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Does the history of the simulation matter?ΒΆ

I want to know if the history of the simulation matters with respect to the PV test. More specifically, I want to know if the PV test will be different between a first simulation run with, say, 1200-s time step (without satisfying the PV balance) up to day 500 and then run with, say, 30-s time step for another 500 days and a second simulation run with 30-s time step from the beginning.

To answer this question, I am using exp4 that was run with 1200-s time step and did not satisfy well the PV balance (see this note). I run exp4 for 160 more days starting from day 640 with 1) 1200-s time step and 2) 30-s time step, and I perform the potential vorticity (PV) test for 4 parcels. The result is mixed. For two parcels, the PV balance is well satisfied in the 30-s run and not in the 1200-s run while for the other two, it is more respected but still with a significant error (Figs. 1 and 2). [update: The error in the right-hand panels is as large as in the left-hand panels. Thus, the results are not mixed, as stated. We can a priori restart a run that has not satisfied the PV balance with a smaller time step without worrying that the history of the simulation will matter.]

To know if the history of the simulation –the previous 640 days– matters, I look at exp8, a simulation similar to exp4 (especially, the SPLIT option was used), except that it was run with 30-s time step from the beginning. In this case, the PV balance is better respected for the two problematic parcels, suggesting that the history of the simulation does matter to some degree.

../../../../../_images/PV_test_exp4_d680d760_dt1200s.png

Figure 1: PV test for 4 parcels in exp4 re-run with 1200-s time step.

../../../../../_images/PV_test_exp4_d680d760_dt30s.png

Figure 2: PV test for 4 parcels in exp4 re-run with 30-s time step.

../../../../../_images/PV_test_exp8_d680d760_dt30s.png

Figure 3: PV test for 4 parcels in exp8 re-run with 30-s time step.

It is not clear, however, how it matters. One possible reason is that between Figs. 2 and 3, not the same parcels are studied –consistent with the fact that the behavior of the PV time series differs qualitatively between the two simulations although the chosen parcels have the same initial position and time. Indeed, Fig. 4 shows the time series of U and V at 2.1084E and 23.5N for exp4 with 1200-s and 30-s time step after day 640 and exp8 run with 30-s time step from day 1. It shows that all time series differ after day 640 in terms of amplitude and phase. Thus, to fairly judged if ``exp4`` run after day 640 with 30-s time step respect or not the PV balance, the PV test needs to be done over a domain, not just for a couple of parcels.

This remark applies to exp8. Althoug exp8 was shown in in this note to satisfy well the PV balance using 4 parcels, we see that this is not the case for two parcels in Fig. 3. Again, the PV test needs to be applied over a domain. [update: This remark is not founded. The vertical axis are not the same between all panels of Fig. 3. When they are, the error in the right-hand panels is as large as in the left-hand panels.]

../../../../../_images/U_V_2E_23_5N_exp4_exp8.png

Figure 4: (a) U and (b) V at 2.1084E and 23.5N for exp4 with 1200-s and 30-s time step after day 640 and exp8 run with 30-s time step from day 1.


See RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp4/160d_with1200s and RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp4/160d_with30s for exp4, and RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp8/160d_with30s for exp8. The PV test was made in each case with analysis_4_script.m located in each of these directories.