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My Climate Science Journal

By

Ian Beardsley

Copyright © 2014 by Ian Beardsley

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I am taking Climate Science online at MIT. I take copious notes,and try to put things in the most understandable terms formyself. I would like to share what I am learning, because I thinkhumanity does not face a more important subject than this one,today. I find, with a little work, some of the basic conceptsbehind the climate process really can be made more accessibleto the non-scientist beyond just saying burning fossil fuelswarms the planet. I think putting things in their simplestterms, without losing the dynamics, which can be done with alittle work, is key to the success of humanity.

Ian BeardsleyMarch 14, 2014

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How Climate Works

The incoming radiation from the sun is about 1370 watts persquare meter as determined by the energy per second emittedby the sun reduced by the inverse square law at earth orbit.  Wecalculate the total absorbed energy intercepted by the Earth'sdisc (pi)r^2, its distribution over its surface area 4(pi)r^2 andtake into account that about 30% of that is reflected back intospace, so the effective radiation hitting the Earth's surface isabout 70% of the incoming radiation reduced by four. Radiativeenergy is equal to temperature to the fourth power by theStefan-boltzmann constant. However, the effective incomingradiation is also trapped by greenhouse gases and emitted downtowards the surface of the earth (as well as emitted up towardsspace from this lower atmosphere called the troposphere), themost powerful greenhouse gas being CO2 (Carbon Dioxide) andmost abundant and important is water vapour.  This doubles theradiation warming the surface of the planet.  The atmosphere ispredominately Nitrogen gas (N2) and Oxygen gas (O2), about95 percent.  These gases, however, are not greenhouse gases. The greenhouse gas CO2, though only exists in trace amounts,and water vapour, bring the temperature of the Earth up fromminus 18 degrees centigrade (18 below freezing) to an observedaverage of plus 15 degrees centigrade (15 degrees abovefreezing). Without these crucial greenhouse gases, the Earthwould be frozen.  They have this enormous effect on warmingthe planet even with CO2 existing only at 400 parts per million. It occurs naturally and makes life on Earth possible.  However,too much of it and the Earth can be too warm, and we are nowseeing amounts beyond the natural levels throughanthropogenic sources, that are making the Earth warmer thanis favorable for the conditions best for life to be maximallysustainable.  We see this increase in CO2 beginning with theindustrial era.  The sectors most responsible for the increase arepower, industry, and transportation.  Looking at records of CO2amounts we see that it was 315 parts per million in 1958 androse to 390 parts per million in 2010.  It rose above 400 in2013. Other greenhouse gases are methane (CH4) and NitrousOxide (N2O). Agricultural activities dominate emissions fornitrous oxide and methane.  A healthy earth is one that is in

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radiative equilibrium, that is, it loses as much radiation as itreceives. Currently we are slightly out of radiative balance, theEarth absorbs about one watt per square meter more than itloses.  That means its temperature is not steady, but increasing.

The solar luminosity is:

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L0 = 3.9 ×1026J /s

The average distance of the Earth from the Sun is:

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1.5 ×1011m

Therefore the solar constant is:

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S0 =3.9 ×1026

4π(1.5 ×1011)2=1,370watts /meter2

That is the amount of energy per second per square meterhitting the Earth.

The radiation, F, is proportional to the temperature, T to thefourth power, and equal by the Stefan-Boltzman constant,sigma:

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F =σT 4

σ = 5.67 ×10−8Wm−2K −4

This gives the temperature, T, at the top of the Sun’sphotosphere is:

T=6,000 degrees Kelvin

The planetary albedo, a, is the amount of radiation from the Sunthat the Earth reflects back into space which is 30%. Thereforea=0.3 is the planetary albedo. Therefore the Earth receives 70%of the Sun’s light, or, in other words:

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S0(1− a)πr2

4πr2=S04(1− a) =σT 4

T = 255K = −18oC

That is the temperature the Earth would be if it had noatmosphere, minus eighteen degrees centigrade. The observedaverage temperature is:

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T =15oC

Fifteen degrees centigrade.

