# 06.03.2013: Comparison of `exp32` and `exp36`

`exp32` and `exp36` are identical (KH=50 m2/s) except that the latter has doubled spatial resolution.

## Did the experiments reach a statistically steady state?

Yes

## LPV analysis

Because the flow is chaotic, trajectories are obviously different between the two simulations even if we start at the same date. Figs. 5 and 8 show an histogram of the error in the LPV analysis. The error is reduced (but not totally) with the higher resolution run.

## Issue of the period chosen to get the Lagrangian-mean flow

There is an issue over the period to choose to compute the ensemble-mean Lagrangian-mean flow. The mean changes depending on the period chosen (Fig. 9). Note that in Fig. 9, the mean flow presented has converged over the period chosen (so that the difference between the mean flows is not due to a lack of convergence of the ensemble mean). The consequence of this is that we cannot compare in details the mean flow obtained in `exp32` with that obtained in `exp36`.

Note, however, that the bigger the period, the less noisy the mean flow appears.

## Lagrangian-mean flow

Despite the issue mentioned above, the smoothed version of the Lagrangian mean seems to be the same in both experiments (Fig. 12). The conclusion that I draw is that, with lower and lower KH, the model error with respect to the LPV continuously increases. There is not a sharp transition where the model is suddenly wrong in many aspects. Hence, even if `exp32` does not satisfy well LPV (given some criterion), the Lagrangian-mean flow that it produces (the quantity that matters the most) is not fundamentally different from that obtained in a less incorrect simulation (in this case, `exp36`).

## GLM analysis

I have the files for the average over 20 cycles for both `exp32` and `exp36` and over days 4000-4500 but we still do not get a stationary steady state after 20 cycles and I am not sure it is worthy to run the expensive `exp36` simulation for many more days.

The different routines, Matlab files and script to produce the different figures are in `RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp32/` and `RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp36/` on the main disk on `ipu1`.