Introduction to Radar Doppler Spectra

ERAD2014-Research Applications of Radar Doppler Spectra

Introduction to Radar Doppler Spectra

A. Battaglia with contributions from P. Kollias, E. Luke, S. Kneifel, M.Maahn,F. Fabry

ERAD2014-Research Applications of Radar Doppler Spectra 2

Doppler Radar spectra: a review back in ’73

Why bothering you with Doppler radars after more than 40 years?


Some research on Doppler spectra since1973182 peer reviewed paper citations (58 since 2010)+553 google scholar citations+many more

1. Nick Guy, David P. Jorgensen, Kinematic and Precipitation Characteristics of Convective Systems Observed by Airborne Doppler Radar during the Life Cycle of a Madden–Julian Oscillation in the Indian Ocean, Monthly Weather Review, 2014, 142, 4, 1385.

2. G. Yu, J. Verlinde, E. E. Clothiaux, Y.-S. Chen, Mixed-phase cloud phase partitioning using mm wavelength cloud radar Doppler velocity spectra, Journal of Geophysical Research: Atmospheres, 2014, 119, 12

3. Frédéric Tridon, Alessandro Battaglia, Pavlos Kollias, Disentangling Mie and attenuation effects in rain using a Ka-W dual-wavelength Doppler spectral ratio technique, Geophysical Research Letters, 2013, 40, 20

4. Edward P. Luke, Pavlos Kollias, Separating Cloud and Drizzle Radar Moments during Precipitation Onset Using Doppler Spectra, Journal of Atmospheric and Oceanic Technology, 2013, 30, 8, 1656

5. Dong-Kyun Kim, Yeon-Hee Kim, Kwan-Young Chung, Vertical structure and microphysical characteristics of Typhoon Kompasu (2010) at landfall, Asia-Pacific Journal of Atmospheric Sciences, 2013, 49, 2, 161

6. Christopher R. Williams, Simultaneous ambient air motion and raindrop size distributions retrieved from UHF vertical incident profiler observations, Radio Science, 2002, 37, 2

7. Peter T. May, A. R. Jameson, Thomas D. Keenan, Paul E. Johnston, Chris Lucas, Combined Wind Profiler/Polarimetric Radar Studies of the Vertical Motion and Microphysical Characteristics of Tropical Sea-Breeze Thunderstorms, Monthly Weather Review, 2002, 130, 9, 2228

8. Robert Schafer, Susan Avery, Peter May, Deepak Rajopadhyaya, Christopher Williams, Estimation of Rainfall Drop Size Distributions from Dual-Frequency Wind Profiler Spectra Using Deconvolution and a Nonlinear Least Squares Fitting Technique, Journal of Atmospheric and Oceanic Technology, 2002, 19, 6, 864

9. Pavlos Kollias, R. Lhermitte, B. A. Albrecht, Vertical air motion and raindrop size distributions in convective systems using a 94 GHz radar, Geophysical Research Letters, 1999, 26, 20

10. P. E. Currier, S. K. Avery, B. B. Balsley, K. S. Gage, W. L. Ecklund, Combined use of 50 MHz and 915 MHz wind profilers in the estimation of raindrop size distributions, Geophysical Research Letters, 1992, 19, 10


Some research on Doppler spectra since1973

182 peer reviewed paper citations (58 since 2010)+553 google scholar citations1. Nick Guy, David P. Jorgensen, Kinematic and Precipitation Characteristics of Convective Systems Observed

by Airborne Doppler Radar during the Life Cycle of a Madden–Julian Oscillation in the Indian Ocean, Monthly Weather Review, 2014, 142, 4, 1385.

2. G. Yu, J. Verlinde, E. E. Clothiaux, Y.-S. Chen, Mixed-phase cloud phase partitioning using mm wavelength cloud radar Doppler velocity spectra, Journal of Geophysical Research: Atmospheres, 2014, 119, 12

3. Frédéric Tridon, Alessandro Battaglia, Pavlos Kollias, Disentangling Mie and attenuation effects in rain using a Ka-W dual-wavelength Doppler spectral ratio technique, Geophysical Research Letters, 2013, 40, 20

4. Edward P. Luke, Pavlos Kollias, Separating Cloud and Drizzle Radar Moments during Precipitation Onset Using Doppler Spectra, Journal of Atmospheric and Oceanic Technology, 2013, 30, 8, 1656

