Supplementary Information for
Horizontal eddy energy flux in the world oceans diagnosed from altimetry data
Chi Xu
State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology,
Chinese Academy of Sciences, Guangzhou, China, 510301
Xiao-Dong Shang (Corresponding author)
State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology,
Chinese Academy of Sciences, Guangzhou, China, 510301 e-mail: xdshang@scsio.ac.cn
tel: +86-20-89024731 fax:+86-20-89024731
Rui Xin Huang
Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
Supplementary Discussion; Supplementary Figures S1; Supplementary Figures
S2; Supplementary Figures S3; Supplementary Table S1
Supplementary Discussion provides a comparison with estimates based on the cube92 version of the CS510 runs of the ECCO2 (Estimating the Circulation and
Climate of the Ocean, phase II) and a discussion about the difference between this estimate and other published results.
Supplementary Figure S1 shows that intense eddy-energy dissipations and generations occur basin wide, although strong eddy energy sink may locate near the western boundaries.
Supplementary Figure S2 shows smoothed EEF vector (arrows) together with their divergence (shading) plotted separately for cyclonic and anticyclonic eddies (cf. Fig.
1

4).
Supplementary Figure S3 shows the trajectories and the multi-year averaged zonal
EEFs of mesoscale eddies with different lifetimes.
Supplementary Table S1 lists mean meridionally-integrated zonal EEF of 5 latitudinal bands estimated based on altimetry data with hydrographic climatology or model outputs.
2

Supplementary Discussion
Apparently, the averaged volume of eddy energy and its change rates are much larger than what were published in the previous study
18
(0.38 EJ for eddy energy and
0.203 TW for its change rates). Different spatial filtering approach and more suitable half-power cutoffs in the present pretreatment of the SSHA fields are the main reasons for this large difference, and it was tested in two ways. One is that nine cases of calculation based on different scales of spatial filter (with half-power cutoffs at 5°,
10° and 15°) and different thresholds of closed contour of SSHA (at ±4cm, ±5cm and
±6cm) are introduced. The reservoirs of eddy energy fall within the range of 1.40 ~
3.25 EJ, and the associated sources/sinks fall within the range of 0.57 ~ 1.26 TW. The lower bounds are still larger than numbers we presented in the previous study, meaning Ref. 18 might underestimate these quantities as the authors stated in their summary. The estimated EEFs in five zonal bands are listed in column 1&2 of Table
S1. As displayed in Fig 5&6, large standard deviations of EEFs in subtropical bands are attributed to large errors when deriving the geostrophic currents near the equator and to the tropical instability waves captured in the filtered SSHA fields.
The other way is applying these methods to an eddy-permitting model output and making a comparison. The cube92 version of the CS510 runs in the Estimating the
Circulation and Climate of the Ocean, phase II: high resolution global-ocean and sea-ice data synthesis (ECCO2) state estimate
S1
was selected here as it is a global eddy-permitting model and several studies have used the ECCO2 state estimate to study mesoscale eddies S2 . Daily SSH outputs were chosen to perform eddy detection
3

and auto-tracking, and the scale of spatial filter and the threshold of SSHA contours are the same as what applied to the altimetry data. Monthly salinity and potential temperature were used to derive the interfacial depth which is described in the
Methods section, indicating that the equivalent interface depth is time-dependent.
Results are as follows: mean amount of eddy energy is ~1.60 EJ, mean generation/dissipation rate is ~0.59 TW and the net transports of eddy energy in five zonal bands are listed in column 3 of Table S1. The estimates based on outputs of model are almost half of the estimates result from the altimetry data. Main reason is that the magnitudes of upper layer thickness derived from the outputs of ECCO2 are generally smaller than those diagnosed from WOA01. Hence, a more direct calculation and a systematic analysis are still clearly needed for further study.
Ref. S3 has evaluated global eddy energy based on model estimates. They counted all temporal variability as "eddies" and therefore the eddy energy in the present study should be smaller than that of Ref. S3. Nevertheless, eddy energy in the present study is larger. This discrepancy may be partly due to the lack of information on vertical structure. In addition, it is noted that temporal filters will significantly influence the estimates as stated in Ref. S3 because “eddies” in Ref. S3 denote temporal variability. On the other hand, if “eddies” refer to coherent vortex structures propagating and rotating in the ocean as in present study, spatial filters will be more influential in eddy identification and energy estimates.
4

Table S1 Mean meridionally-integrated zonal EEF of 5 latitudinal bands estimated based on altimetry data with hydrographic climatology (columns 1 & 2) or model outputs (column 3). Unit is GW and negative means westward.
Zonal bands
Altimetry Data with hydrographic climatology
10° cutoffs
±5cm threshold
Average and spread of the 9 cases
(mean ±standard deviation)
Model outputs
ECCO2
10° cutoffs
±5cm threshold
45N~60N
25N~44N
-0.6
-5.2
-0.5 ± 0.2
-4.5 ± 1.8
-0.2
-2.4
5N~24N
5S~44S
45S~60S
-6.4
-15.7
3.7
-8.3 ± 6.9
-14.6 ± 7.3
3.2 ± 1.1
-3.1
-10.6
1.8
5

0
-5
120E
12
8 c
4
0
-4
-8
150E
150 a
100
50
0
-50
135E
10 b
5
135E
165E
150E
150E
165E
165E
180E
180E
165W
165W
150W
150W 135W
180E 165W 150W 135W 120W 105W
135W
120W
90W
120W
75W
Figure 1 (Supplementary Figure S1: mean eddy-energy generation rates (red), mean dissipation rates (blue) and energy balance (black) due to eddies (with lifetimes no less than 2 weeks) along several zonal sections, in unit of mW/m
2
).
a, 35°N (130°E ~
120
°
W); b. 22
°
N (120°E ~ 110°W); c. 28°S (150°E ~ 75°W).
6

7

Figure 2 (Supplementary Figure S2: Eddy energy flux vectors normalized by EEF ((KW/degree)
1/2
; arrows) and its divergence (mW/m
2
; shading). Both fields are smoothed.) a, long-lived cyclonic eddies; b, long-lived anticyclonic eddies. MATLAB R2011a
( http://www.mathworks.com/ ) with M_Map (a mapping package, http://www.eos.ubc.ca/~rich/map.html
) was used to create the map.
8

Figure 3 (Supplementary Figure S3: upper panels: the trajectories of tracked nonlinear eddies in 18 years, red lines for anticyclonic eddies and blue lines for cyclonic eddies; lower panels: the multi-year averaged zonal eddy energy fluxes induced by both cyclonic and anticyclonic eddies, in unit of MW/degree.) a &d for mesoscale eddies with lifetimes from 4 weeks to 8 weeks; b & e for mesoscale eddies with lifetimes from 9 weeks to 16 weeks; c & f for mesoscale eddies with lifetimes no less than 17 weeks. MATLAB R2011a ( http://www.mathworks.com/ ) with M_Map
(a mapping package, http://www.eos.ubc.ca/~rich/map.html
) was used to create the map.
9

References
S1. Chen, R. Energy pathways and structures of oceanic eddies from the ECCO2 state estimate and simplified models. Ph.D. Thesis, MIT-WHOI Joint Program, Cambridge, MA (2013).
S2. Menemenlis, D. et al. ECCO2: High resolution global ocean and sea ice data synthesis.
Mercator Ocean Quarterly Newsletter, 31 , 13-21 (2008).
S3. Aiki, H. and K. J. Richards. Energetics of the global ocean: the role of layer-thickness form drag. J. Phys. Oceanogr.
38 , 1845-1869 (2008).
10