**ATMS 411 Homework [Main Page] [Daily Notes]**

Homework style example.

Homework style example with a graph.

**ONLINE ASSIGNMENTS ARE GIVEN IN WEBCAMPUS.
**

** TEAMS FOR HOMEWORK ASSIGNMENTS WHEN REQUIRED.
Team Korian: **Tayebeh, Mohammed, Bin

Team Rock and Ice:

**Homework 5.** Read chapter 4. The first two problems are related to climate and radiation issues.

1. Do problem 4.21.

2. Do problem 4.29.

3. **A.** This problem uses the one dimensional radiation transfer equation we discussed in class in weeks 12 and 13. 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.

4. This problem refers to the 1 layer atmosphere model discussed during week 11, 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 used in the theory.

**A.** What are the surface and atmospheric temperatures when the solar transmissivity is equal to 1? Explain why the surface temperature in this case is higher than the surface 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 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. Extra credit.** What mass concentration of black carbon aerosol is needed to obtain the solar transmissivity given in part B, assuming a mass absorption efficiency of 10 square meters per gram, and that the aerosol is in a 5 km thick layer (assume constant air density for this calculation). Is this mass concentration ever likely to be found in the atmosphere?

5. 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?

6. 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.** READ problem 4.11 first, page 145. Read chapter 4. Do problem 4.11. It has many parts, so start early. This presentation lists the problems.

Note: There is an error in the description of problem 4.11q.

**Here are the Team Presentation Assignments: Each student will a problem (everyone pitches in).
Team Korian: Present problems 4.11 a, b, c
Team Crafty: Present problems 4.11 d, e, f
Team Cirrus: Present problems 4.11 g, h, i
Team Rock and Ice: Present problems 4.11 j, k, l
Team Purple Bears: Present problems 4.11 m, n, o
Team Isobars: Present problems 4.11 p, q, r, s NOTE: There is an error in problem q.
Team A-Team: Present problems 4.11 t, u, v
Team Greased-Lightning: Present problems 4.11 w, x, y
Team F-sharp minor: Present problems 4.11 z, aa, bb
Everyone Contributes an Opinion to this problem:
cc**

Here is some solar radiation from the DRI weather station, and all sky camera images that correspond to this time frame.

**In addition, each person will separately turn in to web campus a solution for all parts of problem 4.11 (individual assignment).
Use MSword or PDF file format for your submittal to web campus.
You can do the assignment on paper and scan it when finished, using a cell phone app or other means for scanning.**

**Homework 3.** Each * team* will do a report and a presentation for the following. (One report and presentation from each team).

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).

a. Identify the level of free convection and the equilibrium level.

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.

(Here's the updated version we worked on in class; it also has the calculation of the moist adiabatic lapse rate.)

c. Make a graph of the vertical distribution of potential temperature (THTA in the sounding text) and equivalent potential temperature (THTE in the sounding text).

These graphs will look like the height vs temperature graphs we did in homework assignment 1.

In your discussion, identify stable, unstable, and neutrally stable regions.

Here's an example from our Barrow, Rochambeu study**;** however, just make your plot to the equilibrium level.**
**Also, just plot the data for THTA and THTE in the sounding, not the model curves.

Potential temperature and equivalent potential temperature for summer in Barrow and Rochambeau.

d. Obtain the 500 mb height map from reanalysis for your sounding, or from the University of Wyoming, 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.

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.

**Report**:

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. 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 *θ _{E}* for your air parcel (from the spreadsheet). This value is constant for the entire trajectory of the air parcel lifted from the surface.

b. Lifting condensation level height and pressure.

c. Level of free convection in meters and pressure value for it.

d. Equilibrium level height and pressure.

e. Your calculated CAPE value in Joules/kg.

f. Your calculated vertical velocity in meters/second at the equilibrium level based on use of your CAPE value.

g. Your precipitable water amount in mm.

Use one table with data from all team members.

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.

Each team member will explain their own skewT graph.

One team member can do the section 2 discussion.

**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.

**Homework 2.** Read chapter 3. Do problems 3.18, 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*: Not all of the online solutions for the latter problems are correct, especially 3.23.

**Here are the Team Presentation Assignments: Each student will present part or all of a problem (everyone pitches in).
Team Korian: Present problems 3.18a, b, c
Team Crafty: Present problems 3.18d, e, f
Team Cirrus: Present problems 3.18g, h, i
Team Rock and Ice: Present problems 3.18j, k, l
Team Purple Bears: Present problems 3.18m, n, o
Team Isobars: Present problems 3.18p, q, r
Team A-Team: Present problems 3.18s, t, u
Team Greased-Lightning: Present problems 3.18v, w, and 3.20
Team F-sharp minor: 3.23, 3.26, 3.28
**

**Homework 1**. Turn in this homework assignment through webCampus.

Read chapter 1.

A.
Do problem 1.6. Write your answers into the first part of the MSword document you will be turning in for this assignment.

B. Prepare a short report using Google Earth, MSword, and Excel to explore the following:

**Meteorology of the world: Use Google Earth to view these two locations, Rochambeau French Guiana and Barrow Alaska USA.**

**Look at data for 12Z, 24 January 2017**

Near equator: Rochambeau French Guiana (get sounding for SOCA from the Wyoming site, plot pressure and temperature vs height, calculate density and plot versus height)

Near north pole: Barrow Alaska (get sounding for PABR from the Wyoming site, plot pressure and temperature vs height, calculate density and plot versus height)

Then fit a trendline for ln(Pressure) vs height to obtain the scale height of the atmosphere at these two locations, considering data to a height of 2 km.

Observe the lapse rate Γ=-dT/dz from the slope of the temperature versus height graph and interpret.

Compare and contrast the difference in the meteorology between these two sites for 24 January 2017.

**Graduate students, also discuss the difference in meteorology between these two sites for 24 August 2017 that we did in class (undergrads can do so for extra credit).**

**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 accomlished.

C. Provide figures, each figure with a number and 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

E. Any equations should be offset, as in a textbook, and each equation should have a number. Refer to equations by number.

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.

**TOOLS**:

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.

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