radar polarimetric retrievals. anthony illingworth university of reading, uk
TRANSCRIPT
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Radar Polarimetric Retrievals.
Anthony Illingworth
University of Reading, UK
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RADAR REFLECTIVITY, Z FOR RAIN Z = N D6 (mm6 m-3 )
SIXTH MOMENT: dBZ = 10log(Z)
RAINRATE: R = N D3.67
3.67TH MOMENT
EMPIRICALLY Z = aRb “Z= 200 R1.6”
ERROR ‘FACTOR OF TWO’
Z has no information on hydrometeor characteristics
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WHAT IF TARGET IS ICE? Z = (Kice/Kwater)2 N D6
(Kwater)2 = 0.93 and Kice = (ice) 0.205
So K of fluffy snow is very low,
now, mass = * volume
so for dry ice Z prop to mass 2
If ice is wet: K2 =0.93 so Z much higher:
So melting snow: high Z – bright band.
HAIL – D large – Z = 60dBZ
So Z= 200 R1.6 Gives R=200mm/hr
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WHAT CAN POLARISATION ADD?
TRANSMIT AND RECEIVE HORIZONTALLY AND VERTICALLY POLARISED WAVE.
FOUR NEW PARAMETERS.
Consider at low elevation
1. DIFFERENTIAL REFLECTIVITY: ZDR
MEASURE REFLECTIVITY WITH HORIZONTAL (ZH) AND VERTICAL (ZV) POLARISATION
ZDR = 10 LOG(ZH/ZV)
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ZDR MESURES MEAN PARTICLE SHAPE – e.g. RAIN.
1mm
3mm
5mm
ZH > ZV ZDR = 2dB
ZH >>ZV ZDR = 4 dB
• RAIN: ZDR IS A MEASURE OF MEAN DROP SHAPE/SIZE • HAIL: TUMBLES SO ZDR=0dB• SNOW/AGGREGATES: look spherical to radar, ZDR=0dB.
ZH =ZV ZDR = 10LOG(ZH/ZV)=0dB
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2. DIFFERENTIAL PHASE SHIFT, KDP
OBLATE HYDROMETEORS (E.G LARGE RAINDROPS) DELAY H WAVE MORE THAN V WAVE.
PHASE DIFFERENCE, DP, INCREASES WITH RANGE KDP is grad of dp in deg/km
RAIN – KDP R: HAIL NO KDPAGGREGATES – NO KDP PRISTINE XLS – SOME KDP
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ZDR AND KDP IN RAIN
Z >40dBZIn heavy rain
ZDR>2dBIn heavy rain
Phase shift 40degs thru heavy rain
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3. LINEAR DEPOLARISATION RATIO, LDRTransmit H, receive H (copolar) and V (x-polar)
LDR = 10 log(x-polar/copolar)
X-polar return only from oblate particles falling an angle to H or V
Highest return for high K – if particles are wet
Wet snowflakes LDR = -12dB Dry Pristine Crystals -24dB Dry snow flakes and rain LDR < - 30dB
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4. Copolar correlation, (hv)the correlation between time series of ZH and ZV
If particles all the same shape = 1
Variety of shapes, variety of ratio ah/av then < 1
Rain: >0.98 bright band: approx 0.9
Ground clutter and anaprop (Mie scatter): = 0.
t=1
T=2
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POLARISATION PARAMETERS FROM CLOUDS
LIQUID DROPLETS <1mm SPHERICAL – NO SIGNAL
LOW DENSITY AGGREGATES – LOOK SPHERICAL TO THE RADAR – NO SIGNAL FROM MOST ICE CLOUDS.
PRISTINE CRYSTALS – viewed at low elevation
can have high ZDR and some kdp when viewed at low elevation.
If aggregates present then ZDR=0dB, but kdp unaffected
Can’t use kdp to estimate iwc because iwc dominated by aggregates.
Special case of crystals aligned in electric field in thunderstorm:
Where field vertical - negative kdp.
Where field at 45 degs – get ldr
Can ‘map’ out field – see our web site.
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POLARISATION PARAMETERS FROM CLOUDS
PRISTINE CRYSTALS – viewed at zenith
NO ZDR OF KDP
(except when alignment in electric field)
THEY CAN GIVE LDR OF ABOUT –24dB
But X-POLAR RETURN USUALLY BELOW DETECTION LIMIT
AT ZENITH IDENTIFY MELTING LAYER LDR= -13dB
IN PRECIPTATING CLOUDS CAN IDENTIFY GRAUPEL FROM SNOW BY DIFFERENT LDR WHEN THEY MELT.
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WHAT USE IS RADAR FOR LWC AND IWC?
