RADAR OBSERVATIONS OF DENDRITIC GROWTH ZONES IN …

The Pennsylvania State University

The Graduate School

College of Earth and Mineral Sciences

RADAR OBSERVATIONS OF DENDRITIC GROWTH ZONES

IN COLORADO WINTER STORMS

A Thesis in

Meteorology

by

Robert S. Schrom

© 2015 Robert S. Schrom

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Master of Science

May 2015

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The thesis of Robert S. Schrom was reviewed and approved* by the following:

Matthew R. Kumjian

Assistant Professor of Meteorology

Thesis Advisor

Eugene E. Clothiaux

Professor of Meteorology

Johannes Verlinde

Professor of Meteorology

Associate Head, Graduate Program in Meteorology

*Signatures are on file in the Graduate School.

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ABSTRACT

X-band polarimetric radar observations of winter storms in northeastern Colorado on 20-21

February, 9 March, and 9 April 2013 are examined. These observations were taken by the Colorado

State University-University of Chicago-Illinois State Water Survey (CSU-CHILL) radar during

the Front Range Orographic Storms (FROST) project. The polarization radar moments of

reflectivity factor at horizontal polarization (ZH), differential reflectivity (ZDR), and specific

differential phase (KDP) exhibit a range of signatures at different times near the -15° C temperature

level favored for dendritic ice crystal growth. Generally, KDP is enhanced in dendritic ice crystal

growth region with ZDR decreasing and ZH increasing towards the ground, suggestive of

aggregation (or riming). The largest ZDR values (~3.5-5.5 dB) are found during periods of

significant low-level upslope flow. Convective features observed when the upslope flow was

weaker have the highest KDP (> 1.5 deg km-1) and ZH (> 20 dBz) values.

Vertically-pointing observations of radial velocity (VR) taken by NCAR’s X-band polarimetric

radar (NCAR-XPOL) are analyzed along with the polarimetric observations from the CSU-CHILL

radar. The magnitude of VR is found to decrease towards the ground near the -15 °C temperature

level, indicating a decrease in the mean particle fall speed. ZH increases towards the ground in this

region, indicating an increase in the mean particle size. These signatures are found to be consistent

with the growth and subsequent aggregation of dendrites.

Electromagnetic scattering calculations using the Generalized Multi-particle Mie (GMM)

method are used to determine whether these radar signatures are consistent with dendrites. Particle

size distributions (PSDs) are retrieved for a variety of cases using these scattering calculations and

the corresponding radar observations. The PSDs are found to be reasonably consistent with

previous observations of ice particle size distributions. Observations of enhanced KDP, decreasing

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ZDR, and increasing ZH towards the ground may therefore be useful in identifying regions of rapidly

collecting dendrites and thus increased surface snowfall rates.

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TABLE OF CONTENTS

List of Tables……………………………………………………………………………. vi

List of Figures…………………………………………………………………………... vii

Preface………………………………………………………………………………….. xii

Acknowledgements…………………………………………………………………..... xiii

Chapter 1. INTRODUCTION…………………………………………………………..... 1

1.1 Dendritic Ice Crystal Growth and Aggregation……………………………… 1

1.2 Polarimetric Weather Radar Background.………………………………….... 3

1.3 Previous Polarimetric Observations of Pristine Ice Crystals............................ 7

Chapter 2. DATA AND METHODS…………………………………………………… 10

Chapter 3. OVERVIEW OF WINTER STORM CASES………………………………. 13

Chapter 4. RADAR SIGNATURES OF DENDRITIC GROWTH…………………….. 23

Chapter 5. VERTICAL PROFILES OF RADAR OBSERVATIONS…………………. 33

5.1 Signatures of Riming, Dendritic Growth and Aggregation……..………….. 33

5.2 Radar Observations with Temperature………………………..……………. 36

Chapter 6. ELECTROMAGNETIC SCATTERING CALCULATIONS………….…... 44

6.1 Description and Monodisperse Distribution Calculations…………….…..... 44

6.2 Ice PSD retrieval with Mixtures of Aggregates…………………………...... 47

Chapter 7. DISCUSSION……………………………………………………………..... 61

Chapter 8. CONCLUSIONS…………………………………………………………..... 72

Appendix A: ALTERNATIVE KDP ESTIMATION PROCEDURE………………....... 75

References……………………………………………………………………………..... 78

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LIST OF TABLES

Table 6.1 Description of the plates and dendrites from the database shown in Botta (2013). Adapted

from Lu et al. (2014)…………………………………………………………………………...... 53

Table 6.2. Exponential ice PSDs determined from the radar observations listed in columns 2, 5 and

6. An aggregate ZDR of 0.3 dB and σ = 15° are assumed for these calculations………………… 53

Table 7.1. Percentage changes in N0 and λ with respect to the values shown in table 3, for 20%

perturbations in ZDR and KDP……………………………………………………………………. 67

Table 7.2. Percentage changes in N0 and λ with respect to the values shown in table 3, for aggregate

ZDR values of 0.0 and 0.6 dB…………………………………………………………………….. 68

Table 7.3. Percentage changes in N0 and λ with respect to the values shown in table 3, for crystal

types of p1.0 and d0.5. No modification of crystal type was imposed on the 9 April case…...… 68

Table 7.4. Gamma ice PSDs determined from the radar observations listed in columns 2, 5 and 6.

An aggregate ZDR of 0.3 dB and σ = 15° are assumed for these calculations…………………… 69

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LIST OF FIGURES

Figure 2.1. Terrain contours of the northern Colorado region with labels of the locations

mentioned in the text……………………………………………………………………………. 12

Figure 3.1. Plots of 500-hPa height (solid contours), 750-hPa wind and 600-hPa temperature

(dashed color contours with -10 and -15 °C indicated by red and purple, respectively. These

images correspond to a) 20 February 2013 at 21 UTC, b) 21 February 2013 at 12 UTC, c) 9

March 2013 at 12 UTC, d) 9 March 2013 at 18 UTC, e) 9 April 2013 at 09 UTC and f) 9 April

2013 at 18 UTC…………………………………………………………………………………. 16

Figure 3.2. Sounding plots taken at the MFS for a) 21 February 2013 at 00:17 UTC, b) 9 March

2013 at 13:19 UTC and c) 9 April 2013 at 08:20 UTC. Temperature and dew point values are

plotted as black and blue lines, respectively. The wind barbs represent the wind speed in knots,

with the full-length barbs, half-length barbs, and flags corresponding to 5-, 10-, and 50-knot wind

speeds each, respectively……………………………………………………………………....... 17

Figure 3.3. RHI scan taken at 00:58 UTC on 21 February 2013 at an azimuth angle of 181.8° for

a) reflectivity factor at horizontal polarization (ZH), b) differential reflectivity (ZDR), c) radial

velocity (VR), and d) specific differential phase (KDP)…………………………………………... 18

Figure 3.4. Figure 4. RHI scan taken at 17:22 UTC on 9 March 2013 at an azimuth angle of 181.7°

for a) ZH, b) ZDR, c) VR and d) KDP……………………………………………………………… 19

Figure 3.5. RHI scan taken at 12:49 UTC on 9 March 2013 at an azimuth angle of 214.4° for a)

ZH, b) ZDR, c) VR and d) KDP……………………………………………………………………. 20

Figure 3.6. Figure 6. PPI scan taken at 20:44 UTC on 9 March 2013 at an elevation angle of 2.8°

for a) ZH, b) ZDR, c) VR and d) KDP. The rings indicate the range at which the beam height is at -

10, -15 and -18 °C, in order of increasing range. These temperature levels are derived from the

00 UTC sounding taken at DNR on 10 March 2013…………………………………………… 21

Figure 3.7. RHI scan taken at 05:10 UTC on 9 April 2013 at an azimuth angle of 235.8° for a) ZH,

b) ZDR, c) VR and d) KDP…………………………………………………………………………. 22

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Figure 4.1. Frequency diagrams corresponding to the 12:49 UTC RHI taken on 9 March at an

azimuth angle of 214.4°. The data used in these diagrams were extracted from between 49 and 56

km range of the radar. The black line indicates the median value of the particular radar moment at

each height. Analyses are shown here for a) ZDR, b) KDP and c) ZH. The temperature contours

(black dashed lines) are based on the 13:19 UTC sounding taken on 9 March 2013 at the

MFS……………………………………………………………………………………………... 27





(black dashed lines) are based on the 00 UTC sounding taken on 10 March 2013 at DNR…...... 28


ZH, b) ZDR, c) VR and d) KDP…………………………………………………………………….. 29


b) ZDR, c) VR and d) KDP……………………………………………………………………......... 30

Figure 4.5. Frequency diagrams corresponding to the 19:40 UTC RHI taken on 9 April at an




(black dashed lines) are based on the 00 UTC sounding taken on 10 April 2013 at DNR…….... 31

Figure 4.6. Analysis of frequency for the data points contained within bins of ZH and ZDR. These

data are derived from the 19:40 UTC RHI taken on 9 April at an azimuth angle of 181.7° (Fig.

4.4). Only the radar observations between 0 km and 60 km were used in these diagrams.......... 32

Figure 5.1 Time-height profiles of a) ZH, b) ZDR, c) KDP, d) the downward-relative gradient of ZH,

e) the downward-relative gradient of ZDR, and f) the downward-relative gradient of KDP. These

data are based on the CHILL RHI scans along the 220.7° azimuth on 9 March from 10:53 to 21:59

UTC. The yellow dashed contour indicates the height of the -15 °C isotherm while the upper and

lower black dashed contours indicate the -20 °C and -10 °C isotherms, respectively….………. 39

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Figure 5.2 Time-height profiles of a) ZH, b) VR, c) the downward-relative gradient of ZH, d) the

downward-relative gradient of VR. These data are based on the XPOL vertically-pointing scans

taken at the MFS on 9 March from 10:53 to 21:59 UTC. The yellow dashed contour indicates the

height of the -15 °C isotherm while the upper and lower black dashed contours indicate the -20 °C

and -10 °C isotherms, respectively…………………...…………………………………………. 40



data are based on the CHILL RHI scans along the 220.7° azimuth on 20-21 February from

approximately 22:40 to 02:40 UTC. The yellow dashed contour indicates the height of the -15 °C

isotherm while the upper and lower black dashed contours indicate the -20 °C and -10 °C

isotherms, respectively………………………………………………………...………………... 41



taken at the MFS on 20-21 February from approximately 22:20 to 02:20 UTC. The yellow dashed

contour indicates the height of the -15 °C isotherm while the upper and lower black dashed

contours indicate the -20 °C and -10 °C isotherms, respectively………………………………... 42

Figure 5.5 Time-averaged profiles of a) downward-relative |VR| gradient, b) downward-relative ZH

gradient, and c) downward-relative ZDR gradient for 20-21 February (solid line) and 9 March

(dashed line). The time-height profiles use to create the time-averaged profiles shown here

correspond to figures 5.1 and 5.2 for the 20-21 February profiles and figures 5.3 and 5.4 for the 9

March profiles…………………………………………………………………………………... 43

Figure 6.1. Scattering calculations for monodisperse populations of a) dendrites with one half the

reference thickness, b) dendrites of the reference thickness and c) plates twice the reference

thickness based on the empirical relationships found in Auer and Veal (1970). The ZH values for

all data points are 3 dBz. The numbers labeled to the right of the data indicate the maximum

dimension (in mm) and number concentration (in m-3) for the size class of ice particles,

respectively. The color of the points differentiate the crystals sizes for which the scattering

calculations are performed. The size of the markers indicates the canting angle distribution width

(σ) with the largest markers equal to 20° and the smallest markers equal to 1°………………… 54

Figure 6.2. Plot of ZHI given observations of ZH

T and ZDRT, a value of ZDR

I of 5.8 dB and a ZDRA

value of 0.3 dB………………………………………………………………………………....... 55

Figure 6.3. Schematic depicting the iterative process by which a PSD is retrieved from a set of

radar observations. The orange-colored boxes indicate the quantity is observed by the radar, the

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blue-colored boxes indicate the quantity is derived from the radar observations and scattering

calculations and the green-colored box indicates an assumed quantity…………………………. 56

Figure 6.4. Contours of KDPI (blue) and the ZH

I contribution from ice (red) as a function of the

slope and intercept parameters for PSDs of exponential form. ZHI is contoured every 2 dBz from

0 to 20 dBz………………………………………………………………………………………. 57

Figure 6.5. Plot of the number concentration per size (maroon), marginal contribution to Zh

(orange) and marginal contribution to KDP (blue) corresponding to the exponential PSD with N0 =

1.84x105 m3 mm-1 and λ= 3.29 mm-1. Ice particles to the left of the red dashed line are of type p1.0

and of type d1.0 to the right…………………………………………………………………........ 58



5.91x104 m3 mm-1 and λ= 1.87 mm-1. Ice particles to the left of the red dashed line are of type p1.0

and of type d1.0 to the right…………………………………………………………………….... 59



3.85x105 m3 mm-1 and λ= 7.13 mm-1. The ice particles used here are all of type p2.0………….. 60

Figure 7.1. Number concentration per unit size as a function of maximum dimension based several

observational probe studies. The orange curve corresponds to the ice particle observations taken

at temperatures between -10 and -20 °C. From Heymsfield et al. (2013). The dots depict the values

one standard deviation above the mean normalized concentrations at each temperature range and

diameter…………………………………………………………………………………………. 70

Figure 7.2. Plots of the number concentration per size (maroon), marginal contribution to Zh

(orange) and marginal contribution to KDP (blue) for a) particles of type p2.0 and d1.0 and b) type

p2.0 and d0.5. The maroon dashed lines shows the bulk PSD observations adapted from the

Heymsfield et al. (2013) study (Fig. 7.1)…………………………………………………........... 71

Figure A1. Frequency distributions with height of KDP calculated using the a) WC09 estimation

procedure and b) the alternate estimation procedure described in appendix A (identical to Fig.

