6B.6 LINKING OBSERVATIONS OF ZDR AND VERTICAL VELOCITY IN THE -15◦C REGION

DURING STRATIFORM PRECIPITATION

Jonathan M. Vogel∗, Frederic Fabry, and Isztar ZawadzkiDepartment of Atmoshperic and Oceanic Sciences, McGill University, Montreal, QC, Canada

1 INTRODUCTION AND BACKGROUND

Polarimetric radars have been widely used foridentifying different hydrometeor types (e.g. rain,snow, graupel) as well as differentiating betweendifferent growth and transformation mechanisms(e.g. deposition, aggregation, riming, melting)(e.g. Kennedy and Rutledge, 2011; Andric et al.,2013; Bechini et al., 2013; Schneebeli et al., 2013;Schrom et al., 2015; Vogel and Fabry, 2017). Iden-tifying these regions and understanding where theyoccur within clouds can be useful for understandingthe growth of the cloud, distribution and structurewithin the cloud, the formation and growth of differ-ent hydrometeors, and production of precipitation.Together, these can be also be used for improvingmicrophysical constraints within numerical weatherprediction models.

Since stratiform precipitation is generally morespatially homogenous and widespread than con-vective precipitation, it provides more ideal circum-stances for observing these different microphysicalprocesses. Surcel and Zawadzki (2010) initially ob-served the frequent occurrence of a localized veloc-ity minima near the -15◦ region after compiling over300 hours of vertically pointing radar data of strat-iform weather events. Zawadzki (2013), later sug-gested this signature was due to an updraft asso-ciated with the level of nondivergence. Other stud-ies have frequently observed the occurrence of anenhanced ZDR signature near the -15◦C isothermattributing it to dendritic growth (e.g. Kennedy andRutledge, 2011; Andric et al., 2013; Bechini et al.,2013; Schneebeli et al., 2013; Schrom et al., 2015).Schrom et al. (2015) suggested the the signa-tures in this region could be due to the differentialgrowth rates of two modes of crystals. Schrom andKumjian (2016), added further support to the theorysuggesting that, at temperatures colder than -15◦C,

∗Corresponding author address: Jonathan M. Vogel,Atmospheric and Oceanic Sciences, Burnside Hall 805Sherbrooke Street West, Montreal, QC, Canada, H3A0B9, e-mail: jonathan.vogel@mail.mcgill.ca

isometric crystals dominated the signatures; then,in the -15◦C region, smaller crystals grow dentriti-cally and grow faster eventually dominating the sig-natures of ZDR and VD.

In this study, we attempt to add insight to the the-ories of updrafts, crystal habits, and growth regimesin the -15◦C region by combining divergence obser-vations and velocity-azimuth display (VAD) calcula-tions from a scanning S-band radar, vertically point-ing Doppler velocity VD and reflectivity ZX , scan-ning polarimetric reflectivity ZH and differential re-flectivity ZDR, and aircraft particle imagers from theGCPEx campaign.

2 DATA AND METHODOLOGY

2.1 Radar Data Collection

Radars used in this study include the McGill S-band scanning dual-polarization radar located atthe J.S. Marshall Radar Observatory in Ste-Annede Bellevue, Quebec and the vertically pointing X-band Doppler radar (VertiX) located at the McGillCampus in downtown Montreal, Quebec. TheMcGill S-band radar is a 10.4 cm dual-polarizationradar with a beam width of 0.83◦. It completes a fullPPI of 23 elevations from 0.5 to 31.2◦ every 5 min-utes. VertiX is a vertically pointing 3.2 cm X-bandDoppler radar that completes one vertical profile ev-ery 1.5 seconds. Doppler velocity spectra are alsoavailable from VertiX over a 2 minute interval. It islocated at 30 km in range along the 72◦ azimuth ofthe S-band radar.

For the Montreal region, velocity and ZDR signa-tures in the -15◦C region appear to be long livedoften lasting an hour or longer. Since polarimetricobservations as well as VertiX measurements areprone to variability from both dynamical and micro-physical processes on temporal and spatial scaleson the order of 1-15 minutes or kilometers, VertiXand S-band data are averaged over periods of onehour. For this study, 45 one hour periods are usedfrom 2012 and 2013. Additionally, to reduce vari-

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Figure 1: Vertical profiles of VD, ZX , and ZDR for each of the 45 cases in grey and the mean for each in black. Theprofiles are normalized so that the minimum in the velocity reduction is centered at 0 km.

ability and increase the vertical coverage, the polari-metric data is averaged over a region 10◦ in azimuthby 10 km in range. This region is located within 5km of VertiX where ground clutter contamination isat a minimum; however, for data quality, any pixelswith a Z < 0 dBZ, ρHV < 0.90, or a target ID of”ground echo” or ”biological” are removed.

