A physicist’s view on atmospheric and climate models R. Koch Introduction, aims The gardener’s...

A physicist’s view on atmospheric and climate models

R. Koch

• Introduction, aims• The gardener’s greenhouse, greenhouse effect, greenhouse gases,

climate change in a shoebox• Radiative equilibrium of objects in the sun• Textbook absorption / re-radiation (A/RR) theory• The “convective” part of simple “radiative-convective” models• Textbook Consensus Radiation Transfer (CRT) theory• Hard science physics radiation transfer and fluid-kinetic theory and

discussion• More questions about the consensus view on climate

Koch - EPS-EG Rome 23 Sept. 20151

“Greenhouse” does not occur in a greenhouse

2

Experiments have shown that the “greenhouse” effect is not the warming mechanism in a greenhouse. The mechanism is suppression of convection. R.W. Wood Philosophical magazine 19 (1909) 319-320. http://www.drroyspencer.com/2013/08/revisiting-woods-1909-greenhouse-box-experiment-part-i/ http://www.principia-scientific.org/the-famous-wood-s-experiment-fully-explained.html

This fact is well-known to Consensus Climatologists (CC’s): “The next 18 pages of GT09 are devoted to showing that the atmospheric greenhouse effect relies on

different physical processes than the warming in a glass greenhouse. This is a well-known fact that can be found even in popular expositions of the atmospheric greenhouse effect and is mentioned on p. 115 of the 2007 IPCC report.13” [Halpern et al. (2010); Gerlich & Tscheuschner (2009)]

“Radiation from the atmosphere back towards the surface raises its temperature above (…), giving rise to what we (somewhat inaccurately) call the greenhouse effect. [Vardavas & Taylor (2007)]

“the analogy should not be taken too far , but the term is too well-ingrained in the popular literature to ignore it altogether). [Taylor (2005)]

The physics of the “greenhouse box” or of the “climate change in a shoebox” is much more complex than the simple absorption/re-radiation scheme and is even not well understood [Berto, et al (2014); Buxton (2014); Wagoner (2010)]


http://www.drroyspencer.com/2013/08/revisiting-woods-1909-greenhouse-box-experiment-part-i/

http://www.drroyspencer.com/2013/08/revisiting-woods-1909-greenhouse-box-experiment-part-i/

http://www.principia-scientific.org/the-famous-wood-s-experiment-fully-explained.html

Temperature of a surface S at ground in the sun without convection

3

Power radiated normally on a flat disk of radius Rd

Power radiated by the disk

24

2(1 )(1 )s

s s e ese

RP T S

d

4d dP T S

62 Cd s dP P T

0.3; 0.25e e


Temperature on the ground of the Gardener’s greenhouse according to the “greenhouse effect”

100%

100%

100%

200%

1/42 (273 62) 273 125 CdT

This is (schematically) the way atmospheric models incorporate radiative balance (without water feedback [Berger & Tricot (1992)])


Questions and terminology

5Koch - EPS-EG Rome 23 Sept. 2015

Why should the simplistic absorption/re-radiation scheme work better in the very complex situation of the atmosphere than in box experiments?

Why should we believe that this many orders of magnitude more complex problem is fully understood and accurately predictable while it is not in the simple “box” situations?

Why do consensus climatologists insist on continuing to call a cat a dog?

“Greenhouse effect” is a misnomer for the absorption/re-radiation (A/RR) mechanism advocated by CC

A greenhouse gas is a gas that one can find in a greenhouse. Irrelevant to atmosphere or climate.

