ATMS 411 Homework [Main Page] [Daily Notes] [Final Project]

Homework style example.

ONLINE ASSIGNMENTS ARE GIVEN IN WEBCAMPUS.

ASSIGNMENT DUE DATES ARE GIVEN IN WEBCAMPUS.

Homework 6. Chapter 4.
Turn in this homework assignment through webCampus, prepared using Microsoft Word.

Purpose:
Gain familiarity with geoengineering the Earth's climate.
Use a simple model to understand the role of downwelling infrared radiation on making the planet habitable.
Work with the direct, diffuse, and total radiation reflected and transmitted by clouds, and the role of multiple scattering.

1. This problem refers to the 1 layer atmosphere model we discussed in class (Nov 17th 2021, right click, save, and open with OneNote.), and is related to the idea of geo engineering ---
the idea of putting stuff into the atmosphere to reduce the amount of sunlight at the surface, to cool the planet.
Common discussions are about using scattering aerosol to geo engineer by placing them into the stratosphere.
This problem considers a different idea, putting black carbon aerosol into the aerosol that primarily absorb light.
We are actually doing a lot of this planet-wide, as a consequence of incomplete combustion, especially from diesel fueled vehicles and sources.
We'll assume that the affect of aerosol can be modeled by the solar transmissivity τ used in the theory.
Use an atmospheric emissivity of ε=0.8 and albedo A=0.3 for this problem in parts A through C.

A.
i. What are the surface and atmospheric temperatures when the solar transmissivity τ is equal to 1?

ii. Explain why the surface temperature in this case is higher than the radiative temperature found for the astronomical problem
when we considered only the outgoing infrared radiation budget (where we obtained a brightness temperature of 255 K).
Note: Here's Python code you can use to calculate values that can be read into Excel, etc, for making a graph or reading values.
You can use the online Python interface or others.
You'll need to adjust the Python code to use the atmospheric emissivity of ε=0.8.

B.
Now reduce the solar transmissivity τ until the surface temperature is lowered by 1 Kelvin.
i. What is the solar transmissivity that gives a reduction of surface temperature by 1 Kelvin?

ii. What is the corresponding atmosphere temperature?

iii. Comparing the atmospheric temperature difference between parts A and B,
what is likely to happen with the atmosphere that changes temperature by the amount you find?

C.
i. What mass concentration of black carbon aerosol, denoted by BC [units of grams/m³],
is needed to obtain the solar transmissivity τ given in part B,
assuming a mass absorption efficiency of MAE=10 square meters per gram,
and that the aerosol is in a H=5 km thick layer (assume constant air density for this calculation).

ii. Is this mass concentration ever likely to be found in the atmosphere [convert your answer to micrograms/m³ units]?
[Hint: solve for BC from the relationship τ=exp(-BC*MAE*H].

Resources for Problem 1:
Related reference for air pollution in cities.
Reference discussing black carbon aerosol emission from gas flaring.
Reference for air pollution in Dehli.
Single-Layer model of the atmosphere discussion (note: The solar transmissivity is 1 in this model, compared with ours where it's variable, τ).
Our class notes on this problem (right click, save, open with OneNote).

Problem 2

You may copy the problem statement to Microsoft Word and put your answers there.
The Mie theory calculator link in the Resources for Problem 2 will need to be used for this problem.
Here are the class notes for this problem:
Single scattering properties of a single cloud droplet discussion (right click, save, open with OneNote).
Multiple scattering properties of a cloud of droplets discussion (right click, save, open with OneNote).

Problem Statement:
A stratiform cloud fills the sky.
The cloud is 1 km thick, and is a water droplet containing cloud composed of a monodispersion of droplets all having radii = 7 microns.
Assume the droplet single scattering albedo is 1 (no absorption of radiation).
The optical depth at 550 nm is τ_ext=τ_sca=10.

Questions.

a. What is the size parameter?

b. What scattering regime is this?

c. What is the scattering efficiency factor? (Mie theory calculator).

d. What is the asymmetry parameter? (Mie theory calculator).
It is also known as the average cosine of the phase function.

e. What is the number concentration of cloud droplets?
[Hint: Calculate this from the given optical depth and the relationship with number concentration.]

f. What fraction of direct sunlight makes it through this cloud?

g. What fraction of total radiation (diffuse and direct) makes it through this cloud?

h. What fraction is the diffuse radiation to the total radiation coming through this cloud?

i. Would the sun be visible when viewed through this cloud? Briefly discuss your answer.
 
j. What is the liquid water path for this cloud? (total liquid water per unit area).


k. How much water would be collected in a cup of area A swept through the cloud?
(In other words, what is the precipited water in mm, similar to precipitable water vapor).