2.2 Velocity-Azimuth Display

While many studies generally assume the verticalair motion in stratiform precipitation is small com-pared to the fall speeds of hydrometeors, verticalmotion is required for moisture transport as well asto achieve supersaturation. Additionally, a localizedupdraft or an abrupt change in updraft could lead tothe perviously documented observations of a sud-den decrease in Doppler velocity and, therefore, hy-drometeor fall speed. Due to the lack of a wind pro-filer and distrust in localized vertical velocities fromthe RAP model, another method is required to as-certain the vertical motion.

If the azimuthal coverage of Doppler velocity from

a scanning radar is sufficient at a given radius, theprofile of horizontal divergence (and, therefore, ver-tical velocity) can be calculated. By assuming theatmosphere is in hydrostatic balance and only ver-tically compressible, taking the vertical derivative ofthe vertical wind in pressure coordinates is equalto the horizontal divergence on a constant pressuresurface (O’Brien, 1970):

∂ω

∂p= −

(∂u

∂x+∂v

∂y

)p

. (1)

At a given radius r, the radar observed ra-dial Doppler velocity Vr measures the air motion(u, v, w) and hydrometeor fall speed Vf :

Vr(r, θ) = [u sin(θ)+v cos(θ)] cos(β)+[w+Vf ] sin(β)(2)

where θ is the azimuthal angle and β is the elevationangle.

Because radial velocity is periodic, a least-squareFourier expansion can be used to represent the

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Figure 2: Vertical profiles of the gradients of VD, ZX , and ZDR for each of the 45 cases in grey and the mean for eachin black. The profiles are normalized so that the minimum in the velocity reduction is centered at 0 km..

VAD:

Vr(r, θ)− Vf sin(β) =A0 +A1 sin(θ) +B1 cos(θ)+

A2 sin(2θ) +B2 cos(2θ).

(3)

The radial doppler velocity from (2) can be rewrittenwith the horizontal wind and its derivatives:

Vr(r, θ)− Vf sin(β) ={r/2(ux + vy)+

[u0 cos(β)] sin(θ)+

[v0 cos(β)] cos(θ)+

r/2(uy − vx) sin(2θ)+r/2(vy − ux) cos(2θ)} cos(β)+w sin(β)

(4)

where ux, vx, uy, and vy are the partial derivativesof the horizontal wind. By comparing (3) and (4),the horizontal divergence δ can be found using the

A0 term from the Fourier expansion (Browning andWexler, 1968):

δ = (ux + vy) =2A0

r cos(β)(5)

From (5), the divergence is sensitive to the ra-dial distance from the radar while the vertical cov-erage is limited by the spacing of the elevation an-gles. The vertical velocity profile can be determinedby assuming boundary conditions of ω = 0 at thesurface and echo top as well as combining (1) and(5). VAD profiles were calculated from radii be-tween 30 and 40 km in range which eliminate mostof the ground clutter contamination, include rangesnear the VertiX location, and ensure adequate ver-tical coverage. Additionally, sensitivity tests haveshown minimal error to divergence estimates whenazimuthal coverage exceeds 90%.

2.3 GCPEx Data

The Global Precipitation Measurement (GPM)Cold-season Precipitation Experiment (GCPEx)

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Figure 3: The normalized greatest ZDR gradient and itscorresponding normalized velocity gradient for each ofthe 45 cases

field campaign took place from January 17 to Febru-rary 29, 2012 near Ontario, Canada. Among theseveral instruments that were involved in the mis-sion, data was used from the University of NorthDakota Cessna Citation aircraft, the University ofMcGill VertiX radar, and the Environment CanadaKing City dual-polarization C-band radar. The verti-cally pointing VertiX Doppler velocity data was usedto find periods of local velocity minima. The Citationaircraft provided in situ measurements of temper-ature, moisture, saturation, number concentration,and particle imagers during vertical spirals. TheKing City radar provided dual-polarimetric volumescans every 10 minutes. When the Citation con-ducted an observation spiral within the 10 km ofthe VertiX, the data were combined with the nearestpixel of C-band data to determine what crystal habitor collection of crystals contributed to the signaturesobserved both on VertiX and on dual-polarization.

3 OBSERVATIONS

3.1 Average Profiles from the Montreal Region

Data was collected from 45 one hour periodsfrom the McGill VertiX and scanning S-band radars.To focus on the velocity reduction signature, allcases have been normalized in height so that thevelocity minima occurs at 0 km (Figure 1). The ve-locity reduction occurs over a depth of about 1 kmand is quite consistent from case-to-case. The peakZDR maxima occurs at the same height as the ve-locity minima; however, it occurs over a broader re-gion. ZDR shows more variability from case-to-casewith some having an abrupt peak while others showa gradual transition from increasing to decreasing.

