Transcript PHY2505 Lecture 5 - Atmospheric Physics

PHY2505 - Lecture 5
Interaction of solar radiation and the
atmosphere
1
Interaction of the sun and atmosphere
RECALL
I ( * )  I o e

*


*
 J ( ' )e
 ( *  ')

d '
o
Extinction

Where
   kdz

Source (scattering)
and z defined upwards from surface
z
LAST TIME we looked at the variability of the
solar constant S(l,t) ~ Io (l,t)cos qo(t)DW(t).
•
Systematic variability due to orbit: cos qo(t)DW(t).
•
Long term variability due to solar cycles.
•
Short term variability on order of measurement time??
2
Short term variability of Io(t,l)
• How constant is Io(t,l)?
– From satellites we don’t know the absolute value
of S(t,l) better than ±4Wm-2 (~0.3%)
3
Short
term variability
of Io(t,l)
Variability
of S(t,l)
(cont.)
– On top of this is a day to day variability
of order 0.1% – how significant is this?
Will return to this when we look at
remote sensing and retrieval.
– This variability is explained by magnetic
disturbances: sunspots, flares,
prominences. A successful theory
predicting change in magnitude of
S(l,t) due to disturbances has not yet
been developed. The figure shows a
decrease of 0.1% in the solar constant
apparently due to presence of a cluster
of sunspots
– New satellite missions will provide new
information on variability of Io(l,t):
SOHO mission provides first
continuous observations from L1 point
Sunspot blocking:
Figure from Hoyt & Schatten (1997)
4
This time:
Solar absorption and scattering terms
ABSORPTION:
RECALL: energy exchange in the
UV/VIS region produced mainly by
ionization (UV continuum) and
electronic transition processes.
Some transitions are also produced
by coupling of vibrational modes
with electronic transitions
To quantify atmospheric absorption we
need:
–
the composition of the
atmosphere
–
the distribution of atmospheric
constituents
–
the strength of their absorption
coefficients in the solar region
5
Atmospheric composition
+ aerosol and cloud
6
Solar absorption bands
Absorption below 120nm
considered to be insignificant as
solar output so low in EUV
Strongest absorptions:
H2O overtones
O2 coupled vib-electronic transitions
O3 electronic transitions (see fig) 7
Atmospheric structure
8
Absorption with altitude
Plot shows height
at which optical
depth =1
Indicates no solar
radiation reaches
the surface at
wavelengths
lower than about
300nm
9
Scattering
The absorption component of
I(*) can be calculated using a
good line-by-line model (later..)
In some regions of the solar
spectrum the scattering
interaction results in a
reduction of incoming radiation
as great as due to absorption…
10
Scattering
Qualitatively,
If a plane wave meets a particle
small compared to its
wavelength we expect that
most of the wave energy is
transmitted forward
with a small amount of energy
lost in the form of a scattered
wave centred on the particle
Represent scattered energy Is=IoCsca
I
I o P ( ,  )
r2 k2
Thus defining the scattering cross section,
Csca. Can also define absorption cross section
Cabs and extinction cross section Cext in the
same way.
11
Scattering: quantitative approach
Consider the vector nature of the electric field:
Assume applied field, Eo,
induces a dipole moment, po
in a small homogeneous charged particle,
radius r <<l,
poaEo where a=polarizability
The applied electric field generates
oscillations in the induced dipole
which in turn produces plane polarised EM:
the scattered wave.
From electromagnetic theory:
where we can write
Substituting the expressions for P and Po into E we get the expression for scattered field in
terms of incident field
12
Scattering: the scattering matrix
The scattering matrix comes about due to the phase between scattered and incident light.
Can express Eo as parallel Eol
and perpendicular Eor to scattering plane
In the atmosphere these components are
related by a random phase:
the incident solar radiation is unpolarised.
Relate the incident and scattered components by
(see fig)
And rewrite in matrix form, where  is the scattering angle:
Scattering matrix – an
important part of
scattering problems
13
Scattering: Rayleigh scattering formula
RECALL: Intensity of radiation per solid angle (radiance) Io= |Eo|2
Can express the two components of the electric field in terms of radiances:
and the total scattered intensity of the unpolarised sunlight incident on a molecule in the
direction  as
For unpolarised light, Ior=Iol=Io/2, and using k=2p/l we get Rayleigh’s scattering formula
polarizability
distance,r
Scattering angle
1/l4
dependence
14
Scattering: Phase function
For vertically polarized light, Er, scattering is isotropic, independent of  and for horizontally
polarised light, Eol, the scattered intensity depends on cos2
The angular dependence of the Rayleigh scattering patterns for Eor, Eol and Eo is shown:
For more complex problems we define the PHASE FUNCTION, P(cos ) to represent this
angular distribution. This is a normalised non-dimensional parameter integrated over  and 
for Rayleigh this integral gives:
and
15
Scattering: cross section
Scattered flux, f, is found by integrating the scattered intensity over solid angle:
giving
IoDW
We can define the cross section per molecule, s, by f/Fo
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Scattering: polarizability
Polarizability, a: Derived in Liou Appendix A
Where Ns= number of particles per unit volume
m= mr+imi is the refractive index of the particle – notoriously difficult to measure!
Real part
Absorption
imaginary part
scattering
For air, the real part of the refractive index is approximated by
- basis of formulae quoted for
Rayleigh scattering optical17depth