# Net PV change over the whole domain in exp2_w¶

I realized that I could perform the PV test over the whole domain. Fig.1 shows the net PV change after one wave cycle in the middle layer of exp2_w. The different estimates are, as usual, from either using 1-day snapshot or 1-day average and from either using output or by integrating the PV equation in time. I remind that the calcul has been done by following every parcel of the domain during a wave cycle. The result is plotted at the initial position of each parcel.

Figure 1: Net PV change over a wave cycle in the middle layer of exp2_w: (a) from PV output (1-daysnapshot), (b) from PV output (1-day average), (c) from the integration of the PV equation (1-daysnapshot) and (d) from the integration of the PV equation (1-day average). The red dots in (a) show the position of the six parcels that have been used so far for the PV test.

Figure 2: Net PV change over a wave cycle in the middle layer of exp2_w at 10°E.

As you can see, it seems that the model, over one wave cycle, does satisfy the PV equation quite well. The main pattern is north of 30°N (the central latitude of forcing), loss of PV (southward displacement) within the forcing area and gain of PV (northward displacement) along the western boundary, with the pattern reversed south of 30°N; this is consistent with a clockwise circulation north of 30°N and anticlockwise south of 30°N. Notice, however, that there are some secondary recirculations within the forcing area and near the western boundary.

A section of the result along 10°E is shown in Fig. 2: there are some small violation but overall, we could consider that the PV equation is satisfied. The red dots in Fig. 1a shows that the choice of the six parcels used so far to perform the PV test was not the most adequate to perform the PV test. Let’s use two new parcels that have significant net PV change (10°E, 31.55°N and 10°E, 28.45°N), the trajectory of which is shown in Fig. 3. The PV violation for these parcels during a wave cycle, although significant, is not too dramatic (Fig. 4). It would be nice to use the run with higher resolution to see if any of the violation seen here are reduced or not.

Figure 3: The trajectory of two new parcels.

Figure 4: PV test for the new parcels of Fig. 3.