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Do not be led by others,
awaken your own mind,
amass your own experience,
and decide for yourself your own path.
The Atharva Veda

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Brindabella Archives Summary The Brindabella Archives are nonfiction writings on Science, Technology, and Society.

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Personal odds and ends from past sites.

./Dai/photos (1y 4w 3d ago, 9 files)
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./Dai/photos/Digging Sticks.html (1y 4w 3d ago, size: 1382 bytes)
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./Dai/photos/Young Possom.html (1y 4w 3d ago, size: 2079 bytes)
./OCM (1y 5w 1d ago, 6 files)
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Untitled Page The Open Climate Modeller (OCM) is an interactive Javascript visualisation package for exploring the Earth's surface-atmosphere energy dynamics.
Select the OCM.html file to run it now, or download the OCMdemo.zip file.
Unzip it then open in a local browser. Local use recommended for Javascript programmers only. Check code safety for yourself.

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./OCM/OCMdemo.zip (1y 5w 2d ago, size: 158555 bytes)
./OCM/plots (1y 5w 1d ago, 2 files)
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./Science ( 38w 4d ago, 70 files)
./Science/Climate ( 18w 1d ago, 59 files)
./Science/Climate/Atmosphere (1y 8w 5d ago, 6 files)
./Science/Climate/Atmosphere/-Notes (1y 1w 6d ago, 0 files)
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This article, Energy and Atmosphere, looks at the energy dynamics of the Earth's atmosphere. Since the role of radiative gasses has become a political issue that is undermining the stability of industrial economies and denying the many benefits of cheap and reliable energy to billions of people, the precise nature of the energy dynamics of our atmosphere has become a trillion dollar question.

It shows a new derivation for the adiabatic temperature lapse rate in the atmosphere.
It also points to a possible explanation for why the Earth's water thermostat cuts in so suddenly at 30 Cº.

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./Science/Climate/Atmosphere/Energy&Atmosphere.pdf (2y 19w 3d ago, size: 529340 bytes)
./Science/Climate/Atmosphere/Lapse Rates.html (1y 2w , size: 11383 bytes)
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./Science/Climate/Climate PP/-comments.html (2y 18w 3d ago, size: 306 bytes)
./Science/Climate/Climate PP/-summary.html (1y 2w , size: 141 bytes)

Climate – A Personal Perspective is an early overview article looking at things and events that have influenced my views on climate.

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./Science/Climate/ClimateTruth&Certainty/TruthAndCertainty.pdf (2y 17w 2d ago, size: 131955 bytes)
./Science/Climate/Diurnal-Smoothing-Effect.pdf ( 18w 2d ago, size: 238052 bytes)
./Science/Climate/HallOfInfamy.pdf (1y 42w 5d ago, size: 73439 bytes)
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./Science/Climate/IPCC-CO2 (1y 8w 5d ago, 5 files)
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 The IPCC and the Carbon Cycle
We are told by the IPCC that CO2 emissions from burning fossil fuels are causing atmospheric CO2 levels to rise and that these are causing global warming. Of the two links in this chain of reasoning this article addresses the first.

I show that the IPCC view of the carbon cycle is fundamentally flawed in many ways, and is not supportable at any meaningful level of confidence. This is not esoteric science to be left to specialists or ‘great minds’. Any numerate person who cares to look and think can understand the insignificance of our total industrial era CO2 emissions at less than 1% of the carbon cycle and our annual emissions at just 5% of the air-sea fluxes.

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./Science/Climate/IPCC-CO2/IPCC-CO2.pdf (2y 16w 4d ago, size: 956187 bytes)
./Science/Climate/Lapse Rates (1y 8w 5d ago, 6 files)
./Science/Climate/Lapse Rates/-Notes (1y 1w 6d ago, 0 files)
./Science/Climate/Lapse Rates/Lapse Rates.html (2y 16w 3d ago, size: 11534 bytes)

Determination of the gravitational lapse rate

Determination of the gravitational lapse rate

Dai Davies
brindabella.id.au
PERPETUAL DRAFT, 160912a

The fundamental dynamic process in the energy dynamics of the atmosphere is the creation of the lapse rate – the rate that the temperature drops with increasing altitude in the troposphere – below the tropopause marked by a dotted line in Figure 1 where the Earth curve follows a straight line. The tropopause is not a fixed height. It can vary from close to zero altitude at the poles to over 20 km at the equator. It varies in time, and thunderstorms can push it up locally. A typical height is said to be 11 km.

Some people think that the lapse rate is entirely due to radiative gasses (aka greenhouse gasses) and without them the atmosphere would have a constant temperature all the way up – be isothermal. The Postmodern view of the radiative dynamics of the atmosphere is based on this assertion.

It is a plausible first assumption, since we know that hot air rises. We might even expect to have cold air at the bottom and hot at the top, except that the atmosphere is mainly heated from the bottom. The problem is that these views are based on thermodynamics for laboratory conditions, which generally ignores gravity because the effect of gravity over small height changes is negligible. 


