OSOcean ScienceOSOcean Sci.1812-0792Copernicus PublicationsGöttingen, Germany10.5194/os-13-235-2017Validation of an ocean shelf model for the prediction of mixed-layer
properties in the Mediterranean Sea west of SardiniaOnkenReinerreiner.onken@hzg.deHelmholtz-Zentrum Geesthacht (HZG), Centre for Materials and Coastal Research, Max-Planck-Straße 1, 21502 Geesthacht, GermanyReiner Onken (reiner.onken@hzg.de)3April201713223525721October201628October201614March201715March2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://os.copernicus.org/articles/13/235/2017/os-13-235-2017.htmlThe full text article is available as a PDF file from https://os.copernicus.org/articles/13/235/2017/os-13-235-2017.pdf
The Regional Ocean Modeling System (ROMS) has been employed to
explore the sensitivity of the forecast skill of mixed-layer
properties to initial conditions, boundary conditions, and
vertical mixing parameterisations. The initial and lateral boundary
conditions were provided by the Mediterranean Forecasting System
(MFS) or by the MERCATOR global ocean circulation model via one-way
nesting; the initial conditions were additionally updated through the
assimilation of observations. Nowcasts and forecasts from the weather
forecast models COSMO-ME and COSMO-IT, partly melded with
observations, served as surface boundary conditions. The vertical
mixing was parameterised by the GLS (generic length scale)
scheme in four different set-ups. All ROMS
forecasts were validated against the observations which were taken during
the REP14-MED survey to the west of Sardinia. Nesting
ROMS in MERCATOR and updating the initial conditions through data
assimilation provided the best agreement of the predicted mixed-layer properties with the time series from a moored
thermistor chain. Further improvement was obtained by the usage of
COSMO-ME atmospheric forcing, which was melded with real observations,
and by the application of the k-ω vertical mixing scheme with
increased vertical eddy diffusivity. The predicted temporal
variability of the mixed-layer temperature was reasonably well
correlated with the observed variability, while the modelled
variability of the mixed-layer depth exhibited only agreement with the
observations near the diurnal frequency peak. For the forecasted
horizontal variability, reasonable agreement was found with
observations from a ScanFish section, but only for the mesoscale
wave number band; the observed sub-mesoscale variability was not
reproduced by ROMS.
Introduction
In ocean acoustics research, the diagnostics and prediction of
selected mixed-layer properties, such as the mixed-layer depth and
the mixed-layer temperature, are of primary interest because they
have a profound impact on the propagation of sound in the ocean. In
this article, a high-resolution ocean circulation numerical model is
presented which provides nowcasts and forecasts of these
properties. The objectives are (i) to evaluate the sensitivity of the
properties to different set-ups of the initial conditions, lateral boundary
conditions, atmospheric forcing patterns, vertical grid, and
vertical mixing parameterisations and (ii) to find a set-up which
reproduces and best predicts the depth and the temperature of the
mixed layer and the associated spatio-temporal variabilities
obtained from observations.
By definition, temperature and salinity are constant in the
mixed layer, and the sound speed increases slightly with depth due to
the pressure effect . Therefore, sound rays in
the mixed layer are refracted upwards and reflected at the sea
surface. Hence, the mixed layer acts as a surface duct
. On the other hand, at a depth greater than
the mixed-layer depth and because of the decreasing temperature, the
rays are refracted in the other direction, i.e. towards greater
depths. Consequently, in terms of passive acoustic monitoring, if a
sound source is within the mixed layer, the sound cannot be “heard”
at depths greater than the mixed-layer depth. If the sound source
is located below the mixed layer, it cannot be heard in the
mixed layer. The equivalent is true for the location of objects by
active sonar: if the sonar is within the mixed layer, the acoustic
signal can hardly reach an object at a greater depth, and vice
versa. This is, of course, an idealised model based on ray theory
which does not take account of the non-linear and frequency-dependent
effects, but it clearly emphasises that knowledge about the depth of
the mixed layer is mandatory for the planning and conduction of
acoustic experiments.
The sound speed c in seawater is a function of temperature T,
salinity S, and pressure p. Hence, small changes dc in the
sound speed can be described by the total differential
dc=∂c∂TS0,p0dT+∂c∂ST0,p0dS+∂c∂pT0,S0dp,
where the subscripts T0, S0, and p0 indicate that T, S, and
p, respectively, are held constant during the execution of the
partial differential. For the mid-latitudes and close to the sea surface
(T0=15∘C, S0=35, p0=0 dbar), the partial differentials
in Eq. (1) yield ∂c/∂T≈3.2 m s-1∘C-1 and
∂c/∂S≈1.2 m s-1, which means that the fractional change in the sound
speed with temperature is about 3 times larger than the change
with salinity . Moreover, as typical spatio-temporal
variations in temperature are O(10 ∘C), but those of salinity
are only O(1) at best, the first two terms in Eq. (1) yield
31.2 and 1.2 m s-1. Hence, changes in the sound
speed are largely controlled by changes in the temperature, and the
impact of salinity variations in the mixed layer can confidently be
ignored for the calculation of the sound speed. However, one may note
that this is only true for the open ocean. In coastal areas,
estuaries, and in polar regions, the salinity variations are
frequently larger and the concurrent variations in temperature smaller.
Besides the temperature and the depth of the mixed layer, the temporal
and horizontal variability of these two quantities require special
attention . The temporal variability at a fixed
location is affected by temporal changes in the following:
air–sea fluxes in momentum, heat, and fresh water;
sea state conditions and internal waves;
horizontal advection;
vertical motion; and
optical properties of the seawater.
The horizontal variability is due to spatial
differences of the same quantities and, in addition, to the presence of
mesoscale and sub-mesoscale features like fronts, meanders, eddies,
and filaments (e.g. ). Both the temporal and the
horizontal variability impact the sound speed and the
underwater sound propagation.
The objective of this article is to find a model set-up which predicts
in the best possible way the mixed-layer properties and their
spatio-temporal variabilities. While for the temporal variabilities
the main focus of attention is directed at timescales between
O(1 h) and O(10 days), the intention is to
resolve the horizontal variabilities on scales of 10 km
and below. This requires a circulation model with a built-in vertical
mixing scheme that accurately reproduces the diurnal cycle. A
state-of-the-art scheme has recently been published
by . It is an enhancement of the turbulence
closure model of , which is similar to
but additionally takes into account the effects of wave breaking and
Langmuir circulation. developed new numerical
techniques and improved the schemes for the physics in Noh's model, which
amongst others intensified the diurnal amplitude of the simulated sea
surface temperature. incorporated Noh's model into a
global ocean general circulation model, and they could show that the
new mixing scheme helped to correct too-high mixed-layer temperatures
and too-shallow mixed-layer depths in the high-latitude ocean. A
similar approach was pursued by a series of papers by
. In the first publication, a
one-dimensional mixed-layer model was developed based on the K-profile
parameterisation of . The model was forced with
observed fluxes from a mooring in the tropical Pacific Ocean, and it
qualitatively reproduced the observed diurnal variability in the sea
surface temperature over a period of about 4 months. However,
most of the time, the modelled temperature was higher than the
observed one by up to 1 ∘C. implemented
the turbulent kinetic energy scheme of in an ocean
circulation model, and this circulation model was coupled with
an atmospheric circulation model . The major outcome
of the latter publication was that the inclusion of the diurnal cycle
leads to a tropic-wide increase in the mean sea surface temperature, and, in
addition, the authors could demonstrate that the modelled diurnal cycle was
modulated by intraseasonal variations. The vertical mixing in all
papers mentioned above was accomplished by turbulence closure models.
