1. 0
INITIAL OBSERVATION RESULTS
FOR PRECIPITATION
ON THE KU-BAND BROADBAND RADAR
NETWORK
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

2. 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

3. Introduction
Resolution of Conventional Weather Radar
○Fronts, Hurricanes
×Cumulus,
Tornadoes, ○Mesocyclones,
Microbursts Supercells,
Squall lines
10min △Thunderstorms,
Macrobursts
100m
2

4. Introduction
Resolution of the Ku-BBR Network
○Fronts, Hurricanes
○Cumulus,
Tornadoes, ○Mesocyclones,
Microbursts Supercells,
Squall lines
△Smaller
phenomena? ○Thunderstorms,
Macrobursts
1min
Several meters
3

5. 4
Introduction
The Ku-BBR Network
• 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)
<Conventional Radar> • Multi-Radar Network
⇒ Precipitation attenuation correction
⇒ High resolution grid retrieval
⇒ Wider area

6. 5
Design Concept of the Ku-BBR
High resolution Wide Band Width
solution Pulse compression solution Ku-band
Gain ： BT ・Band width of 80 MHz
Range resolution ： c 2 B ⇒ Range resolution of 2 m (max)
B ：Band width (Hz), T ：Pulse width (sec), ・In C- and X-band, it is difficult to
c ：Light speed (m/sec) obtain wide band width in Japan.
Precipitation Attenuation Wide Area & High Accuracy
solution Short range: 15 km solution Multi-radar network
(Dual-poralization)
・Higher accuracy in overlapped area
・Polarimetric parameters are more
sensitive in Ku-band than other ・Network approach for precipitation
low frequency radars. attenuation correction

7. 6
Configuration
D/A Converter generates IQ signals Bistatic Lens Antenna
arbitrarily. (170 MHz (max), 14 bit) to eliminate blind range
Signal Processing Unit IF Unit Antenna Unit
I Amp Mixer HPA Horn
D/A
IQ
Memory Q
PC Modulator
D/A
14bit Rotary 13.75 Luneberg
170MHz LO 2GHz LO
Joint GHz Lens
I
A/D
DSP IQ De-
Board Q modulator
A/D
Amp Mixer LNA Horn
Digital Baseband IF (2GHz) Ku (15.71-9 GHz)
Real-time Digital Signal Processing
for Pulse Compression and Doppler Spectrum Estimation

8. 7
Signal Processing Unit
Pulse compression Signal Processing Unit Doppler estimation PC
DSP boards
A/D converter
Former process Latter process
I Received signal 32bit 32bit
(I and Q) FFT integer float
Q (32768 points)
16bit integer Pulse Clutter
Power,
compression filter
& Velocity,
IFFT output FFT
Memory (32768 poins) (64 points) Doppler Spectral width
* (I and Q)
moment
32bit float
Reference signal 16bit integer estimation
(I and Q) FFT 64 times 8192 times
(32768 points)
/segment /segment
16bit integer
• 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)
New FPGA system is in the process of production.

9. 8
Fast Scanning System
Luneburg Lens
(φ450 mm)
Azimuth rotation
40 RPM (max)
30 RPM (usual)
Primary
Feed
Elevation rotation

10. 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
9

11. 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
4   2
2
  1  b
Ze  5  ( D)  N ( D)dD N(D): DSD
2  b : Back Scattering coefficient
2 
b    1 2l  1al  bl 
l
from mie scattering
4 l 1

12. 11
Observation Accuracy
Scatter plot
40
Histogram
Zm of BBR (dBZ)
30 20
15
20
(%)
10
10
5
0 0
0 10 20 30 40 -10 -5 0 5 10
Ze of JWD (dBZ) Zm – Ze (dBZ)
• The high resolution reflectivity measurements of the
BBR show fairly good agreement compared with JWD.
– Correlation coefficient: 0.95, Standard deviation: 1.59 dBZ

13. 12
Examples of Ku-BBR Observation
Vertical Pointing Mode
Time-Height Cross Section (Reflectivity)
8
Range resolution
of several meters
6
Height (km)
4 Minimum
observation
Reflectivity (dBZ)
height of 50 m
50 2
0
0 5 10 15 20
0
Time (min)

