Introduction
The assessment of the fluxes at the air/sea interface is an
issue of crucial relevance for many topics in geophysics. A correct
parametrization of such exchanges is relevant for climatic studies, climate
change, weather and ocean forecasting and their applications in marine and
maritime sciences.
Wind stress, which is the medium of the momentum flux
between atmosphere and ocean, is one of the main drivers of the ocean
circulation for a wide range of
spatial and temporal scales. The wind stress (τ) in ocean models, when not directly provided by
atmospheric forecasts, is usually computed through the so-called bulk formulas as described by
, where τ is equal to the square of the wind speed at 10 m times
the air density multiplied by a dimensionless drag coefficient (usually function of wind speed).
, updating their previous work, suggest the use of relative wind
vectors to compute the wind stress, i.e., to take into account ocean currents subtracting them from the absolute wind vectors.
The contribution of the ocean currents in the computation of the wind stress has been neglected in ocean modelling for many years.
The fastest ocean current is 1–2 order of magnitude smaller than the stronger wind: for this reason
the surface current contribution was often neglected in applying bulk formulas, even if an estimation of
surface currents is often easily available from the ocean model itself. Considering that the computation
of the wind stress contains a squared velocity term, it can be easily understood that the relative contribute
of ocean currents is also squared, becoming really relevant for low-wind conditions. Further, as the drag
coefficient is also a function of the wind speed, the inclusion of the surface currents also affects the drag
term, further increasing the impact of such a component. Heat fluxes may also be impacted by including the surface currents, in this
case with a linear relation with wind-current velocities.
By taking into account the surface current component, bulk formulas for momentum, sensible
and latent heat fluxes can be written as:
τ=ρaCd|ua-us|(ua-us)Qs=ρaCpaCs|ua-us|(ta-ts)Ql=ρaLeCl|ua-us|(qa-qs),
where ρa is the air density, ua and us
are the vector velocities for air and sea surface respectively, ta-ts
is the difference in temperature between air (at 10 m) and sea surface,
qa-qs is the difference in humidity, Cpa and Le are
the specific heat of air and the latent heat of water
evaporation respectively, while Cd, Cs and Cl are the
coefficient for momentum, sensible heat and latent heat transfer respectively.
Some recent papers provided evidence of a moderate but actual impact of such a modification on
fluxes at global/oceanic scales. showed that the inclusion of ocean currents
and dominant waves into the drag computation leads to a daily reduction of the drag of
about 10 % at daily scale and for the entire globe, with large variability between
mid-latitude (smaller impact) and tropics. Another model study found that,
for the North Pacific, heat fluxes and wind stress changed about 1–2 % at basin average,
while localized changes (in the tropics) reached up to a 10 % reduction of both momentum
flux and surface currents. In that study the wind power input to ocean surface is reduced
by 27 %, quite in good accordance with previous findings of . In the
Gulf Stream region, this reduction of the wind work was estimated to be around 17 %
. also assessed the effect of coupling currents with winds.
They found a 10 % change in surface currents when considering surface currents velocities
in the bulk formulas, quite in agreement with other authors.All authors found that in the tropics such changes are more relevant than for mid-latitudes.
This is a valid generalization for large scales, while an insight of what happens at
mid-latitude and at regional and coastal scales was not provided yet. To address this
issue we focused our attention in the seas around Sardinia (Western Mediterranean sea),
which is a highly variable and dynamic area interested by several (sub-)mesoscale
structures of different origin
and also affected by strong wind events characterized both by seasonality and high-frequency peaks.
The area is quite heterogeneous in terms of circulation and dynamical characteristics.
The Sardinian Sea, i.e., the continental shelf and slope area west of Sardinia,
is part of the Algero-Provençal Basin. From the basin scale circulation perspective,
the Sardinian sea is located in between the Algerian Basin to the south, dominated by the
inflow of Atlantic water from Gibraltar advected eastward by the Algerian Current,
and the Provençal Basin to the north characterized by the path of the Northern
Current moving south-westward along the Italian and French continental shelf
and where a surface cyclonic gyre drives the northern sub-basin circulation .
The southern branch of this cyclonic gyre contributes to the formation of the North Balearic
front which represents the separation between
the Atlantic water reservoir of the Algerian Basin and the saltier and denser waters of
the Provençal basin e.g.. In a recent paper
we suggested, through the analysis of the outputs of a 3-D assimilative model, that the
upwelling occurring along the SW Sardinian coast was pre-conditioned by the presence of
a quasi-permanent southward current (Western Sardinian Current – WSC) whose origin was
in part due to the approaching of anticyclonic eddies to the western Sardinia shelf.