By contrast, improved the parameterisation of
the absorption of solar radiation in the diurnal heating bulk model of
. This change, combined with a reduction in
accumulated heat and momentum, increased the model's responsiveness to
changes in the surface heat flux and surface stress. Amongst others, the
improved model predicted the vertical temperature profile within the
diurnal thermocline, increased warming at low wind speeds, and
decreased warming at high wind speeds.
The experimental area addressed in this study is situated in the
Mediterranean Sea to the west of Sardinia (see Figs. 3, 4, 5, and
7). Here, the observational data from a June 2014 oceanographic survey
are used to drive the aforementioned ocean circulation model and to
validate the model results .
The reader may note that within this article all dates refer
to the year 2014 and all times are in UTC (Coordinated Universal Time
) except where otherwise stated.
Observational data
The observational data originate from the REP14-MED experiment, which
took place in the eastern Sardo-Balearic Sea in the period of
6–25 June 2014. The collection of in situ data was
accomplished by the NATO Research Vessel Alliance, the Research
Vessel Planet of the German Ministry of Defence, a fleet of
underwater gliders, surface drifters, one sub-surface float, and six
oceanographic moorings. Throughout this article, however, the author
will refer only to the data of one mooring, denoted as M1, and to
the CTD (conductivity–temperature–depth) data collected by the
survey vessels and the gliders. For more details of the observations,
see .
Mooring M1
M1 (Fig. 1) was launched on 8 June at 07:14 at
8∘12.98′ E, 39∘30.80′ N (Fig. 3) and
recovered on 20 June at 13:55. The water depth at the launch position
was ≈ 150 m. M1 consisted of the central mooring M1CTR and
a sideways-extending appendix M1APP floating at the sea
surface. M1CTR was equipped with an upward-looking ADCP (acoustic doppler
current profiler) mounted at a nominal depth of
100 m below the sea surface, a CTD probe at 1 m of depth, and
a meteorological buoy at the surface. The appendix was connected by a
50 m long rope to M1CTR and extended to about 40 m in the
vertical direction. Forty Starmon thermistors (Star-Oddi, Gardabaer, Iceland) were mounted along the vertical cable to record the temperature with high vertical
resolution. In addition, four RBR data loggers (RBR, Ottawa, Canada) determined the actual
depth of the Starmons. The nominal and actual vertical positions and
the recorded parameters of the sensors are summarised in Table .
The design drawing of mooring M1. For explanations, see the text.
The nominal and actual depths
of the Starmon and RBR sensors mounted on the appendix of mooring
M1. For the meaning of the recorded variables, see the text.
(a)
The observed temperature [∘C] at mooring M1 and (b) the
vertical temperature gradient [∘C m-1].
The Starmons recorded time t (10 s) and temperature T in intervals of 10 s. The RBRs
additionally recorded pressure p. The depth
z was calculated internally by the RBR software. As the Starmons did
not have a pressure gauge, their actual vertical position was
evaluated thereafter from the depth records of the RBRs because the
positions of the Starmons relative to the RBRs was known. This was
accomplished in the following way:
the Starmon records at 3.0 and 7.0 m of depth were rejected
because the recorders failed (sensor positions 7 and 15 in
Table );
all records before 8 June at 07:18 and after
20 June at 13:30 were clipped and then sub-sampled in 5 min intervals;
at each instant, a second-order polynomial fit was applied to
the actual depth of the RBRs versus their nominal depth; and
the actual depths of the Starmon recorders were calculated with
the polynomial using the previously calculated coefficients.
This procedure was advisable in order to correct for
potential depth changes of the Starmons due to the actions of waves,
internal waves, horizontal advection, and vertical shear. However, it
turned out that these corrections were rather small: right at the sea
surface at sensor position 1, the actual depth of the Starmon
(Table ) varied between 0 and 1.85 m, and the
depth of the sensors at position 41 varied between 39.89 and
41.81 m. Hence, the applied corrections were around ±1 m.
The time series of the recorded temperature and the vertical
temperature gradient are shown in Fig. 2, several properties of which
may be challenging to reproduce for the circulation model.
The near-surface temperature
varied between about 22 ∘C and more than 24 ∘C. At
the beginning of the recording period, it was around 23 ∘C, then
it rose slowly and reached the maximum value on 12 and
14 June; afterwards, it decreased. The minimum of around
22 ∘C was reached on 17 June, and during the final
3 days, the temperature rose again by about 1 ∘C.
The mixed-layer depth may be defined approximately by means of
the depth at which the vertical temperature gradient is maximal.
Between about 15 and 20 June, there is clear evidence for such a
signal: the mixed-layer depth varied between about 4 m on 15 June and about 13 m on 18 and 19 June. However, between 8 and 14 June,
the signal is rather indistinct: the nighttime mixed-layer
depth ranged from about 2 m on 9 June to about 6 m on 10 June,
but during daylight hours the maximum gradient was sometimes found
right at the surface. Thus, a mixed layer in the “classical” sense
did not exist.
There are clear signals for temporal variability for both
temperature and the depth of the mixed layer. The variability
occurred on all scales between about 2 weeks and the Nyquist period
of 10 min (twice the sampling interval; see above).
Data collected by lowered CTD, gliders, and towed measuring systems
On both survey vessels, casts with lowered CTD probes were conducted
during the entire survey, but only the casts taken during the
7–11 June period were used here (for a more detailed description of the
probes and their calibration, see ). These casts
belonged to the initialisation survey, the purpose of which was to
provide realistic temperature and salinity data for the initialisation
of the numerical models. In total, 108 casts were taken on a regular
horizontal grid with a mesh size of ≈ 10 km (Fig. 3), resolving
the internal Rossby radius of deformation, the first mode of which is
around 13 km . Eleven gliders (for their payloads,
see ) were deployed on 8 and 9 June at
the positions marked “L” in Fig. 4 and directed to their
nominal zonal tracks. The scheduled tracks were arranged parallel to
the CTD sections (Fig. 3) but offset by 5 km in the meridional
direction. For the validation of the model forecasts, Alliance
conducted a survey during 21–24 June with a ScanFish (EIVA, Skanderborg, Denmark). The tracks are shown
in Fig. 5.
The CTD casts taken by Planet and Alliance during 7–11 June
and the position of mooring M1. The colour bar indicates the water
depth [m].
The circulation modelROMS
The employed numerical ocean circulation model is ROMS, the Regional Ocean
Modeling System. ROMS is a hydrostatic,
free-surface, primitive equations ocean model, the algorithms of which
are described in detail in . In the vertical, the primitive equations are
discretised over variable topography using stretched terrain-following
coordinates, or so-called s coordinates . In the
version used for this article, spherical coordinates on a staggered
Arakawa C grid are applied in the horizontal, and the horizontal
mixing of the momentum and the tracers is along isopycnic surfaces. The
vertical mixing is parameterised by means of the GLS (generic
length scale) scheme using the
stability function of . The air–sea
interaction boundary layer in ROMS is based on the bulk
parameterisation of .
The actual glider tracks during 8–23 June. The small circles
along the tracks show the surfacing positions. Each glider is marked
by a different colour. The colour code for the bathymetry is the same
as in Fig. 3.
