ATMOSPHERIC AND OCEANIC SCIENCE LETTERS, 2009, VOL. 2, NO. 3, 148−152
Weak Vertical Diffusion Allows Maintenance of Cold Halocline in
the Central Arctic
Ilker FER
Geophysical Institute, University of Bergen & Bjerknes Centre for Climate Research, Bergen, Norway
Received 27 March 2009; revised 30 April 2009; accepted 6 May 2009; published 16 May 2009
Abstract In spring preceding the record minimum
summer ice cover detailed microstructure measurements
were made from drifting pack ice in the Arctic Ocean, 110
km from the North Pole. Profiles of hydrography, shear,
and temperature microstructure collected in the upper
water column covering the core of the Atlantic Water are
analyzed to determine the diapycnal eddy diffusivity, the
eddy diffusivity for heat, and the turbulent flux of heat.
Turbulence in the bulk of the cold halocline layer was not
strong enough to generate significant buoyancy flux and
mixing. Resulting turbulent heat flux across the upper
cold halocline was not significantly different than zero.
The results show that the low levels of eddy diffusivity in
the upper cold halocline lead to small vertical turbulent
transport of heat, thereby allowing the maintenance of the
cold halocline in the central Arctic.
Keywords: Arctic Ocean, cold halocline layer, turbulence,
mixing, heat flux, Atlantic Water
Citation: Fer, I., 2009: Weak vertical diffusion allows
maintenance of cold halocline in the central Arctic, Atmos.
Oceanic Sci. Lett., 3, 148−152.
1
Introduction
The Arctic ice cover depends on a delicate heat balance
in which the magnitude and distribution of the oceanic
vertical heat flux are important. Thermal and mechanical
forcing, ocean stratification, internal waves, and turbulent
mixing have significant impact on this heat flux. Maintaining the observed thickness of perennial ice requires an
annual average heat flux of about 2 W m−2 at the ice undersurface (Maykut and Untersteiner, 1971; Maykut,
1982). The Atlantic Water (AW) with above zero temperatures can be a considerable source of heat, however it
is insulated from the mixed surface layer and ice by a
layer with nearly uniform cold temperature where the
density change is dominated by increasing salinity (Aagaard et al., 1981; Rudels et al., 1996). This cold halocline layer (CHL) is considered to be a barrier to upward
mixing of heat because of the density stratification. As a
result, solar heating through open leads, thin ice, and melt
ponds is the main source of the ocean heat flux in the
central Arctic basins, rather than from turbulent mixing of
heat from below (Maykut and McPhee, 1995; Perovich
and Elder, 2002).
The Arctic Ocean is a quiescent environment with turbulence levels close to the limits of measurement (RainCorresponding author: Ilker FER, [email protected]
ville and Winsor, 2008). In the absence of enhanced levels
of mixing due to episodic shear events or mesoscale eddies, diffusive layer fluxes dominate over turbulent fluxes
(Padman and Dillon, 1989; Timmermans et al., 2008).
Consistent with a quiescent Arctic interior, recent numerical studies suggest that the observed AW layer circulation in the Arctic Ocean requires low vertical mixing
(Zhang and Steele, 2007). Mixing of AW up towards the
surface is anticipated to be enhanced along the boundaries
(Padman, 1995; Holloway and Proshutinsky, 2007; Rainville and Winsor, 2008).
Recent measurements detected a pulse of anomalously
warm AW which entered the Arctic Ocean from the Fram
Strait and propagated around the basin margins (Polyakov
et al., 2005). It was subsequently of concern whether such
oceanic warming signal could have implications for the
ice cover. A conclusive answer is hampered as the observations of oceanic turbulence in the upper water column
of the Arctic are scarce (Padman et al., 1990; Padman and
Dillon, 1991; Fer and Sundfjord, 2007; Rainville and
Winsor, 2008), and mixing rates are largely unknown.
Numerical simulations and sensitivity studies show that
the increased ocean heat will rise AW temperature in the
Arctic, but will not contribute to the melting of sea ice
significantly (Smedsrud et al., 2008). Here we report new
observations of the thermal microstructure of the upper
Arctic Ocean, in support of this view, collected in April
2007 preceding the record minimum summer ice cover
(Perovich et al., 2008). The focus is on mixing across
CHL, previously not addressed in Arctic turbulence studies, using a data set that is an advance on the recent study
of Rainville and Winsor (2008). Present data are better
sampled in time, increasing confidence on the averages,
and the temperature and shear microstructure are better
resolved allowing for more confident mixing rate estimates.
