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  • View in gallery

    Locations of the NSP data stations

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    Bathymetry (m) of the simulated area and location of the 13 discharge sources. The Dogger Bank is the shallow triangular area in the central North Sea between 54° and 56°N. The deeper Outer Silver Pit (54°N, between 1° and 3°E) is visible to the south of the Dogger Bank. The area north of Germany and east of Denmark is the German Bight where the Old Elbe Valley can be observed by its wedgelike shape

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    Time series for the 10 NSP cruises in 1989 of global parameters averaged over all (a) mixed and (b)–(f) stratified data stations: (a),(b) depth mean temperature, (c) surface temperature, (d) bottom temperature, (e) surface minus bottom temperature difference, and (f) percentage of stratified stations. Values are shown according to the data (solid circles), run A (solid–plus signs), run B (dots–asterisks), run C (dashes–diamonds), run D (dash–dots–triangles), and run E (dash–three dots–squares).

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    Heat flux experiment at station AG: (a) sea surface minus air temperature calculated from run A (solid line) and run C (dashed line); (b) downward surface heat flux from run A minus its value from run C; (c) depth mean temperature difference between runs A and C. All values are averaged over 3 days

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    Heat flux experiment at station CW: (a) downward surface heat flux from run A minus its value from run B and (b) depth mean temperature difference between runs A and B. All values are averaged over 3 days

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    Seasonal temperature evolution (°C) at station CS: (a) observations and (b) run A; Thick line denotes 12°C contour; (c) temperature profile on 30 Aug as given by the observations (plus signs), run A (solid curve), run B (dotted curve), and run D (dash–dotted curve). White areas in (a) indicate missing data

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    (a) Monthly averaged thermocline depth (m) for Aug, defined as the distance to the surface of the point where the temperature exceeds the bottom value by 0.5°C; (b) residual bottom stress (N m−2) for Aug; surface salinity distribution (psu) on (c) 7 Apr and (d) 5 Aug; and (e) daily averaged wind vectors at station BB.>

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    Residual circulation fields for (a)–(c) Mar and (d)–(f) Aug: (a),(d) horizontal current at 15-m depth; (b),(e) circulation along a transect at 55°N; and (c),(f) northward current (m s−1) at the same transect; (c),(f) thick line represents zero current.>

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    Monthly averaged values of the depth mean temperature (°C) obtained from the standard run A minus the corresponding value calculated from run D without temperature advection: (a) Mar and (b) Aug. Contour interval is (a) 0.25°C and (b) 0.5°C. White areas indicate negative temperature differences (advective cooling); gray and black areas represent positive values (advective warming). The plots show the effect of advective transport on the temperature distribution during typical winter and summer months

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    Time series of depth mean temperatures at a number of selected stations as obtained from the observations (solid circles), run A (solid curves), run D (dash–dotted curves), and run E (dash and three-dotted curves).

  • View in gallery

    (Continued)

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    Daily averaged temperature evolution (°C) at station DM for Jul and Aug according to (a) the observations, (b) run A, and (c) run B. Thick line represents 14.5°C contour. Time series of (d) the harmonically analyzed surface amplitude, (e) surface stress, and (f) the daily averaged downward surface heat flux

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    (a) Bottom minus surface density difference (kg m−3) and circulation at 15-m depth on 7 Jul at neaps from run A; (b) as in (a) but for 26 Jul during spring tide; (c) neaps distribution of temperature (°C) along the 55°N transect on 7 Jul from run A; (d) as in (c) but for 26 Jul at spring; (e) as in (c) but for the northward current (m s−1); (f) as in (d) but for the northward current; (g) same as (c) but calculated from run B; (h) same as (f) but obtained from run E. Thick lines delineate the 14°C and zero current contours. The plots are obtained after removal of the M2 tide

  • View in gallery

    (Continued)

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    Fraction of the total computational area where the surface minus bottom temperature difference exceeds 1°C as obtained from all model experiments: run A (solid line), run B (dotted line), run C (dashed line), run D (dash–dotted line), and run E (dash and three-dotted line)

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    Time series (nonaveraged) at station DM from 28 Jul to 3 Aug: (a) observed temperature (°C), (b) modeled temperature, (c) northward current (m s−1), and (d) vertical velocity (10−4 m s−1) from run A. Thick lines represent the 15°C and zero current contours, dashed lines the 12°C contour. Depths below 30 m are omitted for clarity. (a) White areas represent missing data. Harmonically analyzed temperature amplitude at (e) 13-m and (f) 41-m depth for Jul and Aug: data (solid circles), run A (solid curve), and run B (dotted curve)

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A Numerical Study of the Long- and Short-Term Temperature Variability and Thermal Circulation in the North Sea

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  • 1 Management Unit of the Mathematical Models, Brussels, Belgium
  • | 2 Proudman Oceanographic Laboratory, Bidston, United Kingdom
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Abstract

A three-dimensional numerical study is presented of the seasonal, semimonthly, and tidal-inertial cycles of temperature and density-driven circulation within the North Sea. The simulations are conducted using realistic forcing data and are compared with the 1989 data of the North Sea Project. Sensitivity experiments are performed to test the physical and numerical impact of the heat flux parameterizations, turbulence scheme, and advective transport. Parameterizations of the surface fluxes with the Monin–Obukhov similarity theory provide a relaxation mechanism and can partially explain the previously obtained overestimate of the depth mean temperatures in summer. Temperature stratification and thermocline depth are reasonably predicted using a variant of the Mellor–Yamada turbulence closure with limiting conditions for turbulence variables. The results question the common view to adopt a tuned background scheme for internal wave mixing. Two mechanisms are discussed that describe the feedback of the turbulence scheme on the surface forcing and the baroclinic circulation, generated at the tidal mixing fronts. First, an increased vertical mixing increases the depth mean temperature in summer through the surface heat flux, with a restoring mechanism acting during autumn. Second, the magnitude and horizontal shear of the density flow are reduced in response to a higher mixing rate. Thermal and salinity fronts generate a seasonal circulation pattern in the North Sea. Their impact on the horizontal temperature distributions is found to be in good agreement with the observations. It is shown that, in the absence of strong wind forcing, both the vertical temperature distribution and the thermal circulation experience semimonthly variations in response to the spring–neap cycle in tidal mixing. At spring tides, the surface mixed layers are shallower, in agreement with observations at two mooring stations, and the baroclinic circulation intensifies, whereas the opposite occurs at neaps.

