Interaction With the Surface and AtmosphereII

8/2/2019 Interaction With the Surface and AtmosphereII

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Interaction of EMR with theSurface and Atmosphere II


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Conservation of energy at the surface

A + T + R = 1 - sum of the

absorptance, reflectance and

transmittance remains equal 1

Absorptance A = a()/i(),

Reflectance R = r()/i(),

Transmittance T=

t()/

i()

Absorption (a =A /l, m-1) is a loss of energy in a medium at specific

frequency (wavelength). It occurs because of the excitation of atoms and

molecules the energy is transformed to heat. Ex: absorption bychlorophyll in the process of photosynthesis.

Transmission is a propagation of energy through a medium.

i

Ai

Ti

Ri

l

Reflection is the change in direction of a wave front at the boundary oftwo media so that the wave front returns into the medium from which it

originated.


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Conservation of energy in the

volume

z

F0

F

- Incident flux

- Absorbed flux

- Scattered flux

- Transmitted fluxt

a

s

i

a absorption

coefficient, m-1

Fdz

dFa= dzF

dFa=

])(exp[)()( 0 zFF a =

- fraction of theincident power that is

absorbed by the slab

Very frequent form

in optics])(exp[)()( 0 zII a =


4/26

Absorption, scattering and

extinction coefficients

a

absorption coefficient, m-1

s scattering coefficient, m-1

e extinction coefficient, m-1

Scattering is the deflection of electromagnetic radiation without absorption

as a result of its interaction with particles.

The sum of the absorption and scattering represents the loss of energy from

the forward-propagating radiation and is called attenuation or extinction.

)()()( saext +=

])(exp[)()( 0 zII ss =])(exp[)()( 0 zII aa =

])(exp[)()( 0 zII extext =

zext

)()(Optical thickness:

(non-dimensional)

= dzzz

ext

=

0

),()( or

Transmittance: ))(exp())(exp()(

)()(

0

=== z

I

IT ext


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Absorption and scattering by

particles

Absorption cross-section, m2: Naa /)()( =

If N is the number of particles in the volume, 1/m3

or Naa =Scattering cross-section, m2: Nss /(( )=) or Nss =

Extinction cross-section, m2:

Nextsaext /)()()()( =+= or Nextext =

])(exp[)()(0

zNIIa

=

FP a

- Beer-Lambert law

=Cross-section can be considered as the absorbed power P

by the particle per the incident flux F, it can be compared

with the geometrical cross-section of the particle

zNz extext )()()(Optical thickness: === drrNrextext )()(

If the scattering particles have size

distribution, for each :


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Absorption and scattering by

particles

These relationships are true for solid

surfaces (soil, leaves) small penetration

For water (absorption by water itself and

organic components, scattering byphytoplankton and mineral particles)-deeper penetration (1-50 m)

For atmosphere (absorption by gases andwater vapor, scattering by molecules andaerosols) dozens of km


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Fluorescence, Raman scattering

We have considered so far elastic scattering effects in which the wavelength ofthe radiation is unchanged by the scattering process. Fluorescence and Raman

scattering belong to inelastic processes in which excitation wavelengths are

different from the emitting wavelength.

Typical example of

fluorescence is the

chlorophyll fluorescence

which occurs as a result

of illumination of leaves

and phytoplankton inwater. Part of the light

absorbed in the 400-700

nm range is emitted as

fluorescence signal inthe red near 685 nm

Raman scattering is another trans-spectral process: as a result light

emits at higher or lower frequency or at several frequency pairs.

Inelastic effects are useful for tracing specific substances with

known fluorescence or Raman signatures


8/26

Absorption of Gases in the

AtmosphereMechanisms of molecular absorption:

1. Promotion of electrons to higher energy level electronic transitions;

absorption lines appear in UV and VIS

2. Vibration energy levels absorption lines in the thermal infrared region

3. Rotation energy levels absorption lines are in the microwave and far IR

4. Combinations of mechanisms

Line broadening: narrow absorption bands

become broader due to the additional

processes in the atmosphere

Thermal motion (Doppler boadening):

Pressure broadening (collision):

2cMRT

ff

m

=

RTM

pf

m

~


9/26

Scattering by particles

rx

2=

In the most simple case, atmospheric particles can be considered as

small spheres.

The rigorous solution for the scattering of a plane monochromatic

wave by a spherical dielectric particle with an index of refraction n

was derived by Mie.

