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Radar Basics and Estimating Precipitation
Jon W. Zeitler
Science and Operations Officer
National Weather Service
Austin/San Antonio Forecast Office
Radar Beam Basics
Energy Scattering
As pulse volumes within the radar beam encounter targets, energy will be
scattered in all directions. A very small portion of the intercepted energy will be
backscattered toward the radar. The degree or amount of backscatter is
determined by target:
size (radar cross section)
shape (round, oblate, flat, etc.)
state (liquid, frozen, mixed, dry, wet)
concentration (number of particles per unit volume)
We are concerned with two types of scattering, Rayleigh and non-Rayleigh.
Rayleigh scattering occurs with targets whose diameter (D) is much smaller (D <
/16) than the radar wavelength. The WSR-88D's wavelength is approximately
10.7 cm, so Rayleigh scattering occurs with targets whose diameters are less than
or equal to about 7 mm or ~0.4 inch. Raindrops seldom exceed 7 mm so all liquid
drops are Rayleigh scatters.
Potential problem: Nearly all hailstones are non-Rayleigh scatterers due to their
larger diameters.
Probert-Jones Radar Equation
Simplified Radar Equation
Equivalent Reflectivity (Ze)
Since we technically don't know the drop-size distribution or
physical makeup of all targets within a sample volume, radar
meteorologists oftentimes refer to radar reflectivity as
equivalent reflectivity, Ze.
The assumption is that all backscattered energy is coming from
liquid targets whose diameters meet the Rayleigh
approximation. Obviously, this assumption is invalid in those
cases when large, water-coated hailstones are present in a
sample volume. Hence, the term equivalent reflectivity instead
of actual reflectivity is more valid.
Reflectivity (Z) vs.
Decibels of Reflrectivity (dBZ)
(Equation 5)
dBZ = 10log10Z
Beam-Filling
Sending vs. Listening
Sending vs. Listening
99.843% of the time the WSR-88D is listening for signal returns.
The Doppler Dilemna
A low PRF is desirable for target range and power, while a
high PRF is desirable for target velocity. The inability to
satisfy both needs with a single PRF is known as the Doppler
Dilemma. The Doppler Dilemma is addressed by the WSR88D with algorithms.
Range Folding
Subrefraction: dry adiabatic, moisture increases with height. In
addition to underestimated echo heights, this phenomenon tends
to reduce ground clutter in the lowest elevation cuts.
Superrefraction: temperature inversion. In addition to
overestimated echo heights, increases ground clutter in the
lowest elevation cuts and is the cause of what we normally refer
to as anomalous propagation or AP echoes.
The Earth is Round!
Storms Too Close!
Each pulse has a volume with dimensions of ~ 500
meters (~ 1500 meters) in length by ~ 1° wide in short
pulse (long pulse) mode. This means that two targets
along a radial must be at least 250 (750) meters apart for
the radar to be able to distinguish and display them as
two separate targets (i.e., more than H/2 range separation
distance).
Storms or Bats?
Strategies to Fix Problems
Drop Size Distribution
Drop Size Distribution
Rainfall Rate
Rainfall Rate
Rainfall Rate
R(Z) Relationships (Battan 1973)
BREAK!
What is Dual Polarimetric Radar?
Sends and receives horizontal &
vertical polarized radiation
Image courtesy Terry Schuur
Polarimetric Variables Depend
on Several Things
Hydrometeor:
• Shape
• Orientation
• Dielectric constant
• Distribution of sizes
Applications of Dual
Polarization Radar
•Rainfall Estimation (vast improvement)
•Bright Band Detection (vast improvement)
•Clutter Filtering/Data Quality Improvement
(vast improvement)
•Rain/Snow Discrimination (vast improvement)
•Hail Detection (some improvement)
•Updraft Location (some improvement)
•Tornado Detection (some improvement)
Polarimetric Variables
Backscattering:
Zh - reflectivity factor for horizontal polarization
ZDR - differential reflectivity
|ρhv(0)| - co-polar correlation coefficient
Propagation - forward scattering:
ΦDP - differential phase
KDP - specific differential phase (range derivative of
ΦDP)
Shapes of Large Drops in Equilibrium
Differential Reflectivity (ZDR)
• Definition: the ratio of the power returns
from the horizontal and vertical
polarizations
• Units: decibels (dB)
 Z hh 
Z DR  10 log 10  
 Z vv 
Simple ZDR Calculation for a
Sample of Raindrop Sizes
What does ZDR Mean?
