Role of mixed layer depth in surface frontogensis: the Agulhas
Return Current front
Tomoki Tozuka and Meghan F. Cronin
1
Department of Earth and Planetary Science, Graduate School of Science,
The University of Tokyo, Tokyo, Japan
2
NOAA Pacific Marine Environmental Laboratory, Seattle, WA, USA
Supplementary Material
The Monin-Obukhov depth,
ag 0
ò q ( z) dz
r0 c p -H
ag
(Qnet - qd )
2 r0c p
m0u*3 +
H MO =
MO
(1)
[Kraus and Turner, 1967; Niiler and Kraus, 1977; Qiu and Kelley, 1993], is a useful
diagnostic to examine the relative importance of wind speed and surface heat flux in
determining the mixed layer depth (MLD) when the ocean is subject to a positive
buoyancy flux and the mixed layer is in shoaling phase [cf. Morioka et al. 2012]. In fact,
Schneider and Müller [1990] analyzed observational data obtained during the
Hawaii-to-Tahiti Shuttle Experiment and found that the MLD and the Monin-Obukhov
depth are significantly correlated when only data points with surface heat flux into the
ocean are larger than 20 W m-2. Here, m0 is an efficiency coefficient of wind stirring,
and we use m0 = 0.5 following Davis et al. [1981]. The frictional velocity u* is
defined by
(
u* = raCDu102 ro
)
12
,
(2)
where r a is the density of air, CD (=0.00125) is a drag coefficient, u10 is the wind
speed at 10 m height, and g is the acceleration due to gravity. Also, q ( z ) is the
downward shortwave radiation at depth z and parameterized by
1
é
z
zù
(3)
q ( z ) = q ( 0) ê R exp + (1- R) exp ú
g1
g2û
ë
[Paulson and Simpson, 1977], where R (=0.58) is a separation coefficient, and g 1
(=0.35 m) and g 2 (=23.0 m) are attenuation length scales. These values are for the
case of water Type I (clear water) of Jerlov [1976]. In regions where the net surface heat
flux cools the ocean, MLD is not represented by Eq. (1), but instead will tend to deepen
until the surface cooling is balanced by advective processes.
To quantitatively understand the difference in the MLD on both sides of the SST
front in austral summer, we calculate the Monin-Obukhov depth using the atmospheric
data used to force OFES listed in Table 1 for 45°E-50°E. The Monin-Obukhov depth is
38.9 m (21.0 m) in the northern (southern) box, and the shallower mixed layer on the
southern side of the SST front may be explained by the stronger buoyancy gain by net
surface heat flux. This is because if we use wind speed at 10 m height averaged over
both boxes to calculate Monin-Obukhov depth, we obtain 42.5 m (18.7 m) for the
northern (southern) box, but we obtain 24.5 m (29.3 m) if we use net surface heat flux
averaged over both boxes to calculate Monin-Obukhov depth. We note that the
Monin-Obukhov depth is systematically shallower than the simulated MLD of 63.9 m
(39.2 m) in the northern (southern) box [cf. Schneider and Müller; 1990]. This
systematic bias may stem from Ekman advection [Rintoul and England, 2002; Sallée et
al., 2006; Thomas and Lee, 2006].
The westerly winds transport colder and denser water to the north by equatorward
Ekman transport. As a result, water column is destabilized and the mixed layer becomes
deeper [Rintoul and England, 2002; Sallée et al., 2006; Thomas and Lee, 2006]. Since
the Monin-Obukhov depth is derived by assuming that the temperature field is
horizontally uniform, this Ekman transport effect is not taken into account. Moreover,
this effect is stronger on the northern box because the meridional SST gradient is largest
at the southern periphery of the northern box.
We note that Ekman advection must be viewed carefully since Ekman transport
will be modified in a frontal region [Thompson, 2000; Cronin and Kessler, 2009]. This
is because wind stress is balanced by the total surface shear, including both the Ekman
ageostrophic and geostrophic thermal wind components of the shear. However, the
near-surface zonal current shear at 42.25°S in the 45-50°E band in January is 4.78x10-3
s-1, and this is much larger than the surface geostrophic shear of 0.12x10-3 s-1 calculated
2
from the meridional surface density gradient. The main reason for much smaller
contribution from the geostrophic component in this mid-latitude SST front compared
with the SST front in the cold tongue region of the tropical Pacific is that the
geostrophic shear is inversely proportional to the Coriolis parameter and the Coriolis
parameter near the equator is much smaller than at the mid-latitudes. Therefore, the
Ekman transport may partly explain why the Monin-Obukhov depth diagnostics
underestimate the MLD.
3
Tables
Table 1: Wind speed at 10 m height, net shortwave radiation at the sea surface, net
surface heat flux, MLD simulated by OFES, and Monin-Obukhov depth in the
northern and southern boxes in the 45°E-50°E band in January.
u10
q ( 0)
Qnet
H mix
H MO
(m s-1)
(W m-2)
(W m-2)
(m)
(m)
North
6.64
220.0
53.8
63.9
38.9
South
7.57
210.1
124.4
39.2
21.0
4
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