14. 13
Examples of Ku-BBR Observation
Volume Scanning Mode
3D construction of
structure of
strong vortex
(Resolution of several
meters, 1 min)

15. 14
2(3)-BBR Network in Japan
Toyonaka radar
(Dual-pol)
135.455748E
34.804939N
Nagisa radar
135.659029E
34.840145N
SEI radar (from Aug., 2011)
135.435054E
34.676993N
Osaka area, Japan

16. 15
Initial Observation Results
Integration clearly
shows precipitation Integration by using
patterns because of simple geometric
the high temporal weighting average
resolution
13:54:05 09/14/10

17. 16
Initial Observation Results
13:55:09 09/14/10

18. 17
Initial Observation Results
13:56:13 09/14/10

19. 18
Initial Observation Results
13:57:17 09/14/10

20. 19
Initial Observation Results
13:58:21 09/14/10

21. 20
Initial Observation Results
Clear shapes
of precipitation
are retrieved Thin-plate shaped
pattern of the BBR
still remains

22. 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

23. 22
Thank you for listening!
End

24. 23
Initial Observation Results
Integration clearly
shows precipitation Integration by using
patterns because of simple geometric
the high temporal weighting average
resolution
13:54:05 09/14/10

25. 24
Initial Observation Results
13:55:09 09/14/10

26. 25
Initial Observation Results
13:56:13 09/14/10

27. 26
Initial Observation Results
13:57:17 09/14/10

28. 27
Initial Observation Results
13:58:21 09/14/10

29. Introduction
Resolution of the BBR
○Fronts, Hurricanes
○Cumulus,
Tornadoes, ○Mesocyclones，
Microbursts Supercells,
Squall lines
△Smaller
phenomena??
○Thunderstorms,
Macrobursts
1min
Severl meters
Introduction 28

30. 29
Introduction
The BBR Network
○ 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
<Conventional Radar> ○ 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
Introduction

31. 30
Outline
1. The Ku-band BroadBand Radar (The Ku-BBR)
– Theory
– Observation accuracy
– Initial observation result
2. The Ku-BBR Network
– Theory
– Deployment in Osaka
– Initial Observation Result
3. A Kalman Filter Approach for Precipitation
Attenuation Correction in the Ku-BBR Network
– Algorithm
– Simulation Result
Outline

32. 31
Ch.1: The Ku-BBR
1. The Ku-band BroadBand Radar (The Ku-BBR)
– Theory
– Configuration
– Initial observation result
2. The Ku-BBR Network
– Theory
– Deployment in Osaka
– Initial Observation Result
3. A Kalman Filter Approach for Precipitation
Attenuation Correction in the Ku-BBR Network
– Algorithm
– Simulation Result
Chapter 1 The Ku-BBR

33. 32
Concept
High resolution Wide Band Width
solution Pulse compression solution Ku-band
Gain ： BT ・Band width of 80 MHz
c ⇒ Range resolution of 2 m (max)
Range Resolution ：
2B
B ：Band width (Hz), T ：Pulse width (sec), ・In C- and X-band, it is difficult to
c ：Light speed (m/sec) obtain wide band width in Japan.
Precipitation Attenuation Wider Area & Higher Accuracy
solution Designed as a short solution Radar network
range polarimetric radar
・Higher accuracy in overlapped area
・Polarimetric parameters are more
sensitive in Ku-band than other low ・Network approach for precipitation
frequency radars. attenuation correction
Chapter 1 The Ku-BBR

34. 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).
High power &
Low power &
short-duration pulse
long-modulated pulse
Chapter 1 The Ku-BBR 33

35. Pulse Compression for Distributed Particles
• Radar Equation for Precipitation Particles with
Pulse Compression
• Radar equation
P G 2 h c 3  2  1
2 (received power) does
Pr r   10 t
Z
2 ln 2l r   2
2 2 2 NOT actually change.
• High range resolution
responding wide band
width is accomplished.
2 2 c  3
Pt B G  h   2 • High SNR due to long
B  1
Pr r  
pulse reduces to
Z
2 ln 2 l r
10 2 2
 2
2 integrate pulses and
allows one to scan
rapidly.
Chapter 1 The Ku-BBR 34

