x. bosch-lluis 1, h. park 2, a. camps 2, s.c. reising 1, s. sahoo 1, s. padmanabhan 3, n....
TRANSCRIPT
A RADIOMETER CONCEPT TO RETRIEVE 3-D RADIOMETRIC EMISSION FROM ATMOSPHERIC TEMPERATURE AND WATER
VAPOR DENSITY
X. Bosch-Lluis1, H. Park2, A. Camps2, S.C. Reising1, S. Sahoo1, S. Padmanabhan3, N. Rodriguez-Alvarez2, I. Ramos-Perez2, and E. Valencia2
1. Microwave Systems Laboratory - ECE, Colorado State University, Fort Collins, CO, USA.2. Remote Sensing Lab, Dept. Teoria del Senyal i Comunicacions,
Universitat Politècnica de Catalunya and IEEC CRAE/UPC, Barcelona, Spain.3. Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA.
E-mail: [email protected]
IGARSS’11 – Vancouver, Canada, 29th July 2011FR3.T03: Microwave Radiometry Missions and Instrument Performance III
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Presentation Outline
1. Motivation
2. Introduction to Atmospheric Sounding
3. New Concept Proposal
4. Theoretical Development
5. Simulation Results
6. Future Lines and Conclusions
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Radiometric measurements of the atmosphere provide brightness temperatures according to the radiative transfer equation.
Retrieval algorithms are used to obtain information on profiles of atmospheric parameters such as water vapor content (WVC). Weighting functions and in-situ measurements from radiosondes (RAOB) are required to perform such retrievals.
Here we propose a new approach to this problem which may enable the development of new solutions to the atmospheric profile retrieval problem.
Specifically, the goal of this work is to measure the structure of the radiometric emission from the atmosphere using two antennas separated by a certain distance and pointing to the same point in the atmosphere.
Motivation
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Atm
osp
here
Layer 1
Layer N(10 km)
TC
rjj
N
jjabs
rNCA eTKreTT ),0(
1
),0(
Cosmic Background
Atmospheric attenuation
Atmospheric attenuation (from the layer to the ground)
Absorption coefficient
Physical Temperature
dz
ds
ds
Assuming a stratified atmosphere and a pencil beam antenna
Ground level
zenithdzdsr ·sec
Atmospheric Sounding I – Radiative Transfer Equation (RTE) Basis
Discrete RTE
0
),0(),0( )()( dsesTsKeTT sabs
rNCBA
RTE
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Atmospheric Sounding II – Retrieval Algorithm Linearization
)()( oo xxx
FxFy
Weighting Function (MxN) (Jacobian or Kernel)
WVC profile to retrieve(Nx1)
M radiometric measurements(Mx1) @ several frequency channels
Linearization error
Linearization point (measured using RAOB measurements)(Nx1)
Linearization point (Mx1)
The linearization approximation applies only for a certain period of time. It requires the launch of ROAB periodically.
Linearizing the discrete problem for retrievingrj
j
N
jjabs
rNCA eTKreTT ),0(
1
),0(
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Atmospheric Sounding II – Retrieval Algorithm Linearization
• N is the number of atmospheric layers to retrieve• M is the number of uncorrelated channels that the radiometer measures
Usually N >M → ill posed problem
An information content analysis of the measurement determines the quality of the retrieval , i.e. a trade-off between accuracy and spatial resolution
Various inversion methods can be used for retrieving WVC:
1. Newtonian Iteration retrieval 2. Regression retrieval 3. Neural Network4. Bayesian Maximum likelihood
𝑦−𝐹 (𝑥0 )=𝜕𝐹𝜕 𝑥 (𝑥−𝑥0 )+𝜀 𝑥=(𝜕𝐹𝜕 𝑥 )
− 1
(𝑦−𝐹 (𝑥0 ))+𝑥0
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Atm
osp
here
Layer 1
Layer N(10 km)
TCB
Ground level
Baseline
LPFAntenna #1(x1, y1, 0)
Antenna #2(x2, y2, 0)
(x0, y0, z0)
z
x
y
⟨𝑆1𝑝 (𝑡 )𝑆2𝑞∗ ( 𝑡−𝜏𝑑 )⟩
New Concept proposal
True time delay for measuring at points which have different distance with respect Ant1 and Ant2, and sub-overlapping measurements
Measure Brightness temperature using a CROSS-BEAM InterferometerBrightness temperature from different atmospheric volumes could be measured independently, without the cumulative effect of the RTE
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
• .
