An Analysis of the Earth’s Energy Budget

Guest post by Philip Mulholland

1. Introduction.

The following two figures, showing the principal features of the Earth’s Energy Budget, were published in 1997 by the Oklahoma Climatological Survey (OK-First) and are reproduced here with kind permission.

Fig. 1: – Radiation “Budget” for Incoming Solar Radiation (Oklahoma Climatological Survey, 1997).

Fig. 1: – Radiation “Budget” for Incoming Solar Radiation (Oklahoma Climatological Survey, 1997).

Fig. 2: – Globally Averaged Energy Budget (Oklahoma Climatological Survey, 1997).

Fig. 2: – Globally Averaged Energy Budget (Oklahoma Climatological Survey, 1997).

Both of these diagrams when combined provide detailed energy budget information for the Earth’s climate; however, their parameters are recorded as percentages of solar insolation at the top of the atmosphere (TOA). Neither diagram published by OK-First records the actual values of solar power intensity, nor is it demonstrated how they can be used to estimate the global average temperature for the surface of the Earth.

A number of assumptions must be made in order to understand how the OK-First diagrams can be used to estimate the average global temperature under an expected solar insolation radiant power intensity of *1368 W/m2, and the albedo of 0.30 used in Figure 1. *N.B. The standard NASA Earth irradiance is 1361 W/m2 and the Bond albedo is 0.306 (Williams, 2019). However, in 1997 the solar irradiance used by Kiehl and Trenberth (1997) was 1368 W/m2, and so this value is used here to give the most appropriate match to this historic paper (Fig. 3) (reproduced below with kind permission).

Fig. 3: Earth’s Annual Global Mean Energy Budget (Kiehl and Trenberth, 1997 Fig. 7).

Fig. 3: Earth’s Annual Global Mean Energy Budget (Kiehl and Trenberth, 1997 Fig. 7).

2. Filling in the Gaps.

At first sight it is clear that Figure 1 shows that 30% of the solar insolation is bypassed via albedo loss, and so only 70% of the power intensity is available to heat the planet. If we now apply the standard divide by 4 spherical geometry rule to the expected (but not yet confirmed) solar irradiance of 1368 W/m2, then the TOA power intensity will be reduced to 235 W/m2 post-albedo (as per Kiehl and Trenberth, 1997). However, and confusingly, because the percentages relate to the unfiltered TOA power intensity, it follows that the power intensity values in the OK-First diagrams are percentages of the assumed (but not yet confirmed) pre-albedo value of 342 W/m2, and so this power intensity number must be used. By this means consistency in both percentages and also power intensity values will be maintained throughout the OK-First diagrams, the elements of which are presented below in Table 1.

Table 1: Earth's Energy Budget (OK-First).

Table 1: Earth’s Energy Budget (OK-First).

The next assumption we must make is that the standard partition of energy by the atmosphere is being applied. The standard assumption is that for all energy fluxes intercepted by the atmosphere, half of the flux is directed upwards, and lost to space, and half of all captured flux is returned to the surface as back radiation and recycled. This concept is shown in figure 4 (reproduced here with kind permission).

Fig. 4: Equipartition of energy flux by the Atmospheric layer (Jacob, 1999 Fig.7-12)

Because the intercepted energy flux is being recycled this feed-back loop is an endless sum of halves of halves. It has the mathematical form of a geometric series, and is a sum of the descending fractions in the power sequence 2– n, where minus n is a continuous sequence of natural numbers ranging from zero to infinity.

Equation 1: 1/2 + ¼ + 1/8 + 1/16 + 1/32 + …. + 2-n = 1

Equation 1 describes the cumulative effect of the feed-back loop (after an infinite series of additions), where for each turn of the cycle, half the ascending energy flux is passed out to space and lost, and the other half is returned back to the ground surface and then re-emitted. It is a feature of this form of an infinite series that the sum of the series is not itself an infinite number, but in this case the limit is the finite natural number 1.

As a direct consequence of applying Equation 1 to the OK-First atmospheric model we must double the energy flux within the atmosphere, because the atmosphere retains and stores an energy flux equal to that of the total intercepted flux. When we apply the logic of the 50%:50% atmospheric energy flux partition to the OK-First analysis, then we are able to create the following table of percentage atmospheric energy recycling (Table 2): –

Table 2: Earth's Energy Budget (OK-First) including the elements of the atmospheric recycling process.

Table 2: Earth’s Energy Budget (OK-First) including the elements of the atmospheric recycling process.

Table 2 demonstrates that the power intensity experienced by the atmosphere is 128% of the incoming solar beam, and in addition the power intensity flux emitted by the surface, and directly attributable to the high frequency solar insolation, adds another 51% to the planetary energy budget. This means that the total power intensity flux that drives the Earth’s climate is 179% of the pre-albedo TOA insolation according to the OK-First diagram.

In order to justify what is clearly a contentious statement I will now apply the identical process of deconstruction to the accepted diagram of Kiehl and Trenberth, with its recorded power intensity values (Fig. 3), and compare this with the atmospheric absorption elements as listed in Figs. 1 & 2 by OK-First.

Table 3: Earth's Annual Global Mean Energy Budget (K & T, 1997) including the elements of the atmospheric recycling process.

Table 3: Earth’s Annual Global Mean Energy Budget (K & T, 1997) including the elements of the atmospheric recycling process.

Table 3 demonstrates that the total power intensity flux absorbed by the atmosphere in the Kiehl and Trenberth diagram is 195 W/m2, and that this power intensity is then doubled to 390 W/m2 by the process of atmospheric recycling, which includes recycling of both the thermals and also evaporation energy fluxes. Using the standard Stefan-Boltzmann equation to convert irradiance power intensity to thermodynamic temperature

Equation 2: T = (j*/σ)0.25

Where j* is the black body radiant emittance in Watts per square metre, then the average temperature of the Earth’s atmosphere for a total atmospheric power intensity flux of 390 W/m2 is 288 Kelvin (15o Celsius).

Table 4 below demonstrates that the total energy budget for the Earth is driven by 168 W/m2 of surface intercepted and incoming atmospheric absorbed solar insolation. This flux must be added to the intercepted and recycled atmospheric flux of 390 W/m2 (that contains the direct atmospheric solar interception of 67 W/m2) to give a planetary energy budget of 558 W/m2, which equates to a thermodynamic temperature of 315 Kelvin (42o Celsius). The surface fluxes of 1. Surface Longwave Radiation, 2. Thermals and 3. Evaporation are all losses that create surface cooling and so combine to produce the expected Surface Radiation flux of 390 W/m2, which equates to a thermodynamic temperature of 288 Kelvin (15o Celsius).

Table 4: Key Energy Budget Metrics (K & T, 1997).

Table 4: Key Energy Budget Metrics (K & T, 1997).

If at this point you are beginning to wonder why the much-vaunted back radiation has been adjusted, and why some of the returning radiant flux in the Kiehl and Trenberth diagram can be replaced with recycled energy fluxes from the descending air (returned thermals) then please bear with me.

Let us return to the OK-First diagrams (Figs. 1 & 2) now that the table of flux values has been validated using the Kiehl and Trenberth power intensity metrics and apply the same TOA input flux of 342 W/m2 used in Fig. 3 to the table of percentages created from the OK-First diagrams and displayed in Table 2.

Table 5: Suggested Earth Insolation Metrics for OK-First diagrams.

Table 5: Suggested Earth Insolation Metrics for OK-First diagrams.

This insolation power intensity flux of 342 W/m2, when combined with the published percentages of OK-First can be used to create a table of power intensity values (Table 6) and associated thermodynamic temperatures (Table 7).

Table 6: Earth's Energy Budget (inferred from OK-First). Items recorded in W/m2 relative to the intercepted solar beam.

Table 6: Earth’s Energy Budget (inferred from OK-First). Items recorded in W/m2 relative to the intercepted solar beam.

Table 7: Key Energy Budget Metrics (inferred from OK-First).

Table 7: Key Energy Budget Metrics (inferred from OK-First).

The global average surface temperature of 23oC calculated using the OK-First data is higher than that calculated by Kiehl and Trenberth. This temperature difference arises from a number of possible causes.

1. The OK-First model is using a lower Bond albedo.

2. The solar irradiance used by OK-First for the calculation of percentages is unknown but assumed to be the same number as that used by Kiehl and Trenberth.

3. The balance of energy partition fluxes within the OK-First model is different from the canonical model, and this is the most likely cause of the bias towards the calculated higher global average temperature.

3. Discussion.

Kiehl and Trenberth and OK-First, use identical concepts in the formation of their global energy budget diagrams, however both originators present their results in ways that do not clearly demonstrate the commonality or the rigor of the concepts used. In particular both sources fail to illustrate the implicit role of atmospheric mass movement in the process of energy recycling that also heats the surface of our planet. In the presence of a gravity field that binds the atmosphere to the surface of a planet, what goes up must come down. The distribution of energy fluxes in Table 3 show that for the total atmospheric energy budget of 558 W/m2 (Table 4), 63.44% (354 W/m2) is transmitted by radiation fluxes and 36.56% (204 W/m2) is carried by mass motion (Table 8).

Table 8: Relative importance of atmospheric flux transmission mechanisms (based on Fig. 3).

Table 8: Relative importance of atmospheric flux transmission mechanisms (based on Fig. 3).

So clearly mass motion is an important energy carrying process within the Earth’s atmosphere. It is critical to understand at this point that because our energy budget is formulated in terms of power intensity, if the proportion of flux carried by mass motion increases due to an increase in moist convectional overturning, then the proportion of energy transmitted by radiant processes must decrease (and vice versa), a given energy flux cannot do two things at once.

In addition, we find that because the energy budgets of OK-First and also Kiehl and Trenberth are clearly built on the equipartition of energy by the atmosphere (half up and half down), then there are only two ways that the internal energy budget of the Earth’s atmosphere can be increased.

1. The longwave surface to space atmospheric window is closed, which causes more energy to be recycled within the atmosphere.

2. The planetary Bond albedo is decreased which allows more solar energy to enter the climate system.

Issue #1 relates directly to concerns that carbon dioxide emissions increase the opacity of our semi-transparent atmosphere, and will close the atmospheric window (Fig. 5). We can test the effects of closing this window on global average temperature by using Table 3, and diverting the 40 W/m2 direct to space radiant emission into atmospheric capture and heating (Table 9).

Fig. 5: Earth’s infrared atmospheric window. (Public Open Licence reproduction)

Fig. 5: Earth’s infrared atmospheric window. (Public Open Licence reproduction)

Table 9: The impact of blocking the atmospheric window on the Earth's Global Energy Budget.

Table 9: The impact of blocking the atmospheric window on the Earth’s Global Energy Budget.

The impact of closing the Earth’s long wave emission atmospheric window is to raise the global average temperature from 15oC to 29oC (Table 10). This 14oC increase is the maximum possible temperature increase that the Earth can experience by internal energy recycling for a constant Bond albedo of 0.306.

Table 10: The Thermal Effects of Blocking the Earth's Atmospheric Window.

Table 10: The Thermal Effects of Blocking the Earth’s Atmospheric Window.

In order to further raise the Earth’s average global temperature above 29oC to form a Cretaceous hothouse world it is necessary to either increase the atmospheric mass, (thereby raising atmospheric pressure and also the boiling point of water), and/or reduce the planetary brightness by lowering the Earth’s Bond albedo. Assuming total blocking of the atmospheric thermal radiant window and also assuming no increase in atmospheric mass, then it is possible to achieve a Cretaceous global average temperature of 36oC with a planetary Bond albedo of 0.244 (Table 11).

Table 11: Cretaceous World Insolation Metrics.

Table 11: Cretaceous World Insolation Metrics.

This reduction in planetary brightness can be achieved by having a Cretaceous world with no surface icecaps, and also an increased continental surface inundation associated with a high global sea level to create a putative low albedo hothouse world (Table 12).

Table 12: Putative Cretaceous Hothouse World.

Table 12: Putative Cretaceous Hothouse World.

Replacing reflective continental solid land surfaces with a liquid surface of shallow solar energy absorbing seas means that the Earth would capture and transmit more solar energy from the tropics to the poles via the oceanographic currents of a flooded world (e.g. the Tethys Ocean). Assuming a Cretaceous meteorological distribution of energy flux, pro-rata to that of the modern world, then the key energy budget metrics for a 36oC world are speculatively recorded in Table 13.

Table 13: The Cretaceous Hothouse World.

Table 13: The Cretaceous Hothouse World.

4. Conclusions.

There are some fundamental messages that come from this analysis of these diagrams of the Earth’s energy budget: –

Issue #1. Internal energy recycling limits the maximum possible temperature rise to an increase of plus 14oC, assuming total blocking of the longwave atmospheric window and an unchanged Bond albedo. It is impossible for the Earth to experience a runaway greenhouse effect if the total mass of the atmosphere does not increase.

In order to achieve a putative Cretaceous global average temperature of 36oC, it is necessary to both reduce the Earth’s albedo to 0.244, and also to apply total blocking of surface to space longwave radiation (and/or raise the total mass of the atmosphere).

Total blocking of the atmospheric window by Carbon Dioxide may not be possible. This is an issue that was studied by Ferenc Miskolczi (2010) in his paper “The Stable Stationary Value of the Earth’s Global Average Atmospheric Planck-Weighted Greenhouse-Gas Optical Thickness”.

Miskolczi stated his conclusions as: –

New relationships among the flux components have been found and are used to construct a quasi-all-sky model of the earth’s atmospheric energy transfer process. In the 1948-2008 time period the global average annual mean true greenhouse-gas optical thickness is found to be time-stationary. Simulated radiative no-feedback effects of measured actual CO2 change over the 61 years were calculated and found to be of magnitude easily detectable by the empirical data and analytical methods used.

The data negate increase in CO2 in the atmosphere as a hypothetical cause for the apparently observed global warming. A hypothesis of significant positive feedback by water vapor effect on atmospheric infrared absorption is also negated by the observed measurements. Apparently major revision of the physics underlying the greenhouse effect is needed.

Issue #2. Changes in the value of the Earth’s planetary Bond albedo are a valid mechanism by which global warming can occur. Variations in water distribution in the forms of either reflective ice and/or cloud; or absorbing surface water areal variations by either short term sea-ice distribution or long-term geologic ocean distribution (e.g. The Tethys Ocean) is the primary route to change planetary albedo. This dominance of water either in its reflective role of clouds and ice leading to planetary albedo increase, or in its absorptive form as a transparent surface liquid replacing polar sea ice, means that there is no albedo role for atmospheric carbon dioxide to change global average temperatures. Unlike water, carbon dioxide is not a condensing gas in the Earth’s atmosphere, and so it has no impact on insolation energy capture via changes in reflective planetary brightness.

Issue #3. The standard climate model has the following basic features with specific rules applied.

1. The planetary disc intercept rule. – The average solar irradiance is divided by 4 and spread over the surface of the globe.

2. The albedo bypass rule. – A given percentage of the planetary insolation is bypassed by planetary brightness and not used within the climate system.

3. The remaining solar insolation is absorbed by the planet/atmosphere.

4. The planetary atmosphere is leaky. – Low frequency thermal radiation can pass from the surface directly out to space.

5. The atmosphere is an energy reservoir.

6. Energy recycling by the atmosphere doubles the quantity of energy in this reservoir. – The half in / half out rule of back radiation energy flux partition.

7. Rule six limits the maximum possible gain to times 2. –The infinite recycling geometric series limit.

What this all means is that for a planet with a zero albedo surface (that is with 100% insolation high-energy absorption under a totally clear atmosphere) and a totally opaque atmosphere for exiting surface thermal radiation (that is no surface leaks to space and total 100% atmospheric thermal radiant blocking) then the absolute limit of the internal energy budget is 3 times the Solar Irradiance flux divided by 4.

For planet Earth, with a planetary solar irradiance of 1361.0 W/m2 (Williams, 2019), the maximum possible planetary energy budget for a hypothetical Bond albedo of zero and total atmospheric insolation clarity is 1361*0.75 = 1020.75 W/m2. This flux translates into a maximum possible energy budget thermodynamic temperature of 366.3 Kelvin (93.3oC) (Table 14).

Table 14: The Hypothetical Zero Albedo, Total Atmospheric Insolation Clarity, Hothouse Limit.

Table 14: The Hypothetical Zero Albedo, Total Atmospheric Insolation Clarity, Hothouse Limit.

For Venus, with a solar irradiance of 2601.3 W/m2 (Williams, 2018), the maximum possible planetary energy budget for a hypothetical Bond albedo of zero and total atmospheric insolation clarity is 2601.3*0.75 = 1951 W/m2. This flux translates into a maximum possible energy budget thermodynamic temperature of 430.7 Kelvin (157.7oC), but the surface temperature of Venus is 737 Kelvin (464oC) (Williams, 2018).

From this analysis we can deduce that the standard climate model is compromised. The back-radiation concept cannot explain why Venus has a surface temperature of 464oC by atmospheric radiant energy flux recycling. The solar flux captured by the Venusian atmosphere is far too low to produce the observed surface temperature, even if that planet had a Bond albedo of zero and total atmospheric insolation clarity (which it clearly does not have).