This was also supported by the findings of where the same current
(they called Southerly Sardinia Current – SSC) is described as permanent at low-frequency
scales (decadal) bordering a northern branch of the Atlantic water flow in the Western
Mediterranean. In the southern part of the model domain the Sardinian Channel connects
Tyrrhenian and Algerian sub-basins. Here the Algerian Current e.g.
transports Atlantic water towards and across the Sicily Channel. North of Sardinia the
Bonifacio Strait (∼15 km wide) separates Sardinia and Corsica and connects, with
its narrow passage, Algero-Provençal and Tyrrhenian basins. Winds crossing the strait
contribute to the generation of a wind-driven quasi-stable cyclonic gyre
in the northern Tyrrhenian sea, east of Sardinia, that represents the most energetic mesoscale
structure of the northern Tyrrhenian sea .All these different characteristics make this domain a good test case to study the impact
of the inclusion of surface currents on the surface fluxes and their feedback on circulation at regional and coastal scales.
Left: study area with toponyms and main circulation features as known
from literature. Right: model domain and bathymetry. The bathymetry used is the GEBCO at 30′′ of resolution.
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The aim of the present work is to study the impact of the surface currents in the
computation of the surface momentum and heat fluxes, through the bulk formulas
, in turn driving the surface dynamics and surface temperature.
The latter can be modified both through changes in surface heat fluxes and as
a consequence of changes in vertical and horizontal motions. To evaluate such an impact,
we performed a twin experiment with the Regional Ocean Modelling System (ROMS). ROMS
was implemented in the central area of the Western Mediterranean sea, around Sardinia
Island, at 3 km resolution. The chosen resolution allowed to respect the suggested
1 : 3 ratio e.g. between child and parent grid resolution,
as well as to well resolve mesoscale processes (considering that the smallest Rossby
radius of deformation for this area is of the order of about 10 km). Details on the
model implementation and experimental setup are provided in Sect. ,
together with information on the data and analyses performed.Two experiments were conducted, reproducing the circulation of the year 2012,
with and without the contribution of surface currents in the computation of the
momentum and heat fluxes.In Sect. we validate the model vs. satellite SST and compare the
outcomes of the two setups under different points of view. Finally, concluding
remarks are drawn in Sect. .
Methods and data
Numerical model and experiments
The numerical model is an implementation of the Regional Ocean Modelling System
ROMS in its official release from
Rutgers (svn revision 705). Such a release of the code does not include an
option to switch on/off the surface currents in the surface flux computations,
so the original model code was modified in this sense. ROMS is a free surface,
hydrostatic, primitive equation, finite difference model widely used by the
scientific community for many kinds of applications: large-scale circulation
studies e.g., ecological modelling ,
coastal studies e.g., sea-ice modelling and
others. The model was implemented in the seas around Sardinia (Fig. )
in a rectangular grid of 3 km resolution on the horizontal plane and 30 s terrain
following levels. The equation distributing vertical levels allows a robust description
of surface and subsurface layers where most of the dynamical processes occur.
Intermediate and deep layers are discretized with larger (on the vertical) meshes.
Bathymetry was derived from the General Bathymetric Chart of the Oceans (GEBCO),
a global 30-arc-second database, and smoothed with a Shapiro filter to remove
wavelengths of the order of the grid scale. This is in order to minimize the pressure
gradient force error (PGFE) often caused by too steep bathymetric gradients.
Stiffness parameters (rx0 and rx1, respectively 0.27 and 5.97) are well
within the thresholds suggested by developers (ROMS user forum at https://www.myroms.org/forum/).Initial and boundary conditions were provided by the 1/16∘ model of the
Mediterranean Sea MFS-1671 retrieved through the My-Ocean (www.myocean.eu)
data portal. Daily analyses of 3-D fields of velocities, temperature, salinity and elevation
(2-D) have been used for model nesting and initialization. At the boundary the model
uses Flather conditions for the barotropic velocities while
baroclinic velocities and 3-D tracers (T and S) are clamped to the values prescribed
by the outer model. Even though ROMS allows the choice of more advanced BC than a
simple clamped solution e.g.,
we opted for this solution for the present application as radiative conditions are
not recommended by developers when using bulk formulas for flux computations. Short
sensitivity studies to different BC confirmed that some issue exists when we use
radiative conditions, generating spurious upwelling/downwelling features at boundaries.
