initial observation results for precipitation on the ku-band broadband radar network.pdf

Ei-ichi Yoshikawa1, 2, Satoru Yoshida1, Takeshi Morimoto1, Tomoo Ushio1,

Zen Kawasaki1, and Tomoaki Mega3

Osaka University, Osaka, Japan1

Colorado State University, CO., U.S.2

Kyoto University, Kyoto, Japan3

IGARSS 2011, Vancouver-Sendai, Jul. 29, 2011

INITIAL OBSERVATION RESULTS

FOR PRECIPITATION

ON THE KU-BAND BROADBAND RADAR

NETWORK

0

1

Outline

1. Introduction

2. The Ku-band Broadband Radar (Ku-BBR)

– Design concept

– Observation accuracy

– Observation result

3. The Ku-BBR Network

– Deployment in Osaka

– Initial observation Result

4. Conclusion

2

Introduction

Resolution of Conventional Weather Radar

100m

10min

○Fronts, Hurricanes

○Mesocyclones,

Supercells,

Squall lines

△Thunderstorms,

Macrobursts

×Cumulus,

Tornadoes,

Microbursts

3

Introduction

Resolution of the Ku-BBR Network

Several meters

1min


○Mesocyclones,

Supercells,

Squall lines

○Thunderstorms,

Macrobursts

○Cumulus,

Tornadoes,

Microbursts

△Smaller

phenomena?

Introduction

The Ku-BBR Network

<Conventional Radar>

• High resolution ⇒ Range resolution : several meters

3-dB beam width : 3 deg

⇒ Temporal resolution : 1 min/VoS

• Short range (15 km) radar ⇒ Min altitude : 14 m

⇒ Efficient for Troposphere

(8 through 15 km altitude)

• Multi-Radar Network ⇒ Precipitation attenuation correction

⇒ High resolution grid retrieval

⇒ Wider area

4

5

Design Concept of the Ku-BBR

High resolution

Pulse compression

Wide Band Width

Ku-band

Precipitation Attenuation

Short range: 15 km

(Dual-poralization)

Wide Area & High Accuracy

Multi-radar network

Gain

Range resolution

：

： BT

Bc 2

B ：Band width (Hz), ：Light speed (m/sec)

・Band width of 80 MHz

⇒ Range resolution of 2 m (max)

・In C- and X-band, it is difficult to

obtain wide band width in Japan.

・Polarimetric parameters are more

sensitive in Ku-band than other

low frequency radars.

・Higher accuracy in overlapped area

・Network approach for precipitation

attenuation correction

T ：Pulse width (sec),

c

solution solution

solution solution

6

Configuration

Digital Baseband IF (2GHz) Ku (15.71-9 GHz)

D/A Converter generates IQ signals

arbitrarily. (170 MHz (max), 14 bit)

Bistatic Lens Antenna to eliminate blind range

PC

Signal Processing Unit

14bit170MHz

MemoryD/A

D/A

A/D

A/D

DSP Board

IQModulator

IQ De-modulator

LO

I

Q

I

Q

IF Unit

2GHz RotaryJoint

LO13.75GHz

Horn

Antenna Unit

Amp

Amp

HPA

LNA

Mixer

Mixer Horn

Luneberg Lens

Real-time Digital Signal Processing for Pulse Compression and Doppler Spectrum Estimation

32bitinteger

Reference signal(I and Q)

16bit integer

Memory

Received signal(I and Q)

16bit integer

A/D converter

*

FFT(32768 points)

FFT(32768 points)

IFFT(32768 poins)

Former process

DSP boards

Pulse compression

output(I and Q)

16bit integer

Latter process

Clutter filter

&Doppler moment

estimation

FFT(64 points)

32bitfloat


I

Q

PC

Power, Velocity,

Spectral width

32bit float

64 times/segment

8192 times/segment

7


• First: Pulse compression, Second: Doppler spectrum estimation

• Parallel calculation with DSPs

– First: 32 DSPs (32 bit integer, 1 GHz), Second 3 DSPs (Float, 300 MHz)

Pulse compression Doppler estimation

New FPGA system is in the process of production.

