iii

WRF SIMULATIONS OF A SEVERE SQUALL LINE: COMPARISONS AGAINST HIGH-RESOLUTION DUAL- AND QUAD-DOPPLER RADAR MEASUREMENTS FROM

BAMEX

BY

BRYAN ANDREW GUARENTE

B.S., University of Northern Colorado, 2003

THESIS

Submitted in partial fulfillment of the requirements for the degree of Master of Science in Atmospheric Sciences

in the Graduate College of the University of Illinois at Urbana-Champaign, 2007

Urbana, Illinois

iv

ABSTRACT

Historically, quantitative comparisons between modeled mesoscale convective systems

(MCSs) and observations were limited by spatial and temporal variations between the datasets.

Prior studies often compared specific values that characterized the MCSs, such as maximum

rear-inflow jet wind speed, cold pool strength, or average storm motions. Using high-resolution

multi-sensor data collected during the Bow Echo and Mesoscale Convective Vortex Experiment

(BAMEX 2003), we now have an excellent opportunity to compare modeled versus observed

MCS structures. In this thesis, we compare the statistical distribution of the radar reflectivity

and wind fields within a modeled MCS to those from BAMEX observations. Specifically, we

compared airborne dual- and quad-Doppler observations of the June 10 2003 BAMEX MCS

against high-resolution (3 km grid spacing and 54 vertical levels) simulations made with the

Weather Research and Forecasting (WRF) model using contoured-frequency-by-altitude

diagrams (CFADs) and a new method, contoured-frequency-by-distance diagrams (CFDDs).

These diagrams yielded bulk statistical comparisons of how the frequency distributions of the

observed and modeled systems vary with height and distance, respectively.

Comparisons using CFADs and CFDDs of modeled reflectivity and kinematics to those

from airborne dual- and quad-Doppler radar syntheses were used to quantify the simulated squall

line morphology, rear-inflow jet evolution, and microphysics in this storm system. CFADs of

reflectivity showed that the model over-predicted the frequency of > 35 dBZ reflectivities near

the surface with this microphysics package for this specific storm. A “hole” in only the modeled

reflectivity CFADs was noted below the melting level between 5 and 30 dBZ, where there were

no areas with frequencies greater than 1%. CFADs of RIJ-parallel squall-line-relative winds

suggested an overprediction of modeled wind speeds above the melting level. The distance

behind the convective line where the interface between front-to-rear and rear-to-front flow

v

occurred was easily identified on CFDDs from the RIJ-parallel squall-line-relative winds. With

average altitude per bin per distance diagrams, the height of this same interface was readily

demonstrable with time and distance from the convective line, presenting a chance to quantify

the typical slope of the interface over the trailing stratiform region. Using all of the statistical

methods included for comparisons between modeled and observed systems could help to identify

where model parameterizations are lacking a physical understanding of the atmosphere or where

we may need higher resolution observations to continue to test our understanding.

vi

ACKNOWLEDGEMENTS

I would like to acknowledge the advising of Drs. Brian Jewett, Greg McFarquhar, and

Robert Rauber. Without their constant leadership and prodding this project would not have

happened. When I finally was able to take the project into my own hands, their ideas lead to

many of the discoveries involved in this research. My greatest debt of gratitude goes out to them

for letting me make my own mistakes.

Special thanks go to Dr. Brian Jewett for his open-door policy and quick responses to my

e-mails. All questions computer-related were answered to the best of his ability, often going two

steps beyond where my problem actually lay. His quiet humor and mumbles also made BAMEX

meetings run smoother, in my honest opinion.

To Dr. David Jorgensen, I thank you for supplying the radar observations and the code to

convert them to ASCII format.

To the other members of the BAMEX research group, Mrs. Andrea Smith-Guarente and

Mr. Joseph Grim, I would like to thank you both for keeping our advisors in check, and

reviewing all of my work that you possibly could with all the work you had of your own to

complete. I would like to thank Mr. Grim for his aid in making some of the dual- and quad-

Doppler radar images from this BAMEX case. Andrea, I thank you for talking about research so

often, even when there were other things more pressing in your life, and even when it was 3 or 4

a.m. Your help proofreading every draft of my chapters was unmatched. I would like to take this

opportunity to thank you, my wife, for dealing with me finishing my thesis, even when the stress

was getting to you and our unborn son. Thanks for holding him in.

vii

Lastly, I would like to thank my unborn son, for making me complete this project in a

timely manner. Without your “gentle nagging,” I would have been floundering my way to a May

2008 graduation. I’ll have time to hang out with you more often after this thesis is submitted.

The computer time provided by the National Center for Supercomputing Applications

(NCSA) and the grant money provided by the National Science Foundation are obviously

important contributors to my work. Completion of this work was dependent on these grants.

Any opinions, findings, recommendations, or conclusions expressed in the material are

those of the author and do not necessarily reflect the views of the sponsors.

viii

TABLE OF CONTENTS

CHAPTER PAGE

1. INTRODUCTION .........................................................................................................1

1.1. Introduction...........................................................................................................1

2. METHODOLOGY ........................................................................................................6

2.1. Model Description ................................................................................................6

2.2. Observations Description......................................................................................8 2.3. CFADs...................................................................................................................9

2.4. CFDDs ................................................................................................................12

3. COMPARISONS USING CFADS.................................................................................20 3.1. Masked CFADs...................................................................................................20

3.2. RIJ-centered CFADs of Reflectivity ...................................................................28

3.3. RIJ-centered CFADs of Y-axis-parallel Squall-line-relative Wind Speeds.........35

4. COMPARISONS USING CFDDS ................................................................................45

4.1. Contoured-Frequency-by-Distance Diagrams ....................................................45

4.2. Average Altitude per Bin per Distance Diagrams...............................................54

5. CONCLUSIONS............................................................................................................67

5.1. Conclusions.........................................................................................................67

REFERENCES ..................................................................................................................74

1

CHAPTER 1

INTRODUCTION

1.1. Introduction

Mesoscale convective systems (MCSs) inundate the Great Plains with precipitation

during summer, accounting for 30-90% of total rainfall (Fritsch et al., 1986). These systems are

also known to frequently generate damaging winds, small hail, and occasionally, weak tornadoes.

A theory on the maintenance of MCSs (RKW Theory) exists from numerical model simulations

(Weisman and Rotunno 2004), plus an expansion describing the maintenance of bow-echoes and

the role of convectively generated rear-inflow jets (RIJs) (Weisman 1992). A substantial amount

of work has gone into discovering the mechanisms for the development of RIJs (e.g., Smull and

Houze 1985, 1987a, b, Rutledge et al., 1988, Johnson and Hamilton 1988, Houze et al., 1989),

and other studies have explored the mechanisms (dynamical and microphysical) by which the

RIJ descends to the surface (e.g., Biggerstaff and Houze 1991, 1993, Braun and Houze 1994,

1996, Gallus 1996), occasionally causing strong winds and severe damage (Funk et al., 1999,

Atkins et al., 2005, Wakimoto et al., 2006a, b). A number of studies examine this subject from

one of two frameworks: modeling or observations. Each framework has its advantages and

downfalls. A lack of modern high-resolution (temporal and spatial) MCS observations has made

discoveries from observations lag behind discoveries from modeling studies of MCSs. With rare

exception, observational studies lack high-resolution and/or the number of samples necessary to

make statistically significant statements about the overall structure of a typical MCS or deduce

what controls this structure. Although conducting model simulations at high-resolution

overcomes some of these weaknesses, limited evaluation of the results of simulations against

2

observations has led to questions about the robustness of both the simulations and

parameterization schemes. Before 2003, the most recent field campaign initiated to study mid-

latitude continental MCSs was held in 1985.

In May-July 2003, the Bow Echo and Mesoscale Convective Vortex Experiment

(BAMEX, Davis et al., 2004) was held in an attempt to obtain high-resolution observational

datasets of MCSs, bow-echoes, and mesoscale convective vortices through in-situ microphysical,

thermodynamic, and dual- and quad-Doppler radar observations. With these data, a study using

both modeling and observational frameworks with high resolution was possible.

Quantitative comparisons of MCS characteristics have been made in the past using

models, observations, or a combination of the two. Variables like vertical and horizontal

velocity, reflectivity, and rainfall rates have all been used to characterize MCSs (e.g., Smull and

Houze 1987a, b, LeMone and Moncrieff 1994, Caniaux et al., 1994, Grady and Verlinde 1997,

Montmerle et al., 2000, Dawson and Xue 2006, Grams et al., 2006, Pasken and Martinelli 2006,

Wheatley et al., 2006, Storm et al., 2007). While many of these studies examined high-

resolution radar data, none of these studies employed statistical approaches to show the

characteristics of the given variable over certain regions of the MCS, including the convective

line and trailing stratiform region. For example, stratiform horizontal velocities have been

compared from several different storms, with vertical profiles of horizontal velocities either

obtained by averaging over the entire stratiform region or from a single sounding through the

stratiform region (Smull and Houze 1987b). The problem here is that this method may not

portray what is occurring over the entirety of a given MCS region. By averaging over the entire

stratiform region, for instance, one eliminates the inherent variability that may be important to

MCS structure (e.g., the RIJ). Thus, other statistical methods would be appropriate here.

