Problem 1: Severe Thunderstorms
Part 1 -
Strong wind shear is a crucial ingredient for severe thunderstorm development. Wind shear is defined as the change in wind speed and direction with height.
Supercell thunderstorms form most frequently in the Great Plains in the central US. The ideal wind shear profile for a supercell consists of southeast winds at the surface that strengthen and become more westerly with altitude.
Mesoscale Convective Systems (a.k.a. squall lines) can form anywhere in the US. The ideal wind shear profile for squall line is a unidirectional wind shear profile that has increasing wind speed with height.
Shown below are 5 vertical wind profiles taken from 5 different soundings. Circle the letter beneath the ideal vertical wind profile for a supercell? Put a square around the letter beneath the ideal vertical wind profile fro a squall line.
Wind shear is calculated by finding the difference between the wind speed values at two different heights. Using the wind profile you identified as the ideal environment for a supercell, next you will calculate the 0-1 km and 0-5 km wind shear values. This means we will find the difference between the surface wind (lowest wind barb on the sounding) and the speed of the wind at 1km and 5 km. The atmospheric pressure at 1km above sea level is typically very close to 850 mb. The pressure at 5 km above sea level is very close to 500 mb. Please calculate the 0-1 km and 0-5 km wind shear values in knots (kts).
0-1km shear value _________________ 0-5km shear value _________________
Part 2 - Hail Damage
Imagine a huge supercell thunderstorm passed over campus and produced large damaging hail. One of the cars that was damaged was Chancellor Robert Jones' vintage Jaguar E-Type. When his insurance adjuster arrived to assess the situation, she discovered that most of the dents these hailstones left on the hood of his car had two sizes - one set of dents were 3 inches in diameter and the other set was 6 inches in diameter. See if you can use the information below to find the mass, diameter, circumference, fall speed, and total kinetic energy for these two different sized hailstones. Be very careful with the units!! (Show all of your work!)
What you need to know...
- Kinetic Energy = 0.5 * Mass *
- Density of the ice in the hail stones = 57
- The volume of a sphere is (The fall velocity of a hailstone in still air can be approximated using this equation V = k if d (the diameter of the stone) is given in centimeters. V will have units of meters per second (m/s) as long as d is in cm.)
- Diameter of the dent = 1.5 * diameter of the hailstone
- Density = Mass/Volume
Part 3 - 2011 Hail Data
Download the US hail reports from 2011. Using these data complete the following tasks.
1. Create a line graph that shows the cumulative hail reports throughout the year.
2. Create a bar graph that shows the hail reports for each day of the year.
3. What is the total number of hail reports in 2011?
4. Which day had the most hail reports in 2011?
5. What was the largest hail stone size measured in 2011 and in which state(s) did it fall?
Part 4 - Wind Force on a Tree
In my front yard is a huge Pin Oak tree. How fast would the wind need to be in a thunderstorm to uproot this tree and knock it over? The force required to uproot this tree is fast would the wind have to be (in mph) to generate this force against my tree? Use this information below to solve this problem. (Show all of your work and be very careful with units!)
F = Force applied by the wind = 645000 kg mρ = Air Density = 1.225 kg/ A = Area of the leaves on the tree. Each leaf is 12 of the branches and trunk to be negligible.
v = wind speed in m/s
d where k = 20
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Smaller Hailstone
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Larger Hailstone
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Mass in lbs and kg
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Fall Velocity in m/s and mph
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Diameter in inches
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Circumference in inches
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Total Kinetic Energy (kg m2/s2)
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Problem 2 -
Part 1: Track of a Winter Storm
Shown below is a map with a black arrow that represents the path of a low-pressure system (i.e., winter storm, or extra-tropical cyclone). The low-pressure system formed just east of the Rocky Mountains where the arrow begins and tracked toward the east coast along this arrow. Answer the following questions.