4.5b). These distributions correspond to the RHI taken at 19:40 UTC on 9 April at an azimuth

angle of 181.7°. These data have been extracted at ranges between 20 and 30 km. The black dashed

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lines indicate the temperature levels derived from the 00 UTC sounding from DNR on 10

April…………………………………………………………………………………………….. 77

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PREFACE

This thesis contains significant elements from an article of which I am first author, and has

been preliminarily accepted pending major revisions in the Journal of Applied Meteorology and

Climatology. Matt Kumjian and Yinghui Lu are the two listed co-authors of this paper. I

contributed the majority of the elements contained in the Abstract, Chapters 1-5, Chapters 7-8 and

Appendix A. Yinghui Lu provided the scattering calculations appearing in Chapter 6.

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ACKNOWLEDGEMENTS

I would like to thank Patrick C. Kennedy, Steve Rutledge, and Francesc Junyent (CSU) for

help coordinating, collecting, and processing the CSU-CHILL data used in this study. I thank my

advisor Matt Kumjian, thesis committee members Hans Verlinde and Eugene Clothiaux, and

Kultegin Aydin and Jerry Harrington for their insights regarding this work.

I thank Matt Kumjian and Yinghui Lu for their work as co-authors on the paper mentioned

in the preface. Funding for this work (Robert S. Schrom and Matt Kumjian) comes from NSF grant

AGS-1143948. Yinghui Lu is funded through NSF grant AGS-1228180. I acknowledge the

American Meteorological Society as the sole copyright holder of the article comprising a portion

of this thesis.

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CHAPTER 1. INTRODUCTION

Winter storms often have severe impacts on society, both economically and through increased

risks to life and property. However, accurate short-term forecasting of these events remains a

challenge. One of the greatest areas of uncertainty in these forecasts comes from a poor

understanding of the microphysical processes that contribute to the development of heavy snow.

Part of this lack of understanding is a result of the limited observations of ice particles within

winter storms. Several recent studies have attempted to overcome the limited in situ measurements

by examining the polarimetric radar signatures found in the dendritic growth zones of these storms

(e.g. Kennedy and Rutledge 2011; Andrić et al. 2013; Bechini et al. 2013). However, these studies

are themselves limited due to the narrow range of cases explored and a lack of correspondence

between the radar observations and scattering model simulations. Therefore, the need to explore

the variability of the radar signatures and the scattering of ice particles within dendritic growth

zones motivates this study.

1.1 Dendritic Ice Crystal Growth and Aggregation

The processes by which ice particles increase mass are vapor depositional growth, collection

of ice particles, and collection of supercooled water. Snow growth through aggregation is enhanced

when dendritic ice crystals are present. Dendrites are favored to grow in temperatures near -15 °C

and ice supersaturations above 0.15 (e.g., Bailey and Hallett 2009). Aggregates that form rapidly

through the collection of dendrites can increase the snowfall accumulation rate (Lamb and

Verlinde 2011) and decrease visibility near the ground (Rasmussen et al. 1999). Thus, from an

operational perspective, vapor depositional growth of dendrites and aggregation are important

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microphysical processes to identify observationally, improving near-term forecasts of winter

storms.

The growth of ice crystals by vapor deposition is important in the initial development of the

ice particle population within a cloud. These crystals first appear as ice nuclei that accumulate

vapor mass in an environment supersaturated with respect to ice (Pruppacher and Klett 1997, pg.

547). Depending on the temperature of the environment, water vapor will attach to the ice lattice

of a particle preferentially along either the basal or prism faces of the crystal (Lamb and Scott

1972). Dimensions along the basal and prism faces of a hexagonal ice crystal can be defined using

two orthogonal axes: the c-axis, normal to the two hexagonal basal faces, and the a-axis, normal

to one of the six rectangular prism faces. The aspect ratio of an ice crystal can thus be defined as

the ratio of the c- and a-axes; aspect ratios are less than one for plate-like ice crystals. When

temperatures are around -15 °C, the prism faces experience the quickest growth, leading to the

formation of oblate crystals (Chen and Lamb 1994). If these particles continue to grow in

temperatures where the prism faces grow fastest, the gradient in water vapor along these faces

increases with decreasing aspect ratio (Marshall and Langleben 1954). This increased vapor

gradient increases the growth rate of the particle along the prism faces, further decreasing the

aspect ratio.

Once ice crystals are sufficiently large, they begin to collect each other. This mass growth by

collection of ice particles is known as aggregation. One factor determining the aggregation rate is

the relative fall speeds of the faster-falling particles with respect to slower-falling ice crystals to

be collected. The larger their differences in fall speed, the larger the effective volumes that are

swept out by the collecting particles over a given time. These effective volumes also depend on

the cross-sectional areas of the particles.

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Fall speeds of ice are dependent on crystal habit. Laboratory and theoretical studies (e.g.,

Harrington et al. 2013) show a minimum in fall speed for ice crystals growing in temperatures near

-15 °C. These slower fall speeds result from the large cross-sectional area to mass ratio of the low

aspect ratio crystals that form under these conditions. Therefore, collection of these dendritic ice

crystals by snow aggregates will be enhanced due to the increased differential in fall speeds

between the dendrites and snow aggregates.

Another important factor influencing the rate of aggregation is the collection efficiency. This

collection efficiency depends on the properties of both particles interacting during a discrete

collection event. The branched structure found in dendrites enhances the collection efficiency due

to the increased effective roughness of the particles. Connelly et al. (2012) found a maximum in

the collection efficiency at -15 °C by comparing laboratory-grown ice crystals with model

simulations.

1.2 Polarimetric Weather Radar Background

Dual-polarization radar provides information related to the orientation, shape, and diversity of

the sampled hydrometeors. The National Weather Service array of WSR-88D radars has recently

been upgraded to dual-polarization, allowing for this valuable information to be used operationally

(e.g., Doviak and Zrnić 1993; Zrnić and Ryzhkov 1999; Bringi and Chandrasekar 2001; Ryzhkov

et al. 2005a; Kumjian 2013a,b,c and references therein). Thus, information about the microphysics

of precipitation provided by these instruments can be used by weather forecasters operationally.

The scattering properties of hydrometeors allow for the orientation, shape, and diversity

information of the particles to be retrieved from polarimetric radar. As an electromagnetic wave

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interacts with a particle, radiation will be scattered in a way that depends on the incident electric

field and the properties of the particle. These properties include the size of the particle relative to

the wavelength of the radiation (electromagnetic size), and the particle’s density, phase

composition, shape, and orientation. For un-melted ice particles, the effective density of the

particle determines the particle’s effective dielectric constant, ε at a particular wavelength. This

effective dielectric constant is typically modeled as a mixture of ice and air (e.g. Maxwell Garnett

1904), with low density particles having a real part of ε that is small. Therefore, solid ice particles,

such as plate crystals, will have greater values of ε than low-density snow aggregates.

The information of most interest in radar applications is the electromagnetic radiation

backscattered to the antenna at an angle 180° from the propagation direction of the transmitted

radar beam. This backscattered radiation can be expressed as (Bringi and Chandrasekar 2001):

[𝐸ℎ

𝑠

𝐸𝑣𝑠] =

𝑒−𝑗𝑘0𝑟

𝑟[𝑆ℎℎ

𝜋 𝑆𝒉𝒗𝝅

𝑆𝒗𝒉𝝅 𝑆𝒗𝒗

𝝅] [𝐸ℎ

𝑖

𝐸𝑣𝑖], (1.1)

where Sklπ

are the elements of the backscattering amplitude matrix (S) at the incident polarization,

“l”, and scattered polarization, “k”, r is the distance from the radar, and Eh,vs,i is the electric field

component with the subscript denoting the polarization and with the superscript “s” denoting

scattered and “i” denoting incident. Equation (1.1) shows that S transforms the incident

electromagnetic wave to the backscattered electromagnetic wave. S can be estimated using

numerical techniques such as the T-matrix (e.g., Waterman 1971; Mishchenko 2000) or the

Generalized Multi-particle Mie (GMM; Xu 1995, Xu and Gustafson 2001) method.

To better understand the effects of the aspect ratio on the scattering properties of ice

particles, the Rayleigh approximation is used. In this approximation, the incident electric field is

5

assumed to be constant over the particle, with the scattered electric field represented by a dipole

dependent on the particle’s polarizability (van de Hulst 1981). The polarizability can be found

analytically if the particle is modeled as a spheroid. For horizontally oriented spheroids, the cross-

polar elements (Shv and Svh) of the amplitude scattering matrix are equal to zero, further simplifying

the problem. Radar reflectivity factor at horizontal and vertical polarization (Zh,v) for a single

particle is defined as (Doviak and Zrnić 1993):

𝑍ℎ,𝑣 =4𝜆4

𝜋4|𝐾𝑤|2 |𝑆ℎℎ,𝑣𝑣𝜋|

2, (1.2)

where λ is the wavelength and Kw is the dielectric factor of liquid water. In the Rayleigh

approximation, Zh,v is proportional to the equivalent volume diameter of the particle to the sixth

power. The differential reflectivity (Zdr) is related to the ratio of the co-polar elements of S by

(Doviak and Zrnić 1993)

𝑍𝑑𝑟 =|𝑆ℎℎ

𝜋|2

|𝑆𝑣𝑣𝜋|2 . (1.3)

Oblate spheroids will have larger |𝑆ℎℎ| components than |𝑆𝑣𝑣| components and thus positive ZDR,

where ZDR = 10log10(Zdr). ZDR will therefore increase with decreasing aspect ratio.

To retrieve the bulk polarimetric moments defined in (1.2) and (1.3) for a population of

particles, each equation must be integrated over a distribution of sizes and orientations.

Hydrometeors, however, modulate the electromagnetic wave as it propagates from the radar to a

particular sampling volume and back. Both the phase and amplitude of the electromagnetic wave

change as it propagates through the distributed medium of hydrometeors. Given the presence of

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non-spherical hydrometeors, there will be a differential phase shift between the horizontally and

vertically polarized wave components. This differential phase shift (ΦDP) will accumulate through

the entire propagation path of the transmitted signal. To better represent the contribution to ΦDP

from hydrometeors at a particular range, specific differential phase (KDP) is defined as one-half

the range derivative of ΦDP. Propagation effects are defined using the forward scattering

amplitudes of the particles. In the Rayleigh approximation, the forward scattering amplitudes,

𝑆ℎℎ,𝑣𝑣0, are equivalent to 𝑆ℎℎ,𝑣𝑣

𝜋 (Van de Hulst 1981). KDP for a single particle is defined as

(Bringi and Chandrasekar 2001)

𝐾𝐷𝑃 = 180𝜆

𝜋𝑅𝑒[𝑆ℎℎ

𝜋 − 𝑆𝑣𝑣𝜋]. (1.4)

As shown by equation (1.4), oblate spheroids satisfying the Rayleigh approximation will therefore

have positive values of KDP.

For a size distribution N(D) of horizontally-oriented spheroids, equations (1.2), (1.3) and

(1.4) can be written (dropping the “π” superscript) as

𝑍ℎ,𝑣 = 4𝜆4

𝜋4|𝐾𝑤|2 ∫ |𝑆ℎℎ,𝑣𝑣(𝐷)|2

𝑁(𝐷)𝑑𝐷∞

0, (1.5)

𝑍𝑑𝑟 = 𝑍ℎ

𝑍𝑣, (1.6)

𝐾𝐷𝑃 = 180𝜆

𝜋∫ 𝑅𝑒[𝑆ℎℎ(𝐷) − 𝑆𝑣𝑣(𝐷)]

∞

0𝑁(𝐷)𝑑𝐷. (1.7)

From equations (1.5) and (1.6), it can be seen that Zdr will be independent of the number

concentration of hydrometeors present in a sampling volume. However, Zdr will be weighted

7

strongly by the largest particles due to Zh,v being proportional to D6. In contrast, KDP is mass-

weighted because Re(Shh) is proportional to D3, and is dependent on the number concentration of

anisotropic scatterers. For hydrometeors with an orientation distribution, the polarimetric moments

can be determined using angular moments (e.g., Ryzhkov et al. 2011). This limited theoretical

background provides a basis to interpret the radar observations of winter storms at X band.