0.0 0.5 1.0 1.5Velocity [m/s]

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Figure 4: 45 case mean VertiX observed VD in black,velocity profile with no reduction in magenta, and the re-sulting updraft required in red.

Figure 2 shows that the gradients, relative to to-wards the surface, for both velocity and ZDR occuralmost simultaneously, while the gradient of Z be-gins shortly after. The relationship between the nor-malized greatest ZDR gradient and its correspond-ing normalized velocity gradient is shown in Fig-ure 3. These values are take from the 0-1 km nor-malized heights. It depicts a clear trend of increas-ing ZDR growth corresponding with a greater ve-locity reduction. To obtain the normalized velocityand ZDR gradients, the normalization factor is cal-culated from the mean of velocity and ZDR gradi-ents in the 1-2 km normalized height region. Thisnormalization factor is then subtracted from the en-tire profile. This is necessary to remove any back-ground growth rates in both velocity and ZDR andobserve the absolute change immediately abovethe 0 km normalized height.

3.2 GCPEx Cases

Combining the vertically pointing VertiX data forvelocity and Z, the King City C-band radar for ZDR,and in situ particle imager observations from the Ci-tation aircraft, a three (CHECK THIS) cases couldbe compiled of observations during a spiral by theCitation. One example is presented here for brevity,which represents the typical observations from allthe cases (Figure 7). At temperatures cooler than-15◦C, generally around -20◦C, VertiX shows Z lessthan 10 dBZ and VD up to 1.0 m s−1. ZDR valuesfrom the C-band radar are generally around 0.50dB. The particle imager shows a collection of bul-lets, needles, and rosettes; generally, smaller crys-tals with larger area ratio values and lower drag.

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orm

aliz

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eigh

t [km

]

Figure 5: 45 case mean divergence (in black) calculatedfrom VAD observations +/- 1 standard deviation (in blue).Grey lines show the divergence profiles for each of the 45cases. The red line is the expected divergence signaturefor updraft (red line) shown in Figure 4.

Area ratio is defined as the area an ice crystal takesup over a circumscribed disk, so a value of 1 meansthe crystal fills the whole disk while a value closerto 0 generally means a more porous crystal. Atlower altitudes, the temperature is closer to -15◦Cand vertiX shows an increase in Z to about 10 dBZand a decrease in VD to about 0.8 m s−1 coincid-ing with an increase in ZDR to about 0.75 to 0.8dB. At this time, the Citation particle imager ob-serves larger and more complex crystals: crystalswith dendritic-like appendages, capped columns,and some dendrites, all of which have lower arearatio values and more drag than what was observedabove. Then, as temperatures rise about -15◦C,Z increases above 10 dBZ and VD increases backto 1.0 m s−1 coinciding with ZDR decreasing be-low 0.75 dB. The Citation particle image shows thepresence of even larger crystals with varying com-plexity with a majority being aggregates of what wasobserved above with area ratios also higher thanwhat was observed around -15◦C.

4 DISCUSSION

4.1 Localized Updraft

Zawadzki (2013), suggested that the suddenslowdown in velocity observed by all crystals in thevelocity spectra requires a localized updraft to bepresent. For the 45 one hour periods collected,the mean vertical velocity profile was determined bynormalizing the height for each case to the heightof the velocity minima (black line, Figure 4). As-

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Figure 6: Example velocity spectra taken from a 2 minutesample during one of the 45 cases. The abrupt velocityslow down is apparent around 7 km which is also -15◦Cfor this case.

suming an updraft is the cause of this velocity re-duction, the resulting updraft is shown in red onFigure 4. By continuity, for an updraft, or changein updraft speed, to be present of this magnitudea corresponding convergence/divergence signatureshould discernible from VAD observations. By (1),the expected divergence profile can be calculated(red line, Figure 5.

Figure 5 shows that the expected divergence sig-nature (in red) occurs over a vertical depth of about1 km. In Montreal, the velocity reduction often oc-curs near a height of 5 km. Near this altitude, aVAD profile at a single radius could miss such a nar-row signature due to the lack of vertical coverage athigher elevations. However, by combining VAD pro-files at several successive ranges the lack of verticalcoverage is mitigated. Figure 5 shows that on av-erage the divergence profile (in black) indicates abroad updraft spanning several kilometers. While afew cases could have a localized updraft that resultsin uniform slowing of falling crystals, on average itis unlikely to be the source of this common veloc-ity reduction signature. However, the VAD profilesdo show the presence, on average, of a broad up-draft which provides the necessary ingredients forenhanced depositional growth in this region.

