changes to specific internal energy result from integrated inputs over time of heat added to the parcel through external sources like radiation and internal sources like latent heat or dissipation of kinetic energy, less the work the parcel performed against its environment over its path from a point of origin to the present location.[3] This represents an enormous amount of information. It explains the enthusiasm for the 1-D model, radiative-convective equilibrium (RCE), and the preponderance of feedback analysis based on it.
What about RCE?
Though I find the concept of equilibrium dubious, the transport of heat to space by combined radiation and convection we will call RCE as does Caballero and Merlis. The only place I have ever observed the invariant 6.5 K/km lapse rate, which the simple model of greenhouse warming needs, is among the models in MODTRAN.[4] MODTRAN is an excellent learning tool for exploring how atmospheric structure affects the transport of thermal IR radiation. It is a reasonable calculator of thermal IR within certain limitations. It can, for example, show that a doubling of CO2 produces the immediate decrease in outgoing longwave radiation (OLR) of 3.7 W/m2 at the tropopause, which in turn requires an increase of about 1C in surface temperature to restore OLR to its previous value assuming no water vapor feedback.
The limitation of most concern here is that the implementation available to us does not allow building a custom deck of atmospheric structure. Instead we are limited to using a fixed set of atmospheric models with a few adjustments for clouds. All of these models involve a long segment of temperatures at a fixed, constant lapse rate near 6.5 K/km. Changing the surface temperature of a model, changes the entire vertical column by this same adjustment. Thus, MODTRAN enforces an invariant lapse rate, and one model, the U.S Standard Atmosphere of 1976, presents a constant lapse rate of 6.5 K/km all the way from surface to space. It is the embodiment of the simple model of climate warming under discussion here.
The various models that MODTRAN makes available are all fictions. The U.S Standard Atmosphere of 1976, for example, began as the NACA Standard Atmosphere in 1922. It was not meant as a tool for weather and climate, but to provide input into operational and engineering problems of aeronautics. By the 1950s problems of aeronautics broadened into problems of astronautics. This combined with growing understanding of the upper atmosphere initiated a series of updates starting in 1953 to eventually become the U.S Standard Atmosphere of 1976. I don’t know the precise origin of MODTRAN’s other models, but they all originated apparently out of engineering needs in weaponry and instrumentation; not weather and climate. Nonetheless, mission creep has allowed these to enter weather and climate. As an example, the U.S Standard Atmosphere of 1976, provides weighting (contribution functions) on the GOES-R baseline imager.[5]
As a consequence of not being able to design a model atmosphere, using MODTRAN as a calculator of greenhouse effect presents an inconsistency. The specified temperature profile can’t be sustained by radiative transport alone as Figure 2a shows. Other mechanisms implicitly fill the gap, and we can hardly imagine how these operate, or how they impact the story of changing CO2, without other information. Figure 2b shows that the temperatures profiles in MODTRAN demand that heat actually be supplied as advection from lower latitudes if, for example, the subarctic winter model is to have real meaning.
Our understanding of feedbacks in RCE, as reference [1] states, really only clearly involves the “R” part and “C” becomes conjecture.
Figure 2a and 2b.
An occasional contributor to threads on WUWT has taken an interesting, and in my view clever, approach to the “C” part of RCE. I don’t wish to speak for, or identify, this correspondent, but they might volunteer to provide a link to their work, making it visible to readers. In lieu of that, I’ll summarize what I view as pertinent.
Figure 2 implies that radiative transport grows kind-of linearly as the other, unspecified means of transport diminish with altitude. Assuming that the other transport is entirely heat transported vertically from the local surface to space through material motion, a total transport equation from the Schwarzschild equation plus a convective contribution is then written in a parameterized form. A term such as λ = A∗(1 + Bx), with A and B as constants, represents a characteristic length for radiation absorption/emission – greater by a factor (1+AB)/A at the tropopause (x=1) than at the surface. This λ factor multiplies the Schwarzschild transport terms. A term such as κ = C ∗ (1 − Dx) multiplied by temperature gradient, describes the decline with height of convected (sensible plus latent) heat.[6] The numerical solution is via a variational method.
The approach is not without some limitations. First, it makes no allowance for advected heat. Second, it uses a linear gradational gray atmosphere model; whereas the real atmosphere differs from this because water vapor is so concentrated near the surface. Third, it makes no explicit allowance for the work done against the surrounding atmosphere in vertical motion, although I suspect that this third shortcoming is mitigated to some extent by choice of C and D. Nevertheless, despite these shortcomings, a couple of pertinent conclusions arise.
First, the 1-D RCE model produces not a constant lapse rate, but one varying systematically from surface to space. As the correspondent says “While lapse rate variations with altitude might seem testable, actual plots appear visually linear and suggest otherwise.”
Second, small perturbations to λ, k, and surface temperature produce sensitivity values lower than what one would surmise by using MODTRAN and the invariable lapse rate as a calculator.
Interesting!
What about Radiative/Advective Equilibrium (RAE)?
Once again we are not necessarily speaking of equilibrium, but rather just heat transport by radiation and advection. The Caballero and Merlis paper’s focus is on this issue. This paper describes the construction and testing of a very simple model of the north polar heat transfer. The authors say that warming of the poles in response to global forcing is not fully understood and that this
“…motivates interest in developing a minimal model of RAE that robustly captures
the basic physics of high-latitude climate, as a counterpart to single-column RCE for lower latitudes…”
Note, in particular, an implied dichotomy here between an RAE model for polar regions and an RCE model for lower latitudes. I’ll make some comments about this dichotomy later, but for now I will focus on a critique of the content of the paper.
In order to fully model heat transport, one would need a simultaneous solution to several differential equations. The principle one is a statement of the First Law of Thermodynamics. Let’s state this in English rather than mathematics.
We are interested in changes in internal energy of a parcel of air, which comes about through
a summation of 1) radiative transport (Schwarzschild), plus 2) bulk material transport (3-D dot product of material velocity and temperature gradient), plus 3) a diffusion term to smooth the stark temperature gradients (frontal features) that bulk transport alone produces, and finally 4) heat sources and sinks.
There are several challenges to an effort based on this complex set of partial differential equations. First, the least onerous problem is there being a dominating effect on vertical mass transport of the parcel working against the surrounding atmosphere. This suggests that two different but related temperatures are involved; absolute temperature for category 1 and potential temperature for categories 2 and 3.
Second, the more difficult problem is the need for a 3-D velocity. This means that one cannot produce a First Law statement of an RAE model from just a vertical sounding. One requires a reasonable solution over a 3-D domain. This problem is recursive, drawing in progressively larger regions, and soon one is faced with the prospect of a global climate model run innumerable times to fully populate a sort of factorial experiment with results.