Ev
Eh
• ZDR > 0  Horizontallyoriented mean profile
Ev
Eh
Ev
Eh
• ZDR < 0  Vertically-oriented
mean profile
• ZDR ~ 0  Near-spherical
mean profile
Differential Reflectivity (ZDR)
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
Small (Spherical) <<< RAIN >>> Large (Oblate)
Dry <<< GRAUPEL >>> Wet
Dry (Prolate)
<<<<<
HAIL
>>>>>
Melting (Oblate)
Aggregated/Low-Density <<< CRYSTALS >>> Pristine/Well-Oriented
Dry <<< SNOW >>> Wet
GROUND CLUTTER / ANOMALOUS PROPAGATION
BIOLOGICAL SCATTERERS
DEBRIS
CHAFF
6
ZDR is a Good Indicator of:
1. median liquid drop size (ZDR↑,median
drop diameter↑)
2. hail shafts (ZDR ~ 0dB or negative
coincident with high Zh)
3. areas of large rain drops or liquidcoated ice (ZDR ~3-6 dB)
4. convective updrafts (ZDR ~1-5 dB)
above 0oC level
5. tornado debris ball
ZDR Limitations (Gotchas)
•Values are biased towards the larger
hydrometeors (D6 dependence)
•Tumbling/Random orientation will bias
toward 0 ZDR
•Can be noisy if:
-Low / Insufficient sampling (low
SNR)
- Reduced correlation coefficient (CC)
May 9th tornadic
supercell: Intense
ZDR Column
0oC level in-cloud ~17 kft
ρhv
Correlation Coefficient (ρ hv): A correlation between the
reflected horizontal and vertical power returns. It is a good
indicator of regions where there is a mixture of precipitation
types, such as rain and snow.
Affected by:
• Hydrometeor types, phases, shapes,
orientations
• Presence of large hail
ρhv Usage
• Identify hail growth regions in deep moist
convection (mixtures of hydrometeors)
• Reduce ground clutter/AP contamination
(ρhv very low in these areas)
• Identify giant hail ???
ρhv
SNOW
~0.85-1.00
CLUTTER
~0.5-0.85
CHAFF
~0.2-0.5
Reflectivity (Zh)
Correlation Coefficient (rhv)
ρhv Minimum…in Theory
Giant Hail, Protuberances, Mie Scattering: min ρhv
Differential Phase Shift (ΦDP)
• Definition: the difference in the phase shift
between the horizontally and vertically
polarized waves
• Units: degrees (o)
 DP   H  V
Differential Phase Shift fDP
fDP = fh – fv (fh, fv ≥ 0) [deg]
The difference in phase between the horizontallyand vertically-polarized pulses at a given range
along the propagation path.
- Independent of partial beam blockage,
attenuation, absolute radar calibration,
system noise
What Affects Differential Phase?
Forward Propagation has its
Advantages
• Immune to partial (< 40%) beam
blockage, attenuation, calibration,
presence of hail
Gradients Most Important
Specific Differential Phase Shift
(KDP)
• Definition: range derivative of the differential phase
shift
• Units: degrees per kilometer (o/km)
f (r )  f (r )
K 
2r  r 
DP
2
DP
DP
2
1
1
Specific Differential Phase: KDP
Specific Differential Phase (KDP): A comparison of the returned phase
difference between the horizontal and vertical pulses. This phase
difference is caused by the difference in the number of wave cycles
(or wavelengths) along the propagation path for horizontal and
vertically polarized waves. This is the range derivative of
typically calculated in 1-5 km increments along the radial.
f
DP,
• Provides a good estimate of liquid water
in a rain/hail mixture
• Indicates the onset of melting
Specific Differential Phase Shift
(KDP)
-0.5
0
0.5
1
1.5
2
2.5
3
4
Small <<< RAIN >>> Large
Dry <<< GRAUPEL >>> Wet
Dry (Prolate)
<<<<<
HAIL
>>>>>
Melting (Oblate)
Dry/Aggregated <<< CRYSTALS >>> Pristine/Well-Oriented
Dry <<< SNOW >>> Wet
*** Non-meteorological values not shown here because
they are removed anywhere CC < 0.90 (or 0.85) ***
5
Kdp Usage
•
To isolate the presence of rain from hail
 R(Z, Zdr, Kdp) much better than R(Z)
 Most sensitive to amount of liquid water
•
To locate regions of drop shedding, “Kdp columns”
• Drops are shed from melting or growing
hailstones near the updraft, forming a Kdp
column
•
To distinguish between snow/rain
• Kdp in wet, heavy snow is almost always larger
at a fixed value of Zh than that observed for rain
KDP Limitations (Gotchas)
• KDP values set to “No Data” at CC <
0.90, or 0.85)
• Sensitive to non-uniform beam filling
• Unreliable at far ranges
• KDP Smoothing techinque:
Compare Z and
KDP fields at
each gate
1.
