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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
○Fronts, Hurricanes
○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
Signal Processing Unit
I
Q
PC
Power, Velocity,
Spectral width
32bit float
64 times/segment
8192 times/segment
7
Signal Processing Unit
• 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
Initial Observation Results
13:55:09 09/14/10
17
Initial Observation Results
13:56:13 09/14/10
18
Initial Observation Results
13:57:17 09/14/10
19
Initial Observation Results
13:58:21 09/14/10
20
Initial Observation Results
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
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
24
Initial Observation Results
13:55:09 09/14/10
25
Initial Observation Results
13:56:13 09/14/10
26
Initial Observation Results
13:57:17 09/14/10
27
Initial Observation Results
13:58:21 09/14/10
28
Introduction
Resolution of the BBR
Severl meters
1min
○Fronts, Hurricanes
○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
– 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
31
Ch.1: The Ku-BBR
Chapter 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
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
Chapter 1 The Ku-BBR
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
Chapter 1 The Ku-BBR
34
Pulse Compression for Distributed Particles
• Radar Equation for Precipitation Particles with
Pulse Compression
Chapter 1 The Ku-BBR
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
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
Chapter 1 The Ku-BBR
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
Chapter 1 The Ku-BBR
37
Bistatic Lens Antenna System
Azimuth rotation
40 RPM (max)
30 RPM (usual)
Elevation rotation
Chapter 1 The Ku-BBR
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
Signal Processing Unit
I
Q
PC
Power, Velocity,
Spectral width
32bit float
64 times/segment
8192 times/segment
38
Signal Processing Unit
• 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.
Chapter 1 The Ku-BBR
39
Specifications
Chapter 1 The Ku-BBR
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
Chapter 1 The Ku-BBR
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
Chapter 1 The Ku-BBR
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
Chapter 1 The Ku-BBR
43
Observation Result (Time series example)
Toyonaka,
Osaka university
Chapter 1 The Ku-BBR
44
Example –tornado?
Chapter 1 The Ku-BBR
2nd elevation
(in altitudes of 0 m – 270 m, roughly)
45
Example –tornado?
Chapter 1 The Ku-BBR
3rd elevation
(in altitudes of 0 m – 450 m, roughly)
46
Example –tornado?
Chapter 1 The Ku-BBR
4th elevation
(in altitudes of 0 m – 640 m, roughly)
47
Example –tornado?
Chapter 1 The Ku-BBR
5th elevation
(in altitudes of 0 m – 820 m, roughly)
48
Example –tornado?
Chapter 1 The Ku-BBR
6th elevation
(in altitudes of 0 m – 1000 m, roughly)
49
Example –tornado?
Chapter 1 The Ku-BBR
7th elevation
(in altitudes of 0 m – 1190 m, roughly)
50
Example –tornado?
Chapter 1 The Ku-BBR
8th elevation
(in altitudes of 0 m – 1370 m, roughly)
51
Example –tornado?
Chapter 1 The Ku-BBR
9th elevation
(in altitudes of 0 m – 1550 m, roughly)
52
Example –tornado?
Chapter 1 The Ku-BBR
10th elevation
(in altitudes of 0 m – 1610 m, roughly)
53
Summary of Chapter 1
Chapter 1 The Ku-BBR
• 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
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
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
Chapter 2 The Ku-BBR Network
56
Network Approach of the Ku-BBR
• 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.
Chapter 2 The Ku-BBR Network
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,
Chapter 2 The Ku-BBR Network
58
Network Approach of the Ku-BBR
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
A weighting average of
CAFs
is translated to…
Chapter 2 The Ku-BBR Network
A weighting average of
CAFs
59
Evaluation of Spatial Resolution
Chapter 2 The Ku-BBR Network
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
Evaluation of Spatial Resolution
Chapter 2 The Ku-BBR Network
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
Evaluation of Spatial Resolution
Chapter 2 The Ku-BBR Network
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
Chapter 2 The Ku-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
Chapter 2 The Ku-BBR Network
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
Chapter 2 The Ku-BBR Network
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
Chapter 2 The Ku-BBR Network
66
Initial Observation Results
Chapter 2 The Ku-BBR Network
13:54:05 09/14/10
67
Initial Observation Results
Chapter 2 The Ku-BBR Network
13:55:09 09/14/10
68
Initial Observation Results
Chapter 2 The Ku-BBR Network
13:56:13 09/14/10
69
Initial Observation Results
Chapter 2 The Ku-BBR Network
13:57:17 09/14/10
70
Initial Observation Results
Chapter 2 The Ku-BBR Network
13:58:21 09/14/10
71
Summary of Chapter 2
Chapter 2 The Ku-BBR Network
• 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
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
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)
Retrieved Ze on BBR1 (dBZ)
Retrieved Ze on BBR2 (dBZ)
Retrieved Ze on BBR2 (dBZ)
Underestimate Underestimate
Unstable a little Corrected!
Simulation Result – Comparison to HB solution
81
HB
solu
tion
N
etw
ork
ret
riev
al
Retrieved Ze on BBR1 (dBZ)
Retrieved Ze on BBR1 (dBZ)
Retrieved Ze on BBR2 (dBZ)
Retrieved Ze on BBR2 (dBZ)
Overshoot Overshoot
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
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
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network
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
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network
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
・・・
・・・
・・・
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network
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
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network
• 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
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network
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
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network
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
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network
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
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network
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
Chapter 3 A Kalman Filter Approach for Precipitation Attenuation Correction in the Ku-BBR Network
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?
Simulation by a discretized function
of dielectric constant
104
How to focus?
Simulation by a discretized function
of dielectric constant
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
Hybrid Products Division
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)
Hybrid Products Division
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
Hybrid Products Division