5. References.

Jacob, D.J. 1999. Introduction to Atmospheric Chemistry. Princeton University Press.

Kiehl, J.T and K.E. Trenberth, 1997. Earth’s Annual Global Mean Energy Budget. Bulletin of the American Meteorological Society, Vol. 78 (2), 197-208.

Miskolczi, F.M., 2010. The stable stationary value of the earth’s global average atmospheric Planck-weighted greenhouse-gas optical thickness. Energy & Environment, 21(4), pp.243-262.

Oklahoma Climatological Survey 1997 Earth’s Energy Budget.

Williams, D.R. 2018 Venus Fact Sheet.

Williams, D.R. 2019 Earth Fact Sheet.

Post Excel Tables

198 thoughts on “An Analysis of the Earth’s Energy Budget

  1. So, the radiative theory of the so called greenhouse effect fails to account for the surface temperature of Venus.
    I have previously stated here and elsewhere that the greenhouse effect is caused by convective overturning delaying the release of incoming solar radiation back to space.
    Looks like Philip’s work supports that proposition.

    • Of course. The “Greenhouse effect” is simply the extra heat needed to drive the convective overturning a little more strongly. More GHG requires convection to slightly higher altitude and therefore slightly higher surface temperature, however this will also be affected by lower lapse rate and higher albedo (=more clouds) if the amount of water vapor increases.

      Convection can’t really be modelled realistically and is the main problem with GCM:s.

        • Indeed you are correct and I have thought of a simple thought exercise to prove it.

          Both solids and liquids will emit light in the visible range when they reach a temperature just shy of 1,000 F. Something extremely hot, like lava, can be felt some distance away directly from their photon emissions.

          A gas, however, can reach well past 1,000 F and will remain completely invisible – it must reach plasma temperatures or be compressed into a supercritical fluid (like on Venus) to become optically similar to a solid or liquid – so it’s a safe bet that gases in the Earth’s atmosphere will never behave like this. You will not be able to perceive any heat from a hot gas at a distance unless there is a medium to convect the heat to you, the emitted photons will not be felt in natural conditions.

          This is because of quantum mechanical phenomenon, gases ONLY emit radiation corresponding to quantum energy levels directly equal to the energy levels in their molecular modes. So 1,000 F CO2 will still only emit photons of 15 micron photons and other specific wavelengths of light that match the energy levels of the molecule’s internal modes, they DO NOT emit radiation based on the molecules “temperature.” In other words, heating a gas up does not mean that it will emit more of these photons in nature.

          A gases temperature is due to its average translational kinetic energy, which has essentially nothing to due with the intermolecular vibrations of the molecule, but rather the mass and velocity of the molecule. The folks over at NASA that rely on real science and deal in real world consequences understand this.

          https://www.grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/temptr.html

    • No, Philip Mulholland mistakenly assumes 30% reflected up(by clouds, albedo(lost to space)) is separate from 30% reflect both up and down(recycled) when in fact clouds albedo is both up and down.

      In Fig 2. 100% (1368/4) heats the whole system.
      Albedo is for both clouds(30% lost to space) the terrestrial radiation(23% latent heat + 7% sensible heat), 19% absorbed by atmosphere / 21% absorbed by surface(100%).

      44% (51-3(absorbed clouds)-4(reflected by surface)=44(21% direct IR absorbed by surface, 23% indirect (3% by clouds, 20% radiation reflected downward) is 151 W m2 (-46C) as shown in his CERES Image of the Earth’s Radiant Emission to Space( white top of clouds OLR going out). Clear sky is 342(151(top of cloud albedo)+151(bottom of cloud albedo + 40 (atmospheric window) W m2 .

      Greenhouse gases (water. water vapor and CO2) gets heated up through their heat capacities in the same way air is heated up.

      As guess blogger of previous article “Calibrating the CERES Image of the Earth’s Radiant Emission to Space(https://wattsupwiththat.com/2019/05/19/calibrating-the-ceres-image-of-the-earths-radiant-emission-to-space/)”
      showed his Table 6, Cell Average Temperature (global average surface temperature) e.g. Hadley cell average surface temperature as 17*6.5=110.5-83 27.9C(301 K).

      For all three cells 301+279.5+253=833.5/3=278-273=5C equal to 174PW / (4*3.1415) * (earth’s radius) squared =340 W m2 (278 K) (5C). Then says the global temperature is 288 K (174PW / (2*3.1415) * (earth’s radius) squared =390 W m2 (288 K) (15C) is for global illuminated surface (half the earth).

      Half the earth is not the same global average surface temperature 288 (15C) 390 W m2 as 1360 W m2 (divide by 4 spherical geometry rule (whole earth)) to get 340 W m2 (278, 5C). Global average surface temperature is 5C, International Standard Atmosphere temperature is 15C, that doesn’t cover every square metre of the earth.

    • ” All heat is friction ”
      The chinook winds flow down the mountain heating 5.4° for every thousand feet. Day or night, it doesn’t matter. The air cools 5.4° every thousand feet you go up whether it be a drive up the mountain, plane ride, weather balloon then heats up again when you return to your starting point. Air pressure has friction. When a storm comes, air pressure drops causing colder temperatures, Low pressure system equals heat loss, always.
      Thermal dynamics say the closer to the heat source, the hotter the temperatures. Mount Everest is closest to the sun, hottest place on earth? Definitely has more radiation. Death valley should be coldest on earth, farthest from the sun. Theory does not match reality. But high air pressure does match, and is reproducible.
      South pole radiates heat all winter with an average temperature of 70° below zero Fahrenheit. “Zero solar influence”.
      In summer, 24 hour Sun light for three months gives the south pole 40° below zero Fahrenheit average. With 100% solar influence, a 30° rise in temperature. At 10,000 feet, the radiation is high and water vapor virtually does not exist. The model says it should be the hottest place on earth.
      Now compare it to the north pole with one difference. The north pole is at sea level, higher air pressure, with temperatures above freezing.
      The moon has no atmosphere, and average temperature at the equator of a -50°F earths average is 50°F, 100° warmer than the moon or the space station. The earth radiates more heat in to space than it receives from the sun. Just like the gas giants and Venus.
      The planets in our solar system in order of the hottest to the coldest;
      Jupiter, Saturn, Neptune ( furthest from the sun) then Uranus, all hotter than the surface (photosphere) of the Sun.
      Then Venus, were its rotation takes longer than it’s revolution, is 860° Day or night. (Actually with 90 earth atmospheres thick, the surface is in perpetual night) The high temperature is caused by frictional heating, with pressures equivalent to a half a mile under our ocean.
      Number six is mercury, 800° in the sunlight, 300° below zero in the shade. Average temperature at the equator 200°
      Then earth with a 50° average. Mars with 7 mbar of air pressure, very cold. (unless you count Pluto)
      The higher the air pressure, the higher the heat content. Not a model, or a theory, actual measurements reproducible and predictable no matter which planet you’re on.
      How much heat does the sun give you? Subtract the low of the night, from the high of the day. That’s it, that’s all of it.

  2. Excuse my ignorance… Aren’t there other sources like Earth core temperature / Volcanism and upper atmosphere heat losses that also need to be accounted for?

      • @ tty what about atmospheric oxidation of hydrocarbons – methane, pinenes, etc. ?

        • Or the modulation in energy requirement of all the life on the planet.
          Life take solar energy and transfers it to chemical bonds, sequestering solar energy along the way.

          Must be minimal eh, like the lack of energy required to get the human population (and all it’s needs) from 1 billion about 200 years ago to 7-8 billion of today. That didn’t require an additional uptake in solar energy, eh?

          ~~~~~~~~~~~~~
          Also looking at these unrealistic models and their diagrams — last time I check we live on a planet 2/3 covered in water. So adjust the diagrams and all that ‘energy reflected by surface’ idea so it at least looks realistic.

      • @tty May 23, 2019 at 1:46 pm

        Geothermal heat flow is only on the order of 0.1 Wm-2. Negligible.

        The geothermal flux (GF) through the crust is only ~0,065 W/m^2 on average.
        Yet the crust TEMPERATURE is high, and gets hotter the deeper you go.
        https://www.mpoweruk.com/images/geo_temperature.jpg

        Are you saying that these temperatures can be neglected and that the surface temperatures would be the same if Earths interior was cold (like 0K cold) ?

        • “Are you saying that these temperatures can be neglected ”

          In practice yes. The heat flow at the surface is so low that it is insignificant compared to insolation with two exceptions. It is definitely significant under thick glaciers where it can raise the temperature above the pressure freezing point, making the glaciers much more mobile and dynamic than if they are frozen to the surface. It might also have some effect on the thermohaline circulation in the deep sea. Over the c. 1000 years it takes for the water in the deep ocean to be exchanged the geothermal heat flux may have a small but perhaps significant effect on water temperature close to the bottom.

      • Have to wonder about Venus, though. If there is a significantly higher radioactive decay process going on, with the produced energy trapped by a thick atmospheric blanket, it might be enough to throw a wrench in any calculations wrt that planet. Interesting concept to research.
        Need to find any data that implies how active the planet is.

      • @ tty May 23, 2019 at 1:46 pm

        Geothermal heat flow is only on the order of 0.1 Wm-2. Negligible.

        The Geothermal Flux through the crust is only 0,065 W/m^2 on average.
        Yet the crust is hot, and gets hotter the deeper you go.
        https://www.mpoweruk.com/images/geo_temperature.jpg
        For the ENERGY budget the flux can clearly be ignored.
        Are you saying that the crust TEMPERATURE can be ignored as well and that the surface temperatures would be the same if the crust was cold (like 0K cold) ?

        • Ben & tty
          If you have an Orphan Earth wandering in deep space outside the galaxy then a geothermal heat flux of 0.065 W/m^2 translates into a surface thermodynamic temperature of 32.7 Kelvin using the S-B equation.
          (Remember that using S-B equation to convert flux to temperature forms a non-linear curve with its power ^1/4 exponent).

          • @Philip Mulholland May 25, 2019 at 2:41 am

            If you have an Orphan Earth wandering in deep space outside the galaxy then a geothermal heat flux of 0.065 W/m^2 translates into a surface thermodynamic temperature of 32.7 Kelvin using the S-B equation.

            I posted a reply to tty with the same content.
            My post do not show up most of the times.

  3. What’s the margin of error for each metric?

    Now, take the partial derivative of each metric and run it through with the error to find out how many different conclusions you can make.

    TL;DR – we have no way of measuring accurately to see if any model of the earth’s budget is correct enough to predict anything. The model is only useful as a general explanation of how stuff works.

    • First thing that jumped out at me from the diagrams is from figure 1, where it says that when incoming solar impinges on clouds, as much energy is reflected downwards as upwards.
      This seem very doubtful.
      I wonder if t is just semantics. IOW, could the diagram be conflating reflectance with other things?
      Such as solar that simply shines through clouds?
      Or is the assertion that clouds reflect as much light up down as up?

      • “This seem very doubtful.”
        Nicholas,
        Have a look at this diagram “Our Energy Budget” published on line by Professor Patricia Shapley, formerly of The University of Illinois at Urbana-Champaign.
        http://butane.chem.uiuc.edu/pshapley/genchem2/c1/1.html

        This work is a more refined version of Figures 1 & 2 above and more clearly demonstrates the key elements of the process.
        1. The Incoming Elements: –
        Solar Insolation (100%) is divided between albedo losses (8 + 17 + 6 = 31%) and absorption of both the atmosphere and the surface (19 + 4 + 46 = 69%).

        2. Surface Emission: –
        Surface Thermal Radiation is composed of (15 + 7 + 24 = 46%)

        3. The Atmospheric Reservoir: –
        Atmospheric Absorption is composed of (19 + 4 + 6 + 7 + 24 = 60%)

        4. The Outgoing Elements: –
        Planetary Thermal TOA Radiation exiting to space is composed of (9 + 40 + 20 = 69%)
        N.B. The Atmospheric Window accounts for the 9% direct surface to space “leaky” radiation loss.

  4. Kiehl & Trenberth is out of order. The spectral calculations are based on the US Standard Atmosphere 76. I recommend to find out, what it means.

    • It is very close to the ICAO standard atmosphere. It is a good approximation to middle latitude conditions. It is not good for arctic or tropic areas, nor for very wet or very dry conditions.

  5. Except that the earth not a flat plane. It is a sphere (to a good approximation), and it spins, and it is covered by water. and 70% of the solar radiation falls on a circle of 22.5° from the intersection of the line between the earth and the sun with the earths surface.

    • “and 70% of the solar radiation falls on a circle of 22.5° from the intersection of the line between the earth and the sun with the earths surface.”

      When you say falls, does that mean 70% which reaches the surface.

      It’s said the tropics receives more than 1/2 of sunlight reaching the surface of Earth.
      Or 40% of Earth surface is the tropics and and it receives more than 1/ 2 the sunlight or the 60% of surface area which is outside the tropics receives less than less than 1/2 of total energy of sunlight reaching the Earth surface.

      • gbaikie – at 8:43 pm
        “…the 60% of surface area which is outside the tropics receives less than less than 1/2 of total energy of sunlight reaching the Earth surface.”

        Our friends on the left like to pretend that open water in the Arctic is substantially warmed by the sun when sea ice isn’t present.

    • I assume the 70% refers to the ambient intensity, not actual energy absorption. There’s not any conceivable way the sunshine can be funneled onto one latitude line.

      The assumption that the atmosphere and ocean respond in a direct way to the insolation is naive. W. Eschenbach has posted several descriptions documenting, along with other observers, that the atmosphere behaves very differently as a particular spot sees dawn, then reaches the meridian, and then hits sunset. The temperature, humidity, wind speed, vertical circulation, cloud formation, rain, etc. all vary.

      Currently it doesn’t appear that an average of temperature over the day drives the climate(weather average over 30 years). The weather from an average temperature over the whole face of the earth showing to the sun would be decidedly different from the current weather. The change during the day pretty clearly limits the atmospheric temperature to around 30°C, the temperature at altitude where moisture condenses.

  6. CO2 can’t block the “window” no matter how much there is of it. It can only absorb in a relatively narrow band, this will get slightly broader through doppler broadening and pressure broadening, but at the same time radiation from a larger part of the band will extend into the stratosphere and cause net cooling.

    A thicker and therefore deeper atmosphere on the other hand could theoretically cause Venus like temperatures. As a matter of fact an atmosphere as heavy as on Venus (=60 km deeper) even with the same composition as now, would yield a surface temperature of 400 C, simply by extending the lapse rate for 60 more kilometers. No extra greenhouse gases needed.

    • Two very relevant comments.
      Except when low clouds (liquid water droplets) are masking the sun, the atmosphere is partly transparent to IR. It does not behave like a black (nor grey) body.
      And when the temperature of the ground increases, its maximum emission moves into the “atmospheric window”, increasing direct emissions from the ground. It is another stabilizing effect.

    • I agree
      It is the 60 km depth of the atmosphere of Venus which causes the 400C surface temperature.

  7. People are missing the point.
    It appears that by applying the radiative theory on its own terms one cannot explain the surface temperature of Venus.
    Something else is going on.

    • Radiative theory works just fine. You just need to apply it more carefully because the Venusian system is significantly different from Earth.

      Relative to its surface temperature, the behavior of Venus is closer to that of an ideal insulating container (a white body) whose emissions are zero and whose constant temperature is arbitrary. Unlike Earth, whose atmospheric transparency is chaotically semi-transparent in both the LWIR and visible bands, the Venusian atmosphere is nearly completely opaque in both. In principle, the Venusian surface in direct equilibrium with the Sun is high up in its cloud tops where the temperature of the solid surface below is a
      function of the temperature of the clouds and the PVT profile of the dense CO2 ‘ocean’ between the clouds and the solid surface below. Venus is not a case of runaway GHG’s, but one of runaway cloud coverage, where the clouds became a thermodynamic system largely decoupled from the solid surface below. This is analogous to the temperatures of Earth’s deep oceans, which are also decoupled from the temperature of Earth’s virtual surface in direct equilibrium with the Sun, which like Venus, is something other than the solid surface of the planet. For Earth, this virtual surface is the top of the oceans and bits of solid surface that poke through. By way of analogy, the dense CO2 atmosphere of Venus has more in common with Earth’s oceans then with Earth’s atmosphere. It’s even a supercritical fluid at lower altitudes.

      • I have never seen a good explanation of the fact that there are several elements/molecules, that are gaseous at the temperature of Venus and the effect they would have on the global temperature. These would also form aerosols at higher elevations, like H2O on Earth, and thus create other factors to consider.

        • Most of them (e g SO2, H2SO4, CO) are greenhouse gases. We really don’t know enough about Venus atmosphere to understand either the radiative physics or convection there. Plus the CO2 near the surface is probably supercritical. I don’t think anyboday has the faintest idea how a supercritical atmosphere works.

          • The bottom few 100 meters of the Venusian atmosphere is a supercritical fluid. which while technically a gas, has the macroscopic properties of a liquid and most certainly introduces many unknowns. The GHG effect on Venus has its predominate effect on cloud temperatures as the GHG effect is certainly active between clouds tops and space.

