


































Energy and Earth Science 
Vol. 6, No. 3, 2023 

www.scholink.org/ojs/index.php/ees 

ISSN 2578-1359 (Print)   ISSN 2578-1367 (Online) 

 

21 

 

Original Paper 

The Venusian Insolation Atmospheric Topside Thermal Heating 

Pool 

Philip Mulholland
1*

 & Stephen Paul Rathbone Wilde
2
 

1
 Mulholland Geoscience, Edinburgh, UK  

2
 Private Researcher, Wirral, UK 

*
 Philip Mulholland, Mulholland Geoscience, Edinburgh, UK 

 

Received: August 13, 2023     Accepted: August 23, 2023    Online Published: September 1, 2023 

doi:10.22158/ees.v6n3p21               URL: http://dx.doi.org/10.22158/ees.v6n3p21 

 

Abstract 

A 1 metre increment modelled pressure profile is used to study the troposphere of Venus from the 

surface to the lower stratosphere. Using a troposphere model lapse rate profile as the constraint on 

cooling by vertically convecting air, the modelled height of the tropopause convection limit is a close 

match to the level of the observed static atmosphere height for the 250 Kelvin freezing point level of 

75% by weight of concentrated sulphuric acid, the primary condensing volatile in the Venusian 

atmosphere. This relationship suggests that the observed albedo of Venus is a response to and not a 

cause of planetary atmospheric solar radiant forcing. 

Using the thermal lapse rate for the troposphere of Venus in its top-down mode of application, the 

depth below the tropopause that solar irradiance is able to achieve effective heating of the Venusian 

atmosphere is established. This radiant quenching depth delineates a pool of upper tropospheric air 

that both captures and responds to solar radiant forcing. Consequently, this top of the troposphere 

insolation forcing induces a process of full troposphere adiabatic convective overturn and delivers 

solar heated air to the ground via the action of forced air descent in the twin polar vortices of Venus. 

Keywords 

Venus atmosphere, Boyle’s law, spherical shells, thermal heating pool, adiabatic convection 

 

 

 

 

 



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1. Introduction 

Close proximity observations of the planet Venus by the NASA Mariner 10 space probe in 1974 have 

shown that its upper atmosphere displays a set of cloud bands that are part of a global atmospheric 

circulation system, which connects the solar zenith point of maximum solar radiant forcing to both 

polar vortices of the planet (Figure 1). 

 

 

Figure 1. NASA 1974 Mariner 10’s Portrait of Venus 

 

This paper develops the results of the application of the Dynamic-Atmosphere Energy-Transport 

((DAET) mathematical model to a study of the climate of Venus (Mulholland & Wilde, 2020) and 

addresses the following two issues: 

1) That the intensity of the dim sunlight is too weak to fully energise the surface of the planet Venus at 

the base of a 63.4 km thick troposphere. 

2) Consequently, the temperature at the base of the atmosphere of 699 Kelvin (426
O
C) (Singh, 2019, pp. 

1-5) has a value that far exceeds the effective solar radiative thermodynamic temperature of the surface 

insolation received by Venus (Table 1). 

 

 

 

 

 

 



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Table 1. Venus Lit Hemisphere Illumination Interception Geometry 

Location
Latitude 

(Degrees)

Elevation 

Angle 

(Degrees)

Sine Angle

Solar Power 

Intensity 

(W/m2)

Effective Flame 

Temperature 

(Kelvin)

Quenching 

Limit Height 

(Km)

Air Pressure 

(hPa)

North Pole 90.00 0 0.00000000 0.00

Z1: Heating 

Limit 
86.43 3.57 0.06226276 37.25 160.10 110.000

Z1: 85 5 0.08715574 52.15 174.14 88.092 0.37

Z1: 80 10 0.17364818 103.89 206.89 76.617 5.84

Z1: 75 15 0.25881905 154.85 228.60 70.502 20.89

Z1: 70 20 0.34202014 204.63 245.10 64.669 64.11

Z1: 65 25 0.42261826 252.85 258.41 61.065 123.05

Z5: Hemisphere 

Average Flux
60 30 0.50000000 299.15 269.51 58.461 192.90

Z1: 55 35 0.57357644 343.17 278.92 56.454 269.32

Z1: 50 40 0.64278761 384.58 286.97 54.850 348.82

Z1: 45 45 0.70710678 423.06 293.90 53.540 428.56

Z1: 40 50 0.76604444 458.32 299.84 52.461 505.92

Z1: 35 55 0.81915204 490.10 304.91 51.570 578.81

Z1: 30 60 0.86602540 518.14 309.18 50.839 645.33

Z1: 25 65 0.90630779 542.24 312.71 50.247 703.99

Z1: 20 70 0.93969262 562.22 315.55 49.798 751.53

Z1: 15 75 0.96592583 577.91 317.73 49.474 787.52

Z1: 10 80 0.98480775 589.21 319.27 49.244 813.95

Z1: 5 85 0.99619470 596.02 320.19 49.107 830.05

Z1: Equator 0 90 1 598.30 320.50 49.061 835.52

Illumination Intensity versus Solar Elevation

 

 

At its base Venus has a dense atmosphere with a value of 69.69 kg/m
3
 (Table 2), while this is far less 

than the density of liquid water (1,000 kg/m
3
), the oceans of Earth do provide a model as to how the 

topside of a planetary atmosphere can be heated. On Earth the photic zone is that shallow part of the 

ocean (typically less than 200 m water depth) where sunlight energy is absorbed and the water is 

heated. 