Corresponding author address: Dr. Patrick J. Luyten, Management Unit of the Mathematical Models, 100 Gulledelle, B-1200 Brussels, Belgium. Email: p.luyten@mumm.ac.be

Abstract

A three-dimensional numerical study is presented of the seasonal, semimonthly, and tidal-inertial cycles of temperature and density-driven circulation within the North Sea. The simulations are conducted using realistic forcing data and are compared with the 1989 data of the North Sea Project. Sensitivity experiments are performed to test the physical and numerical impact of the heat flux parameterizations, turbulence scheme, and advective transport. Parameterizations of the surface fluxes with the Monin–Obukhov similarity theory provide a relaxation mechanism and can partially explain the previously obtained overestimate of the depth mean temperatures in summer. Temperature stratification and thermocline depth are reasonably predicted using a variant of the Mellor–Yamada turbulence closure with limiting conditions for turbulence variables. The results question the common view to adopt a tuned background scheme for internal wave mixing. Two mechanisms are discussed that describe the feedback of the turbulence scheme on the surface forcing and the baroclinic circulation, generated at the tidal mixing fronts. First, an increased vertical mixing increases the depth mean temperature in summer through the surface heat flux, with a restoring mechanism acting during autumn. Second, the magnitude and horizontal shear of the density flow are reduced in response to a higher mixing rate. Thermal and salinity fronts generate a seasonal circulation pattern in the North Sea. Their impact on the horizontal temperature distributions is found to be in good agreement with the observations. It is shown that, in the absence of strong wind forcing, both the vertical temperature distribution and the thermal circulation experience semimonthly variations in response to the spring–neap cycle in tidal mixing. At spring tides, the surface mixed layers are shallower, in agreement with observations at two mooring stations, and the baroclinic circulation intensifies, whereas the opposite occurs at neaps.

Corresponding author address: Dr. Patrick J. Luyten, Management Unit of the Mathematical Models, 100 Gulledelle, B-1200 Brussels, Belgium. Email: p.luyten@mumm.ac.be

1. Introduction

Density fronts are common features in midlatitude coastal and shelf seas. Thermal fronts arise as a result of a balance between tidal mixing and surface heating (Simpson and Hunter 1974). The structure of these fronts is sensitive to the characteristics of the topography and spatial and temporal variations of the tidal current amplitude. Salinity fronts are created by coastal discharges of freshwater. A frontal flow is generated by the requirement of geostrophic equilibrium and usually takes the form of a coastal current propagating alongshore or alongshelf to the right (looking seaward) of the source in the Northern Hemisphere.

A typical example is the North Sea where tidal mixing fronts appear from spring to autumn in the deeper central and northern parts and a region of freshwater influence is observed throughout the year that extends along the continental coasts of The Netherlands, Germany, and Denmark. The principal components of the tide are the semidiurnal M2 and S2 harmonics yielding a semimonthly modulation of the tidal amplitude of about 30% (Davies et al. 1997). In earlier studies the location of tidal mixing fronts was determined at critical values of the parameter χ = log(H/u3t), where H is the water depth and ut is the amplitude of the depth mean M2 tidal current (Pingree and Griffiths 1978; Simpson and Bowers 1981). Although the method proved to be successful with some scatter, it is clear that a high-resolution three-dimensional model is needed to resolve finescale processes associated with thermal fronts (James 1989; Proctor and James 1996). The density-driven residual circulation in the North Sea can be divided into two main components arising from different origins. First, a coastal current, driven by the nearshore salinity fronts and the prevailing winds, is known to exist at the continental coasts of The Netherlands and Germany and in the German Bight (e.g., Prandle et al. 1993). Second, a thermal circulation along the tidal mixing fronts in summer has been inferred from current and density measurements at the coast of England and in the Dogger Bank area (Prandle and Matthews 1990; Lwiza et al. 1991).

First studies of the seasonal cycle of temperature and stratification in the North Sea were performed using mean forcing data and compared with climatological observations (Elliot and Clarke 1991; Pohlmann 1996). More realistic simulations could be performed when the data from the U.K. Natural Environment Research Council North Sea Project (NSP) became available (Charnock et al. 1994). A series of cruises was performed during 1988–89 covering a complete seasonal cycle providing monthly profiles of temperature and salinity at more than 100 stations throughout the southern and central North Sea (see Fig. 1). Mooring data with a high time resolution from a selected number of fixed stations are also available. In a recent study Holt and James (1999) compared the temperature data of the complete NSP dataset with a three-dimensional model and realistic surface forcing and open boundary data. The temperature cycle was well represented and reasonable agreement was obtained for surface and bottom temperatures and thermocline depths. The coarse resolution of the model (about 22 km) did not provide a detailed picture of the fronts while discrepancies with the data occurred in the German Bight because of the absence of salinity in the simulation. This omission was corrected in the shelf sea simulations of Holt et al. (2001) but the horizontal resolution (about 12 km) is still too coarse to resolve coastal fronts. Besides the variation on a seasonal scale, observations in the North Sea (Van Haren et al. 1999; Van Haren 2000) showed important fluctuations in temperature at the inertial, in response to the wind forcing, and semidiurnal tidal frequencies. As suggested by these authors these modes and their higher-order harmonics generate an important current shear across the thermocline that tends to enhance vertical mixing.

The recently developed three-dimensional baroclinic COHERENS model (Luyten et al. 1999) is applied to study the annual cycle of temperature, thermal fronts, and density circulation in the North Sea. From the forcing, one deduces three different ranges in timescales, which are examined separately: seasonal (long range), semimonthly as given by the spring–neap cycle (medium range), and semidiurnal and inertial (short range). The model resolves the main frontal structures and has the ability to preserve the sharp frontal gradients. A series of simulations has been performed for the year 1989. The choice is motivated by the availability of the NSP data and a fairly complete set of forcing and open boundary data for that particular year, including freshwater input by the main rivers discharging into the area. Although a study of salinity plumes and fronts is not the prime objective, its impact on temperature via stabilization of the water column and plume-driven transport cannot be neglected. The dense spatial coverage of the data stations not only allows the comparison of vertical temperature profiles, but also provides indirect evidence for the existence of a seasonal circulation pattern as derived from the model.

A number of sensitivity experiments is conducted to analyze the separate roles of vertical mixing, surface forcing, and advection. The importance of an adequate formulation for mixing in the thermocline, already apparent from the numerical study of Holt and James (1999), is investigated by comparing different schemes for background mixing. An important outcome will be that, while advective transport affects the vertical structure of the water column, there exists an important feedback from turbulence onto the surface forcing and even the frontal temperature gradients and baroclinic circulation. The general nature of the analysis allows us to extend the results of the study to tidal shelf seas in general.