Let us look at a simple model if there is an atmosphere:

We have same amount of radiation entering system as leaving,that is, sigma T to the fourth effective equals sigma T to thefourth of the atmosphere:

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σTe4 =σTa

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Sigma T of the surface to the fourth = amount of radiationcoming in from the sun, sigma T effective to the fourth plus theamount of radiation coming down from the atmosphere, sigma Tof the atmosphere to the 4.

This is the greenhouse effect.

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Radiative Equilibrium

Top Of Atmosphere:

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σTa4 =

S04(1− ap ) =σTe

4

Surface:

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σTS4 =σTa

4 +S04(1− ap ) = 2σTe

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TS = 21/ 4Te = 303K ≈ 30degC

This is actually warmer than the average annual temperature ofthe surface of the earth. Reasons why are real atmosphere isnot opaque and heat is transported as well by convection.

In reality almost twice as much radiation is received from theatmosphere than from incoming radiation from the sun. Thisshows the power of the greenhouse effect. Most of the cooling isin the evaporation of water, especially in the tropics. Most ofthe radiation is radiated in the subtropics where there are noclouds.

But we have not considered the emissivity, epsilon, of theatmosphere. It is the amount of radiation absorbed by theatmosphere that is emitted. We apply the same principle asabove, but include epsilon:

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S0(1−α)4

= εσT 4 earth

Alpha is the planetary albedo, which is about 33% and S not isthe solar constant, which is closer to 1,350 than our earlierapproximation. Intensity up from atmosphere plus intensitydown from atmosphere equals intensity up from the ground, or:

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2εσT 4atmosphere = εσT 4groundTground = 21/ 4Tatmosphere ≈1.2Tatmosphere

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The calculation yields 295 Kelvin for the Earth, and thatobserved is 251 Kelvin. Thus with a simple one layeratmosphere model, we have closely predicted the planet’stemperature. Venus with an albedo 71% yields 240 Kelvin butin reality is 700 Kelvin. The discrepancy is in its higherabundance of greenhouse gases responsible for a runawaygreenhouse effect. Mars, with an albedo of 17% yields 216degrees Kelvin but is observed to be 240 degrees Kelvin.Venus=2600, Mars=259, and Earth = 1350 for solar constants inwatts per square meter. Epsilon for earth is about 96%-99%.

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Climate Defined: Climate is the statistics of the weatherincluding not just the average weather, but also the statistics ofits variability, commonly calculated over periods of a year ormore. The progression of seasons is not considered an exampleof climate variability. Separating signal from the noise isseparating climate from the weather. That is we can say it willbe warmer in the summer than in the winter, but we can’tforecast the weather for any particular day.

Climate is determined by (1) the energy balance betweenincoming solar radiation and outgoing infrared radiation. Thatbalance is affected by greenhouse gases, or the composition ofthe atmosphere, in other words. (2) atmospheric and oceanicconvection, the flow or transfer of heat within varioussubstances like, water (the ocean) or gases (the atmosphere).(3) Looking at climate change through geologic time, as a recordof climate is embedded in the geological record, the substancesthat were in the atmosphere during an ice age in other wordsare recorded in the strata, which can be dated, so we can usethis information to model where the climate is going.

Climate Cycles

Five billion years ago, when the earth and sun formed, the sunwas much cooler than it is today, with an output of about 0.7 ofits present output. Yet we know that water existed on the earthin liquid form, when it should have been ice. This is known asthe Faint Young Star Paradox; the Earth should have beenfrozen up to 2.5 billion years ago.

Five hundred and fifty million years ago the Earth went throughclimate swings, being a snowball and then free of ice. SnowballEarth can be accounted for by positive feedback. Albedo is thepercent of incoming radiation that is reflected into space. Snowhas a higher albedo, so glaciation, or increased snow, increasesthe albedo of the earth making it emit more radiation back intoa space making it cooler which, in turn, makes more snow,which increases the albedo still more, until you get a runawayicehouse, or Snowball Earth.

