A tropical cyclone is a low-pressure system over tropical or sub-tropical waters with thunderstorm activity and surface wind circulation. Tropical cyclones with maximum sustained surface winds of less than 17 m/s (39 mph) are called "tropical depressions". If winds reach 33 m/s (74 mph), then they are called: a "hurricane" or "typhoon", depending on the geographic location. For the Atlantic basin, USA meteorologists use a scale of 1 (low) to 5 (high) to rate the intensity of hurricanes. A hurricane generates an incredible amount of kinetic or wind energy. With an radius of 60 km and average wind speeds 40m/3, a hurricane can produce 1.5 x 1012 Watts of energy -- equivalent to about half the world-wide electrical generating capacity! Hurricane wind energy of this magnitude can cause enormous property damage directly as a result of the wind, or indirectly from ocean waves, tornadoes, and flooding and storm surge. Human suffering and loss of life is also caused by wind energy (direct and indirect) but often is the result of outbreaks of disease long after the hurricane has passed. The 1926 hurricane in Southeast Florida and Alabama has been estimated to be the most costly in US history -- $83,814,000,000 in today's dollars, while the 1900 hurricane that hit Galveston, TX was the deadliest -- over 8000 people killed. There is considerable debate over the extent to which the severity and frequency of hurricanes will change with global warming because the formation of tropical cyclones depends on a number of ocean and atmospheric variables, including sea surface temperature and air moisture. But with increased sea levels associated with global warming (coupled with the continued worldwide migration of peoples to coastal cities) there is growing concern that hurricanes will cause more property damage and loss of life in the future. These hurricane data were pulled from the Atlantic Tracks File compiled by the US National Hurricane Center. This file consists of loads of data for major storm events from 1851 to 2016. Tropical depression and tropical storm data were omitted from the file, as were all other storm statistics. Each year the hurricane season begins June 1, and all hurricane dates are converted to "weeks of season." The weeks were then binned in 2 week intervals beginning June 1-14 (weeks 1 and 2) and ending in early January (weeks 31 and 32). Data Source: US National Hurricane Center http://www.nhc.noaa.gov/ Please see the complete list of hurricanes at the US National Hurricane Center site.[1] The following table is the grouped frequency table for the hurricanes that occurred in specific time frames starting with Week 1 starting June 1. ( from 1851 to 2016). Weeks Frequency 1-2 9 9 3-4 16 5-6 24 7-8 24 9-10 54 11-12 117 13-14 172 15-16 153 17-18 108 9-20 95 21-22 45 23-24 18 25-26 11 27-28 2 29-30 0 31-32 3 1) Use Excel to draw a Histogram of the above grouped data. Label each axis. Title the graph. Insert excel graph here: 2) What are some of the characteristics of this graph? What does the graph look like? We will assume that the number of hurricanes follows a normal distribution. 3) What is the total number of hurricanes that were recorded here? 4) Find the mean week of the grouped frequency table. Round to the nearest tenth. Show your formula or explain how you find the mean. 5) Let us assume that this data follows a normal distribution with mean from above and standard deviation of 4.7. Draw this normal curve by hand. Using this curve and z scores, answer the following questions: 6) What weeks correspond to (answer to one decimal place) Z=1? Z=2? Z=3? Z=-1? Z=-2? Z=-3? 7) What is the probability that a hurricane will occur after week 22? 8) Between what weeks will 68% of the hurricanes occur (centered around the mean)? Round to the nearest whole number. Which months are included in that time frame? 9) Between what weeks will 95% of the hurricanes occur (centered around the mean)? Round to the nearest whole number. Which months are included in that time frame? 10) Between what weeks will 99.7% of the hurricanes occur (centered around the mean)? Round to the nearest whole number. 11) How likely is it that a hurricane will occur in June (weeks 1-4)? 12) What effect do you think global warming would have on the shape of the graph? [1] Material taken from http://www.seattlecentral.edu/qelp/index.html. Supported by NSF.