3

Methods similar to Smith et al., 2008, where distributions of kinematic and microphysical

variables are coordinated with specific regions of MCSs show how ill suited averaging over an

entire inhomogeneous region can be. A distribution of each variable over each region is better

suited to create an understanding of key MCS variables.

Yuter and Houze (1995), henceforth YH95, introduced contoured-frequency-by-altitude

diagrams (CFADs) for examining statistical changes in vertical distributions of vertical

velocities, reflectivity, and differential reflectivity at small altitude increments obtained at high-

resolution with dual-Doppler radar for an evolving field of cumulonimbus clouds from the

Convection and Precipitation/Electrification Experiment (CaPE). Their statistical method has

been used to quantify vertical variations of numerous variables in many different types of

systems by multiple authors (e.g., Steiner et al., 1995, Smith et al., 1999, Cifelli et al., 2000,

Geerts and Heymsfield 2000, Yuter et al.,, 2005, Mori et al., 2006, Swann et al., 2006, Kingsmill

et al., 2006). However, relatively few authors have applied this method to examine model fields

(e.g., Lang et al., 2003, Rogers et al., 2006). Also, few authors have used this method to

compare observations versus model output (e.g., Rogers et al., 2004, Smedsmo et al., 2005).

Here, we shall show that CFADs are an ideal tool for making comparisons where temporal and

spatial co-location is poor, as often occurs between observations and some model datasets.

In this thesis, we focus on statistical comparisons between high-resolution dual- and

quad-Doppler radar observations from the National Oceanic and Atmospheric Administration

(NOAA) and Naval Research Laboratories (NRL) P-3 airborne radar systems of the 10 June

2003 MCS from the BAMEX field campaign and high-resolution Weather Research and

Forecasting (WRF) model simulations of the 10 June case. CFADs are used in this study to

4

quantify the vertical distributions of reflectivity and horizontal winds from both observations and

model simulations.

While CFADs are useful to explain vertical distributions of observed and modeled fields,

they inherently lack the ability to portray horizontal variations. Some meteorological

phenomena exhibit the largest variability/gradients in the horizontal (e.g., mesoscale gravity

waves, jets, and fronts). In this thesis, we introduce a new statistical tool for characterizing the

variability in this direction. The new method, a contoured-frequency-by-distance diagram

(CFDD), presented herein, extends the concept of YH95's CFADs to a new dimension. CFDDs

were designed to ignore vertical variability. Instead of using increments of altitude to define a

histogram volume, increments of horizontal distance from a given plane are used to define the

histogram volume. This technique is helpful for comparisons of the June 10 2003 system, or any

bow echo, because of their strong horizontal variations (e.g., winds associated with RIJ) behind

the leading convective line. CFADs summarized the vertical distribution of meteorological fields

while ignoring horizontal variability, while CFDDs ignore vertical variability while statistically

summarizing the horizontal structures.

A new methodology for thorough comparison between observations and model

simulations can lead to further studies of MCS structures using numerical models, with an

improved understanding of how well the model replicates certain characteristics of the MCS.

Studies using these statistical techniques can quantify the errors originating from physical

representations within the numerical model.

The remaining sections of this thesis are arranged as follows: Chapter 2 presents the

methods by which CFADs, CFDDs, and other statistical tools are constructed, and provides

background information for the model simulations. Chapter 3 includes information about

5

comparisons of modeled fields to observed fields using CFADs, while Chapter 4 contains

comparisons using CFDDs. Chapter 5 expands on key results and conclusions from this work.

6

CHAPTER 2

METHODOLOGY

2.1. Model Description

We carried out a 36-hour simulation of the 10 June 2003 BAMEX MCS using the fully

compressible non-hydrostatic ARW (Advanced Research WRF) core of the WRF model version

2.1.2 (Skamarock et al., 2005). We selected this case because it had the fastest flight-level winds

recorded during BAMEX (80 kts), yet had few surface wind damage reports, suggesting that a

strong RIJ never impinged on the surface. We ran multiple simulations with differing

initializations, grid layouts, and parameterizations, but selected the simulation whose evolution

was qualitatively the most similar to the observed MCS using timing for initiation and

dissipation of certain squall line features (e.g., convective line, trailing stratiform, and northern

bookend precipitation) and areal coverage of stratiform and convective regions. Times used for

analysis purposes include 0412, 0430, 0448, 0515, 0542, 0600, 0618, 0636, 0654, 0712, 0748,

and 0815 UTC. These analysis times were selected as they maintained the most consistent RIJ

locations and orientations based on automated criterion of the fastest ground-relative wind speed

below five kilometers. This simulation used two-way nested grids with three-tiered 27 – 9 - 3

km grid spacing (Fig. 2.1), and a mass-based, terrain-following, stretched 54 layer vertical grid.

Parameterizations used in this work included the Thompson et al., (2004) microphysics, the

RRTM longwave radiation scheme (Mlawer et al.,, 1997), the Dudhia shortwave radiation

scheme (1989), the Monin-Obukhov surface layer scheme (Janjic, 1996), the Noah land surface

model (Chen and Dudhia, 2001), the Yonsei University planetary boundary layer scheme (Hong

and Pan, 1996 and Hong et al., 2006), and the Betts-Miller-Janjic cumulus parameterization

7

Fig. 2.1. Location of model simulation domains. Domain 1 (D1), domain 2 (D2), domain 3 (D3) have grid spacing of 27, 9, and 3 km respectively.

8

(Janjic, 1994). Convection was parameterized on the 27 and 9 km grids, while it was explicitly

resolved on the 3 km grid. The coarse grid time step was 60 seconds. Initialization and lateral

boundary condition data came from the NCEP Eta model with boundary conditions updated tri-

hourly. The simulation began at 0000 UTC 9 June 2003 with all domains run for 36 hours.

Model data was saved every 9 minutes. Henceforth, we only present data from the innermost

grid using the model horizontal grid spacing and sampling the data at 0.5 km vertical resolution,

which is not always consistent with the vertical grid spacing due to the stretched vertical

coordinate, but matches the vertical grid spacing of the observational dataset. Computations

were carried out on the National Center for Supercomputing Applications machines at the

University of Illinois.

2.2. Observations Description

The observational dataset came from Doppler radars mounted on the NOAA and NRL P-

3 aircraft that were flown on either side of the convective line of the MCS (Jorgensen et al.,

2005). Measurements were taken at the following times on 10 June: 0422-0437, 0439-0458,

0500-0525, 0529-0558, 0600-0617, 0617-0636, 0636-0657, and 0740-0752 UTC. The lack of

radar observations between 0715 and 0740 UTC was due to the NOAA P-3 performing a

microphysical spiral descent where a quad-Doppler synthesis of the wind field was impossible

due to the heading of the NOAA P-3 changing so rapidly. Each radar has a range of 46.2 km, but

this range is rarely used to its fullest, as the objective was to retrieve dual- and quad-Doppler

analyses, which required the sampled areas to overlap at more than just one location. This range

limits the sampled area over which the observed and modeled fields can be compared. Radar

reflectivity and derived horizontal velocity fields were transferred to a Cartesian coordinate

9

system for analysis following techniques from Jorgensen et al., (1996). The grid spacing of the

radar output is 1.5 km in the horizontal and 0.5 km in the vertical. In the observations below 0.5

km, data were not retrievable. A signal may not be accurate in the lowest kilometer of the

atmosphere due to interference by the surface clutter (Jorgensen et al., 1984). Because of these

stipulations, observed radar reflectivity values at altitudes below 0.5 km, and occasionally up to

1 km, were not available. In addition, near the edges of the radar volume, over-estimation of the

derived horizontal wind fields occurred due to a lack of sample points to derive the wind field

properly. These areas have been removed from the analyses, which were provided by Dr. David

Jorgensen.

2.3. CFADs

A key tool employed to evaluate the simulations was the contoured-frequency-by-altitude

diagram (CFAD, YH95). Because the simulated and observed storms were not collocated in

space or time, CFADs provided a quantitative measure for comparing the vertical structure of the

observations and the model. A CFAD is a two dimensional depiction of a collection of

histograms, or frequency distributions, of a particular variable at evenly spaced altitudes (0.5 km

apart in our work). In this study, we used CFADs to compare observed radar reflectivity and

derived horizontal velocity fields obtained by the NOAA and NRL P-3 airborne radar systems

with simulated reflectivity calculated following Stoelinga (2005) and horizontal wind fields from

the model. The simulated reflectivity calculations are consistent with the microphysics package

employed in the model (personal communication with Dr. Greg Thompson). Radar reflectivity

(simulated and observed) and horizontal velocity (simulated and dual- or quad-Doppler derived,

10

where available) data were binned at each altitude within a predefined area using bin sizes of ΔZ

= 5 dBZ and ΔV = 1 m/s, respectively.

