iii
WRF SIMULATIONS OF A SEVERE SQUALL LINE: COMPARISONS AGAINST HIGHRESOLUTION 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.
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-
vi
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.
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.
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
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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 midlatitude 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 highresolution 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 highresolution 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 trihourly. 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 Z
= 5 dBZ and V = 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 twodimensional 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 (Z = 5 dBZ and V = 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-linerelative 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 z, where z = 1 km in this study) where a particular velocity value (binned as V)
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 V that
originate from different altitudes within the slab, making interpretation of the data somewhat
ambiguous. There may also be data points in one bin (V) on the histogram composed primarily
of data from a low altitude while most data points in an adjacent bin (V  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 TOGACOARE 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
6
ZN
(D
)D
dD
(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. (from convective-dominant
to mixed-type). Careful comparison of the panels in Fig. 3.1 shows that the whole system
24
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 (convectivedominant 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%.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
27
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
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
28
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 bimodal 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 RIJcentered 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 convectivedominant 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 overpredicting 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.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
38
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 V = 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 rearto-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 212% 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-tofront 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 preconvective line activity. This however, is only speculative. The location of these stronger rearto-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 V 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 yaxis-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-bydistance 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-linerelative 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-linerelative 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 lowlevel 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
49
Fig. 4.3. CFDD of idealized rear-to-front/front-to-rear flow pattern shown in Fig. 3.8.
50
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
51
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 midlevels.
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
52
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.
53
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 rearto-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
54
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, yaxis-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
55
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.
56
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.
57
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-torear/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-torear 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
58
Fig. 4.6. Same as Fig. 4.1, except average altitude per bin per distance diagrams.
59
Fig. 4.7. Same as Fig. 4.2, except average altitude per bin per distance diagrams.
60
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 to 2.0 km above ground. After 0630Z, the
interface had lowered to between 1.0 and 1.5 km above ground. In the model, the flow interface
descended over time, but only within the last time of the model analysis did it reach 1.5 to 2.0
km, where the observations generally had the interface located. The rear-to-front/front-to-rear
flow interface in the model was always higher than in the observations, suggesting a higher
altitude or less descended RIJ.
When different average altitude intervals occurred at a given distance, this inferred
vertical wind shear between the two altitudes (especially if the altitudes were adjacent) as noted
on Fig. 4.4 as “Vertical Shear.” There can also be vertical wind shear in a single altitude interval,
and this likely occurred, but our altitude interval (1 km) masked some of these possibilities. On
Fig. 4.6 (0430Z), each altitude interval showed discrete vertically aligned streaks in the rear of
the system at a single distance from the convection. At 390 km or 184 km rearward from the
convective line, moving from left to right across the diagram showed increasingly rear-to-front
flow with an increase in altitude. This was an example of vertical wind shear.
In plan views of modeled squall-line-relative wind vectors, there were few locations that
showed significant horizontal wind shear in a given x-z slab (not shown). Horizontal wind shear
61
can be seen by noting a change of wind speed with distance from the convective line (along the
RIJ-axis) at the same altitude. It was impossible however to tell directional from speed shear
(vertical or horizontal) using average altitude diagrams. For instance, at 0712Z on Fig. 4.6, the
0.5 and 1.0 km average altitudes (green asterisks) showed discrete lines in front-to-rear velocity
bins well behind the convective line (approximately 100 km to the back edge of the system). In
a purely y-axis-parallel sense, there was only speed shear, as the winds at each level were of the
same sign but different speeds. In a squall-line-relative sense though, there is directional and/or
speed shear, as the squall-line-relative winds could have been of different directions, different
speeds, or a combination of the two and maintained the same resultant velocity bins at each level
on the average altitude diagram. Average altitude diagrams must be interpreted in the squallline-relative sense to gain a physical understanding of the wind field.
Rotunno et al., (1988) extrapolated that a balance in the horizontal vorticity (vertical
shear) of the cold pool with the pre-storm low-level horizontal vorticity (vertical shear) governed
the verticality of the convective line, thus the longevity of the MCS. Here, we compared the
vertical shear present (from the horizontal components of the wind only) in given layers at given
distances with respect to the convective line by using an average altitude diagram. We used 15
km from the convective-line reflectivity maxima as our analysis location. This location was
close to the convection, but hopefully far enough from the convection to be outside of the
strongest convective downdrafts. Wind shear was calculated by subtracting the maximum and
minimum wind speeds in the lowest two kilometers (excluding the surface).
