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


Homework style example.


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

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.
Determine the optical depth corresponding to optimally bright clouds.

1. This problem refers to the 1 layer atmosphere model we discussed in class (November 23 2020, and previously), 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 and albedo A=0.3 for this problem in parts A through C.

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.

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?

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 for the direct beam, τ=exp(-BC*MAE*H].
Related reference for air pollution in cities.
Reference discussing black carbon aerosol emission from gas flaring.

2. This problem is about the reflection and transmission of shortwave radiation through a cloud.
Notes from class part 1 no ground: part 2 with the ground: and diffuse calculation.
Consider a cloud with droplets that all have a diameter of 17 microns, and a cloud thickess of 1 km.
Use the Mie Theory Calculator to calculate the asymmetry parameter g at a wavelength of 550 nm.
The calculator calls the asymmetry parameter the "average cosine of the phase function". (be sure to look at the shape of the phase function.
You'll need to use the refractive index of water at this wavelength.
This problem uses the one dimensional radiative transfer equation we discussed in class.
You may also want to read this article that describes the theory as well.
Make a graph of the transmitted total, diffuse, and direct fractions as a function of optical depth ranging from 0 to 100.
Use a logarithmic scale for the horizontal axis to help see the overall range best.
i. At that optical depth is most of the direct radiation gone? (This is the optical depth you would no longer see the sun through the cloud.)
ii. At what optical depth is the diffuse radiation maximum? How many cloud droplets per cubic centimeter (cc) are there for a 1 km thick cloud? (The cloud would look brightest at this optical depth).
iii. What fraction of the total and diffuse radiation are transmitted through the cloud at an optical depth of 100?
Note: Here's Python code you can use to calculate values that can be read into Excel, etc, for making a graph. You can use the online Python interface or others.

The image below shows the relative probability of obtaining different cloud optical thicknesses (same as cloud optical depth) in north central Oklahoma .
i. Read and report the cloud optical depth off of the graph that corresponds with the peak counts.
ii. Calculate and report the cloud reflectance at this optical depth when the cloud is above ground that is very dark (has an albedo of zero, A=0).
iii. Calculate and report the cloud reflectance when it is above ground with a surface albedo of A=0.2.

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




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

Observe how relatively simple analysis can lead to climate insight concerning the Earth's radiatian budget and response time to climate change.

Appreciate that we have modeling capability we have for understanding the role of clear sky downwelling infrared radiation in the atmosphere.
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.

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.

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 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.

5. A student has an infrared spectrometer measuring the spectral downwelling infrared radiation from 5 to 20 microns on a clear day.
The spectrometer resolution is about 0.015 microns, also known as 15 nm.
Our goal is to provide insight into that spectrum based on a relatively simple model (that can easily be generalized).
The simple model is stated as follows:
Consider a 100 meter isothermal layer having a temperature of 285 K, a dew point temperature of 275 K so that the RH≈50%, the volume mixing ratio is 0.00812, and the total pressure is 860 mb.
Carbon dioxide had a mixing ratio of 408 ppm and the same total pressure.
No other infrared active gases are present.
Here are the spectral transmittances for water vapor and carbon dioxide for passage through 1 meter length (done at 1 meter to keep the strong lines from saturating) and are in graphical form here for H20 and CO2. It may be useful to right click on the files and save them, and use the Excel:File:Options:Data:From Text (Legacy) to read them in.
A. Calculate and overlay the absorption cross section per molecule (units of cm2 per molecule) for H2O and CO2. Note regions where each molecule has especially strong and weak absorption.
B. Calculate and overlay the spectral transmissivity through the 100 meter layer for both gases combined. Note the spectral ranges for windows (maximum transmission).
C. Calculate the spectral downwelling infrared radiation in units of [W / (m2 Sr μm)] from the product of blackbody emission times the spectral emissivity (note: emissivity = 1 - transmissivity), and note the spectral ranges for maxima and minima.
D. Assuming the Earth's surface is a perfect blackbody at a temperature of 305 K, calculate the spectral upwelling infrared radiation in units of [W / (m2 Sr μm)] going out the top of the isothermal layer, including both the radiation emitted by the layer and that emitted by the Earth and transmitted by the layer. Comment on the layer's impact on the outgoing IR.
E. Derive the relationship for spectral brightness temperature and calculate it for part D spectra. Interpret.
F. Discuss the HITRAN 2016 spectral data base that was used in the GATS software to obtain the spectral transmittances for this problem.
(What is HITRAN? Why does it exist? How many absorption lines are in it?)
Resources for problem 5.
Equation for black body radiation as a function of wavelength, from equation 7 of this reference.