1.3 Previous Studies Using Polarimetric Observations of Pristine Ice Crystals

Enhancements in KDP and ZDR above the melting layer have been observed by a number of

studies (e.g. Ryzhkov and Zrnić 1998; Trapp et al. 2001; Wolde and Vali 2001; Kennedy and

Rutledge 2011; Andrić et al. 2013; Bechini et al. 2013; Schneebeli et al. 2013; Kumjian et al. 2014;

Griffin et al. 2014). This signature has been linked to the presence of dendrites and plate-like ice

crystals.

Kennedy and Rutledge (2011) found ZDR and KDP maxima with S-band radar near the -15° C

level for several winter storm cases. The presence of these enhancements was correlated with

increased snowfall rates at the ground. They compared these radar observables and ZH (where ZH

= 10log10[Zh]) with electromagnetic scattering calculations using the T-matrix method for

distributions of ice particles. The distributions used in their study were based on airplane ice

particle size distribution (PSD) observations (Lo and Passarelli 1982). Observed KDP and ZH values

were reproduced with these PSDs; however, the resulting ZDR signature was greater than that found

in the observations.

Andrić et al. (2013) found similar ZDR and KDP signatures in S-band radar observations of

winter storms. They also performed scattering calculations with PSDs of plates, dendrites, and

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aggregates determined from the results of a one-dimensional microphysical model. The scattering

calculations in this study were based on the Rayleigh approximation. As in Kennedy and Rutledge

(2011), the calculated radar variables failed to reproduce all of the observed polarimetric

signatures. Large concentrations of ice crystals produced through secondary ice generation, not

present in their model, were proposed to explain the discrepancy between the calculated and

observed KDP.

Bechini et al. (2013) also observed enhancements in ZDR and KDP with X- and C-band radars

around the -15 °C level within stratiform precipitation. This signature was attributed to the

presence of dendritic crystals. The observed KDP was found to scale inversely with wavelength and

ZH was found to be independent of wavelength, suggesting these particles were

electromagnetically small. The scattering calculations used to verify this were based on those

performed by Kennedy and Rutledge (2011), with T-matrix calculations for the spheroidal

particles performed at both X and C band. No discussion of the correspondence between the

scattering calculations and the radar observations was provided.

The lack of agreement in these studies between electromagnetic scattering calculations and

radar observations necessitates both a better understanding of the variability of the radar signatures

in regions of possible dendritic growth and a better representation of the scattering of ice crystals,

where the distribution of mass deviates significantly from uniform spheroidal particles. This study

uses X-band polarimetric radar data from several winter storms in Colorado to examine a range of

signatures in regions of dendritic crystal growth. Advanced scattering calculations are also used to

determine PSDs that match each of the observed radar signatures. The physical validity of the

resulting PSDs is assessed by comparison with previous observational studies of ice crystal PSDs.

9

A description of the data used in this study is introduced in the next chapter. An overview of

the meteorological background for the events of study is presented in chapter 3. Chapter 4 provides

a detailed analysis of the radar signatures found within the events and statistics characterizing these

signatures. Chapter 5 is an analysis of the vertically-pointing radar observations and the

polarimetric radar observations at the same location. A description and analysis of the scattering

calculations used in this study are found in chapter 6. Chapter 7 contains a discussion of the

sensitivity and physical implications of the resulting PSDs. The main conclusions of this study are

provided in chapter 8.

10

CHAPTER 2. DATA AND METHODS

For this study, data from the Front Range Orographic Storms project (FROST; Kumjian et al.

2014) in northeastern Colorado are used. Significant winter storm events on 20-21 February, 9

March, and 9 April 2013 are the focus of this paper. Data collected during these events include

radar observations from the CSU-CHILL radar (Brunkow et al. 2000) and soundings launched at

the Marshall Field Site (MFS); these locations are shown in Fig. 2.1. The CHILL radar and MFS

are at elevations of 1432 m and 1742 m MSL, respectively.

The CHILL radar has recently been upgraded to a dual-wavelength system with X- and S-band

frequencies (Junyent et al. 2014). In FROST, the X-band frequency was used due to its smaller

beam width (0.3°) and greater sensitivity to KDP. CHILL data are available between 19:00 UTC

on 20 February to 12:00 UTC on 21 February, 10:29 UTC to 22:02 UTC on 9 March, and 00:41

UTC to 22:33 UTC on 9 April. The radar data contain a series of PPI and RHI scans performed

every ~12 minutes. The PPI and RHI scans were mostly performed at a set of fixed elevation and

azimuth angles, respectively. The azimuth angles of the RHI scans occasionally varied depending

on the appearance of precipitation targets. A full description of this field project can be found in

Kumjian et al. (2014).

During the events on 20-21 February and 9 March, NCAR’s mobile X-band polarimetric radar

(NCAR-XPOL) was scanning concurrently with the CHILL. This radar was located at the MFS

during these events and provided vertically pointing observations, as well as RHI and PPI scans,

of ZH and radial velocity (VR), along with the polarimetric moments. However, at vertical

incidence, most of the shape information content contained in the polarimetric moments is lost.

Vertical scans taken by the XPOL are available from 22:16 UTC to 02:21 UTC on 20-21

February and from 02:59 UTC to 23:51 UTC on 9 March. These data are compiled into time-

11

height cross-sections by averaging ZH and VR over the ~3 minute scans. The period between

consecutive scans is every ~12 minutes, with each time-averaged profile representing one of these

intervals.

To compare the XPOL observations with the polarimetric moments observed by the CHILL

at roughly horizontal incidence, vertical profiles over the XPOL are constructed from CHILL

RHIs. RHIs taken along the 220.7° azimuth of the CHILL passed over the MFS at a range of 73

km and thus are used to create the vertical profiles. These profiles are produced by binning the

RHI gates into 75-m height increments: the same value as the gate width of the XPOL and slightly

greater than the ~51 m beam width of the CHILL at this range. For each height bin, the median

values of all ZH, ZDR, and KDP observations within 1 km of the MFS are taken to represent the

polarimetric moments at that height. Temperature level information comes from the Rapid Refresh

(RAP; Brown et al. 2011) model hourly analyses for each date and time range.

For the processed CSU-CHILL data, KDP is calculated from ΦDP using the Wang and

Chandrasekar (2009; herein WC09) method, which uses an adaptive algorithm to smooth ΦDP to a

degree inversely related to the signal to noise ratio. Before any range derivatives are computed in

the WC09 method, the data are first flagged in regions of high noise using the dispersion of ΦDP

over a number of consecutive gates. These flagged regions are set to KDP = 0 deg km-1, which may

introduce a large number of erroneous zero values that can skew statistical analyses and

microphysical interpretations. In order to eliminate these points, an alternative method of

estimating KDP (described in Appendix A) is used in this study. KDP observations produced with

this new scheme will be presented in later chapters.

12

Figure 2.2. Terrain contours of the northern Colorado region with labels of the locations

mentioned in the text.

13

CHAPTER 3. OVERVIEW OF WINTER STORM CASES

The events included in this study each featured similar synoptic evolutions. Information about

the synoptic-scale meteorological features present during these events is taken from the North

American Regional Reanalysis (NARR; Mesinger et al. 2006). One feature common to all events

is a 500-hPa trough progressing eastward through the central Rocky Mountains (Fig. 3.1). The

motion and position of the trough and its associated surface features helped dictate whether low-

level upslope flow was present in northeast Colorado.

The 20-21 February 2013 event was associated with a broad trough over the Rocky Mountains.

A closed low was present at 500 hPa in southwestern Arizona at 21:00 UTC on 20 February (Fig.

3.1a). At this time the 750-hPa (roughly 1 km above radar level, hereafter ARL) winds were mainly

easterly to southerly in northeastern Colorado. By 12:00 UTC on 21 February, the 500-hPa trough

axis was centered over central New Mexico and the low-level flow had become more northerly

(Fig. 3.1b). Cold-air advection was ongoing throughout the duration of the sampling period. The

height of the -15 °C level decreased from 2.8 km to 2.5 km ARL between 00:00 and 12:00 UTC

on 21 February, based on the radiosondes from Denver, CO (DNR). The sounding taken at the

Marshall Field Site at 00:17 UTC determined the height of the -15 °C level to be at about 2.6 km

ARL (Fig. 3.2a).

One of the notable features visible during this event is a narrow band of enhanced ZH (> 25

dBz) that approached the radar from the southeast between around 23:00 UTC on 20 February and

02:00 UTC on 21 February. An RHI scan taken at 00:58 UTC cutting through the axis of this band

shows enhancements in both ZDR and KDP (> 2.0 dB and 1.5 deg km-1, respectively) between 2.5-

4.0 km ARL and between 28-35 km range (Fig. 3.3). Temperatures within this height range were

14

between approximately -10 °C and -25 °C. After this period, lighter, generally less-organized

echoes are observed as weak upslope flow became the primary contributor to ascent.

At 12:00 UTC on 9 March, which was shortly after the onset of data collection, a closed 500-

hPa low was centered over the four corners region (Fig. 3.1c). There was generally northeasterly

flow at 750 hPa in northeastern CO at this time. By 18:00 UTC, the closed 500-hPa low was

positioned over southern CO, resulting in a stronger northerly component to the 750-hPa wind

within range of the CHILL radar (Fig. 3.1d). This can be seen in the RHI image from CHILL taken

at 17:22 UTC (Fig. 3.4). Between 1.0 km and 1.8 km ARL, the radial velocity is generally > 20 m

s-1, while above this level it is primarily < 10 m s-1 (Fig. 3.4c). This large gradient in radial velocity

is a consequence of the vertical shear between the low-level upslope regime and the mid-level flow

dictated by the synoptic-scale trough. This general flow regime continued through the termination

of data collection.

During the 9 March event, cold-air advection was occurring in northeastern CO. Mandated

soundings taken at DNR indicate the height of the -15 °C level decreased from 3.1 km to 2.6 km

ARL between 12:00 UTC 9 March and 00:00 UTC 10 March. The sounding taken at the MFS at

13:19 UTC (Fig. 3.2b) determined the -15 °C level to be around 3 km ARL.

Between 11:00 UTC and 14:00 UTC on 9 March, relatively more convective structures are

visible in PPI and RHI scans. An example of a significant convective feature found in an RHI

taken at 12:49 UTC is shown in Fig. 3.5. This time period is coincident with weaker, northeasterly

750-hPa flow. As these winds become stronger and more north-northeasterly, PPI scans show a

more stratiform distribution of precipitation. Figure 3.6 shows such a PPI image taken at an

elevation angle of 2.8° at 20:44 UTC on 9 March. Enhancements in ZDR and KDP are visible

between the range rings corresponding to -10 °C and -15 °C. The more northerly location of the

15

radar with respect to DNR may have led to an overestimation of the temperature level heights,

placing the -15 °C ring closer to the KDP and ZDR enhancements.

The 9 April event initiated with a closed 500-hPa trough centered over southern Utah at 03:00

UTC (not shown). The more northern position of this feature relative to the other events allowed

for thunderstorms to develop within range of the CHILL radar. As the 500-hPa trough progressed

eastward, the 750-hPa winds became more northeasterly in northern CO by 09:00 UTC, shown in

Fig. 3.1e. By 18:00 UTC, these winds backed to north-northeasterly, enhancing the upslope flow

component and increasing the advection of cold air (Fig. 3.1f).

Following the thunderstorm observations, ZH > 20 dBz is observed in PPI and RHI scans.

These areas of precipitation mainly translate from southeast to northwest. An RHI scan (Fig. 3.7)

taken at 05:10 UTC through a section of one intense band of ZH shows substantial KDP

enhancements (> 1.5 deg km-1) between 4-7 km ARL and 25-35 km range (Fig. 3.7d). Moderately

elevated ZDR (~1.0-1.5 dB) was also found in this region (Fig. 3.7b). Less intense, northward-

moving echoes were observed between 8:00 and 11:00 UTC on 9 April.