T B❑=K
|¿|(x p)T ph (x p) e12𝜏 (0 , r 2 x
p+ r1 x
p)¿
~r12 (t )≜ e− j2π f 0 t
√B1B20
∞
H 1 (f )H 2∗( f )e j2πft𝑑 f
V 𝑝𝑞 (u12 , v12 )=12
1𝑘B√B1B2√G1G2
⟨𝑆1𝑝 (𝑡 )𝑆2𝑞∗ (𝑡 ) ⟩
• Visibility sample:
(u12 , v12)≜ ( x2−x1 , y2− y1 )/ λ0
Fringe-washing function ~r12 (t )=sinc(Bw τ)
Integration variable, spans the whole atmosphere
Brightness temperature of the point
Theoretical development
Distance from antenna 1 and 2 to the integration variable
Main differences between this concept and interferometric synthetic aperture radiometer:1. Narrower antenna beamwidth2. Only one visibility sample, not a set of visibility samples3. Adjustable true time delay
Visibility sample written in Cartesian coordinates:
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Antenna beamwidth and overlapping volume effect
Main challenge posed by this technique
If the overlapping solid angle decreases in comparison to the solid angles of the beams , the radiometric resolution (standard deviation) of the measurement increases.
To retrieve the brightness temperature the cross-beam interferometric measurement must be multiplied by the inverse of
χ=∑l=−∞
∞
∑m=−∞
∞
∑n=0
∞
√Ω1xp
𝑝 Ω2x p
𝑞
√Ω𝑎1𝑝 Ω𝑎2
𝑞→1
Very narrow beams mitigate this effect, then same order of magnitude between the overlapping solid angle and the beams’ solid angles
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Spatial Resolution 1/2
Horizontal Spatial Resolution (determined by hardware decorrelation time)
The spatial resolution is determined by the bandwidth of both receivers (FWF)
0 1 2 3 4 5
x 109
0
10
20
30
40
50
60Spatial resolution determined by the FWF
System Bandwidth [Hz]
Me
ters
-1 -0.5 0 0.5 1
x 10-8
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Delay
No
rma
lize
d F
WF
FWF spatial filter effect
B
w=100 MHz
Bw
=500 MHz
Bw
=5 GHz
~r12 (t )≜ e− j2π f 0 t
√B𝑤1B𝑤2
0
∞
H1 ( f ) H2∗( f )e j2 πft𝑑 f ~r12 (t )=sinc(𝐵𝑤 τ )
If with rectangular shapes and
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Spatial Resolution 2/2, Horizontal Spatial Resolution
Moreover, it allows several measurements in the same beam-overlapping volume by changing the delay between both receivers
-30 -20 -10 0 10 20 30-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Sub beam overlapping spatial resoltuion, Bw
=500 MHz
meters
No
rma
lize
d F
WF
d = -2 ns
d = 0 ns
d = +2 ns
Beam-overlapping volume (This volume contributes to the measured visibility function.)
Outside overlapping volume (This volume does not contribute to the measured visibility function.)
3 sub beam-overlapping volume measurements obtained changing the relative delay
The overlapped volume depends on the antennas beamwidth () size of both antennas and on their spacing
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Simulation Assumptions and Considerations
Assumptions and considerations for the simulation
1. 2D atmosphere for simplicity2. Stratified atmosphere with dx=dz=33 meters3. Atmosphere dimensions 10x66 Km (303x2000 voxels)4. Van Vleck model for absorption coefficients, using RAOB measurements for the water vapor,
pressure and temperature profile.5. F=22.12 and 24.50 GHz the same channels as the CMR-H radiometers CSU, channels
suitable for WVC retrieval. 6. Gaussian antenna patterns.7. Identical and perfectly rectangular response of both systems
0 2000 4000 6000 8000 100000
1
2
3
4
5
6
7
Z axis - height [m]
WV
(g
r/m
2)
WVC profile
WVC profile used for the synthetic atmosphere, obtained using a RAOB
WV
C [g
r/m
3]
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Simulation Results, Vertical Scans 1/3
6100 6200 6300 6400 6500 66000
1000
2000
3000
4000
5000
6000
X axis [m]
Z a
xis
[m]
Scaning trajectory
Scanned trajectoryAntena #1Antena #2
0 2000 4000 6000 8000 100000
2
4
6
8
10
12
14
16
Central overlapping point - height[m]
Bri
gth
ne
ss te
mp
era
ture
[Ke
lvin
]Cross-Beam Correlation brightness temperature, Beamwidth=0.5 degrees, Spacing=600m
F0=22.12 GHz
F0=24.50 GHz
0 2000 4000 6000 8000 100000
5
10
15
Central overlapping point - height[m]
Bri
gth
ne
ss te
mp
era
ture
[Ke
lvin
]
Cross-Beam Correlation brightness temperature, Beamwidth=0.5 degrees, Spacing=600m
F0=22.12 GHz
F0=24.50 GHz
6000 6200 6400 6600 6800 7000 7200 7400 76000
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
X axis [m]
Z a
xis
[m]
Scaning trajectory
