X. Bosch-Lluis 1 , H. Park 2 , A. Camps 2 , S.C. Reising 1 , S. Sahoo 1 ,

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


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


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


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(


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


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


• .

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:


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


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


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


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]


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


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:


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


Bri

gth

ne

ss te

mp

era

ture

[Ke

lvin

]


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


Brig

thne

ss t

empe

ratu

re [

Kel

vin]


F0=22.12 GHz

F0=24.50 GHz

#1 #2

#1 #2



Simulation Results, Horizontal Scans 1/2

0 2000 4000 6000 8000 10000 12000 140008

9

10

11

12

13

14


Brig

thne

ss t

empe

ratu

re [

Kel

vin]


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


Brig

thne

ss t

empe

ratu

re [

Kel

vin]


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



Simulation Results, Horizontal Scans 2/2


0 2000 4000 6000 8000 10000 12000 140008

9

10

11

12

13

14


Brig

thne

ss t

empe

ratu

re [

Kel

vin]


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


Brig

thne

ss t

empe

ratu

re [

Kel

vin]


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


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


THANK YOU !

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X. Bosch-Lluis 1 , H. Park 2 , A. Camps 2 , S.C. Reising 1 , S. Sahoo 1 ,

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