Modelling the Climate of Noonworld: A New Look at Venus.

Guest Post by Philip Mulholland

Study hard what interests you the most in the most undisciplined, irreverent and original manner possible.” Richard P. Feynman.

1. Introduction: The Science of Climate.

A planetary climate consists of a dynamic mobile-fluid mass-transport and energy delivery system, organised in the form of closed loops or cells, that advects mass and energy over the surface of a terrestrial planet. The mobile-fluid transport system collects energy from a region of net radiation surplus in the tropics (the zone of maximum solar zenith), and delivers it to a region of net radiation deficit towards the poles (the region of minimum solar zenith). At the location of net radiation deficit, the energy transported internally within the climate system is lost to space by thermal radiation from the planet.

As with any mass transport system it must form a closed loop, otherwise all of the energy necessary for the dynamic mass flow will be dissipated and the system will run down. Indeed, if too much energy is lost from the atmosphere at the region of energy deficit, then the transport mechanism will cease, as the mobile fluid carrying the heat freezes. Therefore the planet will lack a viable troposphere (weather layer) and possess only a tenuous gaseous atmosphere, such as is observed with the Atmosphere of Pluto. Consequently, it is a fundamental requirement that sufficient energy is retained by the mobile fluid, for it to return to the original location of incoming energy surplus for replenishment.

On its return to this origin, the mobile fluid is then able to gain additional energy and the mass transport system becomes recharged. This interception of additional solar energy by the planet’s surface reheats the mobile-fluid, and so the cycle that comprises the mass-transport and energy delivery circulation system continue and repeats indefinitely, and is a sustainable system as we see in this NASA image of the Planetary Atmospheric Circulation System of Venus (Fig. 1).

Figure 1: NASA Mariner 10's Portrait of Venus

Figure 1: NASA Mariner 10’s Portrait of Venus

Explanation of Figure 1: On Venus the sun rises in the west and sets in the east. This NASA Mariner 10’s Portrait of Venus shows the Sunrise Terminator, the South Polar Vortex (to the upper right), and the Bow Shockwave impact of the Solar Zenith “blow torch” disruptor dividing the Super-Rotational equatorial upper atmosphere winds. Remember the atmospheric pressure rule for the Earth’s northern hemisphere “Stand with your back to the wind, and the low pressure centre is to your left”. However, Venus rotates in the opposite sense to the Earth, and so this rule applies to the southern hemisphere of our sister planet. The application of this rule confirms the identity of the Venusian south pole in the NASA image.

2. Climate Forward Modelling.

The process of Forward Modelling creates a numerical prediction, that must be matched and verified against external data for the model to be both valid and useful. The modelling process starts with the identification of the set of fundamental principles, that contain the irreducible minimum set of axioms, from which the actions of a system are designed and constructed. With the set of first principles established and measured, then the mathematical algorithm that combines these elements can be created.

With forward modelling studies of a planet’s energy budget, the first and overarching assumption is that the only way that a planet can lose energy is by thermal radiation from the planetary body to space. This assumption is not in dispute, and it leads to the adoption of the Stefan-Boltzmann (S-B) equation of thermal radiation, which is used to establish the direct relationship between power intensity flux in Watts per square metre (W/m2) and the absolute thermal temperature of the emission surface in Kelvin (K).

The second critical assumption made in the analysis of a planet’s energy budget, is that it receives incoming thermal energy in the form of insolation from a single central star. Solar system planets orbit around this central source of light, and consequently all planets have both a lit (day) and a dark (night) hemisphere.

A technique for establishing the energy budget of a planet, and hence how the power being consumed is distributed within its climate system, is a technical challenge that has already been addressed by astronomy. An equation was required that could be used to compute the average surface temperature of any planet, by establishing its thermal emission temperature under a given insolation loading. To solve this problem, a set of modelling assumptions were made that include the following simplifications: –

1. That the planet being observed maintained a constant average surface temperature over a suitably long period of time.

2. To make this assumption valid, the total quantity of solar energy intercepted by the planet is averaged out over its annual orbital year.

3. This annual averaging therefore removes the effect of distance variation from the Sun, inherent for the trajectory of any planet’s elliptical orbit.

Next the complex problem of how a planetary orb intercepts solar energy, and how this sunlight energy is distributed over the planet’s surface, was addressed. Planets contain the following geometric features in common:

1. They are near-spherical globes.

2. They are only lit on one side from a sun that is located at a focus of their orbit’s ellipse.

3. They often (but not always) have a daily rotation rate that is significantly faster than their annual orbital period.

4. They commonly have an obliquity or axial tilt, although each planet’s angle of tilt is unique.

Given the above list of distinct features, it is clear that the computation for the surface capture of solar energy on an orbiting, rotating, axially tilted planet is a complex mathematical calculation. To address this complexity the following simplification was applied: –

That all planets intercept solar energy at their orbital distance, as if they are a disk with a cross-sectional area that is equal to the planet’s radius (i.e. π R2). However, due to daily rotation and seasonal tilt, planets emit radiation from all parts of their surface over the course of each year.

Therefore, the total surface area of the planet that emits thermal radiation to space is four times the surface area of its intercepting disk (i.e. 4π R2). It is this geometric fact that is responsible for the “divide by 4” rule that is contained within the calculation of planetary radiative thermal balance.

Having devised a simplified way of calculating the amount of energy that the total surface of an orbiting, rotating, axially tilted planet would receive during the course of its year, we can now move to the next stage of the calculation. Namely, the computation of the annual average surface temperature associated with this energy flux.

This is achieved by using the Stefan-Boltzmann law to determine the absolute temperature in Kelvin (K), associated with the average radiative power flux in Watts per square metre (W/m2) of the planet’s emitting surface.

Equation 1: j* = σT4

Where j*is the black body radiant emittance in Watts per square metre; σ is the Stefan-Boltzmann constant of proportionality, and T is the absolute thermodynamic temperature raised to the power of 4.

The fundamental equation used in astronomy that results from this work is exemplified by the Vacuum Planet radiation balance equation (corrected from the published error pers comm) used by Sagan and Chyba (1997): –

The equilibrium temperature Te of an airless, rapidly rotating planet is: –

Equation 2: 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 radius (in metres), and S the solar constant (in Watts/m2) at the planet’s distance from the sun.”

However, when we apply this logic to calculate the average surface temperature of the planet with a gaseous atmosphere, such as the planet Venus, then the parameters appropriate for Venus at its average orbital distance from the Sun, do not produced the known surface temperature of 464oC (737 Kelvin) (Williams, 2018). Instead the equation produces a value of -46.4oC (226.6 Kelvin), some 510oC too low. (Table 1).

Table 1: Venus Atmosphere Parameters.

Table 1: Venus Atmosphere Parameters.

The discrepancy between the calculated equilibrium temperature and surface planetary temperature requires explanation. The accepted reason is called “The greenhouse effect”, the process by which radiation from a planet’s atmosphere warms the planet’s surface to a temperature above what it would be without its atmosphere.

The specific mechanism for this process involves back-radiation by greenhouse gases. Greenhouse gases are those polyatomic molecular gases, present in the atmosphere, which intercept and then re-emit thermal radiation by molecular vibration and flexure of their covalent bonds. Greenhouse gases consequently increase atmospheric thermal radiant opacity. Back-radiation is the mechanism by which thermal energy is returned by the atmosphere, and the surface temperature of the planet is consequently enhanced. The process of surface heating by back-radiation from greenhouse gases is the currently accepted paradigm in Climate Science.

3. Introducing “Noonworld”: A Hypothetical Captured-Rotation Solar System Planet.

On all rotating terrestrial planets, the solid ground cools by thermal radiation all of the time (both day and night), but the surface only gains radiant heat during the hours of sunlight throughout the day. It is the effect of daily rotation and annual seasonal axial tilt that distributes the energy intercepted from the Sun over the full surface area of the planet. However, because all planets at all times possess both a lit and an unlit hemisphere, then it is instructive to consider how we might model this intrinsic geometric property of illuminated globes. To achieve this, we must remove the complications associated with rapid daily planetary rotation, and the impact that this rotation has on global atmospheric cell circulation patterns by creating a model world that is tidally locked in its orbit around the Sun. By this means the Coriolis Effect (Persson, 2005) on planetary air motion is minimised.

We will call this hypothetical tidally locked solar system planet “Noonworld”, and like the Moon is to the Earth, for Noonworld the same face is always presented towards the Sun, and so the Sun remains perpetually stationary in the timeless skies of Noonworld. Consequently, one hemisphere is permanently heated and the other hemisphere is in cold perpetual darkness. Therefore, on Noonworld all surface energy distribution must be conducted by atmospheric motion, both vertical convection and horizontal advection, rather than by daily planetary rotation.

3.1. Modelling the Climate System of Noonworld.

The Dynamic-Atmosphere Energy-Transport Model (DAET) of Planetary Climate, presented here, is a 2-dimensional forward model that preserves the dual hemisphere component of planetary illumination (Fig. 2). The forward model represents a planetary globe with two environmentally distinct halves. A dayside lit by a continuous incoming stream of solar energy which creates an energy surplus, and a nightside that 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 is the fundamental requirement of this climate model.

In order to study the process of atmospheric energy transmission within the model climate system of Noonworld, a number of simplifications have been made. The primary one is that the planetary atmosphere in the model has total clarity to incoming solar radiation, it also contains no greenhouse gases and therefore has no opacity to outgoing thermal radiation. The model has a free-flowing atmosphere of pure Nitrogen gas that connects the two hemispheres. Consequently, because the model atmosphere is fully transparent to all wavelengths, it can only gain or lose heat from the solid surface at its base.

Because Noonworld has only one hemisphere that is permanently lit, we need to invoke a “Divide by 2” rule that relates the cross-sectional area of the Noonworld disc’s interception of solar irradiance to the surface area of its single illuminated hemisphere. This divide by 2 relationship is valid for any planet with captured-rotation illuminated by a single sun.

Figure 2: Basic Noonworld Globe with Initial Static Model: Showing Energy Vectors and Start-Up Energy Partitions

Figure 2: Basic Noonworld Globe with Initial Static Model: Showing Energy Vectors and Start-Up Energy Partitions

3.2. Starting the Dynamic-Atmosphere Energy-Transport (DAET) Engine from Cold.

On Noonworld the atmospheric process of energy transmission begins on the sunlit side (Fig. 2). Here the solid surface is illuminated and warms as it receives radiant energy from the sun. As it warms it also warms the air above it by conduction. This warmed air then rises by convection, and because it is fully transparent, and also because it is no longer in contact with the ground, it retains all of its energy internally.

The lit ground surface however does not retain all its energy. It cools in two separate ways; it both loses energy to the air above it by surface conduction, and also transmits radiant energy, through the transparent atmosphere, directly out into space. In the forward modelling process, we assign a partition ratio of 50% to conduction and 50% to radiation to study this dual process of energy loss. This assignment is chosen to permit a first assessment to be made of the impact the energy partition process has on the energy budget of the planet.

On the dark side of the planet the ground surface is continuously emitting thermal radiation directly out to space. As this solid surface cools, it also cools the air above it, creating a surface pool of cold dense air. It is a critical feature of this model that as the air cools it retains its mobility, and does not freeze onto the solid surface below. Consequently, the cold dense gaseous lower atmosphere is able to advect back across the planet’s surface to the sunlit side, where it can again be warmed.

As the cold air moves away across the surface of the planet towards the lit hemisphere, more air from above descends onto the dark cold surface, delivering energy to the ground which is also then lost to space by direct thermal radiation. As with the lit surface, we assign an energy partition ratio of 50% to be retained by the advecting air, and 50% to the ground to study this dual process of energy transfer to, and subsequent radiant loss of energy to space from the dark surface.

The process of energy collection on the lit side; energy delivery to the dark side; energy loss by the unlit surface, and then cold dense air return to the source of heat on the lit side, forms a closed loop of energy transport that can then begin to endlessly cycle (Table 2).

Table 2: Starting the Dynamic-Atmosphere Energy-Transport Engine from Cold.

Table 2: Starting the Dynamic-Atmosphere Energy-Transport Engine from Cold.

The cycling of air driven by thermal imbalance is a characteristic feature of a Hadley Cell. Because for the cycle to be maintained it must retain energy internally, the Hadley Cell therefore has the capacity to form an energy transmission system, capturing and delivering energy across the planet.

3.3. Warming up the Dynamic-Atmosphere Energy-Transport (DAET) Engine.

Because the priming stage of the process completed above retains energy within the atmosphere, the next overturning cycle starts with 1 unit of insolation plus ¼ unit of thermal energy left over from the first cycle. Clearly the retention of energy within the atmospheric system by this first cycle overturn means that the radiant energy loss to space does not balance at this point. However, the endless mass movement recycling by the air and the progressive energy retention by the developing Hadley Cell does not grow indefinitely. Our model has two separate geometric series that both tend to different limits, one for the lit and one for the dark surface.