On Venus the average post-albedo insolation received by the lit hemisphere is 299 W/m
2
, which 

equates to a thermodynamic temperature of 269.5 Kelvin (-3.6
O
C) (Figure 2). This average intensity 

will apparently provide heating for only the upper 5 km of the troposphere at heights above 58.4 Km, 

where the lapse rate reduced air temperature is below the 269.5 Kelvin value (Figure 3). 

 



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Figure 2. Venus Lit Hemisphere Illumination Interception Geometry 

 

At depths in the atmosphere below this average insolation level the average energy contained in the 

sunlight is less than the ambient temperature of the surrounding air, so no heating is apparently possible. 

However, and perhaps more importantly the local intensity of the insolation at solar zenith has 

sufficient power to heat the Venus atmosphere down to a level of 49 km, in a column that is 14.4 km 

thick (Figure 3). 

 

 

Figure 3. Venus Atmospheric Solar Radiant Thermal Heating Pool 

 



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It is this concentration of energy at the solar zenith, heating the upper air that creates the bow-wave 

disruptor observed in the centre of the blue disk, as the thermal impact of the solar zenith travels 

around the planet (Figure 1). 

The energy imparted by the sun into that zenith induced bow-wave powers the circulatory system of the 

upper atmosphere (Limaye, 2010). So, just like the sun heats the top of the Earth’s oceans, the sun 

clearly heats the top of the Venus atmosphere. However, unlike water in the Earth’s oceans the heated 

topside atmosphere of Venus is a compressible gas held at high elevation in a gravity field. This has 

clear implications for the process of surface heating by full troposphere mass-motion solar forced 

convection overturn of a compressible gas in the presence of a gravity field. 

In order to study this circulation process using the DAET climate model a pressure profile model for 

the Venus troposphere at 1 metre increments has been created. This calculation has been applied from 

the surface to the lower stratosphere, a modelled vertical height of 100 kilometres (Mulholland & 

Wilde, 2021). 

Two equations of state are used to achieve this objective, these are the Pressure, Volume, Temperature 

(PVT) version of Boyle’s law, and the application of Newton’s gravity law of spherical shells, used to 

calculate the reduction in strength of the gravity field as the height above the surface of Venus 

increases. For the purpose of this study a set of four linked predictive lapse rate equations based on 

published data has been created (Justus & Braun, 2007). These equations are used as the fundamental 

temperature control of the tropospheric pressure profile. The temperature data that controls these 

equations is calibrated to a surface datum global average temperature for Venus of 699 Kelvin (Singh, 

2019, pp. 1-5). 

 

2. Method 

The spreadsheet analysis of the pressure profile of the Venusian atmosphere presented here is built on 

the following Baseline Parameters (Williams, 2023): 

1) The surface pressure measured in Pascal. 

2) The surface temperature measured in Kelvin. 

3) The Molecular Weight of the Venus atmosphere measured in g/mole. 

4) The surface gravity of Venus measured in m/s
2
. 

5) The planetary mass of Venus in kg. 

6) The mean radius of Venus in metres. 

 



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Figure 4. Venusian Atmosphere: Temperature versus Altitude 

 

7) A set of four predictive temperature Lapse Rate equations for the atmosphere of Venus based 

on published data (Justus & Braun, 2007) measured in K/m and corrected to a surface datum 

value of 699 Kelvin (Singh, 2019, pp. 1-5) (Figure 4). 

8) Using the two physical relationships of Boyle’s gas law, and Newton’s spherical shell gravity 

law, a pressure profile is created for the atmosphere, applying the predictive lapse rate equations 

as temperature control over the relevant height intervals (Figure 5). 

The predictive lapse rate equations used in the pressure profile model are listed in Table 2. 