From 12:00 UTC to 16:00 UTC on 9 April, initially light (~10 dBz) and sparse ZH echoes

gradually intensified to ~20 dBz and increased in areal coverage. These regions of precipitation

are associated with ZDR > 1.5 dB through a layer generally below 2 km ARL. This coincides with

backing, low-level upslope flow and cold-air advection, where 750-hPa temperatures are around -

15 °C in the vicinity of CHILL. By 16:00 UTC, a more significant band of enhanced ZH is observed

moving slowly towards the north-northwest. At around 20:00 UTC, this band extends north of the

radar with enhanced values of ZDR (> 3.0 dB) visible in the PPI scans (not shown).

16

Figure 3.1. Plots of 500-hPa height (solid contours), 750-hPa wind and 600-hPa temperature

(dashed color contours with -10 °C and -15 °C indicated by red and purple, respectively. These

images correspond to a) 20 February 2013 at 21:00 UTC, b) 21 February 2013 at 12:00 UTC, c) 9

March 2013 at 12:00 UTC, d) 9 March 2013 at 18:00 UTC, e) 9 April 2013 at 09:00 UTC and f)

9 April 2013 at 18:00 UTC.

17

Figure 3.2. Sounding plots taken at the MFS for a) 21 February 2013 at 00:17 UTC, b) 9 March

2013 at 13:19 UTC and c) 9 April 2013 at 08:20 UTC. Temperature and dew point values are

plotted as black and blue lines, respectively. The wind barbs represent the wind speed in knots,

with the full-length barbs, half-length barbs, and flags corresponding to 5-, 10-, and 50-knot wind

speeds each, respectively.

18

Figure 3.3. RHI scan taken at 00:58 UTC on 21 February 2013 at an azimuth angle of 181.8° for

a) reflectivity factor at horizontal polarization (ZH), b) differential reflectivity (ZDR), c) radial

velocity (VR), and d) specific differential phase (KDP).

19


ZH, b) ZDR, c) VR and d) KDP.

20



21

Figure 3.6. PPI scan taken at 20:44 UTC on 9 March 2013 at an elevation angle of 2.8° for a) ZH,

b) ZDR, c) VR and d) KDP. The rings indicate the range at which the beam height is at -10 °C, -15

°C and -18 °C, in order of increasing range. These temperature levels are derived from the 00:00

UTC sounding taken at DNR on 10 March 2013.

22


b) ZDR, c) VR and d) KDP.

23

CHAPTER 4. RADAR SIGNATURES OF DENDRITIC GROWTH

In order to explore the variability of the radar observations taken near the dendritic growth

zone, distributions of the radar moments at various heights within several RHI scans are examined.

To perform this analysis, each polarimetric variable is binned into height increments and

increments corresponding to predefined bin widths for each variable. The bin widths for ZH, ZDR,

and KDP are 0.5 dB, 0.1 dB, and 0.05 deg km-1, respectively. The number of radar gates that fall

within each height and radar moment bin are then determined. Only RHI observations between

certain ranges where a particular signature is visible are binned in order to spatially isolate the

polarimetric enhancements associated with the signature.

The first case presented is from 12:49 UTC on 9 March 2013 (hereafter referred to as case 1).

As shown earlier, an intense convective feature is visible south-southwest of the radar at this time

(Fig. 3.5). Within this RHI, data are extracted at all heights between ranges of 49-56 km where

the greatest enhancements in KDP and ZDR are present. Figure 4.1a shows the frequency of radar

gates within each height and ZDR bin. The median ZDR value has a peak of 1.1 dB at a height of

4.2 km ARL. The corresponding frequency distributions for KDP and ZH are shown in Figs. 4.1b

and 4.1c, respectively. The peak median KDP is 1.6 deg km-1 at about 3.7 km ARL. The median ZH

increases from 19 dBz to 23 dBz between 4.2 km and 3.7 km ARL. The sounding-indicated -15

°C level at this time is about 3.3 km ARL, several hundred meters below the ZDR and KDP maxima.

Below their respective peaks, both ZDR and KDP decrease significantly, with ZDR values of 0.5 dB

and KDP near 0 deg km-1 at 1.5 km ARL. ZH decreases within this layer to 19 dBz at 1.5 km ARL,

perhaps due to the wind shear present in this region of the echo.

Enhancements in ZDR and KDP observed during the period of more stratiform, upslope

precipitation at 19:51 UTC on 9 March (hereafter referred to as case 2) are shown in Fig. 4.2.

24

These data are extracted from the corresponding RHI between 10-20 km range (Fig. 4.3). During

this time, the height of the -15 °C level is approximately 2.8 km ARL based on the 00:00 UTC

DNR sounding. A well-defined peak in median ZDR of 1.4 dB occurs at 2.6 km ARL. Values below

2.2 km and above 2.8 km ARL are between 0.5-1.0 dB. The peak in median KDP of 0.8 deg km-1

is found at 2.5 km ARL. This coincides with ZH = 13 dBz at an elevation of 2.6 km ARL. Median

ZH increases steadily towards the surface to around 23 dBz at 1.4 km ARL.

The latter portion of the 9 April event was also mainly driven by low-level upslope flow.

However, one unique signature visible in RHI scans at this time is high (3.5 – 5.5 dB) ZDR

collocated with ZH < 5 dBz (Figs. 4.4a, b; hereafter referred to as case 3). Above 2.5 km ARL,

inbound radial velocities between 5-10 m s-1 are present, with outbound velocities between 2 m s-

1 and 15 m s-1 below 2 km ARL (Fig. 4.4c). KDP is also modestly enhanced at ~0.3 deg km-1 (Fig.

4.4d). It is important to note that KDP estimates shown here are based on the alternative procedure

described in the Appendix.

The distributions with height of the radar variables for this case are shown in Fig. 4.5. These

data have been extracted between ranges of 20-30 km from the RHI depicted in Fig. 4.4. The global

maximum in median ZDR is ~4.5 dB at 3.3 km ARL, with a local maximum of 2.0 dB present at

0.5 km ARL. At 3.3 km ARL, significant frequencies of gates with ZDR values > 4.5 dB are also

found, suggesting a distribution skewed towards higher values. The median ZH at this height is

about 3 dBz and increases towards the ground. The vertical distribution of KDP shows maxima

around 0.7 km and 2.9 km ARL. At the height of the maximum ZDR, median KDP is still enhanced

at around 0.3 deg km-1. Bins containing non-zero frequencies extend from -1.0 deg km-1 to 2.0 deg

km-1, suggesting a high amount of noise in the KDP estimation at this altitude. Note that these data

would be set to 0 deg km-1 using the WC09 scheme.

25

Because the most recent MFS sounding was launched ~11 hours prior to this RHI, the 10 April

00:00 UTC sounding from DNR was used to get a better representation of the temperature profile.

This sounding indicated that nearly the entire profile was below -10 °C. Between roughly 780 hPa

and 650 hPa, temperatures ranged from -20 °C to -15 °C. Above 650 hPa, the temperature

increased to around -13 °C, before decreasing back to -15 °C at about 580 hPa. As a result, two

layers may have been conducive to dendritic or plate-like growth. 750-hPa temperatures

(approximately 1 km ARL) from the NARR model analysis for 18:00 UTC on 9 April were below

-15 °C near the radar (Fig. 3.1f). The northeasterly flow at this time suggests cold air advection,

with the low-level air mass sampled by the DNR sounding likely moving over the radar at an

earlier time. This sounding thus provides a fair representation of the environment in which the RHI

was taken.

According to the 00:00 UTC DNR sounding, the -15 °C levels at 0.7 km and 2.9 km ARL have

relative humidity values with respect to liquid of 80-85% and 70-85%, respectively. A third height

where the temperature is at -15°C is found near 2.0 km ARL; the environment at this level is close

to saturated with respect to water. Therefore, multiple layers are favorable for plate-like growth;

potentially favorable conditions for dendritic growth are found near 2.0 km ARL.

ZDR and ZH within this RHI are negatively correlated, as suggested in Fig. 4.6. In this image,

all of the radar gates at ranges < 60 km where KDP is estimated are extracted from the RHI taken

at 19:40 UTC (Fig. 4.4).These gates are then separated into bins by increments of ZH and ZDR. The

frequency of gates within a certain ZH-ZDR bin gives a sense of the likelihood of that ZH-ZDR pair

occurring within the extracted segment of the RHI. In this example, the bins with maximum

frequency are oriented in such a way that ZDR generally decreases with increasing ZH. For the bins

below about 6 dBz, the relationship between these variables becomes less obvious. This may be a

26

result of the increased noise where ZH values are relatively lower. Also, the two frequency maxima

below 0 dBz suggest different populations of crystals may be present. The higher frequency of

values with ZDR near 0.5 dB may represent more isometric crystals, while the enhanced frequency

of values around 4 dB is more characteristic of nonspherical particles.

Overall, ZH, ZDR and KDP all exhibit a large range of values in regions where temperatures are

conducive to dendritic growth. ZH and ZDR tend to be negatively correlated, a result of the strong

weighting of ZDR by particle size: if aggregation is the dominant factor in hydrometeor growth, the

larger, more isometric aggregates will decrease the ZDR substantially. This will also increase the

observed ZH. How KDP varies with ZDR and ZH is somewhat less well defined since KDP depends

on both number concentration and aspect ratio of the ice particles, and in general is not as affected

by large aggregates. Analyses performed for cases 1 and 2 (not shown) also suggest an inverse

relationship between ZDR and ZH. However, this relationship was not as robust due to the smaller

range in ZDR within these cases.

The high degree of variability within the radar signatures presented above suggests that the

characteristics of the microphysics during these cases are themselves unique. For instance, this

variability may suggest that snow at various stages of growth (e.g., pristine crystals and aggregates)

are mixed together in the same radar gate. Electromagnetic scattering calculations can provide a

basis to further understand the microphysical properties within these regions of possible dendritic

snow growth, and are presented in Chapter 6.

27


azimuth angle of 214.4° (Fig. 3.5). The data used in these diagrams were extracted from between

49 km and 56 km range of the radar. The black line indicates the median value of the particular

radar moment at each height. Analyses are shown here for a) ZDR, b) KDP and c) ZH. The

temperature contours (black dashed lines) are based on the 13:19 UTC sounding taken on 9 March

2013 at the MFS.

28





temperature contours (black dashed lines) are based on the 00:00 UTC sounding taken on 10 March

2013 at DNR.

29



30


b) ZDR, c) VR and d) KDP.

31

Figure 4.5. Frequency diagrams corresponding to the 19:40 UTC RHI taken on 9 April at an




temperature contours (black dashed lines) are based on the 00:00 UTC sounding taken on 10 April

2013 at DNR.

32

Figure 4.6. Analysis of frequency for the data points contained within bins of ZH and ZDR. These

data are derived from the 19:40 UTC RHI taken on 9 April at an azimuth angle of 181.7° (Fig.

4.4). Only the radar observations between 0 km and 60 km were used in these diagrams.

33

CHAPTER 5. VERTICAL PROFILES OF RADAR OBSERVATIONS

During the FROST project, the XPOL radar collected data at the MFS, in addition to that

collected by the CHILL radar. One of the scanning strategies regularly implemented on the XPOL

is the sampling of targets at a nearly vertical orientation relative to the ground. These scans provide

radial velocity, which can be related to the ice particle’s fall velocities, and thus places constraints

on the types of hydrometeors present. In addition to the vertical radial velocity measurements from

the XPOL, measurements of ZH, ZDR and KDP at elevation angles of ~0-5° from the CHILL are

used to further constrain the ice particle types.

5.1 Signatures of Riming, Dendritic Growth and Aggregation

Convective features are observed during the 9 March event between 12:00-14:00 UTC with

elevated values of ZH above 20 dBz (cf. Fig. 4.1). Similar enhancements are also visible in the

time-height profiles over the MFS from the CHILL (Fig. 5.1). Between 13:00 UTC and 14:00

UTC, ZH > 15 dBz is present above 3.5 km (Fig. 5.1a). This corresponds with elevated values of

KDP between 0.5-1.0 deg km-1 and ZDR around 0.5 dB. These values support the presence of a

significant population of oblate ice crystals mixed with aggregates and/or graupel. The

corresponding time-height plot from the XPOL shows enhanced values of |VR| around 2 m s-1

around 13:30 UTC and 4.2 km above the CHILL radar level (ACRL; Fig. 5.2b). Because

hydrometeor motion is almost exclusively downward in these analyses, |VR| is related to the

reflectivity-weighted fall speeds of the particles within the sampling volume. Due to the fall speeds

34

of aggregates and pristine ice being generally < 1.5 m s-1 (e.g., Brandes et al. 2008), more rapidly

falling particles such as graupel are likely present.

