Using an Iterative Adiabatic Model to study the Climate of Titan.

Using an Iterative Adiabatic Model to study the Climate of Titan.

Guest Post by P Mulholland and Stephen Wilde. July 2019

I would rather have questions that can’t be answered than answers that can’t be questioned.” Richard P. Feynman.

Figure 1: Saturn's largest moon - Titan.

Figure 1: Saturn’s largest moon – Titan.

In this dual scene montage, we see on the left in natural colour the moon Titan orbiting above its parent body, the ringed planet Saturn. On the right is a near-infrared false-coloured composite image taken by the Cassini probe of Titan’s north pole. In this rare image of Titan the sunlight glints off the polar hydrocarbon seas, which are partially obscured by stratus clouds of condensed methane. The bright red arrow shape is from the anvil head of frozen methane cirrus clouds located above an actively raining convection storm (see also Schaller et al. 2006).

Abstract.

A mathematical model has been created based on meteorological principles, and intended to be applied as a correlative to the standard radiation balance equation used in current climate studies. The Dynamic-Atmosphere Energy-Transport climate model (DAET) is designed to account for the dual environmental nature of all terrestrial globes and moons, with sufficient mass and surface gravity to hold an atmosphere under a given solar radiation loading. The model consists of two distinct environments, a solar lit hemisphere dominated by surface radiative heating with an energy surplus, and a dark night-time hemisphere of energy deficit dominated by surface cooling, caused by direct through the atmosphere thermal radiative energy loss to space.

Energy exchange between the two hemispheres of energy surplus and energy deficit is mediated by a series of linked atmospheric mass movement processes. On the lit surface of energy surplus adiabatic convection and atmospheric overturning occurs. The lifted energy rich air then undergoes horizontal mass transport in the upper atmosphere. This process, characterized by air movement and energy transport towards the region of surface energy deficit, is representative of a thermal Hadley cell. The energy rich advected air subsequently descends onto the surface of the dark hemisphere which is under the influence of surface diabatic atmospheric cooling, and thermal radiant energy loss to space. This process is representative of the surface induced radiative cooling of a night time thermal environment. Near-surface advection of surface cooled dense air back to the energy rich sunlit environment, then completes the cyclical process of air mass transport and energy delivery.

1. Introduction.

Studies of the atmospheric dynamics of terrestrial solar system planets have a long and detailed history. The fundamental equation for the basis of this work is exemplified by the radiation balance equation used by Sagan and Chyba (1997): –

The equilibrium temperature Te of an airless, rapidly rotating planet (or moon) is: –

Equation 1: Te ≡ [S π R2(1-A)/4 π R2 ε σ]1/4

where σ is the Stefan-Boltzmann Constant, ε the effective surface emissivity, A the wavelength-integrated Bond albedo, R the planet’s (or moon’s) radius (in metres), and S the solar constant (in Watts/m2) at the planet’s (or moon’s) average distance from the sun.”

Using Equation 1 for Titan: – Te = 83.2 K, however the observed mean surface temperature for this moon is Ts = 94 K, therefore the difference Δ T between Te and Ts = 10.8 K, this value is the atmospheric thermal enhancement effect for Titan. (Table 1).

Table 1: The Expected Surface Temperature for an Airless Titan compared with its actual Atmospheric Temperature (after Sagan and Chyba, 1997).

Table 1: The Expected Surface Temperature for an Airless Titan compared with its actual Atmospheric Temperature (after Sagan and Chyba, 1997).

2. Methods.

The Dynamic-Atmosphere Energy-Transport (DAET) climate model used here, is a 2-dimensional mathematical model that preserves the globular dual hemisphere components of daytime illumination and nighttime darkness. The forward model represents a globe with two environmentally distinct halves. The dayside is lit by a continuous incoming stream of solar radiation which creates an energy surplus, while the nightside is dark and has an ongoing energy deficit, due to the continuous exit to space of thermal radiant energy. Consequently, a mobile fluid atmosphere that transports energy from the day to the night side, and then returns again is the fundamental requirement of this model. (Figure 2).

The climate model presented here is designed to represent the meteorological processes of an illuminated globe. The model collects insolation at the surface boundary between the atmosphere and the solid surface of the globe, over the full face of its lit hemisphere. In this first instance of modelling analysis the illuminated surface partitions the captured power intensity flux equally. Half of the power intensity flux is converted to low frequency radiation. This radiant flux then exits the model, passing unimpeded through the overlying atmosphere and out to the vacuum of space.

The remaining half of the power intensity flux is captured by the air and advected to the unlit dark hemisphere. On this unlit side of energy deficit, the air is the only source of power intensity flux. Consequently, on contact with the cold unlit surface the air transfers half of its flux onto the solid ground, which then radiates this flux directly out to space. The now cold air returns back to the lit hemisphere, carrying its remaining part of the internally retained power intensity flux.

The two surfaces of the globe partition the power intensity flux equally (50% radiant flux ; 50% air thermal flux) , but because the absolute values are different the model contains two separate geometric series that tend to different limits, one limit for the lit hemisphere and one for the dark surface.

The geometric series for the lit side energy loss to space is: –

Equation 2: 1/2 +1/8 + 1/32 + 1/128 …. + 2-n (odd) = 2/3

While the geometric series for the dark side energy loss to space is: –

Equation 3: 1/4 +1/16 + 1/64 + 1/256 …. + 2-n (even) = 1/3

Note that the aggregate sum for the limits of both series is of course 1.

On the lit side of the globe the recycled air from the dark side supplies a second source of flux to the environment of the lit hemisphere. The equipartition of flux in the model, and the repetitive cycling of the air under conditions of constant solar radiation on the lit side, creates an infinitely repeating stable cycle of fluid mass motion and transported power intensity flux. The total energy recycling process in this model stores a power intensity flux in the atmosphere equal to that of the solar insolation flux, and so the model has a system gain of 2 (Figure 2).

Figure 2: Dynamic-Atmosphere Energy-Transport (DAET) model of Titan: Showing Stable Diabatic Energy Vectors and Total Energy Distributions.

Figure 2: Dynamic-Atmosphere Energy-Transport (DAET) model of Titan: Showing Stable Diabatic Energy Vectors and Total Energy Distributions.

We call this meteorological model the diabatic model because of the equipartition of power intensity flux at its critical surface boundary.

2.1. Modelling Slowly Rotating Titan.

The Saturnian moon Titan rotates only slowly on its axis, its rotational period is 382.7 hours (15.95 Earth days). This is the same length of time that Titan takes to orbit Saturn, and so the same face of this moon is always turned towards its parent planet. As a consequence of its slow axial rotation the sunlit day on Titan lasts for 191.35 hours, and the atmosphere experiences only a weak Coriolis effect. Like the planet Venus, Titan also has super-rotational winds in its upper atmosphere, and the daylit and nighttime surface temperatures are almost identical.

As with the previous study of the planet Venus, Modelling the Climate of Noonworld: A New Look at Venus, the application of a DAET model to analyse the climate of Titan will first be tested using the diabatic model described above. This meteorological model will be applied to slowly rotating Titan using the standard published atmospheric data (Table 2).

Table 2: The Metrics of Titan (Various Sources).

Table 2: The Metrics of Titan (Various Sources).

2.2.How the Presence of a Dynamic Atmosphere Distributes the Captured Solar Energy Across Titan.

To facilitate the modelling analysis, a number of simplifications have been made. The primary one is that the global atmosphere in the model world of Titan contains a fully radiatively transparent and free-flowing gas that connects the two hemispheres. Consequently, because the model atmosphere is fully transparent, it can only gain or lose heat from the solid surface at its base.

Next, a test is made of how the diabatic atmospheric model behaves when standard Titan Insolation parameters are applied. The solar irradiance that Titan experiences as a moon of Saturn is 14.82 W/m2, and the Bond albedo of Titan is 0.265 (Table 2) so the average post-albedo power irradiance of the lit hemisphere is 5.45 W/m2 (Table 3).

Table 3: Diabatic Model of Titan showing Internal Energy Recycling with Equipartition of Energy for Both Hemispheres.

Table 3: Diabatic Model of Titan showing Internal Energy Recycling with Equipartition of Energy for Both Hemispheres.

The diabatic equipartition energy budget for the lit hemisphere is 7.26 W/m2 and 3.63 W/m2 for the dark hemisphere, giving a total global energy budget for Titan of 10.89 W/m2 (Figure 2). This quantity of flux is a doubling of the post-albedo irradiance experienced by the lit hemisphere, and so the diabatic model has generated a system gain of 2.

The result of applying the standard Vacuum Planet equation of astronomy to Titan is an Expected Te of 83.2 Kelvin (Table 1). The meteorological diabatic forward model of Titan closely mirrors the results of this fundamental equation, it produces a modelled temperature for Titan of 82.3 Kelvin (Table 3), a difference of only 0.9 Kelvin (Figure 3).

Figure 3: The Relationship between the Diabatic Climate Model Surface Temperature (Meteorology) and the Vacuum Planet Equation Top of Atmosphere Radiant Exhaust Temperature (Astronomy).

Figure 3: The Relationship between the Diabatic Climate Model Surface Temperature (Meteorology) and the Vacuum Planet Equation Top of Atmosphere Radiant Exhaust Temperature (Astronomy).

2.3. Establishing the Global Energy Partition Ratio for Titan by Inverse Modelling.

The process of establishing the observed average surface temperature for slowly rotating Titan, in its customary orbit around Saturn, is achieved by applying the mathematical technique of inverse modelling to an equipartition diabatic forward climate model of the moon. The process of inversion adjusts the surface partition ratio in the diabatic model to create an adiabatic model of the moon’s climate, with an internal system gain that is greater than 2.

The following steps describe the logic flow of the modelling analysis: –

Step 1: That the repetitive air recycling process of a Hadley cell retains energy within the atmosphere, and that the quantity of energy retained by the air stabilises when the amount of outgoing radiant energy has the same value as the incoming solar flux (Table 3). This is the diabatic forward model.

Step 2: That on applying Titan’s insolation parameters to the diabatic forward model, an average global air temperature of 82.34 K is achieved. This value is a small underestimation of the Expected Te for a vacuum Titan of 83.2 K that the standard radiative balance equation computes (Figure 3).

Step 3: That by applying the standard geoscience technique of inverse modelling to the basic diabatic atmospheric model of Titan, an adiabatic model can be created. This process has the ability to identify the surface energy partition ratio which determines the thermal enhancement observed in the atmosphere of slowly rotating Titan. It was established that 24 cycles of atmospheric overturn would produce a stable outcome for the DAET adiabatic model, and produce a global energy budget gain of 2.66 times the surface solar energy input (Table 4).

Step 4: Tests were made to try and establish the flux partition ratio for the unlit surface of Titan. However, in the absence of a suitable nighttime air temperature profile to constrain the modelling process, and because published sources report that the day and nighttime surface temperatures on Titan are almost equal (Courtin and Kim, 2002, Fig. 2), a pragmatic solution was adopted to this lack of control data. Consequently, for the purpose of this analysis it is assumed that the surface flux partition ratio is the same for both hemispheres of slowly rotating Titan. This approach of using a common flux partition ratio for both surfaces in the adiabatic model was also previously found to be suitable for the atmosphere of slowly rotating Venus.

Table 4: Adiabatic Energy Partition Test for Titan (~37.6% Thermal Radiant Loss to Space : ~62.4% Atmospheric Energy Retention).

Table 4: Adiabatic Energy Partition Test for Titan (~37.6% Thermal Radiant Loss to Space : ~62.4% Atmospheric Energy Retention).

On applying Titan’s insolation parameters to the adiabatic model, using the energy partition ratio identified by inverse modelling, an average global air temperature of 94 Kelvin (minus 179oC) is achieved for this slowly rotating moon (Table 5).

Table 5: Adiabatic Model of Titan showing Internal Energy Recycling for Both Hemispheres.

Table 5: Adiabatic Model of Titan showing Internal Energy Recycling for Both Hemispheres.

The results of applying the inverse modelling run to Titan, using 25 cycles of internal planetary atmospheric overturn, are shown in Table 5. The surface energy partition ratio that achieved this result is 37.6% of the moon’s surface energy being directly lost to space, and 62.4% of the surface energy being retained by the atmosphere (Figure 4).