This suggested to opt for a simple but robust BC as the clamped one. At the free surface
the Chapman boundary condition was imposed.A third-order upstream horizontal advection of 3-D momentum
and the k-ϵ turbulence closure scheme were used in the
present implementation. At surface, which is the focus of the present work, we
used the 1/8∘ 6-hourly ECMWF ERA-interim analyses fields. 10 m air temperature,
U and V wind momentum components, air pressure, solar short-wave radiation, air
humidity and precipitation were used to compute freshwater, momentum and heat fluxes
by using the above-cited bulk formulas.
Top to bottom: BIAS, RMSE and ACC for BF (blue) and BFC (red dashed)
experiments. Units for BIAS and RMSE are ∘C, while ACC is dimensionless.
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Experiments
Two experiments were performed: the Bulk Fluxes (BF) experiment did not
include surface currents (so in Eqs. (–)
the us term was neglected), while in Bulk Fluxes with Currents (BFC)
the flux computations interactively took into account the surface currents reproduced
by the model. This modification is quite straightforward when done in ROMS source code,
just by taking care of the fact that currents and winds run on staggered grids, and
therefore they have to be “interpolated” before performing subtraction. As a simple
proxy for this, we averaged the i and i+1 velocity points for each wind i
point and then we subtracted such quantities. The simulations were integrated
for 1 year, to simulate the 2012 year with boundaries and surface forced by
the above described analyses fields. Daily averaged fields are then saved in
the output files.The issue related to the data assimilation deserves a little discussion.
Considering that the model boundaries are provided by an assimilative model
we think that for such a domain the information contained in the boundaries
would propagate to the nested model without a substantial loss of information.
On the contrary for larger off-line nested domains it was shown in literature
that assimilation would be needed as information
coming from boundaries quickly dissipates. Further, and maybe more important,
in the present work we aim to observe changes generated by different parametrizations
of surface physics: for this reason we should not hide this signal with any
statistical correction.
Validation data and metrics
Model performances at surface were evaluated by using satellite SST fields.
Satellite SST used is the MyOcean sea surface temperature operational product
for the Mediterranean Sea which is available at http://www.myocean.eu. The daily
gap-free maps (Level 4, Optimally Interpolated) at 1/16∘ of resolution have been used.Three basic metrics, namely Bias, Root Mean Square Error (RMSE) and Anomaly
Correlation Coefficient (ACC) provide a good overview of the quality of the
model in reproducing the observed SST. While RMSE and BIAS describe the model
error in reproducing observed value of the considered variable, ACC measures
the ability of the model in reproducing anomalies of the SST signature detected
by the satellite, partly overlooking their absolute value.
The three metrics are formulated as follows:
BIAS=1N∑i=1N(obsi-modi),RMSE=1N∑i=1N(obsi-modi)2,ACC=∑i=1N(modi-obsi‾)(obsi-obsi‾)∑i=1N(modi-obsi‾)2∑i=1N(obsi-obsi‾)2,
where mod and obs are respectively modelled and observed values of the
variable and the overbar stands for a long-term temporal average. In the
present paper this long temporal average is the AVHRR monthly climatology
(1982–2008).
The removal of the climatology allows to filter off the seasonal signal that
otherwise would hide the response of this metric to the synoptic features. ACC
is a dimensionless number ranging from -1 (worst) to +1 (best).
Map of SST RMSE (whole period) for BF (left) and BFC experiments. Units are ∘C.
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Top to bottom: wind stress, sensible, latent and net heat flux differences
between the two experiments (BFC – BF). Negative sign indicates lower values for BFC in respect to BF.
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To further evaluate the quality of the two simulations, with particular reference
to the dynamical features produced by the two experiments, we compared model
outputs with synoptic observations of the sea surface observed in single swaths (Level 2)
satellite images. Ocean colour and SST collected by MODIS sensors (on board of
TERRA and AQUA satellites) were used for this purpose. Both typology of products
(optical and infrared derived respectively) can provide useful information on
surface and subsurface structures. An example of such data comparison is presented
in Sect. which tries to emphasize differences between the two model
setups and similarities with observed features.
Difference map (BFC-BF) of the time-averaged wind stress (left) and net
heat fluxes (right). Blue values indicate a BFC stress/heat lower than BF. Units
are N m-2 and W m-2 respectively.
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Total (left) and turbulent kinetic energy at surface. Red curve is for BF and green for BFC experiment.
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Mean flow for BF (left) and BFC experiments. Units are m s-1.
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Eddie kinetic energy for BF (left) and BFC experiments. Units are m2 s-2.
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Flow decomposition, kinetics and wind work
In order to investigate the impact of the fluxes on the simulated dynamics, we
separated the stable and the fluctuating part of the velocity field as already
described, for example, in . The time-averaged term u=〈u〉+u′
represents the stable part of the flow, while u′ is its fluctuating part. The fluctuating
components can be used to describe both eddy kinetic energy (EKE =1/2(u′2+v′2))
and the Reynolds stress covariance term (RS =u′v′), i.e., the eddy momentum flux.