What the authors sought instead was a very simple model that captures the essence of energy transport in the Arctic, but which can provide large numbers of simulations with modest resources and good fidelity.
The simple way to accomplish this was to produce a latitude limited model with a single boundary at the arctic/midlatitudes transition, and employing only an energy balance equation. In effect, the Arctic is represented by a single vertical column. The single boundary condition could be made constant in order to perform numerical experiments on internal processes in the Arctic, or manipulated to perform numerical experiments on factors external to the Arctic. The article goes on to establish validity of the model by comparison with reanalysis and global climate model results. Finally conclusions regarding how various forcings and perturbations expected in the future will affect Arctic climate. Those interested in details can consult the open source paper for details.
I am not endorsing the product that resulted. The authors’ goal was to explore Arctic climate change by the usual forcings: change to surface heat, change to CO2 concentration, change to specific humidity, with the advective forcing added as something new. My hope was different. I hoped to see advective heat transfer added as a global feedback in its own right. Mine wasn’t met.
The dichotomy of RAE and RCE based on latitude specific boundaries is not consistent with this hope. Figure 3 shows why.
Figure 3. Heat surpluses/deficits on average over a year on Earth and the implied advective heat transport that a steady climate then requires. [7]
It is obvious that with a surplus of energy input to the tropics and deficit at the poles, RCE alone without advection would lead to increasing tropical temperatures and declining polar temperature. Advection is a global phenomenon, and figuring how it will change with CO2 additions seems pertinent.
My second concern is with limiting analyses to a latitude range, justified by the authors by reference to other work showing …
“…that while the poles respond strongly to forcing applied in lower latitudes, the opposite is not true: midlatitude temperatures are, to a first approximation, unaffected by polar forcing….”
Figure 4 shows a sounding from Dallas-Fort Worth. A Texan I heard once said, “They ain’t nothin’ between Texas and the North Pole, but a barb’ waar fence.” The relevance of this statement to Figure 4 should be obvious. Flows of fluid, air and seawater, into polar regions have to be mass balanced by flows in the opposite direction. Figure 4 shows the consequence of such a flow. Surface temperature in Figure 4 is -17C and from the dew point values the mixing ratio is less than 0.8g/Kg decreasing upward. Normal values of mixing ratio at this season are two to four times higher. Polar air mass has produced significant effects far south of this putative subarctic/midlatitude boundary.
Figure 4.
The so-called surface radiator fin
Caballero and Merlis identify a significant polar cooling mechanism that they say depends on an atmospheric profile like that in Figure 4. A cold surface with a temperature inversion and dry air above it can radiate freely to space because the atmospheric window of IR thermal radiation is open. The atmosphere can exchange energy through both radiation and diffusion with the nearby surface, and the surface, which approximates a blackbody, then radiates to space efficiently through the window.
Never mind that this isn’t what fins do or how they work[8], this same mechanism or some small variation of it works globally. In fact, even if the temperature inversion is not initially present, the presence of dry air and a wide open atmospheric IR window will produce it. Figure 5 shows a late summer example at Santa Teresa, New Mexico; a locality and situation similar to what I presented in this essay. Overnight there has been a systematic cooling of the air column below 730mb and development of an inversion because of the presence of the radiating ground below – the mixing ratio isn’t even especially dry, being around 10-12 g/Kg near surface.
Figure 5
While Figure 4 showed an unusually severe example of the southward flow, Figure 6 shows that shallow domes of polar air flow during winter deep into the tropics. These not only absorb heat along the way, but because of their relatively dry surface air, they also open the atmospheric window to IR radiation directly to space.[9]
Figure 6. Two instances of mobile polar highs penetrating deep into the tropics. I modified this only slightly from the original by shading land areas to make the paths of travel more clear.
Finally to place these into a clearer heat transport context, Figure 7 shows a numerical simulation of Rayleigh-Benard convection which is the prototype model of natural convection. The lower boundary is heated. The upper boundary cooled.
Note that the fluid motion in this instance involves not a smooth, regular overturning of the fluid, but rather consists of discrete blobs of fluid – red ones rising and blue ones sinking. The appearance of blobs versus smooth overturn is a function of the Rayleigh number which in this example is Ra=108, which is far above the onset of fluid overturn.
In the context of the midlatitudes atmosphere, the blue blobs are mobile polar highs gliding equatorward along the Earth’s surface. The red blobs are the warm counterflow of air/moisture travelling poleward in slant convection or some other mechanism that lofts and bulldozes air to higher latitudes. The mobile polar highs take relatively cool air that can absorb some heat and moisture in the midlatitudes and even into the tropics, but more importantly they take with them dry surface air that presents an open IR window in places where one doesn’t otherwise exist.
Figure 7. Numerical simulation of Rayleigh Benard convection. Image from Lappa, Marcello. (2019). On the Nature of Fluid-dynamics. Uploaded to Researchgate by Marcello Lappa.
Conclusions
The effort of Caballero and Merlis, which initiated this essay, failed to produce what I had hoped primarily because their goal was, as usual, demonstrating how CO2 can make the polar regions warmer. Because of this they stopped short of a worthy goal. That goal is to quantify how the resulting warmer polar regions will take heat from the surface to space because a warmer surface radiates more heat via the Stefan-Boltzmann feedback and does so in the driest portions of the atmosphere with a wider atmospheric window.
Advection not only moves heat over the Earth’s surface to where it can travel more easily from surface to space, but the very dry air in the counterflow of cA and cP masses that polar regions produce open the atmospheric window to space along journeys to warmer regions. Global advection deserves more attention than it has received to date.
References and Notes
1-Caballero and Merlis, Polar Feedbacks in Clear-Sky Radiative–Advective Equilibrium from an Airmass Transformation Perspective, Journal of Climate, V 38, p. 3399, 15 JULY 2025
This paper begins thusly, which was my motivation for this current essay.
“The concept of radiative–convective equilibrium (RCE) and its embodiment in a single-column model (Manabe and Strickler 1964; Manabe and Wetherald 1967) are the foundation of our understanding and quantification of climate sensitivity.”
2-internal energy equals heat capacity at constant volume times temperature plus some arbitrary reference value. Heat capacity is a function of temperature as more degrees of freedom become available at higher temperature, thus more ways a molecule has to store energy.
3-focussing on the parcel of atmosphere as our thermodynamic system, the sign convention of mechanical engineering is that heat added to the parcel is positive (thus heat subtracted is negative), while work the parcel does on its environment is positive. Writing the First Law of Thermodynamics as an equation in small quantities; δU = δQ – δW; where U is internal energy. Physicists and chemists more generally reverse the sign convention for work.