36. 35
Configuration
D/A Converter generates IQ signals Bistatic Lens Antenna
arbitrarily. (170 MHz (max), 14 bit) (36 dBi, 3 deg)
Signal Processing Unit IF Unit Antenna Unit
I Amp Mixer HPA Horn
D/A
IQ
Memory Q
PC Modulator
D/A
14bit Rotary 13.75 Luneberg
170MHz LO 2GHz LO
Joint GHz Lens
I
A/D
DSP IQ De-
Board Q modulator
A/D
Amp Mixer LNA Horn
Digital Baseband IF (2GHz) Ku (15.71-9 GHz)
Real-time Digital Signal Processing
for Pulse Compression and Doppler Spectrum Estimation
Chapter 1 The Ku-BBR

37. 36
Bistatic Lens Antenna System
About 1450 mm
Luneburg Lens (φ450 mm)
Primary Feed
Sumitomo Honeycomb Sandwich Redome High Power Transmitter Low Noise Amplifier
• 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
Chapter 1 The Ku-BBR

38. 37
Bistatic Lens Antenna System
Azimuth rotation
40 RPM (max)
30 RPM (usual)
Elevation rotation
Chapter 1 The Ku-BBR

39. 38
Signal Processing Unit
Pulse compression Signal Processing Unit Doppler estimation PC
DSP boards
A/D converter
Former process Latter process
I Received signal 32bit 32bit
(I and Q) FFT integer float
Q (32768 points)
16bit integer Pulse Clutter
Power,
compression filter
& Velocity,
IFFT output FFT
Memory (32768 poins) (64 points) Doppler Spectral width
* (I and Q)
moment
32bit float
Reference signal 16bit integer estimation
(I and Q) FFT 64 times 8192 times
(32768 points)
/segment /segment
16bit integer
• 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)
New FPGA system is in the process of production.
Chapter 1 The Ku-BBR

40. 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
Chapter 1 The Ku-BBR 39

41. 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
4   2
2
  1  b
Ze  5  ( D)  N ( D)dD N(D): DSD
2  b : Back Scattering coefficient
2 
b    1 2l  1al  bl 
l
from mie scattering
4 l 1
Chapter 1 The Ku-BBR

42. 41
Observation Accuracy
Scatter plot
40
Histogram
Zm of BBR (dBZ)
30 20
15
20
(%)
10
10
5
0 0
0 10 20 30 40 -10 -5 0 5 10
Ze of JWD (dBZ) Zm – Ze (dBZ)
• The high resolution reflectivity measurements of the BBR
show fairly good agreement compared with JWD.
– Correlation coefficient: 0.95, Standard deviation: 1.59 dBZ
Chapter 1 The Ku-BBR

43. 42
Comparison to C-band Radar
Highly attenuated
Tanegashima,
Kagoshima
Fine structures
are shown
C-band radar (El = 0.09deg) The Ku-BBR (Base scan)
Chapter 1 The Ku-BBR

44. 43
Observation Result (Time series example)
Toyonaka,
Osaka university
Chapter 1 The Ku-BBR

45. 44
Example –tornado?
2nd elevation
(in altitudes of 0 m – 270 m, roughly)
Chapter 1 The Ku-BBR

46. 45
Example –tornado?
3rd elevation
(in altitudes of 0 m – 450 m, roughly)
Chapter 1 The Ku-BBR

47. 46
Example –tornado?
4th elevation
(in altitudes of 0 m – 640 m, roughly)
Chapter 1 The Ku-BBR

48. 47
Example –tornado?
5th elevation
(in altitudes of 0 m – 820 m, roughly)
Chapter 1 The Ku-BBR

49. 48
Example –tornado?
6th elevation
(in altitudes of 0 m – 1000 m, roughly)
Chapter 1 The Ku-BBR