          • Then there is Phosphorus, Selenium and a multitude of compounds, like tin/lead. aluminium alloys, etc.

      • Convection is the transport of energy by matter. It has little to do with the radiant balance and only redistributes existing energy. Arbitrarily conflating the energy transported by photons with the energy transported by matter is the source of so many misconceptions.

        Regarding Venus, convection in its CO2 atmosphere has little effect, as most of the CO2 molecules are energized and poised to re-emit a photon upon collision or the capture of another photon anyway. The kinetic temperature of the Venusian CO2 atmosphere has no real significance to the radiant balance and its profile is largely a function of a gravitationally induced lapse rate.

        Where the top of the CO2 atmosphere is in contact with the clouds, it’s no longer super dense and at about the same temperature and pressure as the bottom of the clouds, which is close to the freezing point of water and about 1 ATM. This clouds at this boundary are actually the source of the heat that has accumulated in the atmosphere, all the way down to the surface, per the required PVT profile established by gravity, ultimately being offset by photons leaving the top of the CO2 column and being absorbed by the clouds.

        • It redistributes heat to where it can radiate away to space. And it is the dominant heat-transport mechanism in the troposphere.

          Heat can be transported by three mechanisms: radiation, convection and conduction. Taking all three into account is not “conflating”.

          • /There’s only one way to transport heat off the planet, and only one way for heat to arrive to the planet, and this is via the transport by photons (radiation). The point is that non radiant energy entering the atmosphere from the surface can only be returned to the surface, while the absorption of radiant energy is split up and down. To the extent that matter radiates energy into space and/or back to the surface, it replaces radiation otherwire required for balance, but has no effect on what the balance must be.

            The transport of heat by matter has little to no influence on the radiant balance. O2 and N2 don’t radiate LWIR, so the temperature of those gases is irrelevant and all convection does is rearainge these gasses in the atmosphere. Emissions by GHG’s are independent of their kinetic temperature, so again, the kinetic temperature of gas molecules in motion is irrelevant.

    • Temperature is actually a measurement of energy density. Since the atmosphere of Venus is much denser than that of Earth’s, it naturally has a higher temperature. The error comes from not taking this into account when converting from energy to temperature on the surface of Venus.

      • Nonsense. Temperature is a measurement of the kinetic energy of molecules (or ions). It has nothing to do with density. The Sun’s photosphere has a density about a million times lower than the atmosphere at ground level but it is at 5,800 K all the same.

        • tty: “Temperature is a measurement of the kinetic energy of molecules (or ions). It has nothing to do with density.”

          Adiabatic cooling within rising air is a lowering of temperature without a loss of energy. The temperature lowering comes about because the density decreases; any given amount of atmosphere expands to fill a larger volume as it rises. If the energy of the molecules that make up the atmosphere are the same as at a lower altitude and more compressed volume, why/how is the kinetic energy less?

          • “why/how is the kinetic energy less?”

            Because when a parcel of air expands work is done on its surroundings. This is taken from the internal energy of the package.

        • tty,
          You are the one touting nonsense. The Sun’s photosphere is so “hot” because it is a plasma, which is very high energy ions. It is the high energy of those ions that makes it “hot”. If you could somehow contain and compress such a plasma, it would get even hotter. There is a reason that the gas law includes the P and V terms. This makes it impossible to calculate temperature from energy without knowing pressure and volume. Since pressure/volume is density, then by definition temperature must be a density. I know this is not intuitive, but it is a fact.

      • The density profile is what matters for establishing relative temperatures. When LNG is turned into gas, it gets very cold owing to the much lower final pressure. Compressing LNG makes it hot for the same reason, so LNG must be cooled after compression.

    • We are discussing an unknown – in this case, the Venus temperature. How many temperature measurements do we have from the night side of Venus? (None, to my best knowledge. I’ll be glad to learn.) Venus rotates extremely slowly.

  8. The two ‘cartoons,’ Figures 1 and 2, are only (at best) correct for sunlight entering the atmosphere perpendicular to the surface. It is effectively only a small fraction of the hemisphere! The rest of the light has a longer slant-range and, therefore, is subject to more scattering and absorption! So, unless that has been taken into consideration and the average is being presented, the scattering and absorption is greater than shown. The outgoing IR will be everywhere perpendicular to the surface, so those are probably acceptable as presented. Once again, the surface reflectance of the 71% of the surface that is water will be greater than the apparent albedo because of specular reflection. Also, the light reflected specularly will have a greater path length through the atmosphere than light impinging with a normal incidence. That means more absorption and scattering for the reflected light with large angles of incidence. Generally speaking, even diffuse reflectors have a strong forward reflectance lobe that increases in intensity as the angle of incidence increases. I doubt that CERES has properly captured that because Fresnel’s equation shows it is highly non-linear. One might say that the ‘cartoons’ are only representing a special case that probably doesn’t even represent an average.

    • The outgoing IR will be everywhere perpendicular to the surface, so those are probably acceptable as presented.

      Why has to be perpendicular to the surface? I would imagine radiation will go from the ground in all ‘open’ directions.

      • Paramenter
        That is a good question! If you take a look at the picture of the sun that Anthony regularly posts on the home page, the sun is brightest in the center and darkest on the limbs. So, the bulk of the net emissions are probably perpendicular. But, you are right that a point on the surface will radiate in a hemisphere.

        • In discussing radiation FROM the earth and not the sun at ~ 8 light minutes away seems you missed Paramenter’s point. Where the emissions travel from the earth (surface or some given point in the atmosphere) is only to a max of the earth’s outermost atmosphere or most likely considerably less requiring only the level where emission is largely unobstructed. My IR meter will read the same at a point on the surface regardless of being perpendicular to the surface or at an angle of 45 or 60 degrees. It appears that it is radiating in a hemispherical manner. Just think what effect that would have on the base of a cloud if the IR being emitted from the ground to a given point on the underside of the cloud at say 5000 ft. Now consider the surface area of the ground contained within a 1 mile radius of a given point on the cloud striking that given point on the bottom of a cloud. Then consider the potential of emissions radiating from the ground within a radius of say 5 miles. Those towering thunderheads are getting more energy than just warmer ambient air convection. I believe the process is more on the order of a continuous explosion in a sense.

          I used ground/surface to cloud base above as I have been looking at this for some time. Same or similar should apply at the emission levels higher in the atmosphere where the atmosphere is largely transparent. A satellite with an instrument with a very ‘narrow cone of view’ pointed down may be missing a lot.

  9. One thing I never see taken into account in these energy balance charts is the energy used by photosynthesis to make broccoli and corn and trees and grass and plankton. That energy comes in from the sun, but drops out of the heat flux. Photosynthesis is inefficient at ~1 percent give or take, but there’s a lot of it going on.

    • Almost all of that is soon eaten and turned back into H2O, CO2 and heat. Yes, even trees are broken down and metabolized by fungi and bacteria. Only the small fraction that is permanently sequestered is “lost” (and not even that is quite permanent).

    • This is a point that I have made on several occassions.

      In Tropical Rain Forests less than 5% of incoming Solar reaches the surface. In these Forests, Solar is absorbed in the Canopy, and a very large percentage of this must be used in photosynthesis.

      And Tropical Rain Forests happen to be located just where Solar irradiance is at its greatest, ie,’ in and around the equatorial area of the planet, and it covers approximately 13% of the land area of the planet.

      Finally, there are other dense forest.

      • Much of the solar light intercepted by forests is actually used to vaporize water from the foliage. This is very obvious in e. g. Amazonia which has a daily cloud/rain cycle where the vaporized water rains back in the late afternoon/evening. You can almost set your clock by the evening rain.

        This is also a very powerful heat transport mechanism, and the main reason rain forests are much cooler than dry tropical habitats.

        • Right. There have been posts here that much of the plant transpiring-surfaces in typical conditions try to maintain ~70F by regulating their stomata/rate of evaporation. Plants in semi-arid/arid conditions prb’ly can’t maintain that, tho.

  10. Another way to look at rule 7 is that the maximum surface emissions sensitivity is 2 W/m^2 per W/m^2 of solar forcing, where an ideal black body would only be 1 W/m^2 of surface emissions per W/m^2 of forcing. Earth is somewhere in between at about 1.62 W/m^2 of surface emissions per W/m^2 of forcing, where the 620 mw per W/m^2 is the net feedback from all sources, positive, negative, known and unknown, Note as well that only feedback expressed in W/m^2 is meaningful relative to forcing expressed in W/m^2.

    The 2 W/m^2 per W/m^2 of forcing upper bound arises when you consider that if 1 W/m^2 increases surface emissions by 2 W/m^2 and all 2 W/m^2 are absorbed by the atmosphere, half of this must be emitted into space to offset the W/m^2 of incident energy while the remaining half adds replaces the extra W/m^2 of emissions above and beyond what the forcing replaces by itself. BTW, the 50/50 split of absorbed energy is just another application of rule 1, although the most important rule, rule 0, is Conservation of Energy.

    This self evident truth is obfuscated by including non radiant energy in the budget and by expressing the sensitivity incrementally in degrees per W/m^2. Only radiant energy can leave the planet and the effect of all non radiant energy plus its return to the surface is already accounted for by the surface temperature and its corresponding emissions. Specifying the sensitivity incrementally decouples the average gain from the incremental gain making even an infinite incremental gain (runaway) seem plausible, even though incremental Joules are no different than average Joules, while specifying the sensitivity as degrees per W/m^2 unnecessarily introduces the T^4 non linearity between W/m^2 and temperature into the mix. The relationship between W/m^2 of surface emissions and W/m^2 of solar input is for all intents and purposes, constant.

    The required macroscopic behavior of the planet can’t be denied, which is that the average emissions of the planet are given almost exactly by 0.62 times the BB radiation of the surface, independent of the temperature or insolation, moreover; this ratio is the most tightly controlled relationship between any pair of climate related variables and is held to within 10% on a monthly basis and within 2% on a yearly basis across all latitudes from pole to pole. This macroscopic behavior can be quantified exactly as a gray body whose temperature is that of the surface, whose emissivity is 0.62 and whose emissions are that of the planet. The resulting sensitivity is 1/(4*(.62)*o*T^3) which is about 0.3C per W/m^2 for an ECS of about 1.1C for doubling CO2 and smack in the middle if the various ranges predicted by skeptics (presuming the 3.7-4 W/m^2 of equivalent forcing from doubling CO2 is accurate).

  11. Because the intercepted energy flux is being recycled this feed-back loop is an endless sum of halves of halves.

    Sorry, but this basic claim alone seems wrong on so many levels.

    Equation 1: 1/2 + ¼ + 1/8 + 1/16 + 1/32 + …. + 2-n = 1 , thus, seems to be an infinite sum of smaller and smaller falsehoods, leading to one big deception.

    Okay, I know it is risky to say that here, but there, I said it anyway.

    • It is wrong, and it starts here:
      “The next assumption we must make is that the standard partition of energy by the atmosphere is being applied. The standard assumption is that for all energy fluxes intercepted by the atmosphere, half of the flux is directed upwards, and lost to space, and half of all captured flux is returned to the surface as back radiation and recycled.”
      There is no such “standard assumption”. Fig 4 shown is just a teaching example (Willis’ steel greenhouse). No-one sensible assumes that for the real continuum atmosphere, and it doesn’t even make sense there.

      • Nick,
        So, all back-radiation from CO2 is directed downwards only? That seems to be what you are implying. If so, how can you logically support that?

          • Isn’t it radiated in all 360 degrees such that it depends upon the height from where something is radiated as to whether it favours an out into space trajectory/

            Of course, the matyter is complicated by interruptions of absorption and re-radiation.

          • Richard,
            So where does the rule operate? Half of what?
            It’s true that an individual molecule emitting does so isotropically. But how does that add to an evenly split flux? In fact, the distribution of molecules has a density gradient, and emission is reabsorbed. On average, upward radiation gets further then downward before absorption and reemission, and some gets out to space altogether.

            There is no equipartition as claimed here, and the notion of any partition fraction does not make sense.

          • Nick,

            The rule driving the 50/50 split up/down is rule 1. Energy enters the atmosphere from the bottom and leaves through TOA or is returned back to the surface over twice the area that it was absorbed from.

            What it’s half of is the surface radiation directly absorbed by the first GHG molecule it encounters (if it’s the right energy) or the first molecule of liquid or solid water in clouds that it hits. Those photons that are not absorbed by GHG’s or clouds pass through TOA and represent about 23% of the radiant emissions by the surface consequential to its temperature. The magnitude of the transparent window is something Trenberth has very wrong and if you ask him where he got his value, it was an ‘educated guess’ that was backed out of the data based on what he thought it should be.

            The macroscopic math is simple. The surface emits net 390 W/m^2, 77% is absorbed by the atmosphere leaving 90 W/m^2 passing directly into space and 300 W/m^2 absorbed by GHG’s and clouds. Half of 300 is 150 which when added to 90 exactly offsets the 240 W/m^2 of incident solar energy. When the remaining 150 are added to the 240 W/m^2 of incident solar energy, it’s exactly enough to offset the 390 W/m^2 of emissions. Note that if you think the transparent window is smaller than this, then even more than half of what the atmosphere absorbs will need to be emitted into space.

            The next level of detail is a little more complicated owing to clouds, none the less, the top level macroscopic behavior of the system must still conform to the laws of physics as constrained by its geometry.

            Don’t be confused by non radiant energy leaving the surface as latent heat and convection plus the return of that energy to the surface as the effects of all are already accounted for by the average temperature and its SB emissions.

            Between conflating the energy transported by photons with the energy transported by matter, confusing the feedback fraction with the feedback factor and decoupling the incremental sensitivity from the average sensitivity despite the fact that all W/m^2 are the same, it’s no wonder that so many are so confused and as a result so wrong.

          • george,
            ” 300 W/m^2 absorbed by GHG’s and clouds”
            But there isn’t just one absorption. In many wavelength bands IR has a mean path of hundreds of metres, in some even just metres. Philip M gets his thinking from the simple teaching example where the atmosphere is reduced to a thin layer with perfect conduction. But it isn’t really like that at all, and no-one thinks it is.

        • @Nick Stokes May 23, 2019 at 8:15 pm

          And this is why, the mere claim that solar irradiance is essentially a constant (TSI varies little) is misconceived. One has to look at how the wavelength of light varies over time, since the absorption depths are different depending upon wavelength.

          Above, I have made a point regarding Tropicla Rain Forests where all but no solar irradiance reaches the ground (the surface) and where solar irradiance is absorbed in the canopy, where it is consumed, in part, to power photosynthesis. If energy is being used to power vegetation, one would not expect an energy budget to balance without taking that factor into account. One would not expect energy out to equal energy in, but rather the equation balances around Energy In = Energy Consumed (in powering vegation) + Energy Out. On death, some of the energy consumed during life is released, but not all of it. So for example, is the depth of top soil growing, because some of the energy consumed during life, is not fully released upon death, but instead forms part of and/or is buried beneath the surface?

          We know that presently the Sahel is greening, in fact presently the planet is greening. Surely this must mean that over the short term, energy is being consumed and not all energy received is being released. In the long term, this maybe a net energy neutral process, as cycles of greening wax and wane, but materially we are only measuring matters in the short term. We therefore may have a distorted picture of the energy balance equation.

          But a similar issue applies to the oceans. Solar irradiance is absorbed at depth and then distributed in 3 dimensions. Whilst Solar irradiance is absorbed at depth, and we do not know how long it takes the energy that is absorbed at depth to make its way to the surface. The ocean surface temperature could theoretically be the product of wenergy that was absorbed say a thousand years ago when cloud patterns were different.

      • The problem is that he’s got it arse about face. About 50% of the energy being emitted by the atmosphere at altitude comes from energy being convected. Yes, some of that goes as IR back toward ground, but a lot of it never gets there … because like any substance there is continuous internal heat transfer within the substance. That wouldn’t matter as the internal heat just goes back and forth – except there is a heat gradient – and if there is a heat gradient – as everyone knows – there is a net energy flow induced by the heat gradient.

        • … there is a net energy flow induced by the heat gradient.

          This doesn’t seem right either. I didn’t think that energy flow was induced by a heat gradient — rather, it would seem that, if we speak this way, then heat is induced (i.e., defined) by an energy gradient, where the “flow of heat” is from the warmer to the cooler entity.

          • Sorry – it was late – that should be temperature gradient induces a heat energy flow.

            The problem with all these “heat flow” diagrams is that they are nothing of the sort. Instead in a situation where you have incoming and outgoing IR, then that is work done on the system and is not heat flow. So, they are in fact a disorganised and poorly understood combination of heat (internal energy flows) and work (external IR flows).

            Of course, in order to define which is which you need to have very carefully and watertight system boundaries – so that for example, you can point to IR in part of the atmosphere and say whether it is heat (internal flows within the system) or work (flow to and from the system).

