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.