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

Equation 3: 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 4: 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: –

2/3 + 1/3 = 1

and so, the total energy recycling system will now be in radiative balance (Table 3).

Table 3: Building the Dynamic-Atmosphere Energy-Transport Forward Model.

Table 3: Building the Dynamic-Atmosphere Energy-Transport Forward Model.

We can consider that the consequence of this process of infinite recycling is the formation and maintenance of a dynamic machine made of air (Fig. 3).

Figure 3: Basic Globe with a Stable Diabatic Advection Forward Model: Showing Energy Vectors and Unitary Energy Distributions.

Figure 3: Basic Globe with a Stable Diabatic Advection Forward Model: Showing Energy Vectors and Unitary Energy Distributions.

This machine is Noonworld’s single global Hadley Cell, a thermal and mass motion entity formed as the result of diabatic movement of air. The Hadley Cell machine transports air and energy across the planet from a region of energy surplus to a region of energy deficit, and then returns to endlessly repeat the cyclical process of energy transport. (Table 4).

Table 4: Running the Dynamic-Atmosphere Energy-Transport Engine “Warmed Up”.

Table 4: Running the Dynamic-Atmosphere Energy-Transport Engine “Warmed Up”.

3.4. Testing the Computational Algorithm within the Diabatic Model of Noonworld.

Using an Excel spreadsheet, a simple repetitive cyclical computation sum can be created in which the descending series of fractions in the geometric series shown in Equations 3 & 4 can be cascaded to any required degree of precision. The degree of precision in the computational algorithm is controlled by the number of repetitive cycles of addition of the declining fractional elements contained within the geometric series. The cascade algorithm requires 14 cycles of repetitive summation to achieve 8 decimals of precision (Table 5).

Table 5: Testing the Cascade Algorithm of the Diabatic Model of Noonworld

Table 5: Testing the Cascade Algorithm of the Diabatic Model of Noonworld

3.5. How the Presence of an Atmosphere Distributes the Captured Solar Energy Across a Planet.

Having established the required degree of precision, we now need to test how the Noonworld climate model behaves when standard Venus Insolation parameters are applied. The Venusian annual average solar irradiance is 2601.3 W/m2 and the planet’s Bond Albedo is 0.770 (Williams, 2018) which means that the Annual Average Planetary Energy flow that the lit Venusian globe receives is 149.575 W/m2 (Table 1). However, for our hypothetical captured-rotation planet Noonworld, because it only ever receives insolation over one hemisphere, the radiation loading will be double this value (Table 6).

Table 6: Internal Energy Recycling on Venus with Equipartition of Energy for Both Hemispheres.

Table 6: Internal Energy Recycling on Venus with Equipartition of Energy for Both Hemispheres.

It is this energy flux of 299.15 W/m2 (post albedo), that determines the quantity of energy available to drive the Venusian climate system, and this is the insolation energy value that will be used in the Noonworld modelling analysis of Venus, where the “Divide by 2” rule applies.

3.6. Results of Applying the Noonworld Diabatic Model to Venus.

Converting the stable system (Cycle 14) energy values recorded in Table 6 into temperatures in Kelvin by using the S-B equation, shows that the Lit side power intensity flux converts into a day time air temperature of -29.5oC, while the Dark side power intensity flux converts into a night time air temperature of -62.8oC (Table 6). The average of these two temperature values produces a global average air temperature of -48.8oC (Table 6). This temperature is slightly lower than the Vacuum planet temperature for Venus of -46.4oC (Table 1). The discrepancy arises because we have unevenly distributed the energy flux between the two hemispheres, if we sum these two fluxes then the aggregate value is 299.1495 W/m2, which produces a global surface area average of 149.575 W/m2, and the Vacuum Planet relationship is satisfied (Table 1).

The forward modelling study shows that the global atmospheric recycling system of Noonworld, while redistributing energy from the lit to the dark hemisphere (Fig. 3), also stores and retains an additional 100% of the solar influx within the atmosphere to give a global energy budget which is 2 times the intercepted insolation flux (Table 7).

The diabatic recycling system has created a global average air temperature of -48.8oC, however while closely matching the Vacuum Planet relationship (Table 1) the diabatic model has obviously not retained sufficient energy within the atmospheric reservoir to raise the surface Global Air Temperature to the observed Venusian value of 464oC. (Table 7).

Table 7: Stable Energy Values for Noonworld achieved by Global Air recycling using a 50%A:50%S flux partition at the Ground to Air interface.

Table 7: Stable Energy Values for Noonworld achieved by Global Air recycling using a 50%A:50%S flux partition at the Ground to Air interface.

4. Applying Meteorological Principles to the Dynamic-Atmosphere Energy-Transport Climate Model.

Two important facts have now been established about planetary climate on terrestrial globes: –

1. That the presence of a fully transparent mobile-fluid atmosphere can both retain and recycle solar energy within the atmospheric reservoir, and that this recycling achieves a stable energy flow across the planet’s surface.

2. The stable limit of the energy flow within the system is set by the partition ratio of energy between the radiant loss to space of the emitting surface, and the quantity of energy retained and recycled by the air.

We have also established that by using forward modelling techniques to apply an energy partition ratio of 50% surface radiant loss to space, and 50% thermal retention by the air; (hereafter 50S : 50A); the average global air temperature of the Noonworld model of Venus is approximately minus 48.8oC, a value slightly below that achieved by the vacuum planet equation (Equation 2).

Convection is a fluid movement buoyancy process that takes place in the presence of a gravity field. When heated at its base air becomes less dense and more buoyant; because of gravity the warmed air rises away from the source of heat at the surface, to be replaced by cooler air, either arriving from the side (an advection cold front) or from above (convection overturning). The more energy put in to heating the surface the faster the mobile fluid system cycles between hot and cold, in effect the process of convection “steals” energy from the ground. In a dynamic mobile convecting atmosphere a 50S : 50A thermal equilibrium energy partition ratio is only rarely ever achieved; so, the partition of energy on the lit side must always be in favour of the air (conduction loss) and not the ground (radiation loss). Consequently, a lit surface thermal equilibrium ratio of 50S : 50A should not as a general rule be expected or applied.

4.1. Establishing the Energy Partition Ratio for Noonworld by Inverse Modelling using Venusian Climate System Parameters.

Inverse modelling is the process of establishing the value of a given variable within a modelling algorithm, that can be adjusted to achieve a known target result. Put more simply: inverse modelling is used when we already know the answer but are not sure what the question was. The process of inverse modelling was applied to the Noonworld forward climate model. By constructing a cascade algorithm, the initial unknown energy partition ratio of the lit hemisphere of Venus that creates the planet’s average surface temperature of 464oC, can be found.

The value of the unknown surface partition ratio can be determined using the Excel Inverse Modelling Tool called “Goal Seek”, when applied to a suitably designed cascade algorithm with sufficient repetitive length. Initial tests were undertaken to establish the number of iterative cycles that are required to create a stable thermal outcome for a given partition ratio. It was established that the more highly asymmetric the partition ratio, the greater the number of cycles required to achieve stability.

For the example of Venus, where a TOA insolation flux of ~300 W/m2 supports a surface thermal flux of ~17,000 W/m2 (a gain of 56.67), then a partition ratio of 0.8862% radiant loss versus 99.1138% retention by the air is required. The inverse modelling process needed a cascade of 1203 cycles of atmospheric recycling to produce the stable outcome, by which the 737 Kelvin (4640C) target global average surface air temperature of Venus could be achieved (Table 8).

Table 8: Testing the Cascade Algorithm for the Adiabatic Model of Noonworld

Table 8: Testing the Cascade Algorithm for the Adiabatic Model of Noonworld

The total global energy budget for the adiabatic model of Noonworld, using Venusian insolation parameters and a power intensity flux tuned to achieve the Venusian global average temperature of 737 Kelvin (464oC) is 112.840577 units (Fig. 4).

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Figure 4: Inverse Climate Model of Noonworld (Venus Target Temperature): showing Energy Vectors and Final Energy Distributions.

Figure 5 shows the final global energy distribution that is achieved, by applying the NASA values for the Venusian sunlit hemisphere post albedo solar energy interception flux of 299 W/m2 (Williams, 2018) to the final adiabatic convection model of Noonworld

Figure 5: Inverse Climate Model of Venus: showing Energy Vectors and Final Energy Distributions.

Figure 5: Inverse Climate Model of Venus: showing Energy Vectors and Final Energy Distributions.

The total global energy budget is now 33,756 W/m2 (Fig. 5). Table 9 records the thermal effects of this energy partition, and shows that the Venusian global average air temperature has now been achieved.

Table 9: Stable Energy Values for Noonworld achieved by Global Air Recycling using a 0.8662%A: 99.1138%S Flux Partition.

Table 9: Stable Energy Values for Noonworld achieved by Global Air Recycling using a 0.8662%A: 99.1138%S Flux Partition.

4.2. Exploring the Results of the Adiabatic Convection Model that Creates Greenhouse Noonworld.

The results of the inverse modelling process have demonstrated that it is eminently feasible to achieve energy retention, and thermal enhancement within a climate system by repetitive thermal air recycling.

The key insight gained from this analysis is that it is the energy partition in favour of the air, at the surface boundary that achieves this energy boost within a dynamic atmosphere; and that the greenhouse 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, and that the retention of energy by the air is a critical feature of planetary atmospheric thermal cell dynamics.

The DAET Model has its limitations, as does every model. The most critical limitation with the adiabatic model of Noonworld is that the model was populated by a fully radiatively transparent, non-greenhouse gas atmosphere. Consequently, in the model, all radiative loss to space takes place from the ground surface at the base of the atmosphere. If we now apply to the model an opaque atmosphere that can only emit radiation to space from its upper boundary, or Top of Atmosphere (TOA) altitude (as per Robinson & Catling, 2014), in general understanding this would be a greenhouse gas atmosphere. However, we do not need to invoke any back-radiation energy retention process for such an atmosphere. Its radiant opacity merely acts as a delaying mechanism to the transmission of radiant energy, rather than a feed-back amplifier.

By applying a troposphere lapse rate of 6.7 K/Km to the Venusian atmosphere (Justus and Braun, 2007, Table 3.1.2) we can now estimate the thickness of this opaque atmosphere at its TOA altitude. Its topside surface will be emitting energy to space at a point where the lapse rate achieves the same temperature in air, as the model radiant ground surface maintained under the original fully-transparent atmosphere. The thermal separation between the surface air temperature, and the temperature of the radiant emitting surface can be achieved for an opaque atmosphere at an altitude of ~76 Km (Table 10).

This altitude of the thermal emitting surface is above the Venusian Tropopause value of 62.5 km for latitudes 60o to 70o reported by Zasova et al. (2006) based on studies of the Venera-15 and Venera-16 probes. However, the model computes a temperature of ~227 Kelvin (minus ~46oC) for the air at this higher level, which is within the range of estimated values for the lower stratospheric concentrated sulphuric acid cloud tops of Venus reported from Pioneer data by Hammer, (2017, Fig.2).

Table 9: Stable Energy Values for Noonworld achieved by Global Air Recycling using a 0.8662%A: 99.1138%S Flux Partition.

Table 9: Stable Energy Values for Noonworld achieved by Global Air Recycling using a 0.8662%A: 99.1138%S Flux Partition.

5. Conclusions.

1. By applying forward and inverse modelling techniques to the atmospheric dynamics of a hypothetical captured-rotation model planet “Noonworld”, thermal enhancement of the atmosphere can be achieved by a process of power intensity flux recycling within an Atmospheric Reservoir.

2. This study shows that the presence of a thermally radiant opaque atmosphere is not an a priori requirement for the retention of energy within a climate system.

3. By assuming that the surface boundary has an energy partition ratio weighted in favour of the air, the process of atmospheric convective overturn and energy retention by the atmosphere can be explained.

4. By applying a process of inverse modelling, the value of this energy partition ratio for the Venusian planetary environment can be determined.

5. That for Venus it is this >99% energy retention in favour of the air that creates the climatic thermal enhancement observed at the Venusian surface.

6. By applying the same energy partition ratio to both hemispheres of Venus the model replicates the observed isothermal uniformity of surface temperature between night and day

7. The high partition ratio in favour of the air might be a possible cause of the still unexplained high velocity winds in the upper atmosphere of Venus, which have been observed and reported by the European Space Agency (ESA, 2013).

8. By using the appropriate planetary lapse rate for Venus (Justus and Braun 2007, Tab 3.1.2), the inverse modelling process estimates the height of the planet’s Top of Atmosphere radiant emitting surface and locates this within the concentrated sulphuric acid clouds of the lower stratosphere (Hammer, 2017, Fig.4).

