The Eulerian and Lagrangian PV balances have been computed for 4 fixed locations and 4 parcels, respectively, and for each of the simulations described in Tab. 1.
-clinic dt | -tropic dt | SPLIT | |
---|---|---|---|
exp4 | 1200 s | 15 s | YES |
exp6 | 30 s | 15 s | NO |
exp7 | 300 s | 15 s | YES |
exp8 | 30 s | 15 s | YES |
Table 1: Baroclinic and -tropic time step dt for each of the 4 simulations. The use or not of the SPLIT option is shown in the last column
Fig. 1 summarizes the results by showing the error in the respective PV balance. Figs. 2 to 9 show the actual PV balance. Even with a time step reduced by a factor 4 (from exp4 to exp7, the Lagrangian PV balance is not satisfactory (exp7; see also Fig. 7). Only with the time step reduced to 30 s, the Lagrangian PV balance is satisfactory, with or without the SPLIT condition (exp6 and exp8; see also Figs. 5 and 9). The simulation with the SPLIT condition (exp6) gives, however, the smallest error.
Because the PV balances seem to be sensitive to the time resolution of the model, one can ask if they are also sensitive to the time resolution of the output used to compute the trajectories. The answer is yes as Fig. 10 shows for exp6. One can wonder, thus, if exp4 might still satisfy the PV balance if the time resolution of the model output would have been larger.
Finally, does the advective scheme matter? exp9 is similar to exp6 except that the advective scheme of Arakawa and Hsu (energy and enstrophy conserving) is used, instead of Sadourny (energy conserving scheme). It appears that if you use model output u and v only 1) the advective scheme does matter and 2) Sadourny’s scheme might be better (Fig. 11). The reason why this affect only the calculation using model output u and v is not known.