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).
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).
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.
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).
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).
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).
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).
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).
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).
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).
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).
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).
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
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.
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).
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.
“It implies that the greenhouse effect is a pressure dependent effect …” I would disagree with that statement.
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.
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
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?
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.
“Your theory claims that 1/4 of the Earth is receiving the sun’s energy while 3/4 is emitting to dark space,”
Thomas,
Really, are you sure?
The area of a circle is PiR^2
The surface area of a sphere is 4PiR^2
I think that you need to take this up with Archimedes.
https://en.wikipedia.org/wiki/On_the_Sphere_and_Cylinder
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?
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. 😊
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.
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
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.
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”)
Thanks Max,
I have asked a friend to comment on your contribution.
I was not aware of the solar probe.
https://www.nasa.gov/content/goddard/parker-solar-probe