In this assignment you will extend the 2-layer leaky greenhouse (grey radiation) model we analyzed in class to a much larger number of layers, which would be very tedious to try to solve without a computer.
The $N$-layer grey gas atmosphere¶
- Divide the atmosphere up into $N$ equal mass layers.
- Assume the following:
- The surface emits as a blackbody, $\sigma T_s^4$
- Each layer emits $\epsilon \sigma T^4$
- Each layer absorbs a fraction $\epsilon$ of the incident longwave radiation
- In other words, the atmosphere behaves as a grey gas.
- $\epsilon$ is the same in every layer (absorbers are well-mixed).
Your assigment¶
- Write Python code to calculate the OLR given $\epsilon$, $T_s$, and the temperature in each atmospheric layer. Your code should:
- be general enough to work for arbitrary $N$
- calculate the contributions to OLR from the surface and each $N$ atmospheric layer
- Check your code: set $T = T_s$ in every layer. Verify that your code produces $OLR = \sigma T_s^4$.
- Use observed global, annual mean temperatures to tune your model:
- Use the NCEP reanalysis long-term-mean air temperature data, following the previous homework.
- Use a sufficient number of layers in your model to get good resolution of the vertical structure. Try $N=30$.
- Use the data to set the temperatures in your model. You may need to do some interpolation between pressure levels.
- Determine the value of your parameter $\epsilon$ for which your code produces $OLR = 239$ W m$^{-2}$ given the observed temperatures.
- Using your tuned value of $\epsilon$ and the observed temperatures, calculate and plot the contributions from each layer (and the surface) to the OLR.
- Now use your code to calculate the radiative forcing associated with a 1% increase in $\epsilon$ .
- Plot the changes in the contributions to OLR from each layer (and the surface).
- As usual, write up your answers (including text, code and figures) in a new IPython notebook that runs cleanly from start to finish. Save your notebook as
[your last name].ipynb.
- Submit your answers by email before class on Tuesday February 24.