 

 

 

 

 

 

 

 

 

 

 

 



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Table 2. Predictive Lapse Rate Equations 

Item Height (m) Predictive Temperature Lapse Rate Equation
Temperature 

(Kelvin)

Pressure 

(hPa)

Density ρ 

(kg/m3)

LR1: Lapse Rate: Start of 

Troposphere Equation
0 =-7.967*I2/1000+699 699.000 93,219.00 69.69140601

LR1: Lapse Rate Tie Point: End of 

Troposphere Equation
39,220 =-7.967*I39222/1000+699 386.534 3,001.63 4.058083903

LR2: Lapse Rate Tie Point: Start of 

Solar Heating Convection Equation
39,221 = -6.71*I39223/1000 + 649.7 386.527 3,001.27 4.057677378

LR2: Lapse Rate Tie Point: End of 

Solar Heating Convection Equation
50,000 = -6.71*I50002/1000 + 649.7 314.200 729.81 1.213822584

LR2: Lapse Rate Tie Point: Start of 

Tropopause Convection Overshoot  

Equation

50,000 = -6.71*I50002/1000 + 649.7 314.200 729.81 1.213822584

LR2: Lapse Rate: End of Tropopause 

Convection Overshoot  Equation
70,000 = -6.71*C20032/1000 + 649.7 180.000 16.67 0.048388192

LR3: Lapse Rate Tie Point: Start of 

Tropopause Breaking  Equation
50,001

= 0.092*(I50003/1000)^2 - 15.26*I50003/1000 + 

847.2
314.194 729.70 1.213669421

LR3: Lapse Rate Tie Point: End of 

Tropopause Breaking  Equation
70,477

= 0.092*(I70479/1000)^2 - 15.26*I70479/1000 + 

847.2
228.686 20.99 0.04796827

LR4: Lapse Rate Tie Point: Start of 

Stratosphere  Equation
70,478

=( 0.0027*(I70480/1000)^3 - 0.5809*(I70480/1000)^2 

+ 38.611* (I70480/1000)- 537.31)+(-

0.0146*(I70480/1000)^2 + 1.594*(I70480/1000) - 

54.84)

228.683 20.99 0.047959369

LR4: Lapse Rate: End of 

Stratosphere  Equation
100,000

=( 0.0027*(I100002/1000)^3 - 

0.5809*(I100002/1000)^2 + 38.611* (I100002/1000)- 

537.31)+(-0.0146*(I100002/1000)^2 + 

1.594*(I100002/1000) - 54.84)

173.350 0.01588 4.78577E-05

 

 

The datum parameters used for the pressure profile analysis are listed in Table 3. 

 

Table 3. Datum Values 

Surface Pressure 92 Atmospheres

Control used at L2 Surface Pressure 9,321,900 Pascal

Area 1 Square metre

Force 9,321,900 Newton

Used in Column T Universal Gravitational Constant 6.67430E-11 m
3
.kg

-1
 .s

-2

Boltzmann constant 1.38065E-23 J/K

Avagadro constant 6.02214E+23 mol-1

Varied in Column T Venus Gravity 8.87039 m/s2

Used at U2 Atmospheric Mass 1,050,901 Kg

Used in Column M Molecular Weight 43.45 g/mol

Used at M2 Surface Density 69.691 Kg/m3

Notional QC Check Total "Thickness" (Scale Height) 15,079 m

Control used at J2 Surface Temperature 699 Kelvin

STP Temperature 273.15 Kelvin

STP Temperature 0 Celsius

Used in Column J LR1: Lapse Rate (Troposphere) Predictive Equation K/m

Used in Column J LR2: Lapse Rate (Tropopause) Predictive Equation K/m

Used in Column J LR3: Lapse Rate (Stratosphere) Predictive Equation K/m

Z9: Pressure Tropopause 100 hPa or mbar

Z9: Tropopause 100 hPa 62.232 Km

Z9: Tropopause 100 hPa 253.84 Kelvin

Air Properties Earth STP Venus Units

Pressure 101,325 9,321,900 Pascal

Pressure 1,013 93,219 hPa or mbar

Temperature 273.15 699 Kelvin

Temperature 0 425.85 Celsius

Volume 22,414 623.458 cm3

Density 1.939 69.691 Kg/m3

Lapse Rate Convection Troposphere 7.270 K/km

Datum Values

Key Pad

 

 

 

 



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3. Result 

In order to verify the DAET climate model of Venus, the model was first calibrated against the new 

surface datum temperature of 699 Kelvin (Singh, 2019, pp. 1-5). This process was achieved by 

reducing the energy intensity flux partition ratio to an atmosphere retained percentage of 98.071%, 

down from the previously published value of 99.1138% (Mulholland & Wilde, 2020, pp. 20-35). This 

adjustment is in line with the modelling concept that the average global surface temperature of a planet 

is a function of the energy flux partition ratio between the retained atmospheric energy in the 

troposphere, and the radiant energy loss to space from the stratosphere (Table 4). 

 

Table 4. Adiabatic Model of Venus showing Internal Energy Recycling for Both Hemispheres 

 

 

The key results from the Boyle’s Law Pressure Model Analysis for the atmosphere of Venus 

(Mulholland & Wilde, 2021) are listed in Table 5 and displayed in Figure 5. 