Figure 4: Stable Adiabatic Convection Model of Titan: Showing Energy Vectors and Total Energy Distributions.

Figure 4: Stable Adiabatic Convection Model of Titan: Showing Energy Vectors and Total Energy Distributions.

Details of the algorithms used in the diabatic and adiabatic models of Titan’s climate are recorded in the linked Excel Workbook (Mulholland, 2019).

3. Results of Applying the Adiabatic Meteorological Model to Titan.

The adiabatic model of Titan computes a thermal separation of 24.3oC between the radiating surface and the air for the lit side surface (Table 5). In the model of slowly rotating Titan, the hemisphere of energy surplus is a proxy for the moon’s thermal Hadley cell. Using the troposphere 41.5 km gross thermal lapse rate of 0.53K/km for Titan (Figure 5), this temperature difference equates to a physical separation of 45.6 km. This value is the modelled estimate of the height of the radiant emitting surface for the lit hemisphere of Titan (Table 5).

Figure 5: Titan Atmosphere Temperature Profile (Courtin and Kim, 2002 : Table 1).

Figure 5: Titan Atmosphere Temperature Profile (Courtin and Kim, 2002 : Table 1).

The atmospheric profile for Titan shows that the minimum temperature in the moon’s atmosphere occurs at an altitude of 41.4 Km, where a temperature of 70.2 Kelvin (-202.8oC) is recorded (Courtin and Kim, 2002: Table 1).

4. Discussion.

The numerical atmospheric model used here is based on the fundamental astronomical principle that all globes are sun lit on one side only. This fact applies to all solar system planetary bodies and moons of whatever form or type. For an atmospheric model to be valid, it must be capable of being applied to bodies that have all possible types of planetary rotation, including hypothetical bodies that are tidally locked, and always present the same face towards the Sun. To address this problem, a simple geometric model has been devised based on the “divide by 2” rule for a fully lit hemisphere surface illumination, coupled to the “divide by 4” rule of global thermal radiant emission.

Figure 3 demonstrates the close relationship between the standard Vacuum Planet radiative balance equation derived from astronomical principles, and our Dynamic-Atmosphere Energy-Transport climate model derived from meteorological principles. The differences between these two analytical approaches and their appropriate use are listed in Table 6: –

Table 6: A comparison of the approach to climate analysis used by the two different scientific disciplines of astronomy and meteorology.

Table 6: A comparison of the approach to climate analysis used by the two different scientific disciplines of astronomy and meteorology.

The purpose of the diabatic meteorological model is to replicate the form of the standard radiation balance equation, that uses the illumination intensity divide by 4 rule of surface radiant energy distribution (Equation 1), and to apply this concept to a globe that is only lit on one side. For such a model, the sunlit energy is distributed over the surface of a single hemisphere, and so an illumination intensity divide by 2 rule of surface radiant energy capture is applied. In this model the transmission of energy from the lit hemisphere of energy surplus to the unlit side of energy deficit, is mediated by the meteorological atmospheric process of advection. The diabatic mathematical model shows that the system gain which stores this flux within the atmospheric reservoir has a value of 2.

Because an equipartition of energy between a radiatively heated (or cooled) solid surface and an overlying mobile fluid is characteristic of laminar flow, it is clear that this equipartition ratio cannot be used to describe the transmission of energy into (or from) a fluid that is undergoing turbulence at the critical boundary interface. For turbulent fluid motion, that is characteristic of forced radiative heating and adiabatic convection, a partition ratio weighted in favour of the air is the required metric.

The adiabatic model incorporates the numerical process of energy partition in favour of the turbulent air for the sunlit surface boundary. Because the required average surface air temperature for Titan is known a priori, the numerical technique of inverse modelling to establish the energy partition ratio can be applied. This algorithm creates the required thermal enhancement for an atmosphere of any opacity, and directly computes the gain that stores flux within the atmospheric reservoir. Because the model creates a thermal contrast between the surface and the air, this temperature difference can be used to calculate the height of the radiant emission surface, using the appropriate environmental lapse rate obtained from measured data.

The application of the Dynamic-Atmosphere Energy-Transport model to a planet or moon that is not tidally locked, introduces a new variable of surface daylength into the process of climate analysis. Both Titan and most especially Venus have a polar vortex of descending air in each hemisphere. It is apparent that the locus of the nighttime sector of descending air in the conceptual Noonworld model must shift from the antipodal zenith point (Figure 2) to the poles of rotation (Figure 4) for these real-world examples. Consequently, we expect that the polar vortices of Titan to be the primary atmospheric window for surface radiant flux exiting to space, and that the tropopause height will consequently be reduced in these regions. In the absence of polar atmospheric profile data for Titan to constrain our model, this remains a speculative prediction of our analysis.

5. Conclusions.

1. The mathematical model used in this study is designed to retain the critical dual surface element of a lit globe, namely night and day. The simple equipartition diabatic model, when applied to a fully transparent pure Nitrogen atmosphere, closely matches the results of the standard atmosphere equation, which is traditionally applied to an airless world (Sagan and Chyba, 1987).

2. By applying the inverse modelling process to the atmosphere of Titan, and accounting for the fact that there is little surface thermal contrast between day and night on this moon, then the modelling process can determine the global energy partition ratio that accounts for its thermally enhanced atmosphere.

3. By using the appropriate lapse rate for Titan, the inverse modelling process predicts the height of the radiant emission surface for a fully opaque atmosphere. Consequently, the computational dynamics of the adiabatic model with its fully transparent atmosphere demonstrates that the presence of a troposphere that is opaque to thermal radiation is not an a priori requirement for the retention of energy within an atmospheric system.

4. Titan has an atmosphere with a composition of 98.4% nitrogen gas, a surface pressure of 1.45 bar and a greenhouse effect of 10.8 Kelvin. The pure nitrogen model used here is fully valid for the composition of Titan’s atmosphere, and the adiabatic calculation achieves a surface temperature of 94 Kelvin with a much lower partition ratio than that used for the high-pressure environment of Venus.

5. The Bond albedo of Titan is 0.265. Titan is an optically veiled world with a uniform natural orange glow (ESA, 2004). This veil of photochemical smog results from the presence of Tholins in the upper atmosphere of the moon (Waite et al., 2007), and this hydrocarbon haze directly controls the intensity of the surface solar irradiance that drives the climate of Titan.

6. A slowly rotating moon, such as Titan, does not have a counter rotating mechanical Ferrel cell, therefore there is no dynamic restriction on the latitudinal reach of the Hadley cell on Titan, (as per Del Genio and Suozzo, 1987).

7. The atmosphere of Titan holds a number of environmental characteristics in common with the planet Venus:

a. Titan is a slow rotator.

b. Titan has two hemisphere encompassing Hadley cells which link directly into the moon’s two polar vortices.

c. Titan is an optically veiled world.

d. Titan has a super-rotational wind in its upper atmosphere.

e. Titan has similar day and night time surface temperatures.

8. The key insight gained from this analysis is that it is energy partition in favour of the air, at the lit surface boundary that achieves this thermal energy boost within a dynamic atmosphere. Therefore, the energy retention effect is a direct result of the standard meteorological process of convection. Put simply energy retention by surface conduction and buoyancy driven convection wins over energy loss by radiation. Consequently, the retention of energy in the air by the process of convection is a critical feature of planetary atmospheric thermal cell dynamics.

6. References.

Courtin, R. and Kim, S.J., 2002. Mapping of Titan’s tropopause and surface temperatures from Voyager IRIS spectra. Planetary and Space Science, 50(3), pp.309-321.

Del Genio, A.D. and Suozzo, R.J., 1987. A Comparative Study of Rapidly and Slowly Rotating Dynamical Regimes in a Terrestrial General Circulation Model. Journal of the Atmospheric Sciences, Vol. 44 (6), pp. 973-984.

ESA, 2004. Titan’s True Colors. Astrobiology Magazine.

Li, L., Nixon, C.A., Achterberg, R.K., Smith, M.A., Gorius, N.J., Jiang, X., Conrath, B.J., Gierasch, P.J., Simon‐Miller, A.A., Flasar, F.M. and Baines, K.H., 2011. The global energy balance of Titan. NASA Reports Archive.

Limited Science, 2018. Possibility of life on Titan (Largest “Planet” of Saturn) Methane Sea of Titan. Limited Science Space & Universe.

Mulholland, P., 2019. Titan Climate Models 01Jun19 Excel Workbook. Research Gate Project Dynamic-Atmosphere Energy-Transport Climate Model.

NAIF JPL NASA 2019. Titan Occultations WebGeocalc Spice data and software.

Sagan, C. and Chyba, C., 1997. The early faint sun paradox: Organic shielding of ultraviolet-labile greenhouse gases. Science, 276 (5316), pp.1217-1221.

Schaller, E.L., Brown, M.E., Roe, H.G. and Bouchez, A.H., 2006. A large cloud outburst at Titan’s south pole. Icarus, 182(1), pp.224-229.

Waite, J.H., Young, D.T., Cravens, T.E., Coates, A.J., Crary, F.J., Magee, B. and Westlake, J., 2007. The process of tholin formation in Titan’s upper atmosphere. Science, 316(5826), pp.870-875.

Williams, D.R., 2016. Solar System Small Worlds Fact Sheet NASA NSSDCA, Mail Code 690.1, NASA Goddard Space Flight Center, Greenbelt, MD 20771.

Williams, D.R., 2018. Saturn Fact Sheet NASA NSSDCA, Mail Code 690.1, NASA Goddard Space Flight Center, Greenbelt, MD 20771.

Further Reading: –

Coustenis, A. and Taylor, F.W., 2008. Titan: exploring an earthlike world (Vol. 4). World Scientific.

Glossary:

Adiabatic: The process of air movement in which there is no energy exchange with the surroundings.

Advection: The process of horizontal transport of air by the mass motion of the atmosphere.

Albedo: An environmental property of a lit surface that acts as a radiant energy bypass filter. Defined as the ratio of reflected radiant energy to incident radiant energy.

A priori: Proceeding from a known value to deduce the consequential result.

Convection: The process of vertical transport of air by means of differential atmospheric heating and air density contrast.

Diabatic: The process of energy exchange by conduction between two adjacent bodies.

Forward Modelling: The technique of computing the result for an unknown parameter from a set of known measurements using a mathematical model.

Insolation: (Incoming Solar Radiation). The amount of direct sunlight energy received by the surface of a planet or moon.

Inverse Modelling: The mathematical process of determining the value of an unknown input parameter that creates a known measured result.

Lapse Rate: The change of atmospheric temperature with height in a given gravity field. The lapse rate is defined as positive when the temperature decreases with increasing elevation.

Laminar: An atmospheric layer in which air flow is smooth. This layer is usually associated with stable air mass formation and radiative surface boundary cooling.

Opacity: The capacity of a substance to impede the transmission of radiant energy.

Partition Ratio: The ratio of energy distribution at the boundary between two environments.

Terrestrial Planet: A solar system planetary body (or moon) that has a solid surface and is Earth-like in basic composition and form.

Tropopause: The upper limit of the troposphere marked by a transition to a zero or negative lapse rate in the atmospheric layer above.

Troposphere: The weather layer. The lowest layer of a terrestrial planet’s atmosphere dominated by surface daytime heating or nighttime cooling and energy transport by turbulent air motion.

Turbulence: The process of random mixing of air undergoing forced radiant thermal heating at the surface boundary.

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137 thoughts on “Using an Iterative Adiabatic Model to study the Climate of Titan.

  1. Hopefully, this continuing series will gain some traction by demonstrating the usefulness of our model in being able to predict observable features of all atmospheres around planets regardless of the presence or absence of GHGs.
    The simple truth is that convective overturning introduces the necessary delay in the throughput of insolation that results in a surface temperature enhancement above the expectation set by the S – B equation.
    That equation relies on radiative energy transfers only and thus fails as soon as one introduces non-radiative energy transfers working in parallel with radiative processes.
    The non-radiative processes, being slower, will inevitably introduce an energy backup within the planet / atmosphere system which must increase total energy held within the system which then heats the surface.
    Those responsible for the radiative greenhouse effect have much to answer for.

    • “The observed mean surface temperature for this moon is Ts = 94 K.” How do we “observe” a mean surface temperature of Titan? Of Earth? Of Venus? What is the surface temperature of the night side of Venus?