During this time period between 13:00 UTC and 14:00 UTC, another region where |VR| > 2 m

s-1 is found below 2 km ACRL. This coincides with values of ZH around 20 dBz and minimum

ZDR values of -0.3 dB around 1 km ACRL. These negative ZDR values indicate the presence of

prolate particles with a mean vertical orientation. Conical graupel (that can be approximated as a

prolate spheroid) falls with a mean vertical orientation and is known to have intrinsic ZDR values

that are negative (e.g., Aydin et al 1984; Bringi et al. 1986; Oue et al. 2015), and, given the

coincident negative ZDR, negative KDP, and large |VR| observations, is likely present at these times.

During a period of more stratiform precipitation after 14:00 UTC on 9 March, a relatively

persistent signature found in the time-height profiles is |VR| decreasing towards the ground and ZH

increasing towards the ground. This can be seen in the XPOL |VR| and CHILL ZH measurements

(Fig. 5.2b) between 2.5 km and 4.0 km ACRL, where the maximum reductions in |VR| are between

0.1 m s-1 and 0.3 m s-1. This height range also has enhanced values of ZDR between 0.7 dB and 1.5

dB, suggesting oblate ice crystals may be found in this region of the echo. Both the downward-

relative decrease in |VR| and downward-relative increase in ZH generally follow the -15 °C

isotherm (Fig. 5.1a and Fig. 5.2b). The level of highest ZDR also tracks this isotherm relatively

well, suggesting this signature coincides with dendritic or plate-like growth.

Because these ZH and |VR| signatures are most easily identified as vertical changes in the

quantities with respect to height, gradients in these quantities are calculated. The majority of the

radial velocity values observed by the XPOL depict motion towards the radar. Therefore, the

gradients are taken in the direction of the hydrometeor motion, or downward-relative. The

downward-relative direction is also important because the snow growth processes of aggregation

35

and dendritic growth generally occur as the hydrometeors descend. At each time, vertical gradients

are calculated for every height point. For each particular height, the vertical derivative is calculated

using a linear fit of the 7 values centered about that height.

Given the downward motion of the hydrometeors comprising relatively homogeneous

precipitation, positive downward-relative gradients in ZH correspond to increasing ZH with respect

to time. Similarly, negative downward-relative gradients in |VR| are related to decreasing

reflectivity-weighted fall speeds with time. When the downward-relative gradients in ZH are

positive and the downward-relative gradients in |VR| are negative, the reflectivity-weighted particle

size is increasing with decreasing reflectivity-weighted terminal velocity.

As shown in Fig. 5.1d, there is a persistent signature after 14:00 UTC of positive downward-

relative ZH gradients centered near the -15 °C isotherm. Positive downward-relative gradients in

ZDR are also found near this temperature level with negative gradients in ZDR at lower heights (Fig.

5.1e). In the XPOL data at the same time, negative gradients in |VR| are found just above the -15

°C isotherm, transitioning to positive gradients in |VR| below these heights.

During the 20-21 February event, the period at which both radars scanned concurrently is

limited to around three and a half hours. As described in chapter 3, a relatively intense band of

snow propagates northwestward between 23:00 and 02:00 UTC within range of the CHILL. This

feature can be seen in the time-height profile taken from the CHILL in Fig. 5.3. Elevated ZDR and

KDP values of 1.5-2.0 dB and 1.2-1.7 deg km-1, respectively, are found near the -15 °C isotherm

around 00:00 UTC. Another period of enhanced ZDR values around 2.5 dB is found after 01:30

UTC and at a height of 2 km ACRL, 200 m above the -10 °C isotherm (Fig. 5.3b). ZH at this time

is below 15 dBz, lower than the values coincident with the banded feature observed near 00:00

UTC.

36

The XPOL time-height profiles for the February case show another fairly consistent region of

decreasing |VR| towards the ground. This can be seen in the downward-relative |VR| gradient plot

where negative values are found between 3 km and 3.5 km ACRL (Fig. 5.4d). Positive downward-

relative gradients in |VR| are present between 2 km and 3 km ACRL.

5.2 Radar Observations with Temperature

In order to better relate these signatures to crystal habit, the time-height observations of ZDR

and ZH from the CHILL and |VR| from the XPOL (along with their gradients) are mapped to

temperature. These temperature values come from the RAP model hourly analyses for the grid

point closest to the MFS. Each radar variable (ZH, |VR|, and ZDR) is then interpolated from height

coordinates to temperature coordinates at all radar observation times. The radar moments at each

temperature level are averaged in time over the entire period of concurrent CHILL and XPOL

observations to reduce the noise associated with a particular scan.

The time-averaged vertical profiles of the downward-relative gradient in |VR|, the downward-

relative gradient in ZH, and the downward-relative gradient in ZDR are shown in Fig. 5.5 for the

20-21 February and 9 March events. Negative downward-relative gradients in |VR| are found

between -15 °C and -18 °C for both cases, with minima near -17 °C. At temperatures above -15

°C, the downward-relative gradients of |VR| for both cases are positive and increasing, with

maxima near -13 °C (Fig 5.5a).

Consistent signatures between the two cases are also found in the downward-relative ZH

gradients (Fig. 5.5b). Positive values exist for both cases at temperatures lower than -7 °C with

well-defined peaks occurring at -15 °C and -13 °C for the 20-21 February and 9 March events,

37

respectively. A less obvious signal is present in the downward-relative ZDR gradient plots,

especially for the 20-21 February event where a significant amount of noise is still present. This

may be a result of the fewer number of scans used in the time averaging for the February case. In

the March case, where a greater number of scans are used in the averaging procedure, a well-

defined positive peak is present at -15 °C in the downward-relative gradient of ZDR. Moreover,

negative values of the downward-relative gradient of ZDR are present in both cases for temperatures

greater than -11 °C.

As shown in wind tunnel measurements from Fukuta and Takahashi (1999) and numerical

calculations by Chen and Lamb (1994) and Hashino and Tripoli (2007), fall speeds are minimized

for ice crystals growing in temperatures near -15 °C. Isometric plate crystals growing and

descending into warmer temperatures between -18 °C and -12 °C near water saturation may

therefore begin to slow as they take on dendritic characteristics. The negative values of the

downward-relative |VR| gradient observed by the XPOL may be a reflection of this change in ice

crystal habit. If enough dendritic ice crystals are present, these hydrometeors will contribute

enough to the reflectivity-weighted velocity spectrum, producing the observed negative

downward-relative |VR| gradient values. The enhanced values of ZDR in this region also support

the presence of growing oblate ice crystals (Fig. 5.5d).

The maxima in the downward-relative ZH gradient near -15 °C may signify an increase in the

aggregation rate. The enhanced vertical derivatives in ZH suggest a maximum in the change with

height of the reflectivity-weighted mean particle size and thus a maximum in the snow growth

rate. This may be due to the presence of a significant population of dendrites, whose enhanced

collection efficiencies greatly increase the aggregation rate. Aggregation will also be enhanced

due to the larger spread in fall speeds between the slowing dendrites and the young aggregate

38

population. This enhanced aggregation rate is also suggested by the increasing |VR| values below

-15 °C, where the larger, faster-falling aggregates begin to dominate the velocity spectrum. The

negative downward-relative gradients in ZDR at temperatures warmer than -11 °C for the two cases

also suggests the more isometric aggregates increasingly dominate ZDR.

The limited number of cases where the XPOL and CHILL provided concurrent scans makes it

difficult to generalize these results. However, the signature of negative downward-relative |VR|

gradients and positive downward-relative ZH gradients has also been observed in the data presented

by Szyrmer and Zawadzki (2014) and by Surcel and Zawadzki (2010). Whether the vertical

gradients in |VR| and ZH are found to be consistent indicators of dendritic growth and aggregation

will require future observational datasets. Contamination from storm-scale vertical motion could

also play a role in modulating these results, though the time-averaging procedure limits this

potential source of error to some degree. Wind shear, present during both events, may lead to

differential hydrometeor advection and another source of variability in the vertical profiles of the

radar moments. However, this effect is minimized during periods of stratiform precipitation.

Riming will also modulate the ZH and |VR| gradients as growing particles with fall speeds greater

than aggregates are introduced into the radar sampling volumes.

39



data are based on the CHILL RHI scans along the 220.7° azimuth on 9 March from 10:53 UTC to

21:59 UTC. The yellow dashed contour indicates the height of the RAP model analyzed -15 °C

isotherm while the upper and lower black dashed contours indicate the -20 °C and -10 °C

isotherms, respectively.

40



taken at the MFS on 9 March from 10:53 UTC to 21:59 UTC. The yellow dashed contour indicates

the height of the -15 °C isotherm while the upper and lower black dashed contours indicate the -

20 °C and -10 °C isotherms, respectively.

41



data are based on the CHILL RHI scans along the 220.7° azimuth on 20-21 February from

approximately 22:40 UTC to 02:40 UTC. The yellow dashed contour indicates the height of the -

15 °C isotherm while the upper and lower black dashed contours indicate the -20 °C and -10 °C

isotherms, respectively.

42



taken at the MFS on 20-21 February from approximately 22:20 UTC to 02:20 UTC. The yellow

dashed contour indicates the height of the -15 °C isotherm while the upper and lower black dashed

contours indicate the -20 °C and -10 °C isotherms, respectively.

43

Figure 5.5 Time-averaged profiles of a) downward-relative |VR| gradient, b) downward-relative ZH

gradient, and c) downward-relative ZDR gradient for 20-21 February (solid line) and 9 March

(dashed line). The time-height profiles used to create the time-averaged profiles shown here

correspond to Fig. 5.1 and 5.2 for the 20-21 February profiles and Fig. 5.3 and 5.4 for the 9 March

profiles.

44

CHAPTER 6. ELECTROMAGNETIC SCATTERING CALCULATIONS

Based on the results presented in chapters 4 and 5, there is evidence for the presence of

dendritic growth zones within a number of different cases. Forward modeling, in which the radar

signatures of dendritic ice crystals are simulated, can support or reject whether these ice crystals

are present. In order to represent the populations of ice crystals found in the dendritic growth zone,

PSDs are needed.

Previous studies (e.g., Andrić et al. 2013; Kennedy and Rutledge 2011) have used PSDs either

from a microphysical model or an observational study to calculate the radar observables. However,

these studies failed to fully reproduce the observed radar signatures, suggesting there were errors

in the modeling of the ice crystals or in the PSDs. The variability in the radar signatures near -15

°C shown in chapter 4 suggests there is also variability in the ice crystal PSDs associated with

these signatures.

Therefore, to account for PSD error and variability, a different approach is taken in this study

where the PSDs for ice crystals are determined based on the radar observations, after first

separating out the contributions to the polarimetric variables from aggregates. If these ice crystal

PSDs are physically realistic, then they may provide plausible descriptions of the ice particle size

spectrum for certain polarimetric radar signatures in the dendritic growth zones. The first step

necessary in performing this analysis is to calculate the scattering properties of the individual

crystals with size.

6.1 Description and Monodisperse Distribution Calculations

45

The scattering calculations for pristine ice particles are used based on the ice crystal database

described in Botta et al. (2013) and Lu et al. (2014), which employs the Generalized Multi-particle

Mie (GMM) method. The GMM method involves composing a particle of non-overlapping spheres

and solving the scattering of the collection of spheres analytically. In order for this method to be

accurate, the distribution of mass within the particle must be represented well by the collection of

spheres. Further details can be found in Botta et al. (2013) and Lu et al. (2014).

From the variety of ice crystal morphologies within the database, hexagonal plates and

dendrites were chosen to best represent the likely hydrometeors sampled by the radar, based on

prior work and the observed temperatures. The aspect ratios of these crystals are based on the

empirical formulas in Pruppacher and Klett (1997), adapted from Auer and Veal (1970), shown in

Table 6.1. To get a larger range of possible ice crystal dimensions, the crystal thicknesses were

multiplied by 0.5 for dendrites and by 0.5 and 2.0 for plates. The dendrites in the database have

maximum dimensions (D) of 0.5 mm to 5.65 mm. The maximum dimensions of the plates ranged

from 0.10 mm to 3.27 mm (Lu et al. 2014).

In order to calculate ZDR, ZH, and KDP from the simulated scattering amplitudes, assumptions

about the canting of these ice particles were made. The particles were assumed to be oriented

according to a two-dimensional Gaussian distribution of canting angles with the mean canting

angle set to 0° and the standard deviation (σ) varying from 1° to 20°. Previous studies have found

σ to be between 10°-15° for pristine ice crystals (e.g., Matrosov et al. 2005). The radar observables

for each orientation distribution are then calculated using the angular moments from Ryzhkov et

al. (2011).

The scattering calculations for dendrites with thicknesses of 1.0 and 0.5 times that determined

by the empirical size relationship (hereafter d1.0 and d0.5, respectively) and plates with thickness

46

twice that prescribed by the empirical relationship (hereafter referred to as p2.0) are shown in Fig.

