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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

../../../../../_images/statistically_stationary_test_exp32.png

Figure 1: Time series of basin averaged kinetic energy in the middle layer for exp32.

../../../../../_images/statistically_stationary_test_exp36.png

Figure 2: Time series of basin averaged kinetic energy in the middle layer for exp36.

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.

../../../../../_images/LPV_analysis_alltime_d4005d4195_8E11E_30N_mid_exp32_traj.png

Figure 3: Trajectories of 5 parcels in exp32.

../../../../../_images/LPV_analysis_alltime_d4005d4195_8E11E_30N_mid_exp32.png

Figure 4: LPV analysis along the trajectories of the 5 parcels, shown in Fig. 3, in exp32.

../../../../../_images/LPV_analysis_alltime_d4005d4195_8E11E_30N_mid_exp32_error.png

Figure 5: Error in LPV analysis over all trajectories computed (small domain: 8E-11E and 29.7N-30.3N), in exp32.

../../../../../_images/LPV_analysis_alltime_d4005d4195_8E11E_30N_mid_exp36_traj.png

Figure 6: Trajectories of 5 parcels in exp36.

../../../../../_images/LPV_analysis_alltime_d4005d4195_8E11E_30N_mid_exp36.png

Figure 7: LPV analysis along the trajectories of the 5 parcels, shown in Fig. 3, in exp36.

../../../../../_images/LPV_analysis_alltime_d4005d4195_8E11E_30N_mid_exp36_error.png

Figure 8: Error in LPV analysis over all trajectories computed (small domain: 8E-11E and 29.7N-30.3N), in exp36.

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.

../../../../../_images/UL0_VL0_several_cycles_100day_long_rand_exp36.png

Figure 9: Lagrangian-mean flow for different periods, in exp36.

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).

../../../../../_images/Lagrangian_mean_flow_test_conv_rand_day4000to4500_exp32.png

Figure 10: Test of convergence of the Lagrangian mean flow between days 4000 and 4500 in exp32.

../../../../../_images/Lagrangian_mean_flow_test_conv_rand_day4000to4500_exp36.png

Figure 11: Test of convergence of the Lagrangian mean flow between days 4000 and 4500 in exp36.

../../../../../_images/comp_UL0_VL0_20cycles_rand_day4000to4500_exp32_exp36.png

Figure 12: Lagrangian-mean flow averaged over 20 cycles (chosen randomly) over days 4000-4500 in exp32 and 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.