    • Stephen

      I have been trying to introduce this concept to the discussions of ECS and feedbacks by Monckton and the reply titled “Re-mystifying feedbacks”.

      That whole exercise is about the radiative component of the greenhouse effect, and pretends the surface heating of the air has no forcing effect. It is obvious the omission gives misleading results, where the IPCC, for example, says that without GHG’s the air temperature would be the same as the surface of our airless Moon. Gavin Schmidt frequently restates this.

      The comparison of the surface temperature of an airless Moon to the temperature of the air 1.5m above the surface of the Earth with an atmosphere containing GHG’s is obviously inappropriate on several counts. The temperature of the surface is not the same thing as the temperature of the air, and the comparison sidesteps the convective heat transfer component of the ECS.

      Missing from all these discussions is that the temperature of the air would be on Earth if it had the same atmosphere as Titan, reduced to one Bar at the surface. Add rotation, increase the insolation and run the model to equilibrium. What would the air temperature be?

      My own estimation is that it would be well above the current 15 C. In short, that GHG’s provide net cooling of the air (not necessarily of the surface).

      I trust this investigation will continue.

      • Crispin
        My view is that ghgs do produce back radiation and radiation directly to space from within the atmosphere but any imbalances potentially arising are compensated for by a change in the speed of the convective overturning cycle for a zero net effect on surface temperature and system energy content.
        That change in the speed of overturning is a result of ghgs affecting the lapse rate slope which in turn influences the speed of convection.
        I have written a separate analysis of that elsewhere but it is outside the scope of this post.

    • The difficulty with this model is the assumption that the convective cycle goes between the lit and the dark hemisphere. This is probably a good approximation for Titan, but definitely not for the Earth where this convective cycle mostly goes between different parts of the planet over several rotations, or even mostly up and down in the same area during a single day in the wet tropics.

      The huge heat capacity of the ocean even means that there is a fair amount of convection during nights over the tropical ocean, something that is easily seen on moonlit nights.

      And increased energy (enthalpy) of the atmosphere does not automatically entail higher temperature if there is an condensing component in the atmosphere, as there is on both Earth and Titan (but probably not on Venus).

      • tty
        There is no doubt that the average convective flow is from the lit to the unlit side even for relatively rapid rotators such as the Earth.
        However, it is sufficient for regions of energy surplus to be in regions of rising air and regions of energy deficit to be within areas of descending air wherever they may be located around the sphere.
        Therefore, the principle applies to all planets with atmospheres.

      • That is probably true, but it is not because the convecting air moves from the lit to the unlit side, but rather that the unlit side moves to where the convecting air is.

        • It is because the unlit side moves to where the light is !

          There a pre-dawn wind due to heat difference but this is not a major part of the energy flux calculations. The main flux is in and out in a vertical direction as the “nightside” moves into daylight conditions and vice versa.

          • Neat observation. Taking it one step further, the faster the rotation, less of Stevens convective model is needed. The slower the rotation, the greater the need for super strength winds to carry the heat from the warm side to the cool side.

          • “The slower the rotation, the greater the need for super strength winds to carry the heat from the warm side to the cool side.”

            EdB

            That is a very interesting comment. Thanks.
            Ultimately with really slow rotators like Titan and Venus, the only way back to the surface for the high-altitude super rotating air is to go down the “plug holes” of the polar vortices.

      • Tt, Venusian cloud sulphurous to sulphuric acid cyc!ing with h2o. About 50 to 60km iirc. Brett Keane

        • Brett,
          Not only do we have the formation of sulphuric acid droplet clouds at 50 Km in the Venusian atmosphere, (Hammer, 2017 Fig. 2). There is the added effect of sulphuric acid freezing at still higher altitudes in the stratosphere Sulphuric acid freezing point diagram. These solid particles both enhance atmospheric thermal radiation loss to space and also account for the very high albedo of Venus.

    • “The process of establishing the observed average surface temperature for slowly rotating Titan, in its customary orbit around Saturn, is achieved by applying the mathematical technique of inverse modelling to an equipartition diabatic forward climate model of the moon.”

      That’s a whole new meaning of the word “observed”. A Nobel peace prize, maybe?

      • First observed, then the model is created to establish within the model that which has previously been observed.
        We then found that the model accurately predicts other observed parameters thereby confirming its validity.

        • Peter, I am only objecting to your terminology. You can’t observe an average temperature any better than you can observe an average family with 2.6 children.

    • This will be our last modelling post on WUWT.
      We would like to thank Anthony for having the courage to publish our work.
      Further essays in this series of studies on planetary climate will appear on my Research Gate site in due course.
      1. Boiling Water Venus: A study of albedo and atmospheric pressure induced environmental change on a terrestrial planet.

    • Steven,

      Very useful polar calibration data in this paper.
      Thanks.

      The surface temperature near the south pole over this time decreased by 2 K from 91.7 ± 0.3 to 89.7 ± 0.5 K while at the north pole the temperature increased by 1 K from 90.7 ± 0.5 to 91.5 ± 0.2 K.
      The latitude of maximum temperature moved from 19 S to 16 N, tracking the sub-solar latitude. As the latitude changed, the maximum temperature remained constant at 93.65 ± 0.15 K

      93.65 Kelvin for the tropics and 89.7 Kelvin for the south pole. Winter time in the southern hemisphere.

      • “The latitude of maximum temperature moved from 19 S to 16 N, tracking the sub-solar latitude. ”

        Does Titan have an ITCZ one wonders?

        And how do the methane lakes affect convection? And the “ground methane” at lower latitudes?

    • Broken Links,
      The link to Limited Science, 2018 is down. Unfortunately this site is not on the Wayback Machine either.

      The link to my own page on Research Gate is also broken (Apologies).
      Use this one instead
      Dynamic-Atmosphere Energy-Transport Climate Model
      and follow the link to the Project Log for the Method Files.
      Titan Climate Models 08Jul19

    • Titan gives us two shots at finding potential life: one as we know it, in liquid water, and one as we don’t, in liquid methane or ethane.

      As with some other gas giant moons, Titan might harbor a mantle of liquid water under its ice crust. It’s cryogenic volcanoes erupt water lava. Water from impacts however gets hotter and stays liquid in craters longer. Ubiquitous tholins there promptly form amino acids in aqueous solution.

      • Bryan,

        Don’t be too hard on Steven, he did provide a link to a valuable paper I had not previously seen.
        All I need now is to do a calculation of the areal size of the polar vortices indicated by the transects in Figure 1.

  2. Thanks for the interesting post! I have always wondered how the Ideal Gas Laws reconcile with a high ECS. Having CO2 in the lower atmosphere restrict radiative cooling but increase radiative cooling in the upper atmosphere has always left me scratching my head. Isn’t it well established that convective forces dominate heat transfer in the Troposphere and radiative forces dominate in the upper atmosphere. Results from Modtran show that doubling CO2 has almost no impact on ground based temperatures. The fact that CAGW has gained so much support is a sad commentary on the state of science.

    • The fact that CAGW has gained so much support is a sad commentary on the state of science.

      Nelson,
      I agree. A bit of background history for you. When I first started this modelling analysis for Stephen in January of this year, I was surprised and concerned to discover that my first modelling attempt, in which I apportioned the surface insolation intensity flux equally between the overlying atmosphere and direct radiant loss to space, did not create any greenhouse effect. Instead this equipartition atmosphere model (which we now call the diabatic model) closely replicated the Vacuum Planet equation of astronomy (See Figure 3). Figure 3 is the linchpin of our analysis. What it shows is that the Vacuum Planet equation of astronomy, with its intensity flux divisor of 4 generates the export to Space thermodynamic temperature of an illuminated planet. So, by definition this astronomy equation applies in the absence of an atmosphere.

      Our Dynamic-Atmosphere Energy-Transport model with its intensity flux divisor of 2 by definition requires the presence of air, and so must be applied at the base of an atmosphere. The two models generate a synergy in which the physical lag that air mass movement creates requires the retention of intensity flux within the atmosphere. This effect occurs when the process of radiant forced convection is applied to the ground surface of the sunlit hemisphere, and generates an intensity flux retention in favour of the air. This second model that generates atmospheric heating by flux retention within the atmospheric reservoir is the adiabatic model, and it does not require any thermal radiant opacity to function.

  3. 4. Titan has an atmosphere with a composition of 98.4% nitrogen gas, a surface pressure of 1.45 bar and a greenhouse effect of 10.8 Kelvin. The pure nitrogen model used here is fully valid for the composition of Titan’s atmosphere, …

    In the lower atmosphere methane is about 5.65%, much much higher than any greenhouse gas on Earth, including water vapor.

    If the pure nitrogen model works for Titan, with its huge proportion of the supposedly potent greenhouse gas methane, that seems to mean that greenhouse gasses don’t matter that much. yes/no?

    • Abstract
      A minimum atmospheric temperature, or tropopause, occurs at a pressure of around 0.1 bar in the atmospheres of Earth1, Titan2, Jupiter3, Saturn4, Uranus and Neptune4, despite great differences in atmospheric composition, gravity, internal heat and sunlight. In all of these bodies, the tropopause separates a stratosphere with a temperature profile that is controlled by the absorption of short-wave solar radiation, from a region below characterized by convection, weather and clouds5,6. However, it is not obvious why the tropopause occurs at the specific pressure near 0.1 bar. Here we use a simple, physically based model7 to demonstrate that, at atmospheric pressures lower than 0.1 bar, transparency to thermal radiation allows short-wave heating to dominate, creating a stratosphere. At higher pressures, atmospheres become opaque to thermal radiation, causing temperatures to increase with depth and convection to ensue. A common dependence of infrared opacity on pressure, arising from the shared physics of molecular absorption, sets the 0.1 bar tropopause. We reason that a tropopause at a pressure of approximately 0.1 bar is characteristic of many thick atmospheres, including exoplanets and exomoons in our galaxy and beyond. Judicious use of this rule could help constrain the atmospheric structure, and thus the surface environments and habitability, of exoplanets.
      https://www.nature.com/articles/ngeo2020?WT.feed_name=subjects_giant-planets&foxtrotcallback=true

      • “At higher pressures, atmospheres become opaque to thermal radiation, causing temperatures to increase with depth and convection to ensue”

        Is this an example of anti gas law bias? Gravity causes the lapse rate, not thermal radiation. Convection happens for many reasons, such as uneven internal thermal radiation, causing deviations from the lapse rate.

        • My take on this keeps being defined, which is frustrating. Which is cause and which is effect? Currently:

          The lapse rate itself is a function of gravity, height and atmospheric density, ie, pressure.

          Given that the suns radiation is a fixed Planck power input, at an incoming level defined by the distance to the sun, each planet has the same top of the tropopause, ie, 0.1 bar. This may or may not be the same altitude where energy in equals energy out. It is only the altitude where the lapse rate ends. It is of no consequence to the issues of interest.

          All atmospheres gain heat from radiation, conduction, evaporation.

          The GHE(a misnomer but the temperature gain over the GAT with no atmosphere)is a consequence of the heat gain of the atmosphere and overturning process from the lit side to unlit side of a planet.

          If the molar mass density approach, ie, pressure, and distance from the sun, determine the surface temperature, then the partitioning must be the same for each planet. Differences from ideal are the result of inherent inefficiencies. The temperature at 1 bar should be the same.

          I am most assuredly wrong, but I am trying.🙂

          • EdB,

            Nice to have an engineer on the case.
            The missing piece of the puzzle in my view is the link between the energy partition on the lit side and surface atmospheric pressure. Elsewhere I floated the idea that we are dealing with a Boyle’s law PVT relationship of some kind. If turbulence is the issue and pressure is the control then has this relationship already been studied in the design and power output of gas-powered engines?

            On a related point, a friend sent a copy of a text figure based on Emden’s model showing the comparison of the vertical temperature distribution in an atmosphere in (a) radiative equilibrium and (b) convective equilibrium.
            Emden, R. (1913) ÜberStrahlungsgleichgewicht undatmosphärische Strahlung. Ein Beitrag zurTheorie der oberen Inversion. Sitzungsberichte der mathematisch-physikalischen Klasse der Königlich BayerischenAkademie der Wissenschaften zu München.Jahrgang,1913, 55–142.

            I quote his words:-
            “This is a thermodynamic diagram constructed by Richard Emden, a pioneering physicist in atmospheric radiative transfer, who illustrated the importance and dominance of water vapor and its phase changes that control the infrared radiation flux through the troposphere.

