Fall Quarter 2012

Mondays and Wednesdays 1:30-2:50, Hinds 561

Current News and Announcements

 

 

The Final Exam for 2012 is now available here. Download it at your convenience, and turn it in within 48 hours of the time you begin work, but before the end of exam period. The exam is designed to take about 6 hours to do, but your mileage may vary. When you are finished, please turn in your exam to David Taylor in the front office. If you need to hand in your exam on Friday after the front office closes, you may give it directly to me (RTP) by 5PM Friday.

Recordings of selected 2012 lectures are now available here .

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Course Information

• Synopsis: This class will teach the basic physical principles of thermodynamics and radiative transfer needed to build simple models of the climates of Earth and other planets. Examples will be drawn from Earth's climate evolution over the past four billion years, the near and distant future climate of Earth (including global warming), the climates of Solar System planets, and conjectured climates of the newly discovered extrasolar planets.
• Textbook: The textbook for this course is my book, Principles of Planetary Climate. I will be following this book quite closely (primarily Chapters 1-3). Problems will be taken from the problems and projects in the book. See the PlanetaryClimateBook link for information and additional course resources
• Course resources (software, useful links, datasets) are found at the PlanetaryClimateBook  link.
• TA and office hours: Feng Ding (fding.dfdfdf (at) gmail.com). Office hours will be arranged based on demand.
• About Python: The computational exercises in this course will be carried out using the programming language Python, which is free and can be installed on Mac OS, Linux or Windows. No prior programming experience is assumed, and Python will be taught as part of the course. Indeed, this course serves as an introduction to scientific programming. For information on installing and using Python, click on the Python link at PlanetaryClimateBook 
• Labs, problem sessions and Python clinic: Approximately once per week, time and day to be arranged. The primary purpose of these is to help people get used to solving problems using Python. Some of the problem assignments are referred to as "labs," but they can be done on your own computer or over the network whenever it is convenient for you (so long as you meet the due date).
• Problem sets: Approximately once every 10 days (one per three lectures)
• Midterm: None
• Final exam: Take-home
• Prerequisites: Classical mechanics, including energy concepts (kinetic and potential energy, Newton's Joules, Watts and all that). It would be helpful if you have seen some thermodynamics previously, but not strictly necessary. Single-variable calculus, including simple first-order differential equations.

