Cyclonic and anticyclonic contributions to atmospheric energetics

Scientific Reports
| (2021) 11:13202 | 
https://doi.org/10.1038/s41598-021-92548-7
www.nature.com/scientificreports/
Whether such second-order statistics are dominated by contributions from the decomposed vorticity terms and 
those from the “cross terms” are negligible should be verified in future studies.
Evaluating eddy feedback forcing. 
Feedback forcing exerted on quasi-steady background flow by 
eddies migrating along a storm track is estimated locally as a geopotential height tendency that could be induced 
through fluxes of heat and vorticity by transient eddies
25
,
52
,
53
, as follows:
In Eq. (
8
), an overbar denotes a variable for the background flow, which corresponds to the climatological-
mean state in our practice. The feedback forcing by high-frequency transient eddies was estimated through 
the eddy fluxes as evaluated locally from 6-hourly fluctuations through the temporal high-pass filtering. High-
frequency transients are always exerting feedback forcing onto the background state in which they are embedded. 
In the climatological-mean state their feedback forcing must therefore be balanced with other processes. Eddy 
feedback forcing as acceleration (or deceleration) of westerly winds is estimated by calculating westerly wind 
tendency from the geopotential tendency by assuming geostrophic balance.
FORA-WNP30 reanalysis. 
We utilized daily zonal and meridional velocities of ocean currents over the 
western North Pacific obtained from the FORA-WNP30 reanalysis
54
 by the Japan Agency for Marine-Earth 
Science and Technology (JAMSTEC) and Meteorological Research Institute (MRI). The FORA-WNP30 was 
produced by the MRI Multivariate Ocean Variational Estimation system version of 4-dimensional variational 
method (MOVE-4DVAR
55
), and the data assimilation system developed by the JMA/MRI, which uses an eddy-
resolving ocean model for the western North Pacific. Its horizontal resolution is 1/10° × 1/10° with 54 vertical 
levels (0 ~ 6300 m depth). To focus on the structure of oceanic jets and mesoscale eddies, velocity fields have 
been smoothed by performing a 9-point horizontal smoothing (with weights of 0.5 next to the center point and 
0.3 at corners) 15 times for the snapshots plotted in Supplementary Fig. S12.