            The physical assumptions in construction are that all energy transfer between the earth’s interface with the atmosphere is by IR radiation alone. The absorption and emission of IR by water vapor is so powerful and complete in the domain of the IR spectrum that the resulting surface absorption and re-emission through a layer of vapor whose concentration decreases exponentially with height as it does in the real world is so intense, that the ensuing radiational cooling of the layer away from the surface causes enough cooling in exchange for the surface greenhouse effect that the atmosphere’s density actually increases with height in the layer, demanding auto-convective overturn.
            The surface parcel’s resulting latent heat release allows the parcel to remain buoyant with respect to its environment until the moist adiabat re-intersects the environmental temperature again at 8 Km. The vertical velocity obtained by the parcel in ascent is also powerful enough to overshoot thermodynamic equilibrium by 2 Km, creating a tropopause as indicated at 10 Km. This process is with water vapor alone that sets up its own hydrological cycle! No CO2 is involved and the tropopause is close to the pressure altitude of the real earth tropopause.”

            Emden, R. (1913) Radiation Equilibrium and Atmospheric Radiation. A contribution to the theory of the upper inversion. Meeting reports of the mathematical-physical class of the Royal Bavarian Academy of Sciences in Munich. Year, 1913, 55-142.

          • Philip:
            “The missing piece of the puzzle in my view is the link between the energy partition on the lit side and surface atmospheric pressure.”

            Indeed, my thoughts exactly.

            In a closed system, such as a car cylinder, the gas laws are constrained by the walls to work. On a planet, the force of gravity only gives a one dimensional restraint, ie, pressure with height.

            I am going to assume that we have been chasing a lot of irrelevant issues. For example, the effective emission height can be on the surface(transparent atmosphere), at the top of the troposphere, (fully opaque), or anywhere in between. Lets assume that it does not matter, as incoming heat always tries to distort the lapse rate, and this causes mixing to restore the theoretical lapse rate. Even condensing layers should not cause more than a wiggle. The overturning model you developed establishes a “GHE”, using convection as the main driver. That takes the miraculous existence of a GHE off the table. Is it a complication that the equations need to account for the planets rotation rates? What does partitioning mean? Maybe nothing.

            Maybe it all leads to the simple NZ and Holmes formula. If that drives all, then the rest is only work done to balance heat in a planets thermodynamic envelope.

            How good is our empirical data? Take for example, a single probe on earth can give wildly different temperature results. The pressure and lapse rate would be close, but only an instrument in polar orbit can get an accurate GAT.

            Questions, questions.. if I only had the time, and was a lot younger..

          • The overturning model you developed establishes a “GHE”, using convection as the main driver.

            EdB,
            The key insight for this approach came from the realisation that the presence and location of the descending limb of the Hadley cell in the Horse latitudes is not caused by radiative cooling to space of air at the tropopause, rather it is a dynamic process of forced descent linked to the rate of daily planetary rotation.

            Links to these two papers were posted elsewhere by a contributor a few years ago and clearly demonstrate the falsity of the idea than the latitudinal reach of the Hadley cell is a temperature related phenomenon. The temperature of the atmosphere on Titan proves beyond any doubt that it is daily rotation rate that governs the latitudinal reach of the Hadley cell.
            Hunt, B.G. (1979). The Influence of the Earth’s Rotation Rate on the General Circulation of the Atmosphere. Journal of the Atmospheric Sciences, Vol. 36 (8), 1392-1408.
            Del Genio, A.D. & R. J. Suozzo (1987). A Comparative Study of Rapidly and Slowly Rotating Dynamical Regimes in a Terrestrial General Circulation Model. Journal of the Atmospheric Sciences, Vol. 44 (6), 973-984..

            Everything I have done follows from this starting point.

            Another part of the story that needs addressing is the relationship with lapse rate that is bound up in the equation that links gravity to specific heat. I have not been able to find any equation that generates specific heat from first principles for a known gas composition (molar mass).

            In the meantime I continue to explore the outputs from my toy model by curve fitting.
            The hints and insights that this model provides are fascinating.
            Plenty of potential PhDs could come from this for anyone of courage.

          • Philip and EdB,

            “The missing piece of the puzzle in my view is the link between the energy partition on the lit side and surface atmospheric pressure. ”

            Surface atmospheric pressure is directly related to density at the surface.
            Density at the surface sets the efficiency of conduction from solid surface to the mobile gases above.
            The efficiency of such conduction sets the proportion of surface energy that goes to conduction/convection rather than radiation.
            The way to look at the lapse rate slope is to realise that it represents the changing relationship between the efficiencies of radiation and conduction as means of energy transfer as one descends into increasing density.
            With increasing depth into the gaseous medium conduction slowly improves efficiency relative to radiation and the temperature rises until it reaches its maximum at the solid surface beneath.
            That explains why there is a link between the energy partition at the surface and atmospheric pressure.
            The greater the density of the atmosphere at the surface the greater the energy partition in favour of the air and the higher the temperature at the surface.
            It appears that one needs a surface pressure of more than 0.1 bar to get conduction to a point where a partition in favour of the air is produced.

          • ” I have not been able to find any equation that generates specific heat from first principles for a known gas composition (molar mass).”

            I am thinking along the same lines.

            From NZ and Holmes we have the surface temperature(assuming their derivation hold up to further planetary tests)

            From your work we have a an explanation for the ‘GHE’, or apparent heat gain.

            Can one develop a formula for the partitioning? That would be complex. The internal heat transport dynamics are driven by planetary rotations and convection, combined with Coriolis force, to give winds and thus energy transport from the lit side to the dark side. Conduction is enhanced by wind velocity and atmospheric density.

            If one could derive the partitioning from first principles, then the ‘GHE’ is calculated from first principles.

            It looks more like a heat transport finite element modelling problem than a set of solvable equations.

          • EdB,
            One of the most brilliant engineering insights that I know of is George Stephenson’s design for The Rocket. His use of the steam exhaust flux from the driving pistons, directed up the firebox chimney to increase the air influx draft over the fire, is truly brilliant. This design incorporates mechanical feedback, and is so successful that it requires the fitting of a safety valve to the steam reservoir, else the machine was at risk of blowing up.
            A similar mechanical feedback process was used by Frank Whittle in his design of the turbojet engine. Using the engine exhaust to power a turbine fan that increases the air influx into the combustion chamber was also so successful that the first rig to use this design nearly ran out of control.
            From this it is a short step to the realisation that the Hadley cell is a natural example of a mass movement energy retention feedback loop. When account is taken of the fact that bi-molecular gases are poor emitters of thermal radiant energy, and that planetary rotation induces forced air descent, either in mid-latitudes for rapid rotators (Earth) or at the polar vortex for slow rotators (Titan), then the role of ground surface in the control of energy distribution becomes apparent.
            The Hadley cell is a machine that is powered by sunlight, it retains intensity flux in a feedback loop that permits the system to run hot. For highly opaque atmospheres it appears to be the lowest possible freezing point temperature of the condensing volatile that controls the height of the emission surface, and also (for good measure) the albedo.

          • EdB

            “The temperature at 1 bar should be the same.”

            It appears that the temperature of Venus is indeed very close to that for Earth at 1bar pressure after adjusting for distance from the sun.

          • ”I have not been able to find any equation that generates specific heat from first principles for a known gas composition (molar mass).”

            See Dr. Bohren’s 1998 Text “Atmospheric Thermodynamics” Sec. 3.2, p. 99 on specific heats and enthalpy.

          • EdB July 21, 2019 at 8:46 am

            The lapse rate itself is a function of gravity, height and atmospheric density, ie, pressure.
            It is only the altitude where the lapse rate ends.

            Lapse rate is a pretty confusing name. Temperature profile would be better imo.
            The temperature profile of the atmosphere depends on many more factors, eg a front entering the area, a temperature inversion in a high pressure system etc. etc.
            How can a “lapse rate end” at 0,1 bar?
            The tropopauze is the altitude where the temperature profile on average reverses from decreasing to increasing temperature vs altitude.

          • Philip Mulholland July 22, 2019 at 3:18 am

            The key insight for this approach came from the realisation that the presence and location of the descending limb of the Hadley cell in the Horse latitudes is not caused by radiative cooling to space of air at the tropopause, rather it is a dynamic process of forced descent linked to the rate of daily planetary rotation.

            Radiative cooling to space plays a role in the Hadley process. On its way from the (thermal) equator to ~30 N/S the air certainly cools and sinks, creating an intensifying inversion in the process. Traveltime should be several days for the ~1800 nm straight line distance.
            See Trade wind inversion.

          • Stephen Wilde July 22, 2019 at 6:12 am

            Surface atmospheric pressure is directly related to density at the surface.

            Needs some explanation.
            Surface pressure IS directly related to the weight of the column of air above.
            We can have eg 1020 hPa surface pressure at a temperature of + 50C and -50C.
            The density will be quite different in these two examples.

          • ”Plenty of potential PhDs could come from this for anyone of courage.”

            Many have already been accomplished. From Philip’s 3:18am link:

            “The descent of the air in the Hadley cell is necessitated by a dynamical requirement of the atmosphere for the generation of east-west pressure gradients (See Lorenz, 1967, p. 74). “

            A lawyer and amateur meteorologist earlier wrote: “I think the causes of the General Trade-Winds have not been fully explained by any of those who have wrote on that Subject ..” George Hadley (1735).

            Lorenz then goes on to state: “..radiation, the process which is ultimately responsible for the existence of the circulation. Here I feel that the mutual interaction between the field of motion and the field of radiation is so complicated that we are only beginning to appreciate its true importance.”

            http://users.uoa.gr/~pjioannou/historical/Lorenz-1967.pdf

          • Trick July 22, 2019 at 6:45 am
            In another thread we discussed Lunar daytime temperatures being near radiative balance or not.
            A more recent article has the following texts:
            4.1 “The highly insulating nature of the surface, the lack of an appreciable atmosphere to buffer surface temperatures, and slow rotation of the Moon allow daytime temperatures to nearly equilibrate with the solar flux.”
            and
            4.4 “Daytime temperatures on the Moon are approximately in radiative equilibrium. For slowly rotating bodies with low thermal inertias like the Moon, heat diffusion models predict surface temperatures at the equator within ∼1 K of radiative equilibrium between local time hours 8 and 16”

            https://www.researchgate.net/publication/306139945_The_Global_Surface_Temperatures_of_the_Moon_as_Measured_by_the_Diviner_Lunar_Radiometer_Experiment

          • Ben Wouters,
            All the points you are raising relate to the inevitable local and/or short term energy imbalances that occur within any convecting atmosphere.
            Our model acts in the background and provides the baseline around which all that variety occurs.

          • Ben: “Daytime temperatures on the Moon are approximately in radiative equilibrium.”

            “..surface temperatures at the equator within ∼1 K of radiative equilibrium between local time hours 8 and 16..”

            “..sunlit and shaded surfaces can be cooler or warmer respectively than predicted by models assuming equilibrium conditions.”

            “Daytime temperatures are in near-radiative equilibrium..”

            As I previously pointed out, and this paper supports, lunar temperatures shown in the Vasavada 2012 paper Fig.s 5 & 7 do not show brightness temperature equilibrium achieved over the diurnal cycle at the surface. Apollo thermometer data, and some analysis, shows equilibrium temperature achieved several cm.s below the surface (Fig. 7).

            That subsurface regolith depth is the brightness temperature location necessary to compare the 255K multi-period annual Earthian Te ~equilibrium (240in, 240out). From what I’ve read should be somewhat below 255K but not anywhere near as slow as 197K with the natural, proper regolith optical properties. I’ve not seen a paper trying to get the regolith optical properties right (papers all currently use guesses, including and as explained in, Vasavada 2012) since the field isn’t generating much interest for funding.

          • “The greater the density of the atmosphere at the surface the greater the energy partition in favor of the air and the higher the temperature at the surface.”

            Why not take a stab at a linear relationship to produce multiple graphs on the same plot, such that you could place the earth, Venus, etc. on. Something might be visible. If that does nothing, try exponential relationship(s)

            Philip:

            Given that the GAT for these planets in most cases does not exist from hard data, there will be large error bars for the ‘GHE’.

            Good luck.

