Radar Basics and Estimating Precipitation Jon W. Zeitler Science and Operations Officer National Weather Service Austin/San Antonio Forecast Office Science and Operations Officer National Weather Service Austin/San Antonio Forecast Office

Radar Beam Basics

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. 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. Energy Scattering

Probert-Jones Radar Equation

Simplified Radar Equation

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. 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. Equivalent Reflectivity (Ze)

(Equation 5) Reflectivity (Z) vs. Decibels of Reflrectivity (dBZ) Reflectivity (Z) vs. Decibels of Reflrectivity (dBZ) dBZ = 10log 10 Z

Beam-Filling

Sending vs. Listening

99.843% of the time the WSR-88D is listening for signal returns.

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 WSR- 88D with algorithms. The Doppler Dilemna

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. 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!

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 Too Close!

Storms or Bats?

Strategies to Fix Problems

Drop Size Distribution

Rainfall Rate

R(Z) Relationships (Battan 1973)

BREAK!

Sends and receives horizontal & vertical polarized radiation Image courtesy Terry Schuur What is Dual Polarimetric Radar?

Hydrometeor: ShapeShape OrientationOrientation Dielectric constantDielectric constant Distribution of sizesDistribution of sizes Polarimetric Variables Depend on Several Things

Rainfall Estimation (vast improvement)Rainfall Estimation (vast improvement) Bright Band Detection (vast improvement)Bright Band Detection (vast improvement) Clutter Filtering/Data Quality ImprovementClutter Filtering/Data Quality Improvement (vast improvement) (vast improvement) Rain/Snow Discrimination (vast improvement)Rain/Snow Discrimination (vast improvement) Hail Detection (some improvement)Hail Detection (some improvement) Updraft Location (some improvement)Updraft Location (some improvement) Tornado Detection (some improvement)Tornado Detection (some improvement) Rainfall Estimation (vast improvement)Rainfall Estimation (vast improvement) Bright Band Detection (vast improvement)Bright Band Detection (vast improvement) Clutter Filtering/Data Quality ImprovementClutter Filtering/Data Quality Improvement (vast improvement) (vast improvement) Rain/Snow Discrimination (vast improvement)Rain/Snow Discrimination (vast improvement) Hail Detection (some improvement)Hail Detection (some improvement) Updraft Location (some improvement)Updraft Location (some improvement) Tornado Detection (some improvement)Tornado Detection (some improvement) Applications of Dual Polarization Radar

Backscattering: Z h - reflectivity factor for horizontal polarization Z DR - differential reflectivity |ρ hv (0)| - co-polar correlation coefficient Propagation - forward scattering: Φ DP - differential phase K DP - specific differential phase (range derivative of Φ DP ) Backscattering: Z h - reflectivity factor for horizontal polarization Z DR - differential reflectivity |ρ hv (0)| - co-polar correlation coefficient Propagation - forward scattering: Φ DP - differential phase K DP - specific differential phase (range derivative of Φ DP ) Polarimetric Variables

Shapes of Large Drops in Equilibrium

Differential Reflectivity (Z DR ) Definition: the ratio of the power returns from the horizontal and vertical polarizations Units: decibels (dB)

Simple Z DR Calculation for a Sample of Raindrop Sizes

What does Z DR Mean? Z DR > 0  Horizontally- oriented mean profile Z DR < 0  Vertically-oriented mean profile Z DR ~ 0  Near-spherical mean profile Z DR > 0  Horizontally- oriented mean profile Z DR < 0  Vertically-oriented mean profile Z DR ~ 0  Near-spherical mean profile EhEh EvEv EhEh EvEv EhEh EvEv

Small (Spherical) >> Large (Oblate) Dry >> Wet Dry (Prolate) >>>> Melting (Oblate) Aggregated/Low-Density >> Pristine/Well-Oriented Dry >> Wet GROUND CLUTTER / ANOMALOUS PROPAGATION BIOLOGICAL SCATTERERS DEBRIS CHAFF Differential Reflectivity (Z DR )

1.median liquid drop size 1.median liquid drop size (Z DR ↑,median drop diameter↑) 2.hail shafts 2.hail shafts (Z DR ~ 0dB or negative coincident with high Z h ) large rain drops or liquid- coated ice 3.areas of large rain drops or liquid- coated ice (Z DR ~3-6 dB) 4.convective updrafts 4.convective updrafts (Z DR ~1-5 dB) above 0 o C level 5.tornado debris ball Z DR is a Good Indicator of:

Values are biased towards the larger hydrometeors (D 6 dependence) Tumbling/Random orientation will bias toward 0 Z DR Can be noisy if: -Low / Insufficient sampling (low SNR) - Reduced correlation coefficient (CC) Values are biased towards the larger hydrometeors (D 6 dependence) Tumbling/Random orientation will bias toward 0 Z DR Can be noisy if: -Low / Insufficient sampling (low SNR) - Reduced correlation coefficient (CC) Z DR Limitations (Gotchas)

May 9 th tornadic supercell: Intense Z DR Column 0 o C level in-cloud ~17 kft

ρ hv Affected by: Hydrometeor types, phases, shapes, orientations Presence of large hail 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.

ρ hv Usage Identify hail growth regions in deep moist convection (mixtures of hydrometeors) Reduce ground clutter/AP contamination (ρ hv very low in these areas) Identify giant hail ???

