Some helpful references are:
1.) Examining The Seasonal Model Peformance: The question arises as to what extent do random, strong wind events influence the property evolution of the mixed layer in our simple PWP model? Our model is "forced" by climatological, steady, averaged winds while the real ocean feels the effects of storms passing through. The effect of these storms is to push the mixed layer harder, making it unstable and having it turn over. The converse problem would be during lull periods when the mixed layer would tend to stagnate and become very thin (at least in the summer). A simple minded view might be that our turbulent diffusion kind of compensates for this: or the model may need a higher turbulent diffusivity to "simulate" this behavior. Below is a matrix of model runs with varying turbulent diffusivity (the columns) and varying "stochastic forcing".
| Forcing/Diffusivity | 0.50x10-4 | 0.75x10-4 | 1.00x10-4 | 1.25x10-4 | 1.50x10-4 |
| Smooth Winds | d11.mat | d12.mat | d13.mat | d14.mat | d15.mat |
| Half Stochastic | d21.mat | d22.mat | d23.mat | d24.mat | d25.mat |
| Full Stochastic | d31.mat | d32.mat | d33.mat | d34.mat | d35.mat |
| Double Stochastic | d41.mat | d42.mat | d43.mat | d44.mat | d45.mat |
The first row is the model run with the climatological winds. The second and succeeding rows are with varying degrees of stochastic winds. A random component (with a decorrelation time of 4 days) is added to the wind stress. This random component has a seasonal amplitude (it is larger in the winter, smaller in the summer) which is matched to the climatological wind stress variance. "Full stochastic" is this case. Two other cases are presented with half and double the climatological variance. Below is a picture of the zonal wind stress (as an example) for the fully stochastic case. The stochastic wind stress is plotted in green, the climatological in red. Note the winter/summer difference in amplitude.
Each data file is a mat-file containing the temperature from a three year simulation which starts on March 15th. They each contain the same variable name ("Ta") which is a 150 (depth) x 73 (time) temperature array, so if you load more than one of them into MATLAB at the same time, you will need to rename the "Ta" matrix. Download the data (using shift-click) and compare the model runs to the climatological temperature fields. We have kindly provided you with the Levitus climatology for 33N, 65W gridded onto the same space-time grid. Also included in the bdalev.mat file (aside from the temperature, which called "bdat" ) are two vectors (tf and z) which correspond to the time and space coordinates.
a) Compare the model runs to the climatology (hint: you can contour the differences with the command "clabel(contour(tf,-z,Ta-bdat))" after loading in bdalev.mat and one of the runs). Comment on, and speculate/explain any systematic discrepancy between the model and the climatology and the trends with wind forcing/diffusivity.
b) Compute the two most important "global diagnostics" of the model-data differences: the average difference and average squared deviation for each model run, and contour these diagnostics as a function of diffusivity (x-axis) and stochastic forcing (y-axis). For the stochastic forcing axis, you'd use [0 .5 1 2] as your coordinates. Explain the features you see.