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HOW OUTFLOW BOUNDARY SPEED RELATES TO THUNDERSTORM CORE RADAR
REFLECTIVITY
Da’Vel Johnson
Department of Marine and Environmental Systems
Florida Institute of Technology
Melbourne, Florida 32901
Abstract:
During the month of June 2013, twenty-six thunderstorm cells were analyzed using Level II base
radar data in order to derive the speeds of their outflows. These derived outflow boundary speeds
were then related to the storm’s maximum core height and average storm core reflectivity. It was
found that outflow boundary speed has a positive linear relationship to the height of the
thunderstorm core with an equation of y = 0.67x + 2.9 and R² value of 0.62. The reflectivity of
the thunderstorm’s core in decibels (dBZ) has a positive exponential relationship with outflow
boundary speed and a positive linear relationship with outflow boundary speed when reflectivity
is in Z, equation of y = 7*105x + 5.2 with R² = 0.6583. When the majority of the core lies above
5000 feet the relationship is enhanced because the radar is no longer detecting the rain shaft of
the storm. With these R² values around 60%, it was determined that outflow boundary speed has
a positive relationship with storm core reflectivity and height; however, these are not the only
factors that determine outflow boundary speeds.
Introduction:
Thunderstorms are one of the most
active and spectacular meteorological events
that happen on Earth. Though thunderstorms
have been thoroughly studied, many aspects
are still unclear. This paper aims to expand
and quantitate knowledge on one of the
features of a thunderstorm’s structure, the
out flow boundary. Outflow boundary or
gust front forms as the down draft or down
burst cooler air reaches the ground and
expands in all directions (AMS 2013).
Depending on the size of the storm and the
area’s current weather conditions, this
happens either while the thunderstorm is still
in it mature phase or while in its dissipating
phase. This is due to precipitation either
dragging the air down due to friction or
cooling the air from evaporative cooling
making it negatively buoyant (Srivastava,
1985). Once the outflow boundary has
expanded far enough away from the main
convective cells it can be seen on radar as an
expanding circle of cumulus cloud or debris.
The objective of this project was to
use radar data to derive the speed of the
outflows expansion. The next step was to
relate that speed to the thunderstorm’s core
reflectivity and storm core height. A
thunderstorm’s core can be described as the
area where the updraft is strong enough to
suspend ice and liquid water (Wilhelmson,
1974). This core area has a higher
reflectivity than the surrounding air due to
the densely populated area of precipitation.
The higher reflectivity can then be detected
by weather radars.
Figure 1: Thunderstorm vertical cross
section using GR2Analyst. Red indicates
thunderstorm’s core.
Research on thunderstorms and their
outflow boundaries has primarily been on
the formation of convective cells along an
outflow boundary. One such paper on cold
outflow boundary simulations shows how
air which originates below the planetary
boundary layer forms into new cells along
the edge of the boundary (Wilhelmson and
Ching, 1982). Other areas of study include
the formation of major thunderstorms upon
outflow boundary collisions (Wilson and
Schreiber, 1986). However, many studies on
outflows neglect to mention what factors
may drive faster outflow boundary speeds.
This gap in knowledge is what this project
aims to fill. The results of this project will
hopefully show what factors may drive
faster outflow boundaries, and how to
potentially predict these speeds by using the
height of the storm’s core and its maximum
reflectivity.
During the month of June 2013,
synoptic conditions allowed for stagnant
flow over central Florida. This was ideal for
the formation of thunderstorms that would
develop and dissipate in the same areas
allowing for any outflow boundaries to
expand in all directions with negligible
resistance.
Figure 2: Map of Central Florida, USA blue markers depict the location of thunderstorm cell
used for this project during the month of June 2013.
Twenty-six different thunderstorm
systems and their respective outflow
boundaries were analyzed using the WSR-
88D radar towers located in Melbourne,
Florida and Tampa Bay, Florida National
Weather Service (NWS) Weather Forecast
Offices (WFO). This radar data was used to
answer the question posted by this report of
“How does outflow boundary speed relate to
thunderstorm core radar reflectivity?”