These results include the following: 

1) The average post-albedo irradiance for the lit hemisphere of Venus is 299 W/m
2
, this intensity 

(Table 1, Z5) converts to a thermodynamic temperature of 269.5 Kelvin (-3.6
O
C). This 

temperature occurs at an altitude of 58.46 Km and a pressure of 192.9 hPa. By geometry the 

average intensity value of 299 W/m
2
 also occurs at a solar elevation angle of 30

o
 (Figure 2). 



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2) The post-albedo solar zenith irradiance for Venus is 598.3 W/m
2
, this maximum possible 

intensity (Figure 3, Z1) converts to a thermodynamic temperature of 320.5 Kelvin (47.3
O
C). This 

temperature occurs at an altitude of 49.06 Km and a pressure of 835.5 hPa (Table 5). 

 

Table 5. Predicted Pressures 

Item Height (m) Predictive Temperature Lapse Rate Equation
Temperature 

(Kelvin)

Pressure 

(hPa)

Density ρ 

(kg/m3)
PE =mgh (Joules)

Z6: Mean Air Temperature (699 

Kelvin)
0 =-7.967*I2/1000+699 699.000 93,219 69.69140601 0

Z1: Solar Zenith (albedo applied) 49,061 = -6.71*I49063/1000 + 649.7 320.501 835.52 1.362326292 583,372

Z5: Space Incoming Captured 

Radiation (W/m2)
58,461

= 0.092*(I59315/1000)^2 - 15.26*I59315/1000 + 

847.2
269.512 192.90 0.374026892 190,285

Z8: Night Tropopause 63,240 = -6.71*I63242/1000 + 649.7 225.360 76.31 0.176958051 97,234

Z9: Tropopause Ceiling 100 hPa, 

235.84 Kelvin, 62.232 Km
62,232

= 0.092*(I62234/1000)^2 - 15.26*I62234/1000 + 

847.2
253.839 100 0.205873161 111,356

Z10: Mean Tropopause 63,337 = -6.71*C13369/1000 + 649.7 224.709 74.83 0.174025191 95,766

Z11: Lit Tropopause 63,433 = -6.71*C13465/1000 + 649.7 224.065 73.39 0.171162378 94,331

Z12: Dark Side Radiant Partition is  

1.0929% (W/m2)
71,156

=( 0.0027*(I71158/1000)^3 - 0.5809*(I71158/1000)^2 

+ 38.611* (I71158/1000)- 537.31)+(-

0.0146*(I71158/1000)^2 + 1.594*(I71158/1000) - 

54.84)

226.299 18.33 0.042334801 26,106

Z13: Mean Radiant Exit 

Temperature (Kelvin)
71,062

=( 0.0027*(I71064/1000)^3 - 0.5809*(I71064/1000)^2 

+ 38.611* (I71064/1000)- 537.31)+(-

0.0146*(I71064/1000)^2 + 1.594*(I71064/1000) - 

54.84)

226.631 18.68 0.043076419 26,529

Z14: Space Outgoing Radiation 

Balance (W/m2) 
71,062

=( 0.0027*(I71064/1000)^3 - 0.5809*(I71064/1000)^2 

+ 38.611* (I71064/1000)- 537.31)+(-

0.0146*(I71064/1000)^2 + 1.594*(I71064/1000) - 

54.84)

226.631 18.68 0.043076419 26,529

Z15: Vacuum Planet Equation 

Expected Te of Venus (226.627 

Kelvin)

71,063

=( 0.0027*(I71065/1000)^3 - 0.5809*(I71065/1000)^2 

+ 38.611* (I71065/1000)- 537.31)+(-

0.0146*(I71065/1000)^2 + 1.594*(I71065/1000) - 

54.84)

226.627 18.68 0.043068467 26,525

Z16: Lit Side Radiant Partition is  

1.0929% (W/m2)
70,985

=( 0.0027*(I70987/1000)^3 - 0.5809*(I70987/1000)^2 

+ 38.611* (I70987/1000)- 537.31)+(-

0.0146*(I70987/1000)^2 + 1.594*(I70987/1000) - 

54.84)

226.902 18.97 0.043692829 26,880

Z17:r Rising Air Droplet Cloud Tops 

(260 Kelvin)
58,077 = -6.71*C9600/1000 + 649.7 260.003 201.35 0.404689223 204,558

Z17:s Stable Air Droplet Cloud Tops 

(260 Kelvin)
60,673

= 0.092*(I60675/1000)^2 - 15.26*I60675/1000 + 

847.2
260.002 131.82 0.264950232 139,792

Z18:r Rising Air Latent Heat 

Freezing Point of 75%wt H2SO4 

(250.0 Kelvin)

59,568 = -6.71*C9600/1000 + 649.7 249.999 154.26 0.322448865 167,091

Z18:s Stable Air Freezing Point of 

75%wt H2SO4 (250.0 Kelvin)
63,266

= 0.092*(I63268/1000)^2 - 15.26*I63268/1000 + 

847.2
249.999 82.97 0.173424014 95,331

 

 



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Figure 5. Venusian Tropopause: Temperature versus Altitude 

 

3) The DAET adiabatic climate model of Venus predicts for the lit hemisphere a thermal 

emission intensity (Table 4, Z16) of 150.4 W/m
2
 and a thermodynamic temperature of 226.9 

Kelvin (minus 46.3
O
C). This temperature occurs at an elevation of 70.99 Km and at a pressure of 

19 hPa (Table 5). 

