Equation for radar reflectivity in dBZ 

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Context 1

... 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 5 7*10 x + 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. 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 ...

Context 2

... 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 5 7*10 x + 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. 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 ...

Context 3

... 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 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 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 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. 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. 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 ...