Reynolds stress covariance shows where the turbulent part of the flow interacts
with the mean flow, accelerating or deflecting it from its mean direction .
It is likely that changes in surface parametrization of surface fluxes would influence
both the stable and the fluctuating part of the flow, but in different measure. This
suggested us that the two should be investigated separately.Wind stress work P, which is defined as the product of wind stress τ
by the surface ocean currents us was computed in order to assess the
differences in terms of wind power input to the ocean between the two model experiments.
At oceanic scales, including tropical areas, a reduction of about 20–30 % was recorded
when the contribution of surface currents is considered .
Results and discussion
SST validation and intercomparison
Figure shows the three time series for SST RMSE, BIAS and ACC
metrics computed vs. the SST data.
Such spatially averaged metrics do not show dramatic differences between the
two setups, drawing an almost identical trend. However, BFC (i.e., with currents)
setup shows, as the simulation progresses, slightly better performances than BF
in terms of BIAS and RMSE metrics (see Fig. ), while almost no
differences are recorded for ACC. RMSE improvements seem to be mainly due to the
reduction of the BIAS, which is kept closer to zero by the inclusion of currents
term on flux computations. Of course, considering the complexity and the
diversity in dynamics of the study area, some spatial variability of RMSEs
values would be expected. Actually the comparison of RMSE maps (Fig. )
for the two experiments shows quite a large variability over space. Although the
general distribution of the errors is quite similar, there are many spots where
differences are of great magnitude. In general terms, the largest improvement
for BFC solution is shown on the western side of the domain (the windy side),
with an evident reduction of RMSE for the Algero-Provencal basin. Locally,
major improvements for BFC setup are located along the western Sardinia coast
where the offshore extent of the patch with large RMSE is smaller than in BF
(check figure at about 40∘ N, 8∘ E). Central and southern Tyrrhenian sea
also show noticeable improvements, while in northern Thyrrenian the cyclonic
gyre east of Bonifacio strait seems to be better described by the BC setup.
Impact on surface fluxes
All the spatially integrated surface fluxes (momentum, sensible, latent and net
heat, see Fig. ) show an impact of the order of few percentage points
(∼ 2 %) by averaging time series values, but with a distinct high-frequency behaviour.
The small differences in terms of time series underneath quite large differences
in space because of the very nature of the fluxes and the way they are computed
(i.e., interactively during the model integration and with a feedback with ocean
currents for BFC experiment). In this regard significant information is provided
by the time integrated wind stress difference map shown in Fig. .
Such spatial differences, for wind stress, reach a low of -8×10-3 N m-2 in
the proximity of the southern boundary of the domain where the highly unstable
Algerian Current flows. Another low is at the turning point of the Western Sardinia
Current in the SW corner of Sardinia (-6×10-3 N m-2). Negative patches are
quite dominant, as expected. Positive patches are less present, reaching a
maximum of ∼2×10-3 N m-2 and almost entirely located along the eastern
Tyrrhenian coast. In percentage terms these spatial differences range between -15 %
and +20 % on an annual basis, while they are obviously larger considering a daily basis.
The values of net heat flux difference (right panel of Fig. ) are
highly patchy and correlated with areas of improved model performances in terms
of SST (as shown in Fig. ). Near the western Sardinia coast (40∘ N, 8∘ E) the model shows the largest
correction in terms of heat fluxes (negative blue patch).
Impact on the mean and turbulent surface circulation
As expected, wind stress changes generated significant modifications in circulation
and kinetics. Figure shows time series of total kinetic and eddy
kinetic energy for the two experiments.
It is evident that the introduction of the currents on stress
computation (BFC) led to a large (spatially averaged) reduction of the
kinetic energies at surface.
Such a reduction, about 23 %, shows a long period maximum between days 150
and 250, i.e., during summer. This is probably because winds reach their minimum
intensity, then increase the impact of the correction done by surface currents
on momentum flux. The largest part of such a difference between total kinetic
energies at surface (about 65 %) is actually due to the turbulent part of
the flow. Eddy kinetic energy shows (right panel of Fig. ) the
same trend as the total one, with a maximum difference between the two experiments
also during summer.
Time-averaged maps of the above quantities provide an insight of the distribution of such
differences.
Reynolds stress covariance for BF (left) and BFC experiments. Units are m2 s-2.
