124 F. Schütte et al.: Hidden vortices: near-equatorial low-oxygen extremes driven by high-baroclinic-mode vortices 
are considerably weaker and partly misrepresented. North of 
5°N, the velocity structure is generally better captured. 
Despite differences in spatial details and magnitudes the 
basic features of the DO and velocitiy distributions are in 
the upper 200 m of the ETNA, and the GFDL CM2.6 model 
provides a robust physical and biogeochemical background 
state to study the role of eddies in driving local DO defi- 
cient zones. With a nominal ocean resolution of 0.1°, CM2.6 
is mesoscale eddy-resolving and submesoscale-permitting at 
low latitudes, capturing only the larger submesoscale vor- 
tices. The local Rossby radius of deformation (60-150 km; 
Fig. 1) in the area is resolved, but smaller eddies are near the 
lower limit of resolvable scales. However, the model has been 
shown to simulate low-oxygen mesoscale eddies at latitudes 
poleward of about 12° latitude (Frenger et al., 2018) and pro- 
vides as a useful framework in this study to complement the 
observational analysis. Here, we use the last 20 years of this 
model run to study low-oxygen extreme events in the ETNA 
equatorward of 12° N. 
3 Methods 
Different diagnostics have been applied in this study, that al- 
lowed us to associate low-oxygen features with HB Vs and to 
analyze their origin and temporal evolution. The concept of 
vertical baroclinic modes (Sect. 3.1) was used to characterize 
che vertical structure of HBVs, to identify the dominant verti- 
cal modes, and their associated Rossby radius of deformation 
and propagation speed. In Sect. 3.2, we briefly present the 
calculation of PV, which is used as a conservative tracer to 
track and to identify the isolation of different water masses. 
In Sect. 3.3, we describe the different approaches for eddy 
identification from shipboard observations and in the GFDL 
CM2.6 model. 
3.1 Vertical baroclinic modes and Rossby radius of 
deformation 
A powerful way to describe linear wave dynamics in the 
ocean is the decomposition into vertical baroclinic modes 
(Philander, 1978). Each baroclinic mode is associated with 
a specific gravity wave speed and a corresponding Rossby 
cadius of deformation, which defines its characteristic hori- 
zontal length scale. 
3.1.1 Baroclinic mode decomposition 
The concept of baroclinic modes is based on the linearized 
hydrostatic equations of motion, which can be separated into 
a horizontal and a vertical component. Assuming a motion- 
less background state and a flat-bottomed ocean, the vertical 
structures are given by solving the eigenvalue problems (Gill, 
1982): 
d’W.(z)  N*G) 
az + Zn Vz) =0 
Ocean Sei... 22. 119-143. 2026 
where Y„(z) describes the vertical structures of isopycnal 
displacement & or vertical velocity w and z is the vertical 
coordinate. N(z) is the vertical profile of the Brunt-Väisälä 
frequency and c„ the gravity wave speed for mode n € N. 
For the eigenvalue problem (1), we use boundary conditions 
with a free surface and a flat bottom (Gill, 1982), which are 
given as 
Fa dY,, 
Y, = —, atz=0and Y, =0, atz= -H (2) 
2 dz 
where H is the ocean depth and g the gravitational accelera- 
tion. For a continuously stratified ocean, the number of solu- 
tions depends on the vertical resolution of the data used. Any 
perturbances can be described as a superposition of orthog- 
onal vertical baroclinic modes (n = 1,2,3,...). Amplitudes 
of vertical structure functions are normalized such that 
0 
/ Y, Ydz = önm HH 
H 
where S„m 1s the Kronecker delta and nm the modes. The 
gravity wave speed is related to the Rossby radius of defor- 
mation, that can be calculated for the off-equatorial regions 
(poleward of 5° S and 5° N) as 
Cn 
Ran — Tfr 
(3) 
(Gill, 1982 or Chelton et al., 1998), where Ra. is the Rossby 
radius of deformation for the th vertical baroclinic mode, 
and f is the Coriolis parameter. 
3.1.2 Calculation of vertical baroclinic modes and 
modal decomposition 
The main goal is to decompose any disturbed state into the 
set of orthogonal baroclinic modes that solve (1). Each hy- 
drographic profile from an individual CTD-O profile can be 
considered as a perturbation from the mean state. The mean 
state distribution was derived from the 3D climatological hy- 
drographic field (cf. Chelton et al., 1998) that is given by the 
World Ocean Atlas (Sect. 2.4). Given the corresponding den- 
sity profile, we calculated the isopycnal displacement E(z) 
by 
0:8 
E(z)= NZ 
(4) 
with p’(z) = p(z)—Pref(Z), DO = 1025 kg m”? a constant ref- 
grence density and per being the undisturbed profile of po- 
tential density (here taken as the climatological density pro- 
file from the World Ocean Atlas — see also Vic et al., 2021 for 
more details on the method used). The isopycnal displace- 
ment of the disturbed state can be described as a superpo- 
sition of the orthogonal set of vertical baroclinic modes for 
displacement. 1.e. 
https://doi.org/10.5194/o0s-22-119-2026