Assignment #2 If air with precipitation water content of 1 g/m3, assuming mono size distribution (all hydrometeors have same size) How many raindrops would be in 1 m3 (total number density N) if all raindrops have diameter (D) of 1 mm? Calculate 10log(N*D6), units in mm6/m3. How many snowflakes would be in 1 m3 if all snowflakes have diameter of 5 mm and density in 0.3 g/cm3? Calculate 10log(N*D6), units in mm6/m3. How many hails would be in 1 m3 if all hails have diameter of 10 mm and density in 0.9g/cm3? Calculate 10log(N*D6), units in mm6/m3.

Precipitation Content

Basic units: g/m3

Simple interpretation: Mass of water in a unit volume

Extreme values:0.1 gram/m3 in light drizzle10 gram/m3 in rain in hurricane eyewall

Example:A distribution of 1000 1-mm raindrops per cubic

meter would have a precipitation content of about 0.5 grams/m3 .

Relationship of the Reflectivity Factor to other Meteorological Quantities

c

jj

V

D

Z

6

Precipitation content (W): The mass of condensed water substance (water or ice) present in the form of precipitation-sized particles (detectable with radar), per unit volume.

c

jj

c

jj

V

D

V

m

W

3

6 Where:

mj is the contribution to the total mass from each raindrop j

Precipitation Rate

Basic units: m3/(m2sec) = m/sStandard units: mm/hr

Simple interpretation: Depth of accumulated rainfall on a runoff-free surface

Extreme values:0.1 mm/hr in light drizzle1000 mm/hr in a hurricane eyewall

Example:A distribution of 1000 1-mm raindrops per cubic

meter, falling at their terminal fall speed of 4 m/s in the absence of vertical motion, would give a precipitation rate of 2.1 10-6 m/s or about 7.5 mm/hr.

Relationship of the Reflectivity Factor to other Meteorological Quantities

c

jj

V

D

Z

6

Precipitation rate (R): The volume of precipitation passing downward through a horizontal surface, per unit area, per unit time.

c

jjj

c

jj

V

wD

V

r

R

3

6 Where:

rj is the contribution to the rainfall rate from each raindrop j

wj is the fall velocity of each drop j

c

jjj

V

wD

R

3

6

What is the fall velocity of a raindrop?

For drops with diameters between 0-2 mm (most drops) the fall velocity is proportional to diameter

Terminal velocity of raindropsIn still air (Foote and duTroit 1969)

j

DR 4

so what is the relationshipto the radar reflectivity?

Problem:

5.1

46

jj

DD

Illustration of inequality

Consider two drops 1 mm and 2 mm5.1

46

jj

DD

09.701721

65215.15.144

66

Therefore: There is no exactRelationship between rainfallRate and radar reflectivity

Nevertheless, rainfall rates are qualitatively related to the radarreflectivity factor, and radar scientists have sought empirical relationships of the type:

b

R R

RZZ

0

where ZR is the value of Zwhen R = R0

Relationship of Z to Precipitation Rate

Methods of determining Z-R relationships

1. The direct method: Values of Z and R are measured by a radar and raingages. The data are compared using correlation statistics and a Z-R relationship is determined from a best fit.

Relationship of Z to Precipitation Rate

Methods of determining Z-R relationships

2. The indirect method: Values of Z and R are calculated from the same measured raindrop size distribution.

Methods to measure raindrop size distributions

Mechanical: stained filter paper: Uses water stains in filter paper to estimate raindrop sizes (used originally by Marshall and Palmer)

Impact disdrometer: Uses raindrop’s momentum when striking surface to estimate its size.

Ground Based Optical disdrometers

Airborne Optical disdrometers

Foil impactors

Determine drop sizes by shadows recorded on optical arrays

Foil impactors: determine drop sizes from impact craters

Example of raindrop images collected with an airborne optical array spectrometer in a shower in Hawaii with the largest raindropever recorded in nature (courtesy Ken Beard)

Typical measured raindrop size distributions

Measurement Issues

The measurement used to arrive at a Z-R is an issue too………….

Comparison of aircraft 2D-P measurements (truncated and untruncated) to disdrometer (Joss-Waldvogel) measurement.

Truncated (at 1 mm) 2D-P measurement is closer to disdrometer measurement…..small drops?

DSD instrumentation is an issue (e.g., impact-type disdrometers have sensitivity problems at the small drop end of the spectrum e.g., drops < 1 mm diameter).

To estimate Z and R, exponential approximations to raindrop size distributions are often developed

The Marshall-Palmer Distribution

Developed from raindrop samples collected in Canada on powdered sugar filter paper in 1948 by radar pioneers Marshall and Palmer

DnDn exp0

The Marshall-Palmer Distribution

4640 10808.0 mcmn

c

R R

R

0

hrmmR /10 141 cmR

The Marshall-Palmer distribution stood as the standard for many decades although many subsequent studies showed that it was not universally applicable.

