# Net Lagrangian PV change in exp4 and exp6¶

## Conclusion¶

I compute the net Lagrangian PV change (difference in PV between the end and beginning of a cycle of 80 days) for 4 parcels in exp4 and exp6 either using the left or right hand side of the PV equation. I also show the error in each case. Unlike the PV balance during a cycle, the error in exp4 is as small as in exp6. The error is different depending on which type of model output used (either snapshots or averages), which suggests that the error is mainly due to error in the analysis. The same calculation for exp6 but using 1-day instead of 1/2-day model output has a larger error, confirming the previous point.

With respect to the net Eulerian PV change, there is no puzzle of why the error is zero even in exp4. As long as the fields are periodic, even an uncorrect PV or HOR will go back at the end of the cycle to their respective value at the beginning, resulting in a zero net PV change from both sides of the PV equation and thus a zero error in the net PV change.

## exp4¶

Figure 1: Trajectories of 4 parcels between days 330 and 630 in exp4 using the 1/4-day model outputs.

Figure 2: (a) Net Lagrangian PV change for the 4 parcels of Fig. 1: (blue line) from Q computed with snapshots u and v, (blue dots) from Q computed with averaged output Q, (red line) from HOR computed with snapshots u and v, (red dots) from HOR computed with averaged output HOR. (b) Error in the net PV change. Each color corresponds to a parcel: (lines) using u and v snapshots, (dots) using averages. See analysis_2_script.m in RESEARCH/MODELISATION/HIM/studies/PV_and_dissipation/forced_damped_wave/exp4/quarter_of_a_day_output.

## exp6¶

Figure 3: Trajectories of 4 parcels between days 330 and 630 in exp6 using the 1/2-day model outputs.

Figure 4: As in Fig. 2 but for exp6 and the parcels of Fig. 3.