9. This relationship between Global Surface Atmospheric Temperature determined by energy flux partition ratio and atmospheric thickness (i.e. surface pressure), for a given albedo dependent radiant energy input, is a totally unexpected result. It implies that the greenhouse effect is a pressure dependent effect (as per James Clark Maxwell) and not a radiant feed-back effect (contra Svante Arrhenius).

10. This modelling study shows that the opacity of an atmosphere fundamentally controls the height of the radiant emission surface that vents energy to space (as per Robinson and Catling, 2014). However, there is no requirement for opacity to be an atmospheric energy amplifier via radiative feed-back contra Kiehl, and Trenberth, (1997).

6. References

ESA, 2013 The fast winds of Venus are getting faster. Astronomy Magazine.

Hammer, M., 2017 Atmosphere of Venus. Abstract Venus Atmosphere Notes, 9pp.

Justus, C.G. and Braun, R.D., 2007. Atmospheric Environments for Entry, Descent, and Landing (EDL) NASA Natural Environments Branch (EV13).

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

Persson, A.O. (2005). The Coriolis Effect: Four centuries of conflict between common sense and mathematics, Part I: A history to 1885. International Commission on the History of Meteorology 2, 24pp.

Robinson, T. D., & Catling, D. C. (2014). Common 0.1 bar tropopause in thick atmospheres set by pressure-dependent infrared transparency. Nature Geoscience, 7(1), 12-15.

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

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

Zasova, L.V., Moroz, V.I., Linkin, V.M., Khatuntsev, I.V. and Maiorov, B.S., 2006. Structure of the Venusian atmosphere from surface up to 100 km. Cosmic Research, 44(4), pp.364-383.

Further Reading: –

Zasova, L.V., Ignatiev, N., Khatuntsev, I. and Linkin, V., 2007. Structure of the Venus atmosphere. Planetary and Space Science, 55(12), pp.1712-1728.

125 thoughts on “Modelling the Climate of Noonworld: A New Look at Venus.

        • Sorry David. This video doesn’t prove that carbon dioxide doesn’t back radiate. The carbon dioxide is probably convecting heat from the filament to the walls of the apparatus and reducing the temperature of the filament. As the narrator explained and ordinary (Argon-filled) light bulb gets too hot to touch because heat is being conducted from the filament to the glass. The vacuum bulb in this demonstration is remains cool to the touch.

          So why doesn’t the filament in the carbon dioxide filled chamber glow as brightly as an argon filled bulb? The real light bulb has a very thin layer of glass with a low heat capacity that heats up very quickly, and the rate of conduction of heat away from the filament decreases as the glass warms. The chamber filled with CO2 has a much larger heat capacity and a much larger surface area over which to lose heat to the room. So the filament in the CO2 filled chamber never gets hot enough in this experiment to glow brightly. If the walls of the chamber ever got too hot to touch, as they do with an argon filled light bulb, then the filament probably would glow brightly.

          Can we learn anything from a third vessel filled with nitrogen or argon instead of carbon dioxide? Not sure. Non-GHG gases presumably would only reduce the brightness of the filament by conduction. The reduction in brightness would presumably be proportional to the pressure of the gas. A pressure dependent reduction in light output appears to be diagnostic of a convective/conductive mechanism. If heating or cooling the outside of the chamber effected the brightness of the filament, that would also be diagnostic of a convective/conductive mechanism.

        • David: One final question about this absurdly bad experiment. If CO2 did not convect or conduct any heat away from the filament, how much brighter would you expect back radiation emitted by CO2 to make the light? How much power does 0.2? atmosphere of CO2 emit at around 15 um? That, of course, depends on the temperature of the CO2. Blackbody intensity at 300 K is 460 W/m2, but CO2 doesn’t emit much at some wavelengths. The online calculator says that 0.2 atmosphere of CO2 would emit about 200 W/m2. How many square meters of tungsten surface are on the filament in the light bulb and capable of absorbing the thermal emission from CO2. According to Wikipedia, a the tungsten filament in a typical 60 W bulb is 0.045 mm in diameter and 580 mm long. That is a surface area of about 2.5 mm^2 or 4 millionths of a m2 for a 40 W bulb. So the filament would absorb about 0.5 mW from 0.2 atmospheres of CO2 at 300 degK. That obviously isn’t enough to change the amount of light emitted by the filament.

          The CO2 next to the filament can obviously be hotter than 300 K, but raising the temperature will make calculations even more challenging. The main emission will shift from the CO2 bending band to the CO2 stretching band. Even if you knew the exact temperature at various distances from the filament, correctly applying the theory of radiation transfer to this situation would be very complicated. You can’t prove that theory incorrect without first calculating how much of a change in temperature and light output the theory would predict!

          http://climatemodels.uchicago.edu/modtran/

          If we are going to maintain a healthy skepticism about the information that IPCC experts put out, then we should all have an even healthier skepticism about the information produced by skeptics who are often amateurs dabbling in fields they don’t understand. If you don’t scrutinize what skeptics say, then your beliefs are just as religious in nature as the alarmists.

      • “There is no back radiation from GREEN HOUSE GASES.”

        Says you.

        “Yes there is.”

        Says me.

    • “Never mastered the concept of significant figures, did ye?”
      No, definitely not my strong suit.
      The iterative calculations in the model approach their respective limits asymptomatically, so the issue being addressed is precision of calculation and not significance of measurement.

    • Are you referring to numbers from the modelling? They are rounded off when compared with reported measurements.

      Strange how its important now but not when fitting a line to oscillating data.

  1. Interesting as many planets orbiting red dwarfs at close range are prb’ly mostly or completely tidally-locked. Could those planets have survivable climates or not? Inquiring minds want to know.

    • Most Red dwarfs are also flare stars. A red dwarf is defined as a mass below 0.5 solar mass (0.50 M☉) and have a surface temperature of less than 4,000 K. Most red dwarfs are in fact below the 0.35 M☉ limit to have a radiant zone, this they are termed “fully convective.” The base of their convective zone is in contact with the super hot core, and no tachocline forms to provide an orderly organization of the magnetic flux that arises from differential rotation rates, both latitudinal differences and a likely faster spinning core than the convective zone, thus red dwarfs form likely form intense but disorganized and chaotic magnetic fields that is the source of the flaring activity.
      So most red dwarf stars are generally very badly behaved (compared to our mild-mannered Sun), throwing off huge flares and stellar mass ejections that likely regularly cook any nearby rocky planet to a blackened crisp. Even if they can maintain an atmosphere, any ozone would get destroyed by an intense flare, leaving the surface to cook under intense EUV.

      • Thanks Joel — I was aware of these things. Looks more & more like Earth is an extreme “Goldilocks” situation regarding complex life.

  2. Modeling? As in modeling temperatures on Venus?

    Let’s start with the formula for:

    “The equilibrium temperature T⊆ of an airless, rapidly rotating planet is:”

    Only Venus is not a rapidly rotating planet.

    Orbit and Rotation
    Venus’ rotation and orbit
    are unusual in several ways. Venus is one of just two planets that rotate from east to west. Only Venus and Uranus have this “backwards” rotation. It completes one rotation in 243 Earth days

    Just how much insolation is a planet expected to emit over 58 Days of night?
    Or to put that in perspective, how much insolation can a planet absorb over 58 days facing the nearby sun?

    Keep in mind that Venus’s orbit is nearly a perfect circle and that Venus’s axial tilt is just 3&deg. Nor do Venus day/night cycles align with their orbital cycle.
    Leaving Venus with minimal seasonal changes.

  3. Phillip, your #10 conclusion: “However, there is no requirement for opacity to be an atmospheric energy amplifier via radiative feed-back contra Kiehl, and Trenberth, (1997).”

    simply follows from your previous assumption:

    “This warmed air then rises by convection, and because it is fully transparent, and also because it is no longer in contact with the ground, it retains all of its energy internally.”

    which means in your world an N2 atm. doesn’t radiate & in K&T 1997 the atm. does naturally radiate. If you add back that N2 does radiate (feebly) you will find the well-known text book meteorology. Given that the rest of your study rests on this assumption, your study doesn’t improve on your Robinson & Catling cite. Use that cite to understand surface mean temperature due the atm. physics of atm. opacity (optical depth) from surface pressure and mixing ratios of various gaseous atm. absorbers. See also:

    The natural greenhouse effect of atmospheric oxygen (O2) and nitrogen (N2), M. Hopfner et. al., 2012, GEOPHYSICAL RESEARCH LETTERS, VOL. 39, L10706, doi:10.1029/2012GL051409

    • The assumption of a constant TOA is what’s been undercut by the Phillip’s Noonworld model. On Noonworld Trick would still have his whipping boy(s). It would just be N2 and O2 rather than CO2 based on assumptions of TOA.

      It’s going to be a joy to watch your continued rationalization Trick.

  4. Venus has a very long day, about 117 Earth days. That’s almost stationary.

    Venus has very high wind speeds. link The trouble is that wind speed is measured with relation to the planet’s surface.

    The Earth, on the other hand, has relatively low wind speeds. The Earth also moves air from the sunny side to the dark side much faster than is the case on Venus. How can that be? At the equator, the Earth’s surface speed is about 1000 MPH, and that’s about how fast air moves from the sunny side to the dark side. If you look at a planet as a heat exchanger, the Earth is going to be a lot more efficient than Venus.

  5. “The accepted reason is called “The greenhouse effect”, the process by which radiation from a planet’s atmosphere warms the planet’s surface to a temperature above what it would be without its atmosphere.

    The specific mechanism for this process involves back-radiation by greenhouse gases. ”

    This is a common misunderstanding.

    back radiation is an effect not a cause.

    The cause of the “warming” is that the added GHGs raise the effective radiating level of the planet
    ‘leading to a reduced cooling effect– otherwise known as warming.

    • The cause of the “warming” is that the added GHGs raise the effective radiating level of the planet, ‘leading to a reduced cooling effect– otherwise known as warming.

      Seems to me that added GHGs increase the surface area doing the radiating at all levels. More radiation over a larger surface area, thus, seems like cooling. “Effective radiating level” seems like a not-so-good concept, because it seems to force a boundary layer conceptually, when no such boundary layer exists actually. It seems to create this fake boundary layer, so that we can talk about what is underneath it, when really there is no layer where anything underneath exists, so that we can misapply the SB Law in some sophistic, mathemagical, retro-engineering-of-heating effect.

      • So, Robert, how much larger is the surface area of the planet 10 km above the surface compare to the area of the surface itself.

        There is no boundary layer. The effective radiating level of the planet is the altitude from which the AVERAGE photon escaping to space is emitted. Roughly speaking, that is 5 km above the surface where it is 6.5 K/km * 5 km = 33 K cooler than the surface. That makes it 255 K; the blackbody equivalent temperature for our planet. The surface is therefore 33 + 255 K.

        If we add enough GHGs to raise the effective radiating level to 6 km, the surface will be about 39.5 + 255 K. 6.5 K higher than today.

        • Since I am not buying into the boundary-layer, effective emission height idea, the question seems irrelevant. If CO2 is mixed into an atmosphere that is physically in contact with the surface constantly, the increase of CO2 happens in a volume at all heights, not in a higher surface area of a larger sphere.

          Yes, there is no boundary layer, and yet we speak of the height of this imaginary sphere, where some average escaping goes on. I don’t think the emission height increases. I think that it stays the same, and the mass of the atmosphere redistributes around it, if we must speak in these terms.

          How much larger is the effect of a couple more CO2 molecules per thousands of other molecules that intercept the energy of the CO2 vibrational modes and allow these CO2 molecules to “calm down”, via the negligible transfer of collisional energy that some people might call “heat”? How much significant heat could this possibly be? — I’m not seeing much of any.

          • Robert: Sorry that the concept of an effective radiation level is too complicated for you to understand. The rest of us understand that most of the photons (or EM waves, if you prefer) that escape to space are emitted mostly by GHGs above the surface of the Earth. Those photons carry 240 W/m2 of energy to space. We are capable of recognizing that an average altitude or “emission level” exists for the source of those photons. If the number of GHGs capable of absorbing those photons rises, the average photon escaping to space must be emitted from higher to still carry 240 W/m2 to space. Higher means colder, so there must be warming higher to still emit 240 W/m2.

            Robert writes: “I think that [the effective emission level] stays the same, and the mass of the atmosphere redistributes around it, if we must speak in these terms.”

            What does this handwaving mean? The mass of the atmosphere is distributed vertically according to the principle of hydrostatic equilibrium: The pressure on a volume of gas in the atmosphere is equal to the force of gravity acting on the mass of gas above that volume. Mathematically: dP = -density*g*dh. As Robert correctly noted, the density of the atmosphere is not changed significantly by a couple of more CO2 molecules per thousand”.

