Global Warming: Heat transfer model

So much for GHG debate but without calculation model and in-depth theory open for public. Was IPCC tell the truth or was the cool head right? We have no right to judge unless we know the science behind their theory. I write this journal base on self research of Green House Effect mode. This won’t be an easy digest but I made this journal just for the sake of science

Fig. 1: IPCC initial Global temperature extrapolation

At the very origin when term global warming emerge. The very first version of GHG model as in Fig. look like ultimate exponential increase of temperature until the whole planet melt down. How they made this model? Simple extrapolation like all us learn in Form 5 -6. They take data from 1980 – 1999 and make correlation of CO₂ and temperature. Then they project the CO₂ increase per year assume it is all from our energy usage. This model was later found to be totally wrong. So, they move on to newer model with more accuracy.

Fig. 2: Revised model for GHG vs temperature

IPCC learn the effect of heat transfer and  realize the temperature can’t rise without limit. This is about time that the term Green House Effect took the name instead of Global Warming. The famous “Inconvenience Truth” by Algore is  base on this IPCC model. While the model suggested the temperature raise by 8 ^oC, many scientist doubt “was it accurate”.

Green House Effect Modelling

Most Green House Effect result published was influenced from Radiation Heat Transfer model claimed by Global Warming Scientist from Intergovernmental Panel on Climate Change (IPCC). 

This is how it works

• Radiation from Sun at certain wavelength absorbed by the GHG’s band gap. The absorb radiation will be release at all direction in the same manner as Blackbody Radiation.
• Remain radiation from Sun will be absorb and reflect depend on Earth’s Albedo (It absorb 60% of radiation and reflect out 40% of incident Sun light)
• Heat from Earth’s core transfer from Magma under earth to the surface in Conduction heat transfer.
•  Earth’s surface emitted thermal radiation out to space. Some of the radiation will be absorb by GHG regard to GHG’s spectrum band gap.
• Radiation from 4) will add up to earth energy intake and adjust for new Blackbody temperature.
•  Equilibrium temperature obtained when Earth and GHG energy in-out balance with its’ temperature.

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In general, the model would look like this.

Fig. 3: Darth Prin’s Green House Effect model

Knowledge require for construction of GHG model

1. Radiation and Radiation band-gap
2. Maximum absorbable radiation portion of GHG base on spectrum profile of heat source
3. Atmosphere height and overall GHG Absorption
4. Conduction Heat transfer 

Nomenclature

1. Radiation and Radiation band-gap

Radiation from Sun or Earth is form of Black Body Radiation where the energy concentration release varies with wavelength and surface temperature. The Equation as follow.

Construct the graph using Planck's black body radiation, it should notice the peak at 400 nm for the temperature of 5500 K at Sun’s surface. For earth temperature or around 273 K, the peak is at 10,000 nm and is in the infrared region. Higher earth temperature might shift the radiation peak to the left and so the absorption of GHG might be differ from such shift. Point to note here is, emission wavelength depend on the temperature.

Fig. 4: Solar irradiation spectrum

The effect of cloud that reflects off the solar radiation is estimated at 75% of the incident radiation to reflect off by cloud from cloud coverage of earth.

2. Maximum absorbable radiation portion of GHG base on spectrum profile of heat source

Portion of light GHG may absorb must be within the absorption wavelength of such GHG. For CO₂, the portion is around 300 and 400 nm for example. My calculation is base on J.N. Howard data.

Fig. 5: Absorption spectrum of various GHG gases

It is to point out that the Methane band gap at 300 nm and 750 nm was covered by water absorption, at 100% absorption of water band gap and beyond, no future absorption is possible at this wavelength. However, for CO₂, the band gap at approx 400 nm is not covered by water and is contribute to greenhouse effect.

3. Atmosphere height and overall GHG Absorption

Existence of Greenhouse gases in atmosphere can express as the partial pressure and atmospheric height. Absorptivity and Emissivity do effected by temperature. Correlation of emissivity due to the atmospheric height (L), temperature (T) and Partial pressure of water (P_w) and carbondioxide (P_c) is as followed.

Absorptivity is related to emissivity by following relation

The wall temperature refer to the Sun surface which is differ from the temperature of GHG. The temperature scaling of emissivity allows the finding of net absorptivity over path from Sun to Earth. The net absorption and emission from GHG (Water + CO₂) will be in following manner. 

