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Homework assignments

Homework assignments#

Note

Assignments are due via Blackboard by the time specified. Refer to the syllabus for submission and grading policies.

HW1, Hartmann Ch. 1, due Feb. 15th 9:30am#

  • Questions 1-4: Questions 1-4 in Hartmann Ch. 1

  • Question 5: Write out the full derivation of the scale height as we did in class. (Note: this is roughly as complicated as the math will get throughout the course, at least in terms of derivations we’ll go through carefully and that you’re expected to follow.)

HW2, Hartmann Ch. 2, due March 5th 9:30am#

  • Questions 2-5 in Hartmann Ch. 2

HW3, Hartmann Ch. 4 and 5, due March 28th 11:59pm#

(In order, these are slightly modified versions of Question 1, Ch. 4 and Questions 1-3, Ch. 5 of the textbook):

  1. If the top 75 m of ocean warms by 8°C during a 3-month summer period, what is the average rate of net energy flow into the ocean during this period in units of W m\(^{−2}\)? If the atmosphere warms by 25°C during the same period, what is the average rate of net energy flow into the atmosphere?

  2. The approximate volume of water retained in soil moisture and groundwater is given in Table 5.1 of the textbook (also available on the lecture slides). Use the data in Fig. 5.1 from the book (also available on the lecture slides) to calculate the time it would take for precipitation over land to deliver an amount of water equal to the soil water and groundwater. How long would it take to replace the groundwater and soil moisture if only 15% of the runoff could be redirected to replenishing the groundwater?

  3. Use the bulk aerodynamic formula (Hartmann Eq. 4.32) to calculate the evaporation rate from the ocean, assuming that \(C_{DE}=10^{–3}\), \(U=4\) m s\(^{–1}\), the air density is 1.2 kg m\(^{–3}\), and that the reference-level air temperature is always 2.2°C less than the sea surface temperature. Calculate the evaporation rate for the following values of \(T_s\), \(q\), and RH, and then answer: how would you evaluate the importance of relative humidity versus the importance of surface temperature for determining the evaporation rate?

    1. \(T_s=0\)°C, \(q_s^*=4.0\) g kg\(^{−1}\), RH=50%

    2. \(T_s=0\)°C, \(q_s^*=4.0\) g kg\(^{−1}\), RH=100%

    3. \(T_s=30\)°C, \(q_s^*=28\) g kg\(^{−1}\), RH=50%

    4. \(T_s=30\)°C, \(q_s^*=28\) g kg\(^{−1}\), RH=100%

  4. Calculate the Bowen ratio using the bulk aerodynamic formulas for surface temperatures of 0, 14, and 28°C, if the relative humidity of the air at the reference level is 75% and the air–sea temperature difference is 1.8°C. Assume that the transfer coefficients for heat and moisture are equal.

HW4, due May 14th 11:59pm#

  1. (Hartmann Ch. 6 Q4) Calculate the zonal velocity of an air parcel at the equator, if it has conserved angular momentum while moving to the equator from 20°S, where it was initially at rest relative to the surface.

  2. (Hartmann Ch. 7 Q1) Use the data in Figs 7.1 and 7.2 to estimate how much the salinity of the surface water of the Arctic Ocean would need to increase before the surface density would equal the potential density at 1000-m depth. How does this compare with the average salinity of the ocean?

  3. Play around with this online interactive simulator of a double pendulum for a while: https://www.myphysicslab.com/pendulum/double-pendulum-en.html. What settings (initial conditions of each rod, mass of each rod, lengh of each rod, etc.) make it enter the “chaotic” regime? Include two screenshots, one in the non-chaotic regime and one in the chaotic regime.

  4. Using ChatGPT or another LLM of your choice, research the Pacific Decadal Oscillation. After you use the LLM, double check what you’ve learned against a more reliable source such as the textbook in CH. 8 or the wikipedia page on the PDO. Use what you’ve learned from all sources to answer Q10 from Hartmann Ch. 8: “Assemble a list of arguments for and against the following statement. “The PDO is just the low-frequency, extratropical signature of ENSO, nothing more.”

  5. (survey Q) How much did you learn or not learn from the previous question using an LLM? Do you have any ideas of how to effectively incorporate LLMs into this class or other classes?

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