4) The DAET adiabatic climate model of Venus also predicts for the dark hemisphere a thermal 

emission intensity (Table 4, Z12) of 148.75 W/m
2
 and a thermodynamic temperature of 226.3 

Kelvin (minus 46.8
O
C). This temperature occurs at an elevation of 71.15 Km and at a pressure of 

18.33 hPa (Table 5). 

5) The modelled height of the Venusian droplet cloud planetary veil (Z17: s) occurs at an 

elevation of 60.67 Km and a temperature of 260 Kelvin (Young, 1973, pp. 564-582) with an 

associated pressure of 18.33 hPa (Table 5). 

6) The measured freezing point of 75% wt H2SO4 (Z18:s) is 250 Kelvin (-23
O
C) (Young, 1973, 

pp. 564-582). This temperature is found at a model altitude of 63.27 Km, and a pressure of 83 

hPa (Table5). This near association between the stable air freezing point of concentrated 

sulphuric acid, the main condensing volatile in the Venus atmosphere, and the DAET modelled 

height of the convection tropopause warrants further study. Solid aerosol particles are efficient 

thermal emitters and can enhance atmospheric thermal radiation loss to space through the 

transparent lower Stratosphere (Figure 4). 

 



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3.1 The Energy Consequence of Air Convection in a Gravity Field 

At the modelled convection tropopause of Venus, over 63.3 km above the planet’s surface (Table 5, 

Z10), a cubic metre of Venusian air has a mass of 174 g and possesses a potential energy of 95.7 

Kilojoules. All air mass held aloft in a gravity field contains a considerable quantity of potential energy. 

On descent to the surface this air will undergo adiabatic heating and consequent air temperature rise as 

it falls towards the planet’s surface. In doing so it loses potential energy by the process of conversion to 

kinetic energy (Figure 6). 

 

 

Figure 6. Scaled Comparison Chart of Pressure, Gravity, Discrete Mass, Discrete Potential 

Energy (PE) and Cumulative PE Curves for Venus 

 

4. Discussion 

On Venus the solar forced radiant heating of the upper troposphere at the zenith creates a process of 

pole-ward advection of heated air that feed the planet’s polar vortices (Luz et al., 2011). Figure 2 shows 

how the upper atmosphere of the lit hemisphere of Venus intercepts the energy of the sunlight in a 

pattern of concentric rings of intensity centered around the zenith, the point at which the overhead sun 

provides the maximum flux that heats the atmosphere. When the sun heats the cold upper part of the 

Venusian atmosphere it will distort the lapse rate slope to the warm side. That forces the lapse rate 

profile downward. That compression then steepens the lapse rate slope lower down which causes 

convection to accelerate as a negative compensation mechanism. 

 

 



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As Venus slowly turns from east to west, the locus of the solar zenith tracks along the equator towards 

the east creating a point of disturbance in the upper air. This forms a bow shockwave disruptor dividing 

the equatorial flow of the zonal circulating winds which are forced apart and made to track towards 

higher latitudes (Figure 1). 

Due to the conservation of angular momentum associated with the slow planetary rotation of Venus, 

these winds travel faster than the ground surface below them and are called super-rotation winds 

(Zasova et al., 2007). Eventually these circulating winds reach the planet’s poles at a point on the rim 

of the lit hemisphere. Here the illumination intensity of the low angle sun within 5
O
 of the terminator 

does not have sufficient power to heat the tropospheric air. At the poles of Venus, the low power of the 

sunlight, combined with the angular momentum of the super-rotational winds creates a cyclonic vortex 

which drives the air down into the deep atmosphere below (Ignatiev et al., 2009). 

 

 

Figure 7. Planetary Rotation and the Conservation of Angular Momentum 

 

This forced descent of the topside heated air, means that the compressible air undergoes adiabatic 

heating as it falls in the gravity field of Venus. The descending mass flow within the polar vortex 

provides a hydrodynamic piston drive that causes the planet’s air to circulate vertically in a giant 

hemisphere encompassing Hadley cell (Figure 3). By this means the compressed air is heated as it falls 

and the apparent thermal limit set by insolation at the top of the atmosphere is easily surpassed (Lacis 

& Hansen, 1974). 