Where we know q max is portion of radiation visible to such GHG, the value exceed the portion can be told that it absorb to the full quota of absorbable portion of the gas species.

Fig. 6: Combine Radiation band gap

Combine Radiation band gap (fig. 4) with absorption spectra (fig. 5). The Red colour show full spectrum of solar radiation where the blue portion show what can’t be absorb by GHG, The graph would read that, of 1400 W/m² radiation incident on earth,  GHG can effected about 10% of net energy balance. 

4. Conduction Heat transfer from earth core 

Earth core is a fission nuclear reactor and it supply portion of energy to earth surface. The amount of energy transfer to earth surface can estimate from magma temperature and crust thickness. The portion of heat may be considered very small but in any case, it is added for us to see total Earth energy balance.

Since earth thickness is very thin relative to earth diameter, I neglect the shape factor and presume dx = average earth crust thickness = 25,430 km. Magma temperature is 1,473 K in this calculation.

The Simulation

Simulation written by my favourite Ms-Excel. It doesn’t need multi-million software and computer to calculate the GHG model. Every private researcher can make it DIY.

Fig. 7: GHG model calculation

The result

§  Effect of water vapour: Without atmosphere, average earth temperature would be at 3 ^oC. For water vapour of 100 ppm, however, is sufficient to bring earth temperature up to 19 ^oC.

Fig. 8: Effect of Water on global temperature

§  Effect of CO₂: Carbon dioxide mainly effected the return radiation from earth to space. It is found that from current CO₂  level of 380 ppm, if it go up to 1,000 ppm then the net temperature increase is approximately 1.7 ^oC. This value doesn’t agree with IPCC but very agree with the real observation data.

Fig. 9: Effect of Carbon dioxide on global temperature

Fig.10: Compare IPCC with observation data

So.. What is going on here

1. Though I couldn’t accurately know what is in the IPCC model that is differ to observation figure at such extend. However, by adjust the band gap addition of CO₂  and H₂O to my model, it is found the increase of net temperature. I personally suspect IPCC climate model did add the radiation gap of CO₂ that is overlapped with H₂O into calculation. It is possible that IPCC might take methane band gap into calculation, where I already point out that the radiation band gap of methane is totally overlapped with water.
2. It must note that with increase temperature, cloud formation would be thicker and that might be the reasons that even my model, temperature increase is still smaller than actual data. Cloud reflect off solar radiation and the water movement in water cycle is a heat pump transfer heat from ground to the space.
3. Consider the increase of energy transfer, it found that with little temperature it increase (0.3% refer to absolute scale), the energy transfer increase at greater scale in order of 10% from 300 ppm to 600 ppm. It suggests that global warming is not the matter of temperature increase but change of energy equilibrium. Increase of energy transfer would mean more violent tide, rain and storm. The scenario of ice cap melting is possibly bullshit but the El Niño and La Niña... that is very possible.
4. Temperature relation to CO₂  present in ppm is totally wrong. Increase temperature is not linear with ppm CO₂, temperature may go up with CO₂ concentration but limited to no more than +6 ^oC (or even lower if considered cloud effect). It should consider heat transfer increase rather than a degree Celsius of temperature increase.

Fig. 11: Detail global energy balance

In the End

From the construction of model to show the effect of Water and Carbon dioxide contribution to green house effect, it doesn’t need very high or very deep knowledge. The knowledge need is taught in Heat transfer where all Mechanical and Chemical Engineer should have learnt. I hope that any graduated engineer would do research for this matter and understand how PETA bullshit on the methane using IPCC mistake. 

Fig.12: Darth Prin Energy balance

References

• J.P. Holman “Heat Transfer” 7th ED, McGrawHill
• “Perry’s Chemical Engineering Handbook” 8th ED, McGrawHill
• Thermal Radiative Transfer and Properties
• http://www.john-daly.com/artifact.htm
• http://www.btinternet.com/~robertjtucker/gas_emissivity.htm
• http://en.wikipedia.org/wiki/File:Atmospheric_Transmission.png
• http://en.wikipedia.org/wiki/Greenhouse_effect
• http://en.wikipedia.org/wiki/Absorptivity
• http://en.wikipedia.org/wiki/Beer–Lambert_law
• http://asd-www.larc.nasa.gov/~kratz/ref/p14jgr.pdf
• http://csep10.phys.utk.edu/astr162/lect/light/radiation.html
• http://www.meteo.mcgill.ca/bourqui/

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