50. 49
Example –tornado?
7th elevation
(in altitudes of 0 m – 1190 m, roughly)
Chapter 1 The Ku-BBR

51. 50
Example –tornado?
8th elevation
(in altitudes of 0 m – 1370 m, roughly)
Chapter 1 The Ku-BBR

52. 51
Example –tornado?
9th elevation
(in altitudes of 0 m – 1550 m, roughly)
Chapter 1 The Ku-BBR

53. 52
Example –tornado?
10th elevation
(in altitudes of 0 m – 1610 m, roughly)
Chapter 1 The Ku-BBR

54. 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.
Chapter 1 The Ku-BBR

55. 54
Ch.2: The Ku-BBR Network
1. The Ku-band BroadBand Radar (The Ku-BBR)
– Theory
– Observation accuracy
– Initial observation result
2. The Ku-BBR Network
– Theory
– Deployment in Osaka
– Initial Observation Result
3. A Kalman Filter Approach for Precipitation
Attenuation Correction in the Ku-BBR Network
– Algorithm
– Simulation Result
Chapter 2 The Ku-BBR Network

56. 55
Network Approach of the Ku-BBR
• Single BBR
Cross-range 785 m – Range resolution is
resolution in 15 km range very high.
– On the other hand,
524 m
in 10 km range cross-range resolution
is 100 times poorer
262 m than range resolution
in 5 km range in a range of 15 km.
– Composite average
3 deg 7.5 m function (CAF) is a
with 20 MHz BW thin-plate shape.
Range resolution
Chapter 2 The Ku-BBR Network

57. 56
Network Approach of the Ku-BBR
• The Ku-BBR Network
– 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
About 10 x 10 m
Node 1 resolution in 2- or 3-D.
spatial resolution
Node 2
Chapter 2 The Ku-BBR Network

58. 57
Equations
Single Radar Equation
P r0     r I r0 , r dV
Composite Average Function (CAF)
Pt g  f    0 ,   0 Ws r0 , r 
where, 2 2 4 2
I r0 , r  
4 3 l 2 r r 4
Equivalent Reflectivity Factor

 r     b D N D, r dD
0
dV  r 2 dr sin dd
Chapter 2 The Ku-BBR Network

59. 58
Network Approach of the Ku-BBR
A Weighting Average of Received Signals
Obtained by Each Radar Node
ˆ
N A weighting average of
P r0    wn Pn r0  received signals
n 1
N
  wn   r I n r0 , r dV
n 1
N
is translated to…
   r  wn I n r0 , r dV
n 1
   r I r0 , r dV
ˆ A weighting average of
N
CAFs
where, w
n 1
n 1
Chapter 2 The Ku-BBR Network

60. 59
Evaluation of Spatial Resolution
• Simulation in a two-BBR network
on base scan
Meridional
range (km)
Overlapped area
Node 2 Node 1 Zonal
(-7, 0) (7, 0) range (km)
Non-overlapped area
Chapter 2 The Ku-BBR Network

61. 60
Evaluation of Spatial Resolution
• Normalized CAF (NCAF)
– Single radar
Pt g 2 2  2
P r0   Ws r0 , r  f 4  ,  r drdd
r
4 3 r02l 2 r0  0 0 0
2
Pt g 2 2

4  r
3 2 2
l r   Ar , r  r dr
0 NCAF
0 0
– Radar network
ˆ Pt g 2 2 N
P r0    r  2n An r0 , r dr
w
4 3 l 2 r0   n1 r0n Averaged
Pt g 2 2
NCAF
 r Ar0 , r dr
ˆ
4  l r0  
 3 2
Chapter 2 The Ku-BBR Network

62. 61
Evaluation of Spatial Resolution
• Assumptions of Two BBR Simulation
– A Gaussian shape CAF
 r  r0 2  : A Gaussian pulse

