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


Homework style example.


Flat Earth. (Jeremy, Jacob, Christopher)
SEA (Siying, Ethan, Andy)
Earth (us) Fire (California) and Water (Talia, Taylor, Zach)
No Team Name [aka NTM, Aunti M, Wizard of Oz] (Michael, Levi, Garrick, Melinda)
Unicorn (Paul, Thomas
, Aaron)


Homework 8.
1. A. This problem uses the one dimensional radiation transfer equation we discussed in class.
You may also want to read this article that describes the theory as well. At what optical depth do water droplet containing clouds have the greatest amount of diffuse solar radiation transmitted through them?
[Hints: assume that cloud droplets all have a diameter of 17 microns, and use the Mie Theory Calculator to calculate the asymmetry parameter g at a wavelength of 550 nm. You'll need to use the refractive index of water at this wavelength. You can make a plot of diffuse radiation as a function of optical depth and read the peak off the graph, or use the Excel solver to obtain the optical depth.]

B. The image below shows the relative probability of obtaining different cloud optical thicknesses (same as cloud optical depth). Read the cloud optical depth off of the graph that corresponds with the peak counts. Calculate the cloud reflectance (albedo) at this optical depth when the cloud is above ground that is very dark (has an albedo of zero)? Calculate the cloud albedo when it is above ground with a surface albedo of 0.2.

Cloud optical depth from this reference. Click image for larger version

C. Extra credit. Fit the cloud optical thickness curve in part B to a log normal distribution function. From the fit parameters, calculate the average cloud albedo above a dark ground.

D. Second Extra Credit: Consider the top of atmosphere albedo under partly cloudy conditions. Assume that the surface albedo under clear skies is A=0.08. From your result in part C, obtain the cloud fraction fc implied by this model so that the combined albedo under partly cloudy conditions is Rtotal = 0.31.


Homework 7
1. This problem refers to the 1 layer atmosphere model we discussed in class, 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=0.7 for this problem in parts A through C.

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

B. Now adjust the solar transmissivity τ until the surface temperature is lowered by 1 Kelvin. What is the solar transmissivity that gives a reduction of surface temperature by 1 Kelvin?
What is the corresponding atmosphere temperature?
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. 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=5000 meters thick layer (assume constant air density for this calculation).
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 for the direct beam, τ=exp(-BC*MAE*H].

D. Extra credit: Extend the 1 layer atmosphere model to 2 layers having an atmospheric boundary layer coupled to the surface and the free atmosphere above. Check that the model makes sense.
Explore the model predictions for temperature of the two layers and the surface.
By induction, can you see how to extend this model to a N-layer atmosphere?
Answer the important question, does the surface warm or cool when the black carbon aerosol absorber is in the first layer, the second layer, or in equal amounts in each?
You can choose an emissivity of the first layer equal to ε=0.7, and let the second layer have an emissivity of ε=0.6.
Calculate the surface and layer temperatures as a function of the absorption coefficient.


Homework 6.
Read chapter 4. The first two problems are related to climate and radiation issues.
1. Do problem 4.21.

2. A. Do problem 4.29.
B. Extra credit. Estimate also the radiative relaxation time for the Earth's oceans taken together as one body of water.

3. A. What is the ratio of Rayleigh scattering strength for blue light compared with red light by gases in the atmosphere?
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 74 and 92.

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 5:
Read chapter 4.
Do problems 4.11 a, e, f, i, j, k, l, o, n, s, t, u, v, z, aa, cc.
They are given here, part 1 and part 2.

a. Group presentations (be sure to help each other arrive at a reasonable solution). One group member turns in the presentation for all.
Ask questions during presentations if things are not clear (both presenters and audience).

b. Each student turns in the problems through web campus so taking notes during the presentations can be very helpful.

Group presentations are as follows:

Flat Earth. (k, v, s)
SEA (j, o, z)
Earth Fire Water (e, n, aa)
NTM (a, f, l, u)
Unicorn (i, t, cc)


Homework 4. Each team will do a report and a presentation for the following. (One report and presentation from each team).
Preparation for this homework includes our class discussions, the MetEd module, and you may read section 8.3.1a on Deep Convection, pg 344-347 of Wallace and Hobbs.
Group work will allow you to confirm your conclusions with your team, to help each other.

1. For each team member, find an exciting sounding from anywhere and anytime in the world (using the Univ. of Wyoming site) with a lot of convective available potential energy (CAPE).
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.

a. 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.

b. Note the CAPE and precipitable water from your sounding.
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.

c. 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.

d. 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 specific link to use 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 sound, 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 sounding location, Lamont Oklahoma located at about 36.7 North and 97.6 West: Settings and 500 mb plot. Lamont Oklahoma will be in about the center of the image.

In the report, each team member will be listed as a coauthor.
The goal is to make your report as short as possible, but to include everything.
Introduction: Discuss CAPE and precipitable water vapor amount in the introduction, and discuss the importance of each. Be sure to define each variable when using equations.