8

Fast Scanning System

Azimuth rotation

40 RPM (max)

30 RPM (usual)

Elevation rotation

Primary

Feed

Luneburg Lens

(φ450 mm)

Elevation rotation

9

Specifications

Name Specifications Remarks

System Operational Frequency [GHz] 15.75

Operational Mode Spiral, Conical, Fix

Band Width[MHz] 80 (max) 15.71 - 15.79 GHz

Coverage Az / EL [deg] 0-360 / 0-90

Coverage

Range [km] 15 km (16 dBZ) variable

Resolution Az / El [deg] 3 / 3

Range [m] 2 (min) variable

Time/1scan [sec] 60

Power Consumption [kVA] 4kVA (max)

Weight [kg] 500kg (max)

Antenna Luneberg Lens

Gain [dBi] 36

Beam Width [deg] 3

Polarization Linear

Cross Polarization [dB] 25 (min)

Antenna Noise Temp. [K] 75 (typ)

Transmitter Transmission Power [W] 10(max)

& Receiver Duty Ratio variable

Noise figure [dB] 2 (max)

Signal D/A 170MHz - 14bit IQ 2ch

Processiong A/D 170MHz - 14bit IQ 2ch

Range Gate [point] 32768

PRT [us] variable

10

Observation Accuracy

Cross-validation with Joss-

Waldvogel Disdrometer (JWD)

•Impact type disdrometer

•Rain drop diameter: 0.3 - 5.0 mm

•Ze is calculated by Mie theory

dDDNDZ be

)()(

1

22

5

4

N(D): DSD

: Back Scattering coefficient

from mie scattering

b

2

1

2

1214

l

ll

l

b bal

11

Observation Accuracy Z

m o

f B

BR

(d

BZ

)

0 10 20 30 40

10

20

30

40

0

Ze of JWD (dBZ)

Scatter plot

-5 0 5 10 -10 0

5

10

15

20

Zm – Ze (dBZ) (%

)

Histogram

• The high resolution reflectivity measurements of the

BBR show fairly good agreement compared with JWD.

– Correlation coefficient: 0.95, Standard deviation: 1.59 dBZ

12

Examples of Ku-BBR Observation

Vertical Pointing Mode

Heig

ht

(km

)

0 0

0

Time (min)

Time-Height Cross Section (Reflectivity)

5 10 15 20

2

4

6

8

Re

fle

cti

vit

y (

dB

Z)

50

Range resolution

of several meters

Minimum

observation

height of 50 m

13

Examples of Ku-BBR Observation

Volume Scanning Mode

3D construction of

strong vortex (Resolution of several

meters, 1 min)

3D structure of

strong vortex (Resolution of several

meters, 1 min)

14

2(3)-BBR Network in Japan

Toyonaka radar

(Dual-pol) 135.455748E

34.804939N

SEI radar

135.435054E

34.676993N

Nagisa radar 135.659029E

34.840145N

(from Aug., 2011)

Osaka area, Japan

15

Initial Observation Results

13:54:05 09/14/10

Integration clearly

shows precipitation

patterns because of

the high temporal

resolution

Integration by using

simple geometric

weighting average

16


13:55:09 09/14/10

17


13:56:13 09/14/10

18


13:57:17 09/14/10

19


13:58:21 09/14/10

20


Clear shapes

of precipitation

are retrieved Thin-plate shaped

pattern of the BBR

still remains

21

Conclusion

• We developed the Ku-BBR Network, a short-range and

high-resolution weather radar network.

– Range resolution of several meters

– Temporal resolution of 1 min per volume scan (30 elevations)

– Coverage of 50 – 15000 m in range

• Due to the high spatial resolution, reflectivity is

accurately measured.

– Reduction of the error from non-uniform beam filling

– Very low Minimum detectable height

• Precipitation patterns are clearly shown by data

integration

– With a use of a simple weighting average

– Due to the high temporal resolution

– Integrated products will be improved by a network radar signal

processing

End

Thank you for listening!

