Insights into WWII Radar Bands & Scattering Phenomena
Radar Bands
•
Letters chosen during WWII. X-band so-named
b/c it was kept secret during the war.
Multiple scattering in cloud or aerosol
layers
τ=0
τ=τ
*
Fraction absorbed + fraction transmitted + fraction reflected = 1
REFLECTED
ABSORBED
TRANSMITTED
Direct & diffuse transmission
τ=0
τ=τ
*
Fraction absorbed + fraction transmitted + fraction reflected = 1
REFLECTED
ABSORBED
DIFFUSE Transmission:
Scattered at least once
DIRECT Transmission:
Not scattered at all
Monte-Carlo
•
Can simulate each individual photon from sun.
•
Chance of making it through cloud: t*=e
–
τ*/μ
•
Chance of being scattered or absorbed: 1-t*
•
Chance of being scattered:
•
Chance of being absorbed:
•
Low SSA: most absorbed
•
Higher SSA: many still absorbed
(multiple scattering means many
chances to be absorbed!)
•
Many photons reflected than
transmitted (optically thick)
•
A bit unrealistic because g=0
(would be the case for smaller
particles or longer wavelengths)
•
Now SSA = 1 (conservative
scattering). No photon absorption.
•
Higher g, more photons make it
through rather than being reflected
back.
•
g=0.99 is quite unrealistic. g=0.8 to
0.9 for most clouds in the visible.
Two-Stream Approximation
•
Azimuthally averaged radiance field
•
Radiance is constant within a hemisphere. Can be
different between upward & downward
hemispheres.
•
Phase function is parameterized by g only.
•
Can determine
r, t, a
from three variables:
Solving these equations:
…leads to the general solution:
Next apply boundary conditions
•
ie., the underlying surface is black.
•
A known intensity is downwelling upon the TOA (e.g.,
from the sun)
where
General 2-stream equations
where
Assumptions:
•
Incoming flux is diffuse. Amazingly, works okay with solar
illumination as well!
•
Initially do derivation assumng a black underlying surface.
•
Straightforward to add a nonzero surface albedo later.
Limiting Case: Semi-Infinite Cloud
•
Limit when cloud is VERY optically thick (τ* >~ 100)
•
Transmittance t
0. So only absorption and reflectance.
•
Absorption = 1 – reflectance in this case
Limiting Case: Semi-Infinite Cloud
•
Asymmetry parameter g of 0.85 is harder to get back out, so
reflectance is lower.
•
Note that reflectance is not super high even for ssa =0.999! Implies
that MANY scattering events are happening. How many?
Limiting Case: Semi-Infinite Cloud
•
Asymmetry parameter g of 0.85 is harder to get back out, so
reflectance is lower.
•
Note that reflectance is not super high even for ssa =0.999! Implies
that MANY scattering events are happening. How many?
Limiting Case: Non-absorbing cloud
•
Useful for clouds in the visible, where imaginary part of index
of refraction of water & ice is essentially 0 (pure scattering)
•
Reflectance (r) & tramittance (t) only.
•
a=0 ; t=1-r
Limiting Case: Non-absorbing cloud
Typical Cirrus Cloud
Thicker water cloud
•
As we saw in Cloud Radiative forcing, the cloud albedo ( = reflectance) is
important in determining cloud radiative forcing.
•
Even optical depth of 1 still has low reflectance, due to high asymmetry
parameter.
General Case: Reflectance & Transmittance
g=0.85
g=0.85
•
Reflectance not very high even for ssa =~ 0.9 (tops out due to
strong absorption).
General Case: Absorption
g=0.85
•
Strong absorption for ssa <~ 0.99 !
Final notes
•
Can calculate (monochromatic) fluxes & heating rates using
the fact that
•
Can add a non black surface.