Resources for Problem 2:
Model to calculate light scattering and absorption by spherical particles, also known as "Mie Scattering" for the person that developed it.
Theory of multiple scattering in one dimension (an excellent discussion).
Single scattering properties of a single cloud droplet discussion (right click, save, open with OneNote).
Multiple scattering properties of a cloud of droplets discussion (right click, save, open with OneNote).

Homework 5. Chapter 4.
Turn in this homework assignment through webCampus, prepared using Microsoft Word.

Purpose:
Observe how relatively simple analysis can lead to climate insight concerning the Earth's radiatian budget and response time to climate change.
Have a deeper understanding of something we overlook in our daily lives, the blueness of the sky and the polarization of sky light.
Appreciate the radiation deficit from the equator to the poles.

Read chapter 4. The first two problems are related to climate and radiation issues.
1. Do problem 4.21. Notes from class discussion (right click on link and save to disk. Open with OneNote).

2. A. Do problem 4.29. Express your answer for the response time in units of days.
B. Estimate also the response time for the Earth's oceans taken together as one body of water. Express your answer in units of years.
Notes from class on problem discussion.

3. A. What is the ratio of Rayleigh scattering strength for blue light compared with red light by gases in the atmosphere? (You specify wavelengths).
B. How does this affect the color of the sky?
C. Describe the polarization of light seen when looking at 90 degrees from the direction of the sun on a clear day (no clouds or aerosol, just air).
See slides 77-81 and 95-97.
If you have polarized sunglasses you can go out and look at the sky at 90 degrees from the sun direction, and rotate the sunglasses to see this effect (don't look directly at the sun!)

4. Do problem 4.56. This problem is intended to help you think about the Earth's radiation budget shown in Figures 4.34 and 4.35.

Homework 4. CAPE AND SEVERE WEATHER
Chapter 3 and Section 8.3 on deep convection.
Deliverables:
1. Turn in this homework assignment through webCampus, prepared using Microsoft Powerpoint.
2. Do an oral presentation in class or through Zoom.

Purpose:
Become familiar with soundings that can be associated with severe weather and tornado outbreaks.
Investigate stability of the atmosphere using potential temperature and equivalent potential temperature.
Become familiar with reanalysis data for evaluating previous weather events.
Learn how to obtain and interpret archived radar and infrared satellite imagery.
Practice science communication through giving a presentation.

Preparation: for this homework includes our class discussions, the MetEd module, and reading section 8.3.1a on Deep Convection, pg 344-347 of Wallace and Hobbs.

Steps A-G guide you through acquiring your data and intrepreting it.

A. Find an exciting sounding (using the Univ. of Wyoming site) from anywhere in the continental US, after February 28th, 2017, with a lot of convective available potential energy (CAPE).
Preferably find a sounding that was associated with severe weather in the vicinity.
The limitation on date comes from the availabilty of satellite imagery.
Obtain both the GIF skew T image and the text file.The text file will be used for analyzing the sounding, for graphs and reading values from it.
Color your sounding using the Paint program (or other) to illustrate the level of free convection, equilibrium level,
and regions of positive and negative buoyancy (green for positive, red for negative).
Here's an example.
Check your sounding for issues like these.

I will be using the Reno 3July2021 0Z sounding for the in-class example, so this one is not available for use.
Text for the sounding.

B. Identify the level of free convection and the equilibrium level.
These can be read from the sounding indices, or at the intersections given by the lifted surface parcel and environmental air.

C. Note and discuss the CAPE, CIN, and precipitable water from your sounding.
Calculate and report the maximum vertical updraft speed in m/s and mph.
w_EL=(2CAPE)^1/2. Here EL is the equilibrium level.