5. Dong-Kyun Kim, Yeon-Hee Kim, Kwan-Young Chung, Vertical structure and microphysical characteristics of Typhoon Kompasu (2010) at landfall, Asia-Pacific Journal of Atmospheric Sciences, 2013, 49, 2, 161

6. Christopher R. Williams, Simultaneous ambient air motion and raindrop size distributions retrieved from UHF vertical incident profiler observations, Radio Science, 2002, 37, 2

7. Peter T. May, A. R. Jameson, Thomas D. Keenan, Paul E. Johnston, Chris Lucas, Combined Wind Profiler/Polarimetric Radar Studies of the Vertical Motion and Microphysical Characteristics of Tropical Sea-Breeze Thunderstorms, Monthly Weather Review, 2002, 130, 9, 2228

8. Robert Schafer, Susan Avery, Peter May, Deepak Rajopadhyaya, Christopher Williams, Estimation of Rainfall Drop Size Distributions from Dual-Frequency Wind Profiler Spectra Using Deconvolution and a Nonlinear Least Squares Fitting Technique, Journal of Atmospheric and Oceanic Technology, 2002, 19, 6, 864

9. Pavlos Kollias, R. Lhermitte, B. A. Albrecht, Vertical air motion and raindrop size distributions in convective systems using a 94 GHz radar, Geophysical Research Letters, 1999, 26, 20

10. P. E. Currier, S. K. Avery, B. B. Balsley, K. S. Gage, W. L. Ecklund, Combined use of 50 MHz and 915 MHz wind profilers in the estimation of raindrop size distributions, Geophysical Research Letters, 1992, 19, 10

Commonality: exploitation of information in Doppler spectra collected by profiling radars, ranging from wind profilers to cloud radars

and their combinations for cloud and precipitation microphysics and dynamics.


The cloud radar grand challenge

5Summer School - Finland

Projections of future global average surface temperature for various IPCC 4

scenarios. The graph shows temperature changes as compared with the

1980-1999 average.

The “cloud problem”, i.e., the understanding of the

microphysical, dynamical and radiative processes that

act at the cloud scale and their accurate representation

in numerical models.

Clouds are a bit of a wild card in future climate

simulations (variations in cloud forcing/feedbacks between different

climate models can be as large as the entire radiative forcing due to a doubling of

CO2

(4W/m2)

Cloud radars are a key observing platform for

probing clouds (fifty years after the first attempts and despite the

advancements in the retrieval of raindrop size distribution, the retrieval of cloud

droplet and ice crystals SD from Doppler spectra remains still a grand challenge

(but with renewed hopes).

)


Why are clouds so tough?

April 19, 2023

6

• Huge range of space and time scales

• Hard to validate remote sensing of clouds

• Explosive growth – unstable – chaos producers

• Sub-grid scale in climate models

• At the center of the aerosol-cloud-precipitation chain and linking dynamics-thermodynamics and radiative effects

• What cloud variables do people care about?• Coverage and overlap• Phase• Particle concentration• Water content (liquid/ice)• Vertical velocity

microphysics

Observing systems capable of providing improved descriptions of micro- and macro-physical structure of clouds and of cloud processes over a wide range of spatial and temporal scales will advance our understanding of the Earth system


The cloud radar problem

The dependency to D6 - challenges our ability to study transition regimes (cloud to drizzle,

mixed-phase clouds) and to retrieve cloud properties (mass, number concentration)

7Summer School - Finland


Use a specified functional form for the particle size distribution (model or retrieval imposed)

We want lower moments to evaluate numerical models

Mass content (p = 3)Concentration (p = 0)

Radar reflectivity is related to the 6th moment (p = 6)

Extracting lower moments is subject to large errors introduced by the assumed shape of the particle size distribution

Retrieval of lower particle size distribution moments

April 19, 2023

8


Why this research bloom related to Doppler radars?

,26

4

5

Wb KD

Wa KD Im32

Tx: EIK, 1.7/1.7 kWDuty Cycle: 5%/1%Antenna: 0.33°/0.29°Diameter: 1.82/0.9 m

A potpourri of Doppler systems is now available, the majority of which with multi-frequency capabilities (including mm-wave radars).

