Here, I re-perform the LPV analysis for 5 trajectories done in *this note* but using 1/2-day instead of 1-day outputs. No major changes are found.

Using `exp20` and `exp21` for which the LPV analysis is working (that is, the error in the PV balance is much weaker than the genuine PV changes), we found that **the LPV analysis is accurate within 1e-12/1e-11 1/(m.s)**.

The PV changes that we obtain in Fig. 2 are in the order of 1e-10/1e-9 1/(m.s) so that the LPV analysis should be accurate enough to see that. This suggests that the model genuinely does not satisfy the constraint that PV should be balanced along parcel trajectories at least over several cycles. [The only way that conclusion is not true is if the accuracy of the LPV analysis changes also with the regime. I doubt that. Furthermore, the error was the same in two different simulations, `exp20` and `exp21`, although any difference may be subtle].

The LPV analysis was done with `LPV_analysis_all_time_script.m` producing the Matlab file `LPV_analysis_alltime_d4015d4215_8E11E_30N_mid_delta_tday_0_5_exp33_sponge.mat`, all in `RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp33_sponge/` on the main disk on `ipu1`.