The ScanFish tracks of Alliance during 21–24 June. The
colour code for the bathymetry is the same as in Fig. 3.
The model domain and discretisation
The model domain is situated to the west of Sardinia and it is
identical to the area shown in Fig. 3. The west and east
boundaries are at 6∘30.5 and 8∘35.5′ E, while in the
south and north the domain is limited by the 38∘36.4 and
40∘59.6′ N latitude circles, respectively. In the east–west
direction, the domain is separated into 120 grid cells and in the
south–north direction into 178 cells, which yields an average grid
spacing of Δx≈Δy≈ 1500 m in the zonal and
meridional direction, respectively. A comparison with
Fig. 3 reveals that the domain boundaries are kept away
from the observations by about 30 arcmin; this was intended in
order to mitigate a deterioration of the model solution at the
observational sites due to false advection from the open boundaries.
Bathymetry data from the General Bathymetric Chart of the Oceans
(GEBCO) with a spatial resolution of 1 arcmin were provided by
the British Oceanographic Data Centre (BODC), and coastline data
were obtained from NOAA (National Oceanic and Atmospheric
Administration). In order to avoid the crowding of the s coordinates in
shallow water regions, the bathymetry was clipped at 20 m, which is
the minimum allowed water depth. For the smoothing of the
bathymetry, a second-order Shapiro filter was applied. After smoothing,
the so-called rx0 parameter resulted in 0.31, which is about 50 % higher
than the maximum value of 0.2 recommended by .
However, rx0 is still lower than 0.4 as suggested in the ROMS forum
(https://www.myroms.org/forum).
In the vertical direction, the model domain was separated into 70
s layers, the position of which is controlled by three parameters
(θs,θb,hc) and two functions,
Vtr and
Vstr. Here, Vtr is the transformation equation,
Vstr is the vertical stretching function, θs and
θb are the surface and bottom control parameters, and
hc is the critical depth controlling the stretching (for more
details, see https://www.myroms.org/wiki/). For all ROMS runs
shown below, the functions and parameters were selected as Vtr=2,
Vstr=1, θs=5, and
θb=0.4, while hc was kept a variable.
Initialisation
ROMS was initialised from nowcasts of the coarser Mediterranean
Forecasting System (MFS; )
or the MERCATOR global ocean circulation model .
In either case, the downscaling from the parent
to the child was accomplished first by the linear horizontal
interpolation of the prognostic fields on the ROMS grid. As the
maximum horizontal resolution of MFS was close to 7 km
(1/16∘) and that of MERCATOR was 9.25 km (1/12∘), the
scale factors were around 4.7 and 6.2, respectively. Thereafter, all
fields were interpolated vertically from the horizontal depth levels to
the s coordinates. A special issue was the alignment of the land masks
of the parent and the child; if any wet grid cell of the child was
covered by a dry grid cell of the parent, a smooth transition of all
variables was created by taking the average of the surrounding parent
cells. However, as this may lead to a violation of continuity by
non-zero horizontal velocities normal to the land mask, all horizontal
velocities next to the ROMS land mask were set to zero.
Lateral boundary conditions and nesting
The ROMS code includes various methods for the treatment of open
boundaries. After extensive sensitivity studies, it was found that the
following algorithms served best for the posed problem: for the sea
surface elevation, the Chapman condition was selected
, and for all other quantities (i.e. barotropic and
baroclinic momentum, turbulent kinetic energy, temperature, and
salinity), the mixed radiation-nudging conditions after
were applied.
The lateral time-dependent boundary conditions were provided by the
parent by means of one-way nesting. However, the information from the
parent was not instantaneously superimposed to the ROMS solution;
additional nudging was applied to all prognostic variables (except
for the sea surface elevation), which allowed these fields to adjust
slowly to the parent values at the boundaries within an e-folding timescale of 2 days. In addition, a factor of 5 was used for the nudging
timescales, which caused a stronger nudging on the inflow.
Surface boundary conditions
At the sea surface, the boundary conditions for the air–sea exchange of
fresh water, momentum, and heat were evaluated from the outputs of two
numerical weather prediction models and from the measurements of the
meteorological buoy on top of M1 (see Fig. 1). This was accomplished by means of
the wind field at 10 m (2 m for M1) of height, air temperature and
relative humidity at 2 m, air pressure at sea level, total cloud
cover (not available from M1), net shortwave radiation, and
precipitation. The output of the weather prediction models was made
available by the Italian weather service CNMCA (Centro Nazionale
di Meteorologia e Climatologia Aeronautica) in two different
set-ups, COSMO-ME and COSMO-IT. COSMO-ME covers the entire
Mediterranean Sea with a horizontal resolution of 7 km and provided
72 h forecasts, while COSMO-IT encompasses Italy and the adjacent
waters at the very high resolution of 2.2 km; however, the forecast range
was only 24 h. The temporal resolution of both models was 1 h. The time series of all available variables from COSMO-ME,
COSMO-IT, and the meteorological buoy are shown in
Fig. 6 at the M1 position.
Data assimilation
In most of the model runs presented below, the temperature and salinity
data from the shipborne CTD probes and gliders were assimilated using objective analysis (OA; see
). Namely, ROMS includes
a module which enables data assimilation with the 4D-Var
method. However, as 4D-Var is based on variational methods, it is rather
expensive in terms of computer resources; according to parallel ROMS
runs using 4D-Var (A. Funk, personal communication, 2016), the CPU
time increases by about a factor of 10 compared to OA. During the
integration of ROMS, the engine conducting the data assimilation was
invoked every day at midnight, and it was controlled by six
parameters:
W: the width of the time window which determines what data are
assimilated. In all ROMS runs below, W=48 h; this setting was
found to provide the best forecast skill . Hence,
all temperature and salinity data of the previous and the following
24 h were selected for assimilation.
C: the isotropic correlation length scale. C=15 km was used
throughout, which is approximately the internal Rossby radius of the
Western Mediterranean in summer . Isotropic
correlation is a strong assumption, especially close to the
coast. However, according to the observations from the ADCP measurements
(I. Borrione, personal communication, 2016), predominantly meridional
currents prevailed only in a 10 km wide strip along the
Sardinian coast, while the rest of the 180 km wide model domain was
characterised by an eddy field with alternating currents. Here, the
usage of a non-isotropic correlation scale would deteriorate the
results.
δTobs, δSobs: the observational
errors of temperature and salinity, respectively. δTobs=0.5∘C and δSobs=0.16 were used
throughout. These values were obtained from the variance of all CTD
casts in the upper thermocline.
δTclim, δSclim: the climatology
errors. δTclim=5×δTobs=2.5∘C and
δSclim=5×δSobs=0.8 were applied.
The time series of the measured and predicted atmospheric
parameters at the site of mooring M1 from the observations of the
meteorological buoy on top of M1, COSMO-ME, and COSMO-IT. U-wind
and V-wind denominate the zonal and meridional wind components,
respectively. The cloud cover was not recorded at M1. The precipitation is
not shown because no precipitation was predicted or measured during
the entire period.
Integration and output
All ROMS runs presented below were initialised on 1 June at 00:00 and
integrated forward for 24 days until 25 June at 00:00. To satisfy the
horizontal and the vertical CFL criterion, a baroclinic time step
Δt=108 s (800 steps per day) was chosen, and the number of
barotropic time steps between each baroclinic time step was
40. Harmonic mixing along the isopycnals with an eddy diffusivity
coefficient of 5 m2 s-1 was used for the horizontal diffusion
of the tracers T and S, and a horizontal viscosity coefficient of
1 m2 s-1 was selected for the diffusion of momentum. Further
on, a quadratic law using a coefficient of 0.003 was applied for the
bottom friction, and the pressure gradient term was computed using the
standard density Jacobian algorithm of .