D. Make a graph of the vertical distribution of potential temperature (THTAV in the sounding text) and equivalent potential temperature (THTE in the sounding text).
In your discussion, identify stable, unstable, neutrally stable, and convectively unstable regions.
Here's an example; the top height is at just above the equilibrium level.
Plotting these to just above the equilibrium level (and not the top of the sounding) allows us to see the details in the troposphere.

E. Obtain the 500 mb height map from reanalysis for your sounding for the time of the sounding, and including the location of your sounding.
Here is the link for obtaining it from reanalysis.
The latitude and longitude range for your graph can be centered at the balloon observation by finding the latitude and longtitude for it, and going +-20 degrees north and south, and west and east for the bounding box.
Interpret in terms of locations of low and high heights, and wind speed maxima and minima.
Here's an example from the 28July2017 0z, Lamont Oklahoma located at about 36.62 North and 97.48 West: Settings and 500 mb plot. Lamont Oklahoma will be in about the center of the image.
Lamont OK is site location 74646.
Draw an arrow showing the 500 mb wind direction at your site (center of the graph) based on the height contour spacings and compare with your sounding wind speed and direction at 500 mb.

F. Obtain the radar data for your location and its vicinity, and for the time around your sounding.
Use this archived radar data tool and obtain data in and around the time of your sounding.

G. Use the NOAA Weather and Climate Toolkit to get an infrared image for the time of your sounding to use in identifying cold cloud tops associated with convection.
We will likely use GOES 16 data for coverage of the entire continentaly U.S., and for better time coverage.
Here's an example of the query. And here is an example image.
The data is "Clean" Infrared Longwave Window Band. The center wavelength for this band is 10.3 microns, or a wavenumber=970.9 cm^-1. (wavenumber=1/wavelength).
Estimate cloud top temperature for any convection in the area assuming cloud top is a blackbody radiator.
You can hover over locations of interest and read the infrared radiance.
The measured cloud top radiance can be used with the wavenumber in this calculator to get the brightness temperature. Example calculation.

Presentation:
Introduction: Discuss CAPE and precipitable water vapor amount in the introduction.
Be sure to define each variable when using equations, if you use equations.

Section 1. Use Google Earth and the latitude and longitude coordinates of your sounding to create a map of the location in wide enough of an area to give an idea of its climatological context.
You may find useful climate information on your site here. Describe what motivated you to choose your site.

Section 2. Present your skewT graph and its interpretation, including discussion of the wind speed and direction as a function of height; temperature, and dewpoint temperature; and the lifted air parcel. (See step A).

Section 3. Give a table of values for your location and include:
a. Equivalent potential temperature θ_E for your air parcel. This value is constant for the entire trajectory of the air parcel lifted from the surface and can be read from the sounding as ThetaE at the LFC.
b. Lifting condensation level height and pressure.
c. Level of free convection in meters and pressure value for it.
d. Tropopause height in meters and the pressure value for it.
e. Equilibrium level height and pressure.
f. Your CAPE value in Joules/kg.
g. Your calculated vertical velocity, w, in meters/second and mph at the equilibrium level based on use of your CAPE value. The equation is w = (2 * CAPE)^1/2.
h. Your precipitable water amount in mm units.
i. 500 mb wind direction from the sounding and inferred from the 500 mb level graph.

Section 4. Graph with all the potential temperature and equivalent potential temperature curves versus height.
Discuss atmospheric stability using these graphs. (See step D).

Section 5. Prepare a 500 mb level graph and discuss it. (See step E).

Section 6. Obtain the radar data and discuss it. (See step F).

Section 7. Obtain the infrared satellite image for your area and discuss it. (See step G).

Conclusion: Summarize your findings.

Appendix:
a. You may include any related atmospheric data (like maps of other pressure levels, etc) that helps tell your story.

b. OPTIONAL: Using the sounding text, calculate the CAPE in units of Joules/kg, the estimated vertical velocity at the equilibrium level in meters/second and compare with the value on the sounding.
Also, calculate the precipitable water vapor amount in units of mm and compare with the values given on the sounding.
This spreadsheet will help you calculate temperature along the moist adiabat and gives an example for CAPE and precipitable water calculation.
Replace the example sounding with your own and redo the calculations.
(Here's another version; it also has the calculation of the moist adiabatic lapse rate.) I can assist if you would like to work with the program.
You can also make your own program with any language you would like to do this calculation. Explain what program you use, and include it in the report.