A CFAD is constructed by compiling histograms of a particular variable at each altitude

into a single contour plot. Fig. 2.2a is an example of a simulated reflectivity histogram at 10.5

km above ground level (AGL) showing the frequency of occurrence of different reflectivity

values at that altitude within an area enclosed within a two-dimensional horizontal mask. A

mask was necessary to limit the CFAD analysis area to only the MCS. The mask applied to all

CFADs was defined as the horizontal area in which the maximum reflectivity in each grid

column is greater than, or equal to 0 dBZ, regardless of the variable plotted on the CFAD. The

histograms included in each CFAD only used data from within the masked area. Use of this two-

dimensional mask simplified CFAD interpretation since the analysis area (number of points per

histogram) remains constant with height. When masked with this threshold, the CFAD included

data from the trailing stratiform region, convective region, as well as the leading anvil parts of

the storm at all altitudes. Some extraneous information was included in this masked area,

including other convection occurring in the 3 km domain. Another method, discussed later, was

applied to limit the inclusion of these extraneous data points.

Fig. 2.2b shows histograms as a function of altitude plotted as a single three-dimensional

diagram. The CFAD (Fig. 2.2c) represents a contour plot of the frequencies constructed by

looking down the z-axis on the three dimensional diagram and contouring the data as if it were a

topographic map. CFADs portray the bulk characteristics of the vertical profile of the data. For

a given CFAD, each point provides the frequency of occurrence of the data in that bin at a

specific altitude. Each altitude on a CFAD has frequencies that should add up to 100%; those

altitudes with frequencies that do not add up to 100% have horizontal areas that lack applicable

11

Fig. 2.2. Conceptual model of how to build a contoured-frequency-by-altitude diagram (CFAD). All sub-diagrams are from 0712Z in the simulation. a) Histogram of simulated radar reflectivity at 10.5km above ground level. Reflectivity binned using 5 dBZ intervals. b) Isosurface of frequencies of simulated radar reflectivity with altitude increasing into the page. c) CFAD of simulated radar reflectivity within masked area. Frequency interval is 2% beginning at 1%. d) Plan view of maximum reflectivity in a column mask. Northern portion of reflectivity pattern cut off by edge of domain.

12

values (areas that are contained within the 2-D mask but with point values below the 0 dBZ

threshold or did not contain retrievable values of reflectivity). These null value areas are not

plotted on the CFADs, but need to be included when adding up frequencies at a given height to

achieve a cumulative frequency of one hundred percent. In the masked CFADs in this thesis,

such as Fig. 2.2c, the contour interval was two percent beginning at one percent, meaning all

areas that do not constitute at least one percent of the masked area did not appear on the CFADs.

To understand how to interpret the diagrams, consider, for example, the overall upper-level

precipitation mode. As the convection initiates, there would be very little stratiform

precipitation, but a large amount of convective precipitation. On a CFAD, higher percentages

would be found in the higher reflectivity bins (particularly at lower altitudes) indicative of

convective cells, while lower percentages would be found in the lower reflectivity bins indicative

of stratiform precipitation. As the MCS evolves, a stratiform region would begin to develop.

Now on a CFAD, nearly equal percentages would be found in the higher reflectivity bins and the

lower reflectivity bins. Eventually, the MCS outflow would surge away from the convective

line, cutting off the convective updraft, leaving an orphaned stratiform precipitation region. This

CFAD would show lower percentages of higher reflectivity bins with higher percentages

(particularly at higher altitudes) of lower reflectivity bins. With time, a line through the

maximum percentage at each altitude in these CFADs would change from vertically oriented to

negatively tilted with a shift toward lower reflectivity values.

2.4. CFDDs

Contoured-frequency-by-distance diagrams (CFDDs), developed for this study, are an

extension of the YH95 CFAD method. To create CFDDs, we used a rotated coordinate system.

13

Where the y-axis (distance of CFDD) was oriented parallel to the maximum RIJ horizontal wind

vector, the x-axis was oriented perpendicular to the y-axis, and z continued to represent height

AGL. A CFDD is a collection of histograms of a particular variable at each distance (y-axis

point) rearward from the leading edge of the anvil (defined by the mask) compiled into a single

contour plot. The data points composing a single histogram are all points within the mask region

lying in the x-z plane within a small range of y. To visualize the CFDD, we can think of the

analysis volume as a stick of butter, where the y-axis is along the long axis of the butter, and the

x-z plane is a pat of butter containing the data of one histogram (Fig. 2.3). To construct a CFDD,

we built histograms of a specific variable for each x-z slab. The y-width of the x-z slab (along

the y-axis) was chosen in this study to be 3 km for the model simulations, the minimum possible

considering the model grid spacing, and 1 km for the observations. To create the CFDD, the

histograms were assembled as a function of distance in a three-dimensional diagram. As with

the CFAD, looking down the z-axis and contouring the data as if it were a topographic map

produces a CFDD (Fig. 2.4). In the diagrams in this thesis, such as Fig. 2.4, the contour interval

was five percent beginning at one percent, unless otherwise noted.

To restrict our analysis to the RIJ and exclude higher wind speeds characteristic of the

upper atmosphere, the CFDDs presented herein used data only at and below 7 km (which

remained below the strongest front-to-rear squall-line-relative flow in the observed and

simulated MCS). Horizontally, CFDDs only included data within a swath 57 km wide (typically

the width of our model RIJ) centered on the maximum RIJ wind vector. Binning of data was the

same as with CFADs (ΔZ = 5 dBZ and ΔV = 1 m/s). Frequencies at a given distance add up to

one hundred percent as was the case with CFADs when accounting for the null values. CFDD

fields included radar reflectivity (observed and simulated), absolute wind speed, squall-line-

14

Fig. 2.3. Conceptual model of how to build a contoured-frequency-by-distance diagram (CFDD). The volume defined by the larger rectangular prism was the total volume encompassed by the CFDD. The long axis of the rectangular prism was defined parallel to the maximum RIJ wind vector. Note the rotation of the Cartesian coordinate system. The x-dimension of the CFDD volume was chosen to be 57 km. The z-dimension of the CFDD volume was chosen to be 7 km. The y-dimension of the CFDD volume changed depending on the size of the masked area. Each x-z slab (smaller rectangular prism) was 3 km along the y-dimension, consistent with model grid spacing.

15

Fig. 2.4. Contoured-frequency-by-distance diagram (CFDD) of squall-line-relative velocity parallel to the y-axis (m/s) from model simulation at 0712Z June 10. Y-axis begins ahead of the leading convective line and ends at the back edge of the stratiform region. Convection is located where the density of positive wind speeds drastically decreases. Frequency interval is 5% beginning at 1%.

16

relative wind speed, and the y-axis parallel component of both wind speed and squall-line-

relative wind speed.

To construct CFDDs of modeled fields, the local maximum RIJ wind vector was selected

from each horizontal level, and then the absolute maximum was picked from those local maxima

to define the y-axis of the CFDD volume. In the observational dataset, despite quality control,

there remained some false velocities on the edges of the sampled volume. Because these

erroneous data points could have been the maximum velocity from each altitude, selection of the

observed maximum RIJ wind vector was somewhat subjective.

To exclude precipitation areas from the CFADS within the masked area but outside the

MCS, a further step was necessary. Not only was it necessary to exclude extraneous

precipitation areas, but it was necessary to compare CFADs of observed and modeled fields on a

similarly sized domain. The observational domain was smaller than the model domain due to

constraints imposed by the quad-Doppler flight tracks. Because the model domain was larger

than the observational domain, differences in percentages from smaller phenomena may have

occurred in the larger model domain compared to the smaller observational domain where the

smaller phenomena may have been missing. Moreover, different fractions of each domain may

have been occupied by different regions of the MCS (i.e., trailing stratiform or convective line)

when the sizes of the domains were mismatched. When looking at reflectivity images from the

model compared to observations, the model captures a larger scale southerly transport of

stratiform precipitation particles which the observations did not see due to its smaller domain

size. This bias caused interpretation difficulties between the observed and modeled datasets. By

using the “stick of butter” domain taken from the CFDDs when computing a CFAD, data points

from other precipitating systems were excluded so that the volume of the MCS with an active

17

RIJ was isolated. This also makes interpretation of the CFADs consistent across the datasets and

even accounted for orientation differences between the observations and model. All previously

defined variables used for CFADs and CFDDs have been plotted using this method. Shading of

frequencies on these diagrams was by five percent starting at one percent as with CFADs. An

example of this type of diagram is shown in Fig. 2.5.

