Introduction to Radar Doppler Spectra
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Transcript of 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?
ERAD2014-Research Applications of Radar Doppler Spectra 3
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
ERAD2014-Research Applications of Radar Doppler Spectra 4
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.
ERAD2014-Research Applications of Radar Doppler Spectra
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).
)
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra
German Supersites
Summer School - Finland
12
Integrated Observing
Network
MIRA +MRR radars
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra
Coming next …..
Next generation of spaceborne rain/cloud radar will have Doppler capabilities!
ERAD2014-Research Applications of Radar Doppler Spectra
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).
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra 20
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.
ERAD2014-Research Applications of Radar Doppler Spectra
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
ERAD2014-Research Applications of Radar Doppler Spectra 22
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
ERAD2014-Research Applications of Radar Doppler Spectra
Ideal quiet air Doppler spectrum RR=5 mm/h
]/[)()()( 13625
4
msmmm
dv
dDDDn
KvS back
Spectral reflectivity factor
1
41.0
130
0 1.4
8000)(
mmRR
mmmNeNDn D
ERAD2014-Research Applications of Radar Doppler Spectra
Ideal quiet air Doppler spectrum: RR=5 mm/h
]/[)()()( 13625
4
msmmm
dv
dDDDn
KvS back
Spectral reflectivity factor
Mie oscillations sizing info
Rayleigh region
Ice particles: more difficult to compute
sback
(Stefan’s talk)
,26
4
5
Wback KD
ERAD2014-Research Applications of Radar Doppler Spectra
Ideal quiet air Doppler spectrum: RR=5 mm/h
]/[)()()( 13625
4
msmmm
dv
dDDDn
KvS back
Spectral reflectivity factor
Raindrop terminal velocity
Not a good mapping between diameters and velocities: all large raindrops end up in the same velocity bin
ERAD2014-Research Applications of Radar Doppler Spectra
]/[)()()( 13625
4
msmmm
dv
dDDDn
KvS back
Spectral reflectivity factor
Linear units! The dynamic range of rain reflectivity values is strongly reduced at W-band
Ideal quiet air Doppler spectrum: RR=5 mm/h
ERAD2014-Research Applications of Radar Doppler Spectra
]/[)()()( 13625
4
msmmm
dv
dDDDn
KvS back
Spectral reflectivity factor
Linear units! The dynamic range of rain reflectivity values is strongly reduced at W-band
GHzdBZ
GHzdBZ
GHzdBZ
Ideal quiet air Doppler spectrum: RR=5 mm/h
Effectof frequency
ERAD2014-Research Applications of Radar Doppler Spectra
]/[)()()( 13625
4
msmmm
dv
dDDDn
KvS back
Spectral reflectivity factor
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
Ideal quiet air Doppler spectrum: RR=5 mm/h
ERAD2014-Research Applications of Radar Doppler Spectra
]/[)()()( 13625
4
msmmm
dv
dDDDn
KvS back
Spectral reflectivity factor
Kollias et al., 2002: detection of the Mie notch at D = 1.65 mm, i.e. Vfall ~= 5.8 m s-1
Ideal quiet air Doppler spectrum: RR=5 mm/h
ERAD2014-Research Applications of Radar Doppler Spectra
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!
ERAD2014-Research Applications of Radar Doppler Spectra
Moments of rain spectra for RR=5 mm/h
]/[)()()( 13625
4
msmmm
dv
dDDDn
KvS back Spectral reflectivity factor
GHzdBZ
GHzdBZ
GHzdBZ
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
ERAD2014-Research Applications of Radar Doppler Spectra
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
)()(
ERAD2014-Research Applications of Radar Doppler Spectra 33
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.
ERAD2014-Research Applications of Radar Doppler Spectra 34
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
ERAD2014-Research Applications of Radar Doppler Spectra 35
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
ERAD2014-Research Applications of Radar Doppler Spectra 37
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 ,,
ERAD2014-Research Applications of Radar Doppler Spectra 38
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
ERAD2014-Research Applications of Radar Doppler Spectra 39
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
ERAD2014-Research Applications of Radar Doppler Spectra 40
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
ERAD2014-Research Applications of Radar Doppler Spectra 41
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
ERAD2014-Research Applications of Radar Doppler Spectra
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)