Wind shear
associated with only the rear-to-front and front-to-rear flows were used, as contributions from the
other regimes in the given locations would have been associated with phenomena not discussed
in Rotunno et al., (1988). At 0712Z (Fig. 4.6), 15 km behind the convective line in the lowest
62
2.0 km, excluding the surface (for comparison purposes), there were -8 ms-1 of vertical wind
shear from the rear-to-front flow. 15 km ahead of the convective line, there were 5 ms-1 of
vertical wind shear from front-to-rear flow. In the observations at a similar time in the evolution
of the MCS (0610Z on Fig. 4.7), the vertical shear associated with the rear-to-front flow 15 km
behind the convective line was -5 ms-1. While ahead of the convective line, there were 5 ms-1 of
vertical wind shear from the front-to-rear flow. In both datasets, there was significant front-torear flow behind the convective line indicative of the cold pool spreading out along the surface
forward as well as rearward.
By comparison, the modeled and observed vertical shears were similar, with an indication
that the model cold pool or RIJ near the surface produced more vertical shear than in the
observations. According to the average altitude diagrams from 15 km behind the convective line,
the model under-predicted the winds at 0.5 km, and over-predicted the winds at 2.0 km. It can be
inferred that the friction layer of the model was not properly modeled or the rear-to-front flow
penetrated closer to the surface in the observations. Since the contributions of the vertical
velocities are not included in the calculations, horizontal vorticity was not formally calculated.
Horizontal wind shear could be interpreted from average altitude diagrams by noting
velocity changes of a single altitude interval with distance behind the convective line (noted on
Fig. 4.4 as “Horizontal Shear between slabs at same altitude”). Also, where one average altitude
interval occurred in multiple velocity bins at a given distance, one could measure the difference
in wind speed between these velocity bins and find the horizontal wind shear present (Fig. 4.4;
“Horizontal Shear between slabs at same altitude”).
This however, cannot be accurately
determined in our work as our average altitude interval covered multiple heights of the system.
Either of these methods for finding velocity changes could lead to misidentification of the type
63
of change, as these were only average altitude contributions to a single velocity bin, and the
winds contributing to these bins could be located on opposite ends of the x-z slab. Horizontal
shear as noted above could appear as deformation, divergence, or vorticity, but it is impossible to
tell the difference between these three without careful review of plan-views and cross-sections of
the datasets. For this reason, a limited analysis was performed with this data.
To examine wind acceleration, one has to look at the evolution of the winds at similar
distances from the convective line on multiple diagrams. At the same distance, acceleration is
represented by increasing wind speeds at a given altitude. The reason for the acceleration cannot
be deduced. Acceleration could appear as an area of faster wind speeds translated through that
given area, or dynamical/microphysical changes could accelerate the winds locally. Over time
on Fig. 4.6, the maximum rear-to-front flow (assumed RIJ) progressed rearward. This may be
due to increased entrainment in the stratiform region while precipitation expanded rearward or
another local acceleration. This is especially telling when considering the altitude at which the
maximum RIJ wind speeds occurred in the model (6.5 – 7.0 km). With time though, the front to
rear clustering of the average altitude intervals at their respective maximum velocities began to
spread out along the distance axis, suggesting that the highest altitudes plotted here may be
representative of the larger scale flow, not the mesoscale. Lower altitudes were analyzed to
check for a translation of the maximum RIJ wind speeds. Even at 2.5 – 3.0 km, the maximum
RIJ wind speeds showed a trend toward rearward translation. The observations mimic this
action, but with a faster rearward progression, but only at altitudes of 6.0 km and below. Above
6.0 km, the shorter length scale of the observed RIJ-centered box limited the analysis of the
maximum RIJ wind speeds.
64
The maximum RIJ wind speed locations at 2.5 – 3.0 km were closer to the convective
line than the maximum RIJ winds at 6.5 – 7.0 km. This showed that the maximum RIJ wind
speeds were tilted downward with distance toward the convective line, suggesting descent of the
RIJ, albeit not to the surface. The observed average altitude diagrams (Fig. 4.7) maintained this
trend in downward tilt, with only slow rear-to-front wind speeds near the surface.
The most significant finding from these diagrams was the acceleration of rear-to-front
flow occurring at and below 2 km altitude. In both observations and the model, the rear-to-front
flow strengthened. In the model average altitude diagrams (Fig. 4.6) from 0412 until 0815Z,
there was an increase of wind speeds from 10 to 17 ms-1 at 1.5 - 2.0 km, and an increase of the
wind speeds between 0.5 and 1.0 km from -2 ms-1 to 13 ms-1. In the observations (Fig. 4.7) from
0510 to 0750Z, the 1.5 – 2.0 km altitudes varied from 11 to -10 ms-1 non-cyclically in rear-tofront wind speed, and at .5 to 1.0 km, wind speeds fluctuated between -5 to 12 ms-1, showing no
consistent pattern of increase or decrease between analysis times.
Each interval of average altitudes showed discrete bands on average altitude diagrams,
we refer to these bands as altitude streaks. Where there are nearly straight altitude streaks with
distance from the convective line, it was simple to find two separate streaks for the same altitude
interval. These streaks are an effect of the interval containing two altitudes. Occasionally, these
streaks straddle the zero velocity line, meaning the interface between front-to-rear and rear-tofront flow occurred between those two levels. This was evident on the average altitude diagrams
from 0636 and 0712Z in Fig. 4.6 as well as 0540 and 0630Z in Fig. 4.7.