After making CFDDs, it was insightful to plot the average contributing altitude (with an

interval of Δz, where Δz = 1 km in this study) where a particular velocity value (binned as ΔV)

occurred as a function of distance from the leading edge of the anvil. These diagrams are called

average altitude per bin per distance diagrams and were constructed as follows. Consider a

histogram showing the frequency of velocities occurring within the x-z slab on Fig. 2.3. Within

an x-z slab, there may be a number of points occurring within a given velocity bin ΔV that

originate from different altitudes within the slab, making interpretation of the data somewhat

ambiguous. There may also be data points in one bin (ΔV) on the histogram composed primarily

of data from a low altitude while most data points in an adjacent bin (ΔV ± 1) may originate

from a high altitude. A plot of the average altitude for each bin of the histogram allows one to

determine the altitude range that contributes most to the bin. This method is extended to the

entire CFDD by plotting the average altitudes from all x-z slabs on a single diagram (Fig. 2.6).

18

Fig. 2.5. Contoured-frequency-by-altitude diagram (CFAD) of simulated radar reflectivity within contoured-frequency-by-distance diagram (CFDD) area. Frequency interval is 5% beginning at 1%. Note the difference in vertical extent of this CFAD versus the masked CFAD.

19

Fig. 2.6. Same as Fig. 2.4. except average altitude per bin per distance diagram.

20

CHAPTER 3

COMPARISONS USING CFADS

3.1. Masked CFADs

CFADs were produced for the model simulations and the observations just prior to,

during, and after bowing segments occurred. These diagrams compare statistically the

distributions of modeled and observed fields. Model CFADs were constructed for 12 times:

0412, 0430, 0448, 0515, 0542, 0600, 0618, 0636, 0654, 0712, 0748, and 0815Z. These times

were selected because a consistent RIJ region was maintained on the CFDDs (i.e., maximum RIJ

wind remained quasi-stationary with respect to the convective line, with only slight orientation

changes) and nearly steady state CFADs and CFDDs were seen. Times processed from the

observations included 0430, 0450, 0510, 0540, 0610, 0630, 0650, and 0750Z. Observation time

selection depended on the proximity of the two airborne radar systems and sufficiently straight

flight legs for quad-Doppler synthesis. When the NOAA P-3 performed microphysical spirals,

data were not available for analysis as the plane’s heading changed so rapidly. In this chapter,

comparisons of radar reflectivity and wind speeds from the model and observations used masked

CFADs, with the goal of identifying similarities and differences in the systems’

reflectivity/precipitation structures.

The observed data were only available on a small sub-section of the MCS as sampling of

the system was performed with airborne radars that could not view the entire system at one time.

The model, comparatively, contained the whole MCS. Comparisons of model and observations

using the frequencies on a masked CFAD were difficult to interpret, since the domain sizes were

different. For this purpose, we therefore focused on RIJ-centered CFADs for statistical

21

comparisons of distributions for reflectivity and RIJ-parallel, squall-line-relative wind speeds. In

this way, we can compare CFADS from each dataset.

We focus first on masked CFADs of simulated reflectivity (Fig. 3.1) over the entire

model domain within the maximum reflectivity mask (Fig. 3.2), at the model analysis times

listed in Chapter 2. In Fig. 3.1, we see that the maximum frequency of simulated radar

reflectivity at 1 km remained in the same radar reflectivity bin (35-40 dBZ) throughout the

analysis period. Tokay and Short (1996) showed that almost all of the precipitation in tropical

MCSs observed during TOGA-COARE (Tropical Oceans Global Atmosphere – Coupled Ocean

Atmosphere Response Experiment) with reflectivity values above 40 dBZ fell from convective

clouds. In addition, five percent of the stratiform precipitation from Tokay and Short’s TOGA-

COARE cases had reflectivity values above 36 dBZ. Because of the small percentage of

stratiform precipitation particles with reflectivities above 36 dBZ, we will consider all

reflectivity values above 35 dBZ to be convective. The radar reflectivity of an intercepted

volume of precipitation is given by

∫= dDDDNZ 6)( (1.1)

where N(D) is the number distribution function of precipitation particles with maximum

dimension D. In Fig. 3.1, as one travels vertically upward from the surface, the frequency of

convective-dominant precipitation areas, defined as > 35 dBZ radar reflectivity, decreases to

below one percent above approximately 9.5 - 10 km at all analysis times, showing a vertical

transition to mixed-type (stratiform and convective) precipitation. The manifestation of this

transition from convective-dominant precipitation particles to mixed-type precipitation particles

in a CFAD is a negative tilting of the maximum frequency axis at higher altitudes. Over time,

the maximum frequency axis can change showing a temporal transition of the precipitation mode

22

Fig. 3.1. Temporal evolution of masked CFADs of simulated radar reflectivity binned in 5 dBZ intervals. Frequency interval is 2% beginning at 1%.

23

Fig. 3.2. Temporal evolution of model RIJ-centered CFAD locations (thin black box) overlaid on reflectivity at 3.5km. Thin black outline around reflectivity pattern indicates maximum reflectivity in a column mask. The short dimension of the RIJ-centered box is always 57km, with the longer dimension varying with time, depending on mask outline.

24

(from convective-dominant to mixed-type). Careful comparison of the panels in Fig. 3.1 shows

that the whole system became more stratiform as the frequency distributions shifted toward

smaller radar reflectivity values (to the left on progressive CFADs in Fig. 3.1), and the maximum

frequency axis tilted more negatively with time (representing a reduction in the height to which

the convective region penetrated.

Since the model CFAD domain was larger than the observational domain (compare Figs.

3.2 and 3.3, noting the scales on the axes) and, in terms of the MCS size, included the

observational domain, it was only possible to compare the general trend or slope of the frequency

maxima in the CFADs, but not the actual frequencies. The maximum frequency at 1 km in the

observed reflectivity CFADs (Fig. 3.4) varied temporally between 20-25 dBZ and 35-40 dBZ, so

that the observed reflectivity frequency maxima were less than the simulated reflectivity

frequency maxima at all times. Over-prediction of simulated reflectivities consistently occurred

in the model fields as has been noted by other authors simulating tropical cyclones (McFarquhar

et al., 2006 and Rogers et al., 2007). The observed > 35 dBZ reflectivity values (convective-

dominant precipitation) at all analysis times reached higher altitudes (14.0 km) than in the

simulations (11.5 km). Higher reflectivity values at higher altitudes may be attributed to stronger

vertical velocities in the real atmosphere, insufficient vertical resolution in the upper reaches of

the model domain, updraft intensity dependence on horizontal resolution (Weisman et al., 1997

and Bryan et al., 2003), and/or an upshear tilt of the simulated convection which decreased

raindrop collection efficiencies, as noted by Ferrier et al., (1996).

The slope of the frequency maxima in reflectivity was less negative (more vertical) in the

observations (Fig. 3.4) than in the simulations (Fig. 3.1) at low and middle altitudes (< 10 km),

but changed to more negative (more horizontal) in the high altitudes (≥ 10 km). This makes the

25

Fig. 3.3. Temporal evolution of observed RIJ-centered CFAD locations (thin black box) overlaid on reflectivity at 3.5km altitude with ground-relative wind barbs (kts). The short dimension (generally oriented SW to NE) of the RIJ-centered box is always 57km, with the longer dimension varying with time, depending on mask outline.

26

Fig. 3.4. Temporal evolution of masked CFAD of observed radar reflectivity binned in 5 dBZ intervals. Frequency interval is 2% beginning at 1%.

27

average slope approximately the same with a slight negative bias in the simulations because of

the under-predicted heights of the convective reflectivity values. However, the instantaneous

slope of each can vary dramatically from altitude to altitude. Because of the negative bias in the

simulations, these slope differences show the observations as more convective. This however

may be due to the domain differences.

The cumulative frequencies of simulated reflectivity greater than 0 dBZ at 1 km altitude

only accounted for 11-21% of the masked area at their maximum (0600 and 0636Z on Fig. 3.1),

excluding frequencies below 1% of the masked region as they are not plotted on CFADs (note

starting value of legend). This meant that between 11 and 21% of the masked region of the MCS

likely produced surface rainfall in the model. In the observations, the cumulative frequencies of

radar reflectivity greater than 0 dBZ at 1 km accounted for 65-87% of the masked area at their

maximum (0650Z on Fig. 3.4). This disparity may be partially due to domain size differences

and/or lack of color fill of areas smaller than 1% on masked CFADs, especially in the larger

domain of the model.

Below the melting level (located at ~3.5 – 4.0 km in the model and ~3.0 - 3.5 km in

observations), there were few bins with reflectivities less than 35 dBZ at 1 km that exceeded the

one percent threshold on the simulated reflectivity CFADs (Fig. 3.1). The time of greatest

cumulative frequency less than 35 dBZ at 1 km (0815Z) only covered 5-11% of the masked area.