Scanned trajectory
Antena #1
Antena #2
D=600 m
D=600 m
#1 #2
#1 #2
Centers of the overlapping area, scanned sequentially
=0.5 degrees =100 MHz,
Measured temperatures using the cross-beam interferometer:
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Simulation Results, Vertical Scans 3/3
6100 6200 6300 6400 6500 66000
1000
2000
3000
4000
5000
6000
X axis [m]
Z a
xis
[m]
Scaning trajectory
Scanned trajectoryAntena #1Antena #2
0 2000 4000 6000 8000 100000
2
4
6
8
10
12
14
16
Central overlapping point - height[m]
Bri
gth
ne
ss te
mp
era
ture
[Ke
lvin
]
Cross-Beam Correlation brightness temperature, Beamwidth=0.5 degrees, Spacing=600m
F0=22.12 GHz
F0=24.50 GHz
3000 4000 5000 6000 7000 8000 9000 100000
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
X axis [m]
Z a
xis
[m]
Scaning trajectory
Scanned trajectory
Antena #1Antena #2
Antenna spacing change
D=600 m
D=6600 m0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
0
2
4
6
8
10
12
14
Central overlapping point - height[m]
Brig
thne
ss t
empe
ratu
re [
Kel
vin]
Cross-Beam Correlation brightness temperature, Beamwidth=0.5 degrees, Spacing=6600m
F0=22.12 GHz
F0=24.50 GHz
#1 #2
#1 #2
Measured temperatures using the cross-beam interferometer:
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Simulation Results, Horizontal Scans 1/2
0 2000 4000 6000 8000 10000 12000 140008
9
10
11
12
13
14
Central overlapping point - height[m]
Brig
thne
ss t
empe
ratu
re [
Kel
vin]
Cross-Beam Correlation brightness temperature, Beamwidth=0.5 degrees, Spacing=600m
F0=22.12 GHz
F0=24.50 GHz
0 2000 4000 6000 8000 10000 12000 140000
200
400
600
800
1000
1200
1400
1600
X axis [m]
Z a
xis
[m]
Scaning trajectory
Scanned trajectory
Antena #1Antena #2
0 2000 4000 6000 8000 10000 12000 140000
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
X axis [m]
Z a
xis
[m]
Scaning trajectory
Scanned trajectory
Antena #1Antena #2
0 2000 4000 6000 8000 10000 12000 14000
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
Central overlapping point - height[m]
Brig
thne
ss t
empe
ratu
re [
Kel
vin]
Cross-Beam Correlation brightness temperature, Beamwidth=0.5 degrees, Spacing=600m
F0=22.12 GHz
F0=24.50 GHz
Atmosphere attenuation effectD=600 m
D=600 m
#1#2
#1#2
=0.5 degrees =100 MHz,
X axis [m]
X axis [m]
Height
Height
Measured temperatures using the cross-beam interferometer:
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Simulation Results, Horizontal Scans 2/2
Measured temperatures using the cross-beam interferometer:
0 2000 4000 6000 8000 10000 12000 140008
9
10
11
12
13
14
Central overlapping point - height[m]
Brig
thne
ss t
empe
ratu
re [
Kel
vin]
Cross-Beam Correlation brightness temperature, Beamwidth=0.5 degrees, Spacing=600m
F0=22.12 GHz
F0=24.50 GHz
0 2000 4000 6000 8000 10000 12000 140000
200
400
600
800
1000
1200
1400
1600
X axis [m]
Z a
xis
[m]
Scaning trajectory
Scanned trajectory
Antena #1Antena #2
D=600 m
D=6600 m0 2000 4000 6000 8000 10000 12000 14000
6
7
8
9
10
11
12
13
Central overlapping point - height[m]
Brig
thne
ss t
empe
ratu
re [
Kel
vin]
Cross-Beam Correlation brightness temperature, Beamwidth=0.5 degrees, Spacing=6600m
F0=22.12 GHz
F0=24.50 GHz
0 2000 4000 6000 8000 10000 12000 140000
200
400
600
800
1000
1200
1400
1600
X axis [m]
Z a
xis
[m]
Scaning trajectory
Scanned trajectory
Antena #1Antena #2
#1#2
#1#2
X axis [m]
X axis [m]
Height
Height
© RSLab-UPC & MSL-CSU 2011IGARSS 2011, Vancouver, Canada, 24th-29th July 2011
Conclusions And Open Issues
1. A new radiometric for retrieving VWC proposed using interferometric cross-beam techniques.2. The system can measure brightness temperatures independent of the RTE.3. Spatial resolution depends on:
• The horizontal spatial resolution depends on the BW.• The vertical spatial resolution depends on the antenna spacing and beamwidth
Ongoing:
• Keep on studying this technique to better understand its limitations and constraints.• Estimate the radiometric resolution for ±10% error WVC retrieval depending on the altitude.• Determinate methods for calibrate different parts of the system
• Phase• Amplitude• Offset• Radiometric calibration (hot and cold load)
• Perform retrievals from simulated atmospheres (applying techniques such as “onion peeling” instead of a Weighting function approximation).
• Retrieval error compressive study