Tools and Extras
1. Soundings from the University of Wyoming site.
2. You may also obtain archived data for the 500 mb level, and precipitation data from radar imagery here.
3. Historical weather may be obtained here, mostly from surface stations at airports.
4. Archived satellite imagery from around the world can be obtained here.
5. Read section 8.3.1a on Deep Convection, pg 344-347 of Wallace and Hobbs.
6. Skew T plots discussion.
7. Archived weather radar.
8. Ingredients for a thunderstorm.

Homework 3. Chapter 3, part 1.
Turn in this homework assignment through webCampus, prepared using Microsoft Word.

Purpose:
Emphasize understanding of the physical quantities used to describe atmospheric thermodynamics.
Relate atmospheric thermodynamics to hurricane dynamics as a real world application.
Practice using the skewT graph and Python programming for atmospheric thermodynamics.

Make one MSword document that has solutions for problems 1 through 4.

Read chapter 3.
1. Define and discuss the following quantities (in your own words. Read about them from various sources and then from memory/understanding, discuss them).
a. T_v virtual temperature
b. T_dew dew point temperature
c. T_w wet bulb temperature
d. θ potential temperature
e. θ_w wetbulb potential temperature
f. θ_E equivalent potential temperature

2. Explain in words (no diagram needed) how to use Normand's rule to obtain the following:
a. Dewpoint temperature from the temperature, pressure, and wetbulb temperature.
b. Wetbulb temperature the temperature, pressure, and dewpoint temperature.

3. Given these values typical for class room air:
Ambient temperature T_o=21.3 C, wet bulb temperature T_w=12 C and ambient pressure P_o=871 mb.

Deliverables:
a. Skew T diagram showing how Normand's rule, etc, to obtain the quantities listed below, and values entered into the table.
You can copy and paste this table into Microsoft Word and fill it in. You can delete the "Procedure using skewT" column.
Include your skewT diagram showing how you obtained the various quantities as well.

b. Obtain the dewpoint temperature from this Python program by entering the values of P_o, T_o, and T_w and put it in the table where noted.
This program was written for Python 2.7.13. (Add parenthesis around the print statements to make it work for Python 3.x).
You can check the calculation using the National Weather Service water vapor calculator.
The theory for this problem is here.

c. OPTIONAL: Obtain the rest of the table values using this Python program by entering the values of P_o, T_o, and T_dew to the LCL calculator.
This program uses a simple approximation for the equivalent potential temperature, so it's accuracy isn't perfect.
This program was written for Python 2.7.13. (Add parenthesis around the print statements to make it work for Python 3.x).

4. This problem explores hurricane dynamics and thermodynamics.
It will be in short report format as discussed in Homework 2, this time with references.
At the center of a hurricane is a warm core low pressure region, the eye of the hurricane.
This table gives a categorization of hurricanes by maximum wind speed range. (local backup).
Deliverables:
a. Discuss the life cycle of hurricanes: formation, energy source, and dissipation (be sure to cite your references, see Resources.) (one paragraph for each, with inline references to the literature you cite/use).
b. Create a 'hurricane' table with headings Category, Sustained Wind Range (m/s), Eye Pressure Range (mb), Average Eye Temperature Difference (C).
We will use cyclostrophic flow theory in class to show that the pressure difference between the eye and the surroundings is ΔP=1.81ρv² where ρ is surface density and v is maximum hurricane wind speed.
Use the eye and surrounding pressure to assumed to be 1010 mb to obtain the average temperature difference between the atmospheric column above the eye and surroundings (see prob 3.26).
[We showed that ΔT=T_oln(P_o/P_eye)/ln(P_eye/200mb) where T_o=-3 C = 270 K, and P_o=1010 mb.]

Here's an example of the table for the first entry. It's convenient to use Excel for the table.

Resources:
This paper discusses hurricane properties.
You can reference it in your report, comparing your values with those in the paper, and find other references for hurricanes using the Web of Science.
We will discuss in class how to use cloud applications for EndNote and WebOfScience to manage references within Microsoft Word (download and install the Endnote plugin for Word).
We did problem 3.26 in class to develop theory for the average column temperature difference and the hurricane eye pressure given the wind speed.
National Hurricane Center site and data.
Numerous websites talk about the circulation in hurricanes.