The three-dimensional volume of all prognostic fields was written to
an output file at 6 h intervals. For comparison of the ROMS
results with the observed records at mooring M1, the time series of
the vertical temperature profiles right at the position of M1 were
written to an extra file at the full temporal resolution.
Sensitivity of near-surface temperature and mixed-layer depth
The purpose of this section is to investigate the impacts of the following on the temperature between the surface and about 42 m of depth (which was
the vertical range of the M1 observations) and the depth of the
mixed layer:
initialising ROMS from different data sets;
the set-up of the vertical grid;
different atmospheric forcing patterns;
different vertical mixing schemes; and
the background eddy diffusivity.
This was achieved with 5 series of ROMS runs named A–E
(see Table for the parameter settings and the results
of each model run) with a total of 28 runs. The task of each
series was to assess the sensitivity of the ROMS forecast skill to
variations in the mechanisms mentioned in the bullets above. For each
run, the ability of ROMS to predict the temperature was assessed by
means of the root mean square
(rms) difference
ΔT=1N∑1NTROMS-Tobs212
between the observed temperature Tobs and the predicted
temperature TROMS at each depth level of the observations.
ΔT was evaluated for the period of 15 June at 00:00 to 20 June at 13:55
where N observations were available in 5 min intervals
(Sect. 2.1). This interval was selected because it enabled the
comparison of all runs with those which were forced by data
assimilation until 12 June at 00:00. The 3-day lag between the last
assimilation on 12 June and the start of the evaluation period on 15 June
was granted to ROMS in order to recover from “assimilation
shocks” which frequently become noticeable in the form of strong
inertial oscillations. The experience from the precursor model runs has
shown that such oscillations die off after about three to four inertial periods
(18.7 h at 40∘ N). In order to synchronise the modelled and the
observed temperature, TROMS was linearly interpolated in space
and time on the observations. The equivalent method was also applied
to the mixed-layer depth, D, which due to the lack of salinity
observations at the M1 position was defined as the depth at which the
temperature was 1 ∘C colder than the
temperature at the surface for the first time ().
Hence,
ΔD=1N∑1NDROMS-Dobs212
is the rms difference of the mixed-layer depths.
The parameter settings and
results of the ROMS runs in series A–E. The bold text indicates the
parameters or boundary forcing patterns which are varied within
the respective series. The best run in each series is marked by an
asterisk and serves as the control run for the successive
series.
Runhcrx1ParentMixingAVTAtmosphericAssimilationΔTΔT‾ΔD[m]scheme[m2 s-1]forcing[∘C][∘C][m]Series A A11021MFSGLS generic1×10-6COSMO-MEno0.301.163.47A21021MERCATORGLS generic1×10-6COSMO-MEno0.531.122.97A3*1021MERCATORGLS generic1×10-6COSMO-MEyes0.510.902.62Series B B1*1021MERCATORGLS generic1×10-6COSMO-MEyes0.510.902.62B22027MERCATORGLS generic1×10-6COSMO-MEyes0.490.892.67B35023MERCATORGLS generic1×10-6COSMO-MEyes0.490.912.70B410025MERCATORGLS generic1×10-6COSMO-MEyes0.460.892.68B520027MERCATORGLS generic1×10-6COSMO-MEyes0.440.892.75Series C C11021MERCATORGLS generic1×10-6COSMO-MEyes0.510.902.62C21021MERCATORGLS generic1×10-6COSMO-ITyes0.420.983.45C3*1021MERCATORGLS generic1×10-6M1yes0.800.703.28Series D D11021MERCATORGLS generic1×10-6M1yes0.800.703.28D21021MERCATORGLSk-kl1×10-6M1yes0.500.612.86D31021MERCATORGLSk-ϵ1×10-6M1yes0.510.602.95D4*1021MERCATORGLSk-ω1×10-6M1yes0.410.612.71Series E E11021MERCATORGLS k-ω1×10-6M1yes0.410.612.71E21021MERCATORGLS k-ω5×10-6M1yes0.380.622.74E31021MERCATORGLS k-ω1×10-5M1yes0.350.592.60E41021MERCATORGLS k-ω2×10-5M1yes0.310.572.49E51021MERCATORGLS k-ω3×10-5M1yes0.310.562.36E61021MERCATORGLS k-ω4×10-5M1yes0.350.572.25E71021MERCATORGLS k-ω5×10-5M1yes0.440.542.13E81021MERCATORGLS k-ω6×10-5M1yes0.490.562.11E91021MERCATORGLS k-ω7×10-5M1yes0.550.582.05E101021MERCATORGLS k-ω8×10-5M1yes0.660.572.13E111021MERCATORGLS k-ω9×10-5M1yes0.720.552.08E121021MERCATORGLS k-ω1×10-4M1yes0.800.572.15E131021MERCATORGLS k-ω2×10-4M1yes1.370.602.92Series A: initialising ROMS from different data sets
In this series, hc=10 m was selected for the critical depth. In
the first run, referred to as A1, ROMS was initialised from MFS, while
in A2 the initial conditions were provided by MERCATOR. A3 was
initialised from MERCATOR as well, but temperature and
salinity data from the CTD casts and 10 gliders
taken during 7–12 June at 00:00 were additionally assimilated ( Sect. 2.2 and Figs. 3, 4, 7). The
surface boundary conditions of all runs in the A series were provided
by COSMO-ME.
The actual surfacing positions of all assimilated
gliders during 7–11 June. Each glider is marked by a different colour. The
colour code for the bathymetry is the same as in Fig. 3.
ROMS runs A1, A2, and A3: the time series of the (a) near-surface temperature at 0.81 m of depth, (b) the mixed-layer depth (MLD),
and the corresponding observations at mooring M1. The numbers on the
abscissae indicate June dates. The period for which the data are assimilated
is highlighted with grey shading.
Figure 8a shows the time series of the near-surface temperatures at
0.81 m of depth from runs A1–A3 in comparison with the corresponding
observations of the uppermost Starmon sensor in M1 at the same depth
level. In A1 and A2, the predicted temperatures agree reasonably well
with the observations after 15 June, but before then the temperature
exceeds the observations by several degrees. Extreme differences are
visible during 12–14 June with differences of close to 3 ∘C. Figure 6
shows that during this period the predicted and observed wind speeds
were close to 0 m s-1 and the shortwave radiation flux reached
maximum values of more than 800 W m-2. Hence, as these quantities
are the major drivers of the mixed-layer temperature, it is concluded
that the selected parameterisation of the vertical mixing in ROMS is
not adequate for such calm situations. By contrast, as soon as the
wind became stronger after 14 June, the maximum difference between the
predicted and measured temperature is less than 1 ∘C. In A3
before 12 June, there is better agreement between the modelled and
the observed temperature. However, as can be seen from the sudden drop
in the modelled temperature at midnight on 10–12 June, the data
assimilation led to an underestimation of the surface temperature. The
reasons for this are twofold: first, some of the assimilated profiles
started at 2 or even 3 m of depth because the measurements close to the
surface were not reliable. In such cases, the uppermost measurements
were extended to the surface and led to an underestimation of the
near-surface temperature, which was sometimes significant because of
the extremely shallow or even non-existent mixed layer. Second,
the OA “advected” properties from the neighbouring casts which were not
representative for the M1 position. On 13 June, the modelled
temperature again exceeds the observations by almost 2 ∘C, but
the difference is less than in A1 and A2. After 15 June, the A3
temperature is rather close to the temperatures in A1 and A2. As a
skill measure for the forecasted near-surface temperature, ΔT
was evaluated for all runs and resulted in ΔT=0.30∘C in
A1, ΔT=0.53∘C in A2, and ΔT=0.51∘C in A3
(see also the legend box in Fig. 8 and Table ).