The distance rearward from the convective line where each of these altitude streaks began
was coincident with the distance to the rear of the convection where the stratiform precipitation
ended at that level, found using Fig. 3.2 in conjunction with average altitude diagrams.
65
Additionally, the slope of the back edge of the stratiform precipitation can be interpreted from
the average altitudes. As one travels upward through the system, the stratiform precipitation area
should reach farther rearward from the convective line. This slope is demonstrated the same way
as the interface between the front-to-rear/rear-to-front winds.
In the observations, the back edge of the stratiform precipitation region was not visible
due to the limited sampling by the airborne radars. In the model though, the back edge of the
stratiform rain region near the surface (0.5 – 1.0 km) changes with time (42 km rearward shift),
but in a decidedly non-cyclic fashion. In the 2.5 - 3.0 km altitude range, the back edge of the
stratiform precipitation region varied only slightly more (46 km rearward shift), but showed a
strong rearward migration from 0654 to 0815Z.
Both of these altitude interval analyses suggested an expansion of the stratiform
precipitation region, but only a slightly faster migration aloft, which is unexpected since this is
much closer to where ice crystals would have been deposited from the divergence at the
torpopause in the convective updraft.
With average altitude diagrams, it became obvious that most of the front-to-rear flow
behind the convective line in either dataset came from the lower altitudes. In the front-to-rear
flow behind the convective line from observations (Fig. 4.7), the dominant altitude contributions
were from below 1 km altitude, with the model dataset (Fig. 4.6) showing dominant altitudes
below 2 km.
This suggested a generally higher altitude RIJ in the model than in the
observations, as the dominant altitude contributions in the front-to-rear flow were higher for the
model than the observations, likely meaning a thinner cold pool in the observations. As usual,
the observations may not have extended far enough behind the convective line to sample the bulk
of the stratiform region, so comparisons only applied in close proximity to the convective line.
66
CFDDs and average altitude diagrams could be used for a broad range of meteorological
phenomena. Using average altitude diagrams, we gleaned a diverse set of information including
the slope of the rear-to-front/front-to-rear flow interface, slope of the back edge of the trailing
stratiform region, expansion of the trailing stratiform region, horizontal and vertical wind shear,
rearward migration of the maximum RIJ y-axis-parallel squall-line-relative wind speed, and
accelerations at any given altitude over time. In several instances, CFDDs and average altitude
diagrams suggested a model resolution problem, as the simulations occasionally contained
distances up to 3 times greater in length than in the observed fields.
With the help of vertical velocity CFDDs, a field that we did not plot, one could extract
all the contributions to calculate horizontal vorticity values and compare model to observed
vorticity balances, to reinforce some of the points made in RKW Theory (Rotunno et al., 1988).
More information about the cold pool of a MCS and its relationship to the pre-storm
environmental vertical wind shear could result from this analysis. This may be useful as
calculating cold pool strength (perturbation temperatures) can be tough to quantify from an
observational dataset.
67
CHAPTER 5
CONCLUSIONS
5.1.
Conclusions
With a high-resolution observational dataset of an MCS obtained on 10 June 2003 during
the BAMEX field campaign and a similarly high-resolution WRF simulation of the same MCS,
an opportunity to compare statistical distributions of similar meteorological fields. Our intention
was to evaluate the model’s ability to simulate the 10 June system using previously developed
statistical methods and a newly devised method. Comparisons of CFADs and CFDDs using
modeled reflectivity and kinematics to those derived from airborne dual- and quad-Doppler radar
syntheses were used to quantify the simulated squall line morphology, rear-inflow jet evolution,
and bulk cloud properties in this storm system. Comparing these statistical diagrams one can
minimize errors associated with poor spatial and temporal collocation of the model and
observations.
CFADs were used to describe the vertical distributions of reflectivity and horizontal
velocities, ignoring their horizontal location behind the convective line of the MCS. Specific
comparisons conducted using CFADs included the frequencies of reflectivity values at given
altitudes, convective pulses, and the evolution of the frequencies of reflectivity values. In
CFADs masked to include only locations where the reflectivity was greater than 0 dBZ, it was
easily seen that the model over-predicted the frequency of reflectivities above 35 dBZ. In
particular, the model over-predicted the value of the reflectivity bin where the maximum
frequencies occurred. Below the melting level, the modeled reflectivity value of maximum
frequency at all analysis times fell within the range of 30-40 dBZ on masked CFADs, while in
68
the observations the maximum frequency varied from 20 to 40 dBZ. Even using RIJ-centered
CFADs, for which the observations and models have similar domain sizes, the model overpredicted the frequency of reflectivity values above 35 dBZ. In these RIJ-centered CFADs, the
reflectivities at which the peak occurrence frequencies occurred were similar for the model and
observations, but the peak frequencies were higher for the model. For example, frequencies as
high as 31-36% occurred in the model at 1 km, while in the observations the frequencies peaked
at 26-31%. This seemed initially like a similarity. However, closer inspection of the physical
areas that these two RIJ-centered boxes covered showed that the model CFADs covered longer
horizontal distances along their y-axis, meaning many more points were required to give the
same normalized frequency of occurrence as plotted in the CFADs. The peak frequency below 7
km from each dataset was the same, but the extended length of the model RIJ-centered box, still
indicated that there was more such reflectivity area in the model output.. Thus, not only was the
model over-predicting the frequencies of reflectivities > 35 dBZ, but it was also over-predicting
the area covered by them from both masked and RIJ-centered CFADs.