I call a gas that has (does not have) radiation lines in the infrared an infrared active gas or IRA gas or IRAG (an infrared inert gas or IRI gas or IRIG)

The radiative sun-earth balance

6

Power radiated by the sun deposited on the earth surface:

Power radiated by the earth

Balance

24 2

2(1 )s

s s e ese

RP T R

d

4 24e e eP T R

255K 18 Ce s eP P T

Te is the “radiative” temperature of the earth

Agrees with the radiated power flux measured by satellite

However ground temperature 15°C

4 2240 W/mT

4 2390 W/mT


0.3e

Greenhouse theory: the IR is absorbed by gases and re-radiated, partly to ground

7

CO2 radiative forcing F[W/m2]=-6.3 ln(C/C0)

Thermodynamic paradox:

A colder body

Heats a hotter one

RadiationTransfer theory


Greenhouse theory: the IR is absorbed by gases and re-radiated, partly to ground

8

RadiationTransfer theory

100

54

100

146

100

146

4646


Textbook atmosphere in radiative equilibrium


4n nI T

“A third model for the vertical temperature profile is one that assumes dynamical processes are negligible compared to radiation, so the profile is determined by the equilibrium between the heating caused by the absorption of incoming solar radiation, the cooling to space by thermal infrared emission, and the radiative exchange between atmospheric layers at different heights. [Vardavas & Taylor (2007)]Also in [Goody & Walker 1972], [Taylor 2005], [Halpern et al., 2010],

h

In

In

Conservation of power flux:

In-1

In+1

In+11 1n n n nI I I I

One can take 0 ; then

( ) ( ) ( ) ( )I z h I z I z I z h

2

2 20

24

2

( ) ( ) 2

( )lim 0 ( ) 0 h

I z h I z h I z d I

h d

dT z

z dz



[Goody & Walker 1972; Fig.3-8]

“…the true tropospheric profile is not the result of radiative equilibrium alone, since the radiative equilibrium profile is unstable against convection (super-adiabatic). If the air were as cool at say 5 km altitude as radiative equilibrium predicts, it would rapidly sink and be replaced by warmer air from below.” [Taylor 2005]

Þ (1) The radiative flux unbalance present in the real T(z) profile is taken over by fluid (convective) power fluxes

Þ (2) T(z) profiles differing from the actual (adiabatic) one are unstable



Þ (1) The radiative flux unbalance present in the real T(z) profile is taken over by fluid (convective) power fluxes

Þ (2) T(z) profiles differing from the actual (adiabatic) one are unstable

Glass layer, no convection in the material, radiative equilibrium must hold

24

2( ) 0

dT z

dz

z

1 T 2 T

1/44 4 4

1 2 1( ) ( )z

T z T T Tl

l

Heat flux (z), not a static equilibrium

Fourier’s law violated 0 d dT

dz dz

The stability of an (inverted) temperature profile is determined not by adiabaticity or because it is the actually measured one but by the threshold conditions for the onset of Rayleigh-Bénard convection cells. The threshold results from the balance between the buoyancy force that tends to move the fluid upwards and the viscous force that opposes that motion. Viscous forces are never invoked by CC in such stability discussions.

The “convective” part of simple (didactic) radiative-convective models – First version

12

Thermodynamic analysis: the total internal energy (per unit mass) of gas should be conserved in the convective motion

At equilibrium (+ moist air cp nearly constant + initial condition)

Ground temperature: +14.5°C

6.5( 5) 18 [km, °C]p

dT gT z

dz c

0pdU c dT gdz


Te = -18°C at 5 km altitude

The “convective” part of simple (didactic) radiative-convective models – Second version

Koch - LPP-ERM-KMS talk Brussels Jan. 201513

[Vardavas & Taylor (2007)], [Taylor 2005] Heat exchange between an atmosphere parcel and its surroundings

(per mole) during its vertical motion: Adiabatic motion: Ideal gas law: Hydrostatic equation:

Combining:p p

dT Mg g

dz C c

Or from fluid theory:

vdQ C dT pdV

0 ; ; Bp p K p nk T g


0vdQ C dT pdV p ( )p vpV RT dV Vdp C C dT

/ /dp dz g Mg V

The “convective” part of simple (didactic) radiative-convective models – Fluid version

14

The basis of fluid theory is Boltzmann’s equation. Fluid theory follows by taking velocity moments (collisionless version)

Zeroth-order: mass conservation First order: hydrostatic equation The second order (energy) moment: of the Boltzmann equation reads (scalar

pressure approximation, no viscosity, approximate heat flux)

Ideal gas law: (m molecular mass) Adiabatic assumption: heat flux vector =

Leads to exactly the same law as the two other derivations


.( )t

v 0

0p g

.3 5

.( ) 02 2

D

Dt t

Dp p DT

Dt Dt

u

( / )B Bp nk T m k T

0T Q3 5 ( ) 5

0 0; ; constant2 2 3

Dp p D D pp K K

Dt Dt Dt

p

dT g

dz c

Problems with the didactic convective model

15

Theory is incomplete: K unknown (bc T=-18°C at z= 5 km) Because the heat flux is non-zero Contradicts the adiabatic assumption and the static fluid assumption because according to kinetic theory and so The divergence of the heat flux Q not balanced by anything At TOA conductive flux should be converted to radiative flux (IRA gases?)


/ 0dT dz

/ 0dQ dz

/Q dT dz

T

The “convective” part of simple (didactic) radiative-convective models – Kinetic version

16

Instead of starting with (truncated)ideal fluid equations start with Boltzmann’s equation (1-D, collisionless)

General solution: Assume the distribution function at ground level is maxwellian:

The canonical ensemble distribution of statistical mechanics says the same (atmosphere in contact with the ground heat reservoir): distribution is

Also with rotations and vibrations:


zz

f f fv g

t z v

0

2

( , ) ( )2z

z

vf z v F gz

(stationnary)

23

2 ( )2( , ) exp

2

z

zB B

vm gzm

f z vk T k T

(isothermal atmosphere)

21

( , ) exp ; ; hamiltonian 2B

mvf z A H H mgz

k T v

2 2 221

2 2 2 2

mv p qH mgz I

k

The “convective” part of simple (didactic) radiative-convective models – tentative conclusion

17

The thermodynamic adiabatic theory as well as the equivalent fluid theory is incomplete and inconsistent

Kinetic theory as well at canonical ensemble statistical theory predict an isothermal atmosphere

The latter result seems intuitively correct because these descriptions contain no mechanism capable to loose power flux to outer space.

IRA gases are able to do that by radiating electromagnetic energy the model is lacking interaction terms with the photon gas (as well as collision terms)


The radiation transfer equation


2 2

3 2

4 2

0

1

direction of propagation

radiance [W/(m sr Hz)]; irradiance F [W/(m Hz)]

2 /Blackbody radiance (Planck's law)

1

Stefan-Boltzmann's law [W/m ]

B

h

k T

II I

c t

I I

h cB

e

B d T

s.

s

volume emission

extinction coefficient: dI

Ids

The consensus radiative transfer equation (CRTE)


1 II I

c t

s. [Vardavas & Taylor 2007]

[Blundell & Blundell 2010]

cosz

(absorption) (scattering)

“In a state of thermodynamic equilibrium all processes are in equilibrium including radiative equilibrium (RE), and so the emitted and absorbed energy by the element of volume are equal Thus, for a blackbody, the emission coefficient is identical to the absorption coefficient“ [Vardavas & Taylor 2007]

“The amount of radiation it emits(*) at frequency will be proportional to its density and also (because “good absorbers are good emitters)” [Blundell & Blundell 2010]; (*) the medium)

; emission coefficient (no scattering)B

I

cos ( )I

B Iz

cos c

Diffusivity approximation or Schuster-Schwartzschild equation

A/RR theory: radiative equilibrium

20

(1)dI

B Idz

dI

B Idz

0Define :

zdz

dI dIB I B I

d d

Radiative equilibrium ( ) (0) (0)mI I I I IK

2 ; ( ) /I I B d I I d K

1( )(2 )

21

( )( )2

m m

m m

I I

I I

2 ( )(1 )m mIB

mz

m zdz


A/RR theory: radiative equilibriumConsequences

21

3

/2

4 12 ( )(1 )

1Bm m h k TI

hB

c e

( )mz

m zz dz

T(z) is entirely determined by the absorption at frequency (!!?)

For global balance: 4

0( )[1 ( )]m mIT z d

Uniform absorption:4 1/42 ( )[1 ( )] [1 ( )]m m m mIT z z T T z z

Radiative equilibrium does not make sense


CRT theory: solutions and use

22

dIB I

dz

dIB I

dz

0 0TOA:

mz z

mdz dz

( ')

0Upwelling flux at TOA ( ): ( ) (0) ( ') ( ') '

mm

z zm mz z I z B e e z B z dz


Everything solvable by simple quadratures

2

0240 W/m determines (0)( ) m TI z d

( ')

0Downelling flux at ground ( 0): (0) ( ') ( ') '

mz zz I e z B z dz

Schwartzschild-Milne formula

Determines the “greenhouse gas” forcing (additional W/m2 as if coming from sun)May be used in conjunction with GCM’s to take the “greenhouse effect” into account

Disappearing / appearing volume power density 0( )d

I Idz

Not taken into account anywhere

0( )mI z d

Even CRT theory is complex and uncertain

23

Even using the above model frequency per frequency (LBL)

Bending mode giving rise to the 666 cm-1 (f/c) line:

Rotational sidebands

Collisional broadening

Doppler broadening

“Assuming Voigt line shapes greatly overestimates the net CO2 cross section in the wings of the band”. [Happer 2015]


The hard science version of radiative transfer equations


0

23 3

3

ˆ( , , ) Occupation number per energy level, per polarization ( ; / )

1In thermal equilibrium: (Planck's distribution)

1

8Density of states per unit volume : 2 /

P

B

h

k T

f t p p h c

f f

e

F Fd f d p h fdc

p r p s

3

3

3 3 3 2

02 2

8hoton energy density:

2 2 2 /Photon energy flux = ; In thermal equilibrium: =

41

Kinetic equation for the photon density of states:

B

h

k T

hU h F f

c

c h h h cI U f f B

c ce

1ˆ ; ( )[1 ] ( )ln ln n nl l ln

l n

ff N f N f

c t

s.

[Liboff (2003), Pomraning (2003)]

The hard science radiative transfer equations


1ˆ ; ( )[1 ] ( )ln ln n nl l ln

l n

ff N f N f

c t

s.

Number density of molecules in the -th excited state

Cross-section for the transition at frequency (for : Einstein coefficients)

Absorption / emission symmetry: ; degeneracy

n

ln

l ln n nl n

N n

l n I

g g g

of the -th staten

hbE

aE

Two-level system ( )[1 ] ( )ln ab b ba a abl n

N f N f

Equilibrium: /( )0 /( )

10;

1a B

B

E k Tab a a h k T

N g e f fe

(1)

Eq. (1) is a generalization of Planck’s law

Assume thermodynamic equilibrium:/( ) /( ) (1ˆ )

( )

a B BE k T h k Tb bag e e f f

B I

f

s.

“for the CO2 transitions that are most significant in the thermal IR, the lifetimes(*) tend to range from a few milliseconds to a few tenths of a second. In contrast, the typical times between collisions (…) is well under 10-7s.” (*)of the excited states[Pierrehumbert 2011]

The hard science radiative transfer equations


1ˆ ; ( )[1 ] ( )ln ln n nl l ln

l n

ff N f N f

c t

s.

2hbE

aE

(1)

cE - The absorption / radiation process + mechanical collisions displace the radiation spectrum to other (lower) frequencies

- Single-frequency radiation transfer analysis makes no sense (LBL?)

1h

What should be a correct description of a stationary-state equilibrium?


ˆ ; ( )[1 ] ( )lna lna na nla la lnal n

f N f N f

s.

For each possible energy transition (vibration-rotation) of the IRA molecules (species a)

A Boltzmann equation determining each population density Nna (for each type of IRA molecule) and for each type of IRI molecules (species i) [all species s={a,i}]

', ' , , ,

ˆ. ( , ) ( , ) ( , )

( ) ( ) ( )[1 ( )]

( , ) elastic collision operator

( , )

nana e na ls i n a ls i na ls

l s n n l s l s

la lna ln ln na nla nll n

e na ls

i na ls

NN g K N N C N N A N N

N f N f

K N N

C N N

v. zv

creation of a state of molecule of type from a similar molecule

in state ' by inelastic collision with a molecule of type in state

( , ) annihilation of a state i na ls

n a

n s l

A N N n of molecule of type by inelastic collision

with a molecule of type in state

a

s l

This should be more correctly written to take into account that the interaction between a molecule at velocity v sees a photon of frequency propagating in direction at the Doppler-shifted frequency ˆ(1 . / )c v s

s

Summary


The water cycle refrigerator

• CRT equations are incorrect, they do not conserve power flux• Applied to the simple case of a glass thickness (no convective motion of material)

they lead to absurd conclusions• Correct equations describing a static atmospheric equilibrium can be written:

correct RT equations + Boltzmann’s equations for energy level populations of all gas components. Enormous system of equations. Does not imply IRA gases play no role.