Radiation transfer, pages 127-144 of Wallace and Hobbs. Compare figure 4.32 with the brightness temperature in part E.
Great discussion of blackbody radiation, and the reference for the equation we are using for it.
Various cross sections of carbon dioxide.






Homework 3. CAPE and chapter 3.
Turn in this homework assignment through webCampus, prepared using Microsoft Powerpoint.
Also provide an oral presentation through Zoom by sharing your screen, or in class.

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.
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-E guide you through acquiring your data and intrepreting it.

A. 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.
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.

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 the CAPE and precipitable water from your sounding.

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.

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.

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 0. 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 1. 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 2. Give a table of values for your location and include:
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 units.
i. 500 mb wind direction from the sounding and inferred from the 500 mb level graph.

Section 3. Graph with all the potential temperature and equivalent potential temperature curves versus height.
Discuss atmospheric stability using these graphs. (See step D).

Section 4. Prepare a 500 mb level graph and discuss it. (See step E).

Conclusion: Summarize your findings.

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 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.




Homework 2
. Chapter 3, part 1.
Turn in this homework assignment through webCampus, prepared using Microsoft Word.

Cement 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. Tv virtual temperature
b. Tdew dew point temperature
c. Tw wet bulb temperature
d. θ potential temperature
e. θw wetbulb potential temperature
f. θE 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. Create a program using Python for obtaining Tdew given values typical for the class room air To=21.3 C, wet bulb temperature Tw=12 C and Po=871 mb.
We will develop the theory for this problem in class, the pertinent notes are here.
Also report ws(Tdew), ws(Tw), ws(T), RH, θ, θw, θE, and the LCL temperature and pressure.
The LCL calculation requires inputs of Tdew, To, and Po
This program is a starting point, and it has the LCL calculation in it.
Add your code for obtainining the dewpoint, or write a separate program. Theory.
Compare the Python results with values from a skewT diagram.
You can check your dew point calculation with the National Weather Service water vapor calculator.

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.

Problem 3 Table: Given To=21.3 C,
wet bulb temperature Tw=12 C and Po=871 mb
Quantity Units Value from skewT Value from Python Comment
Tdew C     Dewpoint temperature
ws(Tdew) g/kg     water vapor mixing ratio at saturation at the dewpoint temperature
ws(Tw) g/kg     water vapor mixing ratio at saturation at the wetbulb temperature
ws(T) g/kg     water vapor mixing ratio at saturation at the air temperature
RH %     Relative humidity
θ K     Potential Temperature
θw K     Wetbulb Potential Temperature
θE K     Equivalent Potential Temperature
LCL Temperature C     Temperature at the lifting condensation level (LCL)
LCL Pressure mb     Pressure at the LCL

b. Screen shot of Python program and output, and values entered into the table.

4. This problem explores hurricane dynamics and thermodynamics.
It will be in short report format as discussed in Homework 1, 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).
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=Toln(Po/Peye)/ln(Peye/200mb) where To=-3 C = 270 K, and Po=1010 mb.]
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.


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

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.
Look at data from July 2020 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. (Example).

3. Prepare a short report that describes the atmosphere for 00Z, 10 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 (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 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).

Density of dry and moist air

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. Calculate and graph the water vapor density in grams/m3 for Barrow and overlay with the SOCA, 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.

In your report, compare and contrast the difference in the meteorology between these two sites for 10 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. 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.

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.
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. This is similar to problem 1.20. The answer is around 2.5 mm⁄sec. Show that the air speed is v=(dp⁄dt) RE ⁄ Ps where RE is Earth's radius and Ps is the average surface pressure and evaluate using Python (include in your report).
b. Obtain the surface pressure averaged from 1950 - 2019 for Dec/Jan/Feb and for June/July/August from reanalysis (two figures). [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].
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.


Homework 0
Turn in this homework assignment through webCampus, using Microsoft Word.

Skew T lnP Practice homework based on the atmosphere of 27 August 2020:
Instructions: Place your results from parts 2, 3, 4, 5 and 7
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 for pressures in mb of 846, 700, 500, 400, and 250 mb.
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 values at the pressures given in part 2.
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 (passing hurricane) 12Z sounding and compare with the Reno sounding. What do you see that's different?

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





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 or other data of the atmosphere or environment, and explain the Atmospheric Physics connection.
You can use more than one photograph, 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 6th 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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