2. Model description

a. General

The basic equations for momentum, continuity, temperature and salinity, written in spherical polar coordinates using σ-coordinates in the vertical, are discretized on an Arakawa-C grid with a resolution of 1/15° in latitude, 1/10° in longitude (approximately 7.3 km) and 20 σ levels in the vertical. Density is related to temperature and salinity via the United Nations Educational, Scientific and Cultural Organization equation of state of seawater (Millero et al. 1980).

In analogy with the well-known POM model (Blumberg and Mellor 1987) the equations are integrated in time using the mode-splitting technique with a small time step (30 s) for the 2D barotropic mode and a larger time step (10 min) for the 3D baroclinic mode. A predictor–corrector scheme is implemented to ensure consistency between the 2D and 3D modes. The total variation diminishing (TVD) scheme is applied for the advection of momentum and scalars whereby the advective flux is evaluated as a weighted average between the upwind flux and either the Lax–Wendroff in the horizontal or the central flux in the vertical. Compared to simpler schemes, the method has the advantage, at the expense of an increased CPU time, that it enables the simulation of frontal structures with strong horizontal gradients. Horizontal diffusion is neglected in the present study to avoid the broadening of frontal areas by a poorly parameterized physical diffusion and unphysical diffusion across isopycnals. Further details about the governing equations, numerical methods, and discretization schemes are found in Luyten et al. (1999).

Surface stress and heat flux are calculated as a function of wind and sea-air temperature difference using the bulk formulas of Kondo (1975). The meteorological forcing data have been provided at 3-hourly intervals by the U.K. Meteorological Office, except for cloud coverage, which is obtained from satellite data with a daily value taken to be uniform over the whole domain. Solar irradiance is expressed as the sum of an infrared and a shortwave component. The former contains 54% of the incoming radiation and is absorbed at the sea surface whereas the latter decays exponentially with distance to the surface using an inverse attenuation depth of 0.06 m−1.

A quadratic friction law is applied at the seabed using a roughness length of 3.5 mm. The depth-integrated current at open sea boundaries is determined using the method of characteristics (see, e.g., Røed and Cooper 1987). An equation is solved for the outgoing characteristic while the incoming one is prescribed using an harmonic expansion with nine tidal constituents, including the principal semidiurnal, diurnal, and quarterly diurnal components. More details about the procedures are given in Luyten et al. (1999). Residuals at hourly intervals and the other harmonic parameters are obtained from a baroclinic model for the Continental Shelf (Jones et al. 1998). To prevent spurious vertical velocities at open sea boundaries, the 3D horizontal current is computed assuming a zero normal gradient for the velocity deviation.

Salinity is transported inside the domain during inflow using prescribed climatological values (Jones 1994) in the form of an annually varying sine wave. In the absence of reliable data for the simulated period a zero net transport is considered for temperature. River input is provided from 13 sources (see Fig. 2), using daily river discharge values and assuming a uniform discharge at all depths. Temperature data were available for most sources, except for the Wash, Humber, Seine, and Scheldt Rivers for which a zero transport condition is taken.

b. Turbulence formulation

The vertical eddy coefficients νt for momentum and λt for temperature and salinity are expressed in terms of the turbulence energy K and its dissipation rate ε using
i1520-0485-33-1-37-e1
The stability coefficients Su and Sb are functions of the stability parameter αN = K2N22, where N2 is the (squared) Brunt–Väisälä frequency. Their explicit forms, derived from an algebraic stress model, are given by
i1520-0485-33-1-37-e2
The scheme is similar to the Galperin et al. (1988) version of the Mellor and Yamada (1982) turbulence closure. The main difference is that the critical Richardson number where turbulence ceases now takes a higher value of 0.58, compared to 0.2 in the Mellor–Yamada formulation.
Turbulence energy K is obtained by solving the transport equation
i1520-0485-33-1-37-e3
where advection of turbulence has been neglected. The dissipation rate is computed from
0K3/2l.
The mixing length is prescribed algebraically using a formulation similar to the one proposed by Mellor and Yamada (1982), which takes account of both a surface and a bottom boundary layer
i1520-0485-33-1-37-e5
where
i1520-0485-33-1-37-e6
and h and ζ are the mean water depth and surface elevation, respectively.
The constants ε0 and α1 are set to
0α1

As pointed out by, for example, Kantha and Clayson (1994), the Mellor–Yamada type of closures (including the present scheme) does not take account of mixing in the strongly stratified layers where turbulence is generated by the shear and breaking of unresolved internal waves. In the absence of an adequate scheme for internal wave mixing, a uniform diffusion coefficient is usually proposed. No agreement exists about its value or even about its magnitude. Two alternative approaches will be considered in the present study.

The first formulation is based upon limiting conditions for turbulence variables in the case of stable stratification. Following Galperin et al. (1988) an upper bound is imposed for the mixing length
lK1/2N.
The condition (8) is derived from the result, established from laboratory experiments, that the sizes of the largest overturns are limited by stable stratification. If in addition a lower bound Kmin is set for the turbulence energy, the diffusion coefficients νt and λt take a background value proportional to N−1. Burchard et al. (1998) and Luyten et al. (2002) found good agreement with turbulence dissipation measurements in the Irish and North Seas after tuning of the parameter Kmin. The value adopted here is 10−6 J s−1.
The second one is the semiempirical formulation of Large et al. (1994) where background diffusion coefficients are introduced as a function of the gradient Richardson number
i1520-0485-33-1-37-e9
where
i1520-0485-33-1-37-e10
Following Kantha and Clayson (1994), the background coefficients are only introduced when K drops below a lower limit set by 10−6 J s−1. The scheme was successfully applied by Kantha and Clayson (1994) to a variety of oceanic mixed layer problems.

c. Model area

The computational domain (Fig. 2) consists of the northwest European shelf between 4°W and 57°N covering the Channel and the southern and central parts of the North Sea. The simulated period is from 1 January to 25 December 1989.