None of the reflectivity bins between 5 and 30 dBZ at 1 km contained larger than 1%

frequencies. The time of greatest cumulative frequency at 1 km of observed reflectivity values

less than 35 dBZ (0610Z) accounted for 44-56% of the precipitation (Fig. 3.4).

The minimum in the simulated reflectivity CFADs (Fig. 3.1) below 3 km between 5 and

30 dBZ may be due to conversion of particles from sub-freezing to above freezing temperatures

28

in the microphysical parameterization, as the minimum began just below the melting level.

Other studies have suggested that microphysical parameterization may not be the cause of the

low-level simulated reflectivity deficiencies, but rather the boundary layer scheme (Smedsmo et

al.,, 2005). It is uncertain in this case, which of these schemes, if any, was the cause of the

deficiencies. Use of RIJ-centered CFADs will clarify the differences noted here, as the domain

sizes were not the same in this comparison.

Comparing Figs. 3.1 and 3.4, the width of the contoured region at each altitude above the

melting level greater than 0 dBZ reflectivity was consistently wider in the simulated MCS

compared to the observations. Since we cannot compare frequencies due to the domain size

mismatch, it was impossible to compare the amplitudes of these histograms until we looked at

RIJ-centered CFADs. Below the melting level, the model reflectivity distributions became bi-

modal as the reflectivities split into a convective-dominant precipitation mode and mixed-type

mode. Although the observed histograms widened, they never became bi-modal in the lowest 3

km.

3.2. RIJ-centered CFADs of Reflectivity

With RIJ-centered CFADs (Figs. 3.5 and 3.6), it is now possible to compare observed and

modeled frequencies, distribution widths, and the slopes of the frequency maxima because of

comparable domain sizes. On a RIJ-centered CFAD, the frequency interval was 5% beginning at

1%. The highest frequencies present on these CFADs in all times at 1 km occurred between 25

and 45 dBZ for the model (Fig. 3.5) and between 10 and 45 dBZ for the observations (Fig. 3.6).

The shape of the histograms at 1 km altitude from the model showed a long low-frequency tail in

the lower reflectivity values (< 30 dBZ reflectivity), a relatively high frequency in the higher

29

Fig. 3.5. Temporal evolution of RIJ-centered CFAD of simulated radar reflectivity binned at 5 dBZ intervals. Frequency interval is 5% beginning at 1%. Area encompassed in this CFAD is located on corresponding panels on Fig. 3.2.

30

Fig. 3.6. Temporal evolution of RIJ-centered CFAD of observed radar reflectivity binned at 5 dBZ intervals. Frequency interval is 5% beginning at 1%. Area encompassed in this CFAD is located on corresponding panels on Fig. 3.3.

31

reflectivities (> 30 dBZ reflectivity), and a sudden drop off to the right of the convective

frequency peak. This, along with the highest frequencies of 1 km reflectivities from each

dataset, suggested that the model was predicting a lower fraction of stratiform precipitation on

this smaller scale. In the observations (in which quality control often removed below 0 dBZ

reflectivity values), the frequencies climb more gradually to their peak and often have a slower

drop-off in the higher reflectivities making for a longer high reflectivity tail. Despite generally

showing the same maximum reflectivity on these CFADs, the peak frequencies in the

observations often have a lower frequency than the simulations as the longer length (thus greater

horizontal area) of the RIJ-centered box in the CFADs showed lower frequencies. The

convective line would have to take up a much greater area of the RIJ-centered box to account for

the greater frequencies. A change in the orientation of the RIJ-centered box or a bowing in the

convective line can alter the frequencies of convective reflectivities due to non-normal

orientation to the convective line. Verifying this is easy with a check of the box orientation to the

convective line (Figs. 3.2 and 3.3). The simulations consistently over-predicted the frequency of

higher reflectivity values below the melting level altitude, possibly due to assumptions about

conversion from ice crystals to liquid droplets in the model microphysics. At the surface, these

reflectivity values and frequencies may be shifted due to evaporation, collisions, coalescence,

and breakup of precipitation-sized particles.

The changes in the frequency of > 35 dBZ reflectivity values with height discussed with

masked CFADs were not evident on RIJ-centered CFADs, since a vertical limit was imposed to

exclude altitudes that may alter the wind statistics by including synoptic scale flows instead of

just the mesoscale flow patterns associated with the RIJ.

32

In the observed reflectivity RIJ-centered CFADs (Fig. 3.6), the temporal fluctuations of

the maximum frequency axis below the melting level implied a rapid evolution of the MCS and a

change in the amount or shape of the convection. This became most evident with close

comparison of observed reflectivities on Fig. 3.3, where a bowing segment formed around

0510Z, after which the gust front pushed out from below the main convective line between 0630

and 0650Z. The maximum frequency axis of simulated reflectivity CFADs (Fig. 3.5) remained

nearly steady state at 35-40 dBZ throughout the analysis times, suggesting little transition to

post-bowing stages, consistent with Fig. 3.2, which showed consistent reflectivity structure in the

RIJ-centered box, particularly after 0515Z. The model simulation showed a nearly steady state,

with relatively few bowing events, and certainly no gust front surging out ahead of the line as in

the observations.

The maximum frequency on each RIJ-centered CFAD of reflectivity, in either dataset,

seemed to cycle with height and frequency over time giving the perception of multiple

convective updraft pulses. The maximum frequency in all RIJ-centered CFADs (model and

observations) was above the melting level, between 0430Z and 0750Z. In the model (Fig. 3.5),

there were three convective upward pulses, with some of the frequency change between 0636 to

0654Z occurring because the orientation of the RIJ-centered box became less normal to the

convective line, thus including more of the convective region in the CFAD. The peaks of the

convective pulses appeared on RIJ-centered CFADs at 0515, 0654, and 0748Z (Fig. 3.5), which

resulted in an average period of 71 minutes.

Observations from 0430 and 0450Z covered small areas as seen in Fig. 3.3, accounting

for a smaller subsection of the MCS than the other observational analyses. This could have

artificially increased the maximum frequency as the percentage of the area containing 25-30 dBZ

33

reflectivity increased, while the physical area containing 25-30 dBZ reflectivities did not change

significantly. This could have contributed to the appearance of convective pulses simply by

having a smaller analysis area. In the observations (Fig. 3.6), there were likely two convective

pulses one at 0450 and the other at 0610Z. The period of these pulses was 80 minutes. With the

large time interval (> 20 min) between each analysis time, it was possible that documentation of

convective pulses from either dataset was incomplete, making pulses appear to have a longer

period. Without a larger sample population, convective updraft periods presented from the

model and observations are the best guesses possible from the data.

The maximum frequency (51-56%) on the model RIJ-centered CFADs (Fig. 3.5) occurred

in the 35-40 dBZ simulated reflectivity bin. This occurred in two consecutive analysis times:

0748 and 0815Z. In the observations (Fig. 3.6), the maximum frequency is 56-61% and falls in

the 25-30 dBZ bin at 0450Z. However, because of the aforementioned artificial increases in

frequency from the size of the observed area, it is possible 0610Z could have been the time of

maximum frequency with a peak of 51-56% within the 20-25 dBZ reflectivity bin. The peak

frequencies, for analysis purposes, are considered the same between datasets. The difference in

the reflectivity bin of the peak frequency shows that even on a similar domain, the most

frequently occurring reflectivity value was over-predicted in the model compared to the

observations. Comparing either of the times where the model showed its peak frequency, the

model predicted a peak frequency at a lower altitude (5.5 to 6.0 km) than the observed peak (7.0

to 7.5 km). This may have been due to stronger updrafts in the observations or comparing

different times within the convective pulses.

The trend in the maximum frequency of the observed reflectivity below the melting level

(Fig. 3.6, below 3.0 – 3.5 km) showed a vertically oriented maximum frequency axis or a slight

34

negative slope. As one approaches the melting level from below, the maximum frequency axis

becomes positively sloped within 0.5 – 1.0 km. This is one of few areas on observed RIJ-

centered reflectivity CFADs that had a positive slope. In the positively sloped area, this

suggested acceleration of the terminal velocity over a 0.5 – 1.0 km depth (e.g., Fig. 3.6 at 0610

and 0630Z). Above the melting level, the slope of the maximum frequency axis changed to

negative once again for the remainder of the diagram, initially consistent with a change in the

dielectric constant between ice crystals and liquid water droplets as the reflectivity values only

decreased by 5-10 dBZ in all cases through the bright band. This is consistent with the expected

7 dBZ shift from a change in the dielectric constant (Smith 1986). In the observations, the bright

band is visible on radar scans, but it is difficult to locate on RIJ-centered CFADs, as the

reflectivity change is often smaller than the bin size chosen for our analysis. Farther aloft, the

negative slope of the maximum frequency was due to the height of convective penetration and

the decreased size of the precipitation particles with height.