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
A tropical cyclone is a low-pressure system over tropical or sub-tropical waters with thunderstorm activity and surface wind circulation. Tropical cyclones with maximum sustained surface winds of less than 17 m/s (39 mph) are called "tropical depressions". If winds reach 33 m/s (74 mph), then they are called: a "hurricane" or "typhoon", depending on the geographic location. For the Atlantic basin, USA meteorologists use a scale of 1 (low) to 5 (high) to rate the intensity of hurricanes.
A hurricane generates an incredible amount of kinetic or wind energy. With an radius of 60 km and average wind speeds 40m/3, a hurricane can produce 1.5 x 1012 Watts of energy -- equivalent to about half the world-wide electrical generating capacity! Hurricane wind energy of this magnitude can cause enormous property damage directly as a result of the wind, or indirectly from ocean waves, tornadoes, and flooding and storm surge. Human suffering and loss of life is also caused by wind energy (direct and indirect) but often is the result of outbreaks of disease long after the hurricane has passed. The 1926 hurricane in Southeast Florida and Alabama has been estimated to be the most costly in US history -- $83,814,000,000 in today's dollars, while the 1900 hurricane that hit Galveston, TX was the deadliest -- over 8000 people killed.
There is considerable debate over the extent to which the severity and frequency of hurricanes will change with global warming because the formation of tropical cyclones depends on a number of ocean and atmospheric variables, including sea surface temperature and air moisture. But with increased sea levels associated with global warming (coupled with the continued worldwide migration of peoples to coastal cities) there is growing concern that hurricanes will cause more property damage and loss of life in the future.
These hurricane data were pulled from the Atlantic Tracks File compiled by the US National Hurricane Center. This file consists of loads of data for major storm
Each year the hurricane season begins June 1, and all hurricane dates are converted to "weeks of season." The weeks were then binned in 2 week intervals beginning June 1-14 (weeks 1 and 2) and ending in early January (weeks 31 and 32). Data Source: US National Hurricane Center http://www.nhc.noaa.gov/
Please see the complete list of hurricanes at the US National Hurricane Center site.[1]
The following table is the grouped frequency table for the hurricanes that occurred in specific time frames starting with Week 1 starting June 1. ( from 1851 to 2016).
|
Weeks |
Frequency |
|
1-2 |
9 9 |
|
3-4 |
16 |
|
5-6 |
24 |
|
7-8 |
24 |
|
9-10 |
54 |
|
11-12 |
117 |
|
13-14 |
172 |
|
15-16 |
153 |
|
17-18 |
108 |
|
9-20 |
95 |
|
21-22 |
45 |
|
23-24 |
18 |
|
25-26 |
11 |
|
27-28 |
2 |
|
29-30 |
0 |
|
31-32 |
3 |
|
|
|
1) Use Excel to draw a Histogram of the above grouped data. Label each axis. Title the graph.
Insert excel graph here:
2) What are some of the characteristics of this graph? What does the graph look like?
We will assume that the number of hurricanes follows a
3) What is the total number of hurricanes that were recorded here?
4) Find the mean week of the grouped frequency table. Round to the nearest tenth.
Show your formula or explain how you find the mean.
5) Let us assume that this data follows a normal distribution with mean from above
and standard deviation of 4.7. Draw this normal curve by hand.
Using this curve and z scores, answer the following questions:
6) What weeks correspond to (answer to one decimal place)
Z=1? Z=2? Z=3?
Z=-1? Z=-2? Z=-3?
7) What is the probability that a hurricane will occur after week 22?
8) Between what weeks will 68% of the hurricanes occur (centered around the mean)? Round to the nearest whole number.
Which months are included in that time frame?
9) Between what weeks will 95% of the hurricanes occur (centered around the mean)? Round to the nearest whole number.
Which months are included in that time frame?
10) Between what weeks will 99.7% of the hurricanes occur (centered around the mean)? Round to the nearest whole number.
11) How likely is it that a hurricane will occur in June (weeks 1-4)?
12) What effect do you think global warming would have on the shape of the graph?
[1] Material taken from http://www.seattlecentral.edu/qelp/index.html. Supported by NSF.
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