            What is changed by these CO2 molecules is the rate of radiative cooling to space. The change is relatively small, about 3.5 W/m2 for a doubling of CO2, only 1.5% of the 240 W/m2 that reaches space. The change in temperature at equilibrium that would result (if there were not feedbacks) is 4 times smaller, 0.37%. 0.37% of 288 K is only about 1 degK.

            W = eoT^4
            dW/dT = 4eoT^3 = 4*(W/T)
            dW/W = 4*(dT/T)

          • Mosher says: “The cause of the “warming” is that the added GHGs raise the effective radiating level of the planet leading to a reduced cooling effect– otherwise known as warming.”

            Robert says: “Seems to me that added GHGs increase the surface area doing the radiating at all levels. More radiation over a larger surface area, thus, seems like cooling.”

            Frank questions: “So, Robert, how much larger is the surface area of the planet 10 km above the surface compare to the area of the surface itself?”

            Robert replies: “Since I am not buying into the boundary-layer, effective emission height idea, the question seems irrelevant.”

            So first we are told that the problem with a higher effective radiating level is that it provides a large effective radiating surface area. When asked how much larger, Robert says that is irrelevant. He doesn’t “buy” the common sense idea that the average photon escaping to space must be emitted from a higher altitude when there are more GHGs on the path to space. He doesn’t “buy” the idea, because he doesn’t want to face the consequences.

            Robert also writes: “How much larger is the effect of a couple more CO2 molecules per thousands of other molecules that intercept the energy of the CO2 vibrational modes and allow these CO2 molecules to “calm down”, via the negligible transfer of collisional energy that some people might call “heat”? How much significant heat could this possibly be? — I’m not seeing much of any.”

            If only some people call absorbed radiative energy “heat”, what do the others call it? What do you call it, Robert? Is absorbed solar radiation heat? Is absorbed LWR any different when expressed in W/m2? FWIW, calculation in my other response show that the amount of heat is enough to raise temperature by 1 degC (without feedbacks). That amount is significant, but far from catastrophic. The science demonstrating that rising GHGs will cause some warming is valid, but Robert “isn’t seeing much of anything”.

        • Again Steven, you fail to account for the water world on which we live. Negative feedback from enhanced evaporation, thus enhanced TPW can produce enough clouds to increase albedo and also increase convective transport of surface heat to well above your ERL. These are emergent properties that stabilize the climate ssystem.

          Your simple explanation of GHG and a climate system (as you describe it) is dynamically unstable and subject to runaway hothouse. Since that hasn’t happened even during periods of 10X current CO2, the obvious conclusion is unavoidable, that is, strong negative feedback exists to prevent this. And that system is a vast salt water surface with effectively near input infinite depth to absorb and disperse heat energy to near freezing temperatures (at least on the time scale of interglacial periods). And unlike a compressible transparent fluid (air), adiabatic processes and radiative processes are irrelevant with upwelling or downwelling.

          • Joel: Your apparently sensible idea, probably doesn’t work in practice. The following lengthy explanation might show you why. The planet’s radiative imbalance (R) is given by incoming SWR minus outgoing LWR:

            R = (S/4)*(1-a) – eoTs^4

            where S in the average intensity of solar radiation, a is albedo, Ts is surface emissivity, o is the Stefan-Boltzmann constant and e is the planet’s effective emissivity (0.615) for temperature Ts = 288 K . Now let’s take the derivative of this imbalance with respect to changes in surface temperature.

            dR/dTs = -(S/4)*(da/dTs) – 4eoT^3 – (oT^4)*(de/dTs)
            -4eoT^3 = -3.3 W/m2/K at and near Ts = 288 K = Planck feedback

            Since emission by the atmosphere and clouds varies with humidity and lapse rate, we can’t assume de/dTs is zero. You might recognize these three terms as the sum of all SWR feedbacks (including cloud fraction), Planck feedback, and the sum of all LWR feedbacks except Planck feedback. You are focusing our attention on how albedo changes with Ts, a perfectly sensible thing to do.

            When a positive forcing, say about 3.6 W/m2/K from doubling CO2, has been negated by increased radiative cooling to space caused by a warming of W degK and a new steady state with no imbalance has been reached:

            F + W*(dR/dTs) = 0
            W = -F/(dR/dTs)

            When there are no feedbacks besides Planck feedback, dR/dTs = -3.3 W/m2/K and W is slightly more than 1 K. According to the IPCC, the combined water vapor plus lapse rate feedback is about +1 W/m2/K.

            So, no matter how fast cloud cover grows with warming (and how negative da/dTs may be), this mathematics says there will always be some some warming at equilibrium. W can not be zero unless F is.

            The planet reflects about 100 W/m2 of incoming SWR back to space: about 80 W/m2 by clouds plus 20 W/m2 by surface albedo and Rayleigh scattering (which makes the sky appear blue). Some sources say clouds reflect only 60 W/m2 and there is a lot of Rayleigh scattering above clouds. So, a 1% increase in cloud fraction per degK of surface warming (1%/K) translates into a change of -0.8 to -0.60 W/m2/K. (A 1% increase in cloud fraction changes albedo from 0.300 to 0.303.) To change the sum of Planck feedback and other LWR feedbacks appreciably, you need a large change in cloud fraction. 5%/K would be -3 to -4 W/m2/K, which would be enough to cut warming from about 1 K to 0.5 K. However, during the LGM, it was about 6 K colder. 5%/K would mean 30% less cloud cover during the LGM. Changes this large or larger seem unlikely. Now you can postulate non-linear changes in cloud cover with large changes per degK in the warmer direction and much smaller changes in the cooler direction. A Goldilock’s non-linear feedback. Otherwise, changes in cloud fraction with warming probably aren’t likely to have a big impact on the warming produced by 2XCO2. A 1 W/m2/K feedback in either direction seems fairly large to me, taking us from an ECS of 1.8 W/doubling (-2 W/m2/K) to 3.6 K/doubling (-1 W/m2/K). From there, another +1 W/m2/K produces a runaway GHE.

    • In a simplified model that makes sense. When accounting for conduction and convection, as Phillip has done, the “reduced cooling effect” or warming doesn’t make much sense.

    • steven mosher writes “This is a common misunderstanding.”

      Fortunately one need not take your word or my word for it. Take a remote reading infrared thermometer at night outdoors and point it at the sky. When the sky is clear, my thermometer goes to its lowest measurable reading, about -40 C. The underside of a cloud, however, reads about 0 C (depending on the season). Since it is responding to long wave infrared, clearly the cloud is providing “back radiation” and a clear sky is not, at least in the wavelength sensed by the thermometer.

      Near the Earth’s surface the air pressure is such that while CO2 is capable of providing back radiation, apparently it seldom gets a chance to actually do that before it transfers energy to some other molecule by collision and mechanical transfer. The effect is that energy radiated from the surface doesn’t get very far, is absorbed by CO2, transferred mechanically to air, heats the air which then rises convectively and a whole lot slower than the speed of light.

      • “The effect is that energy radiated from the surface doesn’t get very far, is absorbed by CO2, transferred mechanically to air, heats the air “
        So far, so good, in specific wave bands. But the pathway is reversible. The air transfers heat back to the CO2, and maintains the temperature of the CO2 so it can continue to radiate. The CO2 is not a net source of energy to the air, or not much. It radiates about as fast as it absorbs. What the air does is to ensure that the emission isn’t linked to a prior absorption by that same CO2 molecule.

        • “It radiates about as fast as it absorbs”
          Nick,
          From my reading of the following, I am not sure that Professor Harper agrees with your view concerning the equivalence of absorption and emission rates.

          http://www.sealevel.info/Happer_UNC_2014-09-08/Another_question.html

          “In other words, the very widely repeated description of GHG molecules absorbing infrared photons and then re-emitting them in random directions is only correct for about one absorbed photon in a billion. True? [YES, IT IS THIS EXTREME SLOWNESS OF RADIATIVE DECAY RATES THAT ALLOWS THE CO2 MOLECULES IN THE ATMOSPHERE TO HAVE VERY NEARLY THE SAME VIBRATION-ROTATION TEMPERATURE OF THE LOCAL AIR MOLECULES.]”

        • There is easy way to directly measure energy radiated to space by CO2. Whole global warming based on CO2 is based on 4.3um IR window, where CO2 is not colliding/masked with other gases in atmosphere.
          Simply get picture of Earth from satellite on 4.3um and check opacity. If surface features are visible, there is not enough of CO2 to block radiation on this spectrum band. And additional CO2 can make it opaque and retain additional energy.
          If surface is opaque on this wavelength, atmosphere is already keeping energy reradiated by CO2.
          Measuring directly energy on this wavelength can tell us exact Earth energy budget caused by CO2.
          We should exactly see difference in amount of radiation on 4.3um based on annual increase/decrease of CO2 content in atmosphere.
          I tried to find some IR pictures of Earth on 4.3um, but apparently there isn’t. For what I’m very surprised, as presented importance of global warming agenda.
          Closest I found are GOES-13, GOES-15 and Venus Express. But none matched 4.3um band exactly.

    • Mosh wrote: “The cause of the “warming” is that the added GHGs raise the effective radiating level of the planet”

      But he needs to say a little more: “The cause of the “warming” is that the added GHGs raise the effective radiating level of the planet” WHERE IT IS COOLER THAN THE SURFACE. This allows the surface to be warmer than the blackbody equivalent temperature for the planet.

    • The problem being that an emergent behavior likely arises from a complex interaction on a water planet like Earth. With a copious reservoir of surface water to move (adjust) back and forth via phase changes to atmosphere as its own condensing-GHG (water vapor), the feedback from the emergent behavior may cancel the bulk of ERL rise from non-condensing GHG’s alone.
      The inability of satellite and balloon observations to find the water-vapor relevant tropical hotspot fingerprint of non-condensing GHG’s, as predicted by the CMIP3 and CMIP5 models, is certainly a factor that the modelling community refuses to acknowledge. Asuch they simply continue to tune the critical water-dependent responses in their model outputs that control sensitivity hoping that no one notices (or objects to when noticed) their subjective thumbprint on the output.
      Climate modelling via AOGCMs simply has become an clear example of Feynman’s Cargo Cult Science.

      • Joel O’Bryan points out a major problem with climate models that assume a positive feedback for “constant relative humidity”. The modelers assume that if CO2 absorbs IR radiation from the surface and causes air temperature to rise, that relative humidity will remain constant, meaning that warmer air can hold more water vapor, and this water vapor will absorb additional IR radiation.

        The problem overlooked by the modelers is that the increased water vapor requires water to be evaporated from a body of liquid water (ocean or lake) into the atmosphere, which requires heat to be transferred from the atmosphere to the body of water. The amount of heat to be supplied to maintain constant relative humidity depends on the assumed “original” temperature and humidity of the system (which depends on latitude and season), but for typical ocean temperatures between 10 and 30 C, and relative humidities over oceans ranging from 70 to 100%, the energy loss required to maintain constant relative humidity ranges from 50 to 80% of the original energy absorbed by the CO2 to warm the air. This represents a negative feedback ratio of -0.5 to -0.8 in the CO2 warming effect over the oceans, with the feedback becoming more negative over warm tropical oceans than over cooler temperate oceans in autumn and winter.

        Also, the “constant relative humidity” assumption is not valid over land–on a clear day, if it has not rained recently, where does the additional water vapor come from, if there are no bodies of water (even puddles) in contact with the air?

        Climate models that assume “constant relative humidity” and assume the additional water vapor absorbs more IR radiation over-estimate warming due to (1) ignoring the heat loss required to evaporate water over oceans and (2) over-estimating the water-vapor effect over land, where constant absolute humidity should be maintained.

  6. The point is that one can model the surface temperature enhancement caused by convective overturning for a zero GHG world and then apply it to a world with lots of GHGs such as Venus and it still works.

    Philip is demonstrating mathematically the truth of a summary that I posted in another thread on this site some time ago:

    “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.”

    • Yep. Thanks Stephen. I am eagerly awaiting a response from the radiation crowd to Phillips lucid explanation for how and why Conduction and Convection are so important to planetary temperature.

  7. The details are beyond me, so I humbly ask for Conclusion 9 in plain English. It says: “the greenhouse effect is a pressure dependent effect …and not a radiant feed-back effect”.
    Does this mean that the effect is independent of the gas-composition of the atmosphere? That seems to imply that the very phrase “greenhouse gas” might be wrong-headed, in that any old gas or gases will do the trick.
    Now that really would be “totally unexpected”.

    • Hi. Just as predicted recently with rocky worlds with atmospheres within the solar system. The heretics! Atmospheric composition is irrelevant. Whoops! That’s the warmists cooked.

    • It’s been well known for decades that any atmosphere will delay heat escaping , whether it absorbs heat by radiative effects or just by increased bulk movement. My father explained this back in the late 1980s. It was considered a trivial understanding back then. And he didn’t do the quantifying calculations – just the theory.