In the model output, the maximum frequency axis of reflectivity below the melting level

(3.5 – 4.0 km) remained constant with height, except for 0515, 0712, and 0815Z where

maximum frequencies shift ± 5 dBZ over 0.5 km. Half a kilometer below the modeled melting

level, the slope of the maximum frequency axis became positive over 0.5 km. Above the melting

level, all the simulated reflectivity RIJ-centered CFADs indicate a vertical maximum frequency

axis or a vertical axis changing to a slight negative slope in the highest altitude plotted (7 km).

In the simulated reflectivity calculation from the plotting package, there is a correction for ice

particles scattering radiation as if they had a liquid water skin (i.e., melting ice) near the melting

level, so there should be a bright band in the reflectivity pattern. The simulations did not seem to

show a difference in reflectivity based on the scattering differences, but the aforementioned over-

35

prediction of reflectivity values may have over-shadowed this phenomenon, as it is not present in

simulated reflectivity images or clearly defined in reflectivity CFADs.

At the surface, the cumulative percentage of reflectivity values below 35 dBZ varied

dramatically between the model and observations. As was the case with masked CFADs (Figs.

3.1 and 3.4), even at its maximum cumulative percentage, the model RIJ-centered CFAD

contained a smaller percentage of area with reflectivity below 35 dBZ at 1 km (31-61% at

0815Z; Fig. 3.5) than the observed RIJ-centered CFAD at 1 km (81-100% at 0630Z; Fig. 3.6).

More importantly from the same CFADs, 27-37% of the model domain contained convective-

dominant precipitation, while the observations only yielded 7-17% of points containing

convective-dominant precipitation. The model RIJ-centered box had a longer along-RIJ axis

than the observations, thus an even larger area covered with > 35 dBZ reflectivity to account for

such high percentages, yet the RIJ-centered CFADs suggested once again that the model is over-

predicting the percentage of area with higher reflectivity values.

3.3. RIJ-centered CFADs of Y-axis-parallel Squall-line-relative Wind Speeds

To compare the location and intensity of the RIJs, it was insightful to plot y-axis-parallel

squall-line-relative winds from both datasets. These diagrams portray vertical variation in wind

speeds. In Fig. 3.7 or Fig. 3.8, it is important to note that positive wind speeds were from the

rear of the system to the front of the system (rear-to-front flow) while negative wind speeds were

from the front of the system to the back of the system (front-to-rear flow).

To understand how a typical RIJ appears on a CFAD, we have produced an idealized

east-west oriented wind field. This field had a RIJ core (+30 ms-1) descending toward the

surface from the rear of the system to the front. Above the RIJ, there was a similar front-to-rear

36

Fig. 3.7. Temporal evolution of modeled RIJ-centered CFAD of y-axis-parallel line-relative wind speed binned at 1 ms-1. Frequency interval is 5% beginning at 1%. Area encompassed in this CFAD is located on corresponding panels on Fig. 3.2.

37

Fig. 3.8. Temporal evolution of observed RIJ-centered CFAD of y-axis-parallel line-relative wind speed binned at 1 ms-1. Frequency interval is 5% beginning at 1%. Area encompassed in this CFAD is located on corresponding panels on Fig. 3.3.

38

jet core (-30 ms-1) angled toward the rear of the system. A vertical cross section of the idealized

RIJ-parallel line-relative wind speed is shown in Fig. 3.9 with the corresponding RIJ-centered

CFAD in Fig. 3.10. In this idealized situation, one expects to find rear-to-front flow near the

surface, as was seen in Fig. 3.10. As one increases in altitude, the area of the rear-to-front flow

slowly shrinks, filling in with front-to-rear flow, yielding a mix between front-to-rear and rear-to-

front flow below 5 km, leaving solely front-to-rear flow above 5 km. The crossover region from

2.5 – 4.0 km contained contributions from both jets, resulting in the increased spread of

frequencies in that layer in Fig. 3.10. The small gaps (frequencies under 1%) in the frequencies

were due to sampling and the small ΔV = 1 ms-1 bin size for winds.

Low-level positive wind speeds (e.g., below 3 km) in either the model or observations

CFADs generally indicated a contribution from the low-level RIJ or from winds behind the

outflow boundary. It is impossible to separate these phenomena from each other on a CFAD.

The presence of an outflow boundary ahead of the convective line on CFADs is dependent on the

location of the RIJ-centered box. In the observations, the box was only far enough ahead of the

line to see this feature at 0540, 0610, and 0650Z. These times were the only times that showed

significant front-to-rear flow patterns at higher altitudes as the RIJ-centered box will be filled

more frequently by front-to-rear flow (mid-layer inflow) ahead of the convective line.

Winds in the lowest 1 km of observations were irretrievable, making a comparison of

surface winds impossible. From these observations alone, it was impossible to determine the

surface wind field, although the RIJ and gust front boundary likely influenced the wind field near

the surface. Thus, a comparison of the 1 km altitude wind data was conducted.

CFADs of y-axis-parallel squall-line-relative wind speed from the model (Fig. 3.7)

contained a temporal progression at 1 km from percentages less than 1% rear-to-front flow to

39

Fig. 3.9. Vertical cross-section of idealized RIJ-parallel line-relative wind speeds. Wind speeds are in ms-1 with solid contours being positive (rear-to-front) and dashed contours being negative (front-to-rear). The convective line of the system would be off the right side of the diagram.

40

Fig. 3.10. Idealized RIJ-centered CFAD of RIJ-parallel line-relative wind speed binned at 1 ms-1. Frequency interval is 5% beginning at 1%. Area encompassed in this CFAD is located on Fig. 3.9.

41

increasing percentages of rear-to-front flow until 0636Z when the cumulative percentages

decreased to 2-12% at 1 km. Stated differently, the area that was rear-to-front flow only

accounted for 2-12% of the area at 1 km. After 0654Z, the positive trend in cumulative

percentages at 1 km resumed. On the contrary, the observed system (Fig. 3.8) maintained 1 km

altitude rear-to-front flow with a positive trend in cumulative frequencies up to 0630Z where the

cumulative frequencies declined slightly. The cumulative percentages artificially declined at this

time as the RIJ-centered box did not extend ahead of the convective line where rear-to-front flow

may have occurred behind the outflow boundary. At 0650Z, the cumulative percentages of rear-

to-front flow reached their maximum at 1 km. After this time, another decline occurred as the

convective line was not within the RIJ-centered box. The rear-to-front flow varied from being 2-

12% of the RIJ-centered box area to 9-54% at its peak cumulative percentage, and never dropped

below 1%. The cumulative percentage of rear-to-front flow in the model at 1 km rarely exceeded

the cumulative percentage of front-to-rear flow. The same was true in the observations, except

the cumulative percentage of rear-to-front flow never exceeded its front-to-rear counterpart.

The most significant finding from these diagrams is associated with the low-level rear-to-

front flow. In the observations, the wind field CFADs suggested three times in which an outflow

boundary or relatively strong RIJ reached down to 1 km above the surface (0540, 0610, and

0650Z). A plan-view of the 1 km observed reflectivity (contoured) with squall-line-relative wind

barbs is provided for 0610Z in Fig. 3.11 to show the rear-to-front flow. At all other times, the

RIJ-centered box did not extend ahead of the leading convective line, making y-axis-parallel

squall-line-relative wind speed contributions from an outflow boundary to the CFAD impossible.

Since the prominent rear-to-front ‘nose’ in the observation CFADs at 1 km was absent at these

other times, we interpret this to mean that the RIJ had not descended to lower levels at those

42

Fig. 3.11. Plan view of observed reflectivity (contoured; dBZ) and squall-line-relative wind barbs (kts) at 1 km from 0610Z. Included is the RIJ-centered box (thin black outline).

43

times and the only contributions made during 0540, 0610, and 0650Z may have come from pre-

convective line activity. This however, is only speculative. The location of these stronger rear-

to-front winds was indeterminable from a CFAD, but can be determined from CFDDs as shown

in Chapter 4 when the convective-line-relative location of these maxima is derived. By

comparison, the model CFADs never showed the occurrence of faster rear-to-front wind speeds

at low-levels. This suggested that the model may have a weaker cold pool, stronger vertical

wind shear keeping the outflow boundary vertically aligned with the convective towers, or a RIJ

that was not as low in altitude or as fast in y-axis-parallel squall-line-relative wind speed as the

observations, suggesting a possible problem in the treatment of the planetary boundary layer.

Below the melting level, aside from the aforementioned missing low-level rear-to-front

flow in the model, comparisons of the model and observation CFADs show good quantitative

correspondence. From the RIJ-centered CFADs where frequencies are greater than 1%, the

maximum and minimum absolute values of y-axis-parallel squall-line-relative winds at each

altitude are similar in magnitude, not varying more than 3 or 4 ms-1 between datasets.