Ws  exp  ln 2 
 (ζ = 7.5 m (corresponding to B = 20 MHz))
 rh 2
2

    0 2     0 2  : A Gaussian beam
f    0 ,  0   exp 
4
  exp  
ln 2  
  22 ln 2 
  h 2 (ζ = 3 deg)
2
  h 
– A weighting function
rn2
wn  N
:is equivalent to arithmetic average of reflectivity
r
n 1
n
2
factors in anti-log
– Precipitation at a point is simultaneously observed by
each radar node
Chapter 2 The Ku-BBR Network

63. 62
Single BBR vs Two BBR Network
NCAF Averaged NCAF
in Single BBR (Node 1) in Two BBR Network
518 m 10+2 m
cross-range spatial resolution
resolution
7.5 m
range resolution
Thin-plate shaped CAF About 10 x 10 m resolution
Chapter 2 The Ku-BBR Network

64. 63
Two BBR Network vs the Conventional
Averaged NCAF Radar Network
in Two BBR Network with Conventional Radars
Spatial resolution is NOT improved
because the range and cross-range resolutions are comparable.
Chapter 2 The Ku-BBR Network

65. 64
Resolution Map (in 2-D)
Resolution Square on Base Scan A spatial resolution
of 10+2 m2 is
accomplished in
Almost all region
On the other hand,
spatial resolution is
NOT improved
around the base-line
because two CAF
are not crossed.
Chapter 2 The Ku-BBR Network

66. 65
Deployment in Osaka Area, Japan
Toyonaka radar
(polarimetric)
135.455748E
34.804939N
Nagisa radar
135.659029E
34.840145N
SEI radar (from Jun., 2011)
135.435054E
34.676993N
Osaka area, Japan
Chapter 2 The Ku-BBR Network

67. 66
Initial Observation Results
13:54:05 09/14/10
Chapter 2 The Ku-BBR Network

68. 67
Initial Observation Results
13:55:09 09/14/10
Chapter 2 The Ku-BBR Network

69. 68
Initial Observation Results
13:56:13 09/14/10
Chapter 2 The Ku-BBR Network

70. 69
Initial Observation Results
13:57:17 09/14/10
Chapter 2 The Ku-BBR Network

71. 70
Initial Observation Results
13:58:21 09/14/10
Chapter 2 The Ku-BBR Network

72. 71
Summary of Chapter 2
• 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.
Chapter 2 The Ku-BBR Network

73. 72
Ch.3: Precipitation Attenuation Correction
1. The Ku-band BroadBand Radar (The Ku-BBR)
– Theory
– Observation accuracy
– Initial observation result
2. The Ku-BBR Network
– Theory
– Deployment in Osaka
– Initial Observation Result
3. A Kalman Filter Approach for Precipitation
Attenuation Correction in the Ku-BBR Network
– Algorithm
– Simulation Result
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network

74. 73
Background
Hitschfeld – Bordan (HB) solution Path-Integrated
Z m r   Z r  exp 0.2 ln 10 r k s ds 
0
Attenuation (PIA)

 

When assuming
a static k-Z relation,
k  Z 
Z m r   Z r  exp  0.2 ln 10 r Z r  ds 

 0 

The equation is solved as…
Z r   Z m r exp C  0.2 ln 10S r  1 
 S r    Z m s  ds
r 
0
However, it is known that HB solution often outputs large errors…
Z : (un-attenuated ) reflectivity, Z m : measured (attenuated) reflectivity,
k : specific attenuation (dB/km), C : integral constant

75. 74
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.

76. 75
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.

77. 76
Methodology – Basis
<Observation (in dB)> Z e : (un-attenuated) reflectivity (dBZ)
Z m (r )  Z e (r )  PIAr  Z m : measured (attenuated) reflectivity (dB)
 PIAr   2 k s ds
r k : specific attenuation (dB/km)
0 PIA : Path-integrated attenuation (dB)
<Gamma DSD [Ulbrich, 1983]>
N ( D)  N0 D  exp  D  N0  6 103 exp 0.9 
<Extended Kalman Filter>
Prediction : r  r   r   w  exp   : 1 1  exp  
 r  r    r   w
PIAr  r   PIAr   2rk  r , r 
Filtering : Z m r   Ze  r , r   PIA(r )  v(r )