Another key finding was that a “hole” was produced below the melting level in the
masked CFADs of simulated reflectivity. This hole indicated that reflectivity frequencies fell to
below 1% in all the bins between 5 and 30 dBZ, in at least the lowest two kilometers of the
simulation. This suggested that there may be errors in the parameterization of microphysics or
other physical processes that caused the absence of such reflectivity values in the models, but not
in the observations for the 10 June 2003 squall line. The observed masked CFADs all contained
significant portions of their reflectivity structure within this 5 – 30 dBZ range, and sometimes the
peak observed frequencies occurred in this range.
69
The model, for all analysis times, over-predicted the value of the reflectivity bin that
contained the maximum frequency. Over-prediction of reflectivity values could come from
many different sources including: model microphysical parameterizations, tilting of the
convective towers, and/or under-prediction of vertical velocities due to vertical or horizontal grid
spacing. The vertical velocities associated with these convective updrafts were not analyzed, but
the height of the convective pulses was evident on the CFADs. Convective towers reached 2.5
km higher in the observations than in the model, suggesting that the vertical velocities in the
model were under-predicted.
This under-prediction may have resulted from vertical or
horizontal grid spacing or an over-prediction of precipitable mass in the simulated clouds.
Further analysis of the vertical velocities would help identify some of these uncertainties. In the
absence of any other forcing, stronger vertical velocities would be expected to produce greater
amounts of condensate and hence higher reflectivities. Thus, the combination of weaker
velocities and stronger reflectivity in the models compared to observations further suggests thaat
the parameterizations of microphysics in the model may not be accurately portraying what
occurs in nature.
The reflectivity CFADs, either masked or RIJ-centered, showed a rapidly evolving
system in the observations and a nearly steady state in the model, a stark contrast.
The best
example of this has already been stated, the value of the bin in which the maximum frequency
occurred. Over time, the observations showed a strong variation (20 dBZ), while the model
maximum frequency never changed over the analysis period.
Although the melting layer is not visible on average altitude diagrams of y-axis-parallel
squall-line-relative winds, important information can be gleaned from the location of the
transition between the rear-to-front and front-to-rear flow with respect to the melting layer. In
70
the observations, the transition between rear-to-front and front-to-rear flow occurred at generally
between 1.5 and 2.0 km above ground, eventually lowering to 1.0 to 1.5 km above ground. The
interface between these flow regimes was located between 1.0 and 2.0 km below the melting
level. In the model, the interface between the two flow regimes was located at 2.5 to 3.0 km
above ground, which was consistently located 0.5 to 1.0 km below the melting level.
CFADs were used to show the vertical variation of y-axis-parallel squall-line-relative
winds. The winds showed the same differences in evolution, with the model showing steady
state behavior and the observations more dynamic. In the observations at 1 km, the the presence
of RIJ winds or the winds behind an outlfow boundary are shown in all times where the RIJcentered box reaches ahead of the convective line. The winds at 1 km in the model did increase
speed over time, but at no point in the analysis times did it show a similar low-level “nose” from
the RIJ or outflow as seen in the observations. This may have been due to the model planetary
boundary layer scheme, a balance between the horizontal vorticity of the cold pool and the prestorm environment, a weaker cold pool, or a higher altitude RIJ in the model.
Below the melting layer, the observations and the model show very similar patterns of yaxis-parallel squall-line-relative wind speeds, aside from the aforementioned RIJ or outflow
boundary. Above the melting layer in the model, the absolute value of the wind speeds was overpredicted by the model at all levels. Possible explanations include a stronger RIJ at mid-levels in
the model, a non-descending RIJ in the model, horizontal grid spacing too large to simulate the
small scale motions occurring in the observations, and too large a pressure gradient in the model
accompanied by an over-prediction of the friction layer deceleration.
Over time, the below 2 km wind speeds in the model and observations increased directly
behind the convective line. The model showed a larger increase in rear-to-front flow over time
71
than the observed rear-to-front flow, suggesting that the model RIJ descending, the cold pool was
strengthening, or another unknown local acceleration was occurring.