PROS CONS

Strong attenuation in heavy rainBetter sensitivity, clutter suppressionLarge Mie effects (sizing capability)Unprecedented temporal/spatial res/portability

WhmmRR

KhmmRRkmdB a

@/8.0

@/2.0/

25

4

WK

ionNormalizat


The Atmospheric Radiation Measurement (ARM) Climate Research Facility

April 19, 2023

Mather and Voyles, BAMS, 2012

Primary goal is to improve the treatment of cloud and radiation

physics in global climate models in order to improve the climate

simulation capabilities of these models (www.arm.gov)

10

The ARM program has deployed the operational cloud profiling radars• Ka band radar (MMCR) for fifteen years• W-band(WACR) for more than five years The ARM program has recently deployed• Operational scanning radars to facilitate the

research on 3D mapping of c louds and precipitation

• Several scanning dual frequency Doppler radars


Chilbolton, UK

35/94-GHz Doppler cloud radars

EU CloudNet project

Cabauw, The Netherlands

35-GHz cloud radar (KNMI)

SIRTA, Palaiseau (Paris), France

94-GHz Doppler Radar

Summer School - Finland

11


German Supersites

Summer School - Finland

12

Integrated Observing

Network

MIRA +MRR radars


Air- and ship-borne MM-wave Radar Platforms

NCAR High-performance Instrumented Airborne Platform for Environmental Research (HIAPER) NASA DC8/ER-2 & Global Hawk Unmanned Aerospace Vehicles (UAV)NRC CanadaConvair-580 cloud radar (W/X-band)University of WyomingKing Air W-band Europe HALO (Ka)+RASTA (W)

NOAA Stabilized 94-GHz Doppler Radar FMCW 94-GHz Doppler RadarDOE-AMFMAGIC Deployment (2012-2013)

ERAD Short Course on Millimeter Wavelength Radars

13


Coming next …..

Next generation of spaceborne rain/cloud radar will have Doppler capabilities!


Doppler Shift: A frequency shift that occurs in electromagneticwaves due to the motion of scatterers toward or away from the observer (famous example==red shift of star-light).

Analogy: The Doppler shift for sound waves is the frequency shift that occurs as race cars (trains) approach and then recede from a stationary 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 (peculiarity of MW).


00 2cos tfEtE ttThe electric field of a transmitted wave

The returned electric field at some later time back at the radar 11 2cos ttfEtE tr

The time it took to travelc

trt

)(2

Substituting:

11

)(22cos

c

trtfEtE tr

The received frequency can be determined by taking the time derivative of the quantity in parentheses and dividing by 2p

dtrt

tt

ttr ffc

vff

dt

dr

c

ff

c

rtf

dt

df

2222

2

11

Amplitude is affected by range and reflectivity

If the object is moving the range is time-dependent

022

1

tfdt

df tt

phase


Doppler spectraThe Doppler frequency is negative (lower frequency, red shift) for objects receding from the radar (vr>0) RED SHIFT

The Doppler frequency is positive (higher frequency, blue shift) for objects approaching the radar (vr<0) VIOLET SHIFT

r

D

vf 2

In VPR the radial velocity accounts for hydrometeor terminal velocity and vertical wind

)(2

)()()( fSdv

dffSvSfS

NB: there is no consensus on the convention on velocity signs


Magnitude of the Doppler Shift

Transmitted Frequency

W band X band C band S band

94 GHz 9.37 GHz 5.62 GHz 3.0 GHzRadial velocity

1 m/s

10 m/s

50 m/s

625 Hz 62.5 Hz 37.5 Hz 20.0 Hz

6.25 KHz 625 Hz 375 Hz 200 Hz

31.25 KHz 3125 Hz 1876 Hz 1000 Hz

These frequency shifts are very small (compared to the radar-frequency 6 order of magnitude lower): for this reason, Doppler radars must employ very stable transmitters and receivers (klystron or magnetron systems)

r

D

vf 2


Mapping velocities into particle size: rationaleDifferent particles have different velocities with larger particles typically falling faster. This is the key feature for using Doppler spectra in microphysical retrievals. Unambiguous (hydrometeor-type dependent) relationships between particle fall speeds and diameters mirror into an unambiguous relationship between Doppler frequency shifts and diameters profile of Doppler spectra can provide range-resolved information about the size distribution of the particles contained in the radar backscattering volume.