      In fact, if you think about it, the transmission of heat by convection is far more efficient than by radiative effects. And a transparent atmosphere of N2 can move just like an absorbing atmosphere of CO2. That’s why we have winds on this planet.

      This doesn’t mean that the extra radiative effects from a changed atmospheric composition don’t exist. But don’t be surprised if they turn out to be negligible (low climate sensitivity).

      • Changing composition will result in a changed pattern of circulation as convection changes to neutralise the potential thermal effect.
        The surface temperature will remain as before.
        I agree that the basic principle of atmospheric mass being the correct determinant of surface temperature was accepted in the mid 20th century but no one ever felt the need to describe the mechanism in detail.
        With the advent of the incorrect radiative theory it became necessary to explain it in order to show the radiative theory to be false.
        Philip is doing a good job here and in his earlier posts.

    • No, see conclusion 8. There is an effect from greenhouse gasses. They control the emitting height of the atmosphere. On Venus, that is the sulfuric acid cloud layer. On a planet with a transparent atmosphere, that would be the surface. The temperature difference between the emitting layer and the surface is set by the lapse rate, which is closely related to the mass of the atmosphere. (And not by back radiation from CO2 or anything else, with a convective atmosphere that makes no difference.)

      • “There is an effect from greenhouse gasses. They control the emitting height of the atmosphere. On Venus, that is the sulfuric acid cloud layer.”
        Pochas94,
        I have a slightly different take on this. I am leaning more and more to the view that it is the properties of the condensing volatile within a planet’s atmosphere that is important for radiant thermal emission to space. We know that solid crystals are far more efficient emitters of thermal radiation than liquids or gases for the very good reason that solids are effective flexural (shear wave) vibrators. So, on Earth the condensing volatile is water. In our atmosphere the minimum possible temperature for super cooled water is minus 45C. Have a look again at my essay on Calibrating the CERES image.

        Looking at Venus, the link in my essay to concentrated sulphuric acid shows the freezing point curve for this compound. There are three cusp point in this 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 condensing atmospheric volatiles and albedo. Curious eh?

    • On a quick skim of this technical article, that’s how I read it too.

      So if the math holds up, this is seemingly a reasonable “alternative” to the whole idea of greenhouse gases as effective controllers of planetary temperatures!

      Of course, no matter what the details of how atmospheres make planets warmer, there will likely be people referring to any warming mechanisms as “greenhouse effect” forever? Or, might the phrase “greenhouse effect” go out of favor, like “phlogistion” in chemistry?

      • The convective model presented by Philip is still a greenhouse effect because it is caused by descending columns of air suppressing convection just as does a greenhouse roof and creating greater transparency by dissipating clouds so as to let more radiation in just like a greenhouse roof.

  8. Waste of time

    Low spin rate

    No oceans can form

    NO mechanism to remove co2 from atmosphere

    End of story

    • “Low spin rate
      No oceans can form”

      terry,
      Titan, (the subject of my next essay) is a slow rotator. Its atmospheric structure is similar to that of Venus.
      Titan has two hemisphere encompassing Hadley cells (as does Venus).
      Titan is a veiled world (as is Venus).
      Titan has a super-rotational wind (as does Venus).
      Titan has a uniform day and night time surface temperatures (as does Venus).
      Titan has liquid volatiles (methane) on its surface.
      So slow rotation is not a bar to surface liquids.

      Using my model, I estimate the age at which Venus changed from a water world to a CO2 world as being 1.775 Billion years after the planet’s formation (2.825 bya).
      Remember that Venus has 3.5% of Nitrogen in its 93-bar atmosphere. Using Dalton’s Law of Partial Pressures 3.5% of 93 bar is 3.26 bar. This means that Venus now has just over four times the mass of Nitrogen in its atmosphere compared with the modern Earth. So, a billion years after its formation ancient Venus could easily have had surface water oceans under a dense nitrogen atmosphere.

  9. Try and get it through your heads, the surface of the ocean is covered by a force referred to as surface tension. Because of the existence of surface tension physical heat can not penetrate the surface of water , Anthropogenic Global Warming is a myth.

  10. An interesting experiment is here!
    https://www.youtube.com/watch?v=FgjT_665T6U

    The idea of atmospheric heating is obviously flawed, as the loss by convection currents in CO2 is very large. There are probably no “greenhouse” gases at all, the water vapour being simply a transport mechanism for heat and clouds reflectors.

  11. I don’t think I could PROVE it mathematically, but I believe that your Conclusion No. 2 “This study shows that the presence of a thermally radiant opaque atmosphere is not an a priori requirement for the retention of energy within a climate system.” speaks directly to and in support of the control theory arguments that have been made by Christopher Monckton of Brenchley.

  12. On the other hand, the high surface temperature of Venus may just be because it is hot.

  13. Point 9 – isn’t that Zeller and Nikolov’s discovery? Why no reference?

    New Insights on the Physical Nature of the Atmospheric Greenhouse Effect Deduced from an Empirical Planetary Temperature Model

    So we have confirmation apparently.

  14. Impressive Philip and a very satisfyingly readable prentation. I’m not sure I have it all straightened out yet and will need to read the second half over again.

    I thought you were heading in a different direction. Aha, he’s going to take all this convected and advected heatflow and run it logarithmically through the accumulated CO2 doublings and arrive at Venus’s surface temperature. To be clear, do I understand you to be saying, then, that any gas, would do the same thing without the need for absorption and re-emission of LWIR?

    I’m a sceptic of the consensus CO2 control knob idea and think the Le Chatelier Principle acts to resist change (in temperature, or acidity, or…), say by creating clouds or buffering acidification of seawater… Surely, we know that CO2 and a few other gases do indeed absorb and re-emit, slowing down the exit of heat from the planet the question being the magnitude of any residual effect. Do you rule out any effect?

    • “To be clear, do I understand you to be saying, then, that any gas, would do the same thing without the need for absorption and re-emission of LWIR?”
      Gary,
      I created this model in January this year and have been exploring the implications of it since then. In my next post on Titan, I find a similar effect to that modelled for Venus.
      Titan has a nitrogen rich atmosphere (98.4%), a surface pressure of 1.45 bar and a greenhouse effect of 10.2 Kelvin. My nitrogen model is fully valid for Titan and the adiabatic calculation achieves a surface temperature of 94 Kelvin with a much lower partition ratio.
      From this I deduce that the model is indeed valid for any gas and that the greenhouse effect is a pressure dependent phenomenon.

      • “Do you rule out any effect?”
        Gary,
        For me the moment of comprehension arrived when I realised that for a fully transparent adiabatic model atmosphere, the temperature difference between the radiant emitting surface and the temperature of the overlying convecting gas is also a measure of the thermal difference between the surface of-a planet and the TOA for a fully opaque atmosphere. This temperature difference translates directly into TOA elevation when calculated using the appropriate planetary lapse rate.
        From that point on, its game over for the radiative feedback concept.

        • Yes.
          A fully transparent atmosphere radiates from the surface and a fully opaque atmosphere radiates from the top of the atmosphere.
          The reason is the difference between a solid and a gas because full opacity essentially means that the atmosphere is behaving as would a solid with the same temperature from top to bottom and thus no convection.
          As soon as opacity becomes less than 100% you get a lapse rate plus convection and full transparency drops the radiating point to the surface with maximum possible lapse rate and maximum possible convection.
          It is all about the specific properties of gases as per the gas laws.
          Pressure dependence arises because the higher the pressure the closer together are the gas molecules and the more effective is conduction.
          The lapse rate then marks the fall in efficiency of conduction as one moves upwards along the line of decreasing density with height.
          As conduction declines the radiation takes a greater role in the transmission of energy.
          As I have previously explained in other threads the lapse rate simply marks the changing ratio between conduction and radiation as one moves up through the mass of an atmosphere.
          Philip has converted those concepts into a mathematically sound model which works for all planets by varying the way surface kinetic energy is split between transfer to space by radiation and transfer to the atmosphere by conduction and has applied my suggestion that the thermal effect is equal and opposite between rising and falling air masses.
          If there is no lapse rate there is no convection and no thermal enhancement above S-B because then one is dealing with a solid and the top of atmosphere acts as if it were a solid.
          Any level of transparency introduces a lapse rate followed by convection followed by a thermal enhancement.
          The thermal enhancement is an inevitable result of the presence of convection only.
          No radiative gases required.

    • “Impressive Philip and a very satisfyingly readable prentation.”

      I agree. A very understandable presentation.

      I look forward to your study of Titan.

      Of course you know you are upsetting some applecarts with this presentation, Phillip. 🙂

  15. It is very misleading to talk of a non GHG atmosphere and let the albedo be the same as with atmosphere.
    No atmosphere means no clouds, and clouds are a big player in albedo. The surface of the Earth would be around 5C with no atmosphere and not the -18 with cloud albedo.
    The GHG’s have in total only warmed the surface of Earth 10 degrees C relative to no GHG.
    It is interesting that this noonworld somehow come to what we know, but i am not able to follow it in detail.

    By the way. Is there any explantions of why Venus has such a dense atmosphere. The other rockplanets are very different.

    • Geologic and biological processes have pulled most of the CO2 out of the earth’s atmosphere. Venus doesn’t sequester CO2 into oil/coal/limestone/etc.

    • “It is very misleading to talk of a non GHG atmosphere and let the albedo be the same as with atmosphere.”

      Svend,
      I thought long about albedo, I cut the following paragraph from my essay that addressed this point: –

      “It is important to understanding the process of energy retention and thermal enhancement by the climate system, that the planetary Bond albedo, though critical in establishing the average annual energy influx received by the climate system, acts primarily as an external filter. The model presented here is studying the process of internal energy retention, that is independent of the rate of energy supply. The climate system is inherently leaky, it is by slowing down the leaks, by Internal energy recycling within the atmosphere, that the system is able to retain energy. In studying the process of energy retention, the supply of energy as determined by the albedo, is a given.”

      The really fun thing with this adiabatic model of Noonworld is that you can set the albedo to any value you like. The surface albedo can range from jet black zero to brilliant ice white one. Varying the albedo is one way of studying long term climate change under different irradiance values, such as what happens when an ancient Venus with a low-pressure water and nitrogen atmosphere that has a water ice cloud albedo of 0.306 changes to a high-pressure carbon dioxide and nitrogen atmosphere that has bright sulphuric acid clouds with an albedo 0.77.

  16. This is a useful, albeit largely verbal, explanation of how the “greenhouse effect” really works. Energy absorption and back-radiation by the almost-totally-CO2 atmosphere simply is not the reason the surface temperature of Venus is so high.

    There are statements in this post, however, that are distinctly aphysical, such as: “thermal enhancement of the atmosphere can be achieved by a process of power intensity flux recycling. While energy, indeed, can be transported and recycled, power fluxes cannot; they necessarily involve the unstoppable, unstorable factor of time. It behooves the author to clean up such phrasing in order to avoid the impression of basic physical ineptitude, akin to Mosher’s self-contradictory attribution:

    The cause of the “warming” is that the added GHGs raise the effective radiating level of the planet ‘leading to a reduced cooling effect– otherwise known as warming.

  17. Philip Mulholland,
    An excellent treatise on fundamental climate physics, mathematics, and climate modeling!
    Thank You!

    Best of all, no pseudo-science dissembling such as “The cause of the “warming” is that the added GHGs raise the effective radiating level of the planet ‘leading to a reduced cooling effect– otherwise known as warming.” was needed. Very well done!

    • J Mac,

      Mosher is 100% correct. Trenberth cartoon is a farce. 2nd Law is very important. The Earth, surface and atmosphere, is heated by the Sun. The Earth is not a disc, it is a sphere.

      CO2 absorbs and thermalizes 15-micron radiation from the surface. This effect is already saturated at around 10 meters from the surface.

      The entire Atmosphere radiates to Space. CO2 at the TOA absorbs and re-radiates 15 micron IR. The more CO2 the atmosphere contains, the higher the altitude at which the atmosphere is no longer opaque to 15-micron IR, thus raising the altitude at which the Atmosphere freely radiates to space, thus lowering the temperature at which the Atmosphere freely radiates to Space, thus increasing Energy content of the Atmosphere, thus raising temp of the Atmosphere.

      NO ONE can calculate the magnitude of this effect.

      • The more CO2 the atmosphere contains, the higher the altitude at which the atmosphere is no longer opaque to 15-micron IR…

        There’s minimal 15-micron radiation outgoing at TOA. Focusing exclusively on that narrow band ignores the manifold factors that truly govern OLWR. Such totally misleading emphasis is emblematic of alarmist “climate science.”

        • That is not the case. 15-micron radiation is generated by the atmosphere at around -80 C. There is lots of it up there where the air is cold. Why would you say that?