6.1. These calculations use monosdisperse distributions for each crystal corresponding to a total

ZH = 3 dBz (i.e., representative of case 3). As σ increases, ZDR decreases because of the smaller

total projection of the horizontally polarized signal onto the axes of the ice particles’ maximum

dimensions. The largest ice crystals have the lowest KDP values due to their number concentration

being constrained to have a ZH = 3 dBz. Due to Zh (in mm6 m-3) being approximately proportional

to D6, the smallest particles have much larger number concentrations (or total mass) to achieve ZH

= 3 dBz and thus produce KDP values several orders of magnitude higher than the largest particles.

The behavior exhibited by the calculated ZDR is somewhat different between the p2.0 (Fig.

6.1c) and d1.0 (Fig. 6.1b) particles. The dendrites show a minor degree of variance in ZDR with

maximum dimension. For example, the leftmost points with σ = 20° range from about 4.6 dB to

4.8 dB. This variability in ZDR is roughly equal for all other values of σ. The ZDR values for the

plates, however, show a greater range over size with fixed values of σ. For σ = 20°, ZDR ranges

from 2.7 dB for the 0.1-mm crystals to 5.2 dB for the 2.5-mm crystals. The difference in ZDR

between the smallest and largest particles increases to about 4.2 dB for σ = 1°. This relationship

between the maximum dimension of plates and ZDR can be explained by the particles becoming

more oblate with increasing maximum dimension while retaining the same internal distribution of

mass. However, the relative consistency of ZDR with maximum dimension for the dendrites is

likely due to their more complex shape and larger size, resulting in a more heterogeneous

distribution of mass across the particle and thus more complicated scattering behavior.

Based on these results for monodisperse ice crystal particle size distributions (PSDs), only

observed radar signatures with large ZDR can possibly be explained by these calculations alone. In

case 3 above, the peak median ZDR value of 4.5 dB at 3.3 km was associated with a KDP of 0.3 deg

47

km-1 and a ZH of 3 dBz. The scattering calculations for p2.0 show that plates with a maximum

dimension of 0.6 mm, a number concentration ~104 m-3 and σ = 18° best match the observations.

Values of σ closer to 10° result in similar values of KDP and ZDR values around 5.5 dB. Note that

the distribution of ZDR values near 3.3 km ARL (Fig. 4.5a) shows a significant number of points

clustered around 5.0 dB. These values may be a better estimate of the ZDR contribution solely from

pristine ice crystals. Also, the location of the ZDR anomaly near echo top may contain a greater

degree of turbulence and thus more enhanced fluttering of particles, which may increase σ values

over those established in previous studies.

These simple monodisperse PSDs of plates may therefore provide reasonable correspondence

with the observations from case 3. The number concentration (~104 m-3) falls within the range of

observations found in Heymsfield et al. (2013) for temperatures between -15 °C and -20 °C (their

Fig. 4). The other cases described in Chapter 3 were associated with lower ZDR observations and

thus require the addition of a separate class of hydrometeors to decrease the total ZDR.

Monodisperse PSDs are also less physically realistic for a population of ice crystals in a more

mature stage of development when aggregation may play a more considerable role and differential

depositional growth conditions may widen the particle size spectrum.

6.2 PSD retrieval with Mixtures of Aggregates

In this study, we assume that only aggregates and pristine ice crystals are present in the radar

sampling volumes. Therefore, the radar-observed values of ZH, ZDR, and KDP are each composed

of contributions from ice crystals and aggregates. Since the pristine ice crystal PSD is desired, the

contributions to the polarimetric variables from the aggregates must be separated from that of the

ice crystals. This analysis requires knowledge of the ZDR and KDP values associated with a

48

population of snow aggregates, where these particles are monodisperse and thus have a single ZH,

ZDR, and KDP. A population of aggregates makes a negligible contribution to KDP (e.g., Thompson

et al. 2014) due to the effective isometric appearance of these particles as they tumble. Similarly,

aggregates produce small (but non-zero) ZDR values. Observational (e.g., Ryzhkov and Zrnić 1998;

Ryzhkov et al. 2005b; Homeyer and Kumjian 2015) and modeling (e.g., Thompson et al. 2014)

studies have found aggregates to have ZDR between 0.0-0.6 dB at X-, C-, and S-band. Scattering

calculations of aggregates composed of stellar crystals not explicitly used in this study also fell

within this range. Thus, we assume that any population of aggregates, by itself, has a ZDR value

between 0.0-0.6 dB, 0 deg km-1 KDP, and a ZH value to be determined.

Since KDP is generated by the presence of pristine ice, only ZH and ZDR can provide information

about the aggregate contribution to ZH. The expansion of the equations for Zh and Zdr in terms of

the aggregate and ice crystal ZH contributions is shown in the following equations:

𝑍ℎ𝑇 = 𝑍ℎ

𝐴 + 𝑍ℎ𝐼 , (6.1)

𝑍𝑑𝑟𝑇 =

𝑍ℎ𝑇

𝑍𝑣𝑇 =

𝑍ℎ𝑇

𝑍𝑣𝐴+𝑍𝑣

𝐼 = 𝑍ℎ

𝑇

𝑍ℎ𝐴

𝑍𝑑𝑟𝐴 +

𝑍ℎ𝐼

𝑍𝑑𝑟𝐼

, (6.2)

where subscripts ‘dr’, ‘h’, and ‘v’ refer to the radar observables in linear units. The superscripts

‘T’, ‘A’, and ‘I’ refer to the “total” (observed), “aggregate,” and “ice crystal” values, respectively.

An additional parameter, ZdrI, is needed for these equations to become a system of two variables

and two unknowns. This value comes from the scattering calculations of plates and dendrites from

the database. In general, the dependence of ZdrI on the PSD requires the use of an iterative method,

described in subsequent sections. For the d1.0 crystals, however, ZDRI shows little variation with

size and thus is nearly independent of the PSD.

49

Equations (6.1) and (6.2) can be solved for the contribution to Zh by ice crystals, ZhI, using the

observed values of ZhT and Zdr

T, ZdrI from the ice crystal scattering calculations, and an assumption

about ZdrA. The resulting equation for ZH

I is shown below,

𝑍ℎ𝐼 = 𝑍ℎ

𝑇 (𝑍𝑑𝑟

𝐼

𝑍𝑑𝑟𝑇 ) (

𝑍𝑑𝑟𝑇 −𝑍𝑑𝑟

𝐴

𝑍𝑑𝑟𝐼 −𝑍𝑑𝑟

𝐴 ), (6.3)

where ZHI varies from 0 dBz to ZH

T, depending on how close ZDRT is to ZDR

I and ZDRA. ZH

I as a

function of ZDRT and ZH

T is shown in Fig. 6.2 for the labeled values of ZDRI and ZDR

A. The

calculated value of ZHI can now constrain one of the parameters used to define a particular PSD.

Generalized gamma distributions can be used to model these PSDs and are defined by the

equation N(D) = N0Dµexp(-λD), where N0 is the intercept parameter, μ is the shape parameter, and

λ is the slope parameter. The case where µ = 0 is the exponential distribution, which will be used

primarily herein. Another commonly used version of the generalized gamma distribution is where

µ = 2, hereafter referred to as the gamma distribution. Because two parameters are needed to define

these PSDs (λ and N0), another constraining radar moment is required. Since KDPT will be roughly

equal to KDPI due to the minimal contribution from aggregates, KDP

I provides the second constraint

on the PSD. A variety of λ and N0 values can then be used to calculate KDPI and ZH

I for various ice

crystal PSDs. The PSD with λ and N0 that produces KDPI and ZH

I matching the constraining KDPI

and ZHI values can thus be determined. In order for the λ and N0 that produce the given KDP

I and

ZHI constraints to be found, a method for calculating the polarimetric variables from a PSD is

needed.

To determine the ZH and KDP for a PSD of ice crystals from the database, the ZH and KDP values

of single crystals are used. These intrinsic ZH and KDP values for each crystal size in the database

50

are found by dividing the monodisperse ZH (equal to 3 dBz for all the crystals shown in Fig. 6.1)

and KDP values at each size by their corresponding number concentration. The number of particles

contained within each crystal size bin (the increment between consecutive crystal sizes) given by

the PSD is then multiplied by the intrinsic ZH and KDP. The sum of the ZH and KDP values

contributed by each size gives ZHI and KDP

I. As mentioned earlier, the database has crystals

available only for a set of fixed sizes. In order to use exponential or gamma distributions to model

ice PSDs, these sizes must approximate well the contribution to the radar variables over the full,

continuous distribution spanning all possible maximum dimensions. For the ice particles with

maximum dimensions > 0.5 mm, dendrites are used. Plate crystals are used for sizes between 0.1

mm and 0.5 mm. This is also physically realistic because plate crystals are the primary habit

preceding dendritic growth. The exact size where plates begin to show characteristics of dendrites

depends on the specific growth conditions.

For the ice crystals where there is variation in ZDR with size, ZDRI, and thus ZH

I, is dependent

on the PSD. Therefore, an iterative procedure for determining ZDRI is needed. This process (shown

schematically in Fig. 6.3) uses a first guess for ZDRI to find an initial estimate of ZH

I, using the

procedure described earlier. This ZHI estimate is then used with KDP

I to make an initial estimate of

N0 and λ. An updated value of ZDRI is then calculated from these PSD parameters, allowing for

ZHI, and thus N0 and λ to be further refined. This step is depicted as the outermost arrow in Fig.

6.3 extending from the ice PSD parameters to the ZDRI value. Only a few iterations are needed for

the N0 and λ values to converge.

Figure 6.4 shows the relationship between the PSD parameters for the combination of p1.0 and

d1.0 crystals and the resulting KDPI and ZH

I values. The intersection of these two curves gives the

N0 and λ values needed to match the radar observations. Both KDPI and ZH

I increase with increasing

51

N0 as a larger number of ice particles at all sizes are present. Increasing λ with constant N0 leads

to a decrease in both polarimetric variables as both the total number concentration and median

particle size decrease. For a constant λ, increasing N0 leads to an increase in KDPI and ZH

I, with the

KDPI contours becoming more tightly packed. The relatively small angles between the KDP

I and

ZHI curves in Fig. 6.4 imply a high sensitivity of these values to both PSD parameters. This

sensitivity is explored further in chapter 7.

The PSDs resulting from this methodology are shown in Table 6.2, along with the observed

radar variables associated with each case. The retrieved N0 values for the diverse set of radar

signatures vary about an order of magnitude. A large range in λ is evident as well, with a ~5.3 mm-

1 difference between high and low values. The ZHI, ZDR

I, and KDPI computed from the retrieved

PSD parameters for each case combined with the derived ZHA provide exact matches with the

radar-observed values. Thus, unlike previous studies (Kennedy and Rutledge 2011; Andrić et al.

2013; Bechini et al. 2013), the PSDs derived herein are consistent with the suite of polarimetric

radar observations.

The retrieved PSD for the signature observed in case 2 (cf. Fig. 4.3) is plotted in Fig. 6.5. A

relatively high number concentration of smaller particles is derived for this case, with λ = 3.29

mm-1. The greatest contributions to KDPI from this PSD come from ice crystals with maximum

dimensions between ~0.5-1.5 mm. These crystals have moderate values of normalized KDP, but

are in sufficiently high concentration, and thus have a sufficiently large mass, to produce much of

the observed enhancement. At greater maximum dimensions, the marginal contributions to KDPI

decrease substantially. In contrast, dendrites with maximum dimensions between 1.2-1.6 mm

contribute the most towards ZHI with a slower decrease in the marginal contributions to ZH

I with

size. This is due to ZH depending more strongly on particle size.

52

For case 1 (cf. Fig. 3.5), a shallower PSD is retrieved (Fig. 6.6). In this PSD, the greatest

contribution to KDPI comes from the dendrites with maximum dimensions of ~1.5 mm. Relative to

the previous example, a slower decrease with size is seen in the marginal contribution to KDPI. The

greatest contribution to ZHI, however, comes from dendrites with maximum dimensions between

3-4 mm, due to their increased concentrations and the size dependence of ZHI.

The largest λ was observed for the case with largest ZDRT (case 3). As mentioned in the previous

section, these radar observations correspond fairly well to a monodisperse PSD of plates having a

maximum dimension of 0.5 mm. Only the p2.0 crystal type was used here because the lower

normalized ZDRI values of these crystals require lesser ZH

A values to match ZDRT. This reflects the

likely dearth of aggregation ongoing with plate crystals near echo top. The relatively low ZHI and

modest KDPI for these crystals resulted in a slope parameter of 7.13 mm-1 (Fig. 6.7). The sharp

peak in the KDPI contribution centered on the 0.5-mm crystal size bin suggests this PSD behaves

similarly to the monodisperse distribution for plates of this size.