22

23


13:54:05 09/14/10

Integration clearly

shows precipitation

patterns because of

the high temporal

resolution

Integration by using

simple geometric

weighting average

24


13:55:09 09/14/10

25


13:56:13 09/14/10

26


13:57:17 09/14/10

27


13:58:21 09/14/10

28

Introduction

Resolution of the BBR

Severl meters

1min


○Mesocyclones，

Supercells,

Squall lines

○Thunderstorms,

Macrobursts

○Cumulus,

Tornadoes,

Microbursts

△Smaller

phenomena??

Introduction

Introduction

The BBR Network

<Conventional Radar>

○ Unobservable area in low altitudes ⇒ in 0 deg elevation

300 km range : 5 km altitude

100 km range : 0.5 km altitude

15 km range : 14 m altitude

○ Needless area to be observed ⇒ Troposphere is below

8 through 15 km altitude

○ High resolution ⇒ Range resolution : several meters

3-dB beam width : 3 deg

Temporal resolution : 1 min/VoS

○ Cover large area with multi radar

× Precipitation attenuation

29

Introduction

30

Outline

Outline

1. The Ku-band BroadBand Radar (The Ku-BBR)

– Theory


– Initial observation result


– Theory


– Initial Observation Result

3. A Kalman Filter Approach for Precipitation

Attenuation Correction in the Ku-BBR Network

– Algorithm

– Simulation Result

31

Ch.1: The Ku-BBR

Chapter 1 The Ku-BBR


– Theory

– Configuration



– Theory





– Algorithm


32

Concept

High resolution

Pulse compression

Wide Band Width

Ku-band

Precipitation Attenuation

Designed as a short

range polarimetric radar

Wider Area & Higher Accuracy

Radar network

solution

Gain

Range Resolution

：

：

BT

B

c

2

B：Band width (Hz), ：Light speed (m/sec)

solution

・Band width of 80 MHz

⇒ Range resolution of 2 m (max)

・In C- and X-band, it is difficult to

obtain wide band width in Japan.

・Polarimetric parameters are more

sensitive in Ku-band than other low

frequency radars.

・Higher accuracy in overlapped area

・Network approach for precipitation

attenuation correction

solution solution

T ：Pulse width (sec),

c


33

Pulse Compression for Distributed Particles

• Pulse Compression

– gives us sufficient energy on a target for detection with

high range resolution and signal-to-noise ratio (SNR).

– is equivalent to cross correlation between transmitted

and received signals (almost equal to auto correlation).

Low power &

long-modulated pulse

High power &

short-duration pulse


34

Pulse Compression for Distributed Particles

• Radar Equation for Precipitation Particles with

Pulse Compression


Zrl

cGPP ht

r2

1

2ln2 2

2

2210

322

r

Z

rl

B

cGBP

Pht

r2

1

2ln2 2

2

2210

322

r

• Radar equation

(received power) does

NOT actually change.

• High range resolution

responding wide band

width is accomplished.

• High SNR due to long

pulse reduces to

integrate pulses and

allows one to scan

rapidly.

35

Configuration

Digital Baseband IF (2GHz) Ku (15.71-9 GHz)

D/A Converter generates IQ signals

arbitrarily. (170 MHz (max), 14 bit)

Bistatic Lens Antenna (36 dBi, 3 deg)

PC


14bit170MHz

MemoryD/A

D/A

A/D

A/D

DSP Board

IQModulator

IQ De-modulator

LO

I

Q

I

Q

IF Unit

2GHz RotaryJoint

LO13.75GHz

Horn

Antenna Unit

Amp

Amp

HPA

LNA

Mixer

Mixer Horn

Luneberg Lens

Real-time Digital Signal Processing for Pulse Compression and Doppler Spectrum Estimation


36

Bistatic Lens Antenna System

About 1450 mm

Low Noise Amplifier

Primary Feed

Luneburg Lens (φ450 mm)

Sumitomo Honeycomb Sandwich Redome

• Direct Coupling level

– Bistatic antenna (-70 dB) < Monostatic antenna with a duplexer

– The nearest range is 50 m because we don’t need to turn the receiver off.