4-The version I use is available at University of Chicago. I know of only one other version which seems to have all the same limitations.
5-Timothy J. Schmit, et al, 2017, A Closer Look at the ABI on the GOES-R Series, Bulletin of the American Meteorological Society, 01 Apr 2017, p. 681-698.
DOI: https://doi.org/10.1175/BAMS-D-15-00230.1
6-Heat transport by moving fluid is always represented mathematically by a term something like a dot product (vector inner product) between the vectors of fluid velocity and temperature gradient. Thus, the convection as a parameterized velocity (k term) and vertical temperature gradient is appropriate in this 1-d RCE formulation. However, the presence of positive work output of a parcel as it rises suggests that potential temperature is more appropriate.
In a 3-d model the horizontal advection of heat at any height would involve a term like V·∇T; where V is the horizontal velocity vector, ∇ is the horizontal gradient operator (Grad of div, grad, curl fame) and the middle dot represents the horizontal dot-product. The vertical component typically uses omega as the velocity unit.
7-Adam Showman, J. Y-K. Cho, Kristen Menou, 2009, Atmospheric Circulation of Exoplanets, https://www.researchgate.net/publication/45884771; see for example equations 5a through 5e. Note that 5e has the advective/convective terms separated with the convective term written in terms of omega (vertical velocity in pressure coordinates). Omega is much smaller than the horizontal components, and to try to find it through observations by using 5c renders it mostly in error.
8-”Radiating fins” work simply by providing a low conductance path for heat into a broad region where the heat can be disposed of by fluid convection. The typical fin geometry makes a poor true emitter of radiation because each fin has a large view of others at the same temperature.
9-Leroux, M, 1993, The Mobile Polar High a new concept explaining present mechanisms of meridional air-mass and energy exchanges and global propagation of palaeoclimatic changes, Global Planet Change, 7 69-93
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Advection is the horizontal component of the global convective overturning system.
As I have set out previously over a period of many years both here and elsewhere it is the phenomenon of convective overturning of atmospheric mass that raises temperatures above the level predicted from the S-B equation.
The so called greenhouse effect is a product of convection and not radiative gases.
Where radiative material of any sort is present in an atmosphere the speed of overturning will vary to neutralise any thermal effect.
In relation to our emissions the necessary variation would be too small to measure.
Someday, we are going to have to have this dispute out in full. I don’t know that WUWT is the right format for such a debate, but you do know that you and Nick Stokes are arguing for the same thing, do you not?
Nick says that the effect of convective overturning is to raise the surface temperature. See, for instance, https://wattsupwiththat.com/2024/05/28/of-heat-engines-an-addendum/#comment-3917501
I don’t wish to pick on Nick, in this instance, but for him to say that overturning is heating the surface starts the analysis too late. He neglects that the turbulence (KE in the atmosphere) which provides the work input to his putative heat pump, came from thermal convection in the first place.
You are claiming the same. There is a deus ex machina in what you claim, as it seems to me your claim borders on a perpetual motion machine of the first kind.
I don’t think you or Nick get the point.
There is no ‘machine’ perpetual or otherwise.
You both seem to forget that only half a sphere is lit and heated at any given moment.
Warm air on the lit side rises and cools as it does so. The potential energy (PE) thus formed advects towards the night side and the poles where it sinks and warms.
The pattern is all jumbled up between the lit and unlit sides by rotation which leads to the formation of discrete Hadley, Ferrel and Polar cells.
The net effect is that some of the surface KE on the lit side is prevented from radiating to space from the ground because PE cannot radiate away.
Only when it descends again on the unlit side can PE revert to KE and get radiated away.
It is the time taken for the cycle to complete that slows energy loss to space which thus increases system energy content for a net surface warming effect.
The potential energy in the atmospheric gases originally formed when the gases first became suspended off the surface against the downward force of gravity.
All that then happens is that differential surface heating creating density variations recycles KE to PE and back again for as long as there is an atmosphere.
No extra energy is added or removed.
The same principles apply for every liquid or gaseous material in a gravitational field wherever situated and at every scale throughout the universe because heating is never evenly distributed.
“The net effect is that some of the surface KE on the lit side is prevented from radiating to space from the ground because PE cannot radiate away.”
It is quite possible to radiate PE away as long as there are IR active gasses that can radiate within the thermal band. On Earth, as a column of air radiates during the night it shrinks vertically because it cools — its specific volume decreases. This goes on most clearly in the zone of general subsidence at the confluence of the Hadley and Ferrel cells where the upper/middle troposphere is so dry that there is a very wide and open window for radiation to space within the thermal band. Lindzen refers to this as part of his “iris” hypothesis.
I agree with you regarding how heat would be carried by convection on a non-rotating planet lit on only one hemisphere.
IR active gases in rising air only radiate away the KE that has not yet been converted to PE in uplift.
IR active gases in falling air only radiate away the KE that has been converted from PE in descent.
Atmospheric PE cannot be radiated away and remains constant for every planet with an atmosphere of given mass because it is needed to keep the atmosphere permanently suspended off the surface against the downward force of gravity.
Where the air is very dry or otherwise lacking in radiative characteristics then the wide and open window is from surface to space rather than from within the atmosphere.
As a column of air (or rather the radiative material suspended in it) radiates during the night the parcel of air cools and shrinks in all directions becoming denser and thus heavier so it sinks to a lower level. During the sinking process it warms up due to reconversion of PE to KE so radiation from the newly formed KE continues so that it continually cools and sinks and re-warms progressively until it reaches the ground.
It is an adiabatic fully reversible process with no energy added or removed.
It is driven entirely by density differentials in the horizontal plane and is universally inevitable for any unevenly heated gas or liquid or even a solid if the forces are strong enough held within a gravitational field.
The process is present in stars, black holes, giant gas planets, galaxies and probably the entire observable universe as a whole.
It even applies to mobile solids such as the Earth’s mantle.
Any substance that can be moved internally under the force of gravity follows the same convective process.
The more mass that accumulates the higher the temperature rises because there is more PE locked into the process.
The greenhouse effect is simply the thermal manifestation of the presence of PE within a gravitational field.
You are speaking of a hydrostatic state, and it can be radiated away because atmospheric profiles contract toward the surface while radiating, thence cooling. This sort of cooling and local strinkage is what produces “availability” to convert PE into work; That is it produces variations in PE from one locale to another. Don’t confuse PE with availability ’cause they aren’t strictly the same thing.
If energy isn’t added or removed, then how do you handle dissipation? Dissipation occurs in all real flows — plenty occurs in the atmosphere. Moreover, then how would convection transport heat without energy being added in one part of a cycle and removed in another?