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Fifty million years ago the earth reached its thermal maximum(Paleocene-Eocene). It took 20,000 years to develop, and100,000 years to go away. The earth is cooling from thatthermal maximum 50 million years ago.

For the past three million years glacial cycles have been goingon with a periodicity of about 20,000 to 100,000 years. Theyare due to orbital dynamics of the earth. They are the glacial-interglacial cycles caused by eccentricity of the Earth orbit,which is a cycle of one hundred thousand years, the obliquity ofthe earth or change in tilt which is a cycle of 41 thousand years,and precession or wobble of the earth’s spin, which has a cycleof 22 thousand years. The story of the earth has been a story offreezing over for 100,000 years, then briefly warming. We havebeen in one of these short warm periods for the past 10,000years, called the Holocene, and it would seem it is responsiblefor the beginning of civilization 7,000 years ago. The last icecover was about 18,000 years ago.

Composition Of The Atmosphere Through Time

The early Earth Atmosphere was probably predominantlyhydrogen and helium (H2, He) but was lost to space. The lateratmosphere was due to volcanic emissions, and impact bycomets and meteorites (H20, CO2, SO2, CO, S2, Cl2, N2, H2,NH3, CH4). Oxygen came later as a by-product of livingorganisms. The origin of CO2 was volcanic emissions. It wasabsorbed by water forming carbonic acid, was deposited in thesoil, then underwent reactions to become calcium carbonate:

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H2O+CO2 →H2CO3(soil)H2CO3 +CaSiO3 →CaCO3 + SiO2 +H2O

Lifetime of substances in the atmosphere is given by:

Abundance (Gton)/Emissions (Gtons/year) = Lifetime (yr)

CO2 has a lifetime in the atmosphere of 100 years. CO2 exists invegitation, soils, oceans, atmosphere and sediments. Lifetime

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relies in the simple model above relies on abundance andemissions are constant, that they are equilibrium processes.

Structure Of The Atmosphere

Divided by vertical gradient of temperature, there are fourlayers to the Earth Atmosphere:

Troposphere at 10-18 kilometers, Stratosphere ending at 50kilometers, Mesosphere ending at 85 kilometers, then theThermosphere.

80% of the mass is in the troposphere. In climate science wedeal mostly with the troposphere, and a little with thestratosphere.

Heat Distribution Over The Earth, where heat is gained, whereheat is lost.

Most of the warming is in the continents, Africa, South America,Canada, Asia. We should see a cooling of the lower stratospherewhen we have a warming of the lower troposphere as a part ofradiative balance of the planet. Raising the temperature onedegree centigrade of a cubic meter of sea water requires 4,000times more energy input than to raise a cubic meter ofatmosphere one degree. Water has a high specific heat, that is ittakes one calorie to raise a gram of it one degree centigrade.That is one factor that keeps the Earth from getting too warm.The vast majority of change in the energy climate system hasgone into the ocean, mostly into the upper 700 meters. Waterexpands when you increase its temperature, like mostsubstances, and the sea rise we are seeing is in part due to that.But most is due to the melting of land ice. Most of the land massin the Northern Hemisphere, so, in the spring, when there is alot of plant growth in the Northern Hemisphere, there is a dropin CO2. Annually, anthropogenic emissions increase CO2 byabout nine gigatons or 900 terragrams. This is only about 1% ofthe burden, but it must be remembered that is annual andincreases with time.

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Precipitation is the product of condensation of water vapor thatfalls under gravity, like rain, sleet, snow, hail,…

Most of the CO2 is absorbed by the ocean and the decrease itsPH, making it more acidic. What are the effects on the corralreefs and plankton?

The temperature is pretty much constant in the tropicsthroughout the year. Prevalence of ocean in the southernhemisphere keeps that area relatively stable.