            If you don’t do that, then you really have to consider all energy flows, which means IR, convection (both latent and sensible) and CONDUCTION. For fun I produced a diagram which included conduction “heat” flow portrayed in the same way as “backradiation” is portrayed as a “heat flow” (not heat moving about within the system), and it turns out that something like 99% of all the energy flows were conduction. That’s not because a lot of energy moves from around the atmosphere as conduction – but instead, it’s because like internal IR within a gas, there’s a lot of it moving about.

            And of course, if you confuse heat and work flows – then of course you also appear to break thermodynamic laws. LOL

      • The calculation of the Greenhouse Effect seems inconclusive, a work in progress, But what about the heat created by us humans burning all the fuels both fossil and other. While it is well recognized in the Urban Heat Island Effect, it seems to be ignored on the overall global temperature by everyone. The International Energy Agency has good statistics on all the fuel used worldwide so it should be easy to calculate the total heat caused to the earth’s atmosphere by this consumption of all this fuel annually. What is the impact of this on the overall average temperature?

        • I have done that calculation, a few years back. The amount of energy consumed by man, converted to heat, is about 2 orders of magnitude less than observed warming. Even adding in the heat from 7 billion bodies….

        • It is written in various places, which I don’t have at hand, that the solar energy received at TOA is a couple of hours of any day is equal to the energy usage of humans in a year. Therefore, human energy usage, irrespective of CO2 production, is irrelevant to temperature at large. It is only significant within tiny (earth viewpoint) spaces.

      • I am having trouble believing this “standard assumption” as well. If one assumes enough (like assume the Earth is flat) then it probably works…but consider the real context:

        As energy is entering the atmosphere, the pressure is low and interaction with molecules is more rare. Also, the surface of the earth is curved. The average path of energy absorbed and re-emitted is not going to be 50% up and 50% down. Some will be reabsorbed in the downward path, and so have another chance to go upward, while those going upward have less of a chance being reabsorbed. Some paths will be slightly downward but mostly sideways, and so miss the Earth’s surface due to curve. These effects become less important as the energy nears the surface.

        My bigger problem is one seems to be assuming either a completely stable gas atmosphere, or one is assuming convection and currents do not matter. I think they do. In general, if the energy is moving downward and hits the path of an upward air mass (warm and moist) then it chances of being both absorbed and physically moved upward are larger. If the same energy strikes a downward moving cool, dry air mass then because it is dry, it is less likely to be absorbed.

        Now perform the same thought experiment about a cloud. A cloud is constantly in motion…warmer air pushing up and condensing. Also, the quality of water (not vapor but actual water) is changing from liquid to ice. So energy coming in from above is NOT going to interact just like the energy approaching from below. I just do not see how a 50%/50% rule could possibly be assumed on reflection. The net would be to move heat from lower to higher, so the tops most be emitting more than the bottoms.

        Now consider horizontal movement on large scales – like a Hadley Cell. The net effect is more warm moist air moving upward where the light intensity is more direct and cooler dry air where the light is more oblique. Again, I think this must have some consequences for overall absorption of energy for the Earth. If these cells move air even slightly faster, the heat transport is enormous, and I can’t help but think reflection depth would decrease (due to upward moving warm moist air).

        • “I am having trouble with this standard assumption as well”

          Robert of Texas,
          If you are struggling like I did, then let me try and help by detailing my analysis of-the power intensity flux numbers presented in Figure 3 (Kiehl and Trenberth 1997, Fig 7). This diagram clearly shows that the Surface Radiation is 390 W/m^2, Surface Thermals are 24 W/m^2 and Surface Evaporation is 78 W/m^2. These three outgoing components sum to a total surface outgoing flux of (390 + 78 + 24) = 492 W/m^2.

          From the diagram we also know that the two incoming energy fluxes of Insolation Absorbed by Surface (168) and Back Radiation Absorbed by Surface (324) sum to a total Downward Flux reaching the Surface of (168 + 324) = 492 W/m^2.

          Now we find that the surface radiation of 390W/m^2 is clearly labelled in the diagram. Using S-B this flux converts to a thermodynamic surface temperature of 288 Kelvin (15C). We also see in the diagram that from this 390 W/m^2, 40 W/m^2 is lost to space via the Atmospheric Window, which leaves the (390-40) = 350 W/m2^2 of Surface Radiation Absorbed by the Atmosphere. BUT 324W/m^2 is returned to the Surface as Back Radiation. This means that the net back radiation gain to the Atmospheric Reservoir is (350-324) = 26 W/m^2. This value is the Greenhouse Gas Radiant Blocking effect.

          Next, we calculate the fluxes which are Absorbed by the Atmosphere. These are as follows: –
          Solar Insolation Absorbed by the Atmosphere (67), Thermals delivered to the Atmosphere (24) Latent Heat delivered to the Atmosphere (78) and of course the Greenhouse Gas Radiant Blocking mentioned above (26). These four components sum to (67 + 24 + 78 + 26) = 195 W/m^2.

          Let us pause here for a moment.

          Now the target flux is 390 W/m^2 and 195 is half of 390, so where does the other 195 W/m^2 come from? The answer is infinite recycling in a geometric series of halves of halves. So how does that work? Well the atmosphere has a linear gradient loss rate from the surface to the TOA. There is very little loss at the base and total loss at the top. We can collapse this infinite series loss staircase into a single calculation at the mid-point depth. At this level we have half the flux passing up and lost to space, and half the flux passing down and recycled.

          So now we can double the flux in the atmospheric reservoir from 195 W/m^2 to the 390 W/m^2 value reported in the diagram. This is the flux value required to explain the global average temperature of 288 Kelvin (15C).

    • I’m afraid that my initial criticism is on an even more basic level than is being discussed.

      What these sorts of energy-budget diagrams do with fluxes isn’t physically sensible at all. The way they add up fluxes is the same thing as adding temperatures together, and the way they divide them spreads the energy over surface areas over which the specifically defined fluxes NEVER impinge.

      You cannot divide up a flux like that, any more than you can divide up the color, “green” on a leaf, to say that half the leaf is 50% green, while the other half is 50% green, and adding the left half’s 50% green to the right half’s 50% green gives 100% green for the whole leaf.

      • The author agrees with you. He is pointing out that the radiative theory makes no sense because it cannot explain the high surface temperature of Venus.

  12. NASA’s Van Allen Probes Spot Man-Made Barrier Shrouding Earth

    “Humans have long been shaping Earth’s landscape, but now scientists know we can shape our near-space environment as well. A certain type of communications — very low frequency, or VLF, radio communications — have been found to interact with particles in space, affecting how and where they move. At times, these interactions can create a barrier around Earth against natural high energy particle radiation in space. These results, part of a comprehensive paper on human-induced space weather, were recently published in” https://link.springer.com/article/10.1007/s11214-017-0357-5

  13. Decent article. If that is indeed the case that theoretical model of radiative transfer is poorly constructed, failing miserably to predict actual temperatures of the Venus atmosphere, consequences are truly profound. That reminds me work of Lord Monckton et al. where poorly applied feedback mechanisms wreak havoc in the modelling temperature of the atmosphere.

  14. Equation 1 describes the cumulative effect of the feed-back loop (after an infinite series of additions), where for each turn of the cycle, half the ascending energy flux is passed out to space and lost, and the other half is returned back to the ground surface and then re-emitted. It is a feature of this form of an infinite series that the sum of the series is not itself an infinite number, but in this case the limit is the finite natural number 1.

    Do I understand that correctly that in such case most of the incoming radiation is retained in the atmosphere? If total incoming radiation is 1 and this recycling mechanism approaches 1 – in practical terms how much energy is retained then in the atmosphere?

  15. “Issue #3. The standard climate model has the following basic features”
    As so often, no quotes. Who says? Rules 1-5 do seem reasonable enough, but where did the “half in/half out” rule on which the arithmetic is based come from?

    “The back-radiation concept cannot explain why Venus has a surface temperature of 464oC by atmospheric radiant energy flux recycling.”
    That does suggest the model is wrong. But it isn’t anyone’s model but Philip Mulholland’s.

    • Nick

      then you try to Model Venus and enlighten us all or find someone that has that makes sense to you.

  16. Since this seems to support the enormous 324Wm2 back radiation absorption I see no point in bothering with it. Ok, here at 19°C if I leave a spanner on the ground on a clear day I’ll get burnt picking it up without gloves, and I can fry an egg on the lid of a can, but the natural surface isn’t the same. The first metre or so is in a constant state of turbulence. A cheap fogger machine will demonstrate this.

  17. All of these diagrams require S-B BB LWIR upwelling from the surface creating energy out of a calculation.

    Because of the non-radiative heat transfer behavior of the contiguous participating media such BB radiation is simply not possible.

    Emissivity & the Heat Balance
    Emissivity is defined as the amount of radiative heat leaving a surface to the theoretical maximum or BB radiation at the surface temperature. The heat balance defines what enters and leaves a system, i.e.
    Incoming = outgoing, W/m^2 = radiative + conductive + convective + latent
    Emissivity = radiative / total W/m^2 = radiative / (radiative + conductive + convective + latent)
    In a vacuum (conductive + convective + latent) = 0 and emissivity equals 1.0.
    In open air full of molecules other transfer modes reduce radiation’s share and emissivity, e.g.:
    conduction = 15%, convection =35%, latent = 30%, radiation & emissivity = 20%

    The Instruments & Measurements
    But wait, you say, upwelling LWIR power flux is actually measured.
    Well, no it’s not.
    IR instruments, e.g. pyrheliometers, radiometers, etc. don’t directly measure power flux. They measure a relative temperature compared to heated/chilled/calibration/reference thermistors or thermopiles and INFER a power flux using that comparative temperature and ASSUMING an emissivity of 1.0. The Apogee instrument instruction book actually warns the owner/operator about this potential error noting that ground/surface emissivity can be less than 1.0.
    That this warning went unheeded explains why SURFRAD upwelling LWIR with an assumed and uncorrected emissivity of 1.0 measures TWICE as much upwelling LWIR as incoming ISR, a rather egregious breach of energy conservation.
    This also explains why USCRN data shows that the IR (SUR_TEMP) parallels the 1.5 m air temperature, (T_HR_AVG) and not the actual ground (SOIL_TEMP_5). The actual ground is warmer than the air temperature with few exceptions, contradicting the RGHE notion that the air warms the ground.

    Conclusion
    So, the 396 W/m^2 upwelling LWIR and net 333 W/m^2 GHG energy loop of RGHE and the K-T diagram and RGHE claim that the air warms the ground are all illusions due to inappropriate calculations and misunderstood instruments.

    No GHG energy loop = No RGHE theory = No man-caused climate change.

    • Agreed – As yet there is no instrument that measures the Poynting vector that defines radiant flux in the E-M fields. All the power fluxes are calculated based on misapplication of S-B equation.

    • Radiative gases, primarily water vapour and CO2, absorb and emit IR at discrete wavelengths. You seem confused by Blackbody radiation characteristics. If the atmosphere was only N2 and 02, your infrared gun thermometer pointed up would read -270 C, the temperature of outer space. Because of CO2 and H2O emitting IR in the atmosphere, the open sky has a temperature for your IR thermometer to read. Then in the SB equation you can see that q= C (Thot^4 – Tsky ^4) is going to result in less heat sent to outer space. In turn Thot will get warmer to radiate the the constant amount of sunshine to space. That is the so-named atmospheric greenhouse effect.
      Your false claims that it does not exist do a disservice to people trying to understand the effect. You would benefit by a course in radiative heat transfer.

    • “……require S-B BB LWIR upwelling creating energy out of a calculation….such BB radiation is simply not possible……”
      Where do you get such an incorrect idea? The upwelling IR is emitted by the ground that has been warmed by the sun to some temperature warmer than the sky above it, which in turn is warmer than outer space. Not “out of a calculation” instead “can be calculated”. And the ground does emit radiation like a black body (times an emissivity).
      Also the “…RGHE claim that the air warms the ground….” Huh, no, everybody claims the Sun warms the ground, you know, except at night…or when a warm front comes through the cold mountains…..

    • Nick, that is correct. Us farmers deal with grass and surface temps of over 40C on normal average days. Brett Keane

  18. Picture a house in Phoenix.
    The south wall holds several large picture windows.
    Solar energy enters warming the contents which then warm the air.
    The absorbed internal energy leaves in all directions through the insulated walls per Q, kJ/h = 1/R A dT. Walk the insulation aisle at Home Depot. Yeah, it’s that R.
    The rate of energy entering and leaving must balance producing a particular temperature. Less Q leaves than enters, temp goes up. (More AC) More Q leaves than enters, temp goes down. (Furnace)
    But this is Phoenix. How to keep the house cool? Well, draw the drapes reflecting and reducing the amount of energy entering, aka the atmosphere.
    The earth’s atmosphere does not warm, it cools and greenhouse theory goes straight in the trash bucket.
    No GHG LWIR pseudo-thermo hocus pocus needed.

  19. One of the heated issues underlying greenhouse theory is whether space is hot or cold.

    It is neither.

    By definition and application temperature is a relative measurement of the molecular kinetic energy in a substance, i.e. solid, liquid, gas. No molecules (vacuum), no temperature. No kinetic energy (absolute zero), no temperature. In the vacuum of space the terms temperature, hot, cold are meaningless, like dividing by zero, undefined.

    However, any molecular substance capable of kinetic energy (ISS, space walker, satellite, moon, earth) placed in the energetic radiative pathway of the spherical expanding solar photonic gas at the earth’s average orbital distance will be heated per the S-B equation to an equilibrium temperature of: 1,368 W/m^2 = 394 K, 121 C, 250 F.

    Like a blanket held up between a camper and campfire the atmosphere reduces the amount of solar energy heating the terrestrial system and cools the earth compared to no atmosphere.

    This intuitively obvious and calculated scientific reality refutes the greenhouse theory that has the atmosphere warming the earth and no atmosphere producing a frozen ice ball at -430 F.

    No greenhouse effect, no CO2 global warming, no man caused nor cured climate change.

    • Actually space has a “temperature”, thanks to the cosmic microwave background radiation which behaves as blackbody radiation at 3 K. So for all practical reasons space has a temperature, though it is very low.

    • Nick Schroeder

      “Like a blanket held up between a camper and campfire the atmosphere reduces the amount of solar energy heating the terrestrial system and cools the earth compared to no atmosphere.”

      Sorry, this is simply wrong.

      The energy supplied by the Sun to Earth’s system (according to Sun’s temperature: in form of radiation at frequencies around 1 micron wavelength) must be returned back to space (according to Earth’s temperature: in form of radiation at frequencies around 10 microns wavelength), in order to achieve equilibrium: otherwise, the planet would permanently warm or cool.

      A planet with an atmosphere lacking substances able to absorb and reemit its own radiation will be cooler than a planet with such an atmosphere, because all radiation emitted directly reaches outer space.

      Instead of explaining your own theory without any scientific background, you could for example try to contradict the following paper

      Proof of the atmospheric greenhouse effect
      A. P. Smith, 2008

      https://arxiv.org/pdf/0802.4324.pdf

      A somewhat miserable attempt was made by Gerhard Kramm & al.

      https://arxiv.org/pdf/0904.2767.pdf

      Kramm’s allegations were later refuted by A. P. Smith and Chris Ho-Stuart in Joshua Halpern’s blog (you might follow in the comment sections the discussion until Kramm definitely gives up):

      http://rabett.blogspot.com/2009/04/die-fachbegutachtung-below-is-elis.html
      http://rabett.blogspot.com/2009/05/krammed-to-our-misfortune-gerhard-kramm.html

      It is evident that Kramm did not understand that his critique of Smith’s math was a non-sequitur.

      *
      Maybe you do it better?

      • “The energy supplied by the Sun to Earth’s system (according to Sun’s temperature: in form of radiation at frequencies around 1 micron wavelength) must be returned back to space (according to Earth’s temperature: in form of radiation at frequencies around 10 microns wavelength), in order to achieve equilibrium: otherwise, the planet would permanently warm or cool.”

        Two points:
        1. The planet is not at equilibrium. It *is* permanently warming and cooling with the day/night cycle.
        2. If the atmosphere warms the earth as you say, why is the daytime temperature of the Moon (no atmosphere) much higher than the daytime temperature of the Earth (with an atmosphere)?

        • Late answer, 5:20 pm is 02:20 am in UTC+2…

          1. The planet is at equilibrium: what you talk about are minuscule deviations from a mean, as if you would compare a day’s weatherwith a century’s climate.

          What is was talking about id that if it was not, the temperature would continuously either increase or decrease. It does neither.

          2. The question is formally correct, but has no practical substance from my point of view.

          What we must compare ist not a rocky Earth vs. the Moon, but an Earth whose atmospheric IR active substances either have precipitated or have reached some absolute minimum.

          This is what very probably happens when Earth has reached minimal temperatures within one or more concurrent Milankovitch cycle(s).

          In such a case, the Earth is an ice ball with an average albedo of 0.3. According to A. P. Smith, this leads to an average surface temperature of 255K.

          I wouldn’t say “the atmosphere warms the earth”. I would rather say it prevents it from cooling.

          What about reading the intro of Michael F. Modest’s “Radiative heat transfer” ?
          Exists online as Google book, with some pages excluded here and there.