Finally you cannot move material in a cycle with only gravity. Gravity is a conservative force and returns to its original state over a cycle. To make a cycle move you have to have a dissipative process involved. There is no other way. Heat will not “just accumulate”. A spontaneous process has to involve an increase in entropy.
A heat engine!
Transformation of energy between KE and PE creates density differentials.
Within a gravitational field that is enough to create convective overturning because of the differences in weights.
I must have caused a kerfuffle somewhere because there has been a sudden rush of downvotes, presumably from the climate alarmist camp.
The 1967 Manabe and Wetherald climate model is a one dimensional radiative convective (1-D RC) model with a 9 or 18 air layer radiative transfer algorithm that includes the IR absorption/emission of H2O, CO2 and ozone, O3, the near IR (NIR) solar absorption of H2O and CO2 and the UV absorption of O3. Considering the limited spectral data available in the mid 1960s, this radiative transfer algorithm was quite reasonable. Unfortunately, it was sandwiched between two unrealistic mathematical boundaries. The surface was a partially reflecting blackbody surface with zero heat capacity. The solar flux at the top of the model atmosphere (TOMA) had a fixed average value for each model run. The vertical temperature profile was constrained so that the magnitude of the lapse rate did not exceed 6.5 degrees K (or C) per kilometer. In addition, the relative humidity (RH) profile was fixed. When the temperature increased in the model air layers, so did the absolute water vapor concentration.
When the CO2 concentration was doubled in this model, from 300 to 600 ppm there was a small decrease in the outgoing longwave radiation (OLR)returned to space of approximately 4 watts per square meter. This is now called a radiative forcing. This forcing was not used directly in the model. Instead, the model was guided to a steady state ‘equilibrium’ using a time step integration algorithm until the energy flow reached an exact balance at TOMA and the air temperatures were stable.
The radiative transfer algorithm was used to calculate the net LWIR heating flux at each air level in the model. The net LWIR fluxes were divided by the local heat capacities to determine the rate of heating for each level in the model. These heating rates were multiplied by the eight hour time step used in the time integration algorithm to determine the temperature increases. These were added to the existing air layer temperatures to gets a new set of model temperatures. The water vapor concentrations were then adjusted for the new set of temperatures. This process was repeated iteratively until the model reached a steady state. The model required approximately one year or 1100 eight hour time steps to reach the new steady state. For a CO2 doubling, the model created a surface warming of 2.9 °C as a mathematical artifact in the calculation.
In the real world, the surface temperature is changing with the daily and seasonal temperature cycles. The humidity is also changing. In the troposphere at low and mid latitudes, the total cooling rate produced by net LWIR emission is between -2 and -2.5 °C per day [Feldman et al, 2008]. A doubling of the CO2 concentration from 300 to 600 ppm produces a maximum decrease in the LWIR cooling rate or a slight warming of +0.08 °C per day [Iacono et al, 2008]. This is too small to measure and does not accumulate over time. For a lapse rate of -6.5 °C per km, an increase in temperature of +0.08 °C is produced by a decrease in altitude of approximately 12 meters. This is equivalent to riding an elevator down four floors. This is the real warming produced by a CO2 doubling in the troposphere. The small amount of heat released in the troposphere by an increase in greenhouse gases (GHGs) is radiated back to space as wideband LWIR emission, mainly by water vapor. There is almost no change to the energy balance of the earth.
Some form of time integration algorithm has been used to create the GHG warming in all of the climate models since they were first developed in the 1960s. At present the average annual increase in atmospheric CO2 concentration is near 2.5 parts per million (ppm) per year. This produces an increase in the emission downward longwave IR (LWIR) radiation from the lower troposphere to the surface of approximately 40 milliwatts per square meter per year (40 mw m-2 yr-1). It is impossible for this small increase LWIR energy to produce a measurable increase in surface temperature. Nor can it cause any change in the frequency or intensity of ‘extreme weather events’.
For further details see the paper A Nobel Prize for Climate Modeling Errors.
And OLR has increased, despite higher levels of CO2, right?
Harold The Organic Chemist Says:
CO2 Does Not Cause Warming of Air
Shown in the chart (See below) is a plot of the average annual temperatures in Adelaide from 1857 to 1999. The chart also shows there was a slight cooling since 1857. In 1857 the concentration of CO2 in dry air was ca. 280 ppmv (0.55 g CO2/cu. m.) and by 1999, it had increased to ca. 370 ppmv (0.73 g CO2/cu. m.), but there was no corresponding increase in air temperature. The reason there was no increase in air temperature is that there is too little CO2 in the air to absorb out going long wavelength IR light to cause heating of the air.
In 1999 the average annual temperature in Adelaide was 16.9° C when the concentration of CO2 was 370 ppmv. In 2024 the concentration of CO2 was 424 ppmv (0.83 g CO2/cu. m.), and the average annual temperature was 17.4° C. Although there was a modest increase in the concentration of CO2 of 13%, the increase in temperature was only
0.5°C or 3% In summary the empirical data shows CO2 has no effect on air temperature in Adelaide.
NB: The chart was obtained from the late John Daly’s website:
“Still Waiting for Greenhouse” available at: http://www.john-daly.com.
John Daly found over 200 weather stations located around the world that
showed no warming up to 2002. From the home page, page down to the end and click on “Station Temperature Data”. On the “World Map”, click on
“Australia”. There is displayed the temperature charts for the cities of Australia.
The temperature data for Adelaide from 2000 to 2024 was obtained from:
https://extremeweatherwatch.com/cities/adelaide.
This new website has search function that obtains and displays temperature and climate data form cities and from any site in the world that are in NOAA’s data base.
NB: If you click on the chart, it will expand and become clear. Click on the
“X” in the circle to return comment text.
A really good summary, Roy. Thanks for taking the time to discuss it. As you say,
Sometimes the entire physics of a problem is in the boundary conditions. In this case there is so much going on in the region from 10cm below the surface to 10m or even more above the surface on a daily cycle, that one could despair of ever getting all the physics done right — try reconciling what a downward facing pyrgeometer measures against 2m air temperatures for instance.
Then, as I have said in commentary here, the upper boundary ranges over an enormous vertical distance. I live at 2200m AMSL and the cold of space is never far away. It may reach near 80F at midday at the surface here in October, but even before the Sun sets the temperature is dropping fast and may go into the high 30sF before dawn. Forget about an imagined surface at 10km above the ground, we are part of the real upper boundary at 2.2km.
Rarely talked about is the rate and height at which clouds can form, a warm day can produce thunderheads within hours…..Our planet 70% ocean covered plus snow and rain. At altitude the planet is also about 65% cloud covered (coincidence?)