Meanwhile, above the melting level, the datasets’ absolute maxima and minima diverge.

Using only the locations on RIJ-centered CFADs where the frequency of occurrence was

greater than 1%, the model over-predicted the absolute maximum wind speeds at most levels,

with the largest disagreement at or near the melting level (as much as 10 ms-1 greater in the

model fields). However, the absolute minimum was predicted well (within 3 or 4 ms-1) near the

melting level, with the greatest discrepancies 2.0 – 3.0 km above the melting level (9 to 10 ms-1)

again biased toward model over-prediction of the absolute wind speed. It is not clear from a

CFAD whether it was the magnitude or the direction of the winds that caused the absolute

magnitude differences. The model may have artificially enlarged the mesoscale phenomena due

44

to too large (relative to the radar) grid spacing to properly resolve the smaller phenomena. The

model RIJ-centered box was longer in the y-dimension (along RIJ) making the populations at

each altitude larger, which would enlarge the area required to be represented on a CFAD. This

means that there would need to be a larger number of points in any given ΔV bin to produce a

statistical representation on a CFAD. As there are larger absolute maxima, there are also larger

samples of those faster absolute wind speeds since their representation appeared on CFADs.

Another possible reason for the over-prediction of wind speeds was an improper squall line

motion vector from the model, causing the storm motion calculations to contain a bias solely

from “poor” selection of a squall line motion vector. The manifestation of this in the model

CFADs is the orientation of the RIJ-centered box, which determines the y-axis-parallel wind

speeds.

CFADs have provided useful statistics for comparison of modeled and observed fields.

CFADs showed that the model over-predicted radar reflectivity below the melting level and y-

axis-parallel squall-line-relative wind speeds above the melting level. It was also noted that the

model did not produce an outflow boundary ahead of the convective line or a strong RIJ at the

surface. Although CFADs hold great value in summarizing the vertical profiles of variables, they

were not designed to study phenomena that show strong gradients in their horizontal dimension.

Another statistical method is required for analysis in this direction: contoured-frequency-by-

distance diagrams. In the next chapter, we discuss our use of CFDDs.

45

CHAPTER 4

COMPARISONS USING CFDDS

4.1. Contoured-Frequency-by-Distance Diagrams

CFDDs were produced for the model simulations and the observations at similar stages

(just prior to, during, and after bowing segments occurred) of the MCS’s evolution. The purpose

of these diagrams was to compare statistically the horizontal distributions of modeled and

observed fields. Model CFDDs were constructed for 12 times: 0412, 0430, 0448, 0515, 0542,

0600, 0618, 0636, 0654, 0712, 0748, and 0815Z. Model times selected maintained a consistent

RIJ region from the maximum RIJ wind below 5km, which produced nearly steady state CFDDs

over time. Times processed from the observations included 0430, 0450, 0510, 0540, 0610, 0630,

0650, and 0750Z. Observation time selection depended on the proximity of the two airborne

radar systems and sufficiently straight flight legs for quad-Doppler synthesis. When the NOAA

P-3 performed microphysical spirals, data were not available for analysis as the plane’s heading

was changing so rapidly. Herein, comparisons of y-axis-parallel squall-line-relative wind speed

from the model and observations used CFDDs made to characterize similarities and differences

in the systems’ kinematic structures specifically with respect to the RIJ.

Care must be used when interpreting CFDDs presented in this chapter as the distance

covered along the y-axis varies, sometimes dramatically, between the model and the

observations. On a CFDD, be it model or observations, a dot-dashed black horizontal line

indicates the location of the convective-line reflectivity maximum, as in Figs. 4.1 and 4.2. If

there is no black line on the diagram, the convective line reflectivity maximum is off the bottom

of the diagram, as in observational analyses from 0430 and 0450Z. Also indicated is a standard

46

Fig. 4.1. Contoured-frequency-by-distance diagram (CFDD) of y-axis-parallel squall-line-relative wind speeds from the model simulation. Frequencies colored according to the legend. Time of each panel indicated in top right corner of each panel. Distance defined in kilometers. Wind speeds are ms-1, with 0 ms-1 indicated with the vertical black dashed line. Note the change in y-axis distances when viewing each panel. The dot-dashed horizontal black line indicates the location of the convective line (identified by the maximum reflectivity).

47

Fig. 4.2. Same as Fig. 4.1, except data are from observations. Where no dot-dashed horizontal black line occurs, the convective line is not located within the RIJ-centered box and occurs below zero kilometers distance on the diagram.

48

horizontal distance of twenty-five kilometers to depict similar length scales on each diagram.

CFDDs from the model spanned the entire width of the MCS, while observation CFDDs spanned

the entirety of the observations at most, with CFDDs for most analysis times not reaching the

back edge of the stratiform region. Thus, the region best suited for comparing observed and

modeled CFDDs was adjacent to and within the convective line, where the most consistent

retrieval of observations occurred. For discussion purposes, the volume was split into regions

ahead of and behind the convective line.

CFDDs show different phenomena that we will focus on. We will discuss the

significance of these diagrams referring to the clustering of points, histogram ranges at a given

distance, absolute maximum wind speeds, discrete “streaks” of consistent wind speeds, and their

temporal evolution. For reference, the CFDD from the idealized rear-to-front/front-to-rear flow

example (Fig. 3.8) from the previous chapter has been included here as Fig. 4.3. On Fig. 4.3,

positive wind speeds are rear-to-front and negative wind speeds are front-to-rear flow.

On CFDDs of y-axis-parallel squall-line-relative wind speed, the density or clustering of

positive or negative velocities at any given distance revealed similar y-axis-parallel squall-line-

relative wind speeds with little variation in winds. It is uncertain from these diagrams whether

wide distributions were an effect of friction near the surface, a vertically deep, contiguous low-

level jet, a stable atmosphere conducive of minimal mixing, or another mesoscale phenomenon.

A loose grouping (low density of points) represents a distance including varying y-axis-parallel

squall-line-relative wind speeds that have variable winds. Ahead of the convective line in the

simulated field (Fig. 4.1), the CFDDs for all times showed a distinct clustering of rear-to-front

flow (V ranges between 1 and 21 ms-1), which widened approaching the convective line. With

time, the widening lessened with approach to the convective line, suggesting the rear-to-front

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Fig. 4.3. CFDD of idealized rear-to-front/front-to-rear flow pattern shown in Fig. 3.8.

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flow ahead of the line became more organized. The front-to-rear flow ahead of the convective

line consistently showed a varying wind field (V ranges between -19 and -26 ms-1). In the

observations ahead of the convective line (Fig. 4.2), CFDDs contained a relatively wide

distribution of rear-to-front flow (V ranges between 8 and 21 ms-1) as well as a generally

clustered distribution (V ranges between 1 and 25 ms-1) of front-to-rear flow, likely due to a

small population size per distance.

The density pattern may be reversed between the model and observations because the

model grid spacing may not be small enough to resolve some of the smaller phenomena causing

variations in the wind field. In addition, the planetary boundary layer parameterization may be

over-mixing the atmosphere leading to homogeneity.

Modeled front-to-rear flow did not show large changes in histogram ranges from ahead of

to behind the convective line (1-26 ms-1 and 1-31 ms-1, respectively), meaning there was some

consistency between winds ahead of and behind the convective line. This, however, may have

depicted winds from different altitudes that coincidentally have similar histogram widths and

were centered in approximately the same velocity bin. Use of average altitude per bin per

distance diagrams aid in the interpretation of this change from ahead of to behind the convective

line. Significant widening of the rear-to-front flow distributions occurred across the convective

line in both the model and observations as shown by visual inspection of CFDDs. Behind the

convective line in the simulations, all CFDDs showed generally wide distributions with

histogram ranges from 4 to 31 ms-1 for rear-to-front and 1 to 31 ms-1 for front-to-rear flows.

The changes from ahead of to behind the convective line were dramatic. Although

histogram ranges are relatively consistent, the mean velocity with distance behind the convective

line was approximately 12 ms-1 and approximately 22 ms-1 ahead of the convective line in the

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model. This shift in mean velocity was also present in the observations, where there were

retrieved data points ahead of the convective line, but with a smaller shift from front to rear (-19

ms-1 to -11 ms-1, respectively). What may have occurred though was that the winds ahead of the

line were from low altitudes and the winds behind the line were high altitudes. This could easily

have accounted for a change horizontally through a rear-to-front/front-to-rear couplet. Yet,

without the aid of average altitude per bin per distance diagrams, it was difficult to evaluate the

height from which each velocity bin got its frequencies. Thus, one could not tell whether the

rear-to-front flow ahead of the convective line was at the surface or farther aloft, making

interpretation more complex. A number of physical phenomena might have caused the changes

from ahead of to behind the convective line. The model may not have resolved the smaller scale

variations present, it may be over-mixing the atmosphere, or the winds may have been influenced

by the presence of the convection causing divergence from the convective line even in the mid-

levels.