53

Table 6.1. Description of the plates and dendrites from the database shown in Botta (2013).

Adapted from Lu et al. (2014). D is the maximum dimension of the particles, while h is the

particle thickness and is orthogonal to D.

D (mm) h(cm), D(cm) Thickness Factor

Dendrites 0.5-5.65 h = 9.022 x 10-3D0.377 0.5,1.0

Plates 0.1-3.27 h = 1.41 x 10-2D0.474 0.5,1.0,2.0

Table 6.2. Exponential ice PSDs determined from the radar observations listed in columns 2, 5

and 6. An aggregate ZDR of 0.3 dB, an aggregates KDP of 0 deg km-1, and σ = 15° are assumed

for these calculations.

Case ZHT

(dBz)

ZHI

(dBz)

ZHA

(dBz)

ZDRT

(dB)

KDPT/KDP

I

(deg km-1)

N0

(m-3 mm-1)

λ

(mm-1)

Crystal

Types

2/21/13 00:58 UTC 15 10.2 13.25 1.5 1.3 2.77 x 105 3.21 p1.0,d1.0

Case 1:

3/9/13 12:49 UTC

23 16.1 22.01 1 1.6 5.91 x 104 1.87 p1.0,d1.0

Case 2:

3/9/13 19:51 UTC

13 7.9 11.39 1.4 0.8 1.84 x 105 3.29 p1.0,d1.0

Case 3:

4/9/13 19:40 UTC

3 2.5 -6.64 4.5 0.3 3.85 x 105 7.13 p2.0

54

Figure 6.1. Scattering calculations for monodisperse populations of a) dendrites with one half the

reference thickness, b) dendrites of the reference thickness and c) plates twice the reference

thickness based on the empirical relationships found in Auer and Veal (1970). The ZH values for

all data points are 3 dBz. The numbers to the left of the data indicate the maximum dimension (in

mm) and number concentration (in m-3) for the size class of ice particles, respectively. The color

of the points differentiate the crystals sizes for which the scattering calculations are performed.

The size of the markers indicates the canting angle distribution width (σ) with the largest markers

equal to 20° and the smallest markers equal to 1°.

55

Figure 6.2. Contours of ZHI given observations of ZH

T and ZDRT; ZDR

I is set to 5.8 dB and ZDRA to

0.3 dB.

56

Figure 6.3. Schematic depicting the iterative process by which a PSD is retrieved from a set of

radar observations. The orange-colored boxes indicate the quantity is observed by the radar, the

blue-colored boxes indicate the quantity is derived from the radar observations and scattering

calculations and the green-colored box indicates an assumed quantity.

57

Figure 6.4. Contours of KDPI (blue) and the ZH

I (red) contribution from ice as a function of the

slope and intercept parameters for PSDs of exponential form. ZHI is contoured every 2 dBz from

0 dBz to 20 dBz.

58

Figure 6.5. Plot of the number concentration per size (maroon), marginal contribution to ZhI

(orange) and marginal contribution to KDPI (blue) corresponding to case 2; the exponential PSD

for this case has N0 = 1.84x105 m-3 mm-1 and λ= 3.29 mm-1. Ice particles to the left of the red

dashed line are of type p1.0 and of type d1.0 to the right.

59



for this case has N0 = 5.91x104 m-3 mm-1 and λ= 1.87 mm-1. Ice particles to the left of the red

dashed line are of type p1.0 and of type d1.0 to the right.

60



for this case has N0 = 3.85x105 m-3 mm-1 and λ= 7.13 mm-1. The ice particles used here are all of

type p2.0.

61

CHAPTER 7. DISCUSSION

In contrast with previous studies (Kennedy and Rutledge 2011; Bechini et al. 2013; Andrić et

al. 2013), PSDs, along with a contribution to ZH from aggregates that match the observations of

ZDR, ZH, and KDP have been retrieved. However, the physical validity and correspondence with

observational studies of these ice PSDs needs to be established for them to be considered

reasonable models of the ice crystal size spectrum for each case. Unfortunately, only limited

observational studies are available for ice crystal PSDs. A composite of several recent aircraft

probe studies is presented in Heymsfield et al. (2013). The bulk PSDs based on these observations

are shown in Fig. 7.1. The curve indicating the median of observations made between -10 °C and

-20 °C corresponds well with the derived PSDs.

The comparison between the median observed PSDs and the one retrieved from the CHILL

radar observations is shown in Fig. 7.2a for case 2. The retrieved PSD has a somewhat larger λ

and a larger N0 than the median PSD in Heymsfield et al. (2013). It is important to note that a

range of PSDs were observed in Heymsfield et al. (2013), of which some are likely more

representative of the cases presented here than the bulk median values for each particle size

depicted in Fig. 7.2. Similarly, polarimetric signatures of dendritic growth presented herein

exhibited large case-to-case variability. The variety of PSDs retrieved here from radar observations

at similar temperatures suggests other factors played a large role in the microphysical properties

of these events as well.

As discussed earlier, the retrieved PSD parameters can be quite sensitive to the radar

observations given the generally small angles between the KDPI and ZH

I curves, especially for small

λ (e.g., Fig. 6.4). Therefore, uncertainty in these observations can propagate through to the PSD

62

estimation. To gauge the impact of observational uncertainty on the PSD parameters, 20%

perturbations in ZDRT and KDP

T were imposed on the observations for each case. The percentage

changes due to these modifications can be seen in Table 7.1.

Case 1, which had the highest ZHT and lowest ZDR

T, showed the greatest sensitivity to changes

in ZDRT, whereas case 3 (which had the lowest ZH

T and highest ZDRT) had the smallest percentage

changes. The main impact of these ZDRT perturbations was to change the relative proportions of

ZHT contributed by aggregates and ice crystals. For the 20% decrease in ZDR

T, the ZHI constraint

will decrease due to ice crystals having a high intrinsic ZDRI. As a result, both λ and N0 must

increase to provide higher contributions to KDPI from smaller-sized ice crystals. Perturbing ZDR

T

(and thus the ZHI constraint) has the greatest impact for PSDs with small λ due to the exponential

dependence of the PSD on this parameter.

Perturbations in KDPT had more consistent impacts across the cases compared to the

perturbations in ZDRT. This is due to the ZH

I constraint depending on both ZDRT and ZH

T, while

KDPT (KDP

I) is a direct constraint on the PSD. Increases in KDPT resulted in increases in N0 and λ

of 54-59% and 7-9%, respectively. Both N0 and λ increased due to the greater contribution of

smaller particles needed to produce a larger KDPI with the same ZH

I. Negative perturbations in KDPT

had the inverse effect.

Another source of uncertainty is the assumption of the bulk ZDRA and KDP

A values. Due to the

likely minimal contribution to KDP from aggregates, the resulting changes in PSD parameters will

be very small. However, the assumed ZDRA can have a significant impact on the ZH

I constraint for

the ice crystal PSD. To determine the sensitivity of the PSD parameters to this assumption, PSDs

were determined for each case using ZDRA values of 0.0 dB and 0.6 dB (Table 7.2). Again, resulting

changes in both PSD parameters were largest for case 1, which had the largest ZHT and smallest

63

ZDRT and thus the largest initial ZH

A. The impact of this assumption is amplified when ZDRT is low.

When ZDRA is 0.6 dB, which is relatively close to ZDR

T (1.0 dB), there is a large decrease in ZHI.

This leads to a large increase in λ and N0 in order for the PSD to maintain KDPI = 1.6 deg km-1. In

contrast, very minor changes (< 2%) occur for this same ZDRA increase for case 3 due to the very

low contribution to ZHT by aggregates.

Different choices of the ice crystals between sizes of 0.1 mm and 0.5 mm can also impact the

PSD parameters. Using the p2.0 plates leads to a maximum decrease of 14.7% in N0 and a 2.4%

decrease in λ. These thicker plates have lower ZDRI values, thereby increasing the ZH

I constraint

for the PSD. These changes were minor due to the relatively small impact these particles have on

KDPI, and especially ZH

I. In contrast, large impacts are observed when d0.5 is used instead of d1.0

crystals for particles larger than 0.5 mm (Table 7.3). Decreases in both PSD parameters were seen

with these crystals, with 77-98% decreases in N0 and 49-96% decreases in λ. The exponential

response of the PSD to changes in λ makes these fractional decreases more significant. These

thinner and thus more oblate dendrites mainly affect these parameters through their greater number

concentrations. This can be seen in the monodisperse distribution plots shown in Fig. 6.1.

The number concentrations of the d0.5 monodisperse PSDs are nearly an order of magnitude

larger than those of d1.0. Thus, the d0.5 crystals have lower normalized ZHI values and therefore

the PSD needed to satisfy the ZHI constraint requires a greater contribution from larger particles.

This leads to decreased λ and N0 with marginal contributions to KDPI increasing as well for the

larger crystals.

Figure 7.2 illustrates the differences between the PSDs determined for case 2 using the d0.5

and d1.0 crystals. The overall slope for the d0.5 crystal distribution corresponds well to the slope

of the bulk distributions found in the Heymsfield study (Fig. 7.2b). However, the retrieved PSD

64

has an N0 roughly one order of magnitude greater than the observed median PSD. For dendrites

with maximum dimensions between about 1.0-2.5 mm, the PSD fitting the d1.0 crystals was closer

in value than that for the d0.5 crystals. This size range also exhibited the greatest contributions to

KDPI and ZH

I for both PSDs.

Finally, fitting the radar observations to a gamma distribution instead of an exponential

distribution also leads to differences in the marginal contributions to the radar observables with

size. The gamma PSD parameters that fit the observations for each case are shown in Table 7.4.

Generally, the gamma PSDs had much lower marginal contributions to the ZHI and KDP

I from the

larger particles than the exponential PSDs, which is expected based on the narrower spectral

shapes. For case 2, lower marginal contributions to ZHI and KDP

I are seen for the smallest ice

crystals as well as those > 2 mm. Dendrites with maximum dimensions between 0.5-2.0 mm

provide larger contributions to KDPI and ZH

I to compensate for the decreased contributions from

the other sizes.

These variable radar signatures and the corresponding derived PSDs provide insights into the

ongoing microphysics during these cases. In case 3, the derived PSD suggests a highly sloped

exponential distribution is present with the ice particles clustered within a narrow range of sizes.

This suggests that the early stages of depositional growth was occurring, producing a relatively

narrow distribution of small crystals yet to exhibit dendritic characteristics, and thus yet to exhibit

any substantial degree of aggregation.

The stratiform, upslope-induced case 2 also had a relatively steep slope parameter. However,

the contribution to ZHT from aggregates was greater than that produced by the dendrites. This

suggests a relatively low number concentration of aggregates are present which provide an

65

adequate ZHA contribution yet also allow a large enough concentration of small, oblate particles to

exist and match the KDP and ZDR observations.

A much larger contribution to ZHT from aggregates was determined for case 1. The λ value for

this exponential distribution was shallower than the previous two cases, indicating a much larger

weight towards the largest dendrites. This also suggests that many of smallest crystals in the

distribution had been collected by the larger aggregates. The convective appearance to the radar

echoes in this case, along with the elevated ZHT values, suggest a stronger updraft in the cloud that

could have allowed for a larger growth of dendrites via vapor deposition and thus more efficient

aggregation. Additionally, the analysis in chapter 5.1 suggests that rimed ice crystals may have

also been present. This complicates the interpretation of these radar observations, where riming

could differentially alter the aspect ratios comprising a preexisting ice PSD.

Microphysical models of ice processes require, among other parameters, knowledge about ice

crystal and snow aggregate fall speeds. However, there is a large amount of uncertainty in these

values given the difficulties in observing such properties of real ice particles in the atmosphere.

The signature observed by the vertically pointing XPOL, associated with the dendritic growth and

aggregation of these crystals, can help constrain the range of fall speeds and other microphysical

parameters used in the models.

For the limited number of cases presented in this study, the maximum downward-relative

vertical gradient in ZH was consistently between 3 dB km-1 and 10 dB km-1 and found near the

dendritic growth zone. Maximum ZH gradients in stratiform precipitation events were found by

Surcel and Zawadzki (2010) and Bechini et al. (2013) to be within this range of values as well. If

the downward-relative gradient in ZH falls between 3 dB km-1 and 10 dB km-1 near the dendritic

growth zone for a large sample of stratiform precipitation events, the uncertainty in the treatment

66

of aggregation of dendrites in numerical models can be constrained. Similarly, if found to be

consistent over a large number of cases, the negative downward-relative gradient in |VR| near the

dendritic growth zone, as presented in this study, can be used to reduce the uncertainty in the fall

speeds of aggregates and dendrites. Model simulations of aggregation and vapor deposition in

environments conducive for dendritic growth can be compared with the radar observations using

forward operators for ZH and |VR|. Large deviations between the simulated and constraining ZH

and |VR| gradient values will indicate significant errors in the model parameters. These parameters

(such as fall speed) can then be tuned to better match the ZH and |VR| gradient constraints.