Methods:
Ideal days where storms would
develop and dissipate near the same location
with minimal storm motions were chosen for
outflow speed calculations and radar
reflectivity storm core analysis. Level II
base radar data from WSR-88D radar towers
located in Melbourne, Florida and Tampa
Bay, Florida NWS WFO were used for all
calculations of outflow speeds. The Level II
data was gathered from the National
Climatic Data Center (NCDC) online
achieve and saved onto a laptop. Using the
NCDC toolkit, loops of the Level II radar
data were created and saved as an Audio
Video Interleave (.avi) files. The loops were
then inspected for outflow boundaries and
thunderstorms with potentials for outflow
boundaries.
Once a thunderstorm with an outflow
boundary was located on the loop, the time
where the storm appeared to reach
maximum core reflectivity was recorded
into a spread sheet. The longitude and
latitude of the approximate center of the
storm at this was also recorded onto an excel
spread sheet. Using the program
GR2Analyst, a vertical cross section of the
storm at the time and location of maximum
reflectivity is created. An average of the
nine highest reflective pixels of the storms
core in decibels (dBZ) is then recorded into
the excel sheet. The maximum height of the
thunderstorm’s core is also recorded in
thousands of feet. It was noted if the
majority of the core was below or above
5000 feet. Separation of storms above and
below 5000ft was done because much
research suggests that thunderstorm cloud
base is approximately 1.5km or ~ 5000 feet
(Smith et al., 1999). If the majority of a
thunderstorm’s core reflectivity is found
below 5000ft; then, it is safe to assume the
radar is reflecting the rain shaft and not the
storms core. The radar loop is again run
until the selected storm’s outflow boundary
reaches a distance where boundary appears
to have reached a steady velocity. The time
was then recorded. The coordinates of the
outflow furthest from the storm’s center
were recorded into the same excel spread
sheet.
Figure 3: (left) Thunderstorm located at 28.2368 N, 81.2838 W on June 13, 2013 at 18:52UTC.
(right) Corresponding outflow boundary is marked by the black circle.
Using the two longitude and latitude
coordinates a distance in miles was
calculated and recorded. Using the two
times, a difference in time was recorded in
hours. The miles were then divided by the
hours generate a speed in miles per hour and
was also recorded into the spread sheet. In
the case of storm motion greater than 5
miles per hour, the wind speed at 850mb
was subtracted or added to the derived
outflow boundary speed depending on then
chosen locations. Generally locations
parallel to the storm motion were chosen for
ease of calculations. These steps were
repeated for each storm with a suitable
outflow boundary.
Six graphs were made using the data
gathered in Microsoft excel: speed versus
storm core reflectivity, speed versus storm
core height, speed versus storm core
reflectivity above 5000ft, speed versus storm
core height above 5000ft, speed versus
storm core reflectivity below 5000ft, and
speed versus storm core height below
5000ft.
Wind direction data was also saved
into the excel sheet when a storm’s outflow
boundary was seen passing through one of
the three the HOBO portable weather station
sites located in Rockledge, Florida,
Harmony, Florida, and Melbourne, Florida.
This wind direction data was used to
validate that boundaries did in fact pass
through the area and helped to solidify any claims and conclusions made.
Results:
Figure 4: Height of Thunderstorm cores versus Outflow Boundary Speeds.
A reasonable positive relationship is seen
between the two variables. Higher core
heights seem to result in higher outflow
boundary speeds. A moderate correlation
coefficient of 0.69 is seen after a linear
regression with a coefficient of
determination R-squared of 0.48.
Figure 5: Height of Thunderstorm cores vs Outflow Boundary Speeds with core above 5000ft.
y = 0.5222x + 6.1306
R² = 0.4781
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00
Outflow Speed (mph)
Height In Feet x 1000
y = 0.6694x + 2.9472
R² = 0.6204
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0
Outflow Speed (mph)
Height In Feet x 1000
After removing the outflows which had the
majority of their cores below 5000 feet, the
positive relationship is seen from the first
graph is strengthened. Higher core heights
again seem to result in higher outflow
boundary speeds. In accordance to the
strengthened linear relationship, the
coefficient of determination increases from
0.48 to 0.62 after a linear regression.
Figure 6: Reflectivity of Thunderstorm Cores vs Outflow Boundary Speeds.
With all reflectivity points plotted, a positive
relationship is seen between the two
variables with a slope of 1.3; however much
spreading is seen at higher reflectivities.
