I finally succeeded to correct the PV test –the problem was that the 1-day averaged output PV needed to be averaged over two consecutive time steps to be compared with the PV deduced from *snapshot* U and V. Now, the two estimates of PV –from output snapshots (dashed lines) and from output averages (dotted lines)– are almost the same with the error being much smaller than the error due to the violation of the PV equation (difference between the blue and red curves; Fig. 1). Fig. 1 shows also that PV is not conserved with time because of dissipation. It also shows that the *net* PV change after one cycle is, however, much smaller than the amplitude of change during the cycle.

Fig. 2 shows the net PV changes for the six parcels. For all parcels except the one at 10.15°E and 30.15°N, a positive net change corresponds to a net northward displacement and inversely. Fig. 2 also shows that the error using different estimates (snapshot in squares or average in circles) stays smaller than the actual net PV change and is in most cases smaller than the difference due to the violation of the PV equation (red *versus* blue markers). Interestingly, it also shows that, for half of the parcels, the error due to the violation of the PV equation after one cycle is smaller than the corresponding net PV change; so for these parcels, one could say the PV equation is respected over each cycle.