The main characteristics of the bathymetry are the shallow area in the southern North Sea with small depth variations between 20 and 40 m and two deeper parts located, respectively, in the northwest and southwest area of the computational domain. The former is characterized by steeper gradients of bathymetry with depths ranging from 40 up to 100 m. A notable feature is the shallow Dogger Bank between 54° and 56°N, which takes the form of a triangle with its base at the deep Outer Silver Pit (54°N, 1°–3°E) and its top at 56°N, 5°E. The shallowest parts with depths of about 10 m are localized along the Belgian and Dutch coasts and in the eastern part of the German Bight (north of Germany and east of Denmark). The deeper Old Elbe Valley is visible in the German Bight by its wedgelike shape.

d. Model experiments

The evolution of the temperature field is governed by four different processes. These are 1) surface forcing, 2) vertical distribution of temperature by turbulent mixing, 3) horizontal and vertical advective transport, and 4) absorption of solar heat in the water column. A number of model experiments, summarized in Table 1, has been conducted to assess the role of these processes, both physically and numerically, on the long-, medium- and short-time range. No experiment has been designed to test the formulation of optical attenuance, which in reality should include contributions from salinity, dissolved yellow substances, and small (nonsinking) suspended particles not taken into account in the present study.

A standard simulation (run A) was performed using the model formulations and setup described above. Thermocline mixing is parameterized using limiting conditions for l and K. This formulation is replaced by the internal wave mixing (IWM) scheme of Kantha and Clayson (1994), as given by Eqs. (9)–(10) in a second run B. Run C is similar to the first one except that the sea-air temperature difference is removed in the evaluation of the surface drag and exchange coefficients used for the surface stress and heat fluxes. Two tests were performed to test the role of advection and its parameterization. In the first one (run D) horizontal and vertical advection is canceled in the equation of temperature. In the second one (run E) currents are advected by a more diffusive first-order upwind scheme while retaining the TVD scheme for temperature and salinity. It is remarked that these model intercomparisons are intended in the first place as an illustration of the physical processes and second to validate the numerical schemes quantitatively.

3. Analysis of model results

The results of the different model experiments are compared with the temperature data of the North Sea Project for the 1989 period. The 122 data stations are plotted in Fig. 1 and cover most of the North Sea between 51° and 55°40′N. Temperature profiles were taken at nearly monthly intervals. The start and end dates of the 10 cruises conducted in 1989 are listed in Table 2. The analysis below is split up onto three main sections each dealing with one of the different timescales (seasonal, spring–neaps, semidiurnal/inertial).

a. Seasonal cycle

A general comparison between the models and with the data has been performed by averaging the measured and model data separately over the mixed stations, where the water column remains thermally mixed throughout the whole year, and the deeper stratified stations, where a thermocline forms during spring. The results of the averaging, presented in Fig. 3, will be used as general guidelines throughout the discussions below.

1) Surface forcing

The standard simulation (run A) uses Kondo's (1975) formulation for the latent and sensible heat fluxes. The transfer coefficients CE for the latent and CH for the sensible heat fluxes are expressed as functions of the wind speed and the sea-air temperature difference ΔT = TsTa. The expressions were derived from Monin–Obukhov (MO) similarity theory. The formulation predicts higher values for CE and CH compared to the neutral case ΔT = 0 if ΔT > 0, while the opposite occurs if ΔT < 0. The effect is illustrated in Figs. 4a–c for the case of the shallow water station AG (water depth H = 16.6 m), where the results of run A are compared with those of run C without the ΔT dependence. From late winter to early summer ΔT is mostly negative, while ΔT becomes positive from day 175 until the end of the year (Fig. 4a). During the first period, heating through the sensible and cooling through the latent heat flux are both reduced in run A compared to run C. The net effect is that the cooling rates, predicted by run A, are slightly larger so that the depth mean temperatures (Tm) are somewhat lower during spring (Figs. 4b,c). A different situation arises in summer when ΔT changes sign and the MO formulation increases the cooling via both the latent and sensible heat fluxes, yielding a difference in Tm between the runs upto 1.2°C in the beginning of September. The evolution reverses in autumn when the lower temperatures in run A decrease the value of ΔT and, thus, also the surface cooling at a higher rate compared to run C. One may therefore conclude that, although the MO formulation may not be too significant at the end of a yearly temperature cycle, its impact on the seasonal temperature evolution can be substantial. The previous analysis is confirmed by the station-averaged mean temperature values plotted in Fig. 3a. Although both model experiments underestimate the observed mean temperatures in winter changing into an overestimate during summer, the MO formulation reduces, at least, the errors in the summer season by 20%–30%. A similar analysis applies for the stratified stations, as given in Fig. 3b, although the effects of the surface forcing are reduced because of the larger water depths.

Since the surface heat flux is calculated using the modeled sea surface temperature, there is an indirect influence of the turbulence scheme on the surface forcing and, hence, on the depth mean temperature. From Figs. 3c–e one infers that run B, using the IWM scheme, reduces the vertical stratification, yielding lower surface and higher bottom temperatures during summer in the stratified areas as a result of a larger mixing in the thermocline. In consequence, the cooling rates are lower in summer, compared to run A, giving higher mean temperatures (Fig. 3b). The effect is reversed in late autumn when the water column becomes vertically mixed so that the higher mean temperatures in run B now provide a higher cooling rate than in run A with a consequent larger decrease in mean temperature. The whole evolution is further illustrated in Figs. 5a,b, where the surface heat fluxes and depth mean temperatures from runs A and B are compared at the deep water station CW (H = 89.2 m), and can also be derived from Fig. 3. The station-averaged values show a better agreement with the observations, both for mean temperature as for vertical stratification, in the standard run with limiting conditions than in the simulation using the IWM scheme. The apparent better agreement for the surface temperature in the latter case can therefore not be considered as a real improvement.

2) Vertical stratification

Thermistor chains were deployed during the 1989 North Sea Project at a limited number of stations. Time-depth contours of the daily averaged observed temperatures at station CS (55°31′N, 0°54.5′E) are plotted in Fig. 6a and can be compared with the simulated evolution according to the standard experiment, shown in Fig. 6b. Both the time of onset of stratification and the initial deepening of the thermocline are well predicted by the model. The periodic uprising of the isothermals within and below the thermocline, seen in both the data and the model results, occurs at semimonthly intervals and can be related to the spring neap cycle. This is further discussed below. A notable difference is the underestimation of stratification in the thermocline. The result is, as one may expect on first sight, not due to an inaccurate parameterization of turbulent mixing within the thermocline, but can be explained by important short-time advective effects. This is illustrated in Fig. 6c showing the vertical temperature profiles on 30 August according to the data and simulations A, B, and D. Although run D without advection predicts too large surface and bottom values, the temperature gradients in the surface and thermocline layers are more in agreement with the data than the ones predicted by the other runs where advection is included. The same conclusion can be made by inspecting the averaged values of stratification, represented by the surface minus bottom difference in Fig. 3e. A further explanation will be provided in section 3c.