CFDDs took all the advantages of CFADs and turned them on their side to portray
horizontal distributions instead of vertical distributions. CFDDs helped reinforce some of the
points made by CFADs, plus added a few more key points. CFDDs ignore the vertical variability
that CFADs were designed to capture. We designed CFDDs to show horizontal distributions of
horizontally varying phenomena, such as RIJs. CFDDs of y-axis-parallel squall-line-relative
winds were useful for diagnosing consistent streaks of velocities behind the convective line. The
distance behind the convective line where these discrete bands of velocity formed was nearly 3
times longer in the model than the observations. This may suggest the model grid spacing was
not small enough to properly resolve the winds on this scale or that the trailing stratiform region
in the model was wider also possibly due to horizontal and vertical grid spacing, or that the
orientation of the analysis domain (a function of the RIJ angle to the leading convective line)
differed between the model and the observations and influenced the statistics.
CFDDs of y-axis-parallel squall-line-relative velocities yield information about the
horizontal location where the over-prediction of wind speeds above the melting layer observed in
the CFADs originated. For the same behind line horizontal distance, observed CFDDs showed
faster rear-to-front wind speeds than the model predicted at most times. This suggests that the
fastest rear-to-front wind speeds present in the observations may be present below the melting
level and close to the convective line since the over-prediction of wind speeds in the model was
above the melting level. Another new analysis tool, average altitude per bin per distance
diagrams aided in our look at this phenomenon.
72
Average altitude per bin per distance diagrams show the average altitude which
contributies to the reflectivity frequencies greater than 1% on a CFDD. The interpretation of
these diagrams provides information about the horizontal and vertical shear, accelerations of
wind on a given level, and transitions between flow regimes. Not all of these attributions can be
made using data from the 10 June 2003 case analyzed, but because of the multiple different
pieces of information that can be gained through their use, average altitude per bin per distance
diagrams show great potential for future work on RIJs and other horizontally varying
phenomena.
Some of the fastest rear-to-front wind speeds present on average altitude diagrams are in
fact close to the convective line and below the melting level. This is consistent with the fact that
the observations contained a RIJ that descended closer to the surface and/or an outflow boundary
that pushed under the convective line, but not ahead of the convection.
When comparing the CFDDs of models and observations, it was noted that the consistent
streaks of wind speeds occurred at different distances from the convective line. With average
altitude diagrams, it was shown that the different streaks were actually different altitudes.
Further, the distance, with respect to the convective line, between the two different altitude
intervals helped derive the slope of the back edge of the stratiform precipitation. Slopes of the
back edge of the stratiform region were three fold different between the models and observations,
with the model having a more gradual slope. This again suggests that the horizontal resolution
was not fine enough in the model. In the model as noted on CFDDs, the maximum rear-to-front
winds were located behind where the consistent streaks of wind speeds occurred. Here it is
noted that these two phenomena were indeed occurring at different levels. The consistent streaks
closest to the convective line were from the lowest levels of the system, while the maximum RIJ
73
winds were noted at 6.5 – 7.0 km altitude. Both of these areas, where the lowest consistent
altitude streaks began and where the maximum RIJ winds occurred, migrated rearward over
time. The former suggests that the stratiform region of the storm was enlarging, although slowly,
while the latter suggests that the maximum RIJ winds were moving rearward over time as well,
with a similar rate of backward propagation. This suggests a link between the back edge of the
stratiform region and the maximum RIJ winds.
It has been shown that these statistical diagrams can be used to quantify the robustness of
simulations against high-resolution observations even without spatial or temporal collocation.
Using all of the statistical methods mentioned in this thesis 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. Quantitative statistical analyses performed with these
diagrams represent the bulk characteristics of the system much better by comparing the
distributions with height or distance. After quantifying the model’s ability to represent the
features in question, modelling studies can be used to their full potential, knowing that the
simulations behave in a way that is statistically representative of the physical phenomena.
74
REFERENCES
Atkins, N. T., C. S. Bouchard, R. W. Przybylinski, R. J. Trapp, and G. Schmocker, 2005:
Damaging surface wind mechanisms within the 10 June 2003 Saint Louis bow echo
during BAMEX. Mon. Wea. Rev., 133, 2275–2296.
Belcher, L. R., L. D. Carey, J. M. Davis, J. A. Kankiewicz, and T. H. Vonder Haar, 2003: Mmwave radar structure and microphysical characteristics of mixed phase altocumulus
clouds. 31st International Conference on Radar Meteorology, Seattle, Amer. Meteor. Soc.,
3.6.
Biggerstaff, M. I., and R. A. Houze, 1991: Kinematic and precipitation structure of the 10–11
June 1985 squall line. Mon. Wea. Rev., 119, 3034–3065.
__________, and __________, 1993: Kinematics and microphysics of the transition zone of the
10–11 June 1985 squall line. J. Atmos. Sci., 50, 3091–3110.