This solution establishes for given index of refraction n of particles

relationship between scattering and extinction cross sections and the

parameter

where r is the radius

of the sphere, so

)(xfs = and )(xfext =

Ratio r/ determines the type of scattering

Function which defines probability of light scattering

in various directions called phase function)(pp =


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Comparison of Raleigh and Mie

Scattering Regimes


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Sky is blue

Blue light is most efficiently scattered


16/26

Why are sunsets red ???

Blue

scattered

away

Long Path compared to noon

Green

scattered

away

Yellow

scattered

away

Orangescattered

away


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Clouds in contrast to the blue sky

appear white to achromatic gray.

The water droplets that make up the cloud are much larger than the

molecules of the air and the scattering from them is almost independent

of wavelength in the visible range.

Scattering from the clouds


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Average Composition of the

Atmosphere Below 25 kmCom p on en t Ch em ical Ab b r ev iat ion

Vo lume %( d r y a ir )

Nitrogen N2 78.08

Oxygen O2 20.98

Argon Ar 0.93

Carbon dioxide CO2 0.035

Neon Ne 0.0018

Helium He 0.0005

Hydrogen H2 0.00006

Krypton

Kr 0.0011

Xenon Xe 0.00009

Methane CH4 0.0017

Ozone O3 0.00006

This gaseous mixture remains remarkably uniform in composition, and is the result of

efficient biogeochemical recycling processes and turbulent mixing in the atmosphere.


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Water Vapor

)(Tp

pH

sat

water

=

There is also a significant but variable amount of water vapor (0.1-3%)specified by relative humidity H

waterp

H =0100%

is the partial pressure of the water vapor product of the total

atmospheric pressure with volume fraction of water vapor

)(Tpsat is the saturated vapor pressure of water at temperature T

For t =20C psat = 2.34 kPa, so if total atm pressure is 100 kPa and humidity is

80% the volume fraction of water vapor is f = psat*H*100/ptot = 1.9%


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Atmospheric Vertical Structure of

Temperature and Pressure


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Temperature and Pressure (cont.)

RT

pMm=

Where is the gas density, kg/m3, p is the

pressure, Newton/m2, T- temperature, K, R is

the gas constant, R=8,314 J/K, Mm is the kmole

mass in kg, for air 28.97kg

dzzgzdp )()( =Expression basically states that the difference of

pressure between levels z and z+dz is equal to

the weight of the atmosphere between two

levels

Combining equationsdzRT

Mg

p

dp m=

mgM

RTH =

)/exp()0()( Hzpzp =

Scale height

If T=const pressure decreases exponentially

with altitude. The same is true for density and

number density N (molecules/m3

)(0) = 1.21 kg/m3, p(0) =105Pa

)/exp()0()( Hzz = )/exp()0()( HzNzN =


22/26


Temperature and Pressure (cont.)

The above illustrations assumed an isothermal atmosphere. Usually this

is not exactly true. The change of the atmospheric temperature can be

derived for a simplified case assuming thermal equilibrium. It can be

shown that rate of temperature change is 9.81 K/km.

Actual change is lower and is about 6.5 K/km

At higher altitudes the temperature profile is more complex.

VIIRS, MODIS, FY-1C, AVHRR


23/26

, , ,

H2O

H2OH2O

H2O

O2

CO2

CO2

H2O

O2

O3

H2O

O2

Comparison of Solar and Thermal Radiation


24/26

Comparison of Solar and Thermal Radiation

with Transmission Bands

O ti l Thi k d


25/26

Optical Thickness and

TransmittanceOptical thickness from different materials will add:

total = 1 + 2 + 3 + .

...

321321 ...)( ++

== eeeIeII ooI = IoT1T2T3

Optical thickness is additive, transmittance is multiplicative.

= 1/cos

B L b t L f th


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Beer-Lambert Law for the

atmosphereThe Beer-Lambert law for the atmosphere is usually written as

where each x is the optical depth whose subscript identifies the source of

the absorption or scattering it describes:

a refers to aerosols (that absorb and scatter)

g are uniformly mixed gases (mainly carbon dioxide (CO2) and

molecular oxygen (O2) which only absorb) NO2 is nitrogen dioxide, mainly due to urban pollution (absorption

only)

w is water vapour absorption

O3 is ozone (absorption only) r is Rayleigh scattering from molecular oxygen (O2) and nitrogen

(N2) (responsible for the blue color of the sky).

m is the optical mass or airmass factor, a term approximately equal (for

small and moderate values of) to 1 / cos(), where is the observed

object's zenith angle (the angle measured from the direction perpendicular

to the Earth's surface at the observation site).

))(exp(32

0 rOwNOgamII +++++=

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Interaction With the Surface and AtmosphereII

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