12.02.10: Ratio surface interior mode in the 1/10th and 1/30th deg. OFES simulations

Fig. 1 shows the ratio of the root-mean-squared (rms) of potential density for the surface/interior modes for several 10° by 10° domains between 210-220°E and 10-50°N for the 1/10th and 1/30th deg. OFES simulations and one day snapshot. The result suggests that the surface mode contribution is large in the 1/10th deg. simulation and weak in the 1/30th deg. simulation. Below, some comments and diagnostics are offered in order to investigate the possibility that the difference is due to a problem in the code itself used to perform the decomposition.

Figure 1: Ratio of the root-mean-squared (rms) of potential density for the surface/interior modes for several 10° by 10° domains between 210-220°E and 10-50°N for the (a) 1/10th and (b) 1/30th deg. OFES simulations and one day snapshot. 18 interior modes are used in (a), 33 in (b). Matlab file OFES_surf_normal_mode_decomp_rms_psi_pd_210E220E_sev_lat_20040103.mat and OFES_1_30_surf_normal_mode_decomp_rms_psi_pd_210E220E_sev_lat_20010103.mat in /home/gyoji2/francois/RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/Decomp_Surface_Normal_Modes/analysis/ to plot the upper and lower panels, respectively. They were obtained by using main_script_2.m in RESEARCH/PROJECTS/MARINE_BIOLOGY/SUBMESOSCALE_PROCESSES/Decomp_Surface_Normal_Modes/analysis/OFES_qscat_0_1_global_3day.

So far, I know that:

1. it is not a problem of topography; I corrected how the topography is treated and no significative difference appears.
2. the large contribution of the surface mode in the subarctic is also present west of Hawaii (185-195°E) in the 1/10th deg. simulation.
3. the use of 33, rather than 18 interior modes, with the 1/30th deg. simulation does not modified the result.

Below are the diagnostics asked by Patrice Klein and Guillaume Lapeyre. In all subsequent figures, a quantity from the 1/10th simulation is compared to the same quantity from the 1/30th simulation. Each quantity is from the same snapshot used to compute the surface and interior modes of Fig. 1. Fig. 2, 3 and 4 show the kinetic energy, enstrophy and the ratio N/f (where N is the buoyancy frequency and f is the Coriolis parameter), respectively, zonally averaged between 210°E-220°E. Fig. 5 shows the profile N/f zonally averaged over the same region at 45°N. Finally, Fig. 6 compares the snapshot of potential density at the surface. Interpretations follow.

Figure 2: Kinetic energy averaged between 210°E-220°E (a) on 2004/1/3 in the 1/10th simulation and (b) first day after one year of running the 1/30th simulation.

Figure 3: Same as in Fig. 2 but for enstrophy.

Figure 4: Same as Fig. 2 but for N/f.

Figure 5: Profiles of Fig. 4 at 45°N.

Figure 6: Snapshot of potential density at the surface. The days are the same as in Fig. 2.

My interpretations are:

1. In the subarctic ocean, kinetic energy is stronger at depth (Fig. 2) and the potential density anomaly has larger horizontal scale (Fig. 6) in the 1/10th than in the 1/30th OFES simulation, which might both explain the larger contribution of the surface mode in the 1/10th than in the 1/30th OFES simulation (Fig. 1).
2. However, N/F is slightly stronger in the 1/10th than in the 1/30th OFES simulation, which contradicts the difference of Fig. 1.

Are the characteristics described in the first point sufficient, nonetheless, to explain the difference in Fig. 1?