BASIC RADIATIVE TRANSFER

RADIATION & BLACKBODIES

Objects that absorb 100% of incoming radiation are called blackbodies

For blackbodies, emission () is given by the Planck function:

max = hc/5kT Wien’s law

Function of Tonly!

max

2

5

4

2

e 1

hc

kT

hcB

B T

Radiation Flux (F) [W/m2]Intensity (I) [W/m2/sr]Monochromatic Intensity (I) [W/m2/sr/nm]

B

Kirchoff’s Law: absorptance = emittance

λλ

λ

Iε =

B (T)Emittance: 1 < < 0 for grey bodies (=1 for blackbodies

RADIATIVE TRANSFER EQUATION I

dI-absorptance + emission - scattering out + scattering in

ds

A B C D

A: Absorptance (Beer-Lambert Law)

a

dI( )I

ds

B: Emission (Kirchoff’s Law)

a

dI( )B (T)

ds

C: Scattering Out

s

dI( )I

ds

D: Scattering Incomplex because of scattering from all directions, can be approximated as:

's

dI( ) I

dswhere <I' >is directionally weighted average

'a s a s

dI[ ( ) ( )]I ( , ) ( )B (T) ( ) I

ds

RADIATIVE TRANSFER EQUATION II

'a a s s

'a s

dI- ( )I ( , ) ( )B (T) ( )I ( , ) ( ) I

ds

( ) B (T) I ( , ) ( ) I I ( , )

Absorption and emission(depends on incident intensity and T of layer)

Scattering(increase in outgoing if <I’> > I)

e a s( ) ( ) ( ) Extinction coefficient:

Slant versus Vertical Radiation:s2

slant e

s1

z2

vertical e slant

z1

e

( ,s)ds

( , z)dz

d( ) ( ,s)ds

= optical depth= total column optical depth

EXTINCTION = SCATTERING + ABSORPTION

Scattering from milk, ink, and water on an overhead projector

Transmission through milk, ink, and water projected onto a screen

RADIATIVE TRANSFER EQUATION III

'a s

e e

dI ( ) ( )-I ( , ) B (T) I

d ( ) ( )

Single scattering albedo:

Simplification #1: No Scattering (valid for IR with no clouds)

dI-I ( , ) B (T)

d

Schwarzchild’s Equation:

Can be solved explicitly (first order, linear ODE)

Simplification #2: No Emission(valid for the UV/visible/near-IR)

Requires an understanding of scattering properties to solve

'dI-I ( , ) I

d

IN PRACTICE, THERE ARE MANY CONTRIBUTIONS TO ATMOSPHERIC RADIATION…

AtmosphereAbsorption

Scattering

Absorption on the ground

Scattering / Reflection on the ground

Scattering from a cloud

Transmission through a cloud

Transmission through a cloud

Scattering / reflection oh a cloud

Scattering within a cloud

Aerosol / Molecules

Cloud

Emission from a cloud

Emission from the surface

Emission from molecules

Adapted from Andreas Richter

INTERACTION OF RADIATION WITH GASES

Wavelength λ

I I i I I I I I I I I I I I 1km 100m 10m 1m 0.1m 10cm 1cm 1mm 0.1mm 10μm 1μm 0.1μm 10nm 1nm Radiowaves Microwaves thermal X-ray Infrared Visible Ultraviolet Interaction of electromagnetic Rotation Vibration Electron radiation with matter Transition

Also in UV/vis: Ionization-dissociation

Characterized by discrete spectral lines

Characterized by absorption cross

section

SPECTRA OF ATMOSPHERIC GASES HAVE FINITE WIDTHS

Petty, 2004

Pressure (Lorentz) broadening can obscure individual lines

EXAMPLES OF ABSORPTION SPECTRA

Tra

nsm

ittan

ce

15 m 3.6 m

UV

IR

[Clerbaux et al., ACPD, 2009]

Andreas Richter

SCATTERING

If a photon is absorbed and then immediately re-emitted this is called scattering. It depends on particle shape, size, index of refraction, wavelength of incident radiation and the viewing geometry.

Usually, scattered photons have the same wavelength (elastic scattering) but not the same direction as the original photon.

Scattering regime can be assessed

using the Mie parameter: = 2 r /

Mie-Scattering (0.1 < < 50)

Geometric (optics) scattering ( > 50)

Rayleigh Scattering ( < 0.1)

The phase function P() gives the distribution of scattered intensity as a function of scattering angle; the integral over all wavelengths is 1.

[Petty, 2004]

Reflectivity and Emissivity of Various Surface Types

There can be little relationship between reflectivity at visible and infrared wavelengths!

Surface Type Thermal Infrared Emissivity

Water 92-96

Fresh, dry snow 82-99.5

Sand, dry 84-90

Soil, moist 95-98

Soil, dry 90

Forest and shrubs 90

Skin, human 95

Concrete 71-88

Polished aluminum 1-5

Petty, 2004

SATELLITE ORBITS

POLAR ORBIT

Most composition measurements thus far have been from low-elevation (LEO), sun-synchronous orbits.

Sun-synchronous: satellite precesses at same rate as Earth revolves around Sun (~1°/day)

satellite crosses equator at same local time each day

Pros:(1) Global coverage(2) High signal

Cons:(1) Poor coverage (temporal, clouds)(2) Shorter instrument lifetime

EXAMPLE OF TERRA ORBIT

GMT Local Time = GMT +longitude/15

Terra is daytime descending orbit When converted to local time, can see the same equator cross

over ~10:30 & 22:30

SOLAR OCCULTATION ORBIT

SCISAT-1 Orbit

Pros:(1) Very good signal (new species!)(2) Good vertical resolution(3) No surface term to characterize

Cons:(1) Poor coverage (~30 obs per day)(2) Lower troposphere not observed

Pros:

(1) constant observation (diurnal profiles, cloud contamination less detrimental)

(2) Longer instrument lifetime (less drag)

Cons:

(1) reduced signal

(2) worse spatial resolution limit of spatial resolution possible ~ 1km

GEOSTATIONARY ORBIT

Geostationary orbits (GEO) match the period of satellite rotation with the Earth’s rotation (altitude ~ 35,800 km), fixed over the equator (view up to 60°)

 

GEOSTATIONARY NETWORK OF THE FUTURE?

GEO-CAPENASA: 2016?

Sentinel-4/5ESA: 2017

GEO-AsiaJAXA: 2017?

All three likely to include composition measurements in both UV & IR