    • The 394K is not valid for a sphere.

      The Moon provides a perfect example of what the average temperature of an airless, waterless rock in space is when the same distance from the sun as Earth. It has a mean temperature of 197K.

      Earth’s average temperature is primarily a function of the connectedness of the water masses and the ability of these large bodies of water to absorb and transfer solar heat. Earth would be much cooler on average if there were no oceans. There would be much higher temperature extremes because land has limited ability to store and transfer energy; any energy absorbed during sunlight hours is largely lost at night – the Sahara being a good example of the temperature range.

      Water regulates the average temperature of Earth with a myriad of negative feedbacks in all its phases and tropical ocean connectedness via the Southern Ocean and Arctic Ocean.

      • I always love layman physics and so lets give you real numbers from the ISS which has monitors on it’s skin and it runs -157 C in the dark and 121 C in the light. So your average is -3C.

        So explain how it works from there?

        • The Moon temperature of 197K is area averaged. The maximum measured temperature is 389K and the minimum “measured” is 97K. The arithmetic mean of these two numbers is 243K but that is not an area averaged value.

        • The ISS is a funny shape and takes on all sorts of different angles to the sun yet those numbers remain constant. So clearly the shape doesn’t matter to how hot something is in space and your average is meaningless 🙂

          • The linked paper provides the data for the area averaged moon surface temperature:
            https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4447774/
            Unless you have an area averaged temperature you have a meaningless number when just averaging the hottest and coldest of two points.

            The temperature profile for latitude and longitude of the moon is what the surface of earth would be if it did not have large globally connected water masses.

    • But isn’t the claim that the atmospjere cools the sunlit side of the Earth, but warms the darkside of the Earth, but net overall, the atmosphere produces a higher average temperature of what would otherwise be the average temperature of the two extremes of a no atmosphere planet.

  20. All the energy budget diagrams miss a vital piece of information. None of them state the temperature of the bodies emitting all of those different radiations.

    As an example, if you place a steel ball at 1000 degrees C next to a second steel ball at 500 degrees C then the temperature of the second ball will instantaneously go up. But, if you reverse the order and place a 500 degree C steel ball next to a second steel ball at 1000 degree C, then the temperature of the second ball will not instantaneously go up. That is because a cooler body cannot increase the temperature of a warmer body – only a warmer body can.

    Temperatures are not additive. Combining two bodies with temperatures of 1000 degrees will result in a temperature of 1000 degrees, not 2000 degrees. Thus, adding emissions also tells you nothing about the resulting temperature.

    However, Trenberth et al happily add and subtract emissions in their budgets and pretend that they are somehow equivalent to adding and subtracting temperatures.

    All these energy budgets are useless in deriving temperatures because they tell you nothing about the temperature of the sources of the different emissions.

    So, labeling any new emissions as being CO2 related tells you nothing about the temperature effect of those CO2 emissions. Energy budgets do not prove anything about CO2’s impact on temperature.

    • However in your examples the temperature of the 1000 degree steel ball will decrease more slowly than if the 500 degree ball wasn’t there.

      This is a very simple fact that for some reason seems completely incomprehensible to a lot of people. There is no physical law that prevents photons emitted by a cooler body from being absorbed by a warmer body. The second law of thermodynamics only says that the net flow will always be from the hotter to the colder body.

    • “The standard assumption is that for all energy fluxes intercepted by the atmosphere, half of the flux is directed upwards, and lost to space, and half of all captured flux is returned to the surface as back radiation and recycled.”

      My problem with the recycling assumptions are, when downward radiation is recycled and warms the surface , surface warms and then radiates heat upwards again. But much of that recycled upwards IR is now radiating at frequencies that can escape more readily through the “molecular holes ” So there must be a rapidly diminishing intensity of recycled heat

  21. Apparently major revision of the physics underlying the greenhouse effect is needed.

    The physics does need revision. People who understand physics need to educate those who don’t.

    An EMR power source cannot transmit energy against the electric field gradient (EMR IS ELECTRO-MAGNETIC RADIATION). Earth’s surface cannot receive energy from any part of the atmosphere that is cooler than the surface. Such a process is inconsistent with Maxwell’s equations that define EMR. Energy flow at any point in time and space is unidirectional and is ALWAYS from high potential emitter to lower potential receiver.

    IR back radiation from cold atmosphere to warmer surface is bunkum. The only location where IR back radiation is consistently observed is over Antarctic ice mass where warmer atmosphere radiates to the cooler surface.

    • “Earth’s surface cannot receive energy from any part of the atmosphere that is cooler than the surface.”

      Sure it can. There is nothing to prevent a photon emitted from a colder molecule to be absorbed by a warmer one. Photons don’t carry a sign “only permitted to be absorbed by molecules colder than X degrees”. However the net flow is alway from hot to cold.

      What you claim is essentially that a thermal blanket is impossible. Since it will always be colder than your body, it can’t possibly warm you. But it can, because it shields you from an even colder environment and thereby slows down heat loss.

      Not that I have much hope that this will have any effect. This simple physical effect is apparently utterly incomprehensible to a lot of people.

      • tty:
        What you claim is essentially that a thermal blanket is impossible. Since it will always be colder than your body, it can’t possibly warm you. But it can, because it shields you from an even colder environment and thereby slows down heat loss.

        The blanket example you give is incorrect. Your temperature goes up when you wrap yourself in a blanket because your body has an internal energy source. A steel ball does not have an internal energy source. If you put a blanket around a steel ball at 100 degrees C, the temperature of the ball does not go up!

      • @tty No a blanket does not warm you – unless it’s electric. You warm yourself: the blanket reduces your rate of heat loss. You cannot defrost your frozen dinner any quicker by wrapping it in a blanket.

        • EXACTLY!

          And that is how the greenhouse effect works. Since the atmosphere is partially opaque to LWIR it shields the surface from the cold of space.

          And the amount of the effect depends on how much heat must be transported how high by convection before it is lost to space. And it is the lapse rate that transports the heat.

    • @ RickWill
      I think you need the re-education maxwells equation and theory are wrong or if you want to be nice incomplete a fact known for 100 years. You are trying to apply a variation of maxwells law to a problem it is forbidden because it breaks down.

      Here is why it breaks down for layman. Light leaves a sun 2Million years ago and right now hits earth.
      How does it know if it Earth is warmer or cooler than where it left from?

      Do you see the problem to make your statement true the light has to reach backward 2 Million years in time and 2 Million Light years in distance and do a comparison. Do you think anyone except you is ever going to believe that is possible?

      Done correctly under QM the photon has quantized energy and by extension a temperature under classical physics right here right now and it does not care about it’s history or where it came from 🙂

      • The speed of energy transfer from the sun to earth via the E-M fields is a function of the electric permittivity and magnetic permeability of the intervening space. It takes approximately 8 minutes for the matter, spaced at that distance, to alter the field and respond to each other with the higher potential object transferring energy to the low potential object.

        • 1.) You changed the problem … it still stands you have 8umin retrocausality
          2.) Maxwell does not a speed limit on his fields they are instant across the universe
          3.) The question still stands for the 2Billion year old light how does it know the temperature of the thing it hits versus what it was emitted as?

          So now you have mixed relativity into Maxwells equations you are going great and butchering the hell out of everything and we still have retro-causality.

          • The presence of any matter disturbs the electric field and magnetic field that everything exists in. The higher potential object will transfer energy to the lower potential object as the electric field and magnetic field respond to the presence of both objects. Their interaction is not instantaneous. The interaction occurs at the speed of EMR and is determined by Maxwell’s equations; deriving the speed of light in a vacuum:
            http://www.irregularwebcomic.net/1420.html

        • To give you a heads up to your next problem, I am going to tell you that the sun died in the 2Billion period between and became a black hole. Then you have retro-causality to a non existent object and your physics just continues to get better and better.

          • If the sun died we would know 8 minutes later. At which point we would start to cool and move off on a set path, no longer bound by the influence of the sun in the gravitational field that all matter exists in.

          • Got to love ye olde classical field theory and it’s “potentials” and absolute time and space.
            If you wave your hands enough you can almost convince the kiddies and yourself 🙂

            There is a well known causality problem with you seem hell bent to try and ignore. If you ever do get interested you simply need to search “maxwells equations and causality”.

  22. “The standard assumption is that for all energy fluxes intercepted by the atmosphere, half of the flux is directed upwards, and lost to space, and half of all captured flux is returned to the surface as back radiation and recycled.”

    My problem with the recycling assumptions are, when downward radiation is recycled and warms the surface , surface warms and then radiates heat upwards again. But much of that recycled upwards IR is now radiating at frequencies that can escape more readily through the “molecular holes ” So there must be a rapidly diminishing intensity of recycled heat

    Thus much less heat is recycled after each round of warming

  23. Rick says, “But, if you reverse the order and place a 500 degree C steel ball next to a second steel ball at 1000 degree C, then the temperature of the second ball will not instantaneously go up.”

    Nonetheless that does not mean heat will not radiate from the 500 degree C ball and affect the 1000 C ball. Its a matter of balance.

    The 500 ball will radiate heat a lower intensity than the 1000 ball. The 500 ball will receive heat from the 1000 ball faster than it loses it, and so warms. Conversely, the l000 ball emiys heat faster than to receives heat from the 500 ball , so there is a net cooling.

    Because the ground can emit heat at all IR frequencies it cools more rapidly than the atmosphere. O2 and N2 do not radiate heat. They must collide with a greenhouse gas for their heat to be radiated. Thus the air cools more slowly and an inversion layer often sets up at night and in the winter. Due to this inversion and warmer relatively warmer air temperatures, the atmosphere will radiate heat back to the ground faster than the ground can radiate it upward, and thus warm the ground.

    • Jim,

      Of course all objects emit and absorb emissions. That is not the point. The question is will those emissions raise the temperature of the absorbing body or not?

      You do not know whether emissions will increase the temperature of the absorbing body unless you know both the temperature of the emitting body and the temperature of the absorbing body. For example, if a body is emitting at 400 degrees then it will increase the temperature of another body at 200 degrees but will not increase the temperature of another body at 800 degrees. Unless you know the temperature of both bodies, you cannot predict whether the emissions will increase the temperature of the absorbing body.

      That is why the energy budgets are useless for predicting temperatures. They do not state the temperatures of the emitting and absorbing bodies so the temperature effect of any of the emissions is unknown.

  24. Rick says, “But, if you reverse the order and place a 500 degree C steel ball next to a second steel ball at 1000 degree C, then the temperature of the second ball will not instantaneously go up.”

    Nonetheless that does not mean heat will not radiate from the 500 degree C ball and affect the 1000 C ball. Its a matter of balance.

    The 500 ball will radiate heat a lower intensity than the 1000 ball. The 500 ball will receive heat from the 1000 ball faster than it loses it, and so warms. Conversely, the l000 ball emiys heat faster than to receives heat from the 500 ball , so there is a net cooling.

    Because the ground can emit heat at all IR frequencies it cools more rapidly than the atmosphere. O2 and N2 do not radiate heat. They must collide with a greenhouse gas for their heat to be radiated. Thus the air cools more slowly and an inversion layer often sets up at night and in the winter. Due to this inversion and relatively warmer air temperatures, the atmosphere will radiate heat back to the ground faster than the ground can radiate it upward, and thus warm the ground.

    • ROTFLAMO. “Cretin”?” Stop typing”?

      Says viffer who doesn’t understand physics! Name calling will not make you any more intelligent viffer. Your insults are making fascist alarmists look good.

      Due to probabilities, there is a “net” movement of heat from a hotter object to a colder object. There is absolutely no prohibition that prevents emissions from the colder body from interacting with the hotter body.

      Diffusion is a good analog.

      Molecules always move from high concentration to low concentrations. But that doesn’t mean molecules in the low concentration region do not move into the region of high concentration. It only means it is more likely the molecules in the region of higher concentration are more likely to move to the region of low concentration than the reverse. The molecules in the low concentration will still move into the high concentration region but just at a slower rate. The result is a “net” movement from high to low concentrations.

      The same laws hold true for heat transfer. The heat moves in both directions between warmer and colder regions. There is no prohibition against heat from cooler areas interacting with a hotter object. There is only a higher rate of movement from the warmer object causing a net warming of the cooler object.

      A cooler object will not typically warm a hotter object above its initial temperature, but emissions from the cooler object will cause the hotter body to cool more slowly.

      • Maybe it is nit picking, maybe not. Heat is not transferred in either direction. Energy is transferred. Heat is what energy does in the object.

        It seems obvious enough that if a hot object is losing energy faster than it is receiving it, it will cool, no matter how much energy it is receiving. However, the rate of cooling will be less than it would be if no energy was received.

    • 1000C ball in presence of 500C ball will cool longer than without it.
      Imagine this 1000C be heated cyclically by third source 12h 100%, 12h 0% and you remain with higher final temperature of this previously 1000C ball with presence of 500C ball.

    • Jim, AndyHce and others: It is useful and true to say that individual molecules and photons do not obey the 2LoT; they obey the laws of quantum mechanics. Large numbers of molecules following the laws of quantum mechanics cause 2LoT to be obeyed on macroscopic scale.

      Temperature and heat are not defined for individual molecules and photons. Temperature is proportional to the MEAN kinetic energy of a large group of rapidly colliding molecules. Kinetic energy can be exchanged between two molecules during a collision or by emission and absorption of a photon. Heat flow is the NET transfer of energy two groups of molecules large enough to have a properly defined temperature.

  25. I just wish these ‘energy budgets’ would include the fact the planet is hot and there is a significant flux of nearly unknown magnitude from the planet’s interior. Many say this is a relatively tiny flux but for compleatness it should be included, and realistically there is no true understanding of how this flux varies geographically and through time,

    • Surfer Dave , you can lead a horse to water but you can’t make it drink .
      “About 50% of the heat given off by the Earth is generated by the radioactive decay of elements such as uranium and thorium, and their decay products. That is the conclusion of an international team of physicists that has used the KamLAND detector in Japan to measure the flux of antineutrinos emanating from deep within the Earth. The result, which agrees with previous calculations of the radioactive heating, should help physicists to improve models of how heat is generated in the Earth.”
      https://physicsworld.com/a/radioactive-decay-accounts-for-half-of-earths-heat/

  26. What an incredible read; I give you all credit for discussing some impressive discrepancies of the physics involved in all GHG concepts, and in planetary thermal budgets. This is what science is supposed to look like, from the experience of my career as a geologist.

    However, one observation I certainly can make–‘the science is certainly NOT settled’. After reading the article and the many informed discussions in the comments, anyone making a statement about settled science has to be a fool.

    There exists a self-proclaimed group in which 97% must apparently be fools.

  27. Phil: Figure 4 doesn’t illustrate the correct physics for radiation traveling through an atmosphere. When scattering is negligible (as it is for LWR), the incremental CHANGE in spectral intensity (dI) when radiation of a given wavelength passes an increment of distance (ds) through an atmosphere is given by the Schwarzschild eqn:

    dI = -n*o*I*ds + n*o*B(lambda,T)*ds

    where n is the density of GHG (absorbing/emitting molecules), o is absorption cross-section at wavelength lambda (not the Stefan-Boltzmann constant), I is the spectral intensity of the incoming radiation, and B(lambda,T) is the Planck function for the local temperature T and the wavelength lambda. The first term is the increment of absorption by the layer and the second term is the increment of emission by the layer. To properly calculate the CHANGE in radiation as it passes through an atmosphere, you need to numerically integrate this equation from the surface to space for OLR or from space to the surface for DLR. In the real atmosphere, most of these parameters are functions of altitude: n(z), o(z), I(z) and T(z). If the radiation comes from a filament at several thousand degK in the light source of a laboratory spectrophotometer, the emission term is negligible and this equation simplifies to Beer’s Law. When dI is 0, incremental absorption and emission are equal, and I must equal B(lambda,T). Planck’s Law was derived assuming radiation in equilibrium with its environment with absorption balanced by emission.

    https://en.wikipedia.org/wiki/Schwarzschild%27s_equation_for_radiative_transfer

    The Schwarzschild equation basically says that the intensity of radiation passing through an atmosphere approaches blackbody intensity for the local temperature at a rate proportional to the density of GHGs (n) and its absorption cross-section (o). In our atmosphere, this process can occur within meters for the most strongly absorbed wavelengths and has no effect on the most weakly absorbed wavelengths in the “atmospheric window”.

    It should be obvious that an equation that encompasses both Beer’s Law for absorption and Planck’s Law for emission contains the correct physics for most radiation transfer. The interesting question is whether or not your ad hoc methodology contains the same physics (or a reasonable approximation of the same physics) expressed in very different terms. I’ll try exploring that next.

    • Phil wrote: “The next assumption we must make is that the standard partition of energy by the atmosphere is being applied. The standard assumption is that for all energy fluxes intercepted by the atmosphere, half of the flux is directed upwards, and lost to space, and half of all captured flux is returned to the surface as back radiation and recycled. This concept is shown in figure 4 (reproduced here with kind permission).