Raindrops terminal velocities Saturation of terminal velocities


Velocity-size relationship for other hydrometeors

There is a larger dynamics in terminal velocities for rain than for graupel and snow snow is particularly challenging. On the other hand the difference between different hydrometeors immediately helps in hydrometeor classification.


dDDDn

KZ backe )()(

025

4

Spectral reflectivity factor

Particle size distribution in 1/(m3mm)

2-way attenuation

2r

ZACPP e

radartr

Radar equation for distributed targets

]/[)()()( 13625

4

msmmm

dv

dDDDn

KvS back eZdvvS )(

PSD

rr PdvvP )(

From Mie/scattering theory

When considering the return power at different frequencies we can define the spectral power

Applying the same reasoning to the reflectivity factor we can define a spectral reflectivity factor

Jacobian for mapping D into v

We tend to refer this to the ``Doppler spectrum’’

Radar volume at range r


Broadening of an ideal Doppler spectra for distributed target

Velocity of individual targets in contributing volume vary due to:

3) Wind shear

2) Vertical wind speed and turbulence

1) Differential fall velocity of targets (particularly at high elevation angles, e.g. for vertical incidence)

4) Finite beamwidth


Ideal quiet air Doppler spectrum RR=5 mm/h

]/[)()()( 13625

4

msmmm

dv

dDDDn

KvS back


1

41.0

130

0 1.4

8000)(

mmRR

mmmNeNDn D


Ideal quiet air Doppler spectrum: RR=5 mm/h

]/[)()()( 13625

4

msmmm

dv

dDDDn

KvS back


Mie oscillations sizing info

Rayleigh region

Ice particles: more difficult to compute

sback

(Stefan’s talk)

,26

4

5

Wback KD



]/[)()()( 13625

4

msmmm

dv

dDDDn

KvS back


Raindrop terminal velocity

Not a good mapping between diameters and velocities: all large raindrops end up in the same velocity bin


]/[)()()( 13625

4

msmmm

dv

dDDDn

KvS back


Linear units! The dynamic range of rain reflectivity values is strongly reduced at W-band



]/[)()()( 13625

4

msmmm

dv

dDDDn

KvS back


Linear units! The dynamic range of rain reflectivity values is strongly reduced at W-band

GHzdBZ

GHzdBZ

GHzdBZ

Z [email protected]

[email protected]

[email protected]


Effectof frequency


]/[)()()( 13625

4

msmmm

dv

dDDDn

KvS back


Region wheremulti-frequencyapproach can be

useful

Kollias et al., 2002: detection of the Mie notch at D = 1.65 mm, i.e. Vfall ~= 5.8 m s-1



]/[)()()( 13625

4

msmmm

dv

dDDDn

KvS back


Kollias et al., 2002: detection of the Mie notch at D = 1.65 mm, i.e. Vfall ~= 5.8 m s-1



dvvSdffSZv

v

rde

max

max

r

v

v

r

v

v

r

v

v

r

r P

dvvvS

dvvS

dvvvS

v

max

max

max

max

max

max

22

2

2

max

max

max

max vv

dvvS

dvvSvv

v

v

r

v

v

rr

v

Reflectivity

Mean radial velocity

Spectral width

The moments of the Doppler spectra

Ed will introduce additional spectral moments!


Moments of rain spectra for RR=5 mm/h

]/[)()()( 13625

4

msmmm

dv

dDDDn

KvS back Spectral reflectivity factor

GHzdBZ

GHzdBZ

GHzdBZ

Z [email protected]

[email protected]

[email protected]

GHzsm

GHzsm

GHzsm

vD94@/1.4

35@/3.6

3@/8.6

GHzsm

GHzsm

GHzsm

D

94@/11.1

35@/08.1

3@/35.1

Only due to PSD

MP distribution


Inversion and retrieval of PSD

]/[)()()( 13625

4

msmmm

dv

dDDDn

KvS back Spectral reflectivity factor

If the measured spectrum had this shape then

The particle size distribution N(D) can be directly derived from the radar return power S(V)

Is this inversion possible?

N.B This is what is done in several algorithm, e.g. the MRR retrieval. But Atlas et al. [1973] already recognized that even when updrafts are estimated to better than about 0:25m/s errors in the concentration of raindrops for certain size ranges may exceed a factor of two.

dD

dvKvSDn

back4

25

)()(


Effect of Vertical Air motion and turbulence

One size particles Different size particles

)()()( vSwvSvS airt

The presence of turbulent vertical air motion add a Gaussian distributed random component to the terminal velocity of the raindrops

2

2

2

2

1)( t

v

t

air evSw

In reality there is always turbulent air motions in our radar spectrum: some droplets will be slow down due to turbulent upward motions, some of them accelerate due to downward motions.