Moving toward the rear edge of the stratiform region, the winds adjusted to consistent

frequency clusters or single “streaks” of consistent wind speeds. In the model, these lines start

occurring just behind the stratiform precipitation area at each given level extending to the back

of the mask. In the observations, there is only a hint of this at 0540, 0610, 0630, and 650Z. The

distance covered before the lines orient toward the back of the system changes between each

observation time, but is approximately 30 km behind the convective line. In the model, the

streaks of consistent wind speeds do not form until much farther back, around 80 km from the

convective line. This difference of almost three fold suggested resolution problems in the model

because of the 3 km grid spacing. This could however have been due to a stronger component of

the winds rearward in the model, which transported particles farther backward creating a larger

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stratiform rain region, because the front-to-rear flow in and behind the convective line of the

simulations was approximately twice as fast. Yet, the highest altitude included in a CFDD is

7km, well below where the greatest transport of ice crystals would occur. It may also be possible

that the “streaks” of consistent wind speeds were not yet discrete in the observations. One final

possibility is that the RIJ-centered box was oriented more oblique to the convective line, making

the stratiform region appear wider, which was quite evident when looking at the RIJ-centered

boxes in Figs. 3.2 and 3.3, especially comparing 0654Z from the model (Fig. 3.2) with 0650Z

from the observations (Fig. 3.3). Since the stratiform precipitation area sloped rearward with

height, the streaks that became discrete closer to the convective line are closer to the surface.

Confirmation of this comes with average altitude per bin per distance diagrams.

The speeds associated with the absolute maxima of each wind regime from each dataset

can be compared. In the model, the maximum rear-to-front wind speeds were behind the

convective line at 35 ms-1 compared to a maximum of 29 ms-1 in the observations. The

maximum front-to-rear wind speed behind the convective line in the model was -32 ms-1 while

their observational counterpart was -26 ms-1. As was the case with reflectivity, the absolute

maxima of y-axis-parallel RIJ-centered winds speeds in the model seemed to be over-predicted.

However, when comparing only similar widths of trailing stratiform, the observations often had

faster rear-to-front flows as the fastest rear-to-front flows in the model generally occurred at a

distance farther back in the stratiform region than the observations retrieved. On the other hand,

the front-to-rear flow in the model was greater in general, as the observations show only limited

amounts of front-to-rear flow behind the convective lines. Without a larger observational sample

size, comparisons of front-to-rear flow were not viable.

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A combination of the last two analyses produced an interesting result from the

simulations. The maximum rear-to-front flow behind the convective line at all times was

rearward from the first indications of discrete “streaks” of consistent wind speeds. These two

phenomena were not likely present at the same altitude, as the first indications of discrete

“streaks” are found in the front-to-rear flow, but the altitude was indeterminable from CFDDs.

There was no clear physical explanation for why this was occurring. Average altitude per bin per

distance diagrams make conclusions about these phenomena possible. In the observational

dataset, no definitive statements could be made about these phenomena aside from their location

with respect to each other, as the radar data did not extend far enough back in the system to

indicate the fastest absolute wind speeds. From the observations present, the locations of the

streaks and the maximum RIJ varied wildly with respect to each other.

Ahead of the convective line, the maximum rear-to-front flow in the model (35 ms-1) was

greater than the maximum rear-to-front flow in the observations (29 ms-1). In this case, the rear-

to-front flow in the model was over-predicted as the observational and model dataset maxima

were both within 20 km of the convective line. The front-to-rear flow maxima for the model and

observations are 33 ms-1 at 39 km ahead of the convective line and 27 ms-1 at 31 km ahead of the

convective line respectively. Coincidentally, the model over-predicted all the observed maxima

by 6 ms-1. This may be due to slightly different wind directions ahead of the convective line in

comparison to the observations. A vector more normal to the line may have been present.

It is interesting to note that the location of the rear-to-front flow maxima behind the

convective line in the model did not vary cyclically over time. This may have been an effect of

the RIJ-centered box changing orientation over time. Instead of a forward migration of the RIJ

maximum wind speed, the local maxima just behind the convective line increased in speed with

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time, indicating a local acceleration of winds with time in both datasets, with the caveat that the

absolute maximum RIJ wind speed in the observations was likely not sampled on a CFDD due to

sampling constraints. Again, it was unclear whether these winds were near the surface or aloft.

We will revisit this when talking about average altitude per bin per distance diagrams.

4.2. Average Altitude per Bin per Distance Diagrams

In a given y-axis-parallel squall-line-relative velocity bin on a CFDD, winds could have

been occurring at any altitude present in the volume. It was impossible to determine the altitude

of these winds. For this reason, average altitude per bin per distance diagrams (hereafter,

average altitude diagrams) are valuable. The same locations/patterns on a CFDD were plotted on

an average altitude diagram, but the mean altitude contributing to each velocity bin at each

distance from the front of the RIJ-centered box replaced frequencies. In this thesis, average

altitudes were colored in 1 km intervals starting at 0.5 km from the surface, with the surface as

its own color; in general, any altitude interval could be used. Since an average altitude was

calculated for velocity bins that contained frequencies (as seen on CFDDs), not all areas

amounting to less than 1% of the total RIJ-centered box area were assigned an average altitude.

Average altitude diagrams used the same velocity conventions as CFDDs.

Four patterns emerged from average altitude diagrams of wind speeds (in our case, y-

axis-parallel squall-line-relative) that may not be intuitive at first glance. Fig. 4.4 demonstrates

three of these possible patterns: the slope of the transition between front to rear and rear to front

flow, vertical wind shear, and horizontal wind shear. Fig. 4.5 shows each of these patterns from

the idealized case run in Chapter 3 (Fig. 3.8). The fifth pattern (not shown on Fig. 4.4) is an

acceleration of the wind speeds at a given altitude and distance, seen by comparing diagrams

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Fig. 4.4. Average altitude per bin per distance diagram demonstrating how to interpret information from the diagram about horizontal and vertical wind shear, and the slope of an interface. Colored asterisks indicate altitude intervals defined in the legend. All axes and dashed lines same as from CFDDs.

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Fig. 4.5. Average altitude per bin per distance diagram of idealized rear-to-front/front-to-rear flow pattern shown in Fig. 3.8.

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from different times. The remainder of this chapter is devoted to explanations of these patterns

portrayed in modeled and observed fields.

The pattern of a single altitude interval (single color of asterisk on Figs. 4.4, 4.5, 4.6, and

4.7) reveals a large amount of information. Considering temporal migration of the maximum RIJ

winds, it was best to define locations as a distance relative to the convective line, since the front

of the RIJ-centered box could change location and orientation to the convective line. For

example, on Fig. 4.6 at 0654Z, focusing on the altitude interval from 3.5 to 4.0 km (red

asterisks), moving rearward from the convective line, the flow began as front-to-rear and

transitioned to rear-to-front flow 153 km back from the front of the RIJ-centered box, or 36 km

behind the convective line. This change was likely due to the interface between front-to-

rear/rear-to-front flows with height. At higher altitudes, this transition occurred farther rearward

from the convective line. Between 4.5 and 5.0 km altitude (orange asterisks), the transition

occurs 186 km from the front of the RIJ-centered box, 69 km rearward of the convective line.

The closer together the flow interfaces are with height, the steeper the slope of the interface.

In the observations (Fig. 4.7), due to the constrained area where data were retrieved, it

was not possible to tell where the interface occurred at all altitudes for all times. The best

example of the slope of the interface was at 0630Z. At this time, the transition between front-to-

rear and rear-to-front flows occurred 39 - 51 km behind the convective line at 5.5 km and up.

Using the convective line as the origin and positive distance defined as distance ahead of the

convective line, the average slope of the observed interface was approximately -0.125 km

altitude per km horizontal distance. In the simulation, at 0748Z (similar time in MCS evolution)

the average slope of the front-to-rear/rear-to-front interface was -.048 km altitude per km

horizontal distance and occurred between 63 and 115 km behind the convective line. The slopes

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Fig. 4.6. Same as Fig. 4.1, except average altitude per bin per distance diagrams.

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Fig. 4.7. Same as Fig. 4.2, except average altitude per bin per distance diagrams.

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of the transitions were a factor of 2-3 different, suggesting possibly a grid spacing dependence to

the mismatch. However, these differences may have other explanations. The descent of the RIJ

was also dependent on microphysical and dynamical forcing. The forcing from the microphysics

or dynamics from the model compared to the observations was different. Comparisons of

observed and modeled vertical motions might shed some light on this hypothesis.

We could also compare the heights of the interface between rear-to-front and front-to-rear

flows between the model and the observations. In the observations from 0510 until 0630Z, the

interface between the two flow regimes was 1.5