Pat Arnott, ATMS 749, UNR, 2008 CH 8: ATMOSPHERIC EMISSION: PRACTICAL CONSEQUENCES OF THE SCHWARZSCHILD EQUATION FOR RADIATION TRANSFER WHEN SCATTERING.

Pat Arnott, ATMS 749, UNR, 2008

CH 8: ATMOSPHERIC EMISSION: PRACTICAL CONSEQUENCES OF THE SCHWARZSCHILD

EQUATION FOR RADIATION TRANSFER WHEN SCATTERING IS NEGLIGIBLE

Key Concepts:

• Infrared transmission and emission by the atmosphere gases.

• Learn how to read meteorology in infrared spectra.

• Learn about the basic concepts involved with retrieval of atmospheric temperature and humidity - weighting functions.


Some Energy States of Water Molecules

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

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


Atmospheric Transmission: Beer’s Law: I(x)=I0e(-abs x)

What are the main sources for each gas?

Which gases are infrared active and contribute to greenhouse warming?

Which gases significantly absorb solar radiation?

Nitrous oxide is emitted by bacteria in soils and oceans, and thus has been a part of Earth's atmosphere for eons. Agriculture is the main source of human-produced nitrous oxide: cultivating soil, the use of nitrogen fertilizers, and animal waste handling can all stimulate naturally occurring bacteria to produce more nitrous oxide. The livestock sector (primarily cows, chickens, and pigs) produces 65% of human-related nitrous oxide. [1] Industrial sources make up only about 20% of all anthropogenic sources, and include the production of nylon and nitric acid, and the burning of fossil fuel in internal combustion engines. Human activity is thought to account for somewhat less than 2 teragrams of nitrogen oxides per year, nature for over 15 teragrams.

Gas concentrations from ‘typical’ midlatitude summer atmosphere.


Clouds at Visible and IR (e.g. 10 um) Wavelengths


Optics of N identical (particles / volume)

Light beam area = A

dz

z

z+dz

Power removed in dz: = I(z) N A dz ext

Bouger-Beer“law”(direct beam only!)


CH 8: ATMOSPHERIC EMISSION: PRACTICAL CONSEQUENCES OF THE SCHWARZSCHILD

EQUATION FOR RADIATION TRANSFER WHEN SCATTERING IS NEGLIGIBLE

What process subtracts radiation?What process adds radiation?

What equation is used to calculate optical depth for a gaseous atmosphere?


FTIR Radiance: Atmospheric IR Window

13 microns 8 microns


DEFINITION OF THE BRIGHTNESS TEMPERATURE

TB

Measured Radiance at wavenumber v =Theoretical Radiance of a Black Body at temperature TB


FTIR Brightness Temperatures


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.


Ideal Weighting Function Wi: Where in the atmosphere the main contribution to the radiation at wavenumber i

comes from.


Downwelling Intensity Emitted by the Atmosphere to the Detector (Radiance)

z dz

ftir

emissivity=absdz/cos

=cos

B[T(z)]

blackbody radiance,T = temperature.

emission transmission

weightingfunction


Weighting Functions for Satellite Remote Sensing using the

strong CO2 absorption near 15.4 um. (from Wallace and Hobbs,

2nd edition)

Ii =B(Ts)exp−τ absAll Atmos

( ) (surface)

+ B[T(z)]exp(−τabs(z))0

∞

∫ abs(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


Chapter 8 Homework:

1. Calculate and plot weighting functions as in the previous slide, but for the FTIR spectrometer at the ground looking up.(500 to 850 cm-1 region).

2. Explain in detail, using these weighting function, how we can diagnose the temperature inversion in the Barrow Alaska graph.

3. Bring questions to class related to how this is done.

4. Extra credit: Calculate and plot weighting functions for the stratospheric ozone emission spectral region in the atmospheric window region (spectral region between 1000 and 1100 cm-1.)


Simple Theory for W(z) at the Ground

Where is theHUGEapproximation?Why?


Simple Theory for W(z) at the Ground

Where is theHUGEapproximation?Why?


http://www.spectralcalc.com/calc/spectralcalc.php

volume mixing ratio = 0.01 (CO2) = 0.1 (others)


http://www.spectralcalc.com/calc/spectralcalc.php

volume mixing ratio = 0.01 (CO2)

Can save text file!


Calculate the absorption cross section per molecule from the transmittance calculations and this theory.


CO2 Spectrum: Line Strength and Broadening Effects


CO2 Spectrum: Line Strength and Broadening Effects


abs0, P=1013.25 mb, T=296 K. ONLY CO2!!! =0.5 cm-1.

380 ppm CO2


http://www.spectralcalc.com/atmosphere_browser/atmosphere.php

Calculate N(z), thenNH20(z), Nco2(z), etc.

Calculate abs(z) depth.

Calculate W(z)


RENO FTIR SPECTRA


Weighting Functions for the FTIR at the Ground Looking Up

H=6 km


Weighting Functions for the FTIR at the Satellite Looking Down

H=6 km


Theoretical Absorption Cross Sections for the indicated gases, averaged to 1 cm -1 resolution for clarity.


Theoretical Absorption Cross Sections for the indicated gases, averaged to 1 cm -1 resolution for clarity.


RENO FTIR SPECTRA

Which day is more moist?

Which day is warmer near the surface?


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).


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(−extL)

Diffuse=I0 t−exp(−extL)⎡

⎣

⎢⎢

⎤

⎦

⎥⎥

REFLECTED≡I0 r

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

ZeroScattering(gas)CloudModelt=exp(−absL)e=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

Pat Arnott, ATMS 749, UNR, 2008 CH 8: ATMOSPHERIC EMISSION: PRACTICAL CONSEQUENCES OF THE SCHWARZSCHILD EQUATION FOR RADIATION TRANSFER WHEN SCATTERING.

Documents

pat arnott

orgwikilibration slide

temperature t b slide

atmospheric emission

atmosphere gases

ftir radiance

atmospheric transmission

radiation transfer