Hurricanes Intensity
Hurricanes are natural events that bring destruction in many different ways. They are tropical storms with high wind speeds that can unleash gallons of rain. The high winds may spawn tornadoes and the torrential rains may cause floods and landslides. The destructive nature of hurricanes after making landfall is very devastating, to the extent that houses are wiped off the map and the floods deposit debris of damaged homes. Sometimes human lives are lost through this destructive natural event. As residents in our various communities, it is very important to have some level of knowledge about hurricanes and familiarize ourselves with the best practices and safe measures in the event of a hurricane.A hurricane is an intense cyclonic storm that develops over the warm oceans of the tropics. It usually begins as a tropical disturbance and turns into a tropical depression when the speed of the wind attains 61 kilometers per hour (km/h) or equivalently 38 miles per hour (mph) at the storm center. When the sustained wind speed attains 63 km/h (or 39 mph) the tropical depression becomes a tropical storm. The tropical storm is classified as hurricane when the sustained wind speed reaches 119 km/h (or 74 mph). Using the Saffir-Simpson scale the hurricane is categorized a rating of 1 to 5. In the northern Indian Ocean, the tropical storm is known as a cyclone and in the western Pacific Ocean it is referred to as a typhoon [1]. You can learn about Hurricanes and Tropical Storms at http://www.physicalgeography.net/fundamentals/7u.html
Determining Sustained Wind Speed in a Hurricane
We wish to determine how sustained wind speed in a hurricane is related to the surface pressure of the storm.The goal of this project is to consider the relationship between wind speed and pressure within a hurricane and, to develop a model that describes this relationship. Please use the dataset on maximum sustained wind speeds measured (mph) and pressures (mb) within hurricanes for the period 2000-2005. Using either SPSS or Excel for statistical analysis of this data set, please answer the following questions.
1. Identify the response and explanatory variables. Construct a scatter plot for this data set. What kind of relationship appears to exist, if any, between the two variables? Describe the pattern, direction and the strength of association between the two variables.
2. Determine the linear correlation coefficient. Does the value support your observation in exercise 1?
3. Is the linear correlation coefficient statistically significant at the 5% level? Explain. What does this tell you about the existence of a linear relationship between these two variables?
4. Develop a least squares regression model for the two variables. Graph it along with the scatter plot.
5. Interpret the slope of the least squares’ regression model in the context of wind speed and atmospheric pressure.
6. Determine the coefficient of determination and interpret its meaning in the context of wind speed and atmospheric pressure.
7. Use the least squares regression model to estimate the maximum sustained wind speed in a hurricane when the pressure reading is 950 mb.
8. In 2000 and 2004, hurricanes DEBBY and JEANNE recorded maximum wind speeds of 75 mph and 127 mph, respectively. However, their corresponding pressure readings remain unknown. Use your regression model to predict these pressure readings. Be sure to include appropriate units!
Solution
Question 1
Response variable is the surface pressure.
Explanatory variable is Wind Speed.
Scatter plot
From the scatter plot above, there is a linear relationship between the two variables surface pressure and wind speed. Furthermore, there is a negative relationship between the two variables as shown in the graph which means an increase in one will leads to a decrease in the other variable.
Question 2
Correlations |
|||
Pressure | Windspeed | ||
Pressure | Pearson Correlation | 1 | -.962^{**} |
Sig. (2-tailed) | .000 | ||
N | 49 | 49 | |
Windspeed | Pearson Correlation | -.962^{**} | 1 |
Sig. (2-tailed) | .000 | ||
N | 49 | 49 | |
Question 3
From the table above, the statistical correlation is significant because the p-value of the correlation coefficient (0.00) is lesser than 0.5 level of significance. This means there is a linear relationship between the two variables.
Question 4
Regression model estimate
Coefficient | B(Std. Err.) | t-value | p-value |
Intercept | 1050.205(3.967) | 264.714 | 0.000 |
Windspeed | -0.812(0.034) | -24.079 | 0.000 |
R-SquareAdjusted R-Square | 0.925 0.923 | ||
F-Value | 579.799 | ||
Pr(F>0) | 0.0000 |
Question 5
Interpreting the Slope
From the regression model table above, a unit increase in the independent variable wind speed will cause a 0.812 decrease in the response variable surface pressure.
Question 6
From the table above, the coefficient of determination R-squared is 0.925 which means 92.5% of the variation in the model can be explained by the independent variable wind speed.
Question 7
Y = a + bx
Where Y is pressure reading 950 mb
X is the wind speed which is unknown
a = 1050.205
b = -0.812
950 = 1050.205 – 0.812x
-0.812x = -100.205
X = 100.205/0.812
X = 123.405
Hence, the wind speed when Y = 950mb is 123mph.
Question 8
i. Y = a + bx
Where Y is unknown
X is the wind speed which is 75mph
a = 1050.205
b = -0.812
Y = 1050.205 – 0.812(75)
Y = 1050.205 – 60.9
Y = 989.35.
Hence, when DEBBY records maximum winds as 75mph the surface pressure is 989mb.
ii. Y = a + bx
Where Y is unknown
X is the wind speed which is 127mph
a = 1050.205
b = -0.812
Y = 1050.205 – 0.812(127)
Y = 1050.205 – 103.124
Y = 946.965
Hence, when JEANNE records maximum winds as 127mph the surface pressure is 947mb.