• Simple Construction for Fast Scanning

High Power Transmitter


37

Bistatic Lens Antenna System

Azimuth rotation

40 RPM (max)

30 RPM (usual)

Elevation rotation


32bitinteger

Reference signal(I and Q)

16bit integer

Memory

Received signal(I and Q)

16bit integer

A/D converter

*

FFT(32768 points)

FFT(32768 points)

IFFT(32768 poins)

Former process

DSP boards

Pulse compression

output(I and Q)

16bit integer

Latter process

Clutter filter

&Doppler moment

estimation

FFT(64 points)

32bitfloat


I

Q

PC

Power, Velocity,

Spectral width

32bit float

64 times/segment

8192 times/segment

38


• First: Pulse compression, Second: Doppler spectrum estimation

• Parallel calculation with DSPs

– First: 32 DSPs (32 bit integer, 1 GHz), Second 3 DSPs (Float, 300 MHz)

Pulse compression Doppler estimation

New FPGA system is in the process of production.


39

Specifications


Name Specifications Remarks

System Operational Frequency [GHz] 15.75

Operational Mode Spiral, Conical, Fix

Band Width[MHz] 80 (max) 15.71 - 15.79 GHz

Coverage Az / EL [deg] 0-360 / 0-90

Coverage Range

[km] 15 km (16 dBZ) variable

Resolution Az / El [deg] 3 / 3

Range [m] 2 (min) variable

Time/1scan [sec] 60

Power Consumption [kVA] 4kVA (max)

Weight [kg] 500kg (max)

Antenna Luneberg Lens

Gain [dBi] 36

Beam Width [deg] 3

Polarization Linear

Cross Polarization [dB] 25 (min)

Antenna Noise Temp. [K] 75 (typ)

Transmitter Transmission Power [W] 10(max)

& Receiver Duty Ratio variable

Noise figure [dB] 2 (max)

Signal D/A 170MHz - 14bit IQ 2ch

Processiong A/D 170MHz - 14bit IQ 2ch

Range Gate [point] 32768

PRT [us] variable

40

Observation Accuracy

Cross-validation with Joss-

Waldvogel Disdrometer (JWD)

•Impact type disdrometer

•Rain drop diameter: 0.3 - 5.0 mm

•Ze is calculated by Mie theory

dDDNDZ be

)()(

1

22

5

4

N(D): DSD

: Back Scattering coefficient

from mie scattering

b

2

1

2

1214

l

ll

l

b bal


41

Observation Accuracy Z

m o

f B

BR

(d

BZ

)

0 10 20 30 40

10

20

30

40

0

Ze of JWD (dBZ)

Scatter plot

-5 0 5 10 -10 0

5

10

15

20

Zm – Ze (dBZ) (%

)

Histogram

• The high resolution reflectivity measurements of the BBR

show fairly good agreement compared with JWD.

– Correlation coefficient: 0.95, Standard deviation: 1.59 dBZ


42

Comparison to C-band Radar

C-band radar (El = 0.09deg) The Ku-BBR (Base scan)

Highly attenuated

Fine structures

are shown

Tanegashima,

Kagoshima


43

Observation Result (Time series example)

Toyonaka,

Osaka university


44

Example –tornado?


2nd elevation

(in altitudes of 0 m – 270 m, roughly)

45

Example –tornado?


3rd elevation


46

Example –tornado?


4th elevation


47

Example –tornado?


5th elevation


48

Example –tornado?


6th elevation


49

Example –tornado?


7th elevation


50

Example –tornado?


8th elevation


51

Example –tornado?


9th elevation


52

Example –tornado?


10th elevation


53

Summary of Chapter 1


• We developed the Ku-BBR, a short-range and high-resolution

weather radar.

– Range resolution of several meters

– Temporal resolution of 1 min per volume scan (30 elevations)

– Coverage of 50 – 15000 m in range

• Due to the high spatial resolution, reflectivity is accurately

measured.

– Reduction of the error from non-uniform beam filling

– Very low Minimum detectable height

• The Ku-BBR finely detected a small phenomena not resolved

by a conventional C-band radar.

