Radar Differential Phase Signatures of Ice Orientation for the Prediction of Lightning Initiation and Cessation

1. Photo credit: Gene Blevins Radar Differential Phase Signatures of Ice Orientation for the Prediction of Lightning Initiation and Cessation Space Shuttle Endeavor (STS-127) Lawrence. D. Carey1, Walter. A. Petersen2, and Wiebke Deierling1 1Earth Systems Sciences Center, NSSTC, University of Alabama in Huntsville (UAH), Huntsville, Alabama 2NASA Marshall Space Flight Center, NSSTC, Earth Sciences Office VP-61, Huntsville, Alabama

2. Background • Past research has shown strong evidence for ice crystal orientation signatures in polarimetric radar[differential phase] observations of thunderstorms (e.g., Hendry and McCormick 1976, 1979; Hendry and Antar 1982; Krehbiel et al. 1991, 1992, 1996; Metcalf, 1992, 1995; Caylor and Chandrasekar 1996; Galloway et al. 1997; Scott et al. 2001; Marshall et al. 2009). • Theoretical work by Weinheimer and Few (1987) demonstrated that ice crystals up to 1-2 mm could be vertically aligned by strong vertical electric fields (E-fields) of about 100-200 kV m-1. • Strong motivation for our ongoing work is provided by Krehbiel et al. (1993): “[polarimetric radar] signatures have been found to provide an excellent indicator of the potential for lightning in a storm and we have used them to predict the occurrence of numerous lightning discharges. The [polarimetric] measurements have also been used to detect the initial electrification of storms and to determine when a storm is finished producing lightning.” • Radar differential phase (specific differential phase, Kdp, and its integral dp or PHIDP) is currently measured by many research (e.g., UAH-NASA ARMOR C-band) and operational (e.g., new 45WS CCAFS-KSC Radtec TDR 43‑250 C-band) radars. • Potential for the operational prediction of lightning initiation and cessation, using radar. • Applications for America’s Space Program. Research is funded by NASA MSFC to develop radar tools for improved launch availability at KSC-CCAFS in collaboration with USAF 45 WS.

3. Introduction Ez • Radar differential phase (Kdp, PHIDP) signatures of ice orientation are dependent on • the magnitude of the vertical electric field (E-field), which controls ice orientation angle relative to the horizontal/vertical -> helpful since it provides physical link for predictive capability of lightning potential • ice hydrometeor properties in the radar resolution volume -> can modulate signal in a manner that is unrelated to the E-field and lightning potential…that can be unhelpful. • Radar characteristics -> assumedly, we can control so it should be helpful. • Purpose of this research is to investigate the last 2 of 3 issues above in order to develop better and more robust operational tools for prediction of lightning potential. • Approach: Radar observations and radar models of differential phase (Kdp, PHIDP) and other dual-polarimetric variables routinely available at UAH and CCAFS-KSC (Zh, Zdr). • Focus Today: Radar modeling of ice particle size distribution, ice canting (or orientation) angle, radar elevation angle, radar frequency, ice crystal type, ice aggregate properties, graupel properties and mixture of different ice types (e.g., crystal/aggregates, crystal/graupel).

4. Kdp linearly related to N0 similar to Vivekanandan et al. (1994) Kdp Dependence on Ice Particle Size Distribution (PSD) Properties (N0, D0) • Ice Crystal Type: Hexagonal Plates • PSD: Exponential • N(D)=N0*exp(-3.67*D/D0) • 2×105m-3 cm-1 ≤ N0 ≤ 2×106m-3 cm-1 • 0.03 ≤ D0 ≤ 0.07 cm (Dmax = 0.11 cm) • Shape: Model as Oblate Spheroid • a/b (minor:major): Auer and Veal (1970) • Ice Density: Heymsfield (1972) • Ice Orientation: Vertical (90) • Radar Scattering and Propagation Model • T-matrix for oblate/prolate (e.g., Bringi and Chandrasekar 2001) • Mueller matrix for hydrometeor mixtures, PSD, canting, radar elevation angle etc (Vivekanandan et al. 1991) • C-band (5.5625 GHz, 5.33 cm) Kdp non-linearly related to D0

5. Kdp and Zdr Dependence on Mean Ice Particle Canting Angle • Example: Plate (oblate spheroid), C-band • N0 = 2×106m-3 cm-1 • D0 = 0.07 cm • Lack of mirror symmetry of radar parameters about 45 mean canting angle (e.g., Zdr/Kdp at 0 vs. 90) related to random orientation in direction parallel to radar viewing angle. • Reasonable at low elevation angle since ice would have no preferred orientation in this direction unless there is a strong horizontal field providing a preferred orientation. • Electric Field (E-field) strength, particle size, particle shape, and particle density (among other ice properties) will determine mean canting angle. • Weinheimer and Few (1987) • Complex! Threshold E-field to orient particles “X degrees” is not well known. Hor. Ver. V Kdp and Zdr are function of mean canting angle, which will depend on E-field threshold for each particle type. Critical E-field thresholds for ice particle types are not well known but are O(10-100 kV m-1) for most small ice crystals < 1-2 mm.

