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In this essay we introduce the concept of Noonworld, a hypothetical solar illuminated tidally locked planet. We develop a climate model based on the meteorological principles of a lit daytime hemisphere of energy surplus that is coupled to a dark nighttime hemisphere of energy deficit. In the model the fundamental mechanism of power intensity flux distribution across the surface of Noonworld is mediated by the process of atmospheric mass motion. The capture, distribution and loss to space of solar radiant energy is studied for a hypothetical fully transparent atmosphere. In this first instance the model assumes that all processes of flux transformation are equipartition in type and occur at the solid surface of the planet. Our initial model is diabatic in concept and fully replicates the low temperature atmosphere of the standard Vacuum Planet equation. We next adjust the model to account for the process of sunlit forced convection by partitioning energy capture in favour of the air. Our model now retains additional flux within the atmospheric reservoir, and thereby causes the global atmospheric temperature to rise. We call this process of flux capture and distribution by atmospheric mass motion the adiabatic model.
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Modelling the Climate of Noonworld: A New Look at Venus.
Philip Mulholland and Stephen Paul Rathbone Wilde
June 2019
https://wattsupwiththat.com/2019/06/02/modelling-the-climate-of-
noonworld-a-new-look-at-venus/
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.
In this essay we introduce the concept of Noonworld, a hypothetical solar illuminated tidally locked
planet. We develop a climate model based on the meteorological principles of a lit daytime
hemisphere of energy surplus that is coupled to a dark nighttime hemisphere of energy deficit. In
the model the fundamental mechanism of power intensity flux distribution across the surface of
Noonworld is mediated by the process of atmospheric mass motion. The capture, distribution and
loss to space of solar radiant energy is studied for a hypothetical fully transparent atmosphere. In
this first instance the model assumes that all processes of flux transformation are equipartition in
type and occur at the solid surface of the planet. Our initial model is diabatic in concept and fully
replicates the low temperature atmosphere of the standard Vacuum Planet equation. We next
adjust the model to account for the process of sunlit forced convection by partitioning energy
capture in favour of the air. Our model now retains additional flux within the atmospheric reservoir,
and thereby causes the global atmospheric temperature to rise. We call this process of flux capture
and distribution by atmospheric mass motion the adiabatic model.
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
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.
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
Venusian Energy Budget Items
(Wiliams, D.R., 2018)
Power
Intensity
Watts/m2
Kelvin Celsius
Comments
Planetary Disk Beam Interception 2601.300 Top of the Atmosphere
Venus Bond albedo 0.770 Planetary Brightness
Bond albedo Filter Applied 598.299 Absorbed by the Planet
"Divide by 4" Rule Applied 149.575 Distributed over the full Globe
Total Incoming Absorption 149.575 226.6 -46.4 Vacuum Planet Equilibrium Temperature
Balanced Outgoing Radiation 149.575 226.6 -46.4 TOA Emission Temperature
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
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.
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.
Step
Process Energy Flow
1
Interception of solar energy by the lit surface 1 unit.
2
No initial flow of frozen air from the dark side 0 Unit
3
Energy available to drive the system 1 unit.
4
50S : 50A partition of the intercepted energy between the
ground and the air leading to: -
Litside
partition
5
Direct radiant loss to space from the warm surface ½ unit
6
Retention of energy by the lit air, followed by transport
and delivery of this warm air to the dark side
½ unit
7
50S : 50A partition of the delivered energy between the
ground and the air leading to: -
Darkside
partition
8
Radiant loss to space from the ground on the dark side ¼ unit
9
Return flow of cold surface air from the dark side to the
lit side
¼ unit
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 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.