The exponential distribution has properties that make it useful because it is easy to relate the drop size distribution to rainfall rate, precipitation content, and radar reflectivity

Radar scientists have tried to determine Z-R relationships because of the potential usefulness of radar determined rainfall for

FLASH FLOOD NOWCASTING

WATER MANAGEMENT

AGRICULTURE(irrigation needs/drought impacts)

Z-R Variability: Convective/Stratiform

Z=a1Rb1

Z=a2Rb2

10 lo

g 10

Z

R

N(D)

D

Convective

Stratiform

D0strat > D0conv

There have been hundreds of Z-R relationships published – here are just a few between 1947 and 1960 – there have been 4 more decades of new Z-R relationships to add to this table since!

Z-R relationships are dependent on the type of rainfall (convective, stratiform, mixed), the season (summer, winter), the location (tropics, continental, oceanic, mid-latitudes), cloud type etc.

For the NEXRAD radars , the NWS currently uses five different Z-R relationships and can switch between these depending upon the type of weather event expected.

        Default WSR-88D (Z= 300R1.4)        Rosenfeld tropical (Z=250R1.2)        Marshall/Palmer (Z=200R1.6)         East Cool Season (Z=200R2.0)        West Cool Season (Z=75R2.0)

The single largest problem in applying Z-R relationships has been accounting for effects of the radar bright band

The bright band: The melting level, where large snowflakes become water coated, but have not yet collapsed into small raindrops.

Wet snowflakes scatter energy very effectively back to the radar

D istan c e (km )

R ef le ct iv ity fa cto r (d B Z )

S tr a t i fo rm a rea C on v ec t io n

B BAltitude (km)

The bright band appears as a ring on PPI displays where the radar beam crosses the melting level

SNOW

Few attempts have been made to develop Z-S relationships

1. Snow density varies significantly from storm to storm and within storms2. Scattering by ice is non-Rayleigh (not spheres) and so the relationship

between mass and Z is even less certain3. Radars calibrated for rain (Z determined from K for rain, not ice, even in

winter)

Measurements have been made of the size distributions of snowflakes and related to precipitation rates (melted equivalent), and Z-S relationships have been proposed but these relationships have largely been ignored in practice

Hail

Very few attempts have been made to quantity hailfall from thunderstorms. Most work focuses on trying to identify whether hail is reaching the surface. This work is now focused on studies using polarization radar technology, which we will examine later in the course.

Doppler Radar

From Josh Wurman

NCAR S-POL DOPPLER RADAR

Doppler Shift: A frequency shift that occurs in electromagneticwaves due to the motion of scatterers toward or away from the observer.

Doppler radar: A radar that can determine the frequency shift through measurement of the phase change that occurs in electromagnetic waves during a series of pulses.

Analogy: The Doppler shift for sound waves is the frequency shift that occurs as race cars approach and then recede from a stationary observer

Sign conventions

The Doppler frequency is negative (lower frequency, red shift) for objects receding from the radar

The Doppler frequency is positive (higher frequency, blue shift) for objects approaching the radar

These “color” shift conventions are typically also used on radar displays of Doppler velocity

Blue: Toward radar

Red: Receding from radar

Note that Doppler radars are only sensitive to the radial motion of objects

Air motion is a three dimensional vector: A Doppler radar can only measure oneof these three components – the motion along the beam toward or away from the radar

PROBLEM

More than one Doppler frequency (radial velocity) will always exist that can fit a finite sample of phase values.

The radial velocity determined from the sampled phase values is not unique

EXAMPLE VALUES OF THE MAXIMUM UNAMBIGUOUS DOPPLER VELOCITY

Wavelength Radar PRF (s-1)

cm 200 500 1000 2000

3 1.5 3.75 7.5 15

5 2.5 6.25 12.5 25

10 5.0 12.5 25.0 50

Table shows that Doppler radars capable of measuring a large range of velocities unambiguously

have long wavelength and operate at high PRF

Folded velocities

Can you find the folded velocities in this image?

http://apollo.lsc.vsc.edu/classes/remote/graphics/airborne_radar_images/newcastle_folded.gif

Folded velocities in an RHI Velocities after unfolding

The Doppler Dilema

Ways to circumvent the ambiguity dilema

1. “Bursts” of pulses at alternating low and high pulse repetition frequencies

Measure reflectivity Measure velocity

Low PRF used to measure to long range, high PRF to measure velocity

A Guide to interpreting Doppler Velocity Patterns

Rodger A. Brown and Vincent T. WoodNational Severe Storms Laboratory

NOAA

Assignment #3

Multi Doppler analysis

Glen Romine

When more than one radar views the same region of a storm, the pulse volumes have a different orientation, gain function relative to the particles and are generally not simultaneous…..