Braun, S. A., and R. A. Houze, 1994: The transition zone and secondary maximum of radar
reflectivity behind a midlatitude squall line: results retrieved from Doppler radar data. J.
Atmos. Sci., 51, 2733–2755.
Bryan, G. H., J. C. Wyngaard, and J. M. Fritsch, 2003: Resolution requirements for the
simulation of deep moist convection. Mon. Wea. Rev., 131, 2394–2416.
Caniaux, G., J. L. Redelsperger, and J. P. Lafore, 1994: A numerical study of the stratiform region
of a fast-moving squall line. Part I: general description and water and heat budgets. J.
Atmos. Sci., 51, 2046–2074.
Chen, F., and J. Dudhia, 2001: Coupling an advanced land-surface/ hydrology model with the
Penn State/NCAR MM5 modeling system. Part I: model description and implementation.
Mon. Wea. Rev., 129, 569–585.
Cifelli, R., C. R. Williams, D. K. Rajopadhyaya, S. K. Avery, K. S. Gage, and P. T. May, 2000:
Drop-size distribution characteristics in tropical mesoscale convective systems. J. Appl.
Meteor., 39, 760–777.
Davis, C., N. Atkins, D. Bartels, L. Bosart, M. Coniglio, G. Bryan, W. Cotton, D. Dowell, B.
Jewett, R. Johns, D. Jorgensen, J. Knievel, K. Knupp, W. C. Lee, G. Mcfarquhar, J.
Moore, R. Przybylinski, R. Rauber, B. Smull, R. Trapp, S. Trier, R. Wakimoto, M.
Weisman, and C. Ziegler, 2004: The bow echo and MCV experiment: observations and
opportunities. Bull. Amer. Meteor. Soc., 85, 1075–1093.
Dawson, D. T., and M. Xue, 2006: Numerical forecasts of the 15–16 June 2002 southern plains
mesoscale convective system: impact of mesoscale data and cloud analysis. Mon. Wea.
Rev., 134, 1607–1629.
75
Dudhia, J., 1989: Numerical study of convection observed during the winter monsoon
experiment using a mesoscale two-dimensional model, J. Atmos. Sci., 46, 3077–3107.
Ferrier, B. J., Simpson, and W. K. Tao, 1996: Factors Responsible for Precipitation Efficiencies
in Midlatitude and Tropical Squall Simulations. Mon. Wea. Rev., 124, 2100–2125.
Fritsch, J., R. Kane, and C. Chelius, 1986: The contribution of mesoscale convective weather
systems to the warm-season precipitation in the United States. J. Appl. Meteor., 25, 1333–
1345.
Gallus, W. A., 1996: The influence of microphysics in the formation of intense wake lows: a
numerical modeling study. Mon. Wea. Rev., 124, 2267–2281.
Geerts, B., and G. M. Heymsfield, 2000: High-resolution reflectivity and vertical velocity
profiles in various convectively-generated precipitation systems. 24th Conference on
Hurricanes and Tropical Meteorology,Ft. Lauderdale, Amer. Meteor. Soc., 16B.3.
Grady, R. L., and J. Verlinde, 1997: Triple-Doppler analysis of a discretely propagating, longlived, High Plains squall line. J. Atmos. Sci., 54, 2729–2748.
Grams, J. S., W. A. Gallus, S. E. Koch, L. S. Wharton, A. Loughe, and E. E. Ebert, 2006: The use
of a modified Ebert–McBride technique to evaluate mesoscale model QPF as a function
of convective system morphology during IHOP 2002. Wea. Forecasting, 21, 288–306.
Hong, S.-Y., and H.-L. Pan, 1996: Nonlocal boundary layer vertical diffusion in a medium-range
forecast model, Mon. Wea. Rev., 124, 2322–2339.
__________, Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package with an explicit
treatment of entrainment processes. Mon. Wea. Rev., 134, 2318–2341.
Houze, R. A., M. Biggerstaff, S. Rutledge, and B. Smull, 1989: Interpretation of Doppler weather
Radar displays of midlatitude mesoscale convective systems. Bull. Amer. Meteor. Soc.,
70, 608–619.
Janjic, Z. I., 1994: The step-mountain eta coordinate model: further developments of the
convection, viscous sublayer and turbulence closure schemes, Mon. Wea. Rev., 122, 927–
945.
__________, 1996: The surface layer in the NCEP Eta model, Eleventh Conference on
Numerical Weather Prediction, Norfolk, VA, 19–23 August; Amer. Meteor. Soc., Boston,
MA, 354–355.
Johnson, R. H., and P. J. Hamilton, 1988: The relationship of surface pressure features to the
precipitation and airflow structure of an intense midlatitude squall line. Mon. Wea. Rev.,
116, 1444–1473.