During the spring and summer foliage comes out and absorbsCO2, then when leaves fall, and decay, that CO2 is returned tothe atmosphere in the Fall. Most cooling is in evaporation ofwater, especially in the tropics. Radiation is absorbed in thetropics and emitted in the poles. The Ocean and the atmospheretransport absorption in the tropics to the poles, where it isemitted. The tropics absorb more radiation than they emit andthe poles emit more radiation than they receive.

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If radiation comes in at an angle to a surface, its amount per unit area is the projection ofthe vector upon the normal to the surface, that component which is in that direction, inother words. A beam of radiation with intensity I sub lamda is the amount of radiationpassing through a surface area, dA, within a solid angle d-Omega per wavelength intervalper unit time where dE/dt is the amount of energy per unit time, so we have:

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Iλ =dE

cosθdAdΩdλdt

And, we say the flux density is the normal component of intensity integrated over allsolid angles, or:

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Fλ = IλΩ

∫ cosθdΩ

Total flux density is the flux density integrated over all wavelengths:

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F = Fλ0

∞

∫ dλ

And, the total flux is the integral of the total flux density over area and is the radiantpower in watts:

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f = FdAA∫

A blackbody is one that absorbs all incoming radiation and follows Planck’s Law fortemperature.

Blackbody radiation is the radiant intensity one would observe under ideal conditions oflocal thermodynamic equilibrium. It turns out to be an excellent approximation forabsorption and emission by our atmosphere, except maybe at high latitudes. It followssomething called Planck’s Law:

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Bλ (T) =2hc 2

λ5[ehc /λkT −1]

k is botzmann’s constant, h is planck’s constant, lambda is wavelength, c is the speed oflight, B sub lambda is blackbody radiant intensity, and T is temperature.

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Emission of radiation by atoms is due to incoming light changing the orbit of electronsaround the nucleus. If they fall in from a higher energy orbit to a lower one, they emitphotons at the corresponding wavelength, or color. If light makes them jump to a higherenergy orbit, as in the case of absorption, they absorb at the corresponding wavelength.

Compounds and molecules have more methods of absorbing and emitting than atomsbecause they can move in more ways, however N2 and O2 are transparent to radiationbecause they are homonuclear diatomic (composed of identical atoms). They aretransparent to radiation because there is no dipole moment due symmetricity (nodifference between center of charge and center of mass).

But in other non-symmetric gases they can have many vibrational and rotational modes.There are all kind of energy transitions possible for absorption and emission.

Polyatomic Molecules

3N-6 Vibrational Modes (N the number of atoms)

And many rotational and vibrational modes. Vibrational Modes of the plentifulgreenhouse gas H2O:

O-H symmetric stretchingH-O-H bendingO-H asymmetric stretching

Important to radiative transfer is Kirchoff’s Law. That is emission and absorption are thea same for gases at same temperature:

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aλ = ελ

That is, absorptivity equals emissivity.

Summary:

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Etotal = Eatomic + Evibratonal + Erotational + Etranslational

E is energy.

Scattering Of Radiation (types of scattering)

Rayleigh Scattering, Mie Scattering for small particles, Mi scattering for large particles.

The sky is blue because of scattering of shortwavelenghts. Reddening at sunset isbecause red wave lengths are more penetrative.

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Radiative Equilibrium

Modeling temperature as a function of altitude (Leaving out convection at this stage).How long does it take the atmosphere in a given state to relax to a radiative equilibrium?It takes a long time in the Earth’s atmosphere to be achieved. It takes a few tens of daysfor the troposphere to come into radiative equilibrium. Order of 100 days for thestratosphere. It takes tens if not hundreds of days for an atmosphere out of radiativeequilibrium to come into equilibrium.

The cooling of the stratosphere means global warming is due to CO2 and not a warmingsun, because it should cool when the troposphere warms, by models. Taking out C02leads to warming of the stratosphere because it must get hotter to radiate same amount ofenergy it could with CO2.