ρ hv Correlation Coefficient (  hv ) Reflectivity (Z h ) SNOW ~ CLUTTER ~ CHAFF ~

Giant Hail, Protuberances, Mie Scattering: min ρ hv ρ hv Minimum…in Theory

Differential Phase Shift (Φ DP ) Definition: the difference in the phase shift between the horizontally and vertically polarized waves Units: degrees ( o )

 DP =  h –  v (  h,  v ≥ 0) [deg] The difference in phase between the horizontally- and vertically-polarized pulses at a given range along the propagation path. - Independent of partial beam blockage, attenuation, absolute radar calibration, system noise Differential Phase Shift  DP

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)

Provides a good estimate of liquid water in a rain/hail mixture Indicates the onset of melting Specific Differential Phase (K DP ): 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  DP, typically calculated in 1-5 km increments along the radial. Specific Differential Phase: K DP

Specific Differential Phase Shift (KDP) *** Non-meteorological values not shown here because they are removed anywhere CC < 0.90 (or 0.85) *** Small >> Large Dry >> Wet Dry (Prolate) >>>> Melting (Oblate) Dry/Aggregated >> Pristine/Well-Oriented Dry >> Wet

K dp 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, “K dp columns” Drops are shed from melting or growing hailstones near the updraft, forming a K dp column To distinguish between snow/rain K dp in wet, heavy snow is almost always larger at a fixed value of Z h 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: KDP Smoothing techinque: 1.< 40 dBZ, KDP computed at each gate from 12 adjacent gates either side (6.25 km) 2.> 40 dBZ, KDP computed at each gate from 4 adjacent gates either side (2.25 km) to preserve heavy cores 1.< 40 dBZ, KDP computed at each gate from 12 adjacent gates either side (6.25 km) 2.> 40 dBZ, KDP computed at each gate from 4 adjacent gates either side (2.25 km) to preserve heavy cores Compare Z and KDP fields at each gate

Marginally Severe Supercell

Beam Height ~ 4600 ft AGL Z Z Z DR ρ HV HCA 5.25” diameter hail 14 May 2003

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) Think Spectrum Width for Hydrometeors TM S ij = An element of the backscatter matrix

Correlation Coefficient Values 0.96 ≤ CC ≤ 1  Small hydrometeor diversity* 0.80 ≤ CC < 0.96  Large hydrometeor diversity* CC < 0.70  Non-hydrometeors present 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) Non- Meteorological Regime Meteorological Regime Overlap Large >> Small Large >> Small Wet >> Dry Wet / Large >>>> Dry / Small Wet / Large >>>> Dry / Small CRYSTALS > Wet >> Dry > Wet >> Dry GROUND CLUTTER / ANOMALOUS PROPAGATION BIOLOGICAL SCATTERERS DEBRIS CHAFF

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 What about the rest? All > 0.97 What about the rest? All > 0.97 Insects Precip

CC Limitations (Gotchas) High error in low signal-to-noise ratios (SNR) If low, errors increase in other dual-pol variables

One hour point measurements: Radar estimates vs. gages R(Z) R(Z, K DP, Z DR ) 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?

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 comparisons to a dense network of rain gauges in C. OK

Rate Designation Table R (mm/hr)ConditionsEcho Classes Not computed Nonmeteorological echo (Ground Clutter or Unknown) is classifiedGC,UK 0Classification is No Echo or BiologicalNE, BI R(Z, Z DR )Light/Moderate Rain is classifiedRA R(Z, Z DR )Heavy Rain or Big Drops are classifiedHR, BD R(K DP )Rain/Hail is classified and echo is below the top of the melting layerRH 0.8*R(Z)Rain/Hail is classified and echo is above the top of the melting layerRH 0.8*R(Z)Graupel is classifiedGR 0.6*R(Z)Wet Snow is classifiedWS R(Z)Dry Snow is classified and echo is in or below the top of the melting layer DS 2.8*R(Z)Dry Snow classified and is echo above the top of the melting layerDS 2.8*R(Z)Ice Crystals are classifiedIC

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

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 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 Hydrometeor Classification Algorithm Challenges

Melting Layer Detection Mixed phase hydrometeors: Easy detection for dual-pol! –Z typically increases –Z DR and K DP definitely increase –Coexistence of ice and water will reduce the correlation coefficient (CC ~ )

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 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 Melting Layer Detection Algorithm Methodology

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 RAINSNOW Z < 45 dBZ Z DR 0 to 2 dB -0.5 to 6 dB K DP 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 (Z DR and K DP ) have a direct dependence on Z –Z DR and K DP do not typically increase with height –Almost always a pronounced melting layer above rain Snow –Polarimetric signatures (Z DR and K DP ) do not have dependence on Z –Z DR and K DP 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 –< -5 o C = “Cold” – ~+1 o C > T > -5 o C = “Warm” –> +1 o C = “Wet” Crystals (plates, columns, needles) Aggregate Crystals (Dry) Aggregate Crystals (Wet) Surface. Assume temperatures decrease steadily with height 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

Rain Snow Discrimination Z Z DR K DP CC Snow Rain

One Hour Later… ZZ DR K DP CC -SN

Data Quality Improvement Ground clutter/Anomalous propagation –High reflectivity (Z) -- (> 35 dBZ) –Near zero or slightly negative Z DR –Noisy, lower correlation coefficient (CC) -- (< 0.90) Insects/Biological scatterers –Low reflectivity (Z) -- (< 35 dBZ) –Horizontally-oriented with elongated shape: very high Z DR (> 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 –Z DR 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) ZZ DR CC TDS!

Debris cloud near GM Plant