78. 77
Methodology – Processing (1/2)
BBR1 BBR2
Step 1: Single-path retrieval Step 2:
Retrievals in each beam Trading estimate values
starting with initial condition only at cross points

79. 78
Methodology – Processing (2/2)
Step 3:
Retrievals in each beam
starting with traded cross points
Step 4: Network retrieval
BBR1 Optimal estimation
with use of all filtering

80. 79
Simulation Model
True Ze
True Ze on BBR1 Zm on BBR1
True Ze on BBR2 Zm on BBR2
BBR1 BBR2

81. 80
Simulation Result – Reflectivity
Underestimateon BBR1 (dBZ)
Retrieved Ze Underestimate BBR2 (dBZ)
Retrieved Ze on
Single-path retrieval
Step 1
Retrieved Ze on BBR1 (dBZ) Retrieved Ze on BBR2 (dBZ)
Network retrieval
Unstable a little Corrected!
Step 4

82. 81
Simulation Result – Comparison to HB solution
OvershootZe on BBR1 (dBZ)
Retrieved Overshooton BBR2 (dBZ)
Retrieved Ze
HB solution
Network retrieval
Retrieved Ze on BBR1 (dBZ) Retrieved Ze on BBR2 (dBZ)

83. 82
Summary of Chapter 3
• 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.
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network

84. 83
Thank you for listening!
End

85. 84
Back up

86. 観測可能高度
ref) Houze (1993), Doviak (1993)
地形により更に
制限を受ける．
85

87. 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
r 
c
 2[m]  B  80[MHz]
2B
• アンテナ指向性
2 h  3[deg]
86

88. 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) 87

89. Cバンドレーダとの比較(旧ver.)
88

90. 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.
s
r 2
2 
  s (n,  )  2  (2l  1) Re al  bl
 l 1
2 2
  Function of
Refractive index
e 2  and rain drop
  e (n,  )  2  (2l  1) Re{al  bl } diameter
r 2
 l 1
 s : scattering cross section,  e : extinction cross section,
al , bl : recursion formula for Bessel function,
n : refractive index,   2r 
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network

91. 90
Precipitation Attenuation –Equation
Measured Equivalent Path-Integrated
Reflectivity Reflectivity Attenuation (PIA)
Z m r   Z e r   2 10  k s ds
r
3
k : Specific attenuation (dB/km)
0
range r (m)
Ze
Attenuation
Zm
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network

92. 91
Traditional Method for Correction
Assumptions • B.C.： Z m r0   Z e r0 
known
• k-Z relation： k r   Z e r 
unknown
0 （min range bin） 1 2 ・・・
Zm0 Zm1 Zm2 ・・・
B.C. Ze0=Zm0 Ze1=Zm1+PIA1 Ze2=Zm2+PIA2 ・・・
k-Z relation k0=αZe0β k1=αZe1β k2=αZe2β ・・・
PIA1=k0 PIA2=PIA1+k1 PIA3=PIA2+k2 ・・・
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network

93. 92
What is problem?
• k-Z relation
– is dependent on DSD k-Z relation
Specific attenuation k (dB/km)
101
– yields errors in each Ku
range bin if its coefficients X
100
are constant.
C
10-1
• Attenuation at Ku-band
– 10 – 100 times more than 10-2
C-band
10-3
– 4 – 6 times more than X-
band
10-4
10 20 30 40 50
• Deterministic Approach Reflectivity Ze (dBZ)
– Errors in k-Z relation are accumulated.
⇒Output is more unstable in longer ranges or with heavier precipitation.
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network

94. 93
Proposed Algorithm
• Assuming a Gamma DSD
N ( D)  N0 D  exp  D n n+1
 N0  6 103 exp 0.9 
Nn(D) Nn+1(D)=Nn(D)
• No attenuation in the nearest range
PIA(r0 )  0 PIAn PIAn+1=PIAn+kn
Zmn+1
• Applying an extended Kalman filter
Prediction :  1    w
n n  exp   : 1 1  exp  
n1  n  w
PIAn1  PIAn  2rk n ,  
n
Filtering : Z m n  Z e n ,    PIAn  vn
n
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network