2.
< 40 dBZ, KDP computed at each gate
from 12 adjacent gates either side (6.25
km)
> 40 dBZ, KDP computed at each gate
from 4 adjacent gates either side (2.25
km) to preserve heavy cores
Marginally Severe Supercell
14 May 2003
ρHV
Z
HCA
Z
DR
5.25” diameter hail
Beam Height ~ 4600 ft AGL
Correlation Coefficient (CC)
• Definition: how similarly the horizontally and
vertically polarized backscattered energy are
behaving within a resolution volume for Rayleigh
scattering
• Units: none (0-1.00)
r HV (0) 
*
S vv S hh
 S 2
hh

1/ 2
S
2 1/ 2
vv


Sij = An element of the backscatter matrix
Think Spectrum Width for Hydrometeors
Correlation Coefficient Values
• 0.96 ≤ CC ≤ 1
 Small hydrometeor diversity*
• 0.80 ≤ CC < 0.96
 Large hydrometeor diversity*
• CC < 0.70
 Non-hydrometeors present
* Types, sizes, shapes, orientations, etc.
Correlation Coefficient (CC)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.85
0.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
Large <<< RAIN >>> Small
Wet <<< GRAUPEL >>> Dry
Wet / Large
<<<<<
HAIL
>>>>>
Dry / Small
CRYSTALS
<<Melting Layer>>
Wet <<< SNOW >>> Dry
GROUND CLUTTER / ANOMALOUS PROPAGATION
BIOLOGICAL
SCATTERERS
DEBRIS
CHAFF
NonMeteorological
Regime
Overlap
Meteorological
Regime
1
What is CC Used for?
• Not-met targets (LOW CC < 0.70)
– Best discriminator
• Melting layer detection (Ring of reduced
CC ~ 0.80 – 0.95)
• Giant hail? (LOW CC < 0.70 in the midst
of high Z/Low ZDR)
Marginally Severe Supercell
Precip
What about the re
All > 0.97
Insects
CC Limitations (Gotchas)
• High error in low signal-to-noise
ratios (SNR)
• If low, errors increase in other
dual-pol variables
Polarimetric Rainfall Algorithm vs.
Conventional
One hour point measurements:
Radar estimates vs. gages
R(Z)
R(Z, KDP, ZDR)
Polarimetric Rainfall Algorithm vs.
Conventional
Bias of radar areal rainfall estimates
Spring hail
cases
Cold season
stratiform rain
QPE Process in a Nutshell
Step 1
1. Hybrid scan the
variables into
Polar, 1 degree
azimuth, 250 m
bins
Hybrid Hydroclass
QPE Process in a Nutshell
2. Apply an instantaneous Rate:
R(Z), R(KDP), and R(Z,ZDR)
 But which one is accepted?
R(Z )  0.017 Z
0.714
R( KDP)  44.0 KDP
R(Z , ZDR )  0.0142 Z
0.882
sign ( KDP)
0.770
ZDR
1.67
QPE Process in a Nutshell
3. Assign a variation of 1 of those 3 rates to
each bin based on HCA precip type
 Based on 43 events (179 hrs) of radar rainfall data
Rate Designation Table
R (mm/hr)
Conditions
Echo
Classes
Not
computed
Nonmeteorological echo (Ground Clutter or Unknown) is classified
GC ,UK
0
Classification is No Echo or Biological
NE, BI
R(Z, ZDR)
Light/Moderate Rain is classified
RA
R(Z, ZDR)
Heavy Rain or Big Drops are classified
HR, BD
R(KDP)
Rain/Hail is classified and echo is below the top of the melting layer
RH
0.8*R(Z)
Rain/Hail is classified and echo is above the top of the melting layer
RH
0.8*R(Z)
Graupel is classified
GR
0.6*R(Z)
Wet Snow is classified
WS
R(Z)
Dry Snow is classified and echo is in or below the top of the melting DS
layer
2.8*R(Z)
Dry Snow classified and is echo above the top of the melting layer
DS
2.8*R(Z)
Ice Crystals are classified
IC
QPE Output (all produced via
hybrid scan)
•
•
•
•
4bit, 250 m Hybrid-scan Hydro Class
8bit, 250 m Rate
4 bit, 250 m 1hr Accum
4 bit & 8bit versions of 250 m STP Accum (G-R
bias applied)
• 8 bit, 250 m no G-R bias applied STP
• 8 bit, 250 m User Selectable (will be used for any
and all accumulation time periods)
• 8 bit, 250 m 1hr and STP Difference field vs.