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Figure 7: GCPEx data during an aircraft spiral from 16z on Februrary 18, 2012. On the right, from top to bottom, is Z(VertiX in black, King City C-band in blue), VertiX VD, King City ZDR, and temperature observations form the Citationaircraft ambient temperature probe. A, B, C, and D on the left correspond to Citation 2D-C particle images with a 1.6mm buffer width during the corresponding times shown on the right.

4.2 Two Crystal Habits

Schrom et al. (2015) and Schrom and Kumjian(2016), observed positive gradients in Z and ZDR

and a negative gradient in V , all relative to de-creasing height, and attributed them to differentialgrowth between two crystals habits. Aloft, fasterfalling more isometric crystals dominate the reflec-tivity weighted products. As they enter the -15◦Cregion, the smaller crystals grow faster than thelarger preexisting ones. Based on the Bailey andHallett (2009) habit diagram, they will grow dendrit-ically which will fall slower and contribute to a posi-tive ZDR signature. As they grow large enough theywill dominate the reflectivity weighted products pro-ducing the observed signatures.

Figure 6 shows a typical velocity spectra ob-served by VertiX during the 45 on hour periods. Thelack of a bimodal spectra within the -15◦C regionwhere the velocity slows suggests the lack of twodifferent habits of crystals or the preexisting crys-

tals are now falling at the same velocity as anynew crystals that are produced. While it is possiblefor an occasional bimodal spectra to be observedwithin the -15◦C region, the lack of it regularly oc-curring while other signatures of present suggests itis unlike to be the common source of the signature.

4.3 Microphysical Growth

From the 45 one hour cases, Figures 1, 2, and 3show support of a relationship between velocity de-creasing while Z and ZDR are increasing. Citationaircraft particle images from the GCPEx campaignshow a distinct change in crystal type when movingfrom temperatures colder than -15◦C, to the -15◦Cregion, to temperatures warmer than -15◦C coincid-ing with these radar observations.. It has been pre-viously theorized that ZDR signatures in the -15◦Cregion are likely caused by dendrites based on theBailey and Hallett (2009) habit diagram. Observa-tions from the Citation aircraft support this theory

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as dendritic-like growth was observed in this region(Figure 7).

Dendritic growth can be supported by all previ-ously discussed observations. VAD observationsshow a broad updraft that, while is too broad tosuddenly slow all crystals at this altitude, would pro-vide the necessary moisture to reach supersatura-tion with respect to ice. Crystals that grow dendriti-cally would have higher drag than those seen abovewhich would, at least initially, lead to a reduction invelocity. Dendrites and dendritic growth would in-crease Z while also leading to higher ZDR valuesthan that of the ice crystals observed above. Oncethe ice crystals grow large enough or begin to ag-gregate the velocity will once again continue to in-crease. Once aggregation dominates the growth,ZDR values will also begin to decrease. These tran-sitions between different ice crystal growth habitswere observed during vertical spirals by the Citationaircraft during the GCPEx campaign.

5 SUMMARY AND CONCLUSIONS

By combining observations from a verticallypointing Doppler X-band radar, scanning polari-metric S-band radar, scanning polarimetric C-bandradar, and in situ data from a particle imager on aCitation aircraft new evidence has been provided toseveral theories to what is occurring in the -15◦C re-gion in stratiform precipitation. Divergence and ver-tical velocity calculated from velocity-azimuth dis-play data from the S-band radar show the pres-ence of an updraft that provides moisture for de-positional growth. The observed updraft and diver-gence signatures are much broader than expectedfor a localized updraft to be uniformly slowing allfalling ice crystals. The lack of a regular appear-ance of bimodal spectra in the -15◦C region sug-gests that two habits of crystals growing at differ-ent rates leading to different habits dominating thereflectivity weighted products is unlikely to producethe observed VD and ZDR observations. Finally, ve-locity reduction coincident with Z and ZDR suggestenhanced microphysical growth is producing thesesignatures. In situ particle images above, in, andbelow this region shows evidence distinct changesin dominant crystal growth habits further supportingthe microphysical growth theory.

ACKNOWLEDGEMENTS

This project was undertaken with the financialsupport of the Government of Canada provided

through the Department of Environment and Cli-mate Change and the Natural Sciences and Engi-neering Research Council of Canada. We wouldlike to thank Alamelu Kilambi for help accessing theMcGill radar data and Bernat Puigdomenech Tre-serras for use of the Profilers application for VertiXand S-band data.

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