Figure 3 shows the impact of upper atmosphere heating, the circulation system powered by the solar 

zenith constantly replenishes the forced descent vortex over both poles which heats the surfaces 

beneath. That energy then flows across the entire Venusian surface so that it can reach temperatures 

much higher than predicted by the Stefan-Boltzmann (S-B) radiation equation. The greater the mass of 

the Venus atmosphere the greater the system’s efficiency, and the more heat that will be delivered to 

the surface by the air descent at the poles. 

 



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The piston-like hydrostatic circulation is fuelled by whatever energy is available from any source, but 

can never exceed the amount of energy required to balance the upward pressure gradient force with the 

downward force of gravity. The pattern of differing lapse rate slopes within the vertical plane is 

infinitely variable, but must always average out to the slope dictated by mass and gravity. 

4.1 The Utility of the DAET Climate Model 

The key physical process that the DAET climate model describes is that mobile compressible fluids 

circulating within a gravity field over and above the surface of a rotating terrestrial planet, will at the 

same time capture, store and transport energy in various guises. Not all of these are thermal and so not 

all are subject to radiative loss. While energy can flow from cold to hot (e.g., the meteorological 

process of cooling rain falling onto the surface of a hot desert below), however heat being a directed 

dynamic process cannot flow from cold to hot (e.g., Unconfined rivers of water cannot flow uphill). 

Mass motion is a process that generates a system lag because it is inherently slower than radiative 

processes. Convection is also a process that deals with albedo variations because convection just shifts 

to equalise these perturbations. There is still enough room for internal climate variability as the system 

lags somewhat in response to destabilising influences, but it always gets there quickly enough to retain 

the atmosphere in a dynamically stable state. 

The Venus surface is at the temperature it is simply because that is the temperature needed to balance 

the mass of the atmospheric gases against gravity. It makes no difference what the source of that energy 

is. It is the same for stars in the cold of space and the gas planets far from the sun. Convection always 

settles at a level that keeps the gases suspended against the downward force of gravity. Until, in the 

case of stars, a fusion reaction starts whereupon convection adopts a new equilibrium. 

It is by this mechanism of circulating mass motion of a compressible gas acted on by a gravity field, 

within the context of a rotating spherical planet that surface thermal enhancement is created, and which 

it is proposed here to call the Maxwell Mass Effect after the work of James Clerk Maxwell (Maxwell, 

1868). 

 

 

 

 

 

 

 

 

 

 

 



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5. Conclusion: The Venus Heating Paradox Explained 

In conclusion the matter of the high surface temperature of the planet Venus, and the paradox of the dim 

surface sunlight not being able to create this 699 Kelvin global average temperature will now be 

addressed. 

The process of deep atmospheric convection throughout the whole 62.2 km (100 mbar limit) of the Venus 

troposphere means that sunlight heated air at the top of the atmosphere can and does deliver heat to the 

planet’s surface. Instead of solar radiation, this process of energy delivery to the surface occurs by the 

mechanisms of full troposphere planetary rotation-forced mass-motion, the circulation of polar vortex 

descending air and heating by adiabatic auto compression. 

The warming at the surface of Venus is from the mechanical process of convection, and any potential 

warming effect from downward radiation is neutralised by convective adjustments. Instead, descending 

air heats both itself and the surface beneath via reconversion of Potential Energy (PE) to Kinetic Energy 

(KE). The atmosphere is held aloft by potential energy which is not thermal energy. Heat cannot be 

amplified, but it can be stored in a non-kinetic form as potential energy so that it is not then sensed as 

temperature. 

Potential energy is in effect a form of Latent Heat. This store of energy within mass is then returned again 

as temperature at a later time and critically at a lower elevation. So, as long as there is constant mass 

motion recycling to and fro between PE and KE as the air moves vertically within a gravity field, then the 

surface will receive kinetic energy from the descending air and be warmed. 

To maintain long term hydrostatic equilibrium the total energy retained at the surface must be a dynamic 

equilibrium that is just right to support the weight of atmospheric gases against the downward force of 

gravity. It makes no difference whether the source of the necessary energy is from the sun, the surface, 

volcanic outbreaks, atmospheric opacity, particulate aerosols or anything else. 

It is known that planetary atmospheres vary hugely in composition, and that the way the composition of 

an atmosphere is sorted into differing compositional layers will affect the vertical boundaries between 

those layers. Thus, a tropopause can vary in height somewhat depending on the various compositionally 

induced stratifications within a planet’s atmosphere. However, if an atmosphere is to be retained by a 

planet, then the average lapse rate slope between surface and space must always net out to the slope 

specified by mass and gravity. 

Convection always adjusts in order to balance energy into the system from space with energy out to space 

derived from the net combination of all energy transfer mechanisms between surface and atmosphere. If 

it were not so then the tiniest radiative imbalance would prevent the formation and retention of an 

atmosphere. It is known that atmospheres are ubiquitous and last for geological eons in the absence of 

catastrophe, so it must be that convection neutralises all “normal” radiative imbalances. 