Figure 1: Atmospheric temperatures (1)

There are several definitions of lapse rate and some confusion in their use, so I'll start by giving definitions as I prefer to use them:

The ALR is usually calculated from the thermodynamics of a parcel of air rising up through the troposphere. Air can't be adiabatic. Adiabatic means no energy is lost or gained by the gas parcel, which excludes radiative gasses which would transfer infrared energy in and out of the parcel, so the ‘dry’ is superfluous. The ALR applies only to an idealised mixture of gasses such as nitrogen and oxygen that are not radiative at atmospheric temperatures, so it is a theoretical abstraction. It provides the foundation of the actual lapse rate, which is modified by the addition of RGs. Thermodynamics gives a formula for calculating the lapse rate:

Γth = g/cp(E1)

Where g is the gravitational acceleration and cp is the specific heat of air at constant pressure – a measure of the amount of energy needed to raise the temperature of the gas. 

I find the derivation of this formula too opaque. It hides the basic physics, which has caused a great deal of confusion and controversy (note b). After being resolved over a century ago, the issue has surfaced again in recent years in an effort to exaggerate the role of radiative gasses. 

In this essay I go down to the level of individual molecules and give an alternative derivation for the ALR. The basic physics is simple. If you throw a ball into the air its energy can be given as the sum of its energy of movement – its kinetic energy, EK – and its gravitational potential energy, EP, minus energy lost to friction with the air, which can be ignored if the ball is in a vacuum. It moves up until all its energy is potential energy, then starts to fall and regain it. 

E = EK + EP = mv2/2 + mgh(E2)

Where m is the mass of the ball, v is its velocity or speed, h is its height, and g is the gravitational acceleration. 

An insight into the lapse rate problem can be gained from the fact that a ball falling in a vacuum from a hight of 11 km has a velocity at ground level of 464 m/s, which is precisely the mean velocity of air molecules at 20 Cº (2), and 11 km is a typical hight of the tropopause. This, and the suggestive g in E1, was the starting point that prompted me to try the following analysis. 

Between collisions, the molecules that constitute air behave just like the ball. Having a molecule falling in a vacuum may not seem relevant when we're considering the atmosphere, but between collisions with other molecules they actually are all falling in a vacuum, or close enough for a simple analysis. All the molecules are following a parabolic path and gaining a little downward energy between collisions. Those moving down will gain kinetic energy, and those moving up will lose it. This produces a gradient with the average kinetic energy of molecules decreasing with increasing altitude – in other words, a temperature gradient.

Eventually our falling molecule will hit other ones, and the energy it has gained in falling will be passed on to them. The gravitational energy will be thermalised – added to the random motion of other molecules, to their kinetic energy, until an equilibrium is established. 

If you want to skip the detail, go to E5. The next step is the most technical one because we aren't dealing with billiard balls colliding. We have to divide the added energy among all the degrees of freedom of the molecules, f. This is the standard equipartition rule dictated by entropy – the energy will distribute between all possible modes for storing it. Nitrogen and oxygen have 5 degrees of freedom at atmospheric temperatures. That's 3 for the directions of motion and 2 for rotational motions – spin and tumbling – rotation around the axis joining the two atoms doesn't count. I'll call this fm

During a collision we also have to consider the resulting energy distribution between the two colliding molecules. That's four nuclei and around 30 electrons. This needs to be seen from a quantum mechanical perspective as the transient formation of a four atom molecule which passes – slowly by atomic standards – through a sequence of vibrational and rotational quantum states as it tries to form then breaks up – a process which determines the final distribution of energy between the molecules, and gives 2 more degrees of freedom, fc.

The temperature of a gas is related to its kinetic energy by:

EK = fkT/2(E3)

where T is the temperature and k is Boltzmann's constant. The energy gained by a molecule falling a distance ∆h is mg∆h (the deltas indicating related changes) so partitioning this among the available degrees of freedom we get:

∆E = mg∆h = fk∆T/2(E4)

After a little manipulation we have the temperature gradient or lapse rate as:

Γg = ∆T/∆h = 2mg/(fm + fc)k(E5)

Plugging in some numbers, m is taken as the average mass of nitrogen and oxygen in air weighted by their relative proportions of 79:21. 

Comparing the two approaches, using a value for g adjusted slightly for a mean troposphere altitude of 5.5 km reduces it by about 0.8% from the usual surface value, and cp is taken as the measured value of 1.0035.

E1 gives 9.73 Cº/km. 

E5 gives 9.66 Cº/km.

Within 1% difference they are close, given that the real world doesn't usually comply exactly with simple physical theory. 

Next, I demonstrate the theoretical equivalence of the gravitational lapse rate and the conventional derivation, so if the theoretical value for cp is used in E1 the two approaches give exactly the same result. 

Equating Γth with Γg  – for those who are comfortable with some simple algebra and cryptic physics. I'm assuming a perfect monomolecular gas.

Starting with E5: Γg = 2mg/(fm + fc)k.

