Rain Detection & Attenuation Rain Detection & Attenuation for Remote sensing;for Remote sensing;

& auxiliary sensors& auxiliary sensors

Dr. Sandra Cruz-Pol

INEL 5995

DCAS –network weather radars

Total number of drops per unit volume

DdDNrdrpNv )()(

oDDo

c

eNDN

earrp/

/

)(

)(

in units of mm-3

Reflectivity in other books

36

1-

24

512

/mmmin expressed is

and cmin is where

||

10

Z

ZKwo

For Rayleigh approximation

• The cross sectional areas of a scatterer.

24

652

322

24

652

||D

)Im(D

||3

D 2

wbb

waa

wss

Kr

KrQ

KrQ

D=2r =diameter of drop

Observe scattering in Visible EM; forward scattering vs.

backscattering

Mie scattering by dust particles and aerosols

Rayleigh scattering by water vapor molecules and gases.

Mie forward scattering nos impide ver bien a menos que haya alto contraste.

Volume extinction from clouds

• Total attenuation is due to gases,cloud, and rain

• cloud volume extinction is (eq.5.98)

• Liquid Water Content LWC or mv )

• water density = 106 g/m3

epcega

dDDKdDQ wo

ace3

2

}Im{

dDDdrrm wv363

610

3

4

w

Raindrops symmetry

Volume backscattering from Clouds

• Many applications require the modeling of the radar return.

• For a single drop

• For many drops (cloud)

24

652 ||

D wbb Kr

ZK

dDKdDDN

w

wbvc

24

5

624

5

||

N(D)D||

)(

Reflectivity Factor, Z• Is defined as

so that

• and sometimes expressed in dBZ to cover a wider dynamic range of weather conditions.

• Z is also used for rain and ice measurements.

dDDNZ )(D6 ZKwo

vc2

4

5

||

ZdBZ log10

Reflectivity in other books

36

1-

24

512

/mmmin expressed is

and cmin is where

||

10

Z

ZKwo

Reflectivity & Reflectivity FactorR

efle

ctiv

ity,

[cm

-1]

dBZ

for

1g/

m3

Reflectivity and reflectivity factor produced by 1g/m3 liquid water Divided into drops of same diameter. (from Lhermitte, 2002).

Z (in dB)

Precipitation (Rain)

• Volume extinction

• where Rr is rain rate in mm/hr

[dB/km] and b define an algorithm and can depend on polarization since large drops are not spherical but ~oblong.

0

22

3

)()(8

dp eo

er

Mie coefficients

brR1

1

[dB/km]

Rain Rate [mm/hr]

• If know the rain drop size distribution, each drop has a liquid water mass of

• total mass per unit area and time

• rainfall rate is depth of water per unit time

• a useful formula

dDDDNDvR tr3)()(6/

wDm 3

6

0

3 )()6/()()( dDvDNDdAdtdDDmDN tw

4.88D)(-6.8D2

e-19.25)( Dvt

W-band UMass CPRS radar

Volume Backscattering for Rain

• For many drops in a volume, if we use Rayleigh approximation

• Marshall and Palmer developed

• but need Mie for f>10GHz.

dDbrvr

ewvr ZK 24

5

||

6.1200 rRZ

ZKdDK ww2

4

562

4

5

||

D||

Rain retrieval AlgorithmsSeveral types of algorithms used to retrieve rainfall rate

with polarimetric radars; mainly • R(Zh), • R(Zh, Zdr)• R(Kdp) • R(Kdp, Zdr)where R is rain rate,

Zh is the horizontal co-polar radar reflectivity factor,

Zdr is the differential reflectivity

Kdp is the differential specific phase shift a.k.a. differential propagation phase, defined as

band Xfor 5.40)(ˆ

band Sfor 62.11)(ˆ

85.0

937.0

dpdp

dpdp

KKR

KKR

)(2

)()(

12

12

rr

rrK dpdp

dp

Disdrometer

2-Dimensional video disdrometer

R-Z relation

X-band polarimetric radar simulation -estimator R(KDP) - less sensitive to

natural variations in DSD

Also called Distrometers• http://www.iac.ethz.ch/en/groups/richner/cd/doc/optisch/2d-video-distrometer.jpg

$80K $25K• http://www.imk.uni-karlsruhe.de/download/parsivel.jpg

Rain Gauges

• Tipping bucket - 0.2 mm (0.007 in) falls the lever tips and an electrical signal is sent to the recorder

• Weighing rain gauge-storage bin atop a pen recording the changes of weight on a rotating drum . More expensive than Tipping buckets.

• Optical -These have a row of collection funnels. In an enclosed space below each is a laser diode and a phototransistor detector. When enough water is collected to make a single drop, it drips from the bottom, falling into the laser beam path. The sensor is set at right angles to the laser so that enough light is scattered to be detected as a sudden flash of light. The flashes from these photodetectors are then read and transmitted or recorded.

Water spout at Mayaguez, Sept 2005

Calibrated R-Z for 3 regions

Rain gauge data

NEXrad data

Leonid Tolstoy, UPRM-CSU Collaborative Ph.D. student

R-Z calibration

Puerto Rico Testbed IP3

• Update:1st radar is here http://casa.ece.uprm.edu/index.html