        • I say that because the contribution of CO2 to total planetary emissions at any temperature is minor, even in the 15 micron band which overlaps with water vapor . See a tropical example: dhttps://climateaudit.files.wordpress.com/2008/01/daly_spectra.gif

  18. I’ll give my thoughts: There are a few assumptions that people make. That Venus is/was earth like. It’s atmosphere is completely different. It is 93x as dense, moves on the surface very very slowly, the planet rotates very very slowly, a Venus day is 243 Earth days. The surface of the planet is mostly volcanic that seems to have huge outflows that resurface parts of it, but judging from the craters seems to have had a major resurfacing or perhaps the original cooling crust event about 300-600 million years ago. Sure the top of the atmosphere has some wind speeds that are decent but overall it’s a slow atmosphere exchange as the difference in temperatures from the opposite ends aren’t all that different, within a few degrees – much lower than the Earth. The atmosphere also has major amounts of sulphuric acid which make the planet white in colour and bright in the night sky and reflects 90% of the visible light and much of the energy from the sun. My take on Venus is that it never cooled, the planets atmosphere was dense enough that it never allows enough energy to leave as it bounces around before leaving that it never really cooled, my take is that Venus has never had water (lack of erosion) nor a low pressure atmosphere. Earth and most of the rocky planets lose most of the energy at night and have a high diurnal temperature difference as heat gets expressed to space. When the blanket of the atmosphere of the high atmosphere planet don’t allow much heat to escape over time they are very warm. Neptune the farthest planet in our solar system has a surface at rock temperature of likely many thousands of degrees, it expresses estimated at 2.6x the amount of energy it receives from the sun. Perhaps the Earth rotated fast enough and lost enough energy with forming of the moon that allowed the cooling and began the process of changes to the atmosphere that has allowed the earth to have what we enjoy today. I think the Earth is an odd middle ground between rocky planets that quickly express all their heat and more gassy planets that maintain their heat.

  19. I got an average thermal reading of 541K for a rotating body in Venus’ solar orbit.

    Either I did math wrong or author did math wrong and I simply used inverse-square and NASA’s 45.2F at Earth Solar Orbit.

  20. Well, the math looks OK in the first section, but I don’t think you’ve shown anything. Your diabatic model can’t reproduce the Venus surface temperature, which suggests straight off the bat that it is incorrect. You then arbitrarily adjust your partition coefficient until you get the right answer. Calculation of the partition coefficient requires the atmospheric window which in the case of Venus we can take as zero. Then the partition coefficient is 0.00925, and the atmospheric bulk emissivity is 1. You get this answer from forward modelling, which is way more credible than reverse modelling!
    Cheers!

  21. This would appear to be nonsense. The inverse method that the author uses results in an impossible
    scenario. He has the ground of the lit side of Venus being at a temperature of -46.1 degrees C while the
    air above it is at 464.8 degrees but still 99.2 % of the energy loss from the surface goes to the air while
    only 0.8% is radiated to space. Or at least that is what Table 9 appears to say. Philip needs to say how he
    intends to get around the second law of thermodynamics before posting such rubbish.

    • Izaak Walton, I think you just misread the article. Under the author 3.6 heading for instance, I quote:

      “global average air temperature of -48.8oC (Table 6). This temperature is slightly lower than the Vacuum planet temperature for Venus of -46.4oC (Table 1). The discrepancy arises because we have unevenly distributed the energy flux between the two hemispheres. ..” (etc.)

      — so the -46.1 degree number is not the ground temperature in this model, it is an average emission temperature, with the relevant emission layer being generally somewhere high up near the top of Venus’ clouds —

      I note that the previous commentator ‘Neogene’ has the critique that the author has to adjust what he calls an energy partition coefficient get the observed surface temperature of Venus. Right now, I myself can’t judge whether this is a good mathematical technique or good modelling technique for planets as such. Maybe if I read enough, I’ll eventually get a better understanding of what is meant here. What I notice is that *all* theoretical model makers seem to generally have to just “assume” a very large part of what the model is trying to deal with in the first place!

      So, for the author to have to assume a good part of what his model is “predicting” isn’t necessarily a strike against it. The interesting thing is to ask whether any *new* predictions from this model can be confirmed, or even, does this model help to explain why the conventional “greenhouse” models *fail* in some of their predictions?

      • Just to add a bit to my comment, I have to say that I think that the article writer, Philip Mulholland, may be creating a bit of confusion by being too idealized in his treatment of what he refers to as his “Noonworld” scenario, where an assumed atmosphere of pure nitrogen is also assumed to have *no* ability to radiate infrared? In such a case, we are therefore to develop some sort of realistic Hadley cell based stability for the atmosphere, based on the planet as such radiating all of it’s outgoing heat flux from the *surface*, none from the *atmosphere*? The writer then moves very quickly to describe the Venus situation where lots of the outgoing IR flux is going out from tropospheric layers, and *not* directly from the surface!

        As to the idealized situation of an atmosphere with *no* greenhouse property (i.e., no emissive/absorptive property) I think we are a long way from proving that such an atmosphere would even be stable! I mean, name one planet whose atmosphere is known to be made of molecules with “zero” IR emissivity! If we had a planet with an atmosphere of pure argon, or pure neon, that might come close — but I believe it is true that the laser labs these days can measure *some* IR emissivity even in those “noble” gases?

        If you had an atmosphere of pure argon, and it really were essentially a *zero* for IR activity, maybe the top layers would get so cold as to start freezing out, or maybe it would go the other way, with convective heat rising from the bottom causing the upper layers to dissipate — so the whole atmosphere would just disappear into space in fairly short order? In such idealized scenarios, assuming dynamic stability is assuming quite a lot, it seems to me.

        On real planets, you’ve always got something there in the atmosphere that radiates some significant amount of IR into space from layers higher than the ground. That includes aerosols such as the sulfuric acid droplets in the clouds, in Venus’s case. So, there shouldn’t be a goal here to totally discount the importance of IR emission from the atmosphere as such! What I find plausible is that pressure effects have an equally large impact on what to expect at the surface, as compared to any tinkering with minor differences in IR radiation. If someone adds a bit more IR emissiveness to an atmosphere, by whatever means, do the effective radiating layers become “worse” at emitting heat, “better”, “no change”? Who decides, what’s the corroboration?

        • A zero IR atmosphere would still attain hydrostatic equilibrium. Why should it not?
          The significance of Philip’s model is that it makes no thermal difference whether IR is zero or 100%.
          What does make a difference is the presence or absence of convection.

      • David,
        You are I thinking mistaken. Table 6 is the result of “forward modelling” which shows that an equipartition of energy going into conduction radiation doesn’t work for Venus. The author then does “inverse modelling” to find out what fraction of the energy of the surface must somehow be converted to thermal energy of the air and finds a value of over 99.2%. Such a value violates the second law of thermodyanamics if Table 9 is to be believed and also would appear to suggest that the surface of venus is made of a material as yet unknown to man.

        • Powerful winds supplemented by high density would transport heat upwards from the surface very efficiently hence the very high partition ratio in favour of the air suggested by the inverse modelling procedure.
          I don’t see how there would be any breach of the second law.

          • Stephen,
            If I understand Table 9 correctly and I am not sure I do the author has the ground at -46 degrees and the air above it at 400 or so degrees. Yet the ground
            is still losing 99.2% of its thermal energy to the air which violates the second
            law of thermodynamics since heat flows from a hotter body to a colder.

          • “which violates the second law of thermodynamics”
            Izaak Walton,
            You are asking some very probing questions and raising very valid objections.
            I will try and answer the points you raise.
            First, a little about my educational history. I have a degree in Environmental Science (1974) and as part of my course, I was taught about the greenhouse effect and the vacuum planet equation.
            As I remember it, we were told that this equation involved a mathematical trick, using spherical geometry, to compute the radiant exhaust temperature of an illuminated globe under a given solar irradiance and for a given Bond albedo. If you look at equation 2 (the vacuum planet equation) then it is clear that there is a “divide by 4” rule explicitly stated in this computation.

            So why a rapidly rotating planet? Well, this proviso was to overcome the objection that all globes are only ever illuminated over one hemisphere. The power intensity of this illumination when spread over the surface of the hemisphere is (on average) half of the illumination power cut out from the solar beam by the intercepting planet’s disk shadow. So how do you illuminate and power the night side hemisphere that incorporates the dark half of the planet’s surface? Answer – spin the planet rapidly.

            Clearly there are aspects of this vacuum planet equation that are totally unsatisfactory, the most obvious is this requirement for rapid planetary spin. Venus is a slow rotator and it has an atmosphere; indeed, Venus is the closest approximation we have to Noonworld in our solar system. So, following on from some interesting discussions on another thread last Christmas, I decided to build an atmospheric model for a globe that explicitly did not rotate, and explore the implications for planetary illumination and internal atmospheric energy transport using this model.

            My inspiration for Noonworld came from a science fiction story I read many years ago about a tidally locked inhabited world (I forget who the author was, it might have been Frank Herbert during the empire conquest stage of his Dune novels – someone will be able to correct me). The particular scene involved an inhabitant of this world describing how they could only live in the great circle twilight zone, and how a few hundred miles away on the dark side “the oxygen ran like water”. This idea of a fully condensing atmosphere stuck with me, and while it is not applicable to Venus, it has merit for Titan where it rains methane, and also for Mars, where it snows carbon dioxide.

            The problem with the description above of the fully condensing atmosphere, is that there has to be a surface return flow of liquid oxygen from the dark side, across the twilight zone, and towards the furnace of the lit hemisphere’s sol zenith point – the solar pole of maximum power intensity. These rivers of oxygen would make the twilight zone uninhabitable, but the basic idea has merit.

            All models are wrong, but some models are useful in that they show things that you did not previously know.
            Yes, the Noonworld model is aphysical, however look at what it predicts: –
            1. For Venus the ‘surface’ is not ground level but a point high up in the atmosphere where the temperature is much lower. That’s why I deliberately did not say ground level in table 9.
            2. Basically, in the model there is an illuminated collection surface and a dark emission surface.
            The elephant in the room is that the dark side surface is always only ever an emission surface.
            So, there is no possibility of an isothermal planetary atmosphere, even if we try to imagine it to be so. (the hard-cold numbers of maths trump imagination).

            3. A transparent diabatic atmosphere has the radiating surface at ground level, but a fully opaque atmosphere radiates to space from at or near the top of the atmosphere.

            4. Venus being much brighter than the Earth radiates to space from a higher elevation than Earth does, but at a similar radiant temperature.

            This point about emission temperature is where the Noonworld model is so valuable.
            I. The adiabatic model predicts the height of the emission surface and this height is lapse rate dependent (i.e. controlled by gravity).
            II. The Noonworld model predicts the temperature of the emission surface and this temperature appears to relate to the freezing point of the atmospheric condensing volatile (Sulphuric acid for Venus, Water for the Earth, and Tholin for Titan). https://en.wikipedia.org/wiki/Tholin
            III. This means that it is solid particles in the upper atmosphere that are important for thermal emission, and also that there is a direct relationship back to albedo.
            IV. It appears that albedo, controlled by the freezing point of condensing volatiles, is an emergent property of a climate system.
            V. Anyone who wants to geoengineer the climate of Earth by injecting particles into the upper atmosphere is playing dangerously with a very complex system.

          • Phillip, you need to more carefully read your Robinson & Catling ref. where you will find your 3) statement is not physical: “a fully opaque atmosphere radiates to space from at or near the top of the atmosphere.”

            R&C 2014: “Here we use a simple, physically based model(7) to demonstrate that, at atmospheric pressures lower than 0.1bar, 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.”

            Also, under 4) it is common knowledge in meteorology that Earth surface radiation has atm. windows to space greater than 3 micron and Venus does not. For Venus surface radiation due the higher surface pressure, there are no true atmospheric windows at IR wavelengths greater than 3 micron.

          • Phillip, you’ll need to be a little more specific about the meaning of ‘your horizon’. Your R&C 2014 ref. has a lot of information, based on observations, to understand the basic climate of “marginal” Venus. Feynman’s challenge to “study hard” should extend their work, extend their ‘horizon’. Check your work against it. Explain differences and/or deficiencies.

            The rotation rates of the solar system objects are quite different yet the R&C paper uses observations from all of them to arrive at the results. Though R&C point out: “it may prove inappropriate to apply globally averaged models to rotationally locked bodies, which could possess strong temperature contrasts between day and night hemispheres.” Thus, Noonworld may be inappropriate R&C application, you have an opportunity to extend their work to show where R&C 2014 does or does not apply to Noonworld for future climate interpretation of tidally locked exoplanets with significant atmospheres.

          • “it may prove inappropriate to apply globally averaged models to rotationally locked bodies, which could possess strong temperature contrasts between day and night hemispheres.”