Homework 2. Chapter 1.
Turn in this homework assignment through webCampus, prepared using Microsoft Word.

Purpose:
Study the introductory chapter for an overview of the field.
Access and interpret sounding and reanalysis meteorological data from around the world.
Calculate and graph meteorological variables to investigate their vertical distribution in the atmosphere.
Learn how to make and interpret publication quality graphs for meteorology.
Advance science writing skills.

Make one MSword document that has solutions for problems 1 through 4.

Read chapter 1.
1. Do problem 1.6 parts a, c, d, and i. Write your answers into the first part of the MSword document you will be turning in for this assignment.

2. Do problem 1.12, being sure to express your answer in degree C per kilometer.
Then go to the South Pole and find a sounding that best resembles the features of this problem.
Soundings from the South Pole are at Amundsen-Scott station 89009 in Antarctica.
Look at data from perhaps June through August and find a day with cold surface conditions and a strong inversion calculated from the first two points.
You can put the station number 89009 in the website and press enter to access this data.

3. Prepare a short report that describes the atmosphere for 00Z, 5 January 2021 for these two locations, Rochambeau French Guiana (SOCA, Station 81405) and Barrow Alaska USA (PABR, Station 70026)
a. Use Google Earth to view these two locations, Rochambeau French Guiana (coordinates 4.8222, -52.3653) and Barrow Alaska USA (coordinates 71.2889, -156.7833). Save images of each location and use as figures 1 and 2 in your report.
Include grid lines in these images so you can see the Tropic of Cancer and the Arctic Circle, respectively, and discuss the significance of these geographical demarcations,
both in of themselves and with respect to the amount of solar radiation expected to be seen seasonally in their vicinity.

b. Acquire the png format skew T soundings for PABR and SOCA for this day and time. Make these soundings figures 3 and 4 in your report.
Discuss these soundings. What is the local standard time at each site for the soundings?
Observe the lapse rate Γ=-dT/dz from the slope of the temperature versus height graph and interpret.

c. Near equator: Rochambeau French Guiana (get sounding text for SOCA from the Wyoming site.
Plot pressure and temperature vs height as figure 5 in your report.
Calculate density and plot versus height in a separate graph as figure 6).

Density of dry and moist air

d. Near north pole: Barrow Alaska (PABR).
Get the sounding data for PABR from the Wyoming site.
Overlay pressure and temperature vs height with the SOCA pressure and temperature in figure 5.
Calculate density and overlay with the SOCA density in figure 6.

e. Calculate and graph the water vapor density in grams/m³ for Barrow and overlay with the SOCA water vapor density, as figure 7.
Note that water vapor density is the product of density * w. Discuss.

f. Then make a graph and fit a trendline for the natural logarithm of pressure, ln(Pressure) vs height
to obtain the scale height of the atmosphere at these two locations,
considering data to a height of 2 km.
Include this graph as figure 8.
Here's an example of scale height.

In your report, compare and contrast the difference in the meteorology between these two sites
as a function of height in the atmosphere, both near the surface and throughout the atmosphere.

NOTE: A short report should be written like a short section in a text book.
A. Title for the report. Your name.
B. The first paragraph(s) describes what's in the report, describes what is to be accomplished. References to other literature should be in the name year format, e.g. Smith et. al. 2020.
C. Each figure must have a number and a caption. Figures must be in publication format -- high quality figures with 18 point (or greater) bold black font; tick marks inside. All axes 1 point thick and black.
D. Each figure must be discussed in the text by number, describing the significance of the figure and its relationship to other figures as needed.
E. Any equations should be offset, as in a textbook, and each equation should have a number. Refer to equations by number. Use the equation editor in microsoft word to prepare your equations.
F. The last paragraph should summarize the overall outcome of the report, and possibly discuss your results in comparison with literature results as in part B.
Get started early.
G. List of cited references.
Take advantage of the UNR writing center to have them read your report draft to give you feedback on writing quality.

TOOLS:
A. Meteorological data can be obtained from the University of Wyoming web site. Backup of data in case the website is down.
B. Most (or all) computers readily accessible to all students, using their netID, have Google Earth, MSword, and Excel.
C. Students can download office for their home computer. Excel and Word are available for students and faculty here. Sign in with your UNR netID and download Office to your computer. We will import data using the text wizard: Excel:File:Options, then check this box.
D. Description of balloon soundings of the atmosphere.
E. References to published papers and websites can be easily managed with EndNote. Scroll down to "Manage your references" for instructions.