Thus, more than 70% of local temperature increases are accompanied by water vapor increase (lets’s say 7% per degree at 15C) immediately above the wet surface. This causes fairly significant buoyancy of the humid air…which forms clouds when lofted to cooler highs due to the lapse rate and resultant condensation.. If the clouds form at low level, they are generally white and fluffy with a high albedo….which reflects more incoming sunlight to outer space, plus the lower the top of cloud level is, the more IR that the cloud tops send to outer space through the 8-14 micron atmospheric window.
Any temperature increase above wet or moist surfaces causes this water vapor generation effect. Cloud tops emit many watts of IR to outer space and the height and thus emission temperature depends on the H2O vapor generated at surface and the convected upward (and how much mixing it experiences).
Doubling of CO2 is 3 or 4, or 6 watts depending on whose evaluation you choose…but pales into insignificance when one considers how a little extra surface warmth causes more SW and LW to be sent to outer space by the clouds that must inevitably result. This means that Earthly warming caused by CO2 is going to have much less effect than is generally calculated without considering clouds having an active quick response effect on the system.
Thank you for introducing “clouds” into the discussion. The author makes a near-fatal mistake when he talks about atmospheric “temperature”, namely: “This temperature is a reflection of its specific internal energy.” As we know, the vertical energy transport in the atmosphere is dominated by the water cycle, which transports several orders of magnitude more energy from surface water to clouds and precipitation each day than does a small temperature change in dry air. And you haven’t even mentioned the reflection of sunlight during the day and the stabilizing reflection of surface warmth at night. The internal turbulence of clouds releases energy in lightening bolts up to 500 miles long – enough energy to fry every CO2 molecule within sight! But “climate scientists” concentrate on the arithmetic average of thermometer readings, and ignore clouds – the elephant in the room!
I’m going to stop you right there. This is why Willis often asks people to quote the passage they are speaking of. In this case it is…
There is no near fatal error here as I am addressing the factors that affect temperature, and refer specifically to latent heat, which is where the water cycle impacts temperature. In vertical motion one place where this occurs is the difference between a psuedo-adiabat and a dry adiabat over the region in which water vapor is condensing. Hardly ever mentioned is the additional cooling in places where liquid water (clouds) is evaporating — like in the cold downdraft of thunderstorms.
My uneducated but functioning brain remembers that OLR had in fact increased despite the increased CO2. This runs opposite to the increased CO2= decreased OLR idea.
And it came as a surprise to many.
Anything wrong with this?
Yes, per se more CO2 means less OLR. However that is a temporary or transitional thing, with the resulting warming bringing OLR back up.
The increase in OLR is a) due to less clouds, something that consensus science blames on the reduction of pollution and b) a decrease in albedo, meaning more energy absorbed but also more emitted.
Your functioning brain indeed remembers correctly that climate alarmists have continually had to ‘move the goal posts’ as actual data has undermined their ‘canonical narrative’.
Of course. It’s devastating to “the narrative,” and is therefore to be ignored./sarc
You know, like the GLACIATION the Earth experienced with *ten times* today’s atmospheric CO2 levels.
Observations TRUMP theory. (Love that one!)
“An increased concentration of CO2 in the atmosphere makes the atmosphere more opaque to outgoing infrared radiation from the surface.”
It also makes the atmosphere more opaque to incoming IR radiation from the sun at the CO2 frequency. You can’t have one without the other. There’s no one-way filter in the atmosphere.
“according to the Stefan-Boltzmann law this amounts to a reduction in outgoing radiation by about 4W/m2 (236.3 = σ 2544). There is an energy imbalance that warms the entire atmosphere and surface.”
Part of the problem here is that S=B requires an opaque object with a well-defined surface. Gases do not provide this. The radiation from a gas is emitter quantity dependent. The more emitters per volume the higher radiation from a given volume. The more CO2 you add the more emitters you add.
You just can’t simply relate the S-B intensity at a specific temperature to the radiation from the atmosphere. I’ve never seen this relationship between an opaque object with a defined surface vs the radiation from a gas investigated by climate science. Climate science seems to just assume that S-B works the same for both.
Very little of the sun’s energy is coming in on the bands that are absorbed by CO2, whereas a lot of the outgoing energy from the Earth is on those bands.
Which does not address the fact that the gases don’t follow the S-B relationship. And it *all* adds up, even the small contribution at CO2 frequencies from the sun.
It doesn’t take much absorption to see 2 – 4 w/m². That’s what about 3/1370 ≈ 0.2%
““An increased concentration of CO2 in the atmosphere makes the atmosphere more opaque to outgoing infrared radiation from the surface.”:
Only in a thin weak band. As shown further up, that tiny amount of absorbed radiation is transferred to other bands.
Enhanced CO2 in the atmosphere is like a thicker grade of copper to electrical current.
It is not “despite”.. it is “because of”
CO2 acts as a conduit to transfer radiation to other bands. (As Tom Shula explains in his excellent podcast video)
We see that from measured data, where the increase of CO2 gives slight drop in OLR in that frequency range, leads to a much broader increase in OLR in the adjacent band.
Great chart! What is the source?
More importantly, H2O accounts for almost all of the absorption of surface radiation and emission of radiation to space.
Nice essay. Nice to see the terms gradient and diffusion used to describe the atmosphere. Figure 7 reminds me of what would be a large lava lamp. Equilibrium would never occur and gradients would be required.
“Equilibrium would never occur…” Yes, people seem to confuse the idea of “equilibrium” with a distinctly different concept of “steady state”; then the confusion is compounded further by imagining an “averaged” steady state.
The resident alarmists like to invoke ‘LTE’ a lot. I’ll throw out some chum here to see if any of them surface…
https://scienceworld.wolfram.com/physics/LocalThermodynamicEquilibrium.html
It is nice to see a correct depiction of the GHE here, like the from HS2000. However, there is a little problem with that depiction concerning additional CO2 forcing.
That is based on a wrong assumption on where the 3.7W/m2 come from. As in Myrrhe, Stordal 1997, it is the sum of “fluxes” at the tropopause, about 2.4W/m2 less up, and 1.3W/m2 more downward. Obviously you can not translate the significant share of the downward part into an elevation of the emission altitude. At best you could do this with the tropospheric share of 2.4W/m2, which would then only translate into Ze+90m. MS97 were simply not aware of what CO2 forcing actually is, or how it is derived within the model world respectively.
If have discussed this more profoundly here..
Equally this statement is not true..
You might incidentally get a similar value, but that would be without clouds, which eventually have to be taken into account and will reduce that figure about 1/3. So a 3.6W/m2 will turn into 2.4W/m2, as named above.