Cycle
Number
Space Incoming
Captured
Radiation
(Units)
Heating the Lit
Hemisphere
(Units)
Lit Hemisphere
Thermal Radiation
Loss to Space (50%
Lost)
Hadley Cell Export to
Dark Side (50%
Retained)
Dark Hemisphere
Thermal Radiation
Loss to Space ( 50%
of 50% lost)
Surface Return Loop
from Dark to Lit
Hemisphere (50% of
50% Returned)
Space Outgoing
Radiation Balance
(Units)
1
1 0.5 0.5 0.75
0.25 0.25
1.25
1 0.625 0.625 0.9375
0.3125 0.3125
1.3125
1 0.65625 0.65625 0.984375
0.328125 0.328125
1.328125
1 0.6640625 0.6640625 0.99609375
0.33203125 0.33203125
1.33203125
1 0.666015625 0.666015625 0.999023438
0.333007813 0.333007813
1.333333333
1 0.666666667 0.666666667 1.000000000
0.333333333 0.333333333
Infini te
Series Limi t
Comments
Total Energy
Supply Heating
the Atmosphere
Final Lit Side Radiant
Energy Lost to Space
Total Thermal
Energy Transported
to the Dark Side
Solar Irradiance
Planetary Radiant
Exhaust
5
Primary
2
3
4
Total Thermal Energy
Retained by the
Atmosphere
Final Dark Side
Radiant Energy
Lost to Space
Building the Dynamic-Atmosphere Energy-Transport 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.
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”.
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).
Step
Process
Energy Flow
(Units)
1
Interception of solar energy by the lit surface 1
2
Return flow of cold air from the dark side 0.333333333
3
Total energy available to drive the system 1.333333333
4
50S : 50A partition of the intercepted energy between the
ground and the air leading to: -
Litside
partition
5
Direct radiant loss to space from the warm surface 0.666666667
6
Retention of energy by the lit air, followed by transport
and delivery of this warm air to the dark side
0.666666667
7
50S : 50A partition of the delivered energy between the
ground and the air leading to: -
Darkside
partition
8
Radiant loss to space from the ground on the dark side 0.333333333
9
Return flow of cold surface air from the dark side to the
lit side
0.333333333
10
Total Planetary Radiant Emission to Space 1
11
Total Global Energy Budget (Sum of both hemispheres) 2
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).
Cycle
Space
Incoming
Captured
Radiation
(Units)
Lit Ground
Received
Energy
(Units)
Lit Ground
Partition
(Units)
Lit Air
Partition
(Units)
Dark
Ground
Partition
(Units)
Dark Air
Partition
(Units)
Space
Outgoing
Radiation
Balance
(Units)
50.0000% 50.0000% 50.0000% 50.0000%
0 1
1 1 1.00000000 0.50000000 0.50000000 0.25000000 0.25000000
0.75000000
2 1 1.25000000 0.62500000 0.62500000 0.31250000 0.31250000
0.93750000
3 1 1.31250000 0.65625000 0.65625000 0.32812500 0.32812500
0.98437500
4 1 1.32812500 0.66406250 0.66406250 0.33203125 0.33203125
0.99609375
5 1 1.33203125 0.66601563 0.66601563 0.33300781 0.33300781
0.99902344
6 1 1.33300781 0.66650391 0.66650391 0.33325195 0.33325195
0.99975586
7 1 1.33325195 0.66662598 0.66662598 0.33331299 0.33331299
0.99993896
8 1 1.33331299 0.66665649 0.66665649 0.33332825 0.33332825
0.99998474
9 1 1.33332825 0.66666412 0.66666412 0.33333206 0.33333206
0.99999619
10 1 1.33333206 0.66666603 0.66666603 0.33333302 0.33333302
0.99999905
11 1 1.33333302 0.66666651 0.66666651 0.33333325 0.33333325
0.99999976
12 1 1.33333325 0.66666663 0.66666663 0.33333331 0.33333331
0.99999994
13 1 1.33333331 0.66666666 0.66666666 0.33333333 0.33333333
0.99999999
14 1 1.33333333 0.66666666 0.66666666 0.33333333 0.33333333
1.00000000
Noonworld Cascade Algorithm Partition Test 50%S:50%A
Partition Ratio Test
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
Cycle
Space
Incoming
Captured
Radiation
(W/m2)
Lit Ground
Received
Energy
(W/m2)
Lit Ground
Partition
(W/m2)
Lit Air
Partition
(W/m2)
Dark Ground
Partition
(W/m2)
Dark Air
Partition
(W/m2)
Space
Outgoing
Radiation
Balance
(W/m2)
50.0000% 50.0000% 50.0000% 50.0000%
0 299.1495