Effect of turbulence on W-band spectrum

smw /0

There is a smearing of the no air motion Doppler spectrum, first Mie notch can disappear

First Mie notch

One order ofmagnitude


What controls the magnitude of the broadening σt?

O’Connor et al. 2005; Bouniol et al., 2003, Kollias et al., 2001

Unresolved scales of turbulence

The energy (variance) can be estimated using the variance of the mean Doppler velocity

32

323

2

2

4

2

2

222

3

)(

vt

L

t

La

dkkS

v

Retrieve the eddy dissipation rate ε

st related to the eddy dissipation rate e

smallest scale probed by the Doppler radar

Kolgomorov

vLk

2

1

length scale describing the scattering volume dimension includes large eddies traveling through the sampling volume within the radar dwell time

42

Lk

ERAD2014-Research Applications of Radar Doppler Spectra Kollias et al., 2002

dwellrangebeamwidthft ,,,,

Detailed formulas can be foundIn Frisch and Clifford, JAS, 1974

Turbulence broadening σt


Linear wind fields result in Doppler spectrum broadening (detailed formulas in Doviak-Zrnic).

Discontinuous (step function) wind field profile results in bimodal Doppler spectrum.

Wind shear broadening σsh If the vertical wind is changing inside the radar backscattering volume (either moving parallel or perpendicular to the radar beam) this will add extra broadening to the spectrum

shearwindresrangebeamfsh ,,


Wind shear broadening σsh If the vertical wind is changing inside the radar backscattering volume (either moving parallel or perpendicular to the radar beam) this will add extra broadening to the spectrum

Wind shear of 10-2-10-1 s-1 are possible close to convective core w variation of 10 m/s in 100m

Kollias et al., JAS, 2001


The cross-beam wind velocity induces a broadening proportional to the beamwidth because of the radial component of the cross-beam wind vector pointing in directions away from the beam axis

2ln43

dBB

U

For a 9 degree beamwidth wind profiler (typical 915-MHz) σB is 1.4 ms-1 for a 30 ms-1 cross wind velocity

For a 0.5 degree beamwidth cloud radar (typical cloud radar) σB is 0.08 ms-1

Finite beamwidth broadening σB

U

For a Gaussin circular antennaParticles along the green line appearto recede from the radar


EarthCARE CPR

For the EarthCARE CPR, the beamwidth is 0.095 degrees but the satellite (cross beam wind) is 7,600 ms-1 and σB is 3.7 ms-1

Spaceborne-radars: finite beamwidth broadening σB

smvsatdB

satB /7.3)2(log4

3

The same reasoning applies if the radar moves. LEO satellite moves quite fast huge effect even withSmall beamwidths

Apparently receding

from radar/going downward

Approaching/upward

That’s why Doppler spectra from air-borne andSpace-borne radars are not so useful


Radar Doppler Spectrum

rising particles falling particles

cloud

drizzle

light rain

moderaterain

heavyrain** *

** *

**

***** ice/snow noise

Velocity (m/s)

Rece

ived

Pow

er (d

B)

Particle sizeincreasing

Particle size decreasing

updrafts

downdrafts

turbulenceThe quasi-unique relationship between D and vfall(D) does not translate in a unique relationship between D and Doppler shift because of the presence of vertical wind and broadening effects (turbulence, cross-wind,..)

P


Retrieval: Convolution of Microphysics with Dynamics

Cloud radars don’t “see” the air directly. We must infer air motion through the motion of particles of which we have incomplete understanding.

To gain the best insight into the properties of observed particles, we must understand the motion of the surrounding air.

42

Several techniques proposed for retrieving simultaneously dynamics and microphysics. Doppler techniques can be complemented by multi-wavelength capabilities based on Bragg vs Rayleigh, Rayleigh vs Mie effects. Next talk examples of:• Drizzling warm marine stratocumulus (Ed)• Non precipitating fair weather cumulus (Ed) • Clear air insect clutter (Ed)• Continental stratiform rain (Fred&Ed)• Ice and mixed-phase clouds (Stefan)

Introduction to Radar Doppler Spectra

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Transcript of Introduction to Radar Doppler Spectra