76
Jorgensen, D. P., T. Matejka, and J. D. DuGranrut, 1996: Multi-beam techniques for deriving
wind fields from airborne Doppler radars. J. Meteor. Atmos. Phys, 59, 83-104.
__________, M. A. LeMone, and S. B. Trier, 1997: Structure and evolution of the 22 February
1993 TOGA COARE squall line: aircraft observations of precipitation, circulation, and
surface energy fluxes. J. Atmos. Sci., 54, 1961–1985.
__________, T. R. Shepherd, and A. S. Goldstein, 2000: A dual-pulse repetition frequency
scheme for mitigating velocity ambiguities of the NOAA P-3 airborne Doppler radar. J.
Atmos. Oceanic Technol., 17, 585–594.
__________, H. V. Murphey, and R. M. Wakimoto, 2005: Rear-inflow structure in severe and
non-severe bow-echoes observed by airborne Doppler radar during BAMEX. Preprints,
32nd Conference on Radar Meteorology, Albuquerque, New Mexico, J5J.3.
Kane, R., C. Chelius, and J. Fritsch, 1987: Precipitation characteristics of mesoscale convective
weather systems. J. Appl. Meteor., 26, 1345–1357.
Kingsmill, D. E., P. J. Neiman, F. M. Ralph, and A. B. White, 2006: Synoptic and topographic
variability of northern California precipitation characteristics in landfalling winter storms
observed during CALJET. Mon. Wea. Rev., 134, 2072–2094.
Lang, S., W. K. Tao, J. Simpson, and B. Ferrier, 2003: Modeling of convective–stratiform
precipitation processes: sensitivity to partitioning methods. J. Appl. Meteor., 42, 505–527.
LeMone, M. A., and M. W. Moncrieff, 1994: Momentum and mass transport by convective
bands: comparisons of highly idealized dynamical models to observations. J. Atmos. Sci.,
51, 281–305.
McFarquhar, G. M., H. Zhang, G. Heymsfield, R. Hood, J. Dudhia, J. B. Halverson, and F.
Marks, 2006: Factors affecting the evolution of hurricane Erin (2001) and the distributions of
hydrometeors: role of microphysical processes. J. Atmos. Sci., 63, 127–150.
Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A. Clough, 1997: Radiative
transfer for inhomogeneous atmosphere: RRTM, a validated correlated-k model for the
longwave. J. Geophys. Res., 102 (D14), 16663–16682.
Montmerle, T., J. P. Lafore, and J. L. Redelsperger, 2000: A tropical squall line observed during
TOGA COARE: extended comparisons between simulations and Doppler radar data and
the role of midlevel wind shear. Mon. Wea. Rev., 128, 3709–3730.
Mori, S., Hamada, J. I., Yamanaka, M. D., Kodama, Y. M., Kawashima, M., Shimomai, T.,
Shibagaki, Y., Hashiguchi, H., and Sribimawati, T., 2006: Vertical wind characteristics in
precipitating cloud systems over West Sumatra, Indonesia, observed with Equatorial
77
Atmosphere Radar: case study of 23-24 April 2004 during the first CPEA campaign
period. JMSJ, 84A, 113-131.
Pasken, R. W., and Martinelli, J. T., 2006: High resolution numerical simulations of Midwestern
quasi-linear mesoscale convective systems. 23rd Conference on Severe Local Storms, St.
Louis, Amer. Meteor. Soc., 17.5.
Rogers, R., M. Black, S. S. Chen, and R. Black, 2004: Evaluating microphysical
parameterization schemes for use in hurricane environments. 26th Conference on
Hurricanes and Tropical Meteorology, Miami, Amer. Meteor. Soc., 13C.6.
__________, __________, F. Marks, K. Valde, and S. S. Chen, 2006: A comparison of tropical
cyclone hydrometeor profiles from TRMM, airborne radar, and high-resolution
Simulations. 27th Conference on Hurricanes and Tropical Meteorology, Monterey, Amer.
Meteor. Soc., P5.19.
__________, __________, S. S. Chen, and R. A. Black, 2007: An evaluation of microphysics
fields from mesoscale model simulations of tropical cyclones. Part I: comparisons with
observations. J. Atmos. Sci., 64, 1811–1834.
Rotunno, R., J. B. Klemp, and M. L. Weisman, 1988: A theory for strong, long-lived squall lines.
J. Atmos. Sci., 45, 463–485.
Rutledge, S. A., R. A. Houze, M. I. Biggerstaff, and T. Matejka, 1988: The Oklahoma–Kansas
mesoscale convective system of 10–11 June 1985: precipitation structure and singleDoppler radar analysis. Mon. Wea. Rev., 116, 1409–1430.
Skamarock, W. C., J. B. Klemp, J. Dudhia, D. O. Gill, D. M. Barker, W. Wang and J. G. Powers,
2005: A description of the advanced research WRF version 2. NCAR Tech. Note.