Section 1. Include the skewT graph from the Univ of Wyoming and its interpretation, including discussion of the wind speed and direction as a function of height.
One figure for each team member.

Section 2. Give a table of values for your locations and include values in your table for:
a. Equivalent potential temperature θE 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 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.
Use one table with data from all team members so that you can compare the values.

Section 3. Prepare one graph with all the potential temperature and equivalent potential temperature curves versus height for each team member, to compare them.
You may need to have one graph for potential temperature, and one for equivalent potential temperature if they get too busy to put all on a single graph.
Discuss atmospheric stability in terms of these graphs.

Section 4. Prepare one 500 mb level graph for each team member. Discuss.

Conclusion: Summarize your findings.

Optional extra credit.
a. You may include any related atmospheric data (like archived radar data, maps of other pressure levels, etc) that helps tell your story.

b. 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 the 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.

Each team member will explain their own skewT graph and 500 mb level graph.
One team member can do the section 2 discussion.
The presentation outline is the same as the report, organized by sections, and the Appendix if the choice is made for optional extra credit.
Have each team member provide part of the presentation.

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. Read section 8.3.1a on Deep Convection, pg 344-347 of Wallace and Hobbs.
5. Skew T plots discussion.








Homework 3.
Prepare a mini report to study temperature and potential temperature as follows.
Turn in your MSword document/report through web campus.
Data will be acquired from the Univ of Wyoming balloon sounding server for Reno soundings at local times 5 am and 5 pm on October 1st.

1. Figures 1 and 2 will be the skewT logP gif format soundings for 0Z 2 October 2019 (local time afternoon on the 1st of October), and 12Z 1 October 2019 (morning sounding).

2. Plot the air temperature and potential temperature (Thetav column though convert to Celcius units) on the x axis with height on the y axis, with height in kilometers,
and to a height just above the tropopause for the afternoon sounding, 0Z 2 October 2019. This will be figure 3.
Discuss stability as a function of height by interpreting the potential temperature.
It may be helpful to think about the relationship between temperature and potential temperature (what inversions, well mixed layers, and superadiabatic layers look like from both perspectives).

3. Same 1, but for the morning sounding 12Z 1 October 2019. This will be figure 4.

4. To wrap up, you should be able to look at the soundings in part 1 and identify adiabatic layers, and how they look when plotted as potential temperature layers.




Homework 2.
Part 1. Students will present problems as assigned for their group and will turn in the assignment.
Part 2. Turn in problems of question 2 through web campus.
Parts 1 and 2 should be graded separately.

Read problem 3.18 . Then with these questions in mind, read chapter 3.

1. Present problem 3.18 . (overall we will look at questions b, c, d, e, f, g, h, i, j, l, m, n ,o, p, t, u, v, w)
Presentation Assignments (each person presents at least one problem).

b, c, q, w (Flat Earth)

d, e, f, r (SEA)

g, h, i, s (Earth Fire and Water)

j, l ,m, t, v (NTM)

n, o, p, u (Unicorn)

2. Do problems 3.20, 3.23, 3.26 (also discussed in class), 3.28.
(it will be helpful to read problems 3.21 and 3.22 before doing 3.23).

Note: On problem 3.28, if the energy release, 5x106 J/m2 is from the latent heat released in the formation of a liquid water cloud,
the cloud might have properties as follows: 100 m thick, 600 cloud droplets per cm3, 20 micron cloud radius, liquid water path 2 kg/m2,
since the latent heat release from cloud droplet condensation is 2.5x106 Joules/kg. For those interested, here's a journal article on cloud properties.
(From this information it is possible to calculate the cloud optical depth, albedo, and transmission).






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

Make one MSword document that has solutions for problems 1 through 3.

Read chapter 1.
1. Do problem 1.6. 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.
Include the SkewT LogP graph in your report and discuss it.

3. Prepare a short report that describes the atmosphere for 00Z, 9 January 2019 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 and Barrow Alaska USA. 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 gif 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.
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).

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

e. 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 as figure 7.

In your report, compare and contrast the difference in the meteorology between these two sites for 9 January 2019 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. First paragraph describes what's in the report, describes what is to be accomplished.
C. Each figure must have a number and a caption. Figures must be in publication format -- high quality figures with 16 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.
Get started early.
Take advantage of the UNR writing center to have them read your report draft to give you feedback on writing quality.

A. Meteorological data can be obtained from the University of Wyoming web site.
B. Most (or all) computers readily accessible to all students, using their netID, have Google Earth, MSword, and Excel.
C. You can use your netID to also access these software packages through the UNR remote services application.




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 10 minutes long.

Atmospheric Physics students take photographs of the atmosphere or environment, and explain the Atmospheric Physics connection.
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, etc, to also help tell the story.

ATMS 411 students will do a presentation
ATMS 611 students will do a presentation and a report.

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.

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