      Fig. 4: Equipartition of energy flux by the Atmospheric layer (Jacob, 1999 Fig.7-12)

      Because the intercepted energy flux is being recycled this feed-back loop is an endless sum of halves of halves. It has the mathematical form of a geometric series, and is a sum of the descending fractions in the power sequence 2– n, where minus n is a continuous sequence of natural numbers ranging from zero to infinity.”

      Phil: Figure 4 is a type of figure that is often found in beginning textbooks that allows students to do simple radiative heat transfer calculations that have nothing to do with the real atmosphere. These are sometimes called shell models and the shells are sometimes made of solid material. All such models are grossly wrong. To get heat through a solid or gas shell, there must be a temperature gradient across the shell. Heat only flows from hot to cold, not between places with the same temperature. So, you can’t have the same amount of radiation going up as going down unless you are imagining a very thin layer. So, you model must be comprised of many very thin layers. (That is what one does when integrating the Schwarzschild equation.)

      In the real world, excited states of GHGs produced by absorbing a photon are relaxed by collisions much faster than they can emit a photon. Collision occur in the lower atmosphere occur about once a nano-second, while it takes an average of 1 second for the average excited state of CO2 to emit a photon. So absorbed photons become heat and the local temperature in the troposphere is generally controlled by convection, not radiation. There is NO significant re-emission of absorbed photons.

      The idea that absorbed energy is recycled back to the surface is incorrect, because upward and downward emission from the atmosphere is controlled by the local temperature, not simply by the local absorption of photons from below. Most of the troposphere is in a state of “radiative-convective” equilibrium. When temperature drops too rapidly with altitude – an unstable lapse rate – warm air from below rises because it is less dense until convection restores a stable lapse rate. Convection automatically transports upward whatever solar heat is absorbed by the surface that can’t escape upward fast enough as radiation because the lower troposphere is too opaque to thermal IR.

      Likewise the DLR photons that are absorbed by the surface become heat long before they can be “re-emitted” by the surface and re-cycled upward.

      Finally, the traditional solution to Figure 4 assuming NO CONVECTION doesn’t involve the sum of an infinite series. f is the absorptivity of a layer of atmosphere, which by Kirckhoff’s Law is also equal to its emissivity

      Energy Balance at the TOA:
      F_s*(1-A)/4 = (1-f)*o*T_s^4 + f*o*T_a^4 = o*T_s^4 – f*o*(T_s^4 – T_a^4)

      Energy Balance at the surface:
      F_s*(1-A)/4 = o*T_s^4 + f*o*T_a^4

      The two right hand sides must be equal:
      o*T_s^4 – f*o*(T_s^4 – T_a^4) = o*T_s^4 + f*o*T_a^4

      Simplifying: 2*T_a^4 = T_s^4

      This is an result that is found in many textbooks, possibly including the one you cited. The relationship between T_s and T_a doesn’t depend on f! (If f=0, then we divided both sides of the equation by zero when eliminating the f term from both sides, so this solution isn’t correct for f=0.) Given F_s and A, you can now calculate Ts and Ta.

      As I said before, none of this applies to a real atmosphere with convection

      • Frank,
        Thank you for looking at this with such and even handed and open-minded manner.
        My analysis of this issue started with the following linked diagram: Our Energy Budget published online by Professor Patricia Shapley, formerly of The University of Illinois at Urbana-Champaign.
        http://butane.chem.uiuc.edu/pshapley/genchem2/c1/1.html

        Professor Shapley has now retired from UIUC and I was not able to contact her to obtain permission to publish this diagram. However, she linked this analysis to NOAA who in turn referenced OK-First.

        I invite interested readers to also use this more detailed diagram. My calculation shows that using a none standard solar irradiance of 1300 W/m2 and the albedo of 31% given in this diagram, then the calculated average global surface temperature is 15C (the standard NASA irradiance of 1361 W/m2 generates a temperature of 18C).

        Please note that the figures I am using for my calculations are not my invention, they are implicitly buried within the published diagrams. The half in / half out rule is also hidden there in plain sight as my spreadsheet calculations show (Tables 3 & 4).

        • Phil: The idea that half of the energy absorbed by a “shell” representing GHGs in the atmosphere is returned to the surface is fundamentally incorrect. The shell MODEL allows students to make calculations showing how absorption and “re-emission” of absorbed energy in both directions. These calculations show how such shells can mimic a GHE. However, without atmospheric emission of LWR that depends on the local temperature and without convection determining the local temperature, you aren’t using the correct physics.

          I’m not sure why climate scientists don’t refer to Schwarzschild equation by name when they are discussing radiation transfer calculations and radiation transfer through the atmosphere. (I wrote the article in Wikipedia because there were few useful sources of information about how radiation transfer calculations were actually performed. Useful comments would be appreciated.)

          FWIW: The surface temperature of the Earth is actually controlled by what happens high in the troposphere. At steady state, the downward flux of energy (SWR+DLR) and the upward flux of energy (OLR + latent heat + sensible heat) at ALL altitudes must be the same. At the TOA, both directions average 240 W/m2 and are carried only by radiation. At the surface, both directions average 490 W/m2. Except for the atmospheric window, our atmosphere is almost totally opaque to LWR, but as you go higher in the atmosphere, more and more photons emitted upward escape to space. Near the surface, the average net upward LWR flux is only about 60 W/m2 (390 OLR – 333 DLR) and must be supplemented by 100 W/m2 of latent and convection to balance the 160 W/m2 of SWR that reaches the surface. By the time you get to the tropopause, the atmosphere has become less opaque to LWR and the average net upward radiative flux of LWR (OLR-DLR) is the 240 W/m2 needed to maintain a steady state. Below the tropopause, the upward flux needs to be supplemented by convection – and convection requires an unstable lapse rate. Therefore, from a critical point just below the tropopause, the temperature in the atmosphere is determined by the lapse rate. Let’s assume that critical altitude is 10 km, that the local temperature is 223 K, and that is warm enough for 240 W/m2 of net upward radiation (OLR-DLR) will escape to space from there. If the lapse rate averages 6.5 K/km to the surface, the surface it will be 288K.

          Much more SWR is delivered to the tropics and extra humidity makes the atmosphere more opaque. The critical altitude where LWR alone can carry the necessary outward flux is much higher and colder, say 16 km and 196 K. A 6.5 K/km lapse rate from there to the surface would make the surface 300 K.

          • Frank,
            Happy to talk to you off line.
            You can reach me via Research Gate.
            Phil

      • So absorbed photons become heat and the local temperature in the troposphere is generally controlled by convection, not radiation. There is NO significant re-emission of absorbed photons.

        The idea that absorbed energy is recycled back to the surface is incorrect, because upward and downward emission from the atmosphere is controlled by the local temperature, not simply by the local absorption of photons from below.

        That’s bad, that’s pretty bad if models taught in the schools and universities have little to do with reality.

        • Parameter: These (shell) models allow students to practice simple calculations involving radiation. They show a mechanism by which a planet could be warmed by absorbing outgoing radiation, producing something analogous to a GHE. They are valuable for these purposes.

          Unfortunately, activists want the public to think that the GHE and the anthropogenically enhanced GHE are simple phenomena that anyone can understand. So they don’t make the caveats and limitations of these models clear. They are happy if you believe in the aeGHE for any reason. So when a reasonably intelligent person like the author of this post recognizes some of the limitations of the material he has been taught, he has nowhere to turn for a more complete answer. Unfortunately, the answer Phil devised in this post didn’t begin with a correct description of the physics involved.

          We can calculate from first principles heat transfer by radiation through the atmosphere given its composition and temperature at all locations. However, such calculations require numerical integration of a differential equation that doesn’t have an analytical solution. We can calculate from first principles the steepest stable lapse rate the atmosphere can support, but we can’t used that to directly quantify heat transfer by convection.

    • Since this involves a metastable state it is in practice only excited/de-excited by collisions, so the cited statement by Jim is correct.

      • No, In my paper I have found that electrons and photon exit the O2 and O2 molecules and their IR spectra 1558cm-1 and 2348cm-1. The N2-CO2 laser exploits this and can operate on photons – just what the Sun emits. N2 and O2 absorb IR radiation- better that CO2.
        Besides, collisions is very Newtonian, hardly quantum.

  28. Good morning all.
    93 comments posted before I got out of bed.
    Not sure if I can keep up, but thanks anyway.

  29. Some atmosphere compositions will absorb much more heat than other compositions. Meaning that some will reach equilibrium at a higher temperature.

    J

    • Yes, but it is the specific gravities that matter rather than radiative capability.
      The greenhouse effect is a product of atmospheric mass conducting and convecting and not radiative gases.
      If one increases radiative gases then conduction and convection change ever so slightly to neutralise their effect.

  30. Great. Yet another Energy Budget that side-steps the issue of life on this planet and the energy it stores away.
    Yet more reductionist BS!

    So it take no energy to sustain life?
    OK where’s just where is the bit of energy that it took for humans (and all that they need) to go from about 1 billion 200 years ago and and today’s 8billion or so individuals. Oh, of course it take no energy for populations to increase, humans don’t need energy from the sun that why they eat rocks (sarc).

    Great bladders of unthinking complacent computer modeling prefossilized coprolite, can not see that life itself is one of the main modulators of this planet’s energy budget. Life itself in many forms, sequesters away large chunks of solar energy only to release it again spasmodically at some later date (seconds, hours, weeks, centuries later). Life affect how the carbon and water cycle operate. Life is the conversion of solar energy to chemical bonds!

  31. Hi Philip,

    there is very simple solution to confirm GHG warming theory. Without trying to simulate whole physics on molecular level. You will like it because it needs simple averaging of emission from whole Earth area to one value.
    If Earth is receiving more energy because closing of LWIR window of CO2. It can be very simply confirmed by satellite measurement tuned to this frequency (as I remember it is around 4.5um). If this thermal energy is staying on Earth (and warming it) Earth must be disappearing from IR pictures made on this wavelength and amount of radiation on this wavelength must be decreasing with relation to CO2 amount increase.

    It is simply about one 1 pixel instrument on satellite, sensing at 4.5um whole Earth area. And if GHG theory is true, it MUST detect decrease and increase (CO2 is fluctuating during year) of energy radiated from Earth on 4.5um, and it can tell us directly how much energy on this wavelength is still escaping Earth.

  32. This article along with the debate in comments, clearly show that the ‘greenhouse gas property’ is not being measured. We can’t measure it here on Earth and apparently we can’t even measure CO2’s ‘greenhouse gas property’ on Mars where it makes up 95% of the atmosphere.

    If it can’t be measured, how do we know it exists?

    Since nothing is being directly measured, we can’t derive any formulae to extend our knowledge.

    What other ‘properties’ are there that can’t be measured?

    If this is accurate: “A physical property is any property that is measurable” … then there is no Greenhouse Gas Physical Property because it can’t be measured.

  33. Your analysis is wrong, there is no requirement for equal partition up and down of atmosphere absorbed radiation inferred or implied in the KT radiative model. This changes everything, and makes Venus surface temperature possible.

    • Radiation is emitted in all directions equally which must imply half on an upward trajectory and half on a downward trajectory.
      However, following that rule the high surface temperature of Venus cannot be accounted for so the radiative theory is wrong just as Philip points out.
      The truth is that the upward and downward portions can vary as a result of the intervention of conduction and convection.
      It is that variability that leads to the greenhouse effect and not downward radiation from ghgs.

      • The surface of Venus emits around 17 kW per m2, yes? The atmosphere emits nearly all, but emits only around 160 W/m2 up and about 17 kW down. By what imagination can you say the Venusian atmosphere emits half up and half down?

        • “By what imagination can you say the Venusian atmosphere emits half up and half down?”
          Neogene Geo
          It does so at the mid-point depth.

          The formula for the area of a triangle is: –
          Half base length times perpendicular height.
          or if you prefer: –
          Base length times half perpendicular height.
          At which end do you crack open your boiled egg?
          Jonathan Swift would have loved this.

  34. I was investigating this little bit and I found that this LWIR CO2 window is on 4.3um.
    http://www.cis.rit.edu/files/512_SPIE_2004_Griffin.pdf
    Actually between 4.1 and 4.6um.
    Closest pictures I found are here on 5um
    http://sci.esa.int/rosetta/46276-virtis-view-of-the-earth-ir-2/
    And here combination of three channels of 4.92 µm, 2.25 µm and 1.20 µm, where 4.9 is another absorption maximum for CO2 but masked by H20.
    http://sci.esa.int/rosetta/46274-virtis-view-of-the-earth-ir-1/

    If Earth is opaque on 4.3um there can not be any greenhouse effect, because this window is already saturated. And all reflected IR is on 4.3um is staying on Earth.

  35. @tty May 23, 2019 at 1:46 pm

    Geothermal heat flow is only on the order of 0.1 Wm-2. Negligible.

    The geothermal flux (GF) through the crust is only ~0,065 W/m^2 on average.
    Yet the crust TEMPERATURE is high, and gets hotter the deeper you go.
    https://www.mpoweruk.com/images/geo_temperature.jpg

    Are you saying that these temperatures can be neglected and that the surface temperatures would be the same if Earths interior was cold (like 0K cold) ?

    • You’re right to question the statement you quoted:

      “Geothermal heat flow is only on the order of 0.1 Wm-2. Negligible.”

      Shall we calculate the mass of the Earth which is heated from geothermal heat flow and contrast it with the mass of the atmosphere? What temperature would the oceans be without geothermal heat flow?

      • Thomas Homer

        “What temperature would the oceans be without geothermal heat flow?”

        To obtain an answer to your question you need to compute the effect of 240 W/m² of solar irradiance arriving at ocean’s surface.

        Searching for “ocean heating comparison geothermal flux with solar irradiance” gives as first link:
        https://core.ac.uk/download/pdf/11532717.pdf

        Allez-y, Monsieur.

      • @Thomas Homer May 24, 2019 at 10:05 am

        Shall we calculate the mass of the Earth which is heated from geothermal heat flow and contrast it with the mass of the atmosphere?

        Except for the upper ~10m of crust and the upper ~500m of ocean the entire Earth is hot due to geothermal energy.
        The sun only increases the temperature of these layers a bit to reach our observed surface temperatures.
        At 290K without atmosphere Earth would radiate ~400 W/m^2 directly to space.
        Thanks to the atmosphere we only loose ~240 W/m^2 and have an energy balance with incoming solar energy.
        On the other hand, the atmosphere prevents some 140 W/m^2 of solar from reaching the surface.
        So the idea of the atmosphere “further heating the ground” (*) is pretty absurd imo.

        (*) https://www2.bc.edu/jeremy-shakun/Lacis%20et%20al.,%202010,%20Science.pdf

        • Ben: If the atmosphere can’t “further heat the ground”, what heats Venus. Radioactive decay from deep inside the planet?

          Don’t tell me pressure heats anything. Pressure times a change in volume is work/energy, but pressure alone doesn’t heat anything. The soil under the foundation of a skyscraper is essentially the same temperature as nearby soil. You can heat gases by subjecting them to pressure, but you can’t stop them from cooling (by radiation, convection or conduction) once they are hot.

          • Frank May 25, 2019 at 7:42 pm

            what heats Venus. Radioactive decay from deep inside the planet?

            I’m not very familiar with Venus, but a possible explanation along the same lines as for Earth seems possible.
            Think of the Venus CO2 atmosphere as existing of two parts,:
            – high density, not receiving any solar radiation, like our oceans.
            – low(er) density and receiving solar energy, more like our atmosphere.
            A layer with higher temperatures due to solar energy would block the internal geothermal energy from escaping to space, unless the temperatures of the deep layer (oceans), heated by geothermal, is high enough.
            So yes, the high temperature of the solid surface (~ocean floor) could well be caused by geothermal energy.

            The soil under the foundation of a skyscraper is essentially the same temperature as nearby soil.

            Yes, the soil temperature determines the start temperature of the geothermal gradient.
            In principle the geothermal gradient starts at the average surface temperature at that location. Due to the very low FLUX it takes time for the gradient to adjust to changing temperatures like when coming out of a glacial.
            https://en.wikipedia.org/wiki/Geothermal_gradient#Variations

        • Ben wrote: “So the idea of the atmosphere “further heating the ground” (*) is pretty absurd imo.”

          I’ll try to be clearer this time. Our climate system is heated by the sun (SWR): 240 W/m2 after albedo on the average. Our climate system is cooled by radiative cooling to space (LWR): 240 W/m2 on the average (240-0.7 W/m2 according to ARGO measure of the rate of ocean warming). The heat coming from inside the Earth is negligible (0.1 W/m2, https://en.wikipedia.org/wiki/Earth's_internal_heat_budget).

          Everything else is an INTERNAL transfer of energy. These fluxes don’t heat or cool our climate system; they move energy around inside that system. The atmosphere “further heating” the surface is an internal transfer of energy. The average net radiative transfer of energy from the surface to the atmosphere is: 390 W/m2 emitted by the surface – 40 W/m2 escaping directly from the surface to space through the atmospheric window – 333 W/m2 of DLR reaching the surface of the Earth = 17 W/m2. The net flux of energy is called heat and it always flows from warmer to cooler, as it does here. To this 17 W/m2, you might add 80 W/m2 of latent heat and 20 W/m2 of sensible heat (conduction when cooler air molecules collide with the warmer surface).