          • “Why not take a stab at a linear relationship to produce multiple graphs on the same plot”

            EdB,

            Already had a shot at this. There is no simple or clear relationship.
            My current idea is that because rotation rate determines the presence or absence of the Ferrel cell then this could be a factor in the process.

            Too little data and I am just guessing.

          • Setting up a simple lab experiment for the Hadley circulation v. rotation rate could give Philip some ideas. See Lorenz 1967 Chapter VI page 114: Lab models of the atm. ” mounted on a rotating turntable.” which “exonerated” Hadley from past criticism.

            “There are thus two qualitatively different regimes of flow, a zonally symmetric regime and a zonally asymmetric regime, which Fultz has called the Hadley regime and the Rossby regime. Typical circulation patterns occurring in the Hadley and Rossby regimes are shown in Figures 55 and 56, which are photographs of the free surface.”

          • EdB and Philip

            “The greater the density of the atmosphere at the surface the greater the energy partition in favor of the air and the higher the temperature at the surface.”

            “Why not take a stab at a linear relationship to produce multiple graphs on the same plot, such that you could place the earth, Venus, etc. on. ”

            My guess would be that one needs to take account of the specific gravity of the particular atmospheric composition at the surface for a given planet.
            High specific gravity would produce more conduction at a lower density and vice versa.
            I would be surprised if a linear relationship did not emerge after taking specific gravity into account.

            As for rotation speed I think that only determines the locations of the various ascending and descending columns rather than affecting the underlying partition ratio itself.
            No rotation and a single Hadley cell will suffice but if there is fast rotation the polar and equatorial cells become separated by centrifugal forces and a Ferrel cell is needed to act like a mechanical cog regulating the energy flow rate between the equatorial and polar regions.

          • Philip, Stephen:

            According to NZ and Holmes, the surface pressure determines the surface temperature. It does not tell us anything about the system gain(partition and “GHE”).

            OK.. so what is it we want to know? We want to know how much the GHE is, and how atmospheric composition changes it. What’s the variables for a planet? Surface atmospheric pressure/density is known.(uncertainty is small) Surface temperature is known, but other than the earth and a couple of planets, can have several degrees K of uncertainty. Rotation rate is known. Atmospheric opacity is known(?).

            Surface conductivity might be fairly constant. Our water world is unique, as water vapor returns heat to a night time cooling atmosphere.

            Wind speed is unknown, but could be assumed to be a function of planetary rotation rate, atmospheric density and opacity.

            I suspect climate models could be modified to include a partitioning routine. Do you know a friendly modelling center? Without it, I don’t think there is much hope of a solution. The goal is to get the model to work for several planets, and as a result, determine the sensitivity to the increased opacity due to changing the CO2 concentration.

          • EdB
            Our model does just that.
            It includes the required partitioning aspect.
            Atmospheric composition has no effect on GHE and if it seeks to alter the underlying pressure / temperature relationship by altering the partition ratio then the rate of convective overturning changes to neutralise any effect on surface temperature.
            Otherwise, our model would be unable to produce the correct surface temperatures once the correct partition ratio for a given planet has been deduced from the inverse modelling technique.
            The confirmation is the associated ability of our model to also generate the correct tropopause height in each case.

          • ”Atmospheric composition has no effect on GHE”

            EdB, the meteorology ref.s in the top post (and their ref.s) explain Stephen’s statement is wrong.

            Actually, the top post model produces the correct surface temperature Ts above Te once the correct partition ratio for a given planet has been deduced from the inverse modelling technique by starting with Ts mean surface temperature obtained by another (unnamed Table 1) source from radiative-convective atm. analysis.

    • It would appear yes, but the actual average surface temperature of Titan is no better known than Earth’s. Of course, an error of a degree is a relatively bigger deal there than here.

      • ” No one gas has an anomalous effect on atmospheric temperatures that is significantly more than any other gas. In short; there can be no 33°C ‘greenhouse effect’ on Earth, or any significant ‘greenhouse effect’ on any other planetary body with an atmosphere of >10kPa. Instead, it is a postulate of this hypothesis that the residual temperature difference of 33°C between the S-B effective temperature and the measured near-surface temperature is actually caused by adiabatic auto-compression.”

    • Commie Bob: the atmosphere of Titan is also 50% denser than that of earth, further adding to the problem for CO2 control knob folk. If we can do this kind of work meteorologically on a body 900 million miles away with close to observed results, it seems a huge embarrassment to the earth climate science mainstream fot its fixation on CO2. It certainly needs an answer from CO2 control types.

  4. Gents, very readable and interesting for a non meteorologist/non astrophysicist (geologist- mining engineer). Regarding retained energy and radiated loss to space in each hemisphere using the DAET model, you have used 50% for each. Is there a physical explanation for this neat split? Is it rather deduced from modelling (reverse modelling using measured results)?

    It seems this work begs for a reply from the mainstream climate scientists.

    • Gary, the one that uses the 50:50 split is the diabatic only version which does not produce a greenhouse effect. It is effectively the version currently in use by the radiative theorists so to get a greenhouse effect they need to propose surface heating from back radiation.
      It is only when one introduces a split in favour of the air on the lit side plus a split in favour of the surface on the unlit side that a greenhouse effect arises. You have to have uplift and descent to achieve the effect and back radiation is no longer needed.
      The obvious explanation is that the time delay in mechanically transferring the energy surplus on one side to the area of deficit on the other side causes an accumulation of energy within the system that heats the entire surface.

  5. I recognise that many readers will have difficulty following the rather technical features of our model so to assist I set out below my original concept which Philip kindly offered to try to model for me (with great success):

    “i) Start with a rocky planet surrounded by a non-radiative atmosphere such as 100% Nitrogen with no convection.
    Assume that there is no rotation to confuse matters, ignore equator to pole energy transfers and provide illumination to one side from a nearby sun.
    On the illuminated side the sun heats the surface beneath the gaseous atmosphere and, since surface heating is uneven, gas density differentials arise in the horizontal plane so that warmer, less dense, Nitrogen starts to rise above colder, denser, Nitrogen that flows in beneath and convective overturning of the atmosphere has begun.
    After a while, the entire illuminated side consists of less dense warm rising Nitrogen and the entire dark side consists of descending, denser and colder Nitrogen.
    The Nitrogen on the illuminated side, being non-radiative, heats only by conduction from surface to air and cannot assist cooling of the surface by radiating to space.
    There will be a lapse rate slope whereby the air becomes cooler with height due to expansion (via the Gas Laws) as it rises along the line of decreasing density with height. That density gradient is created by the pull of gravity on the individual molecules of the Nitrogen atmosphere.
    At the top of the rising column the colder denser Nitrogen is pushed aside by the warmer more buoyant and less dense Nitrogen coming up from below and it then flows, at a high level, across to the dark side of the planet where descent occurs back towards the surface.
    During the descent there is warming by compression as the Nitrogen moves back down to the surface and then the Nitrogen flows along the surface back to the base of the rising column on the illuminated side whereupon the cycle repeats.
    Thus we have a very simplified climate system without radiative gases consisting of one large low pressure cell on the illuminated side and one large high pressure cell on the dark side.

    ii) The thermal consequences of convective overturning.
    On the illuminated side, conduction is absorbing energy from the surface the temperature of which as observed from space initially appears to drop below the figure predicted by the S-B equation. Instead of being radiated straight out to space a portion of the kinetic energy at the surface is being diverted into conduction and convection. Assume sufficient insolation to give a surface temperature of 255K without an atmosphere and 33K absorbed from the surface into the atmosphere by conduction. The surface temperature appears to drops to 222K. Those figures are illustrative only since there is dispute about the actual numbers for the scale of the so called greenhouse effect.
    On the dark side the descending Nitrogen warms as it falls to the surface and when it reaches the surface the cold surface will rapidly pull some of that initially conducted energy (obtained from the illuminated side) out of the descending Nitrogen so that the surface and the Nitrogen in contact with it will become warmer than it otherwise would have been, namely by 33K.
    One can see how effectively a cold, solid surface will draw heat from the atmospheric gases by noting the development of radiation fog above cold surfaces on Earth. The cold surface quickly reduces the ground level atmospheric temperature to a point below the dew point.
    That less cold Nitrogen then flows via advection across the surface back to the illuminated side which is then being supplied with Nitrogen at the surface which is 33K warmer than it otherwise would have been.
    That describes the first convective overturning cycle only.
    The key point at that stage is that, as soon as the first cycle completes, the second convective cycle does not need to take any further energy from incoming solar radiation because the necessary energy is being advected in by winds from the unlit side. The full effect of continuing insolation can then be experienced once more so the surface goes back up to 255k from 222k.
    ADDITIONALLY the air moving horizontally from the dark side to the illuminated side is 33K warmer than it otherwise would have been so the average temperature for the whole sphere actually rises to 288K
    Since that 33K flowing across from the dark side goes straight up again via conduction to fuel the next convective overturning cycle and therefore does not radiate out to space, the view from space would show a radiating temperature for the planet of 255K just as it would have done if there were no atmosphere at all.
    In that scenario both sides of the planet’s surface are 33K warmer than they otherwise would have been, the view from space satisfies the S-B equation and radiation in from space equals radiation out to space. Radiative capability within the atmosphere not required.”

    The development of predictive capability within the adiabatic model demonstrates its superiority to the radiative model.

    My first foray into this area of study was back in December 2012:

    https://www.newclimatemodel.com/the-ignoring-of-adiabatic-processes-big-mistake/

    and was first published at Tallbloke’s Talkshop.

    • Stephen Wilde,
      Thanks for adding these clarifications as to how heat convection and conduction couple with the near-surface atmosphere and the physical surface respectively, further aided by advection, to create the convective over-turning cycles that dynamically drive Titan’s atmosphere.

    • The convective overturning concept best describes a slowly rotating planet, giving high winds to distribute the heat from the lit to the unlit (night) side.

      That initial concept has led to a model with mathematics which refutes the greenhouse theory. Congratulations to you both. I hope you both get a grand prize for your thermodynamic breakthrough.

      Now back to the earth with some O/T conjecturing if the moderator allows it.

      Atmospheric heat retention is a tiny fraction of the heat retention of the top ten meters of its oceans and lakes. One could imagine the earth rotating slowly enough that it would have 30C water on the lit side, strong overturning winds carrying heat(mostly latent) to the unlit side, where an ice cap would form.

      Atmospheric density matters, as per NZ and Holmes. The greater the density, the greater the surface heat and its resultant temperature.

      For a final conjecture. On early earth, with a quiet sun, a huge atmospheric density produced a warm earth. As the sun grew more active, stripping away the atmosphere, the density reduced, but was still higher than today, otherwise dinosaurs could not fly. That extra density kept the earth warmer than now. Today we have a lean atmosphere but water still keeps us warm, but plate tectonics restricts water flow to the Arctic and gives us an Greenland and Antartica.

      Through it all, we have tides of many types. Ocean transport heat tides. GCR tides induced from the Suns behaviour. ENSO, PDO, AO, AMOC. Then there is the earths tilt, orbital effects.

      The bottom line to me is that this new planetary warming model breaks a logjam on my thinking. Thanks Steven and Philip.

  6. We call this meteorological model the diabatic model because of the equipartition of power intensity flux at its critical surface boundary.

    Sadly that is not what diabatic means. It is dia + batos , passing through, not di- as in diatomic: diabatic has nothing to do with equipartition.

    • Adiabatic means that it does not pass through. It forms a discrete energy loop and heats the surface in the process.
      One therefore must partition the energy flowing through which is diabatic and the energy entering and leaving the discrete adiabatic loop.

    • “Sadly that is not what diabatic means”

      Greg,
      Diabatic is defined in the glossary.
      Greek diabat(ós) able to be crossed (in both directions).

  7. This process has the ability to identify the surface energy partition ratio which determines the thermal enhancement observed in the atmosphere of slowly rotating Titan.

    This does not “identify” anything. It is called using an unknown, unconstrained parameter as a fudge factor to get the “right” answer. You make a model then frig it to match certain observations.

    This very likely gives you a “right for the wrong reason” result. It does not mean that your model works nor that is useful for anything at all. Neither does it “identify” the correct value for the unknown parameter. You have a model of unknown validity which you have rigged to fit your expectations.