1. Shade in on this map where you would expect to find snow falling along this low-pressure system's track.
2. What is the name of a winter storm that follows this track?
3. What type of precipitation should Chicago, IL expect when a low-pressure system follows this track in winter?
Part 2: Liquid to Snow Ratio
Many of you have probably heard that an inch of rain would make a foot of snow if it were cold enough to snow. This statement is referring to a term/phrase in meteorology that is used all winter long called the "Liquid to Snow Ratio". When weather models predict the total amount of precipitation, it is always done in "inches of liquid equivalent". In other words, the models predict the total amount of water in liquid form that can be precipitated from the atmosphere for a given weather event. Meteorologists turn these values into snowfall totals by applying a "Liquid to Snow Ratio". The most common ratio is 1:10 but the colder the air is when it snows, the higher the ratio.
Imagine a winter storm was heading for Champaign and the forecast models predicted we would get 0.8 inches of liquid equivalent precipitation. Use the liquid to snow ratios for each temperature range given below to calculate the total snow depth in inches. Write your answer in the space to the right of each scenario.
Scenario #1: The temperature will be 30°F and the ratio is 1:7. _________________________________ Scenario #2: The temperature will be 24°F and the ratio is 1:10. _________________________________ Scenario #3: The temperature will be 16°F and the ratio is 1:15. _________________________________ Scenario #4: The temperature will be 8°F and the ratio is 1:20. _________________________________
Part 3: 2011 Groundhog's Day Blizzard
During the winter of 2011, a large and powerful winter storm hit Illinois very hard. Chicago saw a large blizzard that stranded cars on Lake Shore Drive as snowdrifts 3-4 feet tall stopped all traffic. Students at the U of I had to deal with 7 inches of sleet, while just to the south, students at Eastern Illinois University saw 2 inches of ice accumulate from a freezing rain event. Finally, southern Illinois had to deal with flooding rains!
The image below shows 4 separate soundings that are each labeled with a letter. The solid black line on each sounding represents the temperature profile during the height of the winter storm in Illinois on Feb 2, 2011. The red line represents the 0°C (32°F) isotherm. To the right of the red line, temperatures are above freezing and to the left, temperatures are below freezing. Match the sounding to the location based upon the description above.
Chicago Blizzard: _____________ U of I Sleet: _____________
EIU Freezing Rain: _____________ Southern IL Rain: _____________
Snowfall totals across the Chicagoland ranged from 15 inches to over 2 feet during this blizzard. If we assumed that on average, the metro area was covered in 19 inches of snow, what percentage of the volume of the Grand Canyon would this amount of snow fill? Show all of your work!
Information you need:
Area of Chicago and surrounding suburbs: 10,857 Average depth of the snow over Chicago and surrounding suburbs: 19 inches Volume of the Grand Canyon: 4.166
Part 4: Ice Accumulation
I fear an ice storm hitting my house more than any other type of weather except a massive flood. The reason is that I live on about 3⁄4 of an acre and I have 31 trees in my yard. They are beautiful, full grown trees and it is one of the reasons that we bought out house. But, if a huge ice storm were to hit my neighborhood, I would be in serious trouble. Ice storms can do more damage to trees than a powerful tornado simply by adding enormous amounts of weight to the tree as the ice accumulates causing the tree to collapse.
I estimate that my trees have approximately 75,500 square feet of exposed surface onto which ice can accumulate. If an ice storm hits central Illinois and I receive 2.3 inches of ice accumulating on the exposed surface of my trees (i.e., branches, pine needles, leaves that didn't fall off as winter began etc), how much in total additional weight would these trees have to carry once the ice has accumulated? The typical density of ice is about the ice in your freezer because it has some air trapped in it.) Show all of your work!
Part 5: Cooling Rates
One tool that a coroner uses to estimate the time of death for someone who has died while exposed to the environment is Newton's Law of Cooling. This law provides the relationship between the rate of change of the temperature of an object (i.e., the loss of heat) when exposed to the environment. Let's set up the equation: (Note: this equation does not consider the impact of the wind!)
Imagine a woman was walking her dog on a really cold day, and while far from her house, she had a heart attack and died. The dog ran away and got help, but took a long time to do so. When the police discovered the body later that day at 8PM, her body temperature had dropped from 98.6oF to 36oF. The environmental air temperature was 6oF. What time did she die from the heart attack? Show all of your work!
Attachment:- Problems.rar