Multiple Doppler Retrieval of Wind Fields

How Quad Doppler wind retrieval from airborne radars works

SQUALLLINEreflectivityshaded

fore radar scan

aft radar scan

How Quad Doppler wind retrieval from airborne radars works

SQUALLLINEreflectivityshaded

How Quad Doppler wind retrieval from airborne radars works

SQUALLLINEreflectivityshaded

Raw unedited data

ground previously leveled

Final clean edited radar sweep!

Wind Output

@3.5 km

cross-sectionto be shownlater

NRL P-3track

NOAA P-3track

Vertical cross-section

A A’

A

A’

Some real cases during SALLJEX field campaign are available at:http://trmm.chpc.utah.edu/old_web/salljex/

Polarimetric Radar

Long-standing Problems

Distinguishing, ice and liquid phases of precipitation using radar

Identifying specific hydrometeor populations, such as hail or supercooled water

Quantifying, rain, snow and hailfall rates using radar.

Multi-Parameter Measurements

Standard Doppler radar (ZHH, Vr, ) Polarization radar (signals of two different

polarizations are processed): Many parameters can be derived

(Measurements of two or more parameters of the radar signal)

* Note notation: ZHH

Transmitted at horizontal polarization

Received at horizontal polarization

Linear Polarization

(Doviak and Zrnić, 1993)

http://www.nssl.noaa.gov/~schuur/radar.html

E

E

Electromagnetic Waves

Circular Polarization

Practical use of circular polarization: Tracking aircraft in precipitation.Light to moderate rain: removal of a large portion (e.g. 99%) of the precipitation echo (transmitted right-hand circular polarized waves become, when scattered from small spherical drops, left-hand polarized).

E

(Pruppacher and Klett, 1997)

4 mm 3.7 mm 2.9 mm

2.7 mm 1.8 mm 1.4 mm

Differential Reflectivity ZDR

ZDR [dB] = 10 log( )– Depends on axis ratio

oblate: ZDR > 0

prolate: ZDR < 0

– For drops: ZDR ~ drop size (0 - 4 dB)

zHH

zVV

ZDR (cont.)

ZDR = 10 log( )

(Pruppacher and Klett, 1997)

zHH

zVV

– For ice crystals: • columns (1 – 4 dB)• plates, dendrites (2 – 6 dB)

ZDR (cont.)

ZDR = 10 log ( )

(Pruppacher and Klett, 1997)

zHH

zVV

(Hobbs, 1974)

– For hail: (-1 – 0.5 dB)– For graupel: (-0.5 – 1 dB)– For snow: (0 – 1 dB)

ZDR (cont.)

• Independent of calibration• Independent of concentration (but can depend on how the concentration is distributed among various sizes• Is affected by propagation effects (e.g. attenuation)

LDR [dB] = 10log( )

Linear Depolarization Ratio LDR

(Pruppacher and Klett 1997)

4 mm 3.7 mm 2.9 mm

zHV

zHH

• Spheroidal hydrometeors with their major/minor axis aligned or orthogonal to the electric field of the wave: LDR - dB

• Detects tumbling, wobbling, canting angles, phase and irregular shaped hydrometeors:

• large rain drops (> -25 dB)• Hail, hail and rain mixtures (-20 - -10 dB)• wet snow (-13 - -18 dB)

8

Differential Propagation Phase ΦDP

ΦDP [deg.]= ΦHH – ΦVV

ΦHH, ΦVV: cumulative differential phase shift for the total round trip between radar and resolution volume).ΦHH, ΦVV = differential phase shift upon backscatter

+ differential phase shift along the propagation path

(Photos: Scott Ellis)

• NSF funded• S-band dual polarization Doppler radar• Highly mobile (fits in 6 sea containers)• Antenna diameter 8.5 m• Beam width 0.91 deg• Range resolution 150 m

S-Pol (NCAR)

Chill (CSU)• NSF funded• S-band dual polarization Doppler radar• Antenna diameter 8.5 m• Beam width (3 dB) 1.1 deg• Range resolution 50, 75, 150 m

Koun WSR-88D Radar(NSSL Norman, OK)

• Polarimetric upgrade of NEXRAD radar, completed in March 2002

Wyoming King Air Cloud Radar (UW)

• K-band• Dual/single polarization Doppler radar• Beam width 0.4 – 0.8 deg (depending on antenna type)• Antenna configurations down, side, up

Results

Assignment #3

Read the slides from the website:http://trmm.chpc.utah.edu/class/5230/homework.html