Radar Polarimetric Retrievals.

Anthony Illingworth

University of Reading, UK

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

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

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)

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

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

ZDR AND KDP IN RAIN

Z >40dBZIn heavy rain

ZDR>2dBIn heavy rain

Phase shift 40degs thru heavy rain

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

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

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.

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.

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

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/

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!

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

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)

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

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

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.

FOR ZDR AND KDP DROP SHAPE MODEL CRUCIAL

USE ANDSAGER/GODDARD SHAPES

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

KDP ONLY USEFUL FOR HEAVY RAIN e.g. 1deg/km is about 40mm/hr.

difficult to measure lower values of KDP

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

ZDR AND KDP IN RAIN

Z >40dBZIn heavy rain

ZDR>2dBIn heavy rain

Phase shift 40degs thru heavy rain

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.

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.

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.

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

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

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

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

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)

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)

Case Study 9 Oct 2000

Convective area

Stratiform area

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

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

Stratiform case

• Data from square side 4km.

• Nw reduces as Do increases

• Expect b larger than 1.5

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

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

Rainfall maps

• a and b are calculated over small areas and these then used to calculate R form Z=aRb

Zphi method