2
Sampling and processing details
As the 2 m thick pack ice drifted at an average speed of
12 cm s−1 southwestward near the prime meridian (Fig. 1),
we collected 100 microstructure profiles from the
ice-camp Borneo using the loosely tethered free-fall
MSS90L microstructure profiler. The instrument is fitted
with precision CTD (conductivity, temperature, depth),
and fast-response conductivity, pre-emphasized microstructure temperature (FP07) sensors, and two airfoil
shear probes. Data (downcasts only) were recorded from
immediately below the ice to typically 500 m depth at a
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FER: VERTICAL MIXING ACROSS ARCTIC HALOCLINE
we only retain the segments where
149
∂T / ∂z
is greater
than twice its error estimate inferred from the linear regression. We estimate χ by fitting the Batchelor’s form
(Dillon and Caldwell, 1980), constrained by the measured
ε, to the resolved wavenumber band of the T-gradient
spectrum over 4 m segments. The noise level for ε is
5−7×10−10 W kg−1, only adequate to resolve the turbulence
in the upper 200 m, but χ is resolved throughout the profiling depth. The effect of noise level of ε on constraining
the fits to obtain χ is found to be negligible after testing
segments with ε < 7×10−10 W kg−1 by repeating the curve
fitting using ε5 = ε/5 and ε 10 = ε/10. The ratio of χ obtained using ε and ε5 (ε10) is 1.6 (1.9) within the uncertainty of oceanic turbulence measurements.
3
Figure 1 Drift track of Barneo ice camp (red curve). The inset magnifies the drift with circles placed at start of each day of year. The distance
in km is referenced to (89°N, 7°W).
profiling speed of 0.4−0.5 m s−1. Casts were made in five
batches of 15 hours duration interrupted by 9 hours of rest.
In each batch individual casts were made every 50 minutes.
CTD data are averaged in 10 cm vertical bins. The dissipation rate of Turbulence Kinetic Energy (TKE) per unit
mass is calculated using the isotropic relation ε =
7.5ν u z′2 . Here ν is the viscosity of seawater, u z′2 is
the small scale shear variance obtained by iteratively integrating the reliably resolved portion of the shear
wavenumber spectrum of half overlapping 1 second
(about 0.5 m) segments (Fer, 2006). The profiles of ε are
averaged in 1 m vertical bins. The diapycnal eddy diffusivity is calculated as Kρ = 0.2εN−2 (Osborn, 1980) using
the buoyancy frequency, N = [−(g/ρ)( ∂ ρ/ ∂ z)]1/2, where g
is the gravitational acceleration and density ρ is approximated by sorted potential density σθ profiles. The background density, temperature (T), and salinity (S) gradients
are obtained as the slope of the linear regression of depth
on σθ, T, and S, respectively, over 4 m length moving
segments (typically 40 data points). Kρ is ill defined in the
absence of stratification and we exclude the segments
with N < 1.7×10−3 s−1 equivalent to one cycle per hour
(cph).
The eddy diffusivity for heat is obtained from the isotropic relation KT = χ / 2 ∂T / ∂z
2
(Osborn and Cox,
1972), using the dissipation rate of thermal variance,
χ = 2kT 3(∂T ′ / ∂z )2 . Here, kT = 1.4×10−7 m2 s−1 is the
molecular diffusivity for heat,
(∂T ′ / ∂z ) 2
scale temperature gradient variance, and
is the small
∂T / ∂z
is the
background T gradient. Heat flux, in units of W m−2, is
FH = − ρ c p KT ∂T / ∂z , positive upwards. Here cp is the
heat capacity of seawater. In calculations of KT and FH,
3.1
Results and discussion
Survey mean profiles
During the time series in the Amundsen Basin no
prominent frontal structures nor eddies were encountered.
A total stretch of about 50 km long data is analyzed. The
survey mean profiles are presented in Fig. 2. The hydrography is characterized by a 38-m thick, low salinity (S <
33) mixed layer, overlaying a relatively saline isothermal
layer down to 70 m. This upper cold halocline is followed
by the bulk of CHL down to 125 m where the density
change is dominated by the salinity, below which both T
and S increase until a depth of about 250 m, both contributing to the density variation. Atlantic-derived water with
T > 0°C is found below 180 m above two temperature
maxima at about 250 m and 300 m separated by a
well-mixed 50-m thick layer (Fig. 2a).
Dissipation rate ε, decays with distance from the ice to
O(10−9) W kg−1 at about 150 m, is relatively constant
down to about 250 m, before reaching the noise level (Fig.
