Transcript Document

BASIC RADIATIVE TRANSFER
RADIATION & BLACKBODIES
 [W/m2]
 [W/m2/sr]
 [W/m2/sr/nm]
Radiation Flux (F)
Intensity (I)
Monochromatic Intensity (Il)
Objects that absorb 100% of incoming radiation are called blackbodies
For blackbodies, emission (Bl) is given by the Planck function:
2 hc 2
Bl 
 hc 




5
 kT l 
l e
 1




B  T 4
lmax = hc/5kT
Emittance:
ελ =
Function of T
only!
Bl
Wien’s law
Iλ
Bλ (T)
lmax
1 < el< 0 for grey bodies (el=1 for blackbodies)
Kirchoff’s Law: absorptance = emittance
RADIATIVE TRANSFER EQUATION I
dIl
 -absorptance + emission - scattering out + scattering in
ds
A
B
A: Absorptance (Beer-Lambert Law)
dIl
  a (l )Il
ds
B: Emission (Kirchoff’s Law)
dIl
  a (l )Bl (T)
ds
C
D
C: Scattering Out
dIl
  s (l )Il
ds
D: Scattering In
complex because of scattering from all
directions, can be approximated as:
dIl
  s (l )  I'l 
ds
where <I'l >is directionally weighted average
RADIATIVE TRANSFER EQUATION II
dIl
 - a (l )Il ( ,  )   a (l )Bl (T)   s (l )Il ( ,  )   s (l )  Il' 
ds
  a (l )  Bl (T)  Il ( ,  )   s (l )  Il'  Il ( ,  ) 
Absorption and emission
(depends on incident intensity and T of layer)
Scattering
(increase in outgoing if <I’l> > Il)
dIl
 [ a (l )   s (l )]Il ( ,  )   a (l )Bl (T)   s (l )  I l' 
ds
Extinction coefficient:
 e (l )   a (l )   s (l )
Slant versus Vertical Radiation:
s2
 slant    e (l ,s)ds
s1
z2
 vertical    e (l , z)dz   slant
z1
d( l )   e (l ,s)ds
 = optical depth
l= 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

dIl
 (l )
 (l ) '
 -Il ( ,  )  a
Bl (T)  s
I 
d l
 e (l )
 e (l ) l
1w
Single scattering albedo: w
Simplification #1: No Scattering (valid for IR with no clouds)
Schwarzchild’s Equation:

dIl
 -Il ( ,  )  Bl (T)
d l
 Can be solved explicitly (first order, linear ODE)
Simplification #2: No Emission(valid for the UV/visible/near-IR)

dIl
 -Il ( ,  )  w  Il' 
d l
 Requires an understanding of scattering properties to solve
IN PRACTICE, THERE ARE MANY CONTRIBUTIONS
TO ATMOSPHERIC RADIATION…
Emission from
molecules
Absorption
Scattering
from a cloud
Scattering
Aerosol /
Molecules
Transmission
through a
Atmosphere
cloud
Emission from
a cloud
Cloud
Scattering
within a cloud
Scattering /
reflection oh a
cloud
Absorption on
the ground
Transmission
through a
cloud
Scattering / Reflection on the ground
Emission from
the surface
Adapted from Andreas Richter
INTERACTION OF RADIATION WITH GASES
Wavelength λ
I
1km
I
i
100m 10m
I
I
I
1m
0.1m
10cm 1cm
Radiowaves
I
I
I
1mm
0.1mm 10μm 1μm
Microwaves
I
I
thermal
Infrared
I
I
I
0.1μm 10nm 1nm
X -ray
Visible
Ultraviolet
Interaction of electromagnetic
radiation with matter
Rotation
Vibration
Characterized by
discrete spectral lines
Electron
Transition
Also in UV/vis:
Ionization-dissociation
Characterized by
absorption cross
section
SPECTRA OF ATMOSPHERIC GASES HAVE FINITE WIDTHS
Pressure (Lorentz) broadening can obscure individual lines
Petty, 2004
EXAMPLES OF ABSORPTION SPECTRA
UV
IR
Transmittance
Andreas Richter
15 m
3.6 m
[Clerbaux et al., ACPD, 2009]
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.
The phase function P() gives the distribution of
scattered intensity as a function of scattering
angle; the integral over all wavelengths is 1.
Scattering regime can be assessed
using the Mie parameter:  = 2 r / l
Mie-Scattering (0.1 <  < 50)
Geometric (optics) scattering ( > 50)
Rayleigh Scattering ( < 0.1)
[Petty, 2004]
Reflectivity and Emissivity of Various Surface Types
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
There can be little relationship between reflectivity at visible and
infrared wavelengths!
Petty, 2004
SATELLITE ORBITS
POLAR ORBIT
Most composition measurements thus far have been from low-elevation (LEO), sunsynchronous 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
Terra is daytime descending orbit
Local Time = GMT +longitude/15
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
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°)
Pros:
(1)
(2)
Cons:
(1)
(2)
constant observation (diurnal profiles, cloud contamination less detrimental)
Longer instrument lifetime (less drag)
reduced signal
worse spatial resolution  limit of spatial resolution possible ~ 1km
GEOSTATIONARY NETWORK OF THE FUTURE?
GEO-CAPE
NASA: 2016?
Sentinel-4/5
ESA: 2017
GEO-Asia
JAXA: 2017?
All three likely to include composition measurements in both UV & IR