    Step 3: That by applying the standard geoscience technique of inverse modelling to the basic diabatic atmospheric model of Titan, an adiabatic model can be created.

    Yep, that sadly is the “standard” way of doing things. You have provided a very detailed example of exactly what is wrong with climatology, and the all destroying power of CO2 it claims to “prove”.

    • Greg,
      Tuning a model to obtain a single value result is a valid criticism. However, the model I have built contains a number of features which have produced unexpected insights. For example, tuning the adiabatic model creates not just the average temperature of either a circulation cell or that of a whole globe, but also the associated tropopause height. Much more interesting is the clear indication that the tropopause height on the lit hemisphere of convection is associated with the lowest possible freezing point temperature of the primary condensing volatile in a particular planetary (or lunar) atmosphere.

      For example, with the Earth, the condensing volatile is water, the lowest possible temperature of super cooled water is circa 230 Kelvin. In the whole Earth Adiabatic model with an average global temperature of 288 Kelvin this final solidification temperature of 230 Kelvin occurs at an elevation of 17.8 km, assuming an environmental lapse rate of 6K/km (after Simpson, 1928).

      In the case of Venus, the condensing volatile is Sulphuric acid and while there is no unique freezing point, there are three cusp points in this freezing point diagram. One at 70 wt% H2SO4 has a value of minus 43C. In the adiabatic model the radiant emission temperature for Venus is minus 46.6C. Venus is bright sulphur yellow, so there is also a potential relationship between the freezing point of the sulphuric acid volatile and the Venusian albedo.

      For Titan the situation is more complex. Here we have the presence of Tholins creating an atmospheric shroud, but also clear evidence of convection storms producing episodes of brightening associated with the formation of frozen methane cirrus clouds.

      It is self-evident that Bond albedo is a lit hemisphere property, and so an association between surface temperature, environmental lapse rate, condensing volatile type, lit hemisphere tropopause temperature and tropopause height begins to constraint the modelling variables to an extraordinary degree. Perhaps the most intriguing point is the clear evidence that once the atmosphere is cold enough to only contain solid particles, then the process of radiant thermal emission to space is greatly enhanced. This is because solid particles (even small ice crystals) are efficient and effective emitters of long wave radiation.

  8. “I would rather have questions that can’t be answered than answers that can’t be questioned.” Richard P. Feynman.

    Another gem. Many thanks for that quotation.

  9. This nice work by Phillip and Seven adds to the studies of Nikolov and Zeller and also of Holmes, that show from several angles that atmospheric temperature is determined by gravity and convection, and that radiation is not dominant. And composition has little relevance (except condensing clouds).

    https://www.researchgate.net/publication/317570648_New_Insights_on_the_Physical_Nature_of_the_Atmospheric_Greenhouse_Effect_Deduced_from_an_Empirical_Planetary_Temperature_Model

    https://www.researchgate.net/publication/323106609_Molar_Mass_Version_of_the_Ideal_Gas_Law_Points_to_a_Very_Low_Climate_Sensitivity

    It’s obvious that radiation to space will be determined by the vertical temperature structure, which is under direct influence of convection. Turbulent versus laminar boundaries will also have different radiation characteristics. The currently popular radiation dominated (or radiation only) models probably require the assumption of total stasis and no wind.

  10. Greg
    Our model has predictive capability for parameters other then those initially provided.
    The distinction between diabatic and adiabatic is well known and you do not have it right.

    • What kind of response do you get from scientists who lean more toward CAGW?

      It seems likely that some scientists will at some point recommend a denier gibbet for CAGW dissent. This would be viewed by that crowd as conversion therapy.

  11. I wonder how they know surface emissivity = 1? I mean unlike ANY real surface..

    Since it seems mandatory assuming a surface emissivity of 1 to climatologists, I would love to see how they explain surface temperatures of neighboring Enceladus.

  12. This article is way over my head, but I wonder what the great Dr. Feynman would have to say about the concept of a “scientific” climate consensus. Bet he wouldn’t be very complimentary.

  13. Can you use Trenberths energy diagram to calculate the split? It should be equal to your modelled split, should it not?

    • Can you use Trenberths energy diagram to calculate the split?

      EdB,

      Have a look at our previous WUWT post in this series.
      An Analysis of the Earth’s Energy Budget
      Table 3: Earth’s Annual Global Mean Energy Budget (K & T, 1997) including the elements of the atmospheric recycling process shows how it is possible to unpack the 390 W/m^2 black box of Back Radiation in Trenberth’s Fig 7 diagram.

      Table 4: Key Energy Budget Metrics (K & T, 1997) shows that the Total Intensity received by the surface (both high frequency insolation and also low frequency “Back Radiation”) is 558 W/m^2.
      Table 8 shows the split between radiant flux and mass motion flux for this total quantity of intensity received by the surface.

      N.B. The 66 W/m^2 of low frequency surface radiation in Table 3 can be further subdivided into the 40 W/m^2 Atmospheric Window loss, leaving only 26 W/m^2 of solar radiance to directly heat the atmosphere. I have added this refinement to an updated version of Table 3 in the spreadsheet K&T (1997) in my Research Gate posting of the Methods Workbook here:-
      Analysis of Earth Energy Budget Diagrams 21May19

      It should be equal to your modelled split, should it not?

      No, Trenberth models the atmosphere in its opaque state with 67 W/m^2 of insolation being directly absorbed by the air (Vapour, dust, Ozone, & clouds).
      While this approach is clearly more representative of the real-world situation, in our model we are trying to demonstrate the existence of mass motion flux recycling for a fully transparent atmosphere.

      • Glitch:-

        390 W/m^2 black box of Surface Back Radiation in Trenberth’s Fig 7 diagram

      • All these models are like the proclaimed “best car in the world”, which accidentally does not even have an engine. You can not skip the basic necessities and come up with something reasonable.

        The GHE (in theory) can not be explained without the adiabatic lapse rate, which is its very foundation. Therefore these “Energy Budgets” or “Radiation Diagrams” are totally pointless, because they artificially try to explain something with wrong parameters, which they naturally can never explain.

        To understand the problem, just go beyond Earth. If you take a gas giant like Jupiter, you can see how temperatures ever increase the deeper you go into its atmosphere. Now imagine you would want to explain the temperature at any depth with an “Energy Budget”. Except for the most upper layers of the atmosphere, there is essentially no radiative exchange with sun and space. So without the adiabatic lapse rate, there is obviously no way you could explain these temperatures.

        The difference between Jupiter and Earth in this regard is only, that with Jupiter it turns so obvious how this approach can not work, while it seems to make sense for some people in the case of Earth. However, the physics are basically the same, just with different parameters, and thus the GHE can NEVER be explained without the adiabatic lapse rate.

        If you happen to come up with the right result, despite doing the wrong thing, then it is only because you have “parameterized” your model to fit the desired result. In other words, it is one big fake!

        • Leitwolf,
          In the case of the radiative models the ‘fakery’ is in proposing a surface thermal effect from back radiation to offset their error in not including the influence of the adiabatic lapse rate within descending air.
          I’m assuming that you do not aim your criticism at our model since the entire point of it is to give due significance to the adiabatic lapse rate.

          • ”In the case of the radiative models the ‘fakery’ is in proposing a surface thermal effect from back radiation to offset their error in not including the influence of the adiabatic lapse rate within descending air.”

            Really radiative-convective atm. physics Stephen (you missed the word convective) since the global descending air cycle is included in all proper energy budgets over 4-15+ annual observations as discussed in the various energy budget papers by numerous authors. This is just a sign you aren’t able to comprehend the published papers.

            This top post again uses the same curve fitting technique as in a previous post that is without predictive value as it simply tunes a model to a given single value that already includes Titan’s radiative-convective GHE result (picked from nowhere in the ref.s that I can find). Tuning a model to obtain a single value as in the top post is not able to include or predict the radiative-convective effects of Titan’s unique haze layer as mentioned in some of the top post ref.s.

            The 50+ year old radiative-convective atm. time tested physics does ably predict the Titan haze layer effect & w/o curve fitting as is discussed in the top post ref.s. The radiative-convective atm. physics will work on exoplanets for a reasonable global mean near surface temperature to resonably understand if liquid water can be present on the surface; the top post tuning method will not do so.

          • Trick, it seems to me you missed the all important model proposed here, which implies a surface warming without the GHE. Titan is just an example.

            The GHE defenders better come up with a refutation of that model, or the have some serious explaining to do. The evidence is coming from two sides now, the atmosphere pressure effect and now this heat retention gain.

          • EdB, no miss as top post 94K starting point INCLUDES Titan’s natural rGHE composition in Table 1 for Ts “the observed mean surface temperature for this moon” above Te. If you read the ref.s, this Ts also net of the natural GHE of Titan’s atm. composition unique haze layer (~opaque to solar SW but transparent to surface LW radiation) which the top post cannot discern as can radiative-convective analysis techniques.

            There is no refutation needed, as the top post merely curve fits known rGHE data “by applying the mathematical technique of inverse modelling”.

  14. Why isn’t Titan warmer than Miami? It’s atmosphere is methane a notorious super greenhouse gas. That much methane should keep Titan toasty warm.

  15. “33K absorbed from the surface into the atmosphere by conduction”
    Steven this is a very loose statement. What do you mean? Are you quantifying sensible heat transfer, if so why use kelvin? Don’t you want to give that transfer in watts per square meter? I don’t understand where your extra heat flow is coming from to get to average 288K.

    • “I don’t understand where your extra heat flow is coming from”

      Neogene Geo.

      Consider this example.
      There is a river of water flowing past your land.
      On the bank of the river you build a water wheel that is turned by the flow of the river.
      The wheel is designed to lift small buckets of water out and above the level of the river, and to direct a flow of the lifted water from the wheel onto the surface of your land.
      You then direct this small flow of lifted water to return back to the river so that it joins the main river flow upstream of the wheel.
      Simple question: Does the flow of water in the river going past the wheel now increase?

    • Neogene,
      The use of 33k rather than expressing it in Wm2 is to link the concept with the generally accepted starting point that the surface is 33K warmer than it ‘should’ be.
      In effect, I am referring to the number of Wm2 that would produce a surface 33k warmer than it ‘should’ be.
      Since it is constantly recirculating adiabatically it adds to total system heat content (over and above the heat content produced diabatically) and therefore must warm the surface.

  16. Interestingly, whilst watching the BBC show ‘The Planets’ with Brian Cox I noticed that episode 2 asserted that Mars was once a warm planet with water oceans and a denser atmosphere but that it changed when the magnetic field faded away so that the atmosphere was no longer protected from the depredations of the solar wind.
    The lighter molecules were stripped away by the solar wind which left mostly heavier CO2.
    My point being that the current coldness of Mars was a result of a reduction in atmospheric mass and NOT a reduction in CO2.
    Since Cox is an AGW believer he must have completely missed the significance of his words which totally contradict the radiative theory and support my mass induced greenhouse effect hypothesis.
    It seems that there are those within the scientific establishment who are aware of the truth but they have never challenged the radiative theory.
    Now that Philip and I have provided the mechanism and a mathematically modelled demonstration I think the establishment needs to address the issues arising.
    One can only hope that someone in authority will see this work and run with it.

    • I’m not sure that you can claim “my mass induced greenhouse effect hypothesis” . How about “Surface temperature gain using a thermally induced planetary convection model”.

      • That is a reasonable suggestion which I may adopt in the future.
        For current purposes my main concern was to clearly distinguish between the usual radiation induced GHE and that which results from atmospheric mass.
        You have a firm grip on the concepts involved. May I ask what your skill set is ?

        • Mech Eng. My design experience is quite varied. As someone previously said, the first challenge of design when faced with a new challenge is to correctly formulate the problem. Then you use your mathematics. The evidence of a failed approach to the climate challenge has been there since the late 90’s missing hot spot. Obviously one can still get it wrong, but when a new approach such as formulated above can demonstrate both the no atmosphere temperature and the GHE, that is attention grabbing.

          • “when a new approach such as formulated above can demonstrate both the no atmosphere temperature and the GHE, that is attention grabbing.”

            One would think so but it is being ignored by established scientists and policy makers thus far.

    • Stephen Wilde July 20, 2019 at 10:10 am

      My point being that the current coldness of Mars was a result of a reduction in atmospheric mass and NOT a reduction in CO2.