2c). In a stratified environment, turbulent stirring must be
strong enough to overcome the stratification to be able to
produce a significant net buoyancy flux resulting in turbulent mixing. Turbulence produces negligible buoyancy
flux when the intermittency factor I = εν−1N−2 is less than
about 19, although the exact threshold is not well-defined
(Thorpe, 2005). Observed profiles of I (not shown) decrease exponentially from O(105) close to the ice down to
the threshold value of I = 19 at 70 m, and average to 13 ±
4 (± one standard deviation) between 70 and 180 m, suggesting negligible net buoyancy flux within and below the
CHL. For such low I, the assumption of local isotropy is
doubtful and the factor 0.2 used in calculating Kρ is uncertain (most likely an overestimate). As a result below 50
m, ε and Kρ can be considered an upper limit which nonetheless reinforces the statement that stirring below 70 m
does not mix heat and salt across the isopycnals. Diapycnal diffusivity Kρ decreases by one order of magnitude
from the base of the mixed layer to 10−5 m2 s−1 at 70 m,
and averages to (5±2)×10−6 m2 s−1 between 70–220 m. Kρ
is marginally above its noise level below CHL, and below
220 m double diffusion and noise dominate. The
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VOL. 2
Figure 2 Survey averaged profiles of (a) potential temperature θ (black) and salinity S (red), (b) σθ (black) and buoyancy frequency N (red), (c)
dissipation rates ε (red line) and χ (black shading), and (d) eddy diffusivities KT (black shading), Kρ (thick red), and its noise level (thin red). In (d), Kρ
is plotted only when N > 1 cph. Lower axis limits for ε and KT are the noise level and the molecular level, respectively.
largest values of χ are observed in the thermocline between the base of CHL and the AW core where KT is extremely low, as a result of the strong vertical temperature
gradient, and averages to (6±3)×10−7 m2 s−1 merely 4
times the molecular level. Significantly larger values are
inferred in the upper layers, decreasing from about 10−3
m2 s−1 at the foot of the mixed layer to O(10−6) m2 s−1 at
80 m. The model used to obtain KT is unaffected by double diffusion, but again assumes local isotropy, however,
the conclusions here are drawn from data in the upper
layers unaffected by noise or isotropy.
3.2
Heat flux
The salinity stratification in the cold upper layer is
clearly seen in the profiles against the density (Fig. 3a).
The heat flux, FH, averaged in bins of σθ (Fig. 3b) shows
that in the layers below the upper cold halocline FH is
negligible (< 0.05 W m−2). FH is slightly enhanced, significant at 95% confidence, between isopycnals 26.7–26.9
and increases by one order of magnitude in the uppermost
layer covering both the top of CHL and the upper mixed
layer. This increase is mostly due to the shortwave radiation as the following analysis shows that the upward turbulent diffusion of heat across the upper CHL is negligible. Using a combination of drifting buoy observations,
climatology, and parameterization, Krishfield and Perovich
(2005) estimate annual oceanic FH between 3 and 4 W m−2
to the Arctic Ocean pack ice, dominated by large values in
summer. Our observations, reaching 0.5 W m−2 as the ice is
approached, are thus comparable to, but likely lower than
the basin average for the corresponding days of the year.
Figure 3 Average profiles as a function of σθ of (a) potential temperature θ (black) and salinity S (red), (b) upward heat flux FH, averaged
between indicated isopycnals (dashed) with mean depth on the right. In
the upper two layers a total of 577 and 221, respectively, 4-m segments
are averaged. In deeper layers the number of samples exceeds 3200. The
shading shows the 95% bootstrap confidence intervals.
