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B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Remote Sensing IAtmospheric Microwave Remote Sensing
Summer 2007
Björn-Martin SinnhuberRoom NW1 - U3215Tel. [email protected]/~bms
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Contents
Chapter 1 Introduction
Chapter 2 Electromagnetic Radiation
Chapter 3 Radiative Transfer through the Atmosphere
Chapter 4 Weighting Functions and Retrieval Techniques
Chapter 5 Atmospheric Microwave Remote Sensing:
A short review of spectroscopy
Chapter 6 Atmospheric UV/visible Remote Sensing
Chapter 7 Radar and Sea Ice Remote Sensing
Chapter 8 Remote Sensing of Ocean Colour
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Chapter 5 Atmospheric Microwave Remote Sensing
• Ground-based microwave remote sensing
• A short review of microwave spectroscopy
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Radiometer for Atmospheric Measurements (RAM)
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
NDSC Stadion at Ny-Alesund, Spitsbergen (79°N)
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Observations in Spitsbergen (79°N)
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Principle of the Radiometer for Atmospheric Measurements
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Measured Microwave Spectrum by the RAM
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Pressure Broadening of Spectral Lines
50km / 0.5 hPa
20km / 50 hPa
10km / 200 hPa
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Weighting Functions for Ozone Retrieval
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Retrieval techniques / Inverse Modelling
xy F
xKy
Assume that the measured spectrum y is a known function of the atmospheric profile x plus some noise ε.
Linearize F (also known as the forward model):
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
However,
can not be directly inverted (ill-posed problem)
Optimal Estimation
xKy
aT
aT
aa KxySKKSKSxx 1
ˆ
A-priori profile
A-priori profile covariance matrix
Measurement error covariance matrix
Best guess profile
Best estimate given by Optimal Estimation solution:
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Example Ozone Profile: RAM vs. Ozonesonde
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Optimal Estimation: Averaging Kernels
aT
aT
aa KxySKKSKSxx 1
ˆ
1 SKKSKSG T
aT
a
aa xxKGxx̂
GxxAxx aaˆ
GxAIAx a
Optimal estimation solution:
Define:
Then:
Define Averaging Kernel Matrix A = GK:
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Averaging Kernel Functions
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Chapter 5 Atmospheric Microwave Remote Sensing
• Ground-based microwave remote sensing
• A short review of microwave spectroscopy
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Molecular Rotations
Diatomic molecule:
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Rotational Energy (classical)
q
qqqIT 2
2
1 q qq
q
I
J
2
2
rotational Energy
qqqq IJ angular momentum
moment of inertia
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Molecular Rotations: Moments of Inertia
Diatomic molecule:
210 rrr 2211 rmrm
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Molecular Rotations: Moments of Inertia
i
iirmI 2
2121
211122
222
211
mmrr
rrmrrm
rmrmI
210 rrr 2211 rmrm
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Molecular Rotations: Moments of Inertia
21
012
21
021 and
mm
rmr
mm
rmr
20
20
21
21 rrmm
mmI
21
21
mm
mm
reduced mass:
21
111
mm
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Rotational Energy (classical)
q qq
q
I
JT
2
2
zz
z
yy
y
xx
x
I
J
I
J
I
J
222
222
classically:
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Rotational Energy (quantum mechanics)
zz
z
yy
y
xx
x
III 222
222 JJJH
Quantum mechanics:
I2
2JH
For linear molecules:
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Rotation: Energy Levels
,2,1,0with12
2
JJJI
EJ
I2
2JH
Angular momentum is quantized:
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Rotation: Energy Levels
12
2
JJI
EJ
Express energy in terms of wave numbers:
14
JJIc
JF
hc
E~remember:
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Rotation: Energy Levels
cIB
4
with Rotational Constant B:
24 rc
14
JJIc
JF
1 JBJJFwrite as
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Rotational Energy Levels
J F(J)
)0()1(~01 JFJFJJ
)0()1(~01 FF
]cm[202~ 101
BB
]cm[426~ 112
BBB
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Rotational Transitions
121~1 JBJJJBJJ
JJJJB 22 23
12 JB
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Rotational Transitions
12~1 JBJJ
allowed transitions:
1J
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Microwave Spectrum of HCl
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Rotational Constant
22 rc
hB
with μ the (reduced) mass ofthe molecule and r the bond length.
Difference between two rotational linesgiven by 2B, where B is the rotational constant:
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Microwave Spectrum of ClO
22 rc
hB
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Intensities of Rotational Lines
•Probability for transition between level l and level udepends on the difference of molecules in level l and u•In thermal equilibrium given by Boltzmann distribution:
TkEN
NBJ
l
u exp
TkJBhcJ B1exp
(tends to decrease with increasing J)
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Intensities of Rotational Lines
•Depends also on degenaracies of the levels:
12 Jg J
(tends to increase with increasing J)
Why?
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Degeneracies of Rotations
posibleorientations
12 J
J=1
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Degeneracies of Rotations
J=2 J=3
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Intensities of Rotational Lines
•Depends also on degenaracies of the levels:
12 Jg J
(tends to increase with increasing J)
Overall proportional to:
TkJBhcJJ B1exp12
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Intensities of Rotational Lines
May be used to derivetemperature from observedspectrum
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Microwave Spectrum of ClO
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Microwave Spectrum of N2O
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Microwave Spectrum of H2O
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
The N2O Molecule
NN O
N2O is a linear molecule
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
The Water Molecule
O
H H
0.09578 nm
104.48°
B.-M. Sinnhuber, Remote Sensing I, University of Bremen, Summer 2007
Microwave Spectrum of Ozone