      Confirmation bias perhaps? If the mass of the atmosphere was the major reason for the high surface temperatures on Mars with oceans, you’re implicitly saying that that atmosphere warmed the oceans.
      Seems the other way around is much more plausible.

      • The mass of the atmosphere bearing down on the water surface controls the amount of energy that the oceans can hold by affecting the amount of energy required to effect the phase change from liquid to vapour so, no, not confirmation bias by me.

        • Stephen Wilde July 21, 2019 at 7:22 am

          Doesn’t explain how the DEEP oceans became so hot on Earth (~275K).
          Unless of course you agree that they are heated by Earths hot interior, in which case the little solar energy that reaches their surface (~161 W/m^2 avg according K&T) is enough to warm the surface layer to the observed SST’s.
          Obviously the atmosphere in that case only has to reduce the energy loss from the surface to space, what it actually is doing 😉

  17. General question about Titan:
    is geothermal energy ruled out completely? (interior same or lower temperature than the surface)
    For Earth and also our moon the surface temperatures would be ~25-50K without sun due to the very small flux that escapes to the surface to be radiated away to space.

    • If geothermal energy leaks out to the surface and is then conducted to the air then the convective overturning cycle speeds up in order to eject that extra energy to space and thereby avoid unbalancing hydrostatic equilibrium for the atmosphere as a whole.

      • Stephen Wilde July 21, 2019 at 8:11 am
        Reading about cryovolcanoes gives the impression that Titan is geothermally active.
        Even a small flux like on Earth can create a continuous surface temperature of ~25-40K, without sun or atmosphere. This could be a significant part of the explanation of the average surface temp (94K?)
        So why only consider solar energy and atmospheric effects?
        Another question: how long is Titan in the shadow of Saturn during its orbit?

        • “Another question: how long is Titan in the shadow of Saturn during its orbit?”

          Ben,
          I checked this question out with NASA and the answer is “surprisingly little and not very often”.
          My contact kindly provided a link to the NAIF JPL NASA 2019. Titan Occultations WebGeocalc Spice data and software. (see references above for the link).

          The Geocalc Code that generates the occultations output for a solar based observer (it is the sun than causes the eclipses) is on the Sources worksheet of my methods workbook TitanClimateModels08Jul19

        • Ben,

          I believe that you are a fan of geothermal heating of the deep oceans. You may be interested in this paper by Zhang, L. et al. 2019 The evolution of latitudinal temperature gradients from the latest Cretaceous through the Present

          Using data kindly supplied by Dr Zhang I am able to calculate that the global marine average surface temperature for the latest Cretaceous was 24 Celsius.
          The paleolatitude transect for the latest Cretaceous shows a link to the influence of the Hadley, Ferrel and Polar cells. Testing this temperature data with a whole earth model requires an albedo of 0.214 to achieve the global average temperature of 24 Celsius. The Polar cell has an average annual temperature of 13 Celsius and this cannot be explained by latitudinal solar heating alone, as the required Bond albedo for a parallel DAET model becomes less than zero. Clearly the high latitude Cretaceous world had a major component of heating from ocean waters. How these ocean waters were heated needs to be the subject of a separate study.

          • Bear in mind that the ocean heat content at any given level of insolation is set by the weight of atmosphere bearing down on the surface and that internal ocean cycles introduce thermal inertia and considerable variability.
            The extent to which the oceans cause variations around the baseline temperature in our model would be a separate area of study.
            I would not expect any geothermal contribution to affect surface temperature because it would simply be neutralised by convective adjustments in the same way that all other potential disruptions are successfully neutralised including any effect from ghgs.

          • Philip Mulholland July 25, 2019 at 3:37 pm
            Ok Phillip, thanks. I requested the paper.
            Relevant for the same subject seems this:
            https://www.researchgate.net/publication/275277369_Some_Thoughts_on_Global_Climate_Change_The_Transition_for_Icehouse_to_Hothouse_Conditions

            Clearly the high latitude Cretaceous world had a major component of heating from ocean waters. How these ocean waters were heated needs to be the subject of a separate study.

            I’m convinced that the high temperatures on Earth are not due to a GHE, but due to our hot deep oceans, heated by geothermal energy.
            The mechanism is very elegant imo.
            From this position a “stumbled” upon the Cretaceous and its hot climate.
            I posted on the subject some years ago:
            https://tallbloke.wordpress.com/2014/03/03/ben-wouters-influence-of-geothermal-heat-on-past-and-present-climate/

          • Philip Mulholland July 25, 2019 at 3:37 pm
            In my post I write

            The events marked in red total around 136 million km3. The total volume of the oceans is ~1.400 million km3. Assuming magma being 1000K warmer than deep ocean water, and the specific heat capacity of water being 4 times that of magma, these events have the potential to warm all ocean water ~ 24K.

            Since then I did some calculations, and now I would state that 1 million km^3 magma cooling in the deep oceans delivers enough energy to warm ALL ocean water 1K.

  18. Just an observation from someone who is not a scientist and isn’t familiar with your Latin scientific terms or math.

    Wikipedia says that titan receives 1% of the sunlight earth receives. (1% of 250°F= 2.5°) The atmosphere (inversion layer?) filters out 90% of that 1%… For the surface of titan to be 288K (near 60°F, 10° warmer than earth average) it would have nothing but minimal connection to watts per meter squared, the sun or anything we are familiar with.
    There are also other factors involved which are not considered. For instance Saturn emits 2 1/2 times more heat than it receives from the sun. Titan may receive as much reflected sunlight and heat from Saturn as it does from the sun. (still not enough heat to melt Saturns rings) This means for a few years of Saturns 30 year orbit, titan is receiving solar radiation on one side, reflected solar radiation and heat from Saturn on the other. 24 hour energy during this part of Titan’s Saturn orbit.
    As it revolves behind Saturn, the far side is exposed to deep black space, and when it falls into Saturns shadow… Movie “Pitch black” comes to mind. This is only possible when Saturns rings are in alignment or on edge with the sun. (next in 2025) As I understand it, most of the moons orbit in alignment with the rings and Saturns rotation, which is at a 26° tilt too orbital plane. (appearing over on its side making Saturn look like a large eyeball) Titan receives 24 hour sunlight on its northern hemisphere, like Saturn, for half of the 30 year cycle as it transitions to the southern hemisphere. Since titan is in tidel lock with Saturn, approximately 1/4 of the atmosphere is in complete darkness for nearly 10 years. Double energy in the exposed portion during the same time period. Which still amounts to 10% which makes it through the atmosphere to the surface, of the 1%, that Saturn receives less than earth average, from being 9 to 10 AU from the sun.

    It would appear that Titan, like all the planets with a significant atmosphere, (including Earth) radiate more energy than it receives from the sun.
    If the model does not satisfy and explain the actual measurements, then an incomplete picture is formed, like the blind men describing an elephant from the vantage point of the surface area they are touching, thinking they have a complete picture when it’s only a part of the whole.

    I would also note that “convection”, as described in this article, is not occurring in real life. Yes, hot air rises but it needs a “greenhouse” insulator and a heat source, like a hot air balloon, to prevent the air from mixing with cold air and being neutralized. Without a container, air expands and always cools in lower air pressure, stopping the convection. The mountain, where I go camping 10 miles from my home, is 80° at 8000 feet, compared to 100° at 5000 feet at my house today. The mountain is surrounded by high temperatures yet the hot air never reaches the summit. (There is still snow up there) Day or night, the top of the mountain is always colder relative to the “barometric pressure”. Weather balloon temperature readings verify this, no matter where on the planet you are. A 5.4° temperature drop, depending on humidity, for every thousand feet the balloon goes up.
    Even the convection of the “Seabreeze” of hot air rising on land during the day, then the airflow reversing itself at night along the coastline is limited to a few miles. It’s a local event.
    The doldrums, on each side of the equator, receive more energy than average and is very warm, no air movement, no convection? No simple explanation for this.
    Is the heat of the equator too far from the cold of Antarctica?
    Saturn has wind speeds over 1000 mph with similar gravity to earth. (10% more gravity)
    I know, comparing apples to potatoes but I needed an extreme example to show that convection is not the main driver or it would be occurring in a very noticeable way.
    I’ve lived north of the Arctic Circle and the wind only blows there when there’s an approaching storm. Completely different than the sea near Antarctica where the wind never stops blowing due to the Polar vortex. The heavy cold air dropping off a continent (which averages near 10,000 feet, falling to Sea level) will heat the air, caused by atmospheric compression, 60°F+/- but will still be below freezing to extend the ice shelf miles beyond the continent.
    My point is, that even with 24 hour sunlight, four months a year in Antarctica, miles closer to the sun, barometric pressure has more influence on heat than watts per meter squared. Titan seems to verify this model beening warmer than earth having more atmosphere, with less gravity. Virtually no heat from the sun.

    • “The doldrums, on each side of the equator, receive more energy than average and is very warm, no air movement, no convection? No simple explanation for this.
      Is the heat of the equator too far from the cold of Antarctica?
      Saturn has wind speeds over 1000 mph with similar gravity to earth. (10% more gravity)”

      Wind is a result of pressure/density differences.

  19. Stephen & Phillip,
    Nice paper.
    It’s ridiculous that we have had to put up with the IPCC’s nonsense of a constant 239W/m2, beating down on a flat Earth for so long!

    My final proof that the greenhouse effect does not exist in any thick atmosphere (one of >10kPa) is as follows;

    Postulates
    • The Ideal Gas Law is correct.
    • The same external conditions such as insolation and auto-compression prevail.

    My papers show that for a GHE to occur in a convecting atmosphere (one of >10kPa), a large anomalous change must happen in the density, pressure or both.
    No anomalous changes of this magnitude have been seen in any planetary atmospheres.
    This is not really a surprise, since anomalous changes are actually forbidden by the ideal gas law and its derivatives like the molar mass version, which treat all gases equally.
    To provide more detail;

    Different concentrations of gases at the same or at different times can provide the same temperature or different temperatures;

    BUT – the same concentrations of gases cannot provide different temperatures at different times. The formula T = P M / R ρ forbids it.

    This fact disproves the greenhouse gas hypothesis, as it is presented by the IPCC*.

    *Because there is said to exist a time delay to reach ‘equilibration’, due to the (ECS) climate sensitivity to CO2 being in the range of 1.5C – 4.5C.
    The IPCC reports state that if there was a sudden doubling in the atmospheric greenhouse gas CO2, the greenhouse effect from this would operate slowly, causing an eventual ~3c of warming over centuries to millennia.
    Therefore the claim is that the temperature would rise significantly over time, with the same prevailing atmospheric gas concentrations, and there would be no rapid equilibration, as the Ideal Gas Law demands.
    This represents a terminal conflict between the IPCC’s greenhouse effect and the molar mass version of the ideal gas law.
    Therefore the climate sensitivity to, for example, a doubling of atmospheric CO2, must be very close to zero. Essentially, it means that there is no GHE – as per your paper.
    Dr Robert Holmes

    • Hi Robert,
      That seems sound to me. The only quibble is that in my view there is a GHE but it is a consequence of atmospheric mass moving up and down via convection within a gravity field and not radiation back from atmosphere to surface.

      • ”Therefore the climate sensitivity to, for example, a doubling of atmospheric CO2, must be very close to zero.”

        As measured on avg. ~.01C/yr monotonic climate sensitivity due observed ppm CO2 increase over the ~75 years up to 2013 is “very close to zero” but nonzero.

        More accurately it means that there is very close to zero or on avg. 0.01C/yr observed change in Earth observed GHE due added ppm CO2 as per above paper (Ts-Te In Table 1).

      • Hi Steven,
        I agree entirely that there is a surface thermal enhancement caused by the presence of an atmosphere, using the mechanism you describe, but I do not call it a ‘greenhouse effect’ – mainly to lessen confusion.
        Robert

        • Robert 5:06am, there is a major problem with Stephen’s imagination that there is a GHE but it is a consequence of atmospheric mass moving up and down via convection within a gravity field.

          It is easily shown (cf. Haurwitz 1941) that the potential and internal energies within a column extending to the top of the atmosphere bear a constant ratio to each other, to the extent that hydrostatic equilibrium prevails. Hence, net gains of kinetic energy occur in general at the expense of both potential and internal energy, in this same ratio at least to the extent that hydrostatic equilibrium prevails.