            Trick,
            Both slowly rotating Titan and also even more slowly rotating Venus, clearly show that this conjecture of “strong temperature contrasts between day and night hemispheres” by Robinson and Catling is simply wrong. Have a look at the Mariner 10 Portrait of Venus, the super-rotational winds crossing the sunrise terminator get forced apart as the circulation approaches the point of maximum solar influx. I call this the “blow torch disruptor” effect and liken it to the impact on fluid flow of the prow of a moving ship causing a bow shock wave. A similar effect is seen in the tropics of Earth where the noonday sun disturbs the atmospheric circulation on our fast rotating world.

            Two modelling studies of the impact of daily rotation rate on the latitudinal reach of a Hadley cell are also relevant here.
            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.
            and
            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), 973-986

            Fast rotating Earth and Mars both have latitudinally constrained Hadley cells, and both of these planets also possess mechanical Ferrel Cells that disconnect the two thermal cells (Hadley and Polar). For the fast rotators, the greenhouse effect on low pressure Mars is tiny compared with 1 bar Earth. For the slow rotators low pressure Titan is less than high pressure Venus, so is the greenhouse effect a pressure dependent phenomenon mediated by rotation rate?

            It also appears to me that rapid rotation leads to better planetary shedding of captured solar energy back to space. I liken this to the effect of a roasting spit, the faster the rotation of the cooking spit the less the meat burns.

            And then there is the issue of planetary albedo and the freezing point of condensing volatiles. Is albedo an emergent property of planetary climates? So much to study from the application of an aphysical model.

          • ”strong temperature contrasts between day and night hemispheres” by Robinson and Catling is simply wrong.”

            You left off R&C “which could possess strong temperature contrasts between day and night hemispheres.”

            This contrast is not true for Venus surface due observations but could be true for Noonworld (and exoplanets) when the R&C approach is used for exoplanetary climate inferences. There is no way to know this temperature contrast a priori for exoplanets and Noonworld (it can’t be observed, maybe estimated) so R&C “inappropriate” stands as true warning.

            The super rotational winds on Venus are at high altitude, not at surface where winds are observed calm. Hadley et. al. cells redistribute existing energy in the system, there is nil effect on global mean multi-annual surface temperature or the cell’s speed would be seen as a needed component of planetary energy budgets.

            ”so is the greenhouse effect a pressure dependent phenomenon mediated by rotation rate?”

            Local hi and lo T yes for rotation, but not for global mean multi-annual planetary surface temperature which for a given illumination, given albedo is a function of surface pressure and the mixing ratios, mass extinction coefficients of the various gaseous absorbers (See R&C eqn. S12, and up, and Fig. S3 P-T for Titan).

            Yes, slow enough rotation rate burns your turkey, but doesn’t affect equilibrium mean T for the turkey surface, at least until a very low rate or you stop the spit completely. When stopped, mean surface T has a 2 input divisor not a 4 input divisor; rotation rate increase progressively takes it up from 2 to 4 pretty quickly as a function of heat capacity and mass until the limit. This is likely root cause of R&C “inappropriate” warning.

            ”Is albedo an emergent property of planetary climates?” Albedo emerged in 1760, has been used in optics ever since “Photometria” by J. Lambert in that year. Planetary albedo is very Lambertian except when surface particle diameters approach the wavelength of illumination being studied. For more on this see Andre Danjon, 1954: Albedo, color, and polarization of the Earth, in “The Earth as a Planet”, University of Chicago Press, pp. 726–38.

            “So much to study”…Yes.

          • @Phillip,
            If I am remembering correctly, Isaac Asimov had a “ribbonworld” essay that is quite similar to what you are describing.

          • cdquarles,

            Thank you.
            Frank at June 4, 2019 at 2:27 pm also reminded me of this story of “ribbonworld” by the great SF writer Isaac Asimov as being the source of my inspiration.

    • “Philip needs to say how he intends to get around the second law of thermodynamics before posting such rubbish.”
      Izaak Walton,

      The issue is one of power intensity. Start with NASA’s value of the solar irradiance at the orbit of Venus. This is 2601.3 W/m^2, even if we use this value then this converts to a thermodynamic temperature of 463 Kelvin, a value that is 274 degrees lower than the 737 Kelvin surface atmospheric temperature of Venus. Now apply the 0.77 Venusian planetary albedo and the maximum possible flux at solar zenith reduces to 598 W/m^2. This value converts to a thermodynamic temperature of 320.5 Kelvin, we are clearly going in the wrong direction.

      The problem we are addressing is similar to the problem in hydrology, where a water being delivered by a shallow river is captured and stored in a reservoir with a leaky dam. The water will be partially impounded within the reservoir, before eventually over topping the leaky dam and continuing on to the sea. The depth of water stored within the reservoir is much larger that the depth of water in the river.

      This is why I use the descriptor “atmospheric reservoir”; it too is a leaky reservoir and the issue becomes one of flux recycling that raises the store of power intensity flux within the atmosphere to a higher level. Once the required dynamic equilibrium is achieved the atmospheric reservoir finally outflows to space at a rate equivalent to the influx rate.

      The key point of issue is what is the mechanism that causes this flux recycling? Standard theory says radiation recycling, however the process of thermal recycling by air mass motion is clearly a mechanism that occurs within the troposphere. The model presented here explores the limits of this dynamic mass motion process, and suggests new lines of inquiry for scientific study of the complex phenomenon of planetary climate

      Welcome to the world of climate modelling.

      • And the model clearly demonstrates that the surface temperature enhancement for every planet with an atmosphere can be accounted for without back radiation simply by varying the ratio between surface energy loss to space via radiation and surface energy loss to the mass of an atmosphere via conduction and convection.
        What is left of the radiative theory ?

    • Chad, you can learn in the top post that the GHE is indeed, in part, a pressure dependent effect by reading thru the top post ref. of Catling & Robinson.

  22. From the article “the total surface area of the planet that emits thermal radiation to space is four times the surface area of its intercepting disk (i.e. 4π R2). It is this geometric fact that is responsible for the “divide by 4” rule that is contained within the calculation of planetary radiative thermal balance.”

    The ‘intercepting disk’ is theoretical, it does not actually exist. But it can be used to help determine how much of the sun’s energy is intercepted by half the Earth. So the sun is illuminating half the Earth, but the entire Earth is emitting thermal radiation. No where does the ‘divide by 4’ rule apply.

    • I think you have to divide by four instead of two because of spherical geometry whereby the angle of incidence is oblique across most of the illuminated half.

    • “No where does the ‘divide by 4’ rule apply”
      Thomas,
      The surface area of a sphere is four times the area of a disk of equivalent radius.
      All spherical planets cut out a shadow from the solar beam with a cross-sectional area that illuminates a hemisphere. This is correct. BUT the surface area of the illuminated hemisphere is twice the area of the cut-out beam. So, divide by two. But again, we have to supply energy to the dark night side of the globe which is another two times the surface area of the beam, so in total divide by four.
      All this is basic geometry and should not be in dispute.

      However, and this is the rub, at no time is any globe anywhere ever illuminated on both sides at the same time. Yet the standard vacuum equation does just that. That’s why the vacuum planet is supposed to be rapidly rotating.
      I prefer to model climate with spherical Noonworld geometry and not with planar Diskworld geometry.

      • Philip Mulholland – (not sure why my earlier reply is shown as a separate comment below)

        If we were to consider a solar eclipse when the Moon casts a shadow on Earth and applied your logic to find the area of the shadow …
        The illuminated portion of the Moon is a hemisphere that is twice the area of a cross section of the Moon’s shadow, therefore “divide by two’????

        • “and applied your logic to find the area of the shadow”
          Thomas,
          And just how much energy does a shadow deliver to the surface of the Moon?
          Strike two.

          • Philip Mulholland “And just how much energy does a shadow deliver to the surface of the Moon?
            Strike two.”

            Two – is that how many dimensions you’re comfortable with, I suggest you consider three dimensions. For example, there are two hemispheres in a three dimensional sphere.

            I understand you’re flustered, but I get one more strike, so please defend your claim: ” … the total surface area of the planet that emits thermal radiation to space is four times the surface area of its intercepting disk ” – there is no actual ‘intercepting disk’, correct? It’s theoretical. There is an actual intercepting hemisphere. And the total surface area of the planet that emits thermal radiation to space is twice the area of the intercepting hemisphere.

          • Thomas Homer

            I understand you’re flustered, but I get one more strike, so please defend your claim: ” … the total surface area of the planet that emits thermal radiation to space is four times the surface area of its intercepting disk ” – there is no actual ‘intercepting disk’, correct? It’s theoretical. There is an actual intercepting hemisphere. And the total surface area of the planet that emits thermal radiation to space is twice the area of the intercepting hemisphere.

            Careful.
            The CAGW’s “flat earth” theory of a “perpetual balance of radiation equilibrium” does work. For an “average flat plate grey-body perfect Earth” illuminated on only one side, radiating all energy received on that one side back to an infinite cold black space.

            But notice my qualifiers!

            A perfect grey-body flat earth.
            An average perfect grey body flat earth, radiating its received energy back at a single global average temperature.

            Forget seasons and the axial tilt for a moment.
            To be even more unrealistic, forget clouds and that inconvenient 30-70 earth-water mix of surface temperatures and emissivities and coefficients of heat transfers and exchanges.
            Trenberth’s flat earth analogy does (sort of) work – but only for an average 35-45 degree latitude band and an average year-round temperature and an average sky and an average TSI/TOA radiation value.

            The Real Earth (may I be forgiven the capital letters?) is a hemisphere of varying cloud cover and a greatly varying earth-water balance between the north and south hemispheres.

            The Real Earth receives solar radiation over a hemisphere – with less at both poles and greater amounts in the mid-latitudes.
            The Real Earth has significantly greater mid-Latitude temperatures (moderated by a huge mid-Latitude water body of near-uniform temperature), and tremendous northern and southern local surface temperature differences, radiating to space from the entire area of the sphere.

            Further, its varying northern ice is concentrated between the north pole and 70 north latitude (with almost no land ice up there at any season of the year!), and a southern ice field of permanent land ice and shelf ice between 90 south and 70 south, and a varying sea ice field between 70 south and 65 south latitudes. So little land is south of the equator that, at time of maximum sea ice, there is more ice south of the equator than all land area … combined.

            Your attempt to correct the reader is needed. But it is incomplete.
            Do you want to discuss “global average flat earth temperatures” or specific Real World temperatures and climates?

        • (not sure why my earlier reply is shown as a separate comment below)
          Because like you it’s out of order.

          • Philip Mulholland “Because like you it’s out of order.”

            I may be ‘out of order’ but why can’t you defend your geometrically challenged position?

            When not in shadow, half the Earth is intercepting energy from the Sun. Is this true?

          • Half the Earth is intercepting the solar beam but the increase in temperature that will be attained is related to the amount of surface area available to absorb that solar beam.
            For a three dimensional object there is double the surface area available as compared to a flat disc so the energy in the beam will only raise the temperature half as much.
            This is well established since Archimedes and known to be true so this is the last response you are getting from me on this topic.

          • Stephen Wilde – Thank you for your recent response – at least I finally have some insight to what you’re trying to defend. In effect, it sounds as though similar to the mechanics of an ‘inclined plane’ are being applied to the sun heating a hemisphere.

            I continue to be skeptical and I recognize my need to refine my questions.

            Looks like RACookPE1978 has provided context in a comment above.

      • Philip, don’t waste any more time on Thomas Homer. He’s a hopeless case who is incapable of understanding basic geometry. Months ago I wasted way more time than I should have, trying to explain the “divide by 4” issue to him. He would hijack an obscure thread and go off on a rant, putting his ignorance on display. I’m afraid he’s a lost cause.

        • Floyd Doughty – Are you prepared to defend your ‘basic geometry’ by producing something of sunstance? Or is my ignorance so powerful it renders you incapable of defending your claims?

  23. Philip Mulholland – Thank you for your response

    “BUT the surface area of the illuminated hemisphere is twice the area of the cut-out beam. So, divide by two”

    Why? Half the sphere is intercepting the sun’s energy. It doesn’t matter about the ‘oblique angle of incidence’ (Stephen Wilde) The difference between night and day is a Boolean, not a gradient. The fact that the hemisphere receiving the sun’s energy is a gradient makes the calculations for the total of the Sun’s energy intercepted by the Earth difficult. The concept of a flat disk of the Earth’s shadow is a good one to help determine the amount of energy received by half the Earth. It is a theoretical concept, the flat disk does not exist but it helps to simplify the calculations.

    “All this is basic geometry and should not be in dispute.” Exactly! It’s amazing that all of this is based on the idea of dividing the energy received by half a sphere (illuminated hemisphere), by 4, to average it over the other half.