Legacy
Hydrometeor Classification Algorithm
Challenges
• Typical Radar sampling limitations (snow at
2000 ft AGL may not be snow at the surface)
• Verification
• “Fuzzy” Logic and cross over between types
• Differentiating between light rain and dry snow
in weak echoes
 Melting layer detection can
help
Melting Layer Detection
• Mixed phase hydrometeors: Easy
detection for dual-pol!
– Z typically increases
– ZDR and KDP definitely increase
– Coexistence of ice and water will reduce the
correlation coefficient (CC ~0.95-0.85)
Melting Layer Detection Algorithm
Methodology
• Precipitation echoes – stratiform or
convective regions – with high SNR
• Middle tilts (4°-10° elevation angles)
• Limitation: Overshoot precip
• “Project” results to other tilts in time and
space
ML Product in AWIPS
Hail Detection
• Dual-Pol Hail Signature
– High Z (> 45 dBZ)
– Low ZDR (-0.5 to 1 dB), Low KDP (-0.5 to
1 o/km) if dry or mostly dry
– Reduced CC (0.85 to 0.95)
• Limitations
– Size detection?
– Hail signatures may get diluted by
• Rain mixing with hail
• Far range
Rain/Snow Discrimination
Z
RAIN
< 45 dBZ
SNOW
< 45 dBZ
ZDR
0 to 2 dB
-0.5 to 6 dB
KDP
0 to 0.6 deg/km
-0.6 to 1 deg/km
CC
>0.95
>0.95 (can be less if
wet)
If the variables overlap so much, how can polarimetric radar
discriminate between rain and snow???
Rain/Snow Discrimination: It’s all
in trends with height
• Rain
– Polarimetric signatures (ZDR and KDP) have a direct
dependence on Z
– ZDR and KDP do not typically increase with height
– Almost always a pronounced melting layer above rain
• Snow
– Polarimetric signatures (ZDR and KDP) do not have
dependence on Z
– ZDR and KDP typically increase with height
– Differences between “warm” and “cold” snow
• “Cold” snow has higher polarimetric variables than “warm”
snow
Warm vs. Cold vs. Wet Snow
• Temperature determines this
– < -5oC = “Cold”
– ~+1oC > T > -5oC = “Warm”
– > +1oC = “Wet”
Crystals (plates, columns, needles)
Aggregate Crystals (Dry)
Aggregate Crystals (Wet)
Radar Cross Section
Characteristics
Z/ZDR/CC
Characteristics
High Density
High Concentration
Oblate, Horizontal Orientation
Small size
Z < 35 dBZ
ZDR 0-6 dB
CC > 0.95
Decreasing density
Decreasing Concentration
Less oblate
Larger size
Z increasing
ZDR decreasing
0 > ZDR > 0.5 dB
CC > 0.95
Rapid increase in density
Rapid increase in oblateness
Z increasing but < 45
dBZ
ZDR rapidly increasing
0.50 > CC > 0.9
Surface. Assume temperatures decrease steadily with height
Rain Snow Discrimination
Z
Snow
ZDR
Rain
KDP
CC
One Hour Later…
Z
-SN
KDP
ZDR
CC
Data Quality Improvement
• Ground clutter/Anomalous propagation
– High reflectivity (Z) -- (> 35 dBZ)
– Near zero or slightly negative ZDR
– Noisy, lower correlation coefficient (CC) -- (< 0.90)
• Insects/Biological scatterers
– Low reflectivity (Z) -- (< 35 dBZ)
– Horizontally-oriented with elongated shape: very high
ZDR (> 2 dB up to 6 dB)
– Heterogeneity causes very low correlation coefficients
(< 0.70)
Tornado Detection
• Tornado debris is large (from radar perspective),
irregularly shaped and randomly oriented
– Z > 45 dBZ
– ZDR near 0 dB
– CC very low (< 0.8)
• A good sign that a tornado is already in progress!
– Diagnostic ONLY
– Has only been verified for EF-1 or greater
tornadoes at relatively close ranges
Tornadic Debris Signature (TDS)
Z
ZDR
TDS!
CC
Debris cloud near GM Plant
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