          Evidently the total potential energy is not a good measure of the amount of energy available for conversion into kinetic energy under adiabatic flow.

          Consider first an atmosphere whose density stratification is everywhere horizontal i.e. hydrostatic. In this case, although total potential energy is plentiful, none at all is available for conversion into kinetic energy.

          Next suppose that a horizontally stratified atmosphere becomes warmed above ambient in a restricted region as Stephen argues. This increase in temperature, decrease in density adds total potential energy to the system, and also disturbs the stratification, thus creating horizontal pressure forces which may convert some total potential energy into kinetic energy.

          BUT next suppose that a horizontally stratified atmosphere loses internal KE becomes cooled rather than warmed in a region. The cooling removes total potential energy from the system, but it still disturbs the stratification, thus creating horizontal pressure forces which may convert total potential energy into kinetic energy. Evidently removal of energy is sometimes as effective as addition of energy in making more kinetic energy available. So these arguments basically cancel each other on avg. within lo and hi pressure systems globally.

          You and Stephen therefore desire a quantity which measures the energy available for conversion into kinetic energy under adiabatic flow to show that there is a GHE but it is a consequence of atmospheric mass moving up and down via convection within a gravity field.

          This means to convince critical readers you & Stephen simply need to show there is on avg. 0.01C/yr observed change in Earth observed GHE in the 75 years prior 2013 due atmospheric mass moving up and down via convection within a gravity field for Earth and Titan as per above paper (Ts-Te In Table 1).

          All this has been covered in the existing meteorological literature (cf. Lorenz 1955 et. al.) so you have many sources to draw upon to prove/disprove your points to informed, critical readers.

        • Robert,
          Welcome to the thread.
          The key issue in the application of the DAET model is the nature of the relationship between partition ratio and atmospheric parameters (pressure and molecular composition). Trick (who will be along shortly) tries to downplay the most important aspect of this relationship by claiming that the inverse modelling process that I use is just “curve fitting”.
          The real surprise however is that the average surface temperature for the tuned model predicts the height of the tropopause. The only way that this can occur, given that we have three planetary bodies; Venus, Earth and Titan, each with different gravity, albedo, gas composition, surface pressure and insolation loading, is that the surface temperature “knows about” and combines the effect of each of these distinct environmental variables.
          It follows therefore that lapse rate, which is a function of gravity and specific heat, is somehow encapsulated within the model. Therefore, the most likely relationship is that partition ratio links through to specific heat, which in turn links to gas composition (molar mass).

          So, if we have atmospheric molecular composition as the primary variable and compute the specific heat, then for a given planetary gravity field and insolation loading the relationship to the partition ratio and the mass of the atmosphere (and hence the height of the tropopause) can be established.

          The take home message of our model is that opacity is not the primary control of planetary climate.

          • The real surprise would be that the average surface temperature for your UNtuned model predicts the height of the tropopause.

            Philip, you really are curve fitting. If the height of tropopause, global Ts and Te were unknowns you do not have enough independent eqn.s to solve for them. So you start with the knowns.

            Radiative-convective atm. analysis does obtain enough independent eqn.s to solve for unknown global mean planetary atm. Ts, tropopause height ever since the seminal papers in the 1960s.

  20. Why? You started with Ts, tuned the general circulation partition model to fit that Ts, then used the known environmental lapse to compute troposphere height.

    If you didn’t know a priori Ts and lapse ( as in the case of an exoplanet) your method would be useless.

    Radiative-convective analysis from observed irradiation, atm. composition and pressures works to reasonably compute Ts, Te, troposphere height. This methodology (now LBLRTM) has enough eqn.s to reasonably compute Ts, Te, troposphere height and above & has been reasonably applied to many exoplanets and solar system objects with substantial atm.s.

    • As far as I can see, no so-called radiative-convective model allows any surface energy to fuel ongoing convective overturning.
      They appear to assume it just happens by magic.
      You cannot have the same unit of surface energy being in two places at once or doing two jobs at once otherwise there is a breach of conservation of energy. Energy conducted cannot be radiated and energy radiated cannot be conducted.
      Trick says:
      “Radiative-convective analysis from observed irradiation, atm. composition and pressures works to reasonably compute Ts, Te, troposphere height. ”
      but of course that is so because he invokes pressure as a relevant parameter. As soon as one does that then one is actually accepting my proposed mechanism because it involves atmospheric mass and the specific gravity of the atmospheric constituents.
      The standard radiative model gives no relevance to pressure and fails to explain convection.

      • Yes, Stephen, higher atm. surface pressure makes the IR active species composition increasingly IR band opaque. Due this high surface pressure for example, Venus has no IR surface windows greater than 3micron thus is opaque to IR above that wavelength. More mass of grey absorbers leads to increasing surface pressure and thus more surface atm. opacity.

        Below a certain pressure (0.1 to 0.2 bar), the opacity from pressure declines enough to allow a wider IR band window no matter the atm. composition – this occurs as observed above the tropopause.

        The radiative-convective analysis DOES allow for convective overturning without double counting which is where the name comes from all the way back in the 1960s and it has stood the test of time.

        ”The standard radiative model gives no relevance to pressure and fails to explain convection.”

        This is just Stephen showing his inability to comprehend basic meteorology papers and texts that explain how the standard radiative model gives relevance to pressure along with the mixing ratios of the various grey absorbing species in planetary atmospheres. Of course, they also go about explaining convection/geostrophic winds hence explain radiative-convective atm. analysis. Which is all very useful for reasonable assessments of exoplanet’s Ts and Te thus Ts-Te (as in Table 1 paper above).

        • Trick says:

          ” surface pressure makes the IR active species composition increasingly IR band opaque.”

          That is the established theory. So why does our model work without any IR active species at all ?

          The reason is that surface pressure makes NON-IR active species composition increasingly IR band opaque by increasing the efficiency of conduction and convection relative to radiation.
          Which is where the energy partitioning between conduction and radiation becomes relevant.

          And you must have such energy partitioning otherwise surface energy cannot provide the necessary fuel for continuous convective overturning.
          Radiation alone doesn’t cause convection, only conduction will do it and such conduction must be at the expense of radiation otherwise you breach conservation of energy.

          • Stephen asks: ”So why does our model work without any IR active species at all ?”

            Because your Earth & Titan models start with observed (thermometer or brightness) Ts which includes ALL the active IR grey absorber species at ALL the observed gas mixing ratios and ALL the natural pressures to tune each partition.

            ”The reason is that surface pressure makes NON-IR active species composition increasingly IR band opaque by increasing the efficiency of conduction and convection relative to radiation.”

            Only in Stephen’s imagination not in first course meteorology. Convection will efficiently occur in any fluid warmed from below in a gravitation field. Convection essentially stops above the tropopause (on Earth for about 9km height at mid-latitude STP) because the fluid becomes warmed from above.

            Radiation doesn’t cause convection as such; radiation warms the surface which warms the fluid from below in a gravity field which causes convection. In the lower stratosphere, radiation warms the fluid from above and convection essentially ceases in close to the same gravity field. No breach of energy conservation.

          • Trick says:
            “Radiation doesn’t cause convection as such; radiation warms the surface which warms the fluid from below in a gravity field which causes convection.”

            So, the radiatively warmed surface warms the fluid from below how exactly ?
            That is achieved via conduction.
            But a single unit of energy transferred from surface to atmospheric gases via conduction cannot radiate out simultaneously.
            Hence the need for partitioning between conduction and radiation.
            Meanwhile, the surface stays at an elevated temperature because, at equilibrium, the energy conducted up is constantly replenished by fresh energy from advection as per our model.
            Any other scenario is a breach of conservation of energy.

          • ”Meanwhile, the surface stays at an elevated temperature because, at equilibrium”

            Then it’s not at steady state equilibrium Stephen. The convected air from surface is replaced laterally by ambient air due mass continuity so remains near equilibrium Ts.

    • “You started with Ts, tuned the general circulation partition model to fit that Ts, then used the known environmental lapse to compute troposphere height”
      Trick
      That is not an answer to the question Why?

      The DAET model does not incorporate the lapse rate into its structure.
      It requires the following three parameters that can all be measured a priori: –

      1. The average surface temperature of the planet – this can be measured by atmospheric probes.
      2. The lit hemisphere albedo – this can be measured from space.
      3. The solar irradiance at the planet’s orbital distance from the sun.

      From these three data points my model can compute the thermal separation of the lit surface and the radiant exhaust temperature.

      If we now add the lapse rate from the atmospheric probe’s profile data, then the elevation of the TOA is established.
      This is not an obvious result. The lapse rate incorporates gravity (obviously) but it is not a requirement in the primary computation. It is a secondary result.
      So once again, Why?

      • Why again? Philip – As I wrote & you confirm, top paper starts with Ts, tuned the general circulation partition model to fit that Ts, then used the known environmental lapse to compute troposphere height.

        In your own 11:25am words you confirm partition was “tuned” using:
        1. (Ts) can be measured by atmospheric probes.
        2. (albedo) can be measured from space.
        3. (To measured) at the planet’s orbital distance from the sun.

        If we now add the (known env.) lapse rate from the atmospheric probe’s profile data, then the elevation of the (not TOA but tropopause) is established.

        These are all obvious as they are measured data! Which is n.a. for an exoplanet.

        So, pick a known exoplanet beyond the capability of today’s ‘scopes. Use your method to come up with its Ts, Te, lapse. Then when today’s ‘scopes are improved upon, and the radiative-convective (LBLRTM) analysis is possible due to then known atm. composition by spectroscopy, compare your answers. If your method is reasonably close to radiative-convective analysis reults, you win the Kewpie Doll.

        This won’t & can’t happen because you will first need the text book radiative-convective (LBLRTM) calculations for exoplanet Ts, Te, and environment lapse with which to “tune” your partition of its general circulation.

        Spin rate of the exoplanet will matter too. If it is tidally locked, then divide by 2, if spinning fast enough, then divide by 4. Anywhere in between: get out the heat capacity tables for the various component materials.

        • Well Trick,

          Te is the diabatic model, so that is already established.
          Lapse rate is a function of gravity (planetary mass and size) and specific heat, for that you need the atmospheric composition (more spectroscopic data needed here).
          Both techniques require albedo (astronomy) and stellar irradiance (astronomy).
          So, the only unknown variable is Ts.
          But without any knowledge of the atmospheric mass can anything be established?
          We can of course use atmospheric occultation data to establish planetary atmospheric thickness, so now with only one unknown left, job done.

          But why does this work?

          • ”We can of course use atmospheric occultation data to establish planetary atmospheric thickness, so now with only one unknown left, job done.”

            There’s another unknown. Spectroscopy will also tell the needed exoplanet atm. composition from the absorption lines of the constituent gases illuminated by the star(s) spectrum the planet is orbiting.

            “Why this works” for unknown Ts solar system objects with substantial atm.s is explained in detail in the appendix of your ref. Robinson and Catling. Te is only known if the guess that the object is in near steady state equilibrium is good enough, otherwise Te would be unknown (e.g. exoplanets like Neptune where Te is only known from flybys & good enough existing ‘scopes for brightness measurements & optical properties of the H2, He gas).

            ”But without any knowledge of the atmospheric mass can anything be established?”

            Sure, Te and Ts, whether there are more general circulation cells than just Hadley type. If the planet is spinning fast enough (e.g. Earth), total atm. mass is not a necessary known as heat capacity is not needed in the calculation, just dividing by 4 works well enough, for solar system objects with substantial atm.s that are in near steady state equilibrium surface and TOA (e.g. Venus, Earth, Titan).

            Philip, it should interest you to study the R&C paper appendix more closely. For Stephen, that is a stretch as he avoids taking the time & doing the work to learn the basic meteorology principles. Stephen has long been imagining things – that time would have been better spent by Stephen studying R&C and Lorenz 1955 while learning what he needs to understand their work.

          • Trick,

            I think that you missed my proviso about spectroscopy earlier in my last statement.

            If the question why? is answered by a description of how a process works, then this is not an explanation. The question why can only be answered with a knowledge that derives from an understanding of the structure of the process – how it is built, and not a description of its utility – how it works. How something works requires no explanatory knowledge of the process of its creation, merely knowledge of the structure of its form. You can know how to use a mobile ‘phone, without any knowledge of how that ‘phone was constructed.

            I will now leave you to make the last comment as always.

            Good night.
            Philip

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