67

Table 7.1. Percentage changes in N0 and λ with respect to the values shown in table 6.2, for 20%

perturbations in ZDR and KDP.

+20% Kdp Percentage Change in N0 Percentage Change in λ

2/21/13 00:58 UTC 56.3 8.4

Case 1: 3/9/13 12:49 UTC 59.2 9.1

Case 2: 3/9/13 19:51 UTC 56.0 8.2

Case 3: 4/9/13 19:40 UTC 53.8 7.0

Mean 56.3 8.2

-20% Kdp

2/21/13 00:58 UTC -42.6 -9.7

Case 1: 3/9/13 12:49 UTC -44.0 -10.7

Case 2: 3/9/13 19:51 UTC -42.4 -9.7

Case 3: 4/9/13 19:40 UTC -40.8 -7.9

Mean -42.4 -9.5

+20% Zdr

2/21/13 00:58 UTC -24.5 -8.1

Case 1: 3/9/13 12:49 UTC -30.6 -11.2

Case 2: 3/9/13 19:51 UTC -25.0 -8.5

Case 3: 4/9/13 19:40 UTC -13.5 -3.9

Mean -23.4 -7.9

-20% Zdr

2/21/13 00:58 UTC 44.4 11.8

Case 1: 3/9/13 12:49 UTC 62.4 16.0

Case 2: 3/9/13 19:51 UTC 45.1 12.2

Case 3: 4/9/13 19:40 UTC 22.9 5.9

Mean 43.7 11.5

68

Table 7.2. Percentage changes in N0 and λ with respect to the values shown in table 3, for

aggregate ZDR values of 0.0 and 0.6 dB.

Aggregate ZDR = 0.0 dB Percentage Change in N0 Percentage Change in λ

2/21/13 00:58 UTC -21.7 -7.2

Case 1: 3/9/13 12:49 UTC -38.2 -14.4

Case 2: 3/9/13 19:51 UTC -23.9 -7.9

Case 3: 4/9/13 19:40 UTC -1.3 -0.4

Mean -27.9 -9.8

Aggregate ZDR = 0.6 dB

2/21/13 00:58 UTC 38.6 10.6

Case 1: 3/9/13 12:49 UTC 114.9 26.7

Case 2: 3/9/13 19:51 UTC 44.0 11.9

Case 3: 4/9/13 19:40 UTC 1.8 0.6

Mean 65.8 16.4

Table 7.3. Percentage changes in N0 and λ with respect to the values shown in table 3, for crystal

types of p1.0 and d0.5. No modification of crystal type was imposed on the 9 April case.

Crystal Types: p1.0,d0.5 Percentage Change in N0 Percentage Change in λ

2/21/13 00:58 UTC -77.83 -49.84

Case 1: 3/9/13 12:49 UTC -97.83 -95.72

Case 2: 3/9/13 19:51 UTC -76.85 -48.63

Case 3: 4/9/13 19:40 UTC

Mean -84.17 -64.73

69

Table 7.4. Gamma ice PSDs determined from the radar observations listed in columns 2, 5 and 6.

An aggregate ZDR of 0.3 dB and σ = 15° are assumed for these calculations.

Case ZHT

(dBz)

ZHI

(dBz)

ZHA

(dBz)

ZDRT

(dB)

KDPT/KDP

I

(deg km-1)

N0

(m-3 mm-1)

λ

(mm-1)

Crystal

Types

2/21/13 00:58 UTC 15 10.2 13.25 1.5 1.3 2.08 x 106 4.97 p1.0,d1.0

Case 1:

3/9/13 12:49 UTC

23 16.1 22.01 1 1.6 1.43 x 105 2.88 p1.0,d1.0

Case 2:

3/9/13 19:51 UTC

13 7.9 11.39 1.4 0.8 1.44 x 106 5.08 p1.0,d1.0

Case 3:

4/9/13 19:40 UTC

3 2.5 -6.64 4.5 0.3 9.67 x 106 10.4 p2.0

70

Figure 7.1. Number concentration per unit size as a function of maximum dimension based on

several in situ aircraft probe studies. The orange curve shows the ice particle observations taken at

temperatures between -10 °C and -20 °C. From Heymsfield et al. (2013). The dots depict the values

one standard deviation above the mean normalized concentrations at each temperature range and

diameter.

71

Figure 7.2. Plots of the number concentration per size (maroon), marginal contribution to Zh

(orange) and marginal contribution to KDP (blue) for a) particles of type p2.0 and d1.0 and b) type

p2.0 and d0.5 corresponding to case 2. The maroon dashed lines shows the bulk PSD observations

adapted from the Heymsfield et al. (2013) study (Fig. 7.1).

72

CHAPTER 8. CONCLUSIONS

X-band polarimetric and vertically-pointing radar observations collected during several winter

storm events in northern Colorado were analyzed, with particular focus on the signatures found

within regions favored for dendritic growth. A large variability in the observed ZH, ZDR, and KDP

was found. This variability may be partially explained by the differing meteorological conditions

found between and during each event. Periods of significant upslope flow tended to be associated

with more stratiform precipitation and, at times, substantial ZDR enhancements. Features with a

more convective appearance mostly developed with less significant low-level upslope flow. These

cases often exhibited larger ZH but smaller ZDR (indicative of more aggregation), yet large KDP

enhancements suggesting a sizeable population of dendritic crystals. This could include both rapid

growth of dendrites in large supersaturations and/or a larger number concentration of dendrites.

Likely due to aggregation, ZDR generally was negatively correlated to ZH, with the highest ZDR

observed with lower ZH. Enhancements in KDP were observed within regions of elevated ZDR

and/or elevated ZH. Since KDP is related to both the total mass and aspect ratio of a sample of

hydrometeors, increases in ZH and/or ZDR can increase its value. The most significant

enhancements, however, were associated with increased ZH. The addition of aggregates will leave

KDP relatively unchanged while decreasing the observed ZDR.

Negative downward-relative gradients in |VR| were observed by the vertically pointing XPOL

near the dendritic growth zone. These values are thought to be related to the onset of dendritic

characteristics during vapor depositional growth. Another persistent signature found near -15 °C

was the maximum in the profile of the downward-relative ZH gradient. These increased ZH

gradients support a maximum in the aggregation rate at this temperature level and provide further

73

evidence for the presence of dendrites due to the enhanced collection efficiencies of these particles.

The greater variation in fall speed between dendrites and aggregates also increases the aggregation

rate. Values of the downward-relative gradient in ZDR were positive at temperatures above -11 °C

and negative at warmer temperatures. This indicates that dendrites growing through vapor

deposition increase ZDR initially, before aggregation dominates the snow growth process. This

lowers ZDR as mass is transferred from the oblate dendrite population to the more isometric

aggregates.

Scattering calculations were performed using the GMM method, with ZH, ZDR, and KDP

calculated using realistic assumptions about the canting behavior of the ensemble of particles. A

monodisperse distribution of plate-like crystals matched relatively well to the observed

polarimetric radar signatures for a case of observed large ZDR. The slope and intercept parameters

for exponential and gamma distributions were retrieved from the radar observations for a variety

of cases. The resulting PSDs corresponded well to previously reported aircraft probe

measurements of ice PSD. The range of PSDs retrieved from the highly variable radar signatures

suggest that these distributions are plausible models to characterize ice crystal size distributions,

given the presence of aggregates. Further evidence these PSDs are physically realistic is that the

property of observed ZDR being positively correlated to λ (Kennedy and Rutledge 2011) is satisfied.

The sensitivity of the derived PSDs to the radar observations, the crystal types used in the

scattering calculations, and assumptions about the scattering properties of aggregates was tested.

The aspect ratio of dendrites made significant impacts on the calculated radar observables and thus

the retrieved PSDs. Electromagnetic scattering calculations for dendrites with aspect ratios that

depend on environmental growth conditions (e.g., Harrington et al. 2013; Sulia et al. 2013, 2014)

may determine PSDs constrained by the radar observations that better fit the limited observational

74

studies of ice PSDs. This also underscores the need for ice crystal observations to better constrain

axis ratio relationships for dendritic and plate-like crystals.

Some information about the microphysical processes associated with certain polarimetric radar

signatures can be inferred. If conditions are unfavorable for riming (i.e., weak vertical motion), ZH

and ZDR can be used to determine the relative contributions of aggregates and ice crystals to the

observed ZH. Enhanced values of KDP in these regions likely suggest that these aggregates rapidly

grow through the collection of dendrites. The greater the observed values of KDP, the greater the

rate of dendritic growth and thus the greater the efficiency in aggregate growth. The PSDs derived

using ZH, ZDR, and KDP can also be compared to gain some information about the growth of snow

through aggregation. For example, shallower slopes indicate collection of the smallest ice particles

by the larger aggregates. The use of scattering calculations of aggregates composed of pristine ice

crystals may be useful in further understanding aggregation processes.

The polarimetric signature of elevated KDP, increasing ZH, and decreasing ZDR towards the

ground, found in the ice-producing region of clouds, is related to the presence of dendritic ice

crystals. Thus, regions where these crystals may be growing can be identified using polarimetric

radar. Further confidence about the presence of these dendrites can be attained if this signature is

observed in a layer saturated with respect to liquid and with temperatures near -15 °C. Due to the

rapid aggregation of these dendrites, these radar observations may be useful in indicating the

occurrence of enhanced snowfall rates.

75

APPENDIX A. ALTERNATIVE KDP ESTIMATION PROCEDURE

In regions where ΦDP is particularly noisy, often where ZH is relatively low, the WC09

estimation procedure sets KDP to 0 deg km-1. Substantial ZDR enhancements due to the presence of

pristine ice crystals at these locations may therefore be incorrectly associated with KDP values close

to 0 deg km-1. In order to better quantify the KDP associated with these ZDR and ZH values, an

alternate method for estimating KDP is introduced. Since this procedure is applied in radar scans

exclusively sampling ice particles, no folding of ΦDP occurs. Also, the backscatter differential

phase shift is considered small, given the high probability that the particles in these high-noise

regions of the echo likely satisfy the Rayleigh approximation.

The first step in this method is removing the data containing primarily noise. A gate is

considered noise when it has a normalized coherent power (NCP) value < 0.4. NCP is a measure

of the predictability of the phase between pulses (Dixon and Hubbert 2012), where values near

one are considered to be mostly signal and those near zero mostly noise. After masking the gates

of high noise, a low-pass range filter is applied to the ΦDP field. The Lanczos filter (Duchon 1979)

was used in this case. This filter is computed using the Fourier transform of a rectangular function

in frequency space and a factor of “sigma,” which minimizes the Gibbs oscillations that occur with

Fourier representations of discrete data. Once the filter is calculated using 2n+1 gates, the resulting

weights can be applied to the range profile of ΦDP. At each gate j, a weighted average of the ΦDP

values from gate j-n to j+n is calculated using the weights determined by the filter. This filtered

value of ΦDP at gate j can only be determined if none of the gates from j-n to j+n have been flagged

as noise.

76

The low-pass cut-off (the width of the rectangular response function) used in this case is the

frequency of oscillations in the KDP field estimated using the WC09 method, corresponding to

approximately 1 peak every 53 gates. Thirty-one points (n = 15) were used to create the Lanczos

filter weights. Gates close to the radar and near echo top with less than 15 ΦDP values at greater

and/or lesser ranges were removed. A linear regression centered on each gate was used to calculate

the slope of the filtered ΦDP profile. While this scheme decreases the overall number of KDP

estimates, estimates are now provided for some of the gates previously flagged as noise (and thus

set to zero) in the WC09 algorithm.

The gates for which estimates of KDP were originally provided (i.e., regions of low noise) by

the WC09 scheme are well correlated with those using this estimation procedure. A comparison

of the vertical profiles of KDP (as in Fig. 4.5b) estimated using the alternate and WC09 methods is

shown in Fig. A1. Below 2.8 km ARL, the median KDP values are nearly identical with slightly

narrower widths and similar shapes to the distributions seen in the alternate KDP estimation.

77

Figure A1. Frequency distributions with height of KDP calculated using the a) WC09 estimation

procedure and b) the alternate estimation procedure described in appendix A (identical to Fig.

4.5b). These distributions correspond to the RHI taken at 19:40 UTC on 9 April at an azimuth

angle of 181.7°. These data have been extracted at ranges between 20 and 30 km. The black dashed

lines indicate the temperature levels derived from the 00 UTC sounding from DNR on 10 April.

78

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