 

 



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However, the DAET concept needs to apply to every scenario, whatever the density or opacity of an 

atmosphere the final outcome must be the same, and the cause will be a combination of heating of upper 

levels and heating of the surface with the proportions related to atmospheric opacity to radiation. It is a 

universal rule of meteorology that any temperature induced density variations in the vertical plane will 

lead to convective overturning in the entire depth of an atmosphere, with consequent heating of the 

surface. 

When the energy present in a mass aloft is converted from PE (not thermal) to KE (thermal) by forced 

descent then that solves the problem of the apparent radiative limit. Radiation does not limit the 

mechanical transformation of energy between PE and KE in convection. Climate theorists who have been 

fixated on radiation miss this point. Potential energy is a form of latent heat. Kinetic energy (motive heat) 

is the direct consequence of the conversion of potential energy during the descending phase of convective 

overturning. 

As the case of Venus proves insolation does not need to reach the surface to provoke planetwide deep 

convection. It is sufficient if insolation beneath the solar zenith creates density differentials at any point 

within the mass of an atmosphere. Convection can achieve that because radiative imbalances alter the 

lapse rate slope and the rate of convection changes in a negative response to this forcing (Wilde, 2012).  

 

References 

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Almeida, M., & Manoel, N. (2009). Altimetry of the Venus cloud tops from the Venus Express 

observations. Journal of Geophysical Research: Planets, 114(E9). 

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Jenkins, J. M., Steffes, P. G., Hinson, D. P., Twicken, J. D., & Tyler, G. L. (1994). Radio occultation 

studies of the Venus atmosphere with the Magellan spacecraft: 2. Results from the October 1991 

experiments. Icarus, 110(1), 79-94. https://doi.org/10.1006/icar.1994.1108 

Justus, C. G., & Braun, R. D. (2007). Atmospheric Environments for Entry, Descent, and Landing 

(EDL). NASA Natural Environments Branch (EV13). 

Lacis, A. A., & Hansen, J. E. (1974). Atmosphere of Venus: Implications of Venera 8 Sunlight 

Measurements. Science, 184(4140), 979-982. https://doi.org/10.1126/science.184.4140.979 

Limaye, S. S. (2010). Measuring winds on Venus and other planets. In 10th International Wind 

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Maxwell, J. C. (2009). 1868. XXII. On the dynamical theory of gases. The London, Edinburgh, and 

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Mulholland, P., & Wilde, S. P. R. (2020). Inverse Climate Modelling Study of the Planet Venus. 

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Singh, D. (2019). Venus nightside surface temperature. Scientific reports, 9(1), 1-5. 

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Wilde, S. P. R. (2012). The ignoring of Adiabatic Processes—Big Mistake. Tallbloke’s Talkshop. 

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Williams, D. R. (2023). NASA Venus Fact Sheet Venus/Earth Comparison Fact Sheet NSSDCA. Mail 

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Appendix 

The Pressure Profile Calculation Method: 

Starting with the Gas Equation: 

P1.V1/T1 = P2 V2/T2  Equation 1 

Where: 

P1 Is the Initial Gas Pressure measured in Pascal. 

V1 Is the Initial Gas Volume measured in Litres. 

T1 Is the Initial Gas Temperature measured in Kelvin. 

P2 Is the Final Gas Pressure measured in Pascal. 

V2 Is the Final Gas Volume measured in Litres. 

T2 Is the Final Gas Temperature measured in Kelvin. 

In the Troposphere as height above the surface increases, air pressure and air temperature both decrease. 

In the open atmosphere the air pressure decrease is a function of air mass and gravity, while the 

temperature decrease, the Lapse Rate, is a measured known parameter (Jenkins et al., Fig. 4., 1994). 

This then leaves the change in volume with height as the one variable to be calculated. 

Equation 1 can be rearranged to give Volume in terms of Pressure and Temperature 

https://doi.org/10.1080/14786446808639963
https://doi.org/10.11648/j.ijaos.20200401.13
https://doi.org/10.1038/s41598-018-38117-x
https://doi.org/10.1016/0019-1035(73)90059-6
https://doi.org/10.1016/j.pss.2007.01.011


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V2 = P1.V1.T2/T1 /P2  Equation 2 

The next issue to be resolved is to determine the rate of pressure reduction with height. 

In a column of air, the pressure is a function of the overlying mass, so if that the atmosphere is 

modelled as a stack of one metre cubes of air, then for each one metre rise in height the mass of the 

overlying column will be less, and so this mass reduction will cause a pressure reduction which can be 

calculated. 

Pressure is a force; it is defined as the product of mass times acceleration. In the atmosphere the 

acceleration acting on the air parcel at rest in the column is the planet’s gravity at that level, and this 

can be determined by Newton’s gravity law of spherical shells. The value of the surface gravity of a 

planet can be calculated by using the Universal Gravity Equation, and knowing the planet’s mass and 

its average radius. 

