Transcript Lesson27.ppt

METO 621
Lesson 27
Albedo 200 – 400 nm
Solar Backscatter Ultraviolet (SBUV)
• The previous slide shows the albedo of the earth viewed from
the nadir. Note that the y axis is on a log scale.
• The albedo shows a very low minimum near 260 nm, but has
risen to about 20% at 330 nm and above.
• The large dip in the albedo matches the absorption cross
section for ozone, shown in the next slide.
• The SBUV method takes advantage of the relation between the
rapid change in the albedo and the ozone cross section to
derive an altitude profile for ozone between 30 and 60 km
altitude.
Solar Backscatter Ultraviolet (SBUV)
Solar Backscatter Ultraviolet (SBUV)
• SBUV is a satellite spectrometer designed to retrieve the
altitude profile of ozone between 25 and 50 km.
• Above about 25 km the absorption due to Rayleigh scattering
is small, and we can ignore multiple scattering.
• Let the solar zenith angle be q0 ., and the angle between the
viewing direction from the spacecraft and nadir be q
• We define the column amount of ozone at an altitude z to be
X(z). Let the atmospheric pressure at z be P(z)
• If we choose wavelengths below 300 nm, then all of the solar
radiation is absorbed before it reaches the tropopause, hence
there is no upward radiation from the ground.
Solar Backscatter Ultraviolet (SBUV)
At a given wave length the solar flux that reaches z is given by
F  Fs0 exp(  0 / 0 ) where  0  X ( z )  P( z ) 
where  is the ozone absorption coefficien t and  is the
Rayleigh scattering cross section.
1

  ( )dP
S
I ( ) 
d p ( 0 ,  ) F exp(  ) exp(  )

4 0
0


1
 ( ) F d p ( 0 , )


I ( ) 
exp(  ) exp(  )dP

4 cos( )
0

0
S
1
dI/FS vs altitude, 245 to 305 nm
Solar Backscatter Ultraviolet (SBUV)
We now define a parameter Q( ) where
Q ( ) 
*
4 cos( )
I ( )   exp  (sec( 0 )  sec( )  dP
S
 ( ) F d p( 0 ,  )
0
• Q() is called the normalized radiance. Note that 0 and 
can be calculated knowing the orbital parameters.
• The next slide shows the same figure as the previous slide,
only for Q. The upper parts of each wavelength curve now lie
on top of each other.
dQ vs altitude, 245 to 295 nm
Solar Backscatter Ultraviolet (SBUV)
• The next figure plots dQ/dz for a single wavelength.
• Also plotted is the dQ/dz that would be obtained if there were
no ozone absorption i.e. Rayleigh scattering only.
• The horizontal line is the altitude at which  = 1.0
• The area B is almost equal to area C, hence the area within the
curve (A+B) is equivalent to the area under the Rayleigh curve
down to the horizontal line (A+C).
• The area A+C can be simply related to the pressure at the
horizontal line. But the optical depth for ozone absorption is
much greater than that for Rayleigh scattering.
• Hence Q at each wavelength can be related to the column
density of ozone at an optical depth of one, versus the pressure
altitude at that point.
• For wavelength chosen, Q=.00122, pressure altitude=.00135
dQ versus altitude for 275 nm
Contribution function and resolution
• The shape of the curve shown in the previous slide is called
the contribution function, and the half width in altitude is a
measure of the resolution of the method.
• However, it should be noted that the contribution at high
altitudes follows the increase in pressure as the altitude
becomes smaller. It is only when the optical depth due to
ozone approaches one, that the contribution begins to fall off.
• If we subtract the contribution functions for two consecutive
wavelengths then we get the next figure. The resolution of this
contribution function is much smaller.
• It should be noted that there is a limit to the resolution that
can be obtained – the scale height of ozone.
dQ vs altitude, for 265 and 275 nm
dQ vs altitude, for 265 and 275 nm
‘Difference’ for wavelengths, 245 to 285 nm
Effect of scattering and reflection on the
photolysis rates
• As mentioned before most dissociation processes are limited
to the ultraviolet.
• At these wavelengths the Rayleigh cross section is high.
• Hence scattering can become an important issue in calculating
dissociation rates.
• In addition we must also consider the effect of the radiation
that is reflected by the Earth’s surface and clouds.
• The next figure shows the effect of a change in the earth’s
albedo on the dissociation rate at the ground. What is plotted is
the enhancement factor i.e. the ratio of the dissociation at a
given altitude to that at the top of the atmosphere (ф/ф∞).
There is no enhancement at wavelengths below 330 nm, as the
solar flux at these wavelengths does not reach the ground.
Enhancement factors vs albedo
Enhancement factors in the stratosphere
• The following three figures show the enhancement factors for
particular wavelengths for three cases (1) no scattering or
albedo, (2) with scattering added, and (3) with both scattering
and albedo added.
• The figures are taken from Meier et. al, (1982)
• The albedo chosen for the calculations is 0.5. There is a broad
range observed, from 10% for the ground up to 100% for
optically thick non absorbing clouds.
Enhancement factor as a function of
altitude for absorption only
Absorption and multiple scattering
With absorption, multiple scattering, and
albedo