6. Kdp and Zdr Dependence on Radar Elevation Angle • Ice Crystal Example: Plate (oblate), C-band • N0 = 2×106m-3 cm-1 • D0 = 0.07 cm • Vertically Oriented (90) • Ice orientation signatures in dual-polarimetric variables are insensitive to radar elevation angle up to about 15 • Decrease in magnitude of ice orientation signatures above 15 is apparent and could have an impact on even qualitative inferences, especially with weak signatures. • Consistent with well known results in radar community (e.g., associated with rain studies). Ice orientation signatures insensitive to changes in radar elevation angle up to 15.

7. Kdp Dependence on Radar Frequency Radar Bands and their Wavelengths () S: 10.71 cm, C: 5.33 cm, X: 3.17 cm, Ku:2.24 cm, Ka: 0.84 cm • Examples: Plate-type (oblate) ice crystal • N0 = 1×106m-3 cm-1 • D0 = 0.03 and 0.07 cm • Vertically Oriented (90) • Rayleigh scattering theory predicts Kdp is linearly proportional to radar frequency (f). Kdp ~ f • Rayleigh: particle is small compared to wavelength, D < 0.1 • Rayleigh is an excellent approximation for ice crystals up to Ka frequency (error < 5%). • ice is optically soft (low density, low dielectric) so some ice particles for D > 0.1  are well approximated by Rayleigh. • Desirable because radar response should be related to actual particle shape, size and orientation and thus E-field. • Larger ice particles like some aggregates, most graupel, and all hail are not well approximated by Rayleigh at Ka (not shown). Further investigation required to assess impact on ice orientation Kdp signatures. Kdp is linearly proportional to radar frequency. All else being equal, higher frequencyradars are better tools for detection of ice orientation signatures in Kdp (signal may often be in the “noise” at S-band/WSR-88D).

8. Zdr is function of crystal type. Kdp and Zdr Dependence on Ice Crystal Type • Ice orientation signatures of vertically oriented plate (oblate), dendrite (oblate) and column (prolate) type ice crystals. • Typical literature values of ice shape (a/b) and density as a function of particle size (Auer and Veal 1970, Heymsfield 1972). • Exponential PSD with same range of N0, D0 as shown earlier. • Results for C-band shown. • Zdr depends on particle type. For range of ice crystal sizes tested, only dendrites show strong relationship between Zdr and Zh (really size, D0). For single particle types, Zdr is independent of N0. • Behavior of Kdp vs. Zh depends moderately on ice crystal type (mostly density difference) but is primarily a strong a function of N0 (concentration) and D0 (size) as shown earlier. Kdp less sensitive to crystal type (plates and columns same, dendrites 15-30% less).

9. Kdp and Zdr Dependence on Ice Aggregate Properties • Ice aggregates (oblate), exponential PSD • N(D)=N0*exp(-3.67*D/D0) • 1×104 m-3 cm-1 ≤ N0 ≤ 1×105 m-3 cm-1 • 0.3 ≤ D0 ≤ 0.7 cm (Dmax = 1.5 cm) • Ice density: Brown and Francis (1995) • Shape: a/b = 0.3 or 0.8 • Orientation: Gaussian distribution of ice particle canting angles. • Mean : Hor. (H, 0) and Vert. (V, 90). • For H-oriented snow not influenced by electric field,  canting angle was set at 5 (slight) or 30 (moderate). • More oblate (a/b=0.3) and less canted (=5)particles have larger signatures. • Kdp and Zdr responses to H- or V-oriented low density aggregates are significantly less than most pristine ice crystals (because of low density). • IF aggregates orient vertically in strong E-field, signature might be weak. • Horizontally oriented aggregates should NOT strongly mask Kdp orientation signatures of ice crystals (see next). Kdp and Zdr orientation signatures of ice aggregates (low density) are small compared to most ice crystal types.