Reflectivities show a relatively large range
of associated outflow speeds. For example a
reflectivity of 55dBZ could produce an
outflow boundary speed of 7 mph to 26
mph. This mathematically translates to a
weak coefficient of determination of 0.32 is
seen after a linear regression.
y = 1.2919x - 52.015
R² = 0.3245
0.0
5.0
10.0
15.0
20.0
25.0
30.0
40 42 44 46 48 50 52 54 56
Outflow Speed (mph)
Reflectivity in dBZ
Figure 7: Reflectivity (dBZ) of Thunderstorm cores versus Outflow Boundary Speeds with cores
above 5000ft.
As seen in Figure 5, upon removing the
outflows which had the majority of their
cores below 5000 feet, the positive
relationship is strengthened. The correlation
coefficient is 0.75 with a coefficient of
determination of 0.56 after a linear
regression; however, points seem to have an
exponential shape. This could be due to
reflectivity in decibels is a logarithmic
function.
Figure 8: Equation for radar reflectivity in
dBZ
y = 1.9196x - 82.615
R² = 0.5618
0.0
5.0
10.0
15.0
20.0
25.0
30.0
40.0 42.0 44.0 46.0 48.0 50.0 52.0 54.0 56.0
Outflow Speed (mph)
Reflectivity in dBZ
Figure 9: Reflectivity (Z) of Thunderstorm cores versus Outflow Boundary Speeds with cores
above 5000ft.
After using the Reflectivity equation
in Figure 8 to convert dBZ values to Z, a
linear graph was created. This graph has a
moderate correlation coefficient of 0.81 and
a coefficient of determination of 0.65 and
proves that the dBZ to outflow boundary
speed relationship in Figure 7 is exponential
in nature.
Table 1: Rockledge, Florida HOBO data during Outflow Boundary
Passage
Time, Coordinated Universal
Time
Temp,
*F
Gust Speed,
mph
Wind
Dir,
6/11/2013 20:50
82.26
1.6
126
6/11/2013 20:55
81.95
1.3
108
6/11/2013 21:00
81.55
2
323
6/11/2013 21:05
78.33
12.5
309
6/11/2013 21:10
76.68
11.6
324
Table 1 depicts the passage of an outflow boundary on 6/11/13 captured by the HOBO portable
weather station in Rockledge, Florida. Points of interest are the 145 degree wind shift from south
easterly to north westerly, the gust increase from 2mph to 12.5 mph and the temperature drop
from 82°F to 76°
y = 7E-05x + 5.2484
R² = 0.6583
0.0
5.0
10.0
15.0
20.0
25.0
30.0
0 50000 100000 150000 200000 250000 300000 350000
Outflow Speed (mph)
Reflectivity (Z)
Discussion:
Confirmation of Outflow boundary passage:
Located in Rockledge, Florida the
HOBO portable weather station recorded an
outflow boundary passage on 6/11/13. Three
main factors can confirm an outflow
boundary passage, a change in wind
direction an increase in wind speed, and a
drop in temperatures. All three factors were
seen at the HOBO station on June 6th 2013
from 20:50UTC to 21:10UTC seen in Table
1. The wind direction backs 145 degrees
from south-easterly to north-westerly in
accordance with the main storm cell being
north of the location. The wind gusts maxes
at 12mph after being steady at 1.3mph.
Finally the temperature drops in from 82
degrees to 76.7 degrees. This 5 degree
decrease in temperature in 20 minutes shows
the colder air from the outflow boundary has
passed through the area. This kind of
confirmation was seen multiple times
throughout the sample period at the three
HOBO locations. Confirmation of outflow
boundaries is important because it shows
that outflow boundaries were detected in
ways other than radar detection.
Discussion of Height of thunderstorm core
vs outflow boundary speeds graphs:
Overall thunderstorm core height
appears to have a moderate to strong
positive linear relationship with the speed of
the outflow boundary. Both Figure 4 and
Figure 5 show this phenomenon. With a
coefficient of determination of 0.48 in
Figure 4, this means that 48% of the outflow
boundary speeds are explained but the
equation y = 0.52x + 6.1. This is improved
by the removal of thunderstorm core
reflectivities that appear to be heavy rain
appearing on the radar. Seen in Figure 5, the
coefficient of determination is 0.62 which
means 62% of the observations are now
explained by the equation 0.67x + 2.9.
Higher storm core heights yield
faster outflow boundary speeds. Higher
heights enhance two major components of
the thunderstorm downdraft, speed of the
downdraft at the surface and the momentum
it carries. Objects released from any height
above the surface will accelerate towards the
ground due to gravity until it reaches
terminal velocity. Higher core heights allow
more time for air parcels to accelerate
towards the ground. In the absence of
friction, this result in faster downdrafts and
by relation faster outflow boundary speeds
(Bernardet, 1998). The momentum of the
downdraft is also increased with higher
heights. Precipitation has more time to apply
a frictional force to the air around it.