• The BBR is a strong tool to detect, analyze and predict these

small scale phenomena.

54

Ch.2: The Ku-BBR Network

Chapter 2 The Ku-BBR Network


– Theory




– Theory





– Algorithm


55

Network Approach of the Ku-BBR

7.5 m with 20 MHz BW

262 m in 5 km range

524 m in 10 km range

785 m in 15 km range

• Single BBR

– Range resolution is

very high.

– On the other hand,

cross-range resolution

is 100 times poorer

than range resolution

in a range of 15 km.

– Composite average

function (CAF) is a

thin-plate shape.

Cross-range

resolution

Range resolution

3 deg


56


• The Ku-BBR Network

About 10 x 10 m

spatial resolution Node 1

Node 2

– CAFs of two radar

nodes are overlapped.

– A weighting average

of the two received

powers is equivalent

to that of the two

CAFs.

– Overlapping two thin-

plate shapes achieves

several meter

resolution in 2- or 3-D.


57

Equations

dVIP rrrr ,00

423

2

000

422

04

,,,

rl

rrWfgPI

st

rrr

0

, dDDNDb rr

dddrrdV sin2

Single Radar Equation

Composite Average Function (CAF)

Equivalent Reflectivity Factor

where,


58


A Weighting Average of Received Signals

Obtained by Each Radar Node

dVI

dVIw

dVIw

PwP

N

n

nn

N

n

nn

N

n

nn

rrr

rrr

rrr

rr

,ˆ

,

,

ˆ

0

1

0

1

0

1

00

11

N

n

nwwhere,

A weighting average of

received signals


CAFs

is translated to…



CAFs

59

Evaluation of Spatial Resolution


Zonal

range (km)

Meridional

range (km)

(7, 0) (-7, 0)

Node 1 Node 2

• Simulation in a two-BBR network

on base scan

Non-overlapped area

Overlapped area

Non-overlapped area

• Normalized CAF (NCAF)

– Single radar

– Radar network

60



rrrrr

rrrr

r

dAlr

gP

ddrdfWlr

gPP

t

r

st

,4

,,4

0

0

22

0

3

22

0 0

2

0

42

0

0

22

0

3

22

0

NCAF

rrrrr

rrrrr

r

dAl

gP

dAr

w

l

gPP

t

N

n

n

n

nt

,ˆ4

,4

ˆ

0

0

23

22

1

02

00

23

22

0

Averaged

NCAF

Averaged

NCAF

• Assumptions of Two BBR Simulation

– A Gaussian shape CAF

– A weighting function

– Precipitation at a point is simultaneously observed by

each radar node

61



2ln

2exp2ln

2exp,

2

2

0

2

2

000

4

hh

f

2ln

2exp

2

2

0

h

sr

rrW

N

n

n

nn

r

rw

1

2

2

: A Gaussian pulse

(ζ = 7.5 m (corresponding to B = 20 MHz))

: A Gaussian beam

(ζ = 3 deg)

:is equivalent to arithmetic average of reflectivity

factors in anti-log

62

Single BBR vs Two BBR Network


NCAF

in Single BBR (Node 1)

Averaged NCAF

in Two BBR Network

Thin-plate shaped CAF About 10 x 10 m resolution

7.5 m range resolution

518 m cross-range

resolution

10+2 m spatial resolution

63

Two BBR Network vs the Conventional


Averaged NCAF

in Two BBR Network

Radar Network

with Conventional Radars

Spatial resolution is NOT improved

because the range and cross-range resolutions are comparable.

64

Resolution Map (in 2-D)

On the other hand,

spatial resolution is

NOT improved

around the base-line

because two CAF

are not crossed.