3) Fronts and residual circulation

A well-known phenomenon in the North Sea is the presence of tidal mixing fronts from spring to autumn. Thermal stratification arises during summer north of 54°N and in the western section of the Channel (west of 2.5°W), as can be observed from the distribution of thermocline depths (Fig. 7a), obtained using the monthly averaged temperature profiles for August. The mean position of the fronts in the central North Sea first extends along the British coast and detaches from the coast near Flamborough Head at 0.5°W. A first branch surrounds the Dogger Bank while a southern branch extends along 54°N upto 4°E where it curves northeastward along the German Bight. These frontal positions are in good agreement with the climatological data analyzed by Elliot and Clarke (1991) and the numerical simulations of Holt and James (1999). A known criterion for locating tidal mixing fronts is via critical values of the parameter χ = H/u3t where ut represents the depth mean amplitude of the semidiurnal current. Comparing the position of the front in the central part with the bathymetry in Fig. 2, one observes that the front is located at a critical depth close to the 35-m isobath. This is explained by the nearly homogeneous distribution of tidal mixing in the central North Sea (Fig. 7b) so that χ only varies with the water depth. Contrary to the open ocean where the depth of the thermocline is determined by the surface forcing, the deepening of the thermocline in tidal shelf seas is limited from below because of the presence of a tidally mixed bottom layer. A bottom-layer thickness of about 35 m, except for the deepest parts, can be deduced after comparing thermocline and water depths.

Although a detailed study of salinity fronts is beyond the scope of the present study, they are the driving force of density currents along the coast that advect the temperature field. The intensity and direction of the salinity-induced residual circulation depend on the wind forcing (Chao 1987, 1988). During the winter and early spring the prevailing winds are strong and mainly blowing from southwesterly to westerly directions (Fig. 7e). They are thus downwelling favorable for plumes at the continental coast. The result is a narrowing of the coastal plumes, which, in combination with the high river discharges in March and April, yields stronger offshore gradients in surface salinity (Fig. 7c) and an intense northward coastal jet current (Fig. 8a). From the end of April until August the wind speeds are reduced by a factor of 2. Easterly winds are now more prevailing giving upwelling favorable conditions for continental plumes. As a result the plumes expand in offshore direction whereas the alongshore intrusion of freshwater is slowed down (Fig. 7d).

The simultaneous presence of thermal and salinity fronts in shelf seas, such as the North Sea, induces an intrinsic pattern of residual circulation with variations on a seasonal scale. The residual currents are obtained from an harmonic analysis with a least squares fitting on a monthly basis, which filters out the most important harmonics of the barotropic tide. The residual velocity fields at 15-m depth and along a transect at 55°N are plotted in Fig. 8 for March and August, which can be considered as typical for the winter and summer seasons. The circulation in March (Fig. 8a) is characterized by a strong northward coastal current within the shallow southern bight and the German Bight, as resulting from the westerly winds in winter and the plume-driven circulation. The residual pattern above 53°N can be described as a cyclonic rotation with a southeastward flow in the western part, turning eastward in the central and northward in the eastern part (similar to Holt et al. 2001). The onshore winds generate a transverse circulation in the freshwater plume of the German Bight with onshore surface flow, offshore bottom flow, and downwelling within the plume front (Fig. 8b). The alongshore coastal jet is mainly barotropic with a maximum of about 8 cm s−1 (Fig. 8c). West of and above the Dogger Bank the eastward current first accelerates and then decelerates generating associated upwellings and downwellings.

The surface circulation for August (Fig. 8d) shows a dominant feature in the form of an anticyclonic gyre along the thermal front around the center of the Dogger Bank. The sense of the rotation can be deduced from geostrophic equilibrium, which creates a flow with the warmer (mixed) water to the right and colder (stratified) water to the left. A second thermally induced circulation is the southward flow along the coast of Britain branching eastward at 54.0°N just below the Outer Silver Pit (south of the Dogger Bank). Compared to the winter situation the salinity current in the German Bight is reduced in magnitude and deflected northwestward by the offshore winds. The jet stream along the western side of the Dogger Bank (0.75°E) has a maximum of 11 cm s−1 within the thermocline at 20-m depth (Fig. 8f). The result is in good agreement with the value of 13–15 cm s−1 measured in 1988 and reported in Lwiza et al. (1991). An important upwelling is generated on the stratified side of the front, changing toward downwelling at the mixed side (Fig. 8e). In analogy with the well-known estuarine circulation, a flow, transverse to the front, is produced by tidal friction. The effect is to reduce the alongfrontal jet and a motion directed toward the inner mixed side of the front. A southward return flow, concentrated toward the surface, is observed along the eastern side of the Dogger Bank at 3.5°E although with a lesser magnitude, since the transect cuts the front there at an angle of about 45° and the depth gradients are smaller at the eastern compared to the western side of the Dogger Bank. This results in smaller cross-frontal currents and upwellings.

4) Advective transport

The present simulations revealed the existence of seasonally dependent circulation patterns in the North Sea affecting the horizontal and vertical distributions of temperature. The high density of the NSP stations in the southern North Sea, the German Bight, and the frontal areas at the western branch of the Dogger Bank and along the British coast allows us to derive some general patterns of circulation from the temperature data. The relative importance of seasonal advection with respect to the surface forcing can be deduced by subtracting the monthly averaged mean temperatures obtained by run D, without temperature advection, from the corresponding values for the standard run A. The results are illustrated in Figs. 9a,b for March and August. The winter distribution shows the advection of warm water along the path of the coastal jet current. Higher temperatures are observed within the Dogger Bank and an extended area of shallow water in front of the Humber estuary. This is explained by the advection from deeper areas, which generally have higher temperatures in winter than shallower ones. Advective effects are more localized in summer but larger in value, as reflected by the larger contour intervals in Fig. 9b. The main features are induced by the frontal circulation, displayed in Fig. 8d. This explains the higher temperatures observed at the Outer Silver Pit (south of the Dogger Bank), the western boundary of the Dogger Bank, and a band extending northeastward along the northern boundary of the Dogger Bank, while cooler water flows southward along the narrow coastal front at the British coast branching eastward in front of the Humber estuary. Tendencies are, as expected, less obvious in the German Bight in view of the spring-neap modulations of the residual circulation pattern, which is further discussed below.