The temporal evolution of the mixed-layer depth is displayed in
Fig. 8b. As revealed by the decreasing rms differences ΔD between the modelled and observed mixed-layer depths, the forecast
skill increases from A1 to A2 and from A2 to A3. The
close agreement between the observed and modelled mixed-layer depth in
A3 before 12 June, which was forced by the assimilation, is noteworthy.
The mismatch between the model and the observations during 12–15 June is
also remarkable as
another indication of an inadequate parameterisation of the
mixed-layer dynamics at low wind speeds.
The vertical distribution of the rms temperature differences
ΔT of all runs in the A series is shown in
Fig. 9. It is demonstrated that at most depth
levels, ΔT is lower or equal in A2 compared to A1. The
assimilation in A3 led to a further significant decrease between about
4 and 35 m of depth; only above 4 m and below 35 m of depth is ΔT
higher in A3. The generally better forecast skill of A3 is also
supported by ΔT‾, the vertical mean of ΔT,
which is greater than 1 ∘C in A1 and A2 but only
0.90 ∘C in A3 (see also Table ). In summary,
nesting ROMS in MERCATOR and assimilating CTD profiles provided the
best forecasts for the temperature and the depth of the mixed layer
and the thermocline temperature below about 4 m of depth. Therefore, all
runs in the B series will be based on A3.
ROMS runs A1, A2, and A3: the rms temperature
differences ΔT [∘C] between the modelled temperature
TROMS and the observed temperature Tobs evaluated at the
actual depths of the observations. The vertical mean ΔT‾ is
written in the second column of the legend box. ΔT
was computed only for the period after 15 June at 00:00.
The temporal evolution of the modelled temperature in A3 at the
position of mooring M1 is shown in Fig. 10b. In comparison with
Fig. 10a, the modelled temperature close to the sea surface is too
high on 13 and 14 June, while at depths greater than about 3–10 m,
TA3 appears too low. This is confirmed by Fig. 10c, which exhibits
the temperature difference TA3-TM1: in approximately the upper
2 m depth range, TA3 partly exceeds TM1 by about
2 ∘C on these days, and just below, TA3 is up to more
than 3 ∘C lower than the observed temperature. This aberrant
cold layer can be identified during the whole model run. Apparently,
the modelled mixed-layer depth is shallower than the observed
one. This is illustrated by the vertical temperature gradient in
Fig. 10e. Namely, a comparison with Fig. 10d reveals that the generally
descending trend of the maximum gradient is similar, but the depth of
the modelled maximum is always less than the observed one. Moreover,
the observed variability is significantly higher than the modelled
one. While for the entire period there is clear evidence of a strong
diurnal variability in the observations (e.g. the deep mixed layer in
the early morning and the shallow mixed layer in the afternoon), the
modelled variability is much less pronounced. Another feature worth
mentioning is that the thermocline is too warm during the assimilation
phase before 12 June (Fig. 10c). It has been verified that this was
caused by the assimilation of the glider data because this feature is not
present in a run where only casts from lowered CTD were assimilated
(not shown). As can be seen from Figs. 3 and 7, two CTD casts were
taken exactly at the M1 position, while numerous glider casts are close
to M1 (note that the meridional offset of the glider tracks with
respect to the CTD meridional sections was 5 km). Thus, as the
correlation scale of the OA was 15 km, the modelled temperature at M1
was primarily determined by the glider measurements because the large
number of glider profiles reduced the statistical weight of the two
CTD casts.
(a) The observed temperature at mooring M1, (b) the modelled
temperature from ROMS run A3, and (c) the difference between
the modelled and the observed temperature. The vertical temperature
gradient from (d) the observations and (e) from A3. The instant of the
last data assimilation is indicated by the the grey dashed vertical
line.
Series B: sensitivity to the set-up of the vertical grid
If the transformation equation, the vertical stretching function, and
the total number of layers are held constant, the layer thicknesses of
the ROMS vertical grid are controlled by the surface and bottom control
parameters, θs and θB, and the critical depth,
hc. For mixed-layer modelling in shelf areas, it would be desirable
to have a high vertical resolution close to the surface, which can be
achieved by either increasing θs or decreasing hc. However,
as increasing θs would make the vertical transformation more
non-linear, it was decided to keep θs=5 constant and vary only
hc. In this series, the sensitivity of the ROMS results to five
different settings of the critical depth is investigated using
hc∈{10,20,50,100,200} m. For each of these choices, the
impact on the layer thicknesses at the position of mooring M1 is
illustrated in Fig. 11. A minimum layer thickness of
0.27 m right at the sea surface is achieved by hc=10 m in run
B1, while the thickness of that layer gradually increases in
B2–B5. In the latter (hc=200 m), the thickness is close to 1.3 m.
B1, because it is identical to A3, is the control run.
For all runs in this series, the temporal evolution of the mixed-layer
properties is displayed in Fig. 12. Although still too high around 14
June, the near-surface temperatures in all runs of this series
most resemble the observations during the entire integration period,
which is also expressed by the corresponding low values for ΔT; the minimum ΔT=0.44∘C is obtained from B5, while
the highest is found in B1 (ΔT=0.51∘C). For the
mixed-layer depth, there is no clear evidence of which run might do
best. ΔD varies only in a rather narrow range between 2.62 m
in B1 and 2.75 m in B5. The vertical distributions of ΔT
(Fig. 13) and the vertical averages ΔT‾ are
almost identical for all runs. However, right at the surface, ΔT is
minimal in B5 as shown in Fig. 12a. As the above results did
not reveal a clear tendency of which choice for hc yielded the best
results, it was decided to continue with B1 (hc=10 m) as the control
run in series C below. This decision was guided by ,
who asserted that a minimum vertical resolution of 1 m is mandatory to
resolve the diurnal cycle of the sea surface temperature. Another
criterion for this decision was the rx1 grid parameter (i.e. the
Haney condition, after ) being at a minimum in B1
(see Table ).
The layer thicknesses at the position of mooring M1
for various assumptions of the critical depth hc.
ROMS runs B1–B5: the time series of (a) the near-surface
temperature at 0.81 m of depth, (b) the mixed-layer depth (MLD), and the
corresponding observations at mooring M1. The numbers on the abscissae
indicate June dates. The period for which the data are assimilated is
highlighted with grey shading.
ROMS runs B1–B5: the rms temperature differences
ΔT [∘C] between the modelled temperature TROMS
and the observed temperature Tobs evaluated at the actual depths
of the observations. The vertical mean ΔT‾ is
written in the second column of the legend box. ΔT was
computed only for the period after 15 June at 00:00.