A spatial resolution

of 10+2 m2 is

accomplished in

Almost all region

Resolution Square on Base Scan


65

Deployment in Osaka Area, Japan

Toyonaka radar

(polarimetric) 135.455748E

34.804939N

SEI radar

135.435054E

34.676993N

Nagisa radar 135.659029E

34.840145N

(from Jun., 2011)

Osaka area, Japan


66



13:54:05 09/14/10

67



13:55:09 09/14/10

68



13:56:13 09/14/10

69



13:57:17 09/14/10

70



13:58:21 09/14/10

71



• The Ku-BBR network accomplishes high spatial resolution in

2- or 3-D.

– Crossed pattern of several thin-plate shaped CAFs accomplishes high

spatial resolution of tens of meters in 2- or 3-D.

– But spatial resolution around the baseline between two Ku-BBRs is not

improved.

– Three or more-BBR network accomplishes high spatial resolution in 3-

D anywhere except for around the ground.

• Initial observation results showed high quality images.

– Precipitation patterns are clearly shown.

– Validation of the integrated data is one of our near future works.

72

Ch.3: Precipitation Attenuation Correction

Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network


– Theory




– Theory





– Algorithm


When assuming

a static k-Z relation,

Background

　

r

m dsskrZrZ0

10ln2.0exp

ZmZ: (un-attenuated ) reflectivity, : measured (attenuated) reflectivity,

k : specific attenuation (dB/km),

The equation is solved as…

However, it is known that HB solution often outputs large errors…

Zk

　

r

m dsrZrZrZ0

10ln2.0exp

110ln2.0exp 　rSCrZrZ m dssZrS

r

m 0

C : integral constant

Hitschfeld – Bordan (HB) solution

73

Path-Integrated

Attenuation (PIA)

What is the problem?

• Deterministic approach ｰ Deterministic approaches (represented by HB solution) accumulate

estimate errors in each range bin, as processing in range.

ｰ The solution is frequently unstable and overshoots.

⇒ Stochastic approach is better [Haddad et al., 1996].

• k-Z relation ｰ Using a constant k-Z relation generates estimate errors of k in each range

bin.

• Raindrop size distribution (DSD) ｰ DSD is the most important parameter in radar meteorology.

ｰ DSD determines k, Z, and so on (including rainfall rate, liquid water

content…).

ｰ However, it is very difficult to estimate DSD in each range bin.

74

Proposal

• Stochastic approach ｰ A Kalman filter approach is applied.

ｰ Uncertainties of estimates are also obtained.

• Network ｰ Assuming the same profile at cross points of beams from two radars,

estimates of two BBRs are integrated with use of corresponding uncertainties.

ｰ Uncertainty is also important for data assimilation into weather numerical

models (Our future work).

• DSD estimation ｰ In the BBR, DSD in the lowest altitude of 50 m is accurately estimated,

compared with a ground-based equipment of disdrometer [Yoshikawa et al.,

2010].

ｰ Thus, the BBR can always obtain the initial condition of DSD.

75

Methodology – Basis

Prediction :

Filtering :

wrrr

)()(, rvrPIArrZrZ em

wrrr

DDNDN exp)( 0

<Observation (in dB)> eZ

mZ

: (un-attenuated) reflectivity (dBZ)

: measured (attenuated) reflectivity (dB)

k : specific attenuation (dB/km)

<Gamma DSD [Ulbrich, 1983]>

<Extended Kalman Filter>

9.0exp106 3

0 N

rrrkrPIArrPIA ,2

exp11:exp

rPIArZrZ em )()(

r

dsskrPIA0

2PIA : Path-integrated attenuation (dB)

76

Methodology – Processing (1/2)

77

BBR2BBR1

Step 1: Single-path retrieval

Retrievals in each beam

starting with initial condition

Step 2:

Trading estimate values

only at cross points

BBR1

Methodology – Processing (2/2)

78

Step 3:

Retrievals in each beam

starting with traded cross points

Step 4: Network retrieval

Optimal estimation

with use of all filtering

Simulation Model 79

Zm on BBR1

True Ze on BBR2 Zm on BBR2

True Ze on BBR1

True Ze

BBR1 BBR2

Simulation Result – Reflectivity

80

Ste

p 1

Sin

gle

-pat

h r

etri

eval

Ste

p 4

Net

work

ret

riev

al

Retrieved Ze on BBR1 (dBZ)




Underestimate Underestimate

Unstable a little Corrected!