To validate the preceding analysis the depth mean temperatures, obtained from runs A, D, and E, are compared with the corresponding data values at a number of selected stations (Fig. 10). In making the comparison one should take into account that the modeled temperatures are too low in winter and too high in summer as a consequence of the surface forcing formulation. Evidence for a warm current along the continental coast during winter is found at stations AV, BN, and CH. The data show agreement about warm advection at stations in the Humber area (DQ, DS) and at or near the Dogger Bank (EB, EJ, EK). The general characteristics of the frontal circulation in summer are confirmed by the data. This applies for the advection of cool water at the coastal stations CY, DA, and DH (with a maximum cooling of more than 4°C in August), DQ, and the stations DS, EJ, and EK in the Humber area. Warm advection is evident at the deeper stratified side of the Dogger Bank mixing front (EI), whereas cold advection is seen at EB within the Dogger Bank. The temperature difference arising from advection has its maximum in July and August and diminishes when the thermal fronts decline in September.

In view of the large impact of residual advection on the temperature evolution near thermal fronts, it is of interest to know to what extent the results are sensitive to the numerical discretization of advection. Time series, obtained from run E using the upwind scheme for advection of momentum, are plotted in Fig. 10 for comparison (dash and three-dotted curves). No difference is seen with the standard case at most stations whereas a slight difference, of the order of a few tenths of degrees, can be observed at the stations EI, FJ, and EK within the Dogger Bank area. Although this may imply that the expensive TVD scheme does not provide a real improvement, it will be shown further below that the magnitude of the thermal circulation is sensitive to the form of the advection scheme.

b. Spring–neap cycle

1) Vertical stratification

To examine the influence of the different mixing processes on the vertical temperature distribution, a further comparison is performed with the mooring data at station DM (54°20′N, 24′E). Compared to CS (H = 74 m) this station has a shallower depth of 58 m resulting in a stronger impact of bottom mixing. In the absence of advection, wind stress and surface cooling mix the surface layer and deepen the thermocline. This is counteracted by tidal mixing in the bottom layer, which limits the deepening of the thermocline. The evolution of the temperature distribution therefore depends on a balance between surface and tidal forcing. While the latter is derived from atmospheric conditions, the former strongly modulates with the spring–neap cycle since the thickness of the bottom layer increases during spring and decreases during neap tide.

Daily averaged contours for July and August, obtained from the observations, the standard run, and experiment B, are plotted in Figs. 11a–c. Time series of the harmonically analyzed surface amplitude, the surface stress, and the net downward surface heat flux, which represent the different forcing parameters, are given in Figs. 11d–f. When the results of the standard model (Fig. 11b) are compared with the tidal evolution (Fig. 11d), one observes a periodic downward and upward lifting of the thermocline, closely related to the spring–neap cycle. Bottom mixing is reduced during neaps allowing deepening of the thermocline. The opposite occurs during spring. Sole exception is the second spring tide when the thermocline continues to deepen. This is explained by an event of strong wind and surface cooling around day 210 (Figs. 11e,f), which effectively opposes the upward expansion of the bottom layer at this spring tide. Although high winds also prevail during the third spring, deepening is now prevented by the stronger tidal mixing. The evolution obtained from run B (Fig. 11c) is qualitatively similar for July but becomes dissimilar in August as a result of the wind event on days 210–212 leading to the complete destruction of the thermocline. As expected from the previous discussions, the evolution, obtained from run A, gives the best agreement with the observations (Fig. 11a). The spring-neap cycle in temperature, clearly seen in the data, is well predicted by the model. A different behavior is, however, observed for the data in August. The low winds during days 215–220 cannot prevent the upward lifting of the thermocline despite the occurrence of a neap tide, while wind deepening dominates during the third spring around days 220–225. This appears to indicate that the model underestimates the effects of the third neap and spring tides, as compared to the surface forcing.

2) Fronts and residual circulation

To examine the influence of the spring–neap cycle on the density fronts and circulation, the M2 tide is eliminated from the field variables using a daily harmonic analysis. Results are discussed for day 187 at neaps and day 206 at spring. The two days are characterized by low winds so that there are minimal effects of wind-driven circulation. The density fronts are plotted as the bottom minus surface density difference Δρ, which represents an efficient way to visualize thermal and salinity fronts at the same time. Figure 12a shows the neap distribution of Δρ with the superimposed circulation at 15-m depth for the central North Sea. Besides the already mentioned anticyclonic rotation around the Dogger Bank, the small gyre around the Silver Pit to the South, and the southward current along the British coast, a strong southward flow is observed in the German Bight, which is related to a tonguelike density front in the Old Elbe Valley (see Fig. 2). The origin of the latter feature is the low tidal mixing at neaps so that not only temperature but also salinity becomes vertically stratified in the deeper parts of the area with a strong density front as a result. The situation at spring (Fig. 12b) is not significantly different from the previous one in the area west of 5°E, except for a strengthening of the fronts and circulation along the western and an opposite weakening along the eastern boundary of the Dogger Bank. The reason for the small variability in the southward locations of the fronts is that the higher tidal mixing rate below 54°N (Fig. 7b) prevents the onset of vertical stratification throughout the semimonthly mixing cycle. The main differences, observed in the German Bight, are the disappearance of the previously mentioned density structure and the complete reversal of the flow from southward toward a north–northeastward-directed current. This is explained as follows. The higher mixing rate during the spring tide suppresses the vertical temperature stratification over the entire Old Elbe Valley where water depths are between 30 and 40 m, giving a consequent weakening of the horizontal temperature gradients. Although vertical salinity stratification is reduced as well, the salinity fronts are not destroyed because of the continuous river outflow. The result is a replacement of the southward thermal flow by a northward coastal plume current. In the absence of wind-driven circulation this periodic flow reversal would be repeated for each semimonthly cycle. The long-term evolution including wind effects, seen in Fig. 8d for August, is a flow dominated by salinity plumes.