NCAR/TN-468+STR, [http://www.mmm.ucar.edu/wrf/users/docs/arw_v2.pdf.]
Smedsmo, J. L., E. Foufoula-Georgiou, V. Vuruputur, F. Kong, and K. Droegemeier, 2005: On
the vertical structure of modeled and observed deep convective storms: insights for
precipitation retrieval and microphysical parameterization. J. Appl. Meteor., 44, 1866–
1884.
Smith, A. M., R. M. Rauber, G. M. McFarquhar, B. F. Jewett, M. S. Timlin, and J. A. Grim, 2008:
Explaining variations in cloud microphysics in BAMEX MCSs using high resolution
radar and optical array probe measurements. Submitted to Mon. Wea. Rev.
Smith, D. K., F. J. Wentz, and C. A. Mears, 1999: Comparison of TRMM TMI sea surface
temperature and wind speed retrievals with measurements from selected NDBC, TAO
and PIRATA buoys. 1999 American Geophysical Union Spring Meeting.
Smith, P. L., 1986: On the sensitivity of weather radars. J. Atmos. Oceanic Technol., 3, 704–713.
78
Smull, B. F., and R. A. Houze, 1985: A midlatitude squall line with a trailing region of stratiform
rain: radar and satellite observations. Mon. Wea. Rev., 113, 117–133.
__________, and __________, 1987a: Dual-Doppler radar analysis of a midlatitude squall line
with a trailing region of stratiform rain. J. Atmos. Sci., 44, 2128–2149.
__________, and __________, 1987b: Rear inflow in squall lines with trailing stratiform
precipitation. Mon. Wea. Rev., 115, 2869–2889.
Steiner, M., R. A. Houze, and S. E. Yuter, 1995: Climatological characterization of threedimensional storm structure from operational radar and rain gauge data. J. Appl. Meteor.,
34, 1978–2007.
Stoelinga, M. T., 2004: An update on post-processing and visualization tools for the WRF
Model. Preprints, 5th WRF / 14th MM5 Users’ Workshop, Boulder, Colorado, NCAR,
168-169.
_________, 2005: Simulated equivalent reflectivity factor as currently formulated in RIP:
description and possible improvements.
[http://www.atmos.washington.edu/~stoeling/RIP_sim_ref.pdf.]
Storm, B. A., M. D. Parker, and D. P. Jorgensen, 2007: A convective line with leading stratiform
precipitation from BAMEX. Mon. Wea. Rev., 135, 1769–1785.
Swann, A., A. H. Sobel, S. E. Yuter, and G. N. Kiladis, 2006: Observed radar reflectivity in
convectively coupled Kelvin and mixed Rossby-gravity waves. Geophys. Res. Lett. 33,
no. 10.
Thompson, G., R. M. Rasmussen, and K. Manning, 2004: Explicit forecasts of winter
precipitation using an improved bulk microphysics scheme. Mon. Wea. Rev., 132, 519542.
Tokay, A., and D. A. Short, 1996: Evidence from tropical raindrop spectra of the origin of rain
from stratiform versus convective clouds. J. Appl. Meteor., 35, 355–371.
Wakimoto, R. M., H. V. Murphey, A. Nester, D. P. Jorgensen, and N. T. Atkins, 2006a: High
winds generated by bow echoes. Part I: overview of the Omaha bow echo 5 July 2003
storm during BAMEX. Mon. Wea. Rev., 134, 2793–2812.
__________, __________, C. A. Davis, and N. T. Atkins, 2006: High winds generated by bow
echoes. Part II: the relationship between the mesovortices and damaging straight-line
winds. Mon. Wea. Rev., 134, 2813–2829.
Weisman, M. L., W. C. Skamarock, and J. B. Klemp, 1997: The resolution dependence of
explicitly modeled convective systems. Mon. Wea. Rev., 125, 527–548.
79
__________, and R. Rotunno, 2004: “A theory for strong long-lived squall lines” revisited. J.
Atmos. Sci., 61, 361–382.
Wheatley, D. M., R. J. Trapp, and N. T. Atkins, 2006: Radar and damage analysis of severe bow
echoes observed during BAMEX. Mon. Wea. Rev., 134, 791–806.
Yang, M. H., and R. A. Houze, 1995: Sensitivity of squall-line rear inflow to ice microphysics
and environmental humidity. Mon. Wea. Rev., 123, 3175–3193.
Yuter, S. E., and Houze Jr., R. A., 1995: Three-dimensional kinematic and microphysical
evolution of Florida cumulonimbus. Part II: frequency distributions of vertical velocity,
reflectivity, and differential reflectivity. Mon. Wea. Rev., 123, 1941-1963.
__________, __________, E.A. Smith, T.T. Wilheit, and E. Zipser, 2005: Physical
characterization of tropical oceanic convection observed in KWAJEX. J. Appl. Meteor.,
44, 385–415.