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March 25, 2014 Climate Science, Convection

We refine our model by including convection. Convection is heat transport by movementof a mass of fluid from one place to another. In climate physics it is the vertical transferof heat by rising warm air and sinking cool air. Our model is too hot at or near thesurface of the earth, too cold at a near tropopause, lapse rate of temperature is too large introposphere, however the stratosphere model is close. We must look at convection, it isvery important. It is as important as radiation in transporting enthalpy in the vertical andcontrols water and vapor clouds, which are the two most important aspects to radiativetransfer. The mechanism is warmer substances are less dense and less dense substancesrise because they have less per volume for gravity to act on them. When they cool, theysink.

Stability

In a valley a ball will roll down a hill until it settles at the lowest point, which is anequilibrium state, or solution. Another equilibrium solution is when the ball is perchedon top of a hill with valleys on either side; it won’t go out of equilibrium until it is pushedin either direction, in which case it would roll down a hill.

Hydrostatic Equilibrium

Gravity accelerates a gas downward, net pressure makes it rise upwards.

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wiegt = −gρδxδyδzρ = densityg = gravityδxδyδz = volume = ΔVpressure : pδxδy − (p +δp)(δxδy)or : pΔA − (p + Δp)(ΔA) = pressureΔA = Area

Pressure is force per unit area and that above is the net pressure, the pressure at thebottom of the box minus that at the top. Pressure being force per unit area gives forcewhen multiplied by area.

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mass = m = ρδxδyδz = ρΔV

dwdt = m d2z

dt 2= −g(ρδxδyδz) − (δpδxδy)

clearlydwdt

= −g −α ∂p∂z

α = specific _volume =1/ρ = volume /mass

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The Ideal Gas Law says pressure is proportional to temperature:

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α =RTp

Combining our two equations (of motion and pressure:

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−g −α ∂p∂z

= −g − RTp∂p∂z

= 0

1p∂p∂z

= −gRT

pressure = pT = temperature

This is the hydrostatic equation for an ideal gas at rest in a gravitational field. Weintegrate the equation, and:

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p = p0e−2 / H

H ≡RTg

= scale_ hieght

For_ Earth _H ≈ 8km

We assert the pressure in the vertical of the atmosphere is approximately exponential.The real atmosphere is not isothermal, the temperature varies, but not over a a hugefraction.

Buoyoancy

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dwdt

= −gρbδxδyδz −δpδxδy

ρb = density _of _ fluiddwdt

= −gαb∂p∂z

∂p∂z

= −g /αe

dwdt

= gαb −αe

αe

≡ B

Alpah sub b and alpha sub e are specific volumes of fluids, b in the sample, e thesurrounding environment. B is buoyancy.

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If the fluid in the box, or sample is less dense than the fluid in the surroundingenvironment (has a larger specific volume) it will accelerate upwards. It is Archimede’slaw. We can determine whether a density in a gravitational field will be stable.

Adibiatic Sample (No Heat Is Added Or Subtracted)

Buoyancy And Entropy

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specific _volume :α =1/ρspecific _entropy : sα = α(p,s)

Specific volume is a function of pressure and entropy. By the chain rule and usingMaxwell’s Law (from first law of thermodynamics):

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(δα)p =∂α∂s

⎛

⎝ ⎜

⎞

⎠ ⎟ p

δs =∂T∂p⎛

⎝ ⎜

⎞

⎠ ⎟ s

δs

B = g(δα)pα

=gα

∂T∂p⎛

⎝ ⎜

⎞

⎠ ⎟ s

δs = −∂T∂z⎛

⎝ ⎜

⎞

⎠ ⎟ s

δs = Γδs

Γ = adiabiatic _ lapse_ rate

The sample will be positively buoyant if its entropy exceeds that of its environment.