          When you have multiple sources of energy, it is impossible to say that one particular source “heated” anything. Likewise, an object can get warmer if you slow down the rate at which it loses heat and keep inputs the same. Because the term “heat” has a special meaning in the 2LoT, it is safer to discuss transfer of energy. According to the law of conservation of energy, if an object gains more energy by all routes than it loses by all routes, the difference between these fluxes becomes “internal energy”. Heat capacity is the factor that converts higher internal energy to higher temperature. If an object loses more energy by all routes than it gains by all routes, the difference between these fluxes comes from the objects “internal energy” – it cools.

          Individual molecules and photons have energy, but they don’t have a temperature or obey the 2LoT. Temperature and heat are terms that only apply to large groups of colliding molecules – their temperature is proportional to their MEAN kinetic energy. The 2LoT is a consequence of large numbers of individual molecules and photons obeying the laws of quantum mechanics.

          • “I’ll try to be clearer this time.”
            Frank,
            Very clear.
            Thank you for providing us with a very useful analysis.
            Philip

        • Ben: For a simple one-dimensional situation between to surfaces, heat transfer is calculated by Fourier’s Law:

          q = -k*(T2-T1)/L

          where q is heat transferred, L is the distance over which heat is transferred, T2 and T1 are the temperatures on each surface and k is thermal conductivity.

          Imagine a layer of granite 1 m thick. Thermal conductivity for granite is 2 W/m/K. So, if it is 1 K warmer at the bottom of this layer, 2 W of heat will be conducted through the granite. If we focus on each square meter of granite, that will be 2 W/m2 of heat flowing through the granite. Replace the granite with polyurethane foam insulation (k = 0.03 W/m/K) and only 0.03 W/m2 of heat will be conducted over this 1 m.

          Now make the granite layer 1 km thick and the temperature difference between the top and bottom 1000 K. 2 W/m2 will still be flowing from the bottom surface to the top surface.

          Now let’s take enough uranium-238 so that radioactive decay produces 100 W. Place it inside a 1m thick shell of granite with a surface are of 10,000 m^2 (ie radius about 28 m. Put the shell and uranium in interstellar space. When the system reaches equilibrium, 0.01 W/m2 of thermal radiation will be leaving the surface of the granite. We will need a temperature difference of only 0.005 K, to drive 0.01 W/m2 through 1 m of granite. Assuming an emissivity of 1, the surface will need to be about 20 K to emit 0.01 W/m2.

          Now let’s look at the our planet. The estimate is that about 50 TW of heat are released inside the Earth by radioactive decay. That is an average of about 0.1 W/m2 of surface. Let’s say that the crust is 10 km of solid granite. The temperature difference across the 10 km of granite would need to be 500 K to drive 0.1 W/m2 of heat through 10 km of granite AT STEADY STATE. Therefore, if the surface temperature of our planet were 288 K, then below a 10 km granite crust the temperature would be 788 K. And that 788 K would only produce a flux from below of 0.1 W/m2 to add to the 160 W/m2 of SWR and 333 W/m2 of DLR that arrive at the surface from above. Negligible. (A 36 K surface with an emissivity of 1 would emit 0.1 W/m2.) 10 km of granite is effective insulation that can keep the interior of the planet at 800 K using a power source equivalent to a 100 W light bulb in a sphere 10 m in radius. A mantle at near 800 K can’t deliver a significant amount of power THROUGH 10 km of granite. Even if we raised the temperature to 8000 K, we would only get 1 W/m2 to the surface.

          To put it more simply (I should have started here), if there is only enough radioactive material inside the Earth to release 0.1 W per m^2 if the planet’s surface, then the surface of the planet can only receive 0.1 W/m2 of power from the interior! The thermal conductivity of the crust determine how much hotter it will be inside the planet than at the surface, not how much power the surface receives from below at steady state. If we make the conductivity of the crust lower or higher, the temperature inside the Earth will change, but the amount of power delivered to the surface will remain the same.

          • Frank May 29, 2019 at 12:38 pm
            Thanks for the extensive reply. Can agree with most of what you write.

            Imo it is possible to distinguish between the influence of the geothermal flux and the solar heating of the solid surface because the sun doesn’t shine continuously.
            Over a year the avg. surface temperature changes typically like in this image:
            https://www.researchgate.net/profile/Murat_Aydin19/publication/286456011/figure/fig1/AS:305488735555588@1449845598381/Ground-temperature-variation-with-depth-at-different-months-for-Maslak-Istanbul-Turkey.png
            In spring and summer the surface gets warmer and this heat penetrates into the soil.
            In autumn and winter the surface cools again and the stored heat from the sun returns to the surface and is lost to space eventually.
            In this example the maximum penetration of solar influence is ~10m.
            Imo is the temperature of the crust below this 10m entirely caused by geothermal heat.

            Without sun the surface would indeed be ~34K to radiate away the geothermal flux (GF) and the crust would be cold. At eg. 3km the temperature would be around 140K.
            Compare this to: https://www.mpoweruk.com/images/geo_temperature.jpg
            Temperature at 3km ~390K
            So the sun heating the surface causes the crust to be so hot that the flux can “flow” , unless the surface gets hotter than the core of course 😉
            Same for our oceans, the seasonal warming/cooling creates a warm mixed surface layer.
            Solar influence in this example is to around 400m deep:
            http://www.climate4you.com/images/ArgoTimeSeriesTemp59N.GIF
            This solar heated layer completely blocks bottom heated water from reaching the surface, unless that surface is as cold as the deep oceans (high latitudes)

            To me it is clear that the heat content of the deep oceans is of geothermal origin.
            Young oceans were hot since they sat on more or less bare magma.
            Since then their temperature has been maintained by geothermal heating (flux and large magma eruptions) minus cooling at high latitude.
            100 mW/m^2 flux is capable of warming the average ocean column 1K every 5000 year.
            Magma eruptions like the Ontong Java one (100 million km^3 magma) deliver enough energy to warm ALL ocean water ~100K.
            Unless enough energy is lost at high latitudes the oceans warm up.
            Last ~85 million years the deep oceans cooled some 17K after the Ontong Java heating,
            eventually bringing us into the current ice age.

            (i’ll stop here to see if my post comes through)

        • Ben wrote: “So the idea of the atmosphere “further heating the ground” (*) is pretty absurd imo.”

          Our climate system is heated by about 240 W/m2 of post-albedo SWR. Our climate system is cooled by 240 W/m2 of LWR escaping to space.

          (If you want to be picky and account for the current warming rate of the ocean, melting of permanent ice, and heat from inside the Earth, radiative cooling is about 0.8 W/m2 less the solar warming.)

          Radiation from the atmosphere to the surface is an INTERNAL transfer of energy. It does NOT ” heat” or cool our climate system (the surface, atmosphere and oceans).

          The term “heat” is tricky because it has a special meaning with regard to the 2LoT. If is safer to say that that atmosphere delivers an average of 333 W/m2 of energy to the surface in the form of absorbed DLR, while the surface is delivering an average of 350 W/m2 of energy to the atmosphere (390 W/m2 of upward thermal radiation, 40 W/m2 of which escapes directly to space through the atmospheric window). Technically, heat is the difference between these two radiative fluxes, 17 W/m2 that is flowing from the warmer Earth to the cooler atmosphere.

          However, when an object is receives and loses energy by multiple mechanisms, it is grossly misleading to say that ANY one of these fluxes “heats” the object. According to conservation of energy, if the sum of the inward fluxes is bigger than the sum of the outward fluxes, the “internal energy of the object rises. Heat capacity tells us how to convert a change in internal energy into a change in temperature. When an object receives less inward energy flux than it losses via outward fluxes, the difference is taken from its internal energy and the object cools. If you insulate an object and slow down the rate at which it LOSES energy, it will get warmer. This is why it is misleading to say that any particular flux “warms” the object when multiple fluxes are involved – even changes in outgoing fluxes can cause a temperature increase.

          In addition to the obvious radiative fluxes, energy leaves the surface of the planet as latent heat (evaporation of water) and sensible heat (conduction when air molecules collide with the surface). And both of these mechanisms are technically the NET result of TWO-WAY transfers, just like radiation. When relative humidity is 100%, water molecules still escape from the surface of the ocean, but just as many are returning to the ocean, meaning NET evaporation is zero. Relative humidity over the oceans is 80%, so the water molecules escaping to the atmosphere carry 400 W/m2 of energy (heat of evaporation) and those returning (without precipitating) carry 320 W/m2. Energy transfer is almost always in two directions, but in thermodynamics NET transfer is called “heat”.

          Finally, individual molecules and photons have energy, but they don’t have a temperature or carry heat. They obey the laws of quantum mechanics, not the 2LoT. Temperature is the MEAN kinetic energy of a large group of rapidly colliding molecules. When large groups of rapidly colliding molecules obey the laws of quantum mechanics, the result is macroscopic behavior consistent with the 2LoT: The NET flux of energy is always from the hotter GROUP to the colder GROUP.

        • Ben wrote: “Imo it is possible to distinguish between the influence of the geothermal flux and the solar heating of the solid surface because the sun doesn’t shine continuously. Over a year the avg. surface temperature changes typically like in this image:

          How far below the surface of the Earth does one need to go before heat transfer from below determines the temperature?

          As you can see from your link, temperature vs depth changes with the seasons only a few meters into the ground. The seasonal change in surface temperature is a little more than 20 degC and about 1.5 m down it is only about 10 degC. Caves famously have the same temperature all year round.

          At Prudhoe Bay, Alaska, the permafrost extends 1.5 km into the ground. So the colder surface temperature in the Arctic than elsewhere on the planet extends far into the ground.

          https://en.wikipedia.org/wiki/Permafrost

          Your linked graph showing temperature vs depth at several locations in Europe shows a gradient of 3.5 degC/100 m, which means that this temperature gradient is to convect 0.1 W/m2, a thermal conductivity of about 3 W/m/K, slightly more than the figure I looked up for granite. The yellow line in France and green line for Italy have much different slopes near the surface, 0.1 K/m and 1 K/m. Their thermal conductivities are 1 and 0.1 W/m/K.

          The plot of Argo data is from 59 degN, 330-360 degE, which I presume means the North Atlantic just south of southern tip of Greenland. It is not typical of the seasonal change in most locations, possibly because this is where the Gulf Stream brings heat from the tropics. The “mixed layer” of the ocean is the average depth that seasonal changes in temperature penetrate the ocean. It is calculated by summing up the heat flux at all depths associated with seasonal temperature change and then dividing by the surface temperature change. The mixed layer averages 50 m: deeper in the SH where the wind is stronger and shallower in equatorial regions where there is little seasonal change. Willis used ARGO data in a WUWT post to calculate the depth of the mixed layer. If you look at the link below, you can see that seasonal surface temperature change can be seen globally at 2.5 m (amplitude of average change 0.6 degK) and at 100 m (amplitude 0.2 degK), but not at 200 m. The other ARGO plots at climate4you are consistent with the idea that the mixed layer is about 50 m.

          http://www.climate4you.com/images/ArgoWorldOceanSince200401%2065N-65S.gif

          Ben wrote: “To me it is clear that the heat content of the deep oceans is of geothermal origin.”

          Most authorities would disagree with you. There are two bodies of water in the deep ocean with temperatures and salinities characteristic of the location where they sink below the surface: Antarctic Bottom Water and North Atlantic Deep Water. There are some hot spots where magma and heat from inside the planet cause local warming (and usual bacteria and other species live). For the most part, the ocean is “stably stratified”, with denser (colder and saltier) water below and less dense (warmer) near the surface. Pushed by deep water formation in the Arctic and Antarctic, the ocean turns over about every 1500 years. The process is called the thermohaline circulation.

          https://www.researchgate.net/profile/Roberto_Violante/publication/321524379/figure/fig12/AS:583405104779264@1516106024044/Schematic-disposition-of-main-water-masses-in-the-Atlantic-Ocean-AABW-Antarctic-Bottom.png

          • Frank June 5, 2019 at 8:45 am

            How far below the surface of the Earth does one need to go before heat transfer from below determines the temperature?

            I haven’t seen anything that shows seasonal influence below ~10m.
            Also the Permafrost example shows no influence deeper down.
            https://upload.wikimedia.org/wikipedia/commons/7/7b/Vertical_Temperature_Profile_in_Permafrost_%28English_Text%29.jpg
            The Geothermal Gradient starts at the average surface temperature, and the temperature steadily increases with depth.
            Without sun the surface would be 30-40K to radiate away the GF. You would have to go some 7 km deep before the temperature reaches 0C.

            The yellow line in France and green line for Italy have much different slopes near the surface, 0.1 K/m and 1 K/m. Their thermal conductivities are 1 and 0.1 W/m/K.

            Probably geologically active areas. Italy for sure. Could be a magma chamber close to the surface.

            The other ARGO plots at climate4you are consistent with the idea that the mixed layer is about 50 m.

            Probably correct, but I needed to show what the maximum depth is where solar influence can be detected. Assuming the plot shows the effect of the Gulfstream, then this is solar heated water that reaches down to ~400m.
            Same for el Nino, solar heated water at some 300 m deep.

            For the most part, the ocean is “stably stratified”, with denser (colder and saltier) water below and less dense (warmer) near the surface. Pushed by deep water formation in the Arctic and Antarctic, the ocean turns over about every 1500 years. The process is called the thermohaline circulation.

            The THC is mostly driven by AABW plunging down into the deep oceans. The second driver is the 0,1 W/m^2 GF that warms the water in contact with the ocean floor. Without heating at the ocean floor the ocean would just fill up with AABW and the THC would stop.
            http://talleylab.ucsd.edu/ltalley/sio210/nov5/schmitz_conveyor.jpg
            0,1 W/m^2 GF is capable of warming ALL ocean water 1K every ~5000 year.
            To warm the deepest ~40 m 1K would take ~50 years.
            Realize that every liter of bottom heated water must be physically transported to the surface at high latitudes before its energy can be transferred to the atmosphere and space.
            http://www.ewoce.org/gallery/P15_TPOT.gif

    • Yes indeed but Erl still accepts the consensus view that an active sun increases ozone whilst a quiet sun reduces ozone which appears not to be correct in that apparently the ozone response to solar variations is reversed above 45 km and over the poles.
      I have a separate hypothesis regarding that which is not directly relevant to this particular thread.

  36. This post has been made twice now, and never showed up:

    @ tty May 24, 2019 at 9:11 am
    The sun heats Earths surface, and blocks the internal heat unless the crust is hot enough to losse heat in winter time.
    https://www.researchgate.net/profile/Murat_Aydin19/publication/286456011/figure/fig1/AS:305488735555588@1449845598381/Ground-temperature-variation-with-depth-at-different-months-for-Maslak-Istanbul-Turkey.png
    Without sun the surface would be ~30-40K to radiate away the GF and the geothermal gradient would start at this surface temperature.

    Same mechanism is true for the oceans. The sun maintains a warm surface layer that prevents geothermal energy from reaching the surface, except at (very) high latitudes.
    Once you realize that the heat content of the oceans is mostly of geothermal origin it is simple to explain our surface temperatures:
    the solar energy that reaches the surface only increases the temperature of the mixed layer a bit above the geothermally heated deep(er) oceans.

    The thermohaline circulation transports bottom “heated” water mostly towards Antarctica, where energy can be exchanged with the atmosphere.

    http://talleylab.ucsd.edu/ltalley/sio210/nov5/schmitz_conveyor.jpg

    Mechanical driver (gravity) seems to be the brine formed during ice creation, that “plunges” towards the ocean floor like a waterfall.

    [Wordpress has for some reason flagged you for deletion. A moderator needs to regularly look in the Trash folder, and pull out those wrongly put on the Blacklist. I will delete your first 2 attempts. Mod]

    • Ben, May 25, 2019 at 2:52 pm
      That is a graph and a diagram that both have lots of interesting features.
      I recommend that you build a post around them and submit your ideas to Anthony, so we can discuss the points you raise on a dedicated thread.
      Philip

      • Philip Mulholland May 26, 2019 at 5:44 am

        I recommend that you build a post around them and submit your ideas to Anthony, so we can discuss the points you raise on a dedicated thread.

        I made a few posts on this subject on “that other site” but it seems I do not strike the right cords to get my ideas across.
        https://tallbloke.wordpress.com/2014/03/03/ben-wouters-influence-of-geothermal-heat-on-past-and-present-climate/
        https://tallbloke.wordpress.com/2014/10/14/ben-wouters-geothermal-flux-and-the-deep-oceans/

        Only change I would make now is adding a calcuation showing that 1 million km^3 magma carries enough energy to warm ALL ocean water 1K.

      • Philip Mulholland

        “That is a graph and a diagram that both have lots of interesting features.”

        Really?