The behavior of the circulation around the Dogger Bank is further examined with the aid of contour plots of the temperature (Figs. 12c,d) and northward current (Figs. 12e,f) along the 55°N transect. Two effects need to be considered. First, at the approach of the spring tide, the water column becomes vertically mixed at larger water depths. The front consequently recedes downslope. Since mixing takes place across σ lines, aligned with respect to the vertical, the water column acquires after mixing a depth mean temperature that is generally different from a neighboring location with a different depth so that an efficient mechanism is provided, whereby vertical stratification is converted into horizontal one. The process is most effective at places where the slopes are largest, such as the western side of the Dogger Bank, resulting in a strengthening of the front. The second mechanism, of less general nature, is related to the deepening of the thermocline, occurring prior to the spring on day 206, which can be inferred from Fig. 12d and which was previously discussed at station DM (see Fig. 11a). This tends to reduce the temperature differences across the lateral fronts and can explain the weakening of the fronts at the eastern slope of the Dogger Bank. The increase of the frontal gradients at the western slope enhances not only the horizontal but also the vertical shear, through the thermal wind relation, of the frontal current. Neglecting the shallow wind-driven surface shear layer, the result is a 19% increase of the maximum current from 9.6 cm s−1 at neaps (Fig. 12e) to 11.4 cm s−1 at spring (Fig. 12f) and a stronger upwelling at the slope boundary, evidenced by the larger updoming of the isothermals.

The sensitivity of the previous results on the model parameterizations is summarized in Figs. 12g,h. The first one is the same as Fig. 12c now obtained from run B using the IWM scheme. The lower degree of vertical stratification and of surface temperatures at the stratified side of the front reduces the frontal gradients and circulation. This is most readily observed by the much smaller updoming of the isopycnals. Figure 12h, to be compared with Fig. 12f, is derived from run E with the TVD scheme for momentum advection replaced by the more diffusive first-order upwind scheme. The consequence is a significant reduction of the shear and magnitude of the horizontal current. The maximum value deduced from the figure is 7.4 cm s−1 or 35% less compared to run A.

The global performances of the different runs are compared in Fig. 13, representing the fraction of the total area, which is thermally stratified, as a function of time. The sharp increase during spring reflects the rapid initial deepening of the thermocline. The semimonthly variations are clearly related to modulations of tidal mixing during the spring-neap cycle. All models behave similarly in spring and summer, except for the lower values in run B as a result of the higher mixing rates in the thermocline. Manifest differences are seen in autumn when the final breakdown of stratification occurs 25 days earlier in run B and 20 days later in run D (without advection of temperature) compared to the standard simulation. The latter result demonstrates the active role of advection in the erosion of the thermal fronts. Tidal advection broadens the horizontal frontal gradients. This is further enhanced by numerical diffusion due to various interpolations on the C grid and the coarse horizontal resolution of the model near-frontal boundaries. Lower cross-frontal density gradients imply a smaller magnitude for the alongfrontal circulation (as discussed above) and a reduced vertical stratification by the thermal wind relation. In this way the thermocline erodes more rapidly in the runs with advection. A further comparison can be made from Fig. 3f showing the percentage of stratified stations as obtained from all model runs and the data. The broadening of the fronts explains the larger number of stratified stations for the runs with advection, except for run B where the higher mixing rate in the thermocline increases the relative fraction of mixed stations. Not surprisingly, the highest fraction of stratified stations is obtained from run E using the diffusive upwind scheme for momentum advection. The best overall agreement during spring and summer is found for run A. In the absence of data after September, no validation can be made for the period, covering the breakdown of stratification, which appeared to be highly sensitive to the model formulation.

c. Semidiurnal and inertial range

Previous observational studies in the North Sea (van Haren et al. 1999; van Haren 2000) revealed an important variability in the temperature field, on timescales up to a few days, primarily due to advection by wind and tidally driven currents. The data analysis, presented by Van Haren et al. (1999), showed that the basic harmonics in the frequency spectrum are the semidiurnal (ω) and inertial (f) modes. Nonlinear interaction between these basic harmonics generates in turn an additional series of peak harmonics (2ωf, 2f, ω + f, M4, …) down to the internal wave spectrum. The existence of such oscillations can be inferred from the (nonaveraged) time series of the vertical temperature distribution (Fig. 14a) and can be clearly observed by the regular upward and downward displacements of the thermocline. The data are displayed between days 208 and 214 covering a spring–neap cycle (see Fig. 14d) and the strong wind event occurring on day 212 (see Fig. 11e). A rigorous inspection of the plotted data shows that the oscillations are mainly semidiurnal during the period of the spring tide when moderate winds apply (days 208, 209). The inertial mode becomes dominant during the wind event. A nonlinear 2f harmonic can be observed during the period of maximum wind stress on day 211. The semidiurnal oscillations reappear after day 212 as a result of a rapid decrease in wind speed.

A similar evolution is obtained from the results with the standard model (Fig. 14b), although semidiurnal harmonics appear to be more dominant throughout the whole period, except on day 211. The lower amplitudes of the vertical temperature fluctuations result from the previously discussed lower temperature gradients in the thermocline.

A notable difference between the model and the observations is that the temperature maxima and minima occur at the same time in the data whereas the modeled temperatures in the lower layer are shifted by about 90°. It is remarked that a phase difference was found in the measurements, reported in Van Haren et al. (1999). No obvious explanation for the data behavior can be provided in the absence of current observations at station DM. The model results can be explained by comparing the temperature distribution with the time series of the horizontal (Fig. 14c) and vertical (Fig. 14d) currents. Since station DM is located south of the Dogger Bank where the horizontal temperature gradient has a main southward component (see Figs. 12a,b), only the northward velocity is considered. Temperature variations in the bottom mixed layer are caused by horizontal advection so that the time of maximum (minimum) temperature coincides with a reversal of the current from northward (southward) to southward (northward). In the thermocline, vertical advection becomes more dominant giving a time of maximum (minimum) temperature when the vertical current reverses from downwelling (upwelling) to upwelling (downwelling). The phase difference between thermocline and lower-layer temperature fluctuations can then be explained by a similar shift seen in the vertical and horizontal components of the current.

The model results show a similar, although smaller, phase shift in the surface layer. The presence of this time delay, not observed in the data plot, induces vertical stratification in the lower part of the surface mixed layer and explains the advective effect at station CS, previously observed in Fig. 6c.

To examine the longer-term evolution of the temperature variability, an harmonic analysis is applied with a least squares procedure. The semidiurnal amplitudes are obtained at daily intervals using hourly averaged temperature profiles. Time series at 13- and 41-m depth are presented in Figs. 14e,f for July and August. The data values in the thermocline layer show a high dominance of the inertial mode. This is observed in Fig. 14e (where data points are plotted at daily intervals) by the repeated beatings occurring at the ωf frequency with a corresponding period of 3.3 days. In the case of run B the oscillations are practically semidiurnal with a superimposed spring–neap modulation. The results for run A represent an intermediate case giving qualitatively a good agreement with the data during most of August and with run B between days 193 and 205. Amplitudes are reasonably predicted except for the period between days 208 and 212, which is shown in the time series plots (Figs. 14a,b). The semidiurnal frequency dominates in the bottom layer (Fig. 14f), yielding a reasonable agreement between models and data. A clear spring–neap signal is now observed in all cases, although some inertial effects are still visible in the data.