•
Can partition the flux transmittance into diffuse & direct
components, using
Diffuse & Direct Cloud Transmittance
Non-Absorbing cloud (ie cloud in visible); g=0.85
Total
Direct
Diffuse
Adding in a reflecting surface
τ=0
τ=τ
*
REFLECTED
ABSORBED
TRANSMITTED
•
We already did this!!
r
sfc
surf
the significance of X-band in WWII radar technology and delve into the principles behind multiple scattering, direct transmission, and Monte-Carlo simulations in cloud layers. Understand the impact of single-scattering albedo variations and the two-stream approximation on radiance fields. Learn how to solve related equations and apply boundary conditions for black surface scenarios.
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Presentation Transcript
Radar Bands Letters chosen during WWII. X-band so-named b/c it was kept secret during the war.
Multiple scattering in cloud or aerosol layers REFLECTED =0 ABSORBED = * TRANSMITTED Fraction absorbed + fraction transmitted + fraction reflected = 1
Direct & diffuse transmission REFLECTED ABSORBED =0 = * DIRECT Transmission: Not scattered at all DIFFUSE Transmission: Scattered at least once Fraction absorbed + fraction transmitted + fraction reflected = 1
Monte-Carlo Can simulate each individual photon from sun. Chance of making it through cloud: t*=e */ Chance of being scattered or absorbed: 1-t* Chance of being scattered: Chance of being absorbed: (1-t*)w0 (1-t*)(1-w0)
Low SSA: most absorbed Higher SSA: many still absorbed (multiple scattering means many chances to be absorbed!) Many photons reflected than transmitted (optically thick) A bit unrealistic because g=0 (would be the case for smaller particles or longer wavelengths)
Now SSA = 1 (conservative scattering). No photon absorption. Higher g, more photons make it through rather than being reflected back. g=0.99 is quite unrealistic. g=0.8 to 0.9 for most clouds in the visible.
Two-Stream Approximation Azimuthally averaged radiance field Radiance is constant within a hemisphere. Can be different between upward & downward hemispheres. Phase function is parameterized by g only. Can determine r, t, a from three variables: t*, w0, g
Solving these equations: leads to the general solution:
Next apply boundary conditions ie., the underlying surface is black. A known intensity is downwelling upon the TOA (e.g., from the sun) where
General 2-stream equations where Assumptions: Incoming flux is diffuse. Amazingly, works okay with solar illumination as well! Initially do derivation assumng a black underlying surface. Straightforward to add a nonzero surface albedo later.
Limiting Case: Semi-Infinite Cloud Limit when cloud is VERY optically thick ( * >~ 100) Transmittance t 0. So only absorption and reflectance. Absorption = 1 reflectance in this case
Limiting Case: Semi-Infinite Cloud Asymmetry parameter g of 0.85 is harder to get back out, so reflectance is lower. Note that reflectance is not super high even for ssa =0.999! Implies that MANY scattering events are happening. How many?
Limiting Case: Semi-Infinite Cloud Asymmetry parameter g of 0.85 is harder to get back out, so reflectance is lower. Note that reflectance is not super high even for ssa =0.999! Implies that MANY scattering events are happening. How many?
Limiting Case: Non-absorbing cloud Useful for clouds in the visible, where imaginary part of index of refraction of water & ice is essentially 0 (pure scattering) Reflectance (r) & tramittance (t) only. a=0 ; t=1-r
Limiting Case: Non-absorbing cloud Thicker water cloud Typical Cirrus Cloud As we saw in Cloud Radiative forcing, the cloud albedo ( = reflectance) is important in determining cloud radiative forcing. Even optical depth of 1 still has low reflectance, due to high asymmetry parameter.
General Case: Reflectance & Transmittance g=0.85 g=0.85 Reflectance not very high even for ssa =~ 0.9 (tops out due to strong absorption).
General Case: Absorption g=0.85 Strong absorption for ssa <~ 0.99 !
Final notes Can calculate (monochromatic) fluxes & heating rates using the fact that Can add a non black surface. Can partition the flux transmittance into diffuse & direct components, using
Diffuse & Direct Cloud Transmittance Non-Absorbing cloud (ie cloud in visible); g=0.85 Total Direct Diffuse
Adding in a reflecting surface REFLECTED =0 ABSORBED = * TRANSMITTED surf rsfc We already did this!!