Adiabatic Lapse Rate (From First Law of Theromodynamics And Ideal Gas Law)

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Q•

= T dsdt

= cv dTdt

+ p dxdt

Q•

= total_ heatingcv = heat _capacity

Q•

= cpdTdt

−αdpdt

= 0 : adiabatic

cpdT + gdz = 0 : hydrostaticdTdz

= −gc≡ Γd : adiabatic _ lapse_ rate ≈1

oC /100m =1K /100m

Γ =gcp

cp = cv + R

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If entropy doesn’t change at all, there is neutral stability. Entropy decreases with altitudethen the sample is positively buoyant (unstable) and accelerates upward. Entropyincreases with altitude results in entropy less than its environment, and would benegatively buoyant and would accelerate downwards, and that state is stable.

The radiative equilibrium of the troposphere if you calculate its entropy, you find itdecreases upward. So with decreasing entropy with altitude, it is unstable. The radiationis constantly driving a state of instability and so you get convection where warm samplesflow upward and cool samples flow downward. With radiation driving instability andconvection working towards stability, you usually get stability. It drives the atmosphereto a neutral state because radiative timescales are long and convective timescales areshort.

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March 27, 2014

Radiative-Convective Equilibrium

Adjusted for convection we have 313 degrees K when model is 333K. Still a little toowarm. The reason is that in the real atmosphere convection involves the phase change ofwater known as moist convection. A cloud is a collection of very tiny condensed waterdoplets, or ice crystals. They are so tiny they can be considered to be in suspension.They are so small their terminal velocities are small compared to air motions. Cloudsform when air expands and cools. Their saturation vapor pressure drops. Water vaporcondenses. This happens when there is higher pressure at the surface and lower pressurehigher in the atmosphere: air rises, expands and cools. When water vapor condenses itreleases latent heat of vaporization and when it freezes it releases the latent heat offusion. Our model has to be adjusted for the heat when water condenses. Condensedwater also evaporates, absorbing latent heat of vaporization or fusion, causing air to cool.

Moist convection redistributes water from the surface up through the atmosphere. Moistconvection is the agent of lofting water and makes the atmosphere moist. Remember,water vapor is the most important greenhouse gas.

At 6 hectopascals, around 0 degrees C, water exists in all three phases. As one increasestemperature on increases saturation vapor pressure, it increases exponentially. As oneapplies pressure to water-ice, one can melt it.

Heterogeneous Nucleation: the condensation of vapor onto pre-existing solid or liquidparticles called aerosols. We don’t need to know how fast this takes place. The time isnominal.

Precipitiation, small water particles in suspension collide, coalesce into sizes heavyenough to fall, called stochastic coalescence. Not very effective.

Saturation Entropy s*

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s* = cp lnTT0

⎛

⎝ ⎜

⎞

⎠ ⎟ − Rd ln

pp0

⎛

⎝ ⎜

⎞

⎠ ⎟ + Lv

q* (T, p)T

⎛

⎝ ⎜

⎞

⎠ ⎟

Lv = latent _ heat _of _vaporizationq* = saturation _ specific _ humidity

The upward flux in the clouds must equal downward flux in between clouds:

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MT =∂Sd∂z

= −Q•

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Amount of water evaporating from the ocean must equal precipitation (water re-enteringocean):

Precipitiation=Evaporization=Radiative Cooling (of atmosphere)

Two Layer Radiative-Convective Model

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σTe4 = effective_ from _ sun

σT14 = radiates_ up_ and _ down _ from _ layer_one

It receives a convective heat flux from the surface

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Fs and it also convects a heat flux,

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Fc ,towards layer two.

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σTs4 = temperature_of _ surface

Layer 2; Emits radiation upward and downward at

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σT24 and receives convective heat

flux from

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Fc .