        1. Did you have a look at the paper hidden behind the graph?

        Experimental and computational performance comparison between different shallow ground heat exchangers

        Aydin & al. 2015

        https://www.researchgate.net/publication/286456011_Experimental_and_computational_performance_comparison_between_different_shallow_ground_heat_exchangers

        From there I downloaded the pdf file and read it carefully.

        The paper has nothing to do with any kind of geothermal heating let alone with a comparison of geothermal vs. solar flux.

        But you don’t need to read the full paper to understand that Ben Wouters misunderstood its goal: the intro is enough. I paste it here (my emphasis in bold):

        Heat pumps have the capability to be integrated with geothermal and renewable resources for heating and cooling load of buildings. They have considerable advantages besides the conventional heating and cooling systems. Ground source heat pumps (GSHPs)
        have great importance because the ground has stable temperature throughout the year.

        The main disadvantage of GSHPs is their high initial cost. The cost of vertical boreholes has an especially large contribution to the total cost. Horizontal Ground Heat Exchangers (GHE) have a relatively lower cost. Horizontal GHE are easy to install and much cheaper than the vertical ones. On the other hand, there are some criticisms on horizontal GHE, like requiring wide spaces and giving poor performance in cold winter times.

        This is in perfect contradiction to what Wouters tried to interpret out of the article.

        The ground heat exchange systems described by the four Turkish scientists operate at a depth of about 2 (two) meters: this is far far above the average depth used for geothermal heat extraction: around 400 (four hundred) meters.

        If the horizontal GHE system doesn’t work during cold winters, then the probability is very high that this technique is based on solar radiation.

        And it is also very probable that it only works in those countries showing an average solar radiation by far higher than e.g. in… the Netherlands 🙂

        2. The little student education web page above the 3D-diagramme does not have anything to do with geothermal heat. It doesn’t even contain that word.

        Look at these picture describing temperature in relation to depth and longitude in the Atlantic:
        http://talleylab.ucsd.edu/ltalley/sio210/nov5/A16_THETA.gif

        … and in the Pacific:
        http://talleylab.ucsd.edu/ltalley/sio210/nov5/p16_ptem.gif

        Interesting, isn’t it? You perfectly see here the amazing contribution of geothermal heat to ocean’s temperatures.

        Sorry: that is what happens when people present information solely intended to match their personal narrative.

        • Bindidon
          “1. Did you have a look at the paper hidden behind the graph?”
          No.
          Did you read my second sentence?
          “I recommend that you build a post around them and submit your ideas to Anthony, so we can discuss the points you raise on a dedicated thread.”
          Philip

        • @Bindidon May 26, 2019 at 3:50 pm
          What I wrote:

          The sun heats Earths surface, and blocks the internal heat unless the crust is hot enough to losse heat in winter time.

          Without sun the surface would be ~30-40K to radiate away the GF and the geothermal gradient would start at this surface temperature.

          Accompanied by an image showing typical temperature vs depth plot over a year, in this case for some place in Turkey.

          In this image some temperature vs depth plots:
          https://www.mpoweruk.com/images/geo_temperature.jpg
          Are you saying that these profiles would be the same when we had no sun warming the surface?

          Interesting, isn’t it? You perfectly see here the amazing contribution of geothermal heat to ocean’s temperatures.

          More convincing:
          http://www.climate4you.com/images/ArgoTimeSeriesTemp59N.GIF
          A plot showing typical seasonal warming/cooling of the mixed surface layer of our oceans over 15 years. No influence of whatever heats the surface below ~400m.
          What is in your opinion the energy source for the oceans below this 400m (or below 1000m to be generous).
          Especially interested in how you explain the very high deep ocean temperatures in the Cretaceous. (ocean floor temperatures up to 17 degrees higher then today)

  37. Like others, I don’t follow the author’s math. In Kiehl and Trenberth 1997’s figure 7 (author’s figure 3), the atmosphere upward flux is 195 W/m^2 and the downward flux is 324 W/m^2. That’s 195 W/m^2 + 324 W/m^2 = 519 W/m^2. As a check (for consistency), we have the total input to the atmosphere as 67 W/m^2 from the Sun, 24 W/m^2 sensible heat flux, 78 W/m^2 latent heat flux, and 350 W/m^2 from the surface, and this also adds to 519 W/m^2. The percentage of downward flux is 324 W/m^2 / 519 W/m^2 = 62.4%. The percentage of upward flux is 195 W/m^2 / 519 W/m^2 = 37.6%. It’s not exactly fifty-fifty.

    I’ve modeled the atmosphere using multiple layers. As the layers get thinner, the fifty-fifty upward-downward radiation assumption of a layer becomes more valid. But taken as a whole, the 40/60 split is more valid for the Earth.

    I also modeled K & T 1997 using a simple EXCEL spreadsheet. To deal with feedback (which EXCEL won’t allow), I created a macro that transfers the contents from one cell to another cell multiple times in a loop. It’s interesting, but this EXCEL model will stabilize at the K & T 1997 numbers.

    As the author mentioned, there are two ways to warm the surface: 1) narrow the IR window (increase the GHE), and 2) reduce the albedo (make the planet darker). In one case, the atmosphere warms first, then the surface warms, then the atmosphere, then the surface, and so on until the system stabilizes. In the other case, the surface warms first, then the atmosphere warms, then the surface, then the atmosphere, and so on until it stabilizes at a new value.

    Is it possible to distinguish between these two cases? My simple EXCEL model isn’t going to do an exact job with the physics, but for very small changes it should be in the ball park.

    We have the heat flux for the atmosphere and the surface. What we need are the emissivities. The surface is close to 1.0, so using 1.0 won’t be too far out-of-line. The atmosphere is another matter. I tend to think its emissivity is around 0.6. I’ve seen some estimates as low as 0.36, whereas 1.0 is probably far too high.

    Using a range of emissivities, and narrowing the IR window until the surface warms by 1 K, I get an atmosphere change of 1.3 K to 1.6 K. If I decrease the albedo until the surface warms by 1 K, I get an atmosphere change of 0.6 K to 0.9 K. So we can distinguish between the two cases.

    I’ve tried to compare actual temperatures, but the surface temperatures are so doctored, that they no longer reflect reality. Even so, it looks like the current warming is being caused by a change in the Earth’s albedo–not a GHE.

    Jim

    • “Like others, I don’t follow the authors math”
      Jim,
      Thank you for posting and for taking up the struggle.

      First where to start? I recommend that you start at ground level. Here we find that there are three upwelling fluxes, these are: –
      1. Surface Radiation which is 390 W/m^2,
      2. Surface Thermals which are 24 W/m^2,
      3. Surface Evaporation which is 78 W/m^2.
      These three outgoing components sum to a total surface outgoing flux of (390 + 78 + 24) = 492 W/m^2.
      From the diagram we also know that the there are two incoming energy fluxes; –
      1. Insolation Absorbed by Surface (168)
      2. Back Radiation Absorbed by Surface (324)
      These two components sum to a total Downward Flux reaching the Surface of (168 + 324) = 492 W/m^2. So, at the surface we have a balance.

      Now we can see that the surface radiation of 390 W/m^2 is clearly labelled in the diagram. Using Stefan-Boltzmann (S-B) this flux converts to a thermodynamic surface temperature of 288 Kelvin (15C). This is the global average temperature that the authors’ list in their paper.

      We also see in the diagram that from this 390 W/m^2, 40 W/m^2 is lost to space via the Atmospheric Window, which leaves the (390-40) = 350 W/m^2 of Surface Radiation Absorbed by the Atmosphere. This is also listed in the diagram, but 324 W/m^2 is returned to the Surface as Back Radiation. This means that the net back radiation gain to the Atmospheric Reservoir is (350-324) = 26 W/m^2. This value is the Greenhouse Gas Radiant Blocking effect.

      Next, we calculate the fluxes which are Absorbed by the Atmosphere. These are as follows: –
      1. Solar Insolation Absorbed by the Atmosphere (67),
      2. Thermals delivered to the Atmosphere (24),
      3. Latent Heat delivered to the Atmosphere (78) and of course
      4. The Greenhouse Gas Radiant Blocking mentioned above (26).
      These four components sum to (67 + 24 + 78 + 26) = 195 W/m^2.

      Now the target flux is 390 W/m^2 and 195 is half of 390, so where does the other 195 W/m^2 come from? The answer is infinite recycling in a geometric series of halves of halves.
      So how does that work? Well the atmosphere has a linear gradient loss rate from the surface to the TOA. There is very little loss at the base and total loss at the top. We can collapse this infinitely thin series loss staircase into a single calculation at the mid-point depth. (Think of standard calculus for computing the area of a triangle for example)
      At this mid-point level, we have half the flux passing up and lost to space, and half the flux passing down and recycled.

      So now we can double the flux in the atmospheric reservoir from 195 W/m^2 to the 390 W/m^2 value reported in the diagram. This doubling occurs because the limit of an infinite geometric series of fractions to the base two (1/2 + 1/4 +1/8 + 1/16 + etc.) =1
      The doubling of the flux within the atmospheric reservoir by infinite recycling creates the flux value of 390 W/m^2 that is required to explain the S-B global average temperature of 288 Kelvin (15C).

      • >>
        Now the target flux is 390 W/m^2 and 195 is half of 390, so where does the other 195 W/m^2 come from? The answer is infinite recycling in a geometric series of halves of halves.
        <<

        Again your math is faulty. You subtracted 324 W/m^2 from the surface-atmosphere loop, so your question should be: “Where does the 324 W/m^2 come from?”

        With the missing 324 W/m^2 (you subtracted it out), then the surface is radiating 26 W/m^2 + 40 W/m^2 = 66 W/m^2. The total energy flux leaving the surface is 24 W/m^2 + 78 W/m^2 + 66 W/m^2 = 168 W/m^2. That’s the exact value that the surface absorbs directly from the Sun. You need to increase the atmosphere from 195 W/m^2 to 519 W/m^2 or 519 W/m^2 – 195 W/m^2 = 324 W/m^2.

        I’m afraid you’re mixing up the atmosphere energy flux with the surface energy flux. You can’t make that 324 W/m^2 up with a fifty-fifty split from the atmosphere–you need something like a 62-38 split.

        Jim

        • “Again your math is faulty. You subtracted 324 W/m^2 from the surface-atmosphere loop, so your question should be: “Where does the 324 W/m^2 come from?””
          Jim,
          I call it like this: –
          1. The Surface Thermals (24 W/m^2) and
          2. The Surface Evaporation (78 W/m^2) are both surface cooling losses
          Both of these processes are powered by solar insolation. Therefore, these two values must be subtracted from the only credible source of energy that can power them, namely solar insolation.
          Solar insolation is 168 W/m^2 so that means we have (168 – 24 -78) = 66 W/m^2 of surface radiant energy left over. Now 40 w/m^2 of this surface radiant energy is lost to space through the atmospheric window, so we have (66 -40) = 26 left over to add to the atmospheric reservoir.

          As before, for the atmospheric reservoir we have we have: –
          1. Solar Insolation Absorbed by the Atmosphere (67),
          2. Thermals delivered to the Atmosphere (24),
          3. Latent Heat delivered to the Atmosphere (78) and of course
          4. The Greenhouse Gas Radiant Blocking mentioned above (26).
          These four components sum to (67 + 24 + 78 + 26) = 195 W/m^2.

          This 195 W/m^2.is the raw power that drives the climate system. Everything else in the system e.g. the 324 W/m^2 of Back Radiation is a consequence of flux recycling. How that flux recycling occurs is a matter for interesting debate. But power intensity flux recycling is what it is.

          • >>
            I call it like this: –
            <<

            And then you reproduce my calculations.

            A surface emitting 66 W/m^2 has a temperature of about 184 K (using Stefan-Boltzmann law). That’s (184 K – 273 K)*(1 °C/K) = -88 °C. It is really cold. Carbon dioxide freezes out at about -78.5 °C at 1 atmosphere. There shouldn’t be any (major) GHGs at that temperature.

            Your numbers (actually K & T 1997’s numbers) are only valid for a surface temperature of 288 K with plenty of water vapor in the atmosphere. You would need a model with lots of physics in it to determine the various fluxes (albedo, sensible heat flux, latent heat flux, IR window, etc.) with such a large change in surface flux. That 66 W/m^2 wouldn’t be correct with 324 W/m^2 missing either. All these fluxes depend on each other in complex ways.

            >>
            How that flux recycling occurs is a matter for interesting debate.
            <<

            It’s simple really: up, down, up, down, up, down, and so on. However, if you use multiple layers and solve them simultaneously, the recycling is taken care of.

            Jim

          • “And then you reproduce my calculations”
            Jim,
            In the diagram K&T show that the surface flux is composed of 3 elements: –
            1. Thermals delivered to the Atmosphere (24),
            2. Latent Heat delivered to the Atmosphere (78)
            3. Surface Radiation (390)
            Together these three elements, clearly shown in the diagram, sum to (24 + 78 + 390) = 492 W/m^2 which provides us with a S-B thermodynamic temperature of 305.2 Kelvin (32.2C).
            All I trying to do is describe the published elements in the K&T diagram using their numbers.
            However, a description is not an explanation.
            For an explanation we needed clarity by the authors’ in the presentation of their ideas.
            To create a diagram that shows Back Radiation in the form given by K&T pretty much boils down to: –
            “And then at this point a miracle occurs.”

    • “Using a range of emissivities, and narrowing the IR window until the surface warms by 1 K, I get an atmosphere change of 1.3 K to 1.6 K. If I decrease the albedo until the surface warms by 1 K, I get an atmosphere change of 0.6 K to 0.9 K. So we can distinguish between the two cases.”
      Jim,
      A really nice piece of analysis, I hope that you persevere.

    • Atmospheric long wave emissivity is easily calculated if upward surface flux and the atmospheric window flux are known. Using the KT diagram above, e= 0.9. The problem is that there is no time-series observation or calculation of AtMWindow, so we cannot see how it changes over time. You need AtmWin to determine the atmospheric partition factor, which as you correctly surmised is 0.38 if you include non-radiative heat transfers into the atmosphere. These kinds of energy budgets don’t have the observational data necessary to solve for emissivity in principle

  38. @Bindidon May 26, 2019 at 3:50 pm
    What I wrote:

    The sun heats Earths surface, and blocks the internal heat unless the crust is hot enough to losse heat in winter time.

    Without sun the surface would be ~30-40K to radiate away the GF and the geothermal gradient would start at this surface temperature.

    Accompanied by an image showing typical temperature vs depth plot over a year, in this case for some place in Turkey.

    In this image some temperature vs depth plots:
    https://www.mpoweruk.com/images/geo_temperature.jpg
    Are you saying that these profiles would be the same when we had no sun warming the surface?

    Interesting, isn’t it? You perfectly see here the amazing contribution of geothermal heat to ocean’s temperatures.

    More convincing:
    http://www.climate4you.com/images/ArgoTimeSeriesTemp59N.GIF
    A plot showing typical seasonal warming/cooling of the mixed surface layer of our oceans over 15 years. No influence of whatever heats the surface below ~400m.
    What is in your opinion the energy source for the oceans below this 400m (or below 1000m to be generous).
    Especially interested in how you explain the very high deep ocean temperatures in the Cretaceous. (ocean floor temperatures up to 17 degrees higher then today)

  39. “Abstract
    Telluric currents are natural electrical phenomena in the Earth or its bodies of water. The strongest electric currents are related to lightning phenomena or space weather. Earth electricity can cause damage to structures, and may be useful for earthquake forecasting and other applications. Thirty-two distinct mechanisms that cause Earth electricity are described, and a broad selection of current research is highlighted. © 2013 by the Istituto Nazionale di Geofisica e Vulcanologia. All rights reserved”
    https://www.researchgate.net/publication/266971680_Earth_electricity_A_review_of_mechanisms_which_cause_telluric_currents_in_the_lithosphere

    “INTRODUCTION
    How does atmospheric electricity affect man and his technological systems? Is our electrical environment
    changing as a result of air pollution, the release of radioactive materials, the construction of high-voltage power lines,
    and other activities? It is clear that modern technological advances can be seriously affected by various atmospheric
    electrical processes and that man is also beginning to affect the electrical environment in which he resides.”
    https://books.google.com.au/books?hl=en&lr=&id=7j4rAAAAYAAJ&oi=fnd&pg=PA232&dq=telluric+currents+wireless+communications+and+remote+sensing&ots=sIlHZNiSd2&sig=KLBr5vaIbBJq8reodTY2zoBPp6Q#v=onepage&q&f=false

    “Telluric Currents and Atmospheric Temperature
    Posted on March 8, 2016 by Louis Hissink
    Philip Callahan is an entomologist, or studies insects, and has written a book for the layman that’s easy to read but he did write a clanger or two when he states that a dimagnetic material is slightly repelled by a magnetic field, and that a paramagnetic one is attracted to a magnetic field.

    The problem is the phrase “magnetic field” – is it the north seeking or south seeking pole of a magnetic field that is causing the observations?

    And while he concentrates on magnetic fields, by omitting the role of electric currents, or telluric currents, miniscule as they might be, in the process also limits comprehension.”
    https://lhcrazyworld.wordpress.com/2016/03/08/telluric-currents-and-atmospheric-temperature/

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