The underestimation of the inertial mode with respect to the semidiurnal one can be explained in two ways. First, vertical stratification is underestimated and mixing overestimated in the thermocline. The result is a larger diffusive coupling between the bottom and surface layers and a resulting conversion of inertial into tidal shear. This can explain, in particular, the behavior seen in run B. Second, surface winds are provided at 3-hourly intervals, which does not allow the generation of inertial waves caused by rapid changes in wind speed and direction.

4. Concluding remarks

The seasonal, spring–neap, and short-time variability of the horizontal and vertical temperature distributions and of the residual current pattern in the North Sea have been investigated with a three-dimensional baroclinic model. The simulations are performed using realistic surface and open boundary data and compared with the 1989 data of the North Sea Project. A series of sensitivity experiments were designed to test the physical role of the heat flux formulations, turbulence scheme, and advective transport. Although applied to a particular area and for a specific year, important aspects of its outcome can be generalized to other shelf seas as well.

The parameterization of the surface heat fluxes via the Monin–Obukhov similarity theory provides a relaxation mechanism for the mean temperature in summer. While improving the results with respect to the data, a significant error still remains. A similar overestimation was obtained by Holt and James (1999) with a different numerical model, but using the same meteorological forcing data. Although some doubts can be cast about the crude climatological data for the cloud coverage, the sensitivity study of the mixing length parameterization in the MO theory, recently conducted by Weidinger et al. (2000), showed important differences in the sensible and latent heat fluxes. An alternative solution, further discussed below, is through the feedback mechanism of turbulent mixing on the surface forcing.

It is shown that advective transport by the density currents has a significant impact on the seasonal temperature distributions. The tendencies, obtained from the model results, are in qualitative agreement with the evolution seen in the observations. Although the form of the numerical scheme for momentum advection is not essential for predicting the global distributions of temperature, a realistic simulation of the frontal circulation requires the implementation of a low-diffusive scheme, such as the TVD scheme.

The study demonstrated that the spring–neap tidal mixing cycle affects the vertical temperature distribution and thermal circulation. In the absence of strong wind forcing, the surface mixed layers are shallower and the magnitude and shear of the baroclinic circulation are intensified at spring while the opposite occurs at neaps. The effect is enhanced (reduced) when strong (weak) winds apply at neaps or when weak (strong) winds prevail during spring tide. The opposing tendencies of the thermally and salinity-induced currents, varying on a semimonthly scale, may be considered as typical for a shelf sea with a freshwater plume near the coast and an offshore thermal front.

An important outcome of the present study is the feedback of the vertical diffusion scheme on the baroclinic circulation and on the surface forcing. First, the magnitude of the density flow is reduced in reaction to a higher mixing rate that weakens the horizontal density gradients at tidal mixing fronts as a result of the larger cross-frontal mixing at the frontal slopes. Second, increasing the vertical mixing in stratified areas reduces the surface temperature in summer but increases the depth mean temperature via the surface heat flux. A restoring mechanism operates in autumn when higher cooling rates tend to lower the mean temperature again. The result is of interest since, even with the standard model, the predicted stratification and surface temperatures are underpredicted, which may partially account for the overestimation of the mean temperature at the stratified stations.

Contrary to previous ocean studies (e.g., Kantha and Clayson 1994; Large et al. 1994), which required a tuned background mixing scheme to simulate the deepening of the thermocline, a better agreement is obtained from a formulation using limiting conditions for turbulence variables. Although less diffusive, the latter scheme still underestimates the stratification and thus overestimates the mixing in the thermocline (cf. Figs. 6a,b or Figs. 14a,b). The overestimation of thermocline mixing with the IWM scheme supports the idea, already suggested by Van Haren et al. (1999), that, in shelf seas as the North Sea, most of the short-time variability in the temperature field can be attributed to the semidiurnal and inertial modes and their first higher-order harmonics. A subgrid-scale turbulence model for the high-frequency spectrum can then be considered of less importance, provided that these basic modes are well resolved by the model. As discussed in the paper, the inertial mode is still underestimated. Improvement for the semidiurnal component can be made with a fine-grid model, resolving both the horizontal and vertical tidal excursion amplitudes of the order of respectively 5 km and a few meters.

Acknowledgments

This work was supported by the European Union's MAST program under Contract MAS3-CT97-0088 (COHERENS). We would like to thank Paul Tett and Karen Wild-Allen from Napier University, Edinburgh, for helpful discussions. The Met Office is acknowledged for providing the surface forcing data.

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Fig. 1.
Fig. 1.

Locations of the NSP data stations

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 2.
Fig. 2.

Bathymetry (m) of the simulated area and location of the 13 discharge sources. The Dogger Bank is the shallow triangular area in the central North Sea between 54° and 56°N. The deeper Outer Silver Pit (54°N, between 1° and 3°E) is visible to the south of the Dogger Bank. The area north of Germany and east of Denmark is the German Bight where the Old Elbe Valley can be observed by its wedgelike shape

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 3.
Fig. 3.

Time series for the 10 NSP cruises in 1989 of global parameters averaged over all (a) mixed and (b)–(f) stratified data stations: (a),(b) depth mean temperature, (c) surface temperature, (d) bottom temperature, (e) surface minus bottom temperature difference, and (f) percentage of stratified stations. Values are shown according to the data (solid circles), run A (solid–plus signs), run B (dots–asterisks), run C (dashes–diamonds), run D (dash–dots–triangles), and run E (dash–three dots–squares).

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 4.
Fig. 4.

Heat flux experiment at station AG: (a) sea surface minus air temperature calculated from run A (solid line) and run C (dashed line); (b) downward surface heat flux from run A minus its value from run C; (c) depth mean temperature difference between runs A and C. All values are averaged over 3 days

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 5.
Fig. 5.

Heat flux experiment at station CW: (a) downward surface heat flux from run A minus its value from run B and (b) depth mean temperature difference between runs A and B. All values are averaged over 3 days

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 6.
Fig. 6.

Seasonal temperature evolution (°C) at station CS: (a) observations and (b) run A; Thick line denotes 12°C contour; (c) temperature profile on 30 Aug as given by the observations (plus signs), