pat arnott, atms 749, unr, 2006. practical consequences of the schwarzschild equation for radiation...

Pat Arnott, ATMS 749, UNR, 2006.

PRACTICAL CONSEQUENCES OF THE SCHWARZSCHILD EQUATION FOR RADIATION

TRANSFER WHEN SCATTERING IS NEGLIGIBLE

From Grant Petty’s Book, A first course in Atmospheric Radiation.


Atmosphere Emission

Measurements, Downwelling

Radiance

Notes:

1. Wavelength range for CO2, H20, O3, CH4.

2. Envelope blackbody curves.

3. Monster inversion in Barrow.

4. Water vapor makes the tropical window dirty.


RENO FTIR SPECTRA


Coincident FTIR Measurements, Down

and Up.


More Examples of FTIR Data from a Satellite


Comments on Figure 8.3.

The very strong CO2 line at 15 microns typically gives the gas temperature closest to the FTIR spectrometer.


Self Study Questions


FTIR Data from the NASA ER2 with Responsible Gases labeled.

IR Window 8-13 microns. IR radiation from

the Earth’s surface escapes

to space (cooling the

Earth). Absorption by

O3 near 9 microns ‘dirties’

the window.

(From Liou, pg 120).


Weighting Functions for Satellite Remote Sensing using the

strong CO2 absorption near 15.4 microns. (from Wallace and

Hobbs, 2nd edition)

Ii=B(Ts)exp−τ absAll Atmos

( ) (surface)

+ B[T(z)]exp(−τabs(z))0

∞

∫ βabs(z)dz (atmos)

or

I i =B(Ts)exp−τ absAll Atmos

( ) (surface)

+ B[T(z)]0

∞

∫ Wi(z)dz (atmos)

TeB(Te)

Satellite with FTIR Looking Down


Atmospheric Temperature Profile: US “Standard” Atmosphere.

From Liou

Cirrus cloud level.High cold clouds, visible optical depth range0.001 to 10, emits IR to surface in the IR window.


Cirrus Clouds: Small Crystals at Top, -40 C to -60 C

nucleation

Growth and fall

Evaporation


FTIR Data from the NASA ER2, Clear and Cloudy Sky. (From Liou’s book). The ice cloud with small ice crystals has emissivity << 1, so the

ground below is partially seen. Clouds reduce the IR making it to space in the atmospheric

window region.

IR Atmospheric window region


Ice Refractive

Index

Red shows the atmospheric window region. The resonance in the window region is useful for remote sensing. The real part goes close to 1, making anomalous diffraction theory a fairly reasonable approach for cross sections.


Skin Depth and Absorption Efficiency


Cloud Emissivity in General and Zero Scattering Approximation.

CLOU

CLOUD

I0 Incident Irradiance

I0 tTransmittedIrradiance

L=

DirectBeam

Diffuse+

1 D ideas....

I0 rReflectedIrradiance

GENERAL CLOUD MODELTRANSMITTED≡I0 tTRANSMITTED=Direct+DiffuseDirectBeam=I0exp(−βextL)

Diffuse=I0 t−exp(−βextL)⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

REFLECTED≡I0 r

Absorptivity(a)=Emissivity(ε)ε=1−t−r=a

ZeroScattering(gas)CloudModelt=exp(−βabsL)ε=1−t


Cirrus with Small Crystals IR Transmission Model

Message: Curve has basic shape of the IR spectrum for small cirrus, primarily a transmission problem of ground radiance through the cloud, with a small emission correction. ASSUMES ZERO SCATTERING.


Cirrus with Small Crystals IR Emission Model

Message: Curve has basic shape of the IR spectrum for small cirrus, primarily a transmission problem of ground radiance through the cloud, with a small emission correction.

Te

B(Te)

Cirrus Cloud


B(Te) tc B(Tc) (1-tc)


Cirrus with Small Crystals IR Emission Model

Te=300 KTcirrus=213 KCrystal D= 10 umCrystal Conc=10,000 / LiCloud Thickness = 1 km

Te

B(Te)

Cirrus Cloud


B(Te) tc B(Tc) (1-tc)


IR Cooling Rates(from Liou)

Message:

Clouds are good absorbers and emitters of IR radiation. MLS is a moist midlatitude profile, SAW is a dry subarctic winter profile.

Cooling rate is from the vertical divergence of the net irradiance absorbed and emitted.

ρcp ∂T∂t=−dFnetdz


Dances of the Molecules in the Atmosphere: Which dance? Depends on temperature, available IR photons.

From Liou


Atmospheric Temperature Profile: US “Standard” Atmosphere.

From Liou

Dances of the Molecules in the Atmosphere: Which dance? Depends on temperature, available IR photons.


Line Strength Temperature Dependence Summary

*** Energy levels are determined from quantum mechanics, electronic, vibration, rotation etc, as related to molecular mass, charge distribution, orientation, number of atoms, etc.

*** # of molecules in each state is determined from statistical mechanics, partition function, thermal energy. Is there sufficient thermal energy to populate the energy levels above the ground state? What is the probability molecules are in a given energy state?


Some Energy States of Water Molecules

http://www.lsbu.ac.uk/water/vibrat.html

http://en.wikipedia.org/wiki/Libration


Is it likely that a molecule can be in energy state El?Water Vapor must be in state El before it can absorb photon with energy h 0c.

Molecules are in lower energy states at lower temperature.

0.00000001

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

0.1

1

0 500 1000 1500 2000 2500

Lower Energy State E

l

(cm

-1

)

Relative Population at 296 K

Relative Population at 196 K

exp[(-E

l

/(k

b

T)]=exp[(-hc ν

l

/(k

b

)]T

: Probability Thermal Energy sufficient to mingle with Photon energy

h ν

0

c

E

l

= h ν

l

c

E

H

= ( h ν

+l

ν

0

) c


Number of Lower Energy States for Water Molecules in Wavenumber bins for the Wavenumber Range 500-750 cm-1.

0

10

20

30

40

50

60

70

80

Lower Energy State (cm

-1

)

h ν

0

c

E

l

= h ν

l

c

E

H

= ( h ν

+l

ν

0

) c

Lower Energy States of Water Vapor Associated with Transitions in the wavenumber range

500 750 -1)to cm


Line Strength Temperature Dependence Water Vapor: Weak Line

0.0E+00

5.0E-25

1.0E-24

1.5E-24

2.0E-24

2.5E-24

3.0E-24

190 210 230 250 270 290

Temperature (K)

Line Strength (cm

2 molecule

-1 cm

-1)

0.032

0.033

0.034

0.035

0.036

0.037

0.038

0.039

g Air Broadened Half Width (cm-1 / atm)

S Line Strength at 296 K

Air Broadened Half Width g to get gammap @296K (cm-1 / atm)

ν0 = 500.035137 -1cm


Line Strength Temperature Dependence Water Vapor: Strong Line

0.0E+00

2.0E-21

4.0E-21

6.0E-21

8.0E-21

1.0E-20

1.2E-20

1.4E-20

1.6E-20

1.8E-20

190 210 230 250 270 290

Temperature (K)

Line Strength (cm

2 molecule

-1 cm

-1)

0.000

0.010

0.020

0.030

0.040

0.050

0.060

g Air Broadened Half Width (cm

-1 /

S Line Strength at 296 K

Air Broadened Half Width g to get gammap @296K (cm-1 / atm)

ν0 = 525.959891 cm -1


Line Strength Temperature Dependence Water Vapor

0.007 0.015 0.030 0.053 0.0910.148

0.232

0.350

0.511

0.724

1.000

0.200.26

0.320.39

0.470.55

0.630.72

0.810.91

1.00

-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.5

190 210 230 250 270 290

Temperature (K)

Relative Line Strength

Relative Line Strength, nu0=500.035 cm-1

Relative Line Strength, nu0=525.960 cm-1

Relatively Strong Line, lower energy state

ν l = 920.2 cm -1 .

Relatively Weak Line lower energy state

ν l = 2248.1 cm -1 .

(P νl) ≈ [-EXP hc νl/( )]kT


Line Strength and Lower Energy States and Temperature

Water Vapor, 500 - 750 cm-1

1.E-33

1.E-32

1.E-31

1.E-30

1.E-29

1.E-28

1.E-27

1.E-26

1.E-25

1.E-24

1.E-23

1.E-22

1.E-21

1.E-20

1.E-19

0 1000 2000 3000 4000 5000 6000

Lower State Energy νl (cm-

( Line Strength cm

2 molecule

-1 cm

-1)

296 S Line Strength at K

196 S Line Strength at K

Detection?Threshold

( ) (290 ) S T grossly related to S K exp [(-hc νl/(k b )]T


Electronic, Vibrational, energy levels and the big break up (dissociation level)

From Liou


Absorption cross sections of O3 and O2 in the UV and Visible.

Strongly affects atmospheric chemistry, thermal structure, and amount of deadly UV that doesn’t make it to the surface.


Depth for abs=[Babs (Ztoa-H)]=1 as a function of wavelength, and the gases responsible for absorption.

H(km)


Classical Stratospheric Ozone Theory of Chapman (1930) (from Liou)


Ozone Number Density: Theory and Measurements.


Solar Spectrum, Top of the Atmosphere and at the Surface

Shaded region is solar irradiance removed by Rayleigh scattering and absorption by gases as indicated. (from Liou).


ERBE View of the radiation

story (Wallace and Hobbs CH4)

Note the IR cold spots near the Equator and the cold poles.


ERBE View of the radiation story (Wallace and Hobbs CH4)


Color, texture, scattering in the visible….

See student pictures also….


Light Scattering Basics (images from Wallace and Hobbs CH4).

Sphere, radius r, complex refractive index n=mr + imi

x

xxLines :

r= x2πλ

Dimensionless Parameters

SizeParameter≡x=2πrλ

ScatteringEfficiency≡Qs=σscaπr2

mr=1.5

Qs

Angular Distribution of scattered radiation (phase function)

x x

xDipole scattering


Geometrical Optics: Interpret Most Atmospheric Optics from Raindrops and lawn sprinklers (from Wallace and Hobbs CH4)

Rainbow from

raindrops

Primary Rainbow Angle: Angle of Minimum Deviation (turning point) for rays incident with 2 chords in raindrops.

Secondary Rainbow Angle: Angle of Minimum Deviation (turning point) for rays incident with 3 chords in raindrops.


Geometrical Optics: Rainbow (from Petty)

Angle of minimum deviation from the forward direction. Focusing or confluence of rays.

x

Distance x is also known as the impact parameter. (Height above the sphere center.)


Geometrical Optics: Interpret Most Atmospheric Optics from Ice Crystals (from Wallace and Hobbs CH4)

22 deg and 45 deg Halos from cirrus crystals of the column or rosette (combinations of columns) types. Both are angle of deviation phenomena like the rainbow. Crystal orientation important. 22 deg halo, more common, thumb rule to measure size of arc.

pat arnott, atms 749, unr, 2006. practical consequences of the schwarzschild equation for radiation...

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