10. Ez Aerodynamics/drag/turbulence dominate Vertical E-field dominates Kdp and Zdr in Mixture of V-oriented Plates and H-oriented Aggregates BACKSCATTER Zdr is a POOR indicator of E-alignment because larger, H-oriented particles dominate PROPAGATION Kdp is a GOOD indicator of E-alignment because smaller, V-oriented particles dominate

11. Kdp/Phidp signatures (bottom row) are above and slightly down wind of convective core. • in low-to-moderate reflectivity (DZ: 20-30 dBZ) (top row) • in “dry snow” as identified by dual-polarimetric particle identification (PD=blue) (top row) • PID algorithms have known deficiency in detecting mixtures of ice…likely ice crystals are there too…negative Kdp might be proof. • OR, could be vertically oriented dry snow by itself. UAH-NASA ARMOR RADAR (C-BAND) EXAMPLE PD DZ Kdp/Phidp signatures – mature phase KDP Phidp ARMOR radar example of negative Kdp (negative Phidp shift) is consistent with electrical alignment of ice-crystals and/or snow into the vertical. 46 degree RHI

12. Kdp and Zdr Dependence on Graupel Properties • Graupel (oblate), exponential PSD, following Bringi et al. (1986) • N(D)=N0*exp(-3.67*D/D0) • 1×104 m-3 cm-1 ≤ N0 ≤ 8×105 m-3 cm4-1 • 0.08 ≤ D0 ≤ 0.32 cm (Dmax = 1.0 cm) • Ice density: 0.3 (low) and 0.6 (moderate) g cm-3 • Shape: a/b = 0.75 • Orientation: Gaussian distribution of ice particle canting angles. • Mean : Hor. (H, 0) and Vert. (V, 90). • NOTE: V-orientation NOT due to E-field !!!! Graupel is typically too big and dense to be aligned by E-field. •  = 45 • Zdr is strongly dependent on density but overall Zdr signature is weak. • Kdp signatures are moderate (N0 effect) and strongly dependent on density. • For larger reflectivity (Zh > 40-45 dBZ), graupel has the potential to mask ice crystal vertical orientation signatures associated with E-field. |Zdr|is small in graupel, regardless of orientation |Kdp| is moderate-to-large for H- and V-oriented graupel at Zh > 40-45 dBZ. Could mask or enhance, respectively, ice crystal orientation signatures associated with E-field.

13. Plates: Vertical E-field dominates Graupel: Aerodynamics, drag, turbulence dominate Ez Kdp of Graupel/Plates Mixture versus Kdp Plates Scenario 1 • PSD and shape same as before • Moderate density : 0.6 g cm-3 • Orientation/canting angle • Scenario 1:Horizontal (Mean 0) • Scenario 2:Vertical (Mean 90) •  = 45 • Graupel orientation is unrelated to strength of E-field (too big, too dense to be affected by E-field). • Masking: Presence of graupel can increase (scenario 1) or decrease (scenario 2) Kdp associated with vertically oriented ice in strong E-field. Scenario 2

14. Kdp/Phidp signatures (bottom row) are in and above convective core. • in moderate-to-high reflectivity (DZ: > 40-45 dBZ) (top row) • in “graupel” as identified by dual-polarimetric particle identification (PD=green) (top row) • as before, PID tends to be dominated by largest particle so crystals are likely present with graupel. • Based on model simulations, it is unclear as to whether these Kdp/Phidp signatures are associated with vertically oriented ice crystals in strong E-field, graupel falling with major axis in vertical or both. • Likely strong E-field is present and phase signature is at least partially associated. UAH-NASA ARMOR RADAR (C-BAND) EXAMPLE PD DZ Kdp/Phidp signatures – mature phase (8 min earlier) KDP Phidp 48 degree RHI

15. Summary of Preliminary Work • Kdp is linearly proportional to radar frequency. All else being equal, higher frequency radars are better tools for detection of ice orientation signatures in Kdp. • Kdp is a function of mean canting angle, which will depend on E-field threshold. • Critical E-field thresholds for ice particle types are not well known but are O(10-100 kV m-1) for most small ice crystals < 1-2 mm. • Kdp linearly and non-linearly related to N0 (concentration) and D0 (size), respectively, of an exponential size distribution of ice particles. • Kdp weakly sensitive to crystal type (plates, columns same; dendrites 15-30% less). • Kdp signatures of aggregates (low density) are relatively small compared to crystals. • Kdp is a good indicator of E-alignment because smaller, V-oriented particles dominate in a mixture of V-oriented crystals and H-oriented aggregates. • |Kdp| is moderate-to-large for H- and V-oriented graupel at Zh > 40-45 dBZ. Since graupel orientation likely NOT connected to E-field, large graupel could mask or enhance, respectively, ice crystal orientation signatures due to E-field in moderate to high dBZ. • E-field threshold for vertical alignment of ice crystals will be related to particle size (D0), shape and density (among other things). Hence, E-field and lightning potential are physically connected to the Kdp alignment signature in dual polarimetric radar. • More work is needed in observations (polarimetric radar, remote E-field strength, and in-situ microphysical and E-field), modeling (radar scattering, cloud microphysics) and theory of particle alignment (follow up to Weinheimer and Few 1987).