Good points, Kevin.
Referring to Figure 3, “Advection is a global phenomenon, and figuring how it will change with CO2 additions seems pertinent.”
Agreed. The spare LW emitter duty is toward the poles. By “spare” I mean that the LW emission to space is maxed out near the equator, but the remainder of the spherical surface is not emitting anywhere near those maximum values. A few years ago I downloaded the CERES SYN1deg hourly values for LW emission for the entire globe. I generated these time-series plots of latitude-ring mean observed LW values to see for myself how this works. The data is for the year 2020.
https://drive.google.com/drive/folders/1aeDEbZXBKj_gDbUx2MCq13dzQG66xWhd?usp=sharing
One implication is that it is absurd to talk about global EEI values in hundreds of milliwatts per square meter, when the global overall emitter performance depends so much on advection. The valid null hypothesis should have been that any minor radiative influence from incremental CO2 would not be detectable from space, nor could it be reliably isolated as a cause of, say, reported ocean warming. That null hypothesis has not been falsified.
One other point. NASA knew very well in 2009 that poleward advection in both ocean and atmosphere circulations matters to the disposition of ALL energy absorbed from the sun. That is a key part of my essay posted here at WUWT in May, 2022.
https://wattsupwiththat.com/2022/05/16/wuwt-contest-runner-up-professional-nasa-knew-better-nasa_knew/
Good points, also, DD. I see you got a favorable mention at the Pragmatic Environmentalist of NY recently. Good of you to take the time to produce a comment. The regulatory bodies need more of this, even if they simply ignore what you have to say.
Thanks for noticing. Roger Caiazza is doing terrific work. I don’t know how he keeps up with it all, but what a contribution he is making!
Those plots of OLR are extremely interesting, but there is so much to ponder that they’ll some time to digest. There is some counterintuitive observations.
Good points, Kevin.
Referring to Figure 3, “Advection is a global phenomenon, and figuring how it will change with CO2 additions seems pertinent.”
Agreed. The spare LW emitter duty is toward the poles. By “spare” I mean that the LW emission to space is maxed out near the equator, but the remainder of the spherical surface is not emitting anywhere near those maximum values. A few years ago I downloaded the CERES SYN1deg hourly values for LW emission for the entire globe. I generated these time-series plots of latitude-ring mean observed LW values to see for myself how this works. The data is for the year 2020.
https://drive.google.com/drive/folders/1aeDEbZXBKj_gDbUx2MCq13dzQG66xWhd?usp=sharing
One implication is that it is absurd to talk about global EEI values in hundreds of milliwatts per square meter, when the global overall emitter performance depends so much on advection. The valid null hypothesis should have been that any minor radiative influence from incremental CO2 would not be detectable from space, nor could it be reliably isolated as a cause of, say, reported ocean warming. That null hypothesis has not been falsified.
One other point. NASA knew very well in 2009 that poleward advection in both ocean and atmosphere circulations matters to the disposition of ALL energy absorbed from the sun. That is a key part of my essay posted here at WUWT in May, 2022.
https://wattsupwiththat.com/2022/05/16/wuwt-contest-runner-up-professional-nasa-knew-better-nasa_knew/
Unintended duplicate. No idea why.
These things happen. Fyi, I ‘upvoted’ both of them.
That’s the way — vote early and often!
Uncanny…… and you were correct both times !! 🙂
I didn’t see any discussion about heat transfer via the atmospheric water cycle and associated convection. I’m of the opinion that Willis Eschenbach is right in that thunderstorms have a significant role in transporting heat from the surface to the upper atmosphere and then radiated to space. On the other hand, modeling thunderstorms is not an easy task.
By “correspondent” I am referring to pdquondam.net who has shown some parameterized solutions of the heat transfer equation including both radiation and convection. His efforts are well worth the time to read.
I believe Kevin has referred to my public Notebook (pdquondam.net). I might add that, in Thermal_Dissipation_V, I’ve offered a 3-D minimum dissipation theorem for a closed surface with arbitrary thermal contacts provided the order in which contacts are made is irrelevant, i.e. path independence. Qualitatively, Nature prefers steady states moving energy from A to B by paths taking the least work (dissipation). Intuition might suggest 10km vertically would be more efficient than first latitudinally and then upward. Gauss’s Theorem correlates internal divergences with normal (perpendicular) surface fluxes.
Kevin,
Thank you for your summary of the Caballero and Merlis paper, which appears to be yet another text book example of what Kuhn referred to as ‘normal’ science’ – in this case attempting to shore up the failing paradigm that CO2 is the ‘control knob’ of the Earth’s climate due to the mistaken assumption that radiative transfer models accurately describe how thermal energy is conveyed through the troposphere.
Also, many thanks for providing a link to your Earth’s Energy Imbalance part II article, which includes a lively exchange of comments among those holding disparate viewpoints on the mechanism underlying this subject.
‘Because of the focus on 1-D geometry, an important question to explore is “What does an atmospheric profile, a 1-D column, tell us about heat transport surface to space?”
The short answer is that it tells us nothing definitive until it is augmented with other information. The reason for this is that any number of processes can arrive at the same atmospheric profile.’
This is excellent! The question to ask at this point is how we got stuck with radiative transfer centric models of tropospheric heat transfer? The short answer, of course, is that by assuming local thermal equilibrium (LTE), these models have been used to greatly simplify the processing of what you correctly point out is an ‘enormous amount of information’ to describe the atmosphere.
Unfortunately, the application of such phenomenological physics not only does not a priori allow for accurate predictions of the atmosphere to be made, but in fact, has provided the Left with a convenient tool with which to tear down Western civilization via their demonization of fossil fuels.
Astute!
However, the invariant gradient of 6.5K/km means the temperature at Ze+150m is lower by about 1K, and according to the Stefan-Boltzmann law this amounts to a reduction in outgoing radiation by about 4W/m^2 (236.3 = σ 254^4).
A fatal flaw so often repeated.
“The Stefan-Boltzmann law states that the total energy radiated per unit surface area of a blackbody is directly proportional to the fourth power of its absolute temperature.”
It does not apply to gases, especially to high altitude low density atmospheric. The lower temperature up high is primarily due to lower density, so for that reason, too, it does not apply.
This is not a comment on the article or the author. We just see too much of this unscientific rhetoric and constantly.
‘It [Stefan-Boltzmann law] does not apply to gases, especially to high altitude low density atmospheric. The lower temperature up high is primarily due to lower density, so for that reason, too, it does not apply.’