But a standard measured quantity of gas is also required. 

To do this the process used by chemists to find the relationship between the mass in grams and the 

volume in litres (dm
3
) at Standard Temperature and Pressure (STP) for one mole of gas has been 

adopted here. 

At 273.15 Kelvin (0
o
C) and 1013.25 hPa (mbar) the volume is 22.414 litres (dm

3
) and so for air with a 

molecular weight of 43.45 g/mol (standard Venus atmospheric composition) the mass contained in 

molecular volume (22.414 dm
3
) will be 43.45g. 

Phase 1: Building the Pressure Ladder for the Venus Atmosphere. 

Step 1: From knowledge of the surface pressure of the Venusian atmosphere and the value of the 

surface gravity of Venus, compute the total atmospheric mass in a column bearing down on 1 square 

metre of the planet’s surface. 

Using the equation of force F = m.a this equation can be restated as Pressure/Gravity = Mass 

For Venus the equation of state is: 

9,321,900/8.87039 = 1,050,990.969 kg (1,051 tonnes/sq metre). 

Step 2: Compute the volume change for I mole of gas from STP at the Earth’s surface to the ambient 

temperature and pressure conditions on the surface of Venus. 

Using the constant Pressure Volume Temperature relationship of P1.V1/T1 = P2.V2/T2 this establishes 

the unknown V2 (the volume of 1 mole of gas at the surface of Venus). 

V2 = P1.V1.T2/T1 /P2 

V2 = 101,325 * 22.414 * 699 / 273.15/9,321,900 = 0.623 Dm
3
 (Litres) 

Step 3: Compute the density of the unit mole of compressed gas at the surface of Venus under ambient 

surface conditions. 

Using the standard formula: Density = Molecular Weight/Volume 

Surface Density = 43.45 / 0.623 = 69.691 Kg/m
3
. 

Step 4: Convert the Gas Density to Discrete Mass of Gas per Unit Metre Cube. 



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Discrete Mass = 69.691 Kg 

Step 5: Establish the Mass of Gas in the Atmospheric Column lying above this Unit Cube. 

Mass Bearing Down = Column Mass minus Unit Mass 

Mass Bearing down at 1 metre elevation = 1,050,900.969 – 69.691 = 1,050,831.277 Kg. 

There is now sufficient information to begin climbing the Pressure Ladder of the Venus Atmospheric 

Profile at Unit Steps of 1 metre increment. 

Phase 2: Climbing the Pressure Ladder of the Venus Atmosphere. 

Step 1: Compute the new P2, The Base Pressure of the Overlying Column of Gas. 

Using the standard equation of Force: F = m.a where m is the mass of the overlying column and a is the 

value of gravity at the surface of Venus. 

P2 = 1,050,831.277 * 8.87039 = 9,321,282 Pascal 

Step 2: Compute the new value of T2 one metre above the base surface temperature of Venus using the 

relevant predictive Tropospheric Lapse Rate equation in K/m and inputting the height value h where h 

is the full distance above the surface in metres. 

T2 = 699-7.967*h/1000= 698.9920 Kelvin 

Step 3: Compute the new value of V2 at one metre elevation using the standard Pressure Volume 

Temperature relationship V2 = P1.V1.T2/T1 /P2 

V2 = 9,321,900 * 623.458 * 698.9920/699.0000 / 9,321,282 = 623.492 cm
3
  

N.B. The Volume increase for V2 is due to the reduction in Pressure P2 (which increases volume) 

dominating over the reduction in Temperature T2 (which decreases volume) in the equation for each step 

up the ladder. 

Step 4: Compute the Density of the New Unit Cube of Gas. 

Using the standard formula: Density = Molecular Weight/Volume 

New Density = 43.45/623.492* 1,000 = 69.68758 Kg/m
3
. 

Step 5: Convert the New Gas Density to Discrete Mass of Gas per Unit Cube. 

Discrete Mass = 69.688 Kg 

Step 6: Subtract the Discrete Unit Cube Mass from the Column Mass at this level to give the overlying 

Column Mass Bearing down on this Unit Cube. 

Overlying Mass = Current Column Mass minus Unit Mass 

Bearing Down Mass = 1,050,831.277 – 69.688 = 1,050,761.590 Kg 

Step 7: Use Newton’s Gravity Law of Spherical Shells and set M2 to be the unit mass to compute the 

reduced value of planetary gravity at this new increment of 1 metre elevation. 

The required information to climb one step of the ladder and continue the calculation cycle is now 

known. The bearing down Mass at the top of the unit cube defines the Pressure at the base of the next 

unit cube above. 

Step 8: Return to Step 1 and continue climbing the Pressure Ladder by 1 metre increments. 