1. DIFFERENTIAL ATTENUATION BETWEEN 94 AND 35GhZ RADAR IN LIQUID CLOUDS IS ABOUT 8dB/km/g/m3
BUT NEED LONGISH DWELLS TO GET PROFILES OF LWC
2. ICE PARTICLE SIZE: 94GHz Mie SCATTERS ONCE D>0.3mm; 35GHz RAYLEIGH SCATTERS SO DUAL WAVELENGTH
REFLECTIVITY RATIO GIVES Do IF Do > 0.3mm
ONCE YOU KNOW Do, THEN Z AT 35GHz GIVES YOU N DERIVE IWC – ERROR DEPENDS ON ICE DENSITY f(D)
GET THIS FROM DUAL DOPPLER VELOCITY DIFFERENCE
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CLOUDNET:
• Two years of 24h/7d radar/lidar observations • Cabauw, Palaiseau, Chilbolton• Categorisation of echoes – ice, liquid, scooled etc. • Derive cloud fraction, iwc, lwc, etc. • + ERRORS
• Model data from ECMWF, MeteoFrance, Met Office, RACMO – over the three stations for two years.
For real time cloud profiles visit:www.met.reading.ac.uk/radar/realtime
And for CloudNET “ /radar/cloudnet/
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Cloud fraction: 10 day comparison with ECMWF model
• Initial comparison suggests that clouds are very well represented by the ECMWF model
• Remember that for 20 m/s wind, one day of data is equivalent to 1700 km of cloud, so very large scale features are being compared here!
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Cloud fraction:12 Months of Chilbolton data
• Too much cloud high levels, too little mid-levels– However, frequency of occurrence is better: suggests
humidity structure is good, but amount when present is not so good
– Low-level clouds are very different in the two models
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Ice water content (from Z) results
• Underestimate of mean mid-level IWC in both models– Seems to be due to factor-of-2 error in mean cloud fraction– Mean in-cloud IWC appears to be reasonably good above 4
km
(g m-3)
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BEST APPLICATION OF POLARISATION
IS FOR BETTER RAINRATES.ZDR GIVES YOU MEAN DROP SIZE + Z GIVES YOU N:
BETTER ESTIMATE OF RAIN SIZE SPECTRA – BETTER R
KDP – PHASE SHIFT – MEASURABLE IN HEAVY RAIN
a) R = f(KDP) GIVES R WHEN HAIL PRESENT.
b) PHASE SHIFT PROPORTIONAL TO Z ATTENUATION
SO
METEO FRANCE AND MET OFFICE WILL INSTALL AN OPERATIONAL POLARISATION RADAR IN 2004
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R from Z alone: major problem is Vertical profile of reflectivity
- melting snow :bright band - rapid fall of Z in the ice - near the ground beam in the rain
OPERATIONAL RADAR – BEAM 1DEG – 2km WIDE AT 100km RANGE.
30dBZ
0dBZ
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SUMMARY OF PROBLEMS (AND SOLUTIONS) OF DERIVING R FROM Z ALONE
• VERTICAL PROFILE OF REFLECTIVITY
- USE LDR TO IDENTIFY THE B BAND?
• ATTENUATION AT C-BAND – USE DIFF PHASE
• ANAPROP AND CLUTTER USE
• ABSOLUTE CALIBRATION OF Z - USE REDUNDANCY OF ZDR AND KDP IN HEAVY RAIN TO CALIB TO 0.5dB.
•BETTER RAINDROP SPECTRA - USE ZDR.
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FOR ZDR AND KDP DROP SHAPE MODEL CRUCIAL
USE ANDSAGER/GODDARD SHAPES
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FOR BETTER RAINRATES NEED
ZDR ACCURATE TO better than 0.2dB
Curves are value of Z for R=1mm/hr for a given ZDR.
If observed Z is xdBHigher then R is xdB Above 1mm/hr
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KDP ONLY USEFUL FOR HEAVY RAIN e.g. 1deg/km is about 40mm/hr.
difficult to measure lower values of KDP
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Z CALIBRATION TECHNIQUE:In rain Z, ZDR and KDP are not independentKDP/Z is a unique function of ZDR:
SO along a ray at each gate from observed Z and ZDR calculate theoretical KDP, find theoretical dp per gate.Adjust Z so computed phase shift agrees with observed phase shift
Correct shapes
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ZDR AND KDP IN RAIN
Z >40dBZIn heavy rain
ZDR>2dBIn heavy rain
Phase shift 40degs thru heavy rain
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CALIBRATION EXAMPLEObserved phase shift along ray is 25 degs.Adjust Z, so that phase shift calculated from observedZ and ZDR agrees with observed phase shift.
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Polarisation Rainfall Technique
• R from Z and Zdr
• Need ZDR to 0.1dB at 3mm/hr for R accurate to 25%
• Operationally ZDR too noisy for accurate gate by gate R.
• Noise due to sidelobe mismatch, triple scattering etc.
• SUGGEST
• Use domain average so noise in ZDR averages to zero.
• Calculate best Z-R domain relation from Z and ZDR.
• Rainfall accuracy of 25% possible for R = 3mm/hr
• See chapter 5 in Peter Meischner’s (Ed.) forthcoming book:
• Weather Radar: Advanced Applications – Springer.