Yes, and the same goes for all other properties of thermal radiation (e.g. Planck’s Law, Wien’s Displacement Law, etc.) because gases don’t act as Black Body radiators, at least under conditions prevalent on this planet.
Except Planck’s Law, Wien’s Displacement Law, etc., deal with electro magnetic energy, not thermal radiation.
They came up with thermal radiation based on elector magnetic energy based on the temperature of a solid surface, but with the purpose of equating heat with IR.
‘Except Planck’s Law, Wien’s Displacement Law, etc., deal with electro magnetic energy, not thermal radiation.’
I ain’t no physicist, so you may well be right. if so, either ‘these guys’ are wrong or I’m misinterpreting what they’re saying:
Thermal radiation is the emission of electromagnetic waves from all objects with a temperature above absolute zero
https://modern-physics.org/thermal-radiation-spectrum/
Grateful for any clarification.
Thermal radiation is electromagnetic radiation. No difference. Different words for the same phenomenon.
Wien’s displacement law provides the peak wavelength of a blackbody spectrum as a function of temperature of the radiating surface. It’s origin is in the study of blackbody radiation even though it applies to surfaces so hot that they emit visible light.
I suppose one should specify that both Planck’s law and the displacement law were derived from observations of cavity radiation, but we often extend the domain of cavity radiation to the situation of radiation from a surface of condensed matter by applying an “emissivity” less than 1.0 that is a function of material and the surface form. Earth materials and water are close to true blackbodies as their emissivity is in the neighborhood of 0.97, as Modtran models them.
“Blackbody” may come from a perfect emitter also being a perfect absorber which would look black. The “cavity radiator” comes from a small hole to a much larger cavity looks black. A perfect blackbody would have a surface resistance of 377 ohms per square, which matches the impedance of free space.
It’s why trying to calculate the surface temperature from the radiation intensity to space is doomed for failure. There isn’t a direct relationship.
Not to mention that much of the IR radiation ‘seen’ by satellites in space doesn’t originate from the surface. However, while I’m thinking about it, I once asked a contributor here if the so-called GAT couldn’t be measured using IR from within the atmospheric window. While I know water vapor has some impact therein, it seems like it would be better to do that than to continue screwing around with the surface thermometer record.
I just posted the same thing. I hadn’t gotten all the way through the thread so I duplicated your post.
The S-B theory requires an opaque object with a defined surface. This doesn’t apply to gases. For gasses the radiation is emitter per volume dependent. More CO2 means more radiation per volume.
The limiting of the lapse rate to a maximum of 6.5K/km is one of the many “not-on-this-planet” and un-scientific things in the climate models.
6.5K/km is the average, not the limit…
… the limit to the natural lapse rate is 9.8K/km in the absence of moisture eg over deserts, poles etc.
Averaging non-linear processes is great way to end up with absolutely wrong answers.
This is not the author’s work. I am quoting others who use this argument to explain the GHE.
Words matter.
“thermal IR radiation”
Thermal radiation involves the kinetic energy exchange due to molecular collisions (in the atmosphere). IR radiation involved electro magnetic fields and waves.
They are not the same as discovered by Eunice Foote in 1850.
This is not a comment on the article or the author. We just see too much of this unscientific rhetoric and constantly.
Thermal IR is a particular band that runs generally from about 8um to 14um for thermal imaging cameras, or 4um to 50um wavelength if we are speaking of pyrgeometers.
Harold The Organic Chemist Says:
RE: The Greenhouse Effect
RE: Greenhouse Gases: H2O vs CO2
At the Mauna Loa Obs. in Hawaii, the concentration of CO2 in dry air is currently 425 ppmv. One cubic meter of this air has a mass of 1.29 kg and contains a mere 0.83 g of CO2 at STP.
In air at 70° F and 70% RH, the concentration of H2O is 17,780 ppmv.
One cubic meter of this air has a mass of 1.20 kg, and contains 14.3 g of H2O and 0.77 g of CO2. To the first approximation and all things being equal, the amount of the greenhouse effect (GHE) due to H2O is given by:
GHE=moles H2O/moles H2O+moles CO2=0.79/0.79+0.017= 0.98 or 98%
This calculation assumes that a molecule of H2O and molecule of CO2 each absorb about the same amount of out-going long wavelength IR light. Actually, H2O absorbs more IR light than CO2 in far IR.
Shown in Fig 7. (See below) is the infrared absorption spectrum of a sample of Philadelphia inner city air from 400 to 4000 wavenumbers
(wns). There are additional peaks for H20 from 400 to 200 wns which are not shown since the cut of the FT IR spectrometer is 400 wns. The GHE active range is from 400 to 700 wns. Note how small and narrow the CO2 peak is and the many peaks there are for H2O. Please keep in mind that 71% of the earth’s surface.
The above empirical data falsifies the claims by the IPCC that CO2 causes “global warming” and is the “control knob of climate change”. The
purpose of these claims is to provide the UN the justification for the distribution of funds, via the UNFCCC and the UN COP, to all the developing (i.e., poor) countries to help them cope with alleged harmful effects of global warming and climate change.
After EPA Administer Lee Zeldin rescinds the 2009 CO2 Endangerment Finding, the greatest scientific fraud since the Piltdown Man will finally come to an end and all the radical environmental NGO’s will go bust.
PS: Fig. 7 was taken from the essay: Climate Change Reexamined by
Joel M. Kauffman. The essay is 26 pages and can be down loaded for free.
NB: If you click on Fig. 7, it will expand and become clear. Click on the “X” in the circle to return to comment text.
The equation shows 1 + 0.017 = 1.017, or are parentheses missing?
Each H20 molecule absorbs photons of many energies, including at 15 micrometer
Each CO2 molecule absorbs photons mainly at 15 micrometer
If all photon energies are added, H20 absorbs about 3 times the energy of a CO2 molecule, plus H20 is many times more abundant than CO2, especially near the surface.
Parentheses are missing.
Why no comment about the UN’s grand plan for the redistribution of wealth from the rich countries to the poor countries? This is what this rhetoric regarding greenhouse emissions from fossil fuels and climate is really about.
The budgets for these UN organizations are now many billions dollars. President Trump will end all funding for these organizations.
RE: The equation shows 1+ 0.017…
Where did you get this? Please explain.
RE : … are the parenthesis missing?
Please explain? What are they missing from?
Only the H2O peaks to the right of the CO2 peak are involved the GHE.
I finally figured out what you guys are talking about. Here is the new equation for the GHE:
GHE=moles H2O/(moles H2O+moles CO2)=0.79/(0.79+0.017)=0.98 or 98%
I thank you all for pointing out the equation was incorrect and confusing.