Simulation Result – Comparison to HB solution

81

HB

solu

tion

N

etw

ork

ret

riev

al





Overshoot Overshoot

82


• A Kalman filter approach for precipitation attenuation

correction in the Ku-BBR network is developed.

– Gamma DSD

– Stochastic approach with a use of Kalman filter

– Cyclic optimization in the radar network environment.

• Simulation shown a high estimate accuracy.

– Ze is accurately retrieved.

– It is difficult to retrieve DSD parameters accurately.

– Under consideration to use polarimetric parameters

• Estimate accuracy depends on variances of DSD parameters

(now under tuning).

• Cross validation with disdrometer is our future work.


End

Thank you for listening!

83

84

Back up

85

観測可能高度

地形により更に制限を受ける．

ref) Houze (1993), Doviak (1993)

86

Ku帯広帯域レーダの観測

空間分解能

• パルス圧縮レーダの距離分解能

• アンテナ指向性

][80][22

MHzBmB

cr

[deg]32 h

87

Cバンドレーダとの比較(旧ver.)

: Zm of C-band radar : Zm of BBR : Retrieved Ze of BBR (an old version)

88

Cバンドレーダとの比較(旧ver.)

Precipitation Attenuation –Mie solution

The solution for back scattering cross section and

absorption cross section for a water particle of dielectric

sphere is due to Mie.

　

1

22}Re{)12(

2),(

l

llee baln

r

　

1

22

22Re)12(

2),(

l

llss baln

r

es

n r2

: extinction cross section, : scattering cross section,

ll ba , : recursion formula for Bessel function,

: refractive index,

Function of

Refractive index

and rain drop

diameter


90

Precipitation Attenuation –Equation

Measured

Reflectivity

Equivalent

Reflectivity

Path-Integrated

Attenuation (PIA)

r

em dsskrZrZ0

3102 k : Specific attenuation (dB/km)

range r (m)

eZ

mZ

Attenuation


91

Traditional Method for Correction

0 （min range bin） 1 2 ・・・

・・・ Zm0 Zm1

Ze0=Zm0

known

unknown

Assumptions • B.C.：

• k-Z relation：

00 rZrZ em

rZrk e

B.C.

k-Z relation k0=αZe0β

PIA1=k0

Ze1=Zm1+PIA1

k1=αZe1β

PIA2=PIA1+k1

Zm2

Ze2=Zm2+PIA2

k2=αZe2β

PIA3=PIA2+k2

・・・

・・・

・・・


92

What is problem?

• k-Z relation

– is dependent on DSD

– yields errors in each

range bin if its coefficients

are constant.

10 20 30 40 50

Reflectivity Ze (dBZ)

10-4

10-3

10-2

10-1

100

101

Sp

ecif

ic a

tten

uati

on

k (

dB

/km

)

Ku

X

C

k-Z relation

• Deterministic Approach

– Errors in k-Z relation are accumulated.

⇒Output is more unstable in longer ranges or with heavier precipitation.

• Attenuation at Ku-band

– 10 – 100 times more than

C-band

– 4 – 6 times more than X-

band


• Assuming a Gamma DSD

• No attenuation in the nearest range

• Applying an extended Kalman filter

93

Proposed Algorithm

Prediction :

Filtering :

wnn 1

nnnnenm vPIAZZ ,

wnn 1

DDNDN exp)( 0

9.0exp106 3

0 N

nnnn rkPIAPIA ,21

exp11:exp

0)( 0 rPIA

n n+1

Nn(D) Nn+1(D)=Nn(D)

PIAn PIAn+1=PIAn+kn

Zmn+1


94

Simulation –in single BBR

Proposed algorithm HB solution

0

5

10

15

mer

idio

na

l (k

m)

-5 0 5 10 -10 zonal (km)

Tru

th

-5 0 5 10 -10 zonal (km)

0

5

10

15

Overestimation ⇒ Infinity Underestimation

behind strong precipitation

• HB solution

– overestimates in large area

– approaches infinity in strong precipitation

• Proposed algorithm

– underestimates behind strong precipitation


95

Algorithm in the BBR Network

BBR2BBR1

Step 1: Single-path retrieval

corrects in each path with the

boundary condition.