Substituting M/NA for m, where M is the molecular mass of the molecule and NA is Avagadro's number gives:

Γg = 2Mg/NA(fm + fc)k(E6)

Substituting R/NA for k, where R is the gas constant, gives:

Γg = 2gM/(fm + fc)R(E7)

Now looking at the conventional derivation in E1: Γth = g/cp

We can derive a theoretical value for cv starting with cvm, the molecular heat capacity:

Combining cvm = fmR/2, cpm = R + cvm, and cp = cpm/M gives:

cp = (fm + 2)R/2M(E8)

Substituting this in E1 we get: 

Γth = 2gM/(fm + 2)R(E9)

So with fc = 2 in E7 we have: 

Γg = Γth(E10)

The two derivations for the adiabatic lapse rate are theoretically equivalent. That these two distinct approaches can be shown to reduce to the same dependence on g provides strong confirmation of the role of gravity in the base lapse rate. 

The addition of radiative gasses produces, effectively instantaneous, energy transfer by radiation over average distances of tens of metres at ground level, increasing to kilometres through to infinity – to outer space –  at the tropopause as the air gets thinner.

References:

  1. Robinson T.D., Catling, D.C., Common 0.1 bar tropopause in thick atmospheres set by pressure-dependent infrared transparency, Nature Geoscience Letters, 8 December 2013 

  2. www.pfeiffer-vacuum.com/en/know-how/introduction-to-vacuum-technology/fundamentals/thermal-velocity/

./Science/Climate/Lapse Rates/Lapse Rates.pdf (2y 18w 3d ago, size: 159006 bytes)
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./Science/Climate/Natural Cycles (1y 8w 5d ago, 4 files)
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Plot from the southern Sea Surface Temperature modelling.
See the SST images archive in the images branch. A description of this project is forthcoming.

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./Science/Climate/RadiativeDelay ( 21w 5d ago, 11 files)
./Science/Climate/RadiativeDelay/-Notes (1y 4w 3d ago, 4 files)
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The article Radiative Delay in Context challenges a core assumption of the contemporary climate science consensus, that the Greenhouse (or Radiative Delay) Effect is the sole mechanism by which the Earth's atmosphere raises the Earth's surface temperature above that which would exist without an atmosphere.

In it I show that the Radiative Delay heating of the atmosphere is negligible, and a well established alternative mechanism arising from atmospheric buffering over the diurnal temperature cycle is capable of producing the temperatures we experience.

The role of Carbon Dioxide is shown to be negligible.

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./Science/Climate/RadiativeDelay/RadiativeDelayInContext180818.pdf ( 21w 6d ago, size: 244143 bytes)
./Science/Climate/Sea Surface Temperature (1y 8w 5d ago, 2 files)
./Science/Climate/Sea Surface Temperature/-Notes (1y 8w 5d ago, 0 files)
./Science/Climate/Sea Surface Temperature/-summary.html (2y 18w 2d ago, size: 109 bytes)

Forthcoming article: a technical description of the SST modelling discussed in the article Natural Cycles.

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This is a personal view of the political nature of the CO2 scare from an environmentalist who has watched on in dismay at the extreme politicisation of the environment. I watched the takeover of the environment movement since the 1970s by the extreme left acting with motives that have nothing to do with reducing our environmental impact.
Moving forward we see the actions of the totalitarian left in the United Nations and associated NGOs forming the Intergovernmental Panel on Climate Change (IPCC), and how this has perverted the already corrupted nexus between science and public policy.

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./Society/Politics/ClimatePolitics.pdf (2y 19w 1d ago, size: 115087 bytes)
./Society/Politics/Empathy and Autism.html (1y 8w 5d ago, size: 10315 bytes)
./Technology ( 29w 3d ago, 18 files)
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Untitled Page

Technology Archives

Most significant article: Personal Archives

Related articles: Knowledge Systems and Conflict,
Knowledge Futures (refers to deprecated WordMuller software)

More technical (Natural language Processing):
nlp-all.pdf, NLP-Parser.pdf, NLP-Inference.pdf

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./Technology/Knowledge Futures.html (1y 2w , size: 8365 bytes)
./Technology/Knowledge Systems and Conflict.html (1y 2w , size: 17910 bytes)
./Technology/LegacySoftware.html ( 29w 4d ago, size: 752 bytes)
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./Technology/NLP-DataStructures.pdf (8y 48w 3d ago, size: 150699 bytes)
./Technology/NLP-Inference.pdf (8y 48w 3d ago, size: 195013 bytes)
./Technology/NLP-Parser.pdf (8y 48w 3d ago, size: 182984 bytes)
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./Technology/PersonalArchives.pdf ( 38w 5d ago, size: 141111 bytes)
./Technology/SLabView.zip (6y 2w 1d ago, size: 351234 bytes)
./Technology/SLabView Intro.html (1y 5w 4d ago, size: 6822 bytes)
./Technology/SpeechDecisionTree.pdf (5y 22w 2d ago, size: 25855 bytes)
./Technology/TWM-Performance-Usability.pdf (5y 22w 1d ago, size: 307247 bytes)
./Technology/Time in ASR.pdf (5y 22w 1d ago, size: 310440 bytes)
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