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Polarisation Rainfall Technique
• R from Z and Zdr
• Need ZDR to 0.1dB at 3mm/hr for R accurate to 25%
• Operationally ZDR too noisy for accurate gate by gate R.
• Noise due to sidelobe mismatch, triple scattering etc.
• Use domain average so noise in ZDR averages to zero.
• Calculate best Z-R domain relation from Z and ZDR.
• Rainfall accuracy of 25% possible for R = 3mm/hr
• Diff phase shifts only good for heavy rain.• Rain of < 30mm/hr caused the flooding of central Europe
• Use Diff phase shift in heavy rain to calibrate Z to 0.5dB.
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Drop Spectra: Normalised Gamma Function
• We assume that the drop spectra can be represented by the normalised gamma distribution
• Do = Median volume drop size• The average size of the drops
• Nw = Normalised drop concentration
• Normalised for constant liquid water content with changes in
• The number of drops
• = width of spectrum• High values correspond to a narrow
drop spectrum – most drops about the same size.
4
67.3
67.3
6 4
4
fWhere:
Drop size (mm)
104
103
102
101
100
10-1
0 0.5 1 1.5 2 2.5
Num
ber
of d
rops
/ m
3 / m
m
Do= 1 mm, Nw= 8000 m-3mm-1
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Z-R if Nw constant• We will now presume =
5• Nw and Do can vary
• Now suppose that as rain gets heavier, Nw remains constant, but Do increases.
• The ‘ZPHI’ method of Testud et al (2000) assumes Nw is constant and derives it and hence a from the integrating along the ray, using Z and the total differential phase shift.
67.4
03
70
6
DNdDDvDDNR
DNdDDDNZ
w
w
5.15.15.1
w
w 1
N
NZ i.e. R
NZR
w
Drop size (mm)
103
102
101
100
0 1 2 3 4 5 6 7
Nw= 8000 m-3mm-1 = 5
Num
ber
of d
rops
/ m
3 / m
m
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Heavier rain Do Increases: Nw Do-1
• If: Nw Do-1
• As drops get bigger, there are less of them.
• This is the UK default
• Stratiform rain. R1.6
• More ice aggregation
• Larger but fewer snowflakes
67.40
70 DNRDNZ ww
6.167.3
6
67.30
60 RZRZ
DR
DZ
104
103
102
101
Drop size (mm) 0 1 2 3 4 5 6 7
Num
ber
of d
rops
/ m
3 / m
m
= 5
10 DNw
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Heavier rain Do Increases: Nw Do2
• If: Nw Do2
• More, larger drops as rain increases
• Similar to the NEXRAD default of Z R1.3
• Convective/tropical rain?
67.40
70 DNRDNZ ww
35.167.6
9
67.60
90 RZRZ
DR
DZ
104
103
102
101
Drop size (mm) 0 1 2 3 4 5 6 7
Num
ber
of d
rops
/ m
3 / m
m
= 5
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R from Z and ZDR
• ZDR is independent of Nw , so gives us Do
• Fixed ZDR normalized gamma Do const.
• For fixed ZDR, Z and R scale with Nw
• For each ZDR calculate Z for R=1mm/hr
• dBZR=1= f (ZDR)
• Use Andsager (‘99) or Goddard(’84) shapes
• Hence, dBR = dBZOBS – f (ZDR)
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Example: dBR = dBZobs – f(ZDR)
1mm/hr
Need ZDR to 0.1dB @ 3mm/hr to 25%
• Observed ZDR=0.65dB
• For this ZDR: R of 1 mm/hr has 26.4dBZ
• Observed 36.4dBZ, so R=10dBR or 10mm/hr
Now use to plot log R – dBZ
space to calculate a and b
dBZobs
f(Zdr)
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Case Study 9 Oct 2000
Convective area
Stratiform area
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Convective case
• Data from a square side 4km.
• Nw less than 8000 m-3 mm-1.
• Nw seems to increase as R increases.
• Expect b < 1.5• Accuracy of
observations• Z 0.7dB• ZDR 0.2dB
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Convective case• Convert Z and ZDR
to log R – dBZ space
• ‘SD - line’• Slope log Z / log R
• Passing dBZ & log R• a from intercept
• b from slope
• Error in R ± std
• For given Z, R changes 3dB which is factor of 2: but SD fit is to within 25%
• This data gives a=340, b=1.37
Z=340R1.3725% spread
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Stratiform case
• Data from square side 4km.
• Nw reduces as Do increases
• Expect b larger than 1.5
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Stratiform case
• Convert Z, ZDR to logR – dBZ space
• Individual Z-R spread gives R spread 5dB.
• S-D line: given Z, R changes 1dB, 25%
• This data gives a=300 & b=1.58
Z=300R1.5825% spread
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Summary• Different Z-R
from domain averaged Z and ZDR.
• Individual Z-ZDR rainfall has big spread.
• Domain average spread in R is 1dB.
• The rain rate calculated from the 2 cases is quite different for rainrates >5mm/hr
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Rainfall maps
• a and b are calculated over small areas and these then used to calculate R form Z=aRb
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Zphi method