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Assignments

• Current Assignment (Assigned 11/28/2012, due 12/5/2012)
  • Using real-gas OLR curves: 4.18,4.19,4.22
  • Kirchhoff's Law: 3.36,3.37,3.38
• (Assigned 11/16/2012, due 11/28/2012: (There will be one more assignment after this, before the take-home final))
  • 3.21, 3.22,3.24
  • Problem S3.1: Since the energy in a photon with frequency nu is h*nu, the blackbody spectrum of photon flux in any give direction is B(nu,T)/(h*nu). Using this formula, compute the net flux of photons of all frequencies through the surface of a blackbody with temperature T. Show that the flux, in numbers of photons per unit area of the body's surface, has the form b*(T**3), and compute the coefficient b. Use this formula to estimate the number of photons per second that a 2m diameter telescope in Earth orbit would receive from an Earth-sized planet having uniform radiating temperature 300K, located at a distancd of 20 parsecs from Earth.
  • Problem S3.2: This problem makes use of the dataset ADLEOrev.txt , which gives the spectrum of the flux from the star AD Leo as observed from Earth. The spectrum is given in units of W/m**2/micron, so notice this is the flux density expressed in wavelength space, not frequency space. Answer the following questions:
    • (a) Why does this measurement yield a "flux per wavelength" rather than a "flux per wavelength per steradian"?
    • (b) Do a crude estimate of the temperature of this star, based on using the Wien Displacement Law on the wavelength where the emission peaks. Remember to take into account the fact that this is the spectrum in wavelength space, so you have to use the proportionality constant appropriate to the wavelength rather than frequency spectrum. (The number you need is given in the text).
    • Write a function Bw(w,T) expressing the Planck density in wavelength space, with wavelength w measured in microns. Find values A and T such that A*Bw(w,T) is a good approximation to the observed spectrum. (It is acceptable to do this by just trial and error and looking at the graphs, but if you can think of a systematic way to determine the best fit, that is even better). Discuss where the deviations from blackbody emission are greatest. How does the ultraviolet emission compare with the blackbody flux? (You'll need to plot the results on a log scale in order to see the details of the weak UV emission).
    • AD Leo is 4.9 parsecs from Earth. Use the coefficient A in your fit above to estimate the luminosity of the star, in units of Solar luminosity. Compare your result with the reported luminosity of AD Leo.
    • Compute the cumulative flux spectrum of AD-Leo from the dataset, and display it in both wavenumber and wavelength space.
  • Problem S3.3: Consider a tide-locked planet in a circular orbit about its star, for which the dayside has uniform temperature T1 and the nightside has uniform temperature T2<T1. The system is located at a distance d from the Earth, and the plane of the orbit is such that the planet transits (i.e. the planet passes directly in front of the star and directly behind it). Compute and plot the time variations of net flux that a a space telescope in Earth orbit would receive when pointed at this system. How would your result change if the observation were carried out on the Jeans tail of the spectrum (h*nu/kT << 1) instead of over the entire emission spectrum of the planet?
  • 3.30, 3.32
  • 3.35 (Daisyworld)
• (Assigned 11/7/2012, due 11/16/2012)
  • More on moist adiabats: 2.54 , 2.56
  • Planck function problems: 3.12, 3.13
  • Radiation balance problems: 3.14, 3.18, 3.19, 3.20
  • Greenhouse effect: 3.27, 3.29
• (Assigned 10/29/2012 . Due 11/7/2012):
  • 2.37, 2.42, 2.45, 2.47, 2.50, 2.52; For Problem 2.52, you need not program up your own integrator using midpoint or Euler. Feel free to just use the integrator class in ClimateUtilities, if you find that more convenient.
  • 3.2, 3.6, 3.10
• (Assigned 10/19/2012 . Due 10/29/2012):
  • Dry thermodynamics and hydrostatics problems: 2.16,2.20,2.24,2.28
  • Data analysis (atmospheric temperature profiles): 2.22, 2.23. (Read the instructions for 2.21, to get some useful Python tips for data analysis)
  • Introductory problems with phase change (moist thermodynamics): 2.31, 2.34
• (Assigned 10/10/2012 . Due 10/19/2012): Send in problems to Feng by email, or leave a printout in Feng's mailbox. The next problem set will be posted 10/19, so check the web that afternoon.
  • Basic physics warm-up problems: 1.9, 1.15, 1.18
  • Some data analysis and numerical toolkit warmups. Before doing these problems, you should create a working directory, download the courseware modules ClimateUtilities.py , ClimateGraphicsMPL.py and put them in that directory. You might as well also download phys.py, and planets.py, since they have physical constants you might find useful in doing the thermodynamics problems. In order for Python to be able to import these scripts, (e.g. using from ClimateUtilities import * in the interpreter or at the start of your script) you must either start up the interpreter while this is your working directory (if you are running interactively), or save your script into this directory before running it. Next week I will show you how to set up Python so you can put these scripts in a central place and have Python find them from wherever you are (if you are already an expert, you probably know how to do this by setting the PYTHONPATH environment variable.
    • As an introduction to simple data analysis and data plotting, do Problem 1.3. The GISS temperature dataset can be downloaded directly from the link under Chapter 1 Data on the Data page of the PlanetaryClimateBook site. See the section on "The Curve() Object and its Uses" in the Python tutorial, and also the Python Tips part of Problem 1.2. (You don't need to do Problem 1.2). Note that the disk icon in the MatPlotLib window allows you to save your graphics as a png file, for inclusion in your write-up. An alternative approach to saving graphics, if you have some problem with that, is to do a screen shot (e.g. using Preview on a Mac).
    • As an introduction to numerical integration of ordinary differential equations, do Problem 1.7 . You should read about the midpoint method in the Numerical Recipes reference available free online (Any of the older free versions will do), and implement it yourself as a loop. The Wikipedia description of the midpoint method is also good. You don't need to implement your own version of Runge-Kutta; you should just learn how to use the integrator class in ClimateUtilities. After doing from ClimateUilities import * , just type help(integrator) for instructions.
  • Atmospheric thermodynamics problems: 2.4, 2.6, 2.8, 2.11, 2.14
• (Assigned 10/1/2012 . Due 10/10/2012): Install Python on your computer if you need to. Read my quick-start Python tutorial found here, Sections 2.1 through 2.2. Try out the basic features of the language, through lists, functions, conditionals and use of the numpy array package. Turn in a copy of your interpreter session(s) as a text file, showing what you have tried out (email it to feng ding). Learn how to use idle to edit, save and run a Python script. To see if your graphics is working properly try the following in the interpreter: first import the graphics by typing: import pylab . If this works and you don't get an error message, create a graph by typing: pylab.plot(range(10));pylab.show() . You should see a window with a graph of a straight line appear on your screen. Read Chapter 1 of textbook through Section 1.6 .