Series C: sensitivity to atmospheric forcing
Series C consists of three model runs, C1, C2, and C3. C1 is identical
to B2; in C2, the surface boundary conditions were provided by
COSMO-IT instead of COSMO-ME. In C3, the atmospheric forcing was
defined by means of the observations of the meteorological buoy on top
of mooring M1. Here, the observations were spread uniformly across the
entire model domain whenever available. If no observations were
available, i.e. before 8 June and after 20 June, the
atmospheric fields of COSMO-ME were used. As observations of cloudiness
were not available from M1, the corresponding fields from COSMO-ME were
used throughout.
According to Fig. 14a, the predicted near-surface temperature from C2
closely resembles that of C1, except for 14–17 June when the
temperatures in C2 are about 1 ∘C higher. Apparently, this was
driven by the different wind forecasts of the weather prediction models
(Fig. 6). Before 14 June, the wind forecasts of both models were
almost identical, but for the following 2 days during a period of
stronger winds, the forecasts differ from each other. Overall, the
near-surface temperature does not appear to be very sensitive to the
choice of the weather forecast models. This is also expressed by
ΔT, which attains similar values of 0.51 and
0.42 ∘C. The signature of the temperature
changes considerably when ROMS was driven by the weather observed at
M1; this is already evident during 8–10 June when the modelled temperature
in C3 is different from C1 and C2. After 15 June, it is mostly
higher than both the observations and the predictions of C1 and C2,
which correspondingly leads to a higher ΔT of
0.80 ∘C. With respect to the modelled mixed-layer depth
(Fig. 14b) and based on the ΔD criterion, C1 is superior to C2
and C3, but the large discrepancies during 12–15 June between the predictions
and the observation are still present in all three runs. This corroborates
the above hypothesis that the mismatch is not caused by the
atmospheric forcing because the most appropriate forcing was applied
in C3.
ROMS runs C1, C2, and C3: the time series of (a) the
near-surface
temperature at 0.81 m of depth, (b) the mixed-layer depth (MLD),
and the corresponding observations at mooring M1. The numbers on the
abscissae indicate June dates. The period for which the data are assimilated
is highlighted with grey shading.
A surprising result was obtained from the vertical structure of the
rms temperature difference (Fig. 15). Below about 3 m of depth,
ΔTC1 is about 0.1 ∘C lower than ΔTC2, but
a considerable improvement in the predicted stratification is provided
by C3. In the entire vertical range below about 5 m, ΔTC3
is up to 0.4 ∘C lower than ΔTC1. Only right at the
surface is ΔTC3 approximately 0.3 ∘C higher than
the corresponding values from C1 and C2, which is obviously due to the
above-mentioned mismatch after 15 June. C3 provides the best results
for the temperature stratification in the thermocline. As the
temperature in this depth range was definitely not affected by the
heat exchange at the sea surface (≈ 90 % of the shortwave
radiation is absorbed in the uppermost 1 m depth range), its
improvement could only be achieved by lateral advection, which is
controlled by the wind; apparently, the wind is better represented in
the observations than in the weather forecasts. To summarise, the
objective skill measure ΔT for the near-surface temperature
and ΔD for the mixed-layer depths indicate that C1 provides
the best forecast, while ΔTC3 is clearly superior to
ΔTC1 and ΔTC2 in the thermocline. The latter
confirms the decision to use C3 as a control run in series D because the
advective processes are obviously reproduced best.
The decision for C3 is supported by Fig. 16. By visual inspection, the
evolution of the predicted temperature pattern in C3 (Fig. 16c)
resembles the observations (Fig. 16a) more than in C1
(Fig. 16b). Namely, the near-surface temperature is too high, but the
thickness of the warm layer during 16–20 June is roughly the same as in the
observations, close to 10 m. Moreover, the depth and the variability
of the maximum vertical temperature gradient in C3 resembles the observed pattern to a
larger degree (Fig. 16d, e, f), although the
vertical temperature gradient is still too weak.
ROMS runs C1, C2, and C3: the rms temperature
differences ΔT between the modelled temperature TROMS and
the observed temperature Tobs evaluated at the actual depths of
the observations. ΔT was computed only for the period after 15
June at 00:00.
(a) The observed temperature at mooring M1, (b) the modelled
temperature from ROMS runs C1 and (c) C3, (d) and the vertical
temperature gradient from M1, (e) C1, and (f) C3. The instant of the
last data assimilation is indicated by the the grey dashed vertical
line.
Series D: sensitivity to the vertical mixing parameterisation
The GLS scheme provides a generalisation of a
class of differential length-scale equations used in turbulence models
for oceanic flows. Commonly used models, like the k-kl model of
, the k-ϵ model , and the
k-ω model , are recovered as special cases of
the generic scheme. Here, k is the turbulent kinetic energy, l is the
length scale of the turbulence, ϵ is the dissipation rate, and
ω is the specific dissipation rate. In series A–C, the GLS
vertical mixing scheme was applied using its generic parameters as
formulated by . In the following, D1 is identical
to C3 serving as the control run, the GLS scheme with
the k-kl parameterisation is applied in D2, the k-ϵ parameters are applied in D3, and
the k-ω parameterisation, which was adjusted to
oceanic conditions by , is applied in D4.
After 12 June, the near-surface temperature of all runs is correlated
with the observations (Fig. 17a), but is mostly still too
high. Moreover, the graphs indicate that the temperatures from D2, D3, and
D4 are closer to the observed ones, which is also expressed by ΔTD2=0.50∘C, ΔTD3=0.51∘C, and ΔTD4=0.41∘C, while ΔTD1=0.80∘C. For the
mixed-layer depth (Fig. 17b), the best agreement with the observations
was obtained from D4 with ΔDD4=2.71 m. However, the
mixed layer was mostly too shallow in all runs in this series. Hence,
based on the ΔT and ΔD criteria, the k-ω mixing
scheme in D4 definitely performs the best. This is also supported by the
vertical structure of ΔT displayed in Fig. 18. There is clear
evidence that the k-kl scheme (D2), the k-ϵ scheme (D3), and
the k-ω scheme (D4) do better than the generic GLS (D1).
Between the surface and about 5 m of depth, the best result was obtained
from D4. Therefore, D4 will serve as the control run in the following
E series.
ROMS runs D1–D4: the time series of (a) the near-surface
temperature at 0.81 m of depth, (b) the mixed-layer depth (MLD), and the
corresponding observations at mooring M1. The numbers on the abscissae
indicate June dates. The period for which the data are assimilated is
highlighted with grey shading.
An indicator of why the k-ω parameterisation performed better than
the other closure schemes is possibly found in the publication of
. Here, a one-dimensional model implemented in a
three-dimensional circulation model was used to investigate physical
and numerical turbulent-mixing behaviour. Amongst others, the k-kl,
the k-ϵ, and the k-ω scheme were compared to each
other. It turned out that the k-ω scheme was the most sensitive to
the vertical resolution. In a coarse (about 10 m) resolution model,
k-kl and k-ϵ clearly did better than k-ω, while at a high
(about 1 m) resolution, all three schemes yielded suitable results. In
the D series, the vertical resolution close to the sea surface is 0.27 m
(see Fig. 11 and Sect. 4.2 above). Hence, one may speculate that
the k-ω formulation becomes superior to the other schemes when
the vertical resolution is increased.
