Exercise - Budgets
Heat budget of the surface mixed layer
- What is the specific heat capacity of water?
- Sketch what the temperature profile below would look like if it lost enough heat so that it was a uniform temperature to 100 m?
- How much heat would have to be lost from the surface of the ocean for this to happen? Estimate from the temperature profile and show how you calculated this.
- What is the average heat flux this heat loss would represent if it occured over 6 months, in W/m^2. Based on the plots in the reading is this a reasonable net surface heat flux?
Interpret the evolution of the surface mixed layer
Based on the following plot, try and answer the following questions:
Q Why does the mixed layer deepen in the winter?
Q Why does it shoal in the spring and summer?
Q Why do you think there is often a spring bloom at Station Papa? Why does it stop?
Diffusive fluxes…
The geometry and units of fluxes are a bit difficult to get clear, so lets practice them here. Consider the following table of data points:
| Depth [m] | Concentration Sulfur [$g\,m^{-3}$] |
| 5 | 2 |
| 15 | 3 |
| 25 | 6 |
| 35 | 6 |
| 45 | 4 |
| 55 | 2 |
Q Sketch the profile of Sulfur with depth.
Q Doing this sort of thing abstractly becomes hard. Lets assume this profile was collected in a column of water that is 65-m high, 1 meter wide and 1 meter deep. Divide the column into 10 x 1 x 1 m^3 blocks centered on our measurements. Approximately, how many grams of Sulfur are there in each of the 6 blocks?
Q Approximate the gradient of Sulfur concentration at each the boundaries of each of the boxes (i.e. 10 m, 20 m, etc..).
Q If the turbulent diffusivity is $K=10^{-3}\ \mathrm{m^2\,s^{-1}}$ what is the diffusive transport across each of the block faces? Make sure you get the direction correct. Report your result in grams/second.
Q Consider any one block. You now should know the value and direction of flux (in $g/s$) across the upper and lower face, and you should know the total grams inside the block. If you assume the flux remains constant for 1000 s, how many grams of Sulfur are in your cell after 1000 s?
Q Repeat for all 6 cells (hint, use a computer!) and plot the new sulfur profile after a 1000 s.
Q repeat the procedure 9 more times to get the gradient after 10000 s; (Hint: really use a computer;). Plot the sulfur profile at each timestep.
Q Do the changes of the profile correspond to your intuition of how diffusion works?