Recordings of selected 2012 lectures

• Monday, 12 November. In part of the middle of the lecture my stylus stopped working and I had to move over to the blackboard. You still have audio, but it's probably best to just fast-forward past this section. The missing part of the lecture is covered on pages 146-150 of the text, and discusses the basic way the greenhouse effect works.
• Wednesday, 14 November. (Sorry I dropped my microphone a few times, so the audio may drop out sometimest).
• Thursday, 15 November. Working with the angular distribution of blackbody radiation, Lambert's law, and the projected area rule. Applications to infrared photometry of extrasolar planetary systems.
• Monday, 19 November
• Wednesday, 21 November

Recordings of Lectures

• Lecture 2
• Lecture 3
• Lecture 4; Sorry, but I forgot to start recording until about a half hour into the lecture. You missed some material on Martian river networks, and on exoplanets with eccentric orbits and the implications of illumination by dim, red stars, but you can pick that up from the relevant sections of Chapter 1. I did manage to record essentially all of my lecture on stable isotope proxies. Note that there is a misprint in the textbook regarding the deuterium concentration in Jupiter and the outer portions of the Sun (should be about 1 in 50,000 molecules , rather than 1 in 1700 as stated. Jupiter is thought to be representative of the primordial composition, and Earth's oceans are very enriched in Deuterium relative to that. Nuclear fusion in stars destroys deuterium, so there should be very little in the deep Sun).
• Video tutorial on where to put modules you want Python to be able to import. You should understand this before downloading the courseware modules.
  • Part 1
  • Part 2
• Lecture 5
• Lecture 6
• Lecture 7 Correction: The discussion of dry static energy should have pointed out that the dry static energy is not a general exact differential of the First Law. The derivation of dry static energy conservation given in the lecture only works if the motion is adiabatic (delta-Q = 0) so that density can be written as a function of pressure alone.
• Lecture 8
• Lecture 9
• Lecture 10
• Lecture 11 (Finished moist thermodynamics and started blackbody radiation)
• Lecture 12
• Lecture 13
• Lecture 14
• Lecture 15
• Lecture 16
  • Part A: Snowball
  • Part B: Angular distribution and exoplanet observations Note that in my haste to finish, I left out a small but critical step towards the end, in my derivation of the emission from a disk, as seen by a distant observer. I wrote the flux from the disk as sigma*T^4, but that already incorporates the angular integral, so you get an extra factor of pi if you try to do it this way. The right way is to use the Planck function B. The disk emission is (pi r^2) B where r is the radius of the disk, and the flux seen by the observer is reduced by 1/ro^2 to account for dOmega, where r0 is the distance to the observer. Then, when you integrate pi*B you get sigma T^4 as desired.
• Lecture 17 (Kirchhoff's law. Optically thin atmospheres. Tropopause height. Skin temperature)
• Lecture 18

Syllabus