• This system is consistent but• Missing: liquid and solid phases of water

Evapor-ation

Latent heat taken from ground

RainSnowhail

Latent heat left in high atmosphere

Mechanical work done by gravityNotice:

most ȻC accept A/RR picture

[Taylor 2009, Moran et al. 2015]

References


Berger A., Tricot Ch., Surveys in Geophysics 13(1992)523.The greenhouse effect

Berto M., Della Volpe C., Gratton L.M., European Journal of Physics, 35(2014) 025016.Climate change in a shoebox: a critical review

Blundell S.J., Blundell K.M., Concepts in thermal physics Oxford University Press (2010)Buxton G.A., Physics Education, 49(2014)171.

The physics behind a simple demonstration of the greenhouse effectGerlich G., Tscheuschner R.D., (2009) International Journal of Modern Physics B, Vol. 23, No. 3 (2009) 275–364

Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of PhysicsGerlich G., Tscheuschner R.D., International Journal of Modern Physics B, 24(2010)1333.

REPLY TO “COMMENT ON ‘FALSIFICATION OF THE ATMOSPHERIC CO2 GREENHOUSE EFFECTS WITHIN THE FRAME OF PHYSICS’Goody R.M., Walker J.C.G., Atmospheres, Prentice-Hall Inc. (1972)Halpern J., Colose C.M., Ho-Stuart C., Shore J.D., Smith A.P., Zimmerman J., International Journal of Modern Physics B, 24(2010)1309.

COMMENT ON “FALSIFICATION OF THE ATMOSPHERIC CO2 GREENHOUSE EFFECTS WITHIN THE FRAME OF PHYSICS”Happer W., in Systematic Errors in Climate Measurements Session 8, Erice, August 21 (2015).

Are Laboratory Measurments of CO2 Adequate to Predict Climate Sensitivity? (A Nerdy Talk)Liboff R.L., Kinetic Theory. Classical, Quantum, and Relativistic Descriptions, Springer (2003)Markó I.E, et al., Climat: 15 vérités qui dérangent Texquis (2013). Moran A. (Ed.) Climate Change The Facts, Stockade books (2015).Pierrehumbert R.T, Physics Today, January(2011)33.

Infrared radiation and planetary temperaturePomraning G.C., The equations of radiation hydrodynamics, Dover (2003)Postma J.E., (2011). http://www.ilovemycarbondioxide.com/pdf/Understanding_the_Atmosphere_Effect.pdf Smith A.P., arXiv:0802.4324 [physics.ao-ph] (2008).

Proof of the Atmospheric Greenhouse EffectSoon W., Connolly R., Connolly M., Earth Science Reviews (2015), doi: 10.1016/j.earscirev.2015.08.010

Reevaluating the role of solar variability on Northern Hemisphere temperature trends since the 19th centuryTaylor F.W., Elementary climate physisc, OUP (2005).Taylor Peter, CHILL A reassessment of global warming theory, Clair view (2009).Vardavas I.M., Taylor F.W., Radiation and Climate Atmospheric energy budget from satellite remote sensing, OUP (2007).Wagoner P., Liu C., Tobin R.G., American Journal of Physics, 78(2010) 536.

Climate change in a shoebox: Right result, wrong physics

http://www.ilovemycarbondioxide.com/pdf/Understanding_the_Atmosphere_Effect.pdf

30

Thank you for yourattention


Date post:	14-Jan-2016
Category:	Documents
Upload:	antonia-doyle
View:	221 times
Download:	0 times

A physicist’s view on atmospheric and climate models R. Koch Introduction, aims The gardener’s...

Documents