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The mean flow (Fig. ) reveals some relevant change in terms of averaged
path of the Western Sardinia Current which shows, surprisingly, a stronger signature
in the BFC configuration. Some important change is evident in terms of mesoscale
circulation: stable eddies footprints appearing in the SW side of the domain
(with probable influence of boundaries) and west of Bonifacio strait, disappear
in the averaged circulation field in favour of streams or a meandering feature.
On the other side, EKE maps (Fig. ) reveal that a large part of
dynamical differences can be ascribed to the fluctuating part of the circulation
as already argued from the time series. Eke values between the two model
solutions shows an averaged reduction of about -23 % for BFC. The largest
differences between the two EKE estimates are ascribed in the area of strongest
mesoscale activity (Algerian Eddies area). Here a qualitative comparison of
modelled fields vs. Level 2 single swath MODIS SST for 29 June 2012
(as an example) elucidates the differences between the two solutions in terms
of mesoscale dynamics (Fig. ).
SST for BF (left), BFC experiments (right) and MODIS SST L2 (bottom panel)
for 29 June 2012. Anticyclone is circled in black. Units are ∘C degrees.
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In this figure the BFC solution better matches, in size and location, the large
anticyclonic Eddy centred at about 38∘ N, 8∘ E, whose signature
is also evident in the satellite image. BF solution on this case draws a less
clear signature of the eddy and of the front on the east side of the eddy that, in the satellite image,
seems also responsible for structuring the path of the WSC south of Sardinia.
This is likely a recurrent correction in the new model solution, as this area
seems highly impacted by the flux correction both in terms of EKE and heat fluxes. Reynolds stress covariance maps (Fig. ) also provide useful information
on the impacts of flux modifications: largest differences are identified in the
area of highest mesoscale activity, i.e., in the Algerian Anticyclonic eddies area.
Alternating negative and positive patches appear, in the BFC solution, close to
the western Sardinia coast: this feature could help to explain the
intensification of the WSC that appears for BFC. In this area BFC provide a
solution, in terms of Reynolds stress covariance, close to the one we previously
found through an interannual experiment performed with a numerical
assimilative model.
Wind stress work difference (BFC – BF). Units are
W m-2. Blue negative patches indicate where the wind power input is
reduced by the feedback of currents on momentum fluxes.
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Conclusions
In the present work the impact of the surface currents in surface flux calculations
at regional/coastal scales was assessed. To do this we performed 1-year long
simulation with a new implementation of ROMS in the seas around Sardinia
(Western Mediterranean Sea) by using two different setups, with and without
the contribution of the currents in the computation of surface fluxes through
bulk formulas.We found, according to bibliography that was mainly related to oceanic and
basin scales, that domain-averaged momentum and net heat flux change by some
few percentage points while more consistent differences are found for surface
kinetic energies (BFC records a 21 % reduction on total surface kinetic
energy in respect to BF). Differences can be observed both in the mean and
fluctuating part of the flow. The latter showed major changes in the SW area
of the domain, where mesoscale eddies are dominant.Inclusion of surface currents determines relevant changes not only in dynamics
but also in the prognosed surface temperature by means of the surface heat fluxes.
Validation with satellite SST reveals that the solution is generally improved,
even if only slightly in spatially averaged terms. Shelf-slope area west of
central Sardinia largely benefits by the correction, while some areas shows
questionable results, as for example the cyclonic area east of Bonifacio strait.
Central and southern Tyrrhenian also show improvements in the BFC solution.While quantitative metrics for SST reveal that net heat fluxes and resulting
SST are improved, it is purely speculative to ascertain (i.e., not quantitatively
validated) if, at these scales, the use of relative winds brings quality to
the simulated dynamics or not. Comparison of synoptic satellite infrared and
optic observations with modelled results did not solve the issue even if it
provided some interesting hint in favour of the BFC solution.
Wind stress work, the product of wind stress and ocean surface currents,
provides an insight of the wind power input to the ocean. Such an input is
reduced for about 14 % as basin average. A difference map between the two
estimates is shown in Fig. . The map shows larger differences
on the left side, which is more windy and dynamic than the Tyrrhenian sea. The
most interesting feature is the localized increase of P in coincidence
with the WSC (slightly shifted westward in BFC in respect to BF) justifying the increased
signature of the WSC we detected in the averaged flow (cfr. Fig. ).
The present study provides evidence that the contribution
of surface currents should not be neglected in the computation of fluxes even at
regional/coastal scales and in temperate regions. This is especially true and important for areas highly
populated by (sub-)mesoscale features, which, in turn, are responsible for the modulation of
relevant physical-biological processes at sea as the triggering of primary
production and the biomass redistribution and export.