    We can see temperature recordings that show a location on Earth begins to warm just before sunrise! That is the very fringes of the illuminated hemisphere that you are claiming is actually receiving none of the sun’s energy and is emitting to dark space.

    Your theory claims that 1/4 of the Earth is receiving the sun’s energy while 3/4 is emitting to dark space, That is clearly wrong. You said yourself that the sun illuminates a hemisphere. How do you average two halves?

    • Thomas
      The oblique angle of incidence matters because it arises due to the curved surface of a three dimensional sphere having double the surface area of a flat disc.
      Thus the portion of the intercepted beam that arrives is spread over double the area and to account for that one must divide by four rather than two.
      Philip’s model recognises that at any given moment half the surface is in energy surplus so that a portion is removed to the atmosphere and not to space whereas the other half is in energy deficit so that a portion is recovered from the surface and radiated to space.
      At hydrostatic equilibrium both halves net out to zero.

      • Stephen Wilde : “the portion of the intercepted beam that arrives is spread over double the area and to account for that one must divide by four rather than two”

        The portion of the intercepted beam is spread over half the Earth. That is self-evident. To average two halves, divide by two. That is self-evident.

        It does not matter what size the surface area is of the theoretical flat disc of the cross section of Earth’s shadow. We are dealing with hemispheres, one in daylight, the other not.

        The oblique angle of incidence does not matter in this case. The sun’s energy is intercepted by half the Earth.

        Perhaps the angle of incidence will become a factor when we attempt to derive a value for
        the Earth’s albedo, but not in averaging the amount of the sun’s energy intercepted by half the Earth. Averaging two halves requires dividing by two.

      • Philip Mulholland – “The area of a circle is PiR^2 The surface area of a sphere is 4PiR^2”

        How many hemispheres make up a sphere?

  24. I read that others too have speculated about how a non IR atmosphere would end up temperature wise.
    The lapse rate would be constant (no condensation) around 10K/km. A parcel of air heated by the surface would rise up and continue because it will be hotter than the surrounding air. The falling air will be heated by the lapse rate and end at the surface a bit colder than the air that went up. On the night side the air is cooled by the surface but will stay at the surface.
    I see two possibilities:
    1) the air will be as hot as the day time surface, but the temperature drops in hight with the lapse rate.
    2) the air will be equally hot in all hights and the convection stops.
    Any comments?

    • Svend
      1) The air descending on the night side would deliver back to the surface all the kinetic energy lost to the air on the day side but the ground would radiate it away to space rapidly so it would cool but slide away horizontally back towards the day side whilst being replaced by more downflowing air with yet more KE that the surface would then radiate to space in a continuous flow. Note that Philip’s model has an energy deficit on the night side where radiation to space is enhanced by energy coming down from above.
      2) The air will never become the same temperature at all heights due to the creation of PE from KE in uplift and the creation of KE from PE in descent.

      • Stephen
        I am not sure #2 would be possible, but imagine that all the air was heated to the maximum day temperature. In that case no convection would take place and the air would never cool and could keep the same temperature all over. I imagine there would be some limited flow of air between cold and hot parts of the surface, but only close to ground where it can be cooled/heated. There would be a globally inversion layer.
        There could still be a temperature gradient close to the lapse rate, but anyway if the convection stops it would be static forever. If the convection stops the air would slowly get the same temperature by conduction except for the layers close to ground.
        This imagination/hypothesis shows the importance of GHG’s for the dynamic of our atmosphere.

        • Svend, convection does stop at night and a temperature inversion forms near the surface as the ground cools by radiation but the air above stays warm, which temporarily disturbs the adiabatic temperature profile. But as soon as the sun comes up convection gins up and everything goes back to normal. 😊

  25. You make the same error that the warmers make. You make the explicit assumption that the only way a planetary body can gain or lose energy is radiation despite the fact that there is ample evidence of other mechanisms at work converting thermal energy to or from other forms. This assumption IS wrong. For example the moon is continuously flexing the earth’s // Venus crust causing friction and perturbing the ocean and atmosphere adding energy, the earth rotation causes an editorial bulge causing fluid migration and friction. Heat differences cause wind that is largely expended in perturbations of the earth’s rotational kinetic energy. Some considerable incoming solar energy is absorbed by photosynthesising plants. Solar wind, Vulcanism, Nuclear decay, phase changes, entropy/enthalpy. There are innumerable gains and losses.

    So, You cannot assume what you assume, it’s incumbent on you to prove that ALL sources of non radiative energy leaking into/out of the thermal environment are inconsequential.

    • Makes no difference.
      Only one surface temperature can hold the atmosphere indefinitely in hydrostatic equilibrium. If any sources other than insolation seek to disturb that baseline temperature then convective changes occur that eliminate the imbalance.

      • Only by establishing a difference between incoming and outgoing energy, radiative balance has to be maintained.

  26. In your initial model, the atmosphere has no GHG’s and therefore cannot absorb longwave (and I assume shortwave) radiation. Therefore it cannot emit any radiation. So the OLR is therefore 100% surface emission. In the equilibrium state, Noonworld bottom of atmosphere temperature equals the surface temperature through conduction and convection, and net heat flow between surface and atmosphere is zero. 150 W/m2 is transported to the dark side, so in equilibrium the surface on the dark side emits 150 W/m2. The surface on the lit side emits 300 W/m2, of which 150 W/m2 ends up on the darkside: so subtract that from OLR on the lit side. So both hemispheres emit average 150 W/m2, which is equal to solar insolation divided by 4. All ok. And surface temperature is 270K on the lit side and 226K on the dark side. Atmospheric partitioning of absorbed energy is 0% out and 100% down. You can only change that partitioning if you allow the atmosphere to have a non-zero longwave emissivity – then there will be a greenhouse effect. In your model, there can be no top of atmosphere radiation outward, you precluded that when you disallowed greenhouse gases. Thus your “reverse engineered” partition factor is bunkum. Yes or no?
    Cheers

  27. Phil: I don’t know what to make of this contribution, but I may have some information that could be useful to you. The lapse-rate on any planet is the whatever process moves heat most rapidly vertically through the atmosphere to space. In Earth’s stratosphere, radiation moves heat much faster than convection. In the troposphere of Earth, bulk convection moves heat vertically more quickly than net radiation, so a moist adiabatic lapse rate dominates in most locations most of the time. (In the early morning hours, however, a thermal inversion a thermal inversion often develops when there is no wind to turbulently mix the boundary layer.) On Venus, there is a nearly constant lapse rate up to about 70 km of 10 K/km which is equal to -g/Cp for the planet.

    For a “gray” atmosphere with equal absorption at all wavelengths with no convection, the vertical temperature profile increases linearly with optical depth as you move deeper into the atmosphere. Since pressure and density increase exponentially with depth, atmospheres the temperature rises linearly with optical. In the traditional plot of T (x-axis) vs altitude (y-axis), this results in a curved plot where T approaches a lowest value at the highest altitude and increases exponentially with depth at the high temperature end. One look at the lapse rate for Venus should tell you that it is controlled by vertical convection of heat, not radiation.

    • Frank,

      Thanks for a very helpful comment. The atmospheric temperature profile data for Venus is published on line by NASA (Justus and Braun, 2007, Table 3.1.2).

      • Philip wrote: “My inspiration for Noonworld came from a science fiction story I read many years ago about a tidally locked inhabited world (I forget who the author was, it might have been Frank Herbert during the empire conquest stage of his Dune novels – someone will be able to correct me). The particular scene involved an inhabitant of this world describing how they could only live in the great circle twilight zone, and how a few hundred miles away on the dark side “the oxygen ran like water”. This idea of a fully condensing atmosphere stuck with me, and while it is not applicable to Venus, it has merit for Titan where it rains methane, and also for Mars, where it snows carbon dioxide.”

        This scene comes from Volume II (Foundation and Empire) of the Foundation Series by Asimov. The planet was called a “ribbon world” and was one of the Independent Trading Worlds considering revolting against Terminus.

        • Thanks Frank,

          Good old Asimov!
          I should have realised that it had to be him.

  28. This has been a well thought out thread with interesting debate. I like to add a twist considering observations of cause-and-effect. I believe you’re looking for the solution in the wrong direction.
    You said;
    “The discrepancy between the calculated equilibrium temperature and surface planetary temperature requires explanation. The accepted reason is called “The greenhouse effect”, the process by which radiation from a planet’s atmosphere warms the planet’s surface to a temperature above what it would be without its atmosphere.”

    The “excepted reason” is because of the wrongful assumption that the “Sun” is the source of all heat. Ultimately “all heat is friction”. Is there alternative to the sun source of heat rendering a greenhouse affect irreverent? You already hinted at the cause without recognizing it;
    ” 9. This relationship between Global Surface Atmospheric Temperature determined by energy flux partition ratio and atmospheric thickness (i.e. surface pressure), for a given albedo dependent radiant energy input, is a totally unexpected result. It implies that the greenhouse effect is a pressure dependent effect (as per James Clark Maxwell) and not a radiant feed-back effect (contra Svante Arrhenius”

    So let’s explore this “pressure dependent effect”. A column of air in a gravity well compresses the air at the bottom of the column creating heat. Venus is a great example of almost no energy from the sun reaching the surface and yet the surface is the hottest part, even hotter than mercury.
    “So not only does Mercury receive four times as much energy-per-unit-area, it absorbs nearly nine times as much of the sunlight it receives as Venus does!”
    On earth, the Chinook winds heat the air coming over the mountain 5.4°F for every thousand feet the air descends creating the desert on the other side. (Solar effect/day or night, is irreverent) As the air warms, air rises, expands and immediately cools, and yet the descending air always heats up… “always”. (this is also true of the weather balloons measurements)
    Which is hotter, Mount Everest which is closer to the sun receiving more radiation. Or death Valley, below sea level, highest air pressure.
    What happens when I apply this earth math to Venus? 865° surface temperature divided by 5.4 =160. 160,000 feet divided by 5280 feet equals 30 miles. Interesting that is also about one bar of pressure/ 70° in Venus atmosphere… (This doesn’t allow for 92% CO2 being heavier than earth normal atmosphere, or gravity is slightly less on Venus. Not scientific but relevant)
    Conclusion: atmosphere greenhouse affect is not consequential to the frictional heat generated continuously by the atmosphere pressure on the surface.
    Big claims require evidence, all I have is examples.
    The temperature at Jupiters core boundary is believed to be 64,000°F, the surface temperature of the sun (the photosphere) is just below 10,000°F. This makes Jupiter, at 5AU, is nearly 7 times hotter than the surface of the sun.
    Saturn is twice as hot as the sun.
    Neptune is furthest out, and yet hotter than the sun.
    Uranus, under its atmosphere, it is estimated about the same temperature as the surface of the sun.
    Mercury averages, with no atmosphere to generate heat, about 300°F.
    The Venus conundrum of over 200° below zero at the top of the atmosphere, with clouds reflecting most of the sunlight. And yet the heat rises as you descend to the lowest point which is over 900°. This occurs In near complete darkness because there is only five wavelengths of energy that can reach through all that atmosphere to the surface. ( I would note that 200 mile an hour winds generates a lot of heat, one can only wonder how much energy is driving the wind to begin with… )
    Noonworld fantasy is an interesting concept. Photosynthesis require sunlight, but not all life requires photosynthesis. If air pressure generates heat (and there is no example where it does not) the entire planet would be warm, and would be capable of life.
    Venus rotates very slowly, it’s day is longer than its year. But because it rotates backwards, ( Think of two runners on the race track with one running in the opposite direction) sunrise to sunrise is 117 days. Now compare this to our north pole and Antarctica. Both receive zero sunlight for half a year nearly 180 days. Longer night then Venus, and yet radiates energy the entire time, with zero solar impact.
    In three months of 100% polar sunlight, why isn’t the poles the hottest places on earth? Because the Suns influence is not as great as the atmospheric pressure. Compare Antarctica’s average temperature during summer is 40° below zero, to where the north pole melts every year. The difference is that Antarctica is at 10,000 feet, the top of a mountain. The north pole is at Sea level.
    It’s not a coincidence that a low pressure storm where air pressure drops, also has a drop in air temperature.
    I’m about to go camping 10 miles from my home on a Mountain at 8000 feet, the temperature is always 20° colder than my home. (Even though I will be closer to the sun)
    I am hoping this observation of real temperature measurements can be utilized in a model that actually predicts climate change fluctuations. Reproducible cause-and-effect. End the greenhouse debate.
    This can be applied even to the sun, the higher you get above the photosphere the colder the temperatures until you reach the 2,000,000°F chromosphere where all light/heat/solar wind comes from. (This temperature anomaly also violates the laws of thermal dynamics indicating a different mechanism is involved here. Hence the reason for the solar probe. The probe is named for the man who theorized “nano flares”)

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