1 299.1495 299.1495 149.5748 149.5748 74.7874 74.7874 224.3621
2 299.1495 373.9369 186.9684 186.9684 93.4842 93.4842 280.4527
3 299.1495 392.6337 196.3169 196.3169 98.1584 98.1584 294.4753
4 299.1495 397.3079 198.6540 198.6540 99.3270 99.3270 297.9809
5 299.1495 398.4765 199.2382 199.2382 99.6191 99.6191 298.8574
6 299.1495 398.7686 199.3843 199.3843 99.6922 99.6922 299.0765
7 299.1495 398.8417 199.4208 199.4208 99.7104 99.7104 299.1312
8 299.1495 398.8599 199.4300 199.4300 99.7150 99.7150 299.1449
9 299.1495 398.8645 199.4322 199.4322 99.7161 99.7161 299.1484
10 299.1495 398.8656 199.4328 199.4328 99.7164 99.7164 299.1492
11 299.1495 398.8659 199.4330 199.4330 99.7165 99.7165 299.1494
12 299.1495 398.8660 199.4330 199.4330 99.7165 99.7165 299.1495
13 299.1495 398.8660 199.4330 199.4330 99.7165 99.7165 299.1495
14 299.1495 398.8660 199.4330 199.4330 99.7165 99.7165 299.1495
S-B 5.67E-08 5.67E-08 5.67E-08 5.67E-08 5.67E-08 5.67E-08 5.67E-08
Kelvin 269.5 289.6 243.5 243.5 204.8 204.8 269.5
Celsius -3.5 16.6 -29.5 -29.5 -68.2 -68.2 -3.5
Metric Sunlight Boosted T Mean Exit T Mean Air T Lit-side Dark-side Global
Kelvin 269.5 289.6 224.2 224.2
W/m2W/m2W/m2
Celsius -3.5 16.6 -48.8 -48.8 398.866 199.433 598.299
Noonworld Diabatic Model using Venusian Insolation Parameters
Partition Ratio Test
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.
Process
Power Intensity
W/m2
Thermodynamic
Temperature
Temperature
(Celsius)
Comments
Incoming Captured
Radiation
299.150 269.5 -3.5
Noonworld post-albedo Lit
Hemisphere Power Intensity
Lit Ground Received
Energy
398.866 289.6 16.6
Solar and recycled thermal
combined
Lit Ground Partition 199.433 243.5 -29.5 Direct radiant loss to Space
Lit Air Partition 199.433 243.5 -29.5
Lit Air Thermal export to Dark
side
Dark Ground
Partition
99.716 204.8 -68.2
Direct radiant loss to Space
Dark Air Partition 99.716 204.8 -68.2
Dark Air Thermal return to Lit
side
Space Outgoing
Radiation Balance
299.149 269.5 -3.5
Sum of Radiant losses
Total Global Energy
Budget
598.299 320.5 47.5
Sum of all 4 components
Average Global Air
Temperature
149.575 224.2 -48.8
Mean of Warm Daytime and
Cold Nighttime air
Vaccum Planet
Equation
149.575 226.6 -46.4
Asumes an even global
distribution power intensity
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.
Cycle
Space
Incoming
Captured
Radiation
(Units)
Lit Ground
Received
Energy (Units)
Lit Ground
Partition is
0.8862%
(Units)
Sun Lit Air
Partition is
99.1138%
(Units)
Dark
Ground
Partition is
0.8862%
(Units)
Dark Air
Partition is
99.1138%
(Units)
Space
Outgoing
Radiation
Balance
(Units)
0.8862% 99.1138% 0.8862% 99.1138%
0 1.0000
1 1.0000 1.0000 0.0089 0.9911 0.0088 0.9824 0.01764558
2 1.0000 1.9824 0.0176 1.9648 0.0174 1.9474 0.03497980
3 1.0000 2.9474 0.0261 2.9213 0.0259 2.8954 0.05200815
4 1.0000 3.8954 0.0345 3.8608 0.0342 3.8266 0.06873602
5 1.0000 4.8266 0.0428 4.7839 0.0424 4.7415 0.08516872
6 1.0000 5.7415 0.0509 5.6906 0.0504 5.6402 0.10131145
7 1.0000 6.6402 0.0588 6.5813 0.0583 6.5230 0.11716933
1197 1.0000 56.671401022 0.502225376 56.169175646 0.497774624 55.67140102 0.999999999
1198 1.0000 56.671401022 0.502225376 56.169175647 0.497774624 55.67140102 0.999999999
1199 1.0000 56.671401023 0.502225376 56.169175647 0.497774624 55.67140102 0.999999999
1200 1.0000 56.671401023 0.502225376 56.169175648 0.497774624 55.67140102 0.999999999
1201 1.0000 56.671401024 0.502225376 56.169175648 0.497774624 55.67140102 0.999999999
1202 1.0000 56.671401025 0.502225376 56.169175649 0.497774624 55.67140103 0.999999999
1203 1.0000 56.671401025 0.502225376 56.169175650 0.497774624 55.67140103
1.000000000
Partition Ratio Target Temperature 737
Kelvin (464oC)
Noonworld Cascade Algorithm Partition Test 0.886%S:99.114%A
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
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.