3.3
Upper cold halocline
In order to obtain an average profile across the upper
CHL, we normalize the depth of each profile using the
thickness h between the base of the well-mixed tempera-
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FER: VERTICAL MIXING ACROSS ARCTIC HALOCLINE
ture (zT) and salinity layers (zS). Sorted T and S profiles in
the upper 100 m are used to detect zT and zS as the depth
when T and S first exceed the average value in the upper
30 m by 0.02 K and 0.05 psu, respectively. The thickness
of the layer between the base of the well-mixed layers, h
= zT – zS, and the mid-depth of this layer, zm = (zT + zS) / 2
are then used to normalize the depth as zn = (z – zm)/h. The
segments between zn = ± 1 are averaged in 0.05 normalized unit bins, successfully covering ± h thick layer across
the center of the cold halocline. On average, zS = 55 ± 9 m,
zT = 71 ± 6 m, and h = 16 ± 8 m. Mixed layer averages
and anomalies are calculated for T and S over the corresponding layer depth. Figure 4 illustrates the mean structure in the upper part of the CHL. While T is close to the
mixed layer value, S gradually increases with depth by
nearly 0.3 psu. Both ε and χ are enhanced at the base of
the well-mixed salinity layer, and decrease towards the
center of the cold halocline. The turbulent parameters are
well above the noise and ensemble averaging further increases the statistical confidence. There is an average upward heat flux of about 0.2 W m−2 above the thermocline,
which cannot penetrate the cold halocline. In the mixed
layer, FH gradually increases toward the ice, reaching
about 0.4 W m−2 by zn = –1. The non-zero divergence of
heat is a result of penetrating shortwave radiation and
turbulent heat exchange across the air–sea–ice interface,
and would heat the mixed layer as time progresses. The
eddy diffusivity KT is between 10−5–10−4 m2 s−1, significantly above the molecular level across the entire upper
cold halocline (–0.5≤zn ≤0.5). Below the isothermal
151
layer, KT approaches 10−6 m2 s−1. Similarly low values
were inferred by Rainville and Winsor (2008) across the
Arctic basins and supports the use of low background
vertical diffusivity in the simulations of Zhang and Steele
(2007) to reproduce the cyclonic AW circulation in the
Canada basin.
3.4
Weak vertical diffusion
Estimates of total annual halocline water production is
between 2.5–5 Sv (Aagaard et al., 1981). If distributed
over the 8×1012 m2 surface area of the deep Polar basin,
this leads to an average upwelling of 3–6×10−7 m s−1. Exponential salinity profile solutions to the steady-state vertical advection-diffusion balance are consistent with Polar
Science Centre Hydrographic Climatology (Steele et al.,
2001), and exponential fit to the annual salinity profile
(averaged for grid points poleward of 80°N with bottom
depth > 500 m) between 30–1100 m yields a vertical eddy
diffusivity of 2.5–5×10−5 m2 s−1 to maintain the steadystate CHL (result is identical for the density profile).
Typical diffusivity in the bulk of CHL reported here is
weak, between 10−6–10−5 m2 s−1 and allow for the maintenance of CHL. Enhanced mixing along the boundaries
will likely increase the basin average towards 10−5 m2 s−1
suggested by the simplified advection-diffusion balance.
If this balance is representative of the steady-state CHL,
basin-averaged diffusivity larger than 5×10−5 m2 s −1
would erode and eventually remove the halocline. In a 3D
ice-ocean coupled model, background mixing of 2.5×10−5
m2 s−1 significantly weakens CHL whereas mixing in the
Figure 4 Average profiles of (a) temperature θa (black) and salinity Sa (red) anomalies, (b) dissipation rates χ (white line) and ε (red line), and (c)
eddy diffusivity KT (white line) and upward heat flux FH (red), centered at mid-depth between the base of isohaline and isothermal layers. For each
normalized depth bin of thickness 0.05, 17 (±3) 4-m segments for χ, KT, and FH, 68 (±4) 1-m segments for ε, 780 (±125) 0.1-m segments for θ, and S
are averaged. The shaded envelopes in (b) and (c) are the 95% bootstrap confidence intervals.
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ATMOSPHERIC AND OCEANIC SCIENCE LETTERS
order of 10−4 m2 s−1 removes it altogether (see Fig. 3 of
Zhang and Steele, 2007; see also “high-mixing” case in
1-D model of Smedsrud et al., 2008).
4
Conclusions
Early spring observations in the Amundsen Basin of
the Arctic Ocean show evidence that in the absence of
storm and eddy events, the oceanic heat flux across the
cold halocline is not significantly different from zero.
Turbulence in the bulk of CHL is not strong enough to
generate significant buoyancy flux and mixing. Resulting
average diffusion is weak and allows for the maintenance
of CHL. The observations form a snapshot from a specific
area away from boundaries. The integral effect of episodic
events that mix the warm AW upward towards the ice as
well as the role of tides, internal waves and enhanced
mixing over topography (Padman, 1995; Holloway and
Proshutinsky, 2007; Rainville and Winsor, 2008) still remain to be quantified and deserve further studies.
Acknowledgments. This work is funded by the Research Council
of Norway, through NORKLIMA Young Investigator grant. This is
publication A228 from the Bjerknes Centre of Climate Research.
The author thanks L. Padman, S. A. Thorpe, B. Rudels, and two
anonymous reviewers for commenting on an earlier version of the
manuscript.
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