Step 2: Data Trade

exchanges corrected

data at cross points


96

Algorithm in the BBR Network

BBR1

Step 3: Retrieval with Traded Data

makes other correction data with Kalman

algorithm starting from each traded data

Step 4: Network retrieval

optimally averages all the correction

data with covariance information


97

Simulation –in the BBR network

Step 4: Network retrieval Step 1: Single-path retrieval

0

5

10

15

mer

idio

na

l (k

m)

-5 0 5 10 -10 zonal (km)

-5 0 5 10 -10 zonal (km)

0

5

10

15

• Errors remaining in Step 1 is properly

re-corrected with a use of radar

network environment. Tru

th


Seminar in CSU

Jun. 24, 2011

Ei-ichi Yoshikawa

Luneburg Lens Antenna

98

99

Lens Antenna Family

http://www.engineering-eye.com/rpt/c003_antenna/popup/04/image020.html

Dielectric (delay) lens E-plane metal plate (fast) lens

100

What is Luneburg Lens?

R.K.Luneberg

“Luneberg lens” is spherical lens for microwave.

Principle

1.0

1.2

1.4

1.6

1.8

2.0

0 0.2 0.4 0.6 0.8 1

Relative radius of lens

(Center) （Surface）

Er ： Dielectric Constant

r ： Radius

R ： Radius of lens Die

lect

ric

const

ant

1944 Proposal as optical lens

1960~ Investigation as lens

for microwave

Microwave

Focal point

Luneberg Lens

Er = 2 - R

r 2

Hybrid Products Division

101

Snell’s law –excerpt from wikipedia

sin 𝜃1sin 𝜃2

=𝑣1𝑣2

=𝑛2𝑛1

Snell's law states that the ratio of the sines

of the angles of incidence and refraction is

equivalent to the ratio of phase velocities in

the two media, or equivalent to the opposite

ratio of the indices of refraction:

𝜃

𝑣

𝑛

: angle measured from the normal

: velocity of light in the respective medium

: refractive index of the respective medium

102

How to focus?

Simulation by a discretized function

of dielectric constant

103

How to focus?



104

How to focus?



105

Focused Beam

106

Many Focal Points

107

Typical Application of Luneburg Lens

Primary feed

Luneberg Lens

Several primary feeds are

installed in advance

Multi-beam Antenna

Move a primary feed

along to lens surface

High Speed beam scanning Antenna

Frequency Range :

VHF - Ka-band

(45MHz) (50GHz)

Polarimetric capability

isolation > 30dB


108

Construction

Ideal construction

1.0 1.2

1.4

1.6 1.8 2.0

0 0.2 0.4 0.6 0.8 1

Relative radius of lens

(Center) （Surface）

Die

lect

ric

const

ant

SEI lens construction

Gradation of dielectric constant ∥

Difficult to form the lens

1.0 1.2

1.4

1.6 1.8 2.0

0 0.2 0.4 0.6 0.8 1

Relative radius of lens D

iele

ctri

c co

nst

ant

Piling up several Layers

An example High accuracy

original analysis tool

(FDTD method)


109

Material

Use special materials

0 0.2 0.4 0.6 0.8 1

1

1.5

2

2.5

Die

lect

ric

const

ant

(Er)

Specific gravity

Impossible to form

SEI material

Special PP+special Ceramic

Special ceramic

= fiber shape

Able to high

dielectric constant

General material (PS) εr≧1.7 Impossible to form

Center layers = High gravity bead foams are adhered by adhesives

Low performance (adhesives: high tanδ)

Hand made →high cost

High weight

Conventional lens

SEI lens

High performance

High productivity

Low weight


initial observation results for precipitation on the ku-band broadband radar network.pdf

Technology

kubbr network deployment

b band width hz

deg temporal resolution

light speed msec band

minvos short range

db beam width

rpm max

kyoto university