Series E: sensitivity to the background vertical eddy diffusivity
The shortcoming of all the model runs conducted so far was that the
mixed layer was too warm and too shallow, and the thermocline was too
cold with respect to the observational data. This is also in agreement
with the findings of . Hence, it was conjectured
that the parameterisation of the vertical transport of heat and/or
momentum was not adequate. Several attempts were undertaken to
fine-tune the D4 results by varying the vertical eddy viscosity
coefficient and the turbulent closure parameters, but the outcomes
were sobering; a significant improvement in the forecast skills for
the mixed-layer properties was not achieved. Hence, in this series,
the background vertical eddy diffusivity AVT was increased
gradually from 1×10-6 m2 s-1 in E1 (which is the
control run identical to D4) to 2 × 10-4 m2 s-1 in
E13. The forecast skill of each run was again assessed by means of
ΔT at 0.81 m of depth and by ΔD. The dependency of these
parameters on AVT is shown in Fig. 19. ΔT exhibits
minimum values of 0.31∘C (≈0.1∘C lower than in
D4) for AVT≤2×10-5≤3×10-5 m2 s-1 in
E4 and E5, which is somewhat higher than (1.7±0.2)×10-5 m2 s-1
obtained from the tracer measurements in the thermocline
during the North Atlantic Tracer Release Experiment
. By contrast, the minimum of ΔD=2.05 m is found in E9 for AVT=7×10-5 m2 s-1.
ROMS runs D1–D4: the rms temperature differences
ΔT between the modelled temperature TROMS and the
observed temperature Tobs evaluated at the actual depths of the
observations. ΔT was computed only for the period after 15 June at 00:00.
Series E: ΔT and ΔD for ROMS runs
E1–E13. Both quantities were computed only for the period after 15 June at 00:00.
The time series of (a) the near-surface temperature at
0.81 m of
depth from E1 and E4, (b) the mixed-layer depth (MLD) from E1 and E9, and
the corresponding observations at mooring M1. The numbers on the
abscissae indicate June dates. The period for which the data are
assimilated is highlighted with grey shading.
Figure 20 shows the near-surface temperature in E4 and the
mixed-layer depth in E9 together with the corresponding quantities of
the control run E1 and the observations. After 15 June, the increase
in AVT from 1×10-6 to 2×10-5 m2 s-1
shifted the near-surface temperature by about
0.1 ∘C closer to the observations. Most of the time, the
modelled signal is correlated with the observations, although the
modelled maximum and minimum temperatures are frequently lagged a few
hours behind the observed extreme values. Similar features were also
described by when comparing time series of
observed sea surface temperatures with those generated by the model of
. In their improved model (see the Introduction), they
demonstrated that the peak warming in the afternoon was shifted
earlier. For the mixed-layer depth, the increase in the eddy
diffusivity to 7×10-5 m2 s-1 caused a significant
reduction in ΔD from 2.71 m in E1 to 2.05 m in E9. While in
the precursor series the mixed layer was always too shallow, it now agrees
remarkably well with the observations, except for large
discrepancies on 19 and 20 June where the predicted mixed layer is up
to 4 m shallower than the observed one. As the M1 wind speed was very
low on these days (Fig. 6), other processes leading to a deepening
of the mixed layer were probably inadequately parameterised, such as
Langmuir circulation and wave breaking ( ).
Temporal variability
In order to assess the modelled temporal variability of the
temperature and the depth of the mixed layer, the normalised spectra
of the near-surface temperature amplitude T^ at 0.81 m of depth and
of the mixed-layer depth amplitude D^ were computed by the Fourier
transform, both from the observations and the ROMS outputs of runs E4
and E9, respectively. To enable a sufficient spectral resolution for
the cycle periods of around 1 day, the entire time series between 8 and
20 June was used as input for the Fourier transform. At first glance,
the modelled spectrum of the near-surface temperature (Fig. 21a1)
resembles the observations in the cycle period range between about 0.1
and 1 days, but significant differences are evident in the bands
between about 0.1 and 0.4 days where the modelled amplitude is
up to 1 order of magnitude different from the observed one. This
mismatch is not surprising, because here the temporal variability is
controlled mainly by internal waves that are either not reproduced or are only partially
reproduced by the model. By contrast, the range of 0.4–0.8 days (10–19 h)
is dominated by tides and inertial
motions. Theoretically, at 40∘ N, the inertial peak is at 18.7 h
(0.78 days), but a correspondingly small peak is only visible in
the modelled spectrum; no such peak is noticeable in the
observations. Probably, the modelled peak is a leftover of the
assimilation shock on 12 June. Additional peaks are found in both the
modelled and the observed spectrum at about 0.4, 0.5, and 0.6–0.7 days
(≈ 10, ≈ 12, and ≈ 14–17 h). While the sources of the first and the latter are unknown, the
12 h peak might be related to a semi-diurnal tidal
component. However, as there was no tidal forcing in the ROMS version
utilised in this study and the MERCATOR forcing at the lateral
boundaries was defined by means of daily averages, the semi-diurnal
variability could only be caused by tides in the atmosphere. Both the
modelled and the observed spectrum are dominated by the diurnal
variability represented by the peak at 1 day. In the red part of
the spectrum between 1 and about 10 days, the modelled and observed
amplitudes exhibit some weak correlation, and they are of about the
same order of magnitude. This matter is not discussed here because it
is potentially impacted by long-period fluctuations in
the forcing at the surface and at the lateral boundaries. More
detailed information on the correlation corrrT^ROMS,T^obs between the modelled and the observed temperature amplitudes
is shown in Fig. 21a2. The correlation coefficient r=0.74
together with the p value p=3.05×10-22 proves a high
significant correlation, and the regression coefficients a0=0 and
a1=1.74 indicate that, in general, the modelled amplitudes are
overestimated. By contrast, there is less but still significant
correlation between the modelled and the observed mixed-layer
amplitudes D^ROMS and D^obs
(Fig. 21b2), which is indicated by corrrD^ROMS,D^obs=0.50,
and p=4.52×10-9. This finding is also
supported by the spectrum (Fig. 21b1) in which a slight correlation of
the amplitudes is only found for the diurnal and semi-diurnal cycles.
The spectra and correlation parameters of the modelled
and observed amplitudes (a)T^ of the near-surface temperature
at 0.81 m of depth from run E4 and (b)D^ of the mixed-layer depth
from run E9. The spectra were evaluated for the entire time series during
8–20 June where observations were available.
The sections along the A05 ScanFish track (cf. Fig. 5)
at 40∘48′ N: (a) the temperature recorded by the ScanFish, (b) the temperature
predicted by ROMS, (c) the sea surface temperature SST, and
(d) the mixed-layer depth evaluated from the ScanFish measurements and
ROMS. No interpolation was used for the contour plots.
The timing and nominal positions of the ScanFish
tracks considered in this study (cf. Fig. 5).
The ROMS analysis determines the instant of the model output which
was used for comparison.
TrackTypeNominal positionStart timeEnd timeDurationROMS analysisA01zonal40∘06′ N21 Jun 14:0321 Jun 18:154:1221 Jun 18:00A03zonal40∘00′ N21 Jun 19:1022 Jun 00:385:2822 Jun 00:00A05zonal39∘48′ N22 Jun 03:0022 Jun 08:005:0022 Jun 06:00A07zonal39∘36′ N22 Jun 12:5722 Jun 18:055:0822 Jun 18:00A09zonal39∘24′ N22 Jun 20:1723 Jun 01:164:5923 Jun 00:00A10*meridional07∘31′ E23 Jun 18:2023 Jun 22:153:5524 Jun 00:00
* Only the strictly meridional fraction
of A10 was utilised.