4. a. Do problem 1.21 in the textbook. This is similar to problem 1.20. The answer is around 2.5 mm⁄sec. Show that the air speed is v=(dp⁄dt) R_E ⁄ P_s where R_E is Earth's radius and P_s is the average surface pressure and evaluate using Python (include in your report).
b. Here are graphs of the surface pressure averaged from 1950 - 2019 for Dec/Jan/Feb and for June/July/August.
[This data is from NCEP/NCAR. One objective of this problem is to become aware of this data].
[Data from NOAA, Physical Science Laboratory, Monthly/Seasonal Climate Composites]. Historical data is available in another form here.
c. Does the pressure distribution support the premise of part a?
d. Discuss the seasonal variation of surface pressure in the Northern hemisphere in summer and winter, locations of highs and lows, and meteorological consequences. (open ended question).
This topic is discussed in this online dynamics textbook near Figure 2.3, the pertinent section is here.
e. Extra credit: Here are data and graphs for 2020. The data is in netCDF format, and it could be averaged to look at this problem analytically.

Homework 1.
Turn in this homework assignment through webCampus, using Microsoft Word.

Skew T lnP Practice homework based on the atmosphere of 17 August 2021:
Reno sounding location is 72489 REV. Slidell Louisiana sounding location is 72233 LIX.
Instructions: Place your results from parts 2, 3, 4, 5 , 7 and 8 into a Microsoft Word Document and submit it to Webcampus.
1. Download the blank skewT graph to Microsoft Paint, or your favorite image program.
2. From the Reno morning sounding, write down the temperature and dewpoint temperature for pressures of mb of 845, 700, 500, 400, and 250 mb. (Local backup).
3. Put these points on the blank skewT graph using Paint and save your skewT image file.
4. Download the actual sounding for the morning and circle the temperature and dewpoint temperature values at the pressures given in part 2. (Local backup).
5. Compare with your skewT from part 3 with the actual sounding in part 4 to make sure you are understanding these charts.
6. Bring questions to class.
7. Download the Slidell Louisiana 12Z sounding and compare with the Reno sounding. (Local backup).
8. What are the local times in Reno and Slidell at the time these soundings?

Resources
Some skewT lnP applications and measurements.
Skew T lnP MetEd Module that covers nearly everything, starting with the basics.

FINAL PROJECT, START NOW!

Deliverables:
ATMS 411 in class presentation and turn in presentation here.
ATMS 611 in class presentation, report, and turn in presentation here.
Presentations are 5 to 20 minutes long depending on the number of observations and types of data used.

Atmospheric Physics students take photographs and/or use other data of the atmosphere or environment, and explain the Atmospheric Physics connection.
You can use more than one photograph or data source, and can look at a variety of phenomena.
For example, blue sky, sky polarization, coronas, halos, rainbows, lenticular clouds, gravity waves, lightning, water phase clouds, ice phase clouds,
inferring air motions and winds from cloud structures, contrails, vortices in contrails, sky color during pollution events, sky color near the horizon, sky color at sunset looking to the east.
Photographs of the dendritic nature of ice growing on windshields on cold days, the shape and nature of icicles, dew on a moist mornings are also possible topics.
Photographs of snow flakes and snow crystals, here's a discussion.
If you have special hobbies or work, like paragliding, Atmospheric Physics related aspects can be included in your project.
You can use soundings, satellite images, weather station data, etc, to also help tell the story.

ATMS 411 students will do a presentation. Presentation hints. 7 secrets of great speakers. Teachable moments.
ATMS 611 students will do a presentation and a report. Report format.

Due Dates:
Presentations: December 1st by 8 am. Presentations start that day. Turn in your presentation through webCampus.
Reports: December 7th by the end of the day. They can be submitted as a second file through webCampus.

Resources that may help

Gravity wave discussion.
Snow crystal/flake observations.
Cloud identification.
NASA WorldView for satellite imagery. You can add layers for additional information.
National Weather Service balloon soundings, served by the Univ of Wyoming.
Weather station data from the Western Regional Climate Center at DRI. In particular, the UNR weather station.

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