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T1 = T2 + ΔTTs = T2 + 2ΔTat _ top_of _ atmosphere :T2 = TeT1 = Te + ΔTTs = Te + 2ΔTSurface :Fs +σTs

4 =σTe4 +σT1

4

Layer2 : 2σTe4 =σT1

4 + Fc

(F_c is convective flux coming from first layer)

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Define : x ≡ ΔTTe

Fs =σTe4[1+ (1+ x)4 − (1+ 2x)4 ]

Fc =σTe4[2 − (1+ x)4 ]

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April 3, 2014

We spoke of heat transfer in the vertical due to radiative transfer and convective transfer,now we talk about motion of both air and water in both the horizontal and verticaldirections, which would be air currents and ocean currents involving the coriolis force oracceleration of air and water due to the rotation of the earth in other words, which is tothe right of its motion in the northern hemisphere and the left in the southern hemisphere.That which we see are things like the westerly trade winds and other winds, with theirassociated eddies. This is important for the motion of air and water from the tropics tothe poles. We begin with the exact solution for a planet like earth, but withoutcontinents.

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dudt

= fv −α ∂p∂x

dvdt

= − fu −α ∂p∂z

α = specific _volumep = pressuref = 2Ωsinθ = coriolis_ parameterΩ = angular_ rotation _earth

(u and v are velocities, east-west and north-south respectively and theta is a measure oflatitude)

Geostrophic Balance

Enough East-West motion to balance the pressure gradient:

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α∂p∂z

= − fu

It is a fundamental balance we see in the real world. This is why we see air circulatingclockwise around high pressure systems and counter clockwise around low pressuresystems. And similarily for east-west pressure gradients:

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α∂p∂x

= fv

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Combining this with hydrostatic balance we have:

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α∂p∂y

= − fu

α∂p∂z

= −g

E liminate_ p_by _cross_ differentiation

f ∂u∂z

= −g ∂ ln(α)∂y

⎛

⎝ ⎜

⎞

⎠ ⎟ = −g

∂ ln(T)∂y

⎛

⎝ ⎜

⎞

⎠ ⎟

Which is the Thermal Wind Equation. This is the vertical derivative of the east-westwind times the coriolis parameter. It says when temperature decrease towards the pole,zonal wind (west-east component of the wind) must increase with altitude. Because theyare west-east winds, they don’t transport energy in the north-south direction. Twopotential problems with this solution: Not enough angular momentum available forrequired east-west wind and equilibrium solution may be unstable.

One must be very careful to distinguish between equilibrium solutions and stability.Warm air extends towards the poles and cold air flows towards the equator. That tends towarm-up high latitudes and cool down low latitudes. A pendulum is stable, it continuesoscillating in the same way, about the center. But moving, it is not in equilibria; that iswhen it is still, hanging straight down. Stable solutions oscillate. Warm moist air movesto the poles, dry cool air to the equator. When warm air moves up, it pushes cool airdown; cool air moving down pushes warm air up. This is oscillatory. Eddies transportenergy away from the equator. Eddies drive the temperature gradients down to about halfof what they would be in the radiative-convective equilibrium solution. It is not exactlyclear how climate change effects eddies, but it is a subject of vigorous research.

The Story So Far.

First we considered an Earth that is in radiative equilibrium, that is, has as much radiationcoming in from the sun, as leaving. We noticed that the temperature of the atmospherewas the same as the effective radiation coming in from the sun and from that we wereable to determine the temperature of the surface of the planet. But that was not goodenough, we next considered an atmosphere with two layers instead of one and brought inthe idea of convective equilibrium, where we get further heat transfer from convection,which is the rising of warm air and sinking of cool air. We also now considered theemmisivity of the atmospheric layers as well. Both radiative and convective heat transferare vertical. We now turned to the horizontal components, which transfer heat. They areocean and air currents. The wind in other words, for one thing. We find there is an exactsolution where we learned wind velocities and directions are determined by the pressureof air, which is determined by its temperature, and are brought about by coriolis forces,which are those forces on the air which are caused by the rotation of the Earth, and theresults depended on latitude.

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So, in order for earth to be in equilibrium it has to lose energy (heat) it gains and it doesthis through the mechanisms of radiating infrared radiation into space (radiative transfer),evaporate ocean water pulling it into the sky as water vapor to make clouds (convection),and create ocean and wind air currents (ocean streams and wind).

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The Keeper Of This Journal