The IPCC has it right:
1) You assume a kg of water and a kg of CO2 have the same GWP. That’s incorrect
2) you assume water vapor contributes to global warming. That’s wrong. It contributes little or nothing because it condenses out, whereas CO2 concentration keeps increasing due to CO2 emissions from fossil fuel burning being absorbed by the atmosphere
3) you assume an avg atmospheric air temp of 70. The bulk of the atmosphere is much colder and therefore holds less water than you’ve assumed.
Most of the graph that you show is irrelevant, the Earth’s emission spectrum would cover the part from 1500-400cm-1 with the peak at 500cm-1
A most pertinent chart, though the significance will escape most. Tyndall, based on his measurements, estimated that at typical temperature and humidity the relative contribution of water vapor as an absorber/emitter relative to CO2 was 16,000:1.
When seeing a
paper like this , I do a quick search forgravity because it is most important to understand that it is the adiabatic tradeoff of gravitational & kinetic energy keeping total energy constant as required by Conservation of Energy which causes the , does it work out to , 6.5K/km temperature gradient . Gravity & mass , nothing to do w spectrum .So , ~
150m is all the greater altitude of final effective transparency to space of CO2 in its bands ?Schwarzschild ( color ) spectra of the planet from outside . I have yet to see a competent calculation of our radiative equilibrium , even as a uniform colored ball .I would like to see actual measured
Why gravity? A neutrally buoyant parcel cares not wit about gravity. The manifestation of gravity is in the pressure gradient. As parcels move vertically they must work against pressure, and without a heat exchange (adiabatic in other words) the parcel can only obtain this work from its internal energy; thus a loss of internal energy equivalent to 9.8K/km. 6.5K/km is the so-called radiative/convective equilibrium lapse rate.
If a Saturn rocket requires work to be done when lifting it thru the gravity well, why wouldn’t a parcel of air require some expenditure of work to do the same? With the Saturn, work is supplied externally, with air, the energy to accomplish the work comes from an internal source.
Since energy conversion from one form to another occurs relatively easily, when using the Conservation of Energy rule, one must be careful to identify the conversions taking place.
The parcel does require work, but it is work against the pressure of the surroundings in order to achieve its new specific volume; and it does, indeed, come from an internal source, as you point out, that source being internal energy. For every parcel of air being lifted another parcel, generally nearby, has to decend. There is no lift of mass in the case of the fluid atmosphere that is like that of a Saturn V from the surface to space.
Here is something even heavier than a Saturn V — a suspension bridge. But the cables suspending the bridge provide an upward force against that of gravity such that the bridge is statically neutral to gravity. Bridges are easy to lift, in the sense of a small, differential quantity, from their static state. It’s why suspension bridges are very lively in the wind, unless additional efforts are made to quash their most flexible modes.
Maybe another way to explain this is that the difference in pressure between the top of a parcel air and its base is, in fact, due to the weight of the intervening air. This pressure is central to atmospheric motion. There is also the same difference in pressure over the height of the Saturn V, but this is a tiny, i’d say negligible, fraction of the weight of the SaturnV. The situations are different.
Maybe I picked the wrong analogy. What I was attempting to say is that work is being done to move upward in the earth’s gravity well. Whether it is a rocket or a parcel ofair, work is required.
The work is being done because the temperature of the parcel changes. Note my explanation to Tom Shula below…
Seriously?
Indeed it does not. That the parameter “g” occurs in the adiabatic lapse rate is simply a reflection of the fact that g determines the pressure gradient in a hydrostatic atmosphere.
Even in cases of extreme upward acceleration of air/ paired with extreme downward acceleration nearby, like in a thunderstorm, the departures of pressure from hydrostatic are very small — a few parts in a thousand maybe
An interesting perspective. You must realize that a hydrostatic atmosphere is purely hypothetical, at least on this planet.
Now I’m curious what you mean when you say,
”6.5K/km is the so-called radiative/convective equilibrium lapse rate”
What is your perception of why the lapse rate is 6.5 instead of 9.8? And what is your perception of the phrase “radiative/convective equilibrium”?
I’m having a bit of trouble with LateX here, so bear with me.
A few arguments:
1) To lift a physical kilogram mass 1 km requires work equal to
but going about this using the lapse rate (use enthalpy to avoid the Pdv work)
As it should be by conservation of energy, but what the parcel experiences is a battle to expand against pressure not work to lift itself against gravity.
I am baffled by you saying the hydrostatic atmosphere is “hypothetical”. Any static fluid in a gravitational field will possess a hydrostatic pressure. At any level this pressure equals the weight of overlying atmosphere — it supports the mass above it. This is more than hypothetical it is engineering statics.
9.8K/km is the adiabatic lapse rate. As I just showed it is related to the work of raising mass or working against pressure without the addition of heat energy. It is the lapse rate of a vigorously convecting atmosphere (or a turbulently mixing one) as long as there is no heat addition during the ascent or during mixing. A lapse rate of 6.5K/km is that which allegedly obtains in a convecting atmosphere that is also free to radiate through a gray gas– I.e. combined radiation and convection. It is a fiction as I have argued here and as “quondam” shows on his pages dealing with the subject at pdquodam.net, and is hard coded into the U.S. Standard atmosphere (see MODTRAN).
I have doubts about calling this “equilibrium” because the system (radiating/convecting atmosphere) is transferring heat and is by definition then, nonequilibrium.
Atmospheric pressure is the result of the gravitational field acting on molecules in the atmosphere. Pressure is the effect, not the cause.
In a true hydrostatic equilibrium, there is no fluid motion in the direction of the applied force. The dynamics of atmospheric circulation are the result of forces that continuously try to drive the atmosphere to a hydrostatic equilibrium that can never be achieved.
Schwarzschild understood and stated explicitly that a radiative equilibrium can only occur in an atmosphere that is free of convection. He constructed a hydrostatic model of the photosphere in order to create his “radiative equilibrium.”
Manabe did not understand this. His oxymoronic “radiative convective equilibrium” was a patch which constrained the temperature to the adiabatic lapse rate in order to force
his model to match the measured atmospheric temperature. This, as you have pointed out, appears in all of the modern models like MODTRAN. All of these models are highly constrained, static boundary value problems with no dynamic components. They are fine for producing a model TOA spectrum, but ignore the dynamic microphysics of the atmosphere which are quite different.
The reduced lapse rate in the troposphere is the result of condensation of water vapor with altitude which releases sensible heat that is quickly redistributed to sensible heat pool of the atmosphere. The altitude where this is “complete” defines the tropopause.
As an aside, if you would like a better alternative to MODTRAN, NASA has an excellent online tool you can find here:
https://psg.gsfc.nasa.gov/index.php