Horizontal variability
In order to assess the capability of ROMS to reproduce and predict the
horizontal variability of mixed-layer properties, the results of run
E9 were analysed along the ScanFish tracks A03, A05, A07, A09, and A10
(see Fig. 5) and compared with the data collected by the towed
device. E9, using AVT=7×10-5 m2 s-1, was selected
for this comparison because both ΔT and ΔD were
acceptable. The details of the ScanFish tracks are summarised in Table .
As ROMS output was only available in 6 h intervals
starting at midnight, in each case the output cycle was used which
fell within the time window when the tracks were conducted. This
assumed synopticity of the ScanFish tracks is justified by the
fact that the maximum duration of the tracks was 5 h 28 min
for A03.
To make the ScanFish observations and the ROMS products comparable,
the ScanFish temperature was interpolated vertically on 1 dbar
standard levels, and the ROMS temperature was mapped on the same
levels. As the upper inflection point of the ScanFish varied between
about 5 and 10 dbar, there was frequently no information on the
near-surface temperature available. In such cases, the temperature at
the inflection level was extended to the surface. The same method was
applied to the ROMS temperature, which was not defined right at the
surface but in the centre of the first s layer below the surface. In
deep-water regions, this was located at about 3 m of depth.
Figure 22a shows a temperature section from the ScanFish
measurements along the central track of A05, and the corresponding
section from ROMS is displayed in Fig. 22b. The overall features of both
sections resemble each other, but the small-scale horizontal
variability of the ScanFish temperature was not reproduced by
ROMS. This is probably due to the smoothing effect of the OA,
the combined action of the horizontal eddy diffusivity, and the numerical
diffusion. However, as the last assimilation cycle was conducted on 12
June, 10 days prior to the ScanFish observations, one may exclude the possibility that
the OA removed the small-scale features. Moreover, the vertical
temperature gradient is much weaker in ROMS, which was already noted
above. Hence, this is apparently not caused by the increased vertical
diffusivity but by the vertical resolution of ROMS. The sea surface
temperatures and the mixed-layer depths from the ScanFish and ROMS are
displayed in Fig. 22c and d. For the surface temperature, the observed
large-scale west–east trend is reproduced by ROMS, but there are
differences of up to 0.5 ∘C in the central portion of
the section. The maximum differences between the modelled and the observed
mixed-layer depth in the 0–20 km range are close to 5 m at 13 km of
distance, while in the eastern half of the section, the modelled and
the observed mixed-layer depths approach each other. However,
the smaller-scale O(1 km) observed variability was not
reproduced by ROMS for both the sea surface temperature and the
mixed-layer depth.
To investigate why the small-scale variability was not predicted
correctly, run E9 was repeated using a smaller horizontal eddy
diffusivity coefficient of 1 m2 s-1 instead of 5 m2 s-1,
which was used for all the model runs so far. However, no
significant changes were noticeable. Thus, one has to settle for the
fact that the present set-up of ROMS is only able to reproduce the
horizontal variability of mixed-layer properties on scales which
are comparable to the Rossby radius.
Conclusions
ROMS has been utilised to diagnose and predict the properties of the ocean
mixed layer. The sensitivity of the model results to the choice of
the initial and boundary conditions, the set-up of the vertical grid,
and the vertical mixing schemes were investigated. The initial and lateral
boundary conditions for ROMS were taken from two different parent
models through one-way nesting. At the surface, ROMS was forced by
two different weather forecasts or by observations. All ROMS nowcasts and
forecasts were validated against observations which were taken in June
2014 to the west of Sardinia in the Mediterranean Sea.
To explore the sensitivity of the near-surface temperature and the
mixed-layer depth to the choice of the initial conditions, ROMS was
alternatively initialised by the Mediterranean Forecasting System
(MFS) and the global MERCATOR model. In addition,
observed temperature and salinity data were assimilated. For
validation, the time series of temperature were compared with the observations
from a mooring. Initialising ROMS from MERCATOR instead of
MFS provided better agreement between the model and the
observations, but significant improvement was obtained from a ROMS
run initialised from MERCATOR and updated with assimilated data from
CTD casts and gliders. This applied both to the near-surface
temperature and the mixed-layer depth as well as to the temperature
distribution in the upper thermocline.
To investigate the impact of the surface boundary conditions,
atmospheric forcing fields were taken from the weather prediction
models COSMO-ME and COSMO-IT and from the observations of a
meteorological buoy acting as a point source. With respect to the
mixed-layer depth, the best agreement with the observations was
obtained from a model run forced with COSMO-ME, while the near-surface
temperature exhibited the best match when ROMS was forced by COSMO-IT.
However, the stratification in the upper thermocline was best
represented when the point source was applied. The obvious reason for
this surprising result is that the momentum forcing was overestimated
by both COSMO-ME and COSMO-IT.
For the vertical mixing, four different configurations of the GLS
scheme of were applied, representing the generic
version: the k-kl model of , the k-ϵ
model , and the k-ω model .
The best performance was obtained from the k-ω model.
Regardless of which initial conditions or surface boundary conditions
were applied, the modelled mixed layer was always too shallow and too
warm. Therefore, the background vertical eddy diffusivity coefficient,
AVT, was varied over more than 1 order of magnitude. The best
agreement of the mixed-layer temperature was obtained for
AVT≈2×10-5 m2 s-1, while
AVT=7×10-5 m2 s-1 provided the best match
of the mixed-layer depth with the observations.
A positive and significant correlation was found between the modelled
and the observed temporal variability in the mixed-layer temperature.
The modelled variability resembled the observed variability
predominantly for cycle periods in the spectral ranges between about
0.5 and 1 days. By contrast, less correlation was found between
the modelled and the observed variability in the mixed-layer depth.
Slight agreement was only found for the diurnal period.
The horizontal variability was validated against measurements from a
high-resolution zonal ScanFish section. Both the modelled mixed-layer
temperature and the mixed-layer depth closely resembled the observations,
but only on the larger scales of O(10 km). Hence, the
mesoscale variability was rather well reproduced, but the sub-mesocale
variability was not.
All work related to this article was done on a Linux workstation under
Kubuntu 16.04. ROMS/TOMS version 3.6 was used for the model runs, the
pre- and post-processing was done with MATLAB R2016b, and the article was
written in LaTeX. The model code and all scripts are available from
the author on request.
All data of the REP14-MED experiment are available on the CMRE data
server at http://geos3.cmre.nato.int/REP14. The data are NATO
UNCLASSIFIED and available only for the
partners of the experiment. However, interested institutions can sign
up for partnership at any time. Requests may be directed to the author
or to geos-webmaster@nurc.nato.int.
The author declares that he has no conflict of interest.
Acknowledgements
The author would like to thank the masters and crews of the NRV Alliance and the RV Planet for their professionalism during the
conduction of the experiments at sea. The data from COSMO-ME and
COSMO-IT were provided by the Italian weather service Centro
Nazionale di Meteorologia e Climatologia Aeronautica, and the MFS
and MERCATOR data sets were downloaded from the Copernicus Marine
Environment Monitoring Service (http://marine.copernicus.eu). REP14-MED
was sponsored by HQ Supreme Allied Command Transformation (Norfolk, VA,
USA).
The article processing charges for this open-access publication
were covered by a Research Centre of the Helmholtz Association.
Edited by: J. Chiggiato
Reviewed by: two anonymous referees
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