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.
Step
Process
Energy Flow
(Units)
Power Intensi ty
Flux (W/m2)
Thermodynamic
Temperature
Temperature
(Celsius)
Comments
1
Interception of solar ene rgy by the lit surface 1 299 269.5 -3.5
Noonworld post-alb edo
Lit Hemisphere Powe r
Intensity
2/9
Return flow of colder air from the dark side 55.671401 16,654 736.2 463.2
Dark Air Thermal return
to Lit side
3
Total energy available to drive the system 56.671401 16,953 739.5 466.5
Solar and recycled
thermal combined
4
0.886%S : 99.114%A partition of the intercepte d energy
betwee n the ground and the air leading to: -
5
Direct radiant loss to space from the lit side 0.502225 150 226.9 -46.1
Direct radiant loss to
Space
6
Retention of e nergy by the lit air, fol lowed by
transport and delivery of this warm air to the dark
side
56.169176 16,803 737.8 464.8
Lit Air Thermal export to
Dark side
7
0.886%S : 99.114%A partition of the deli vered energy
betwee n the ground and the air leading to: -
8
Radiant loss to space from the dark side 0.497775 149 226.4 -46.6
Direct radiant loss to
Space
9/2
Return flow of colder air from the dark side 55.671401 16,654 736.2 463.2
Dark Air Thermal return
to Lit side
10
Total Planetary Radiant Emission to Space 1 299 269.5 -3.5
Space Outgoing Radiation
Balance
11
Total Global Energy Budget (Sum of both
hemispheres)
112.840577 33,756 737.0 464.0
Average Global Air
Temperature: Mean of
Warm Daytime and Cold
Nighttime air
Litside partitio n
Darkside partition
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 10: The Radiant and Atmospheric Thermal Properties of Venus.
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
Metric
Sunlight
Component
Boosted Energy
Mean Radiant Exit Mean Air Retained
W/m2299 16953 150 16728
Kelvin 269.5 739.5 226.6 737.0
Celsius -3.5 466.5 -46.4 464.0
Process
Cyclical
Thermal Boost
Partition Effect
Difference
Boosted Energy
minus Sunlight
Mean Air Retained
minus Radiant Exit
Celsius
470.0 510.4
Lapse rate
K/Km Delta K Km
6.7 512.6 76.2
6.7 511.4 76.0
Lit Thermal Cell
Dark Thermal Cell
Atmospheric Effect
Mean Thermal Impact of the Atmosphere
490.16
Item
Top of Atmosphere (TOA)
Metric
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.
ResearchGate has not been able to resolve any citations for this publication.
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The fast winds of Venus are getting faster
ESA, 2013 The fast winds of Venus are getting faster. Astronomy Magazine.
Abstract Venus Atmosphere Notes
  • M Hammer
Hammer, M., 2017 Atmosphere of Venus. Abstract Venus Atmosphere Notes, 9pp.
Atmospheric Environments for Entry, Descent, and Landing (EDL) NASA Natural Environments Branch (EV13)
  • C G Justus
  • R D Braun
Justus, C.G. and Braun, R.D., 2007. Atmospheric Environments for Entry, Descent, and Landing (EDL) NASA Natural Environments Branch (EV13).
The Coriolis Effect: Four centuries of conflict between common sense and mathematics, Part I: A history to 1885
  • A O Persson
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.
Venus Fact Sheet NASA NSSDCA, Mail Code 690.1, NASA Goddard Space Flight Center
  • D R Williams
Williams, D.R., 2018. Venus Fact Sheet NASA NSSDCA, Mail Code 690.1, NASA Goddard Space Flight Center, Greenbelt, MD 20771.