95. 94
Simulation –in single BBR
• HB solution
– overestimates in large area
Truth
– approaches infinity in strong precipitation
• Proposed algorithm
– underestimates behind strong precipitation
HB solution Proposed algorithm
15 15
meridional (km)
10 10
5 5
Overestimation ⇒ Infinity Underestimation
0 0
behind strong precipitation
-10 -5 0 5 10 -10 -5 0 5 10
zonal (km) zonal (km)
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network

96. 95
Algorithm in the BBR Network
BBR1 BBR2
Step 1: Single-path retrieval Step 2: Data Trade
corrects in each path with the exchanges corrected
boundary condition. data at cross points
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network

97. 96
Algorithm in the BBR Network
Step 3: Retrieval with Traded Data
makes other correction data with Kalman
algorithm starting from each traded data
Step 4: Network retrieval
BBR1 optimally averages all the correction
data with covariance information
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network

98. 97
Simulation –in the BBR network
• Errors remaining in Step 1 is properly
Truth
re-corrected with a use of radar
network environment.
Step 1: Single-path retrieval Step 4: Network retrieval
15 15
meridional (km)
10 10
5 5
0 0
-10 -5 0 5 10 -10 -5 0 5 10
zonal (km) zonal (km)
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network

99. 98
Seminar in CSU
Luneburg Lens Antenna
Jun. 24, 2011
Ei-ichi Yoshikawa

100. Lens Antenna Family
Dielectric (delay) lens E-plane metal plate (fast) lens
http://www.engineering-eye.com/rpt/c003_antenna/popup/04/image020.html
99

101. What is Luneburg Lens?
“Luneberg lens” is spherical lens for microwave.
1944 Proposal as optical lens Principle Luneberg Lens
Microwave
Focal point
Dielectric constant
2
2.0
r
Er = 2 -
1.8 R
1.6
1.4
Er ： Dielectric Constant
R.K.Luneberg 1.2
r ： Radius
1.0
1960~ Investigation as lens R ： Radius of lens
for microwave 0 0.2 0.4 0.6 0.8 1
(Center) （Surface）
Relative radius of lens
Hybrid Products Division 100

102. Snell’s law –excerpt from wikipedia
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:
sin ������1 ������1 ������2
= =
sin ������2 ������2 ������1
������ : angle measured from the normal
������ : velocity of light in the respective medium
������ : refractive index of the respective medium
101

103. How to focus?
Simulation by a discretized function
of dielectric constant
102

104. How to focus?
Simulation by a discretized function
of dielectric constant
103

105. How to focus?
Simulation by a discretized function
of dielectric constant
104

106. Focused Beam
105

107. Many Focal Points
106

108. Typical Application of Luneburg Lens
Luneberg Lens Frequency Range :
VHF - Ka-band
(45MHz) (50GHz)
Polarimetric capability
isolation > 30dB
Primary feed
Several primary feeds are Move a primary feed
installed in advance along to lens surface
Multi-beam Antenna High Speed beam scanning Antenna
Hybrid Products Division 107

109. Construction
Ideal construction SEI lens construction
High accuracy
An example
Dielectric constant
Dielectric constant
original analysis tool
2.0 2.0 (FDTD method)
1.8 1.8
1.6 1.6
1.4 1.4
1.2 1.2
1.0 1.0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
(Center) （Surface） Relative radius of lens
Relative radius of lens
Gradation of dielectric constant
∥
Difficult to form the lens Piling up several Layers
Hybrid Products Division 108

110. Material
SEI material
Use special materials Special PP+special Ceramic
SEI lens
Special ceramic
= fiber shape High performance
High productivity
Able to high Low weight
2.5
Dielectric constant (Er)
dielectric constant
2 General material (PS)
εr≧1.7 Impossible to form
Conventional lens
1.5
Center layers = High gravity bead foams are
Impossible adhered by adhesives
to form
1
0 0.2 0.4 0.6 0.8 1 Low performance (adhesives: high tanδ)
Specific gravity Hand made →high cost
High weight
Hybrid Products Division 109