Florida Institute of Technology. Melbourne, Florida 32901. Abstract: During the .... Rockledge, Florida. Points of interest are the 145 degree wind shift from south.
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 WSR88D 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
claims and conclusions made.
validate that boundaries did in fact pass through the area and helped to solidify any Results:
Outflow Speed (mph)
30.0 25.0 20.0 15.0 10.0
y = 0.5222x + 6.1306 R² = 0.4781
5.0 0.0 0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
Height In Feet x 1000
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.
30.0
Outflow Speed (mph)
25.0 20.0 15.0 10.0
y = 0.6694x + 2.9472 R² = 0.6204
5.0 0.0 0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
Height In Feet x 1000
Figure 5: Height of Thunderstorm cores vs Outflow Boundary Speeds with core above 5000ft.
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.
Outflow Speed (mph)
30.0 25.0 20.0
y = 1.2919x - 52.015 R² = 0.3245
15.0 10.0 5.0 0.0 40
42
44
46
48
50
52
54
56
Reflectivity in dBZ
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.
30.0
Outflow Speed (mph)
25.0 20.0
y = 1.9196x - 82.615 R² = 0.5618
15.0 10.0 5.0 0.0 40.0
42.0
44.0
46.0
48.0
50.0
52.0
54.0
56.0
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
30.0 y = 7E-05x + 5.2484 R² = 0.6583
Outflow Speed (mph)
25.0 20.0
15.0 10.0 5.0 0.0 0
50000
100000
150000 200000 Reflectivity (Z)
250000
300000
350000
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 Temp, Gust Speed, Wind Time *F mph 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°
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 xintercept 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 xintercepts, 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.
PAWLOWSKA-MANKIEWICZ, H. (1987), On the mechanisms of downdraft maintenance in cumulonimbus clouds. Tellus A, 39A: 266–270
References:
Wilhelmson, Robert, 1974: The Life Cycle of a Thunderstorm in Three Dimensions. J. Atmos. Sci., 31, 1629–1651.
American Meteorological Society, cited 2013: “outflow boundary.” Glossary of Meteorology. Bernardet, Lígia R., William R. Cotton, 1998: Multiscale Evolution of a DerechoProducing Mesoscale Convective System. Mon. Wea. Rev., 126, 2991–3015. HAMAN, K. E. and NIEWIADOMSKI, M. (1980), Cold downdrafts in cumulonimbus clouds. Tellus, 32: 525–536.
Sekhon, R. S., R. C. Srivastava, 1971: Doppler Radar Observations of Drop-Size Distributions in a Thunderstorm. J. Atmos. Sci., 28, 983–994. Smith, Paul L., Dennis J. Musil, Andrew G. Detwiler, Rahul Ramachandran, 1999: Observations of Mixed-Phase Precipitation within a CaPE Thunderstorm. J. Appl. Meteor., 38, 145–155. Srivastava, R. C., 1985: A Simple Model of Evaporatively Driven Dowadraft: Application to Microburst Downdraft. J. Atmos. Sci., 42, 1004–1023.
Wilhelmson, Robert B., Ching-Sen Chen, 1982: A Simulation of the Development of Successive Cells Along a Cold Outflow Boundary. J. Atmos. Sci.,39, 1466–1483. Wilson, James W., Wendy E. Schreiber, 1986: Initiation of Convective Storms at Radar-Observed Boundary-Layer Convergence Lines. Mon. Wea. Rev., 114, 2516–2536.