(Haman, 1980) This causes the air to gain
speed and maintain speed as it reaches the
ground and spreads in all directions. Though
Figure 5 shows a 14% improvement in the
coefficient of determination, it is still only
62% accurate. This is because other factors
other than height of the storm core affect the
speed of the outflow.
Discussion of Thunderstorm core
Reflectivity vs outflow boundary speeds
graphs:
Only with storm cores above 5000
feet is a strong positive relationship seen
between the strength of the reflectivity and
the speed of the outflow boundary. This
positive relationship is seen in Figure 6 by
the slope of 1.29. However, the low
coefficient of determination shows how at
higher values of reflectivity the equation
1.3x – 52.0 given by the graph fails to
predict outflow boundary speeds with any
accuracy. The spreading of outflow speeds
seen throughout the graph rules out Figure
6’s linear relationship. As seen in Figure 5,
after removing the cores below 5000 feet
Figure 7’s coefficient of determination
increase from 0.32 in Figure 6 to 0.56 in
Figure 7. Both graphs agree that the x-
intercept is around 40dBZ. This means that
outflow boundaries are not seen with core
reflectivities below 40 dBZ. The adjustment
made in Figure 7 puts more confidence in
the linearity of Figure 7’s graph as 56% of
the points can be explained but its equation
of 1.9x – 82.
However the particular shape of the
points suggests a nonlinear relationship
might better explain the scatter plot. Points
are seen above the trend line of Figure 7,
then dip below the trend line, and finally
ascend above the trend line. This effect is
highly suggestive of an exponential
relationship between storm core reflectivity
in decibels and outflow boundary speed.
The claim of an exponential relationship is
further assured by Figure 8 which is the
equation for dBZ. The reflectivity in dBZ is
a logarithmic relationship. Therefore to
properly correct for this, the inverse of
Figure 8 of 10^(dBZ/10) had to be applied
to all reflectivity values. This is how Figure
9 was generated. After applying a linear
regression to Figure 9’s points, the equation
7*105x + 5.25 with the coefficient of
determination of 0.66 was made. This means
that the store core reflectivity in Z in directly
related to the outflow boundary speed, and
that storm core reflectivity in decibels (dBZ)
is exponentially related to outflow boundary
speed.
Radar reflectivity is proportional to
two other major factors that determine the
speed of the downdraft and by relation the
speed of the outflow boundary. These
factors are the droplet size and density of the
storm core. As mentioned previously
droplets of rain will drag air down as they
fall due to frictional forces. Higher core
reflectivity potentially means larger droplet
sizes (Sekhon and Srivastava, 1971). Larger
droplet sizes create stronger frictional forces
which will result in a faster downdraft and
outflow boundary speed. Density of the rain
also relates to reflectivity. A tighter storm
core could potentially cool the air
surrounding it due to entrainment. Cooler air
is more dense and will also accelerate
towards the ground due to negative
buoyancy (Pawlowska, 1986) This cooler
denser air can persist for miles before it
mixes out. This assists in the outflow
boundary maintaining speed for hours.
However like Figure 5, Figure 9 is not the
sole factor in determining outflow boundary
speeds.
Conclusion:
Outflow boundary speed has a
positive relationship to both the height of the
thunderstorm core and the reflectivity of the
thunderstorm’s core. When the majority of
the core lies above 5000 feet the relationship
is enhanced. According to the derived x-
intercepts, it suggests that outflow
boundaries are not produced from storms
with cores less than 40dBZ. With the height
of the thunderstorm, the relationship is
purely linear. In contrast, the reflectivity of
the storm core in decibels has an exponential
relationship with the outflow boundary
speed. This means that higher decibel
readings exponentially increase the speed of
the outflow boundary. However the height
of the thunderstorm’s core and the
reflectivity of the thunderstorm’s core are
not the only factors that affect the speed of
an outflow boundary. Storm motion plays a
big role in adjusting outflow boundary
speeds and was mathematically subtracted
out in this study. The results of this study
could potentially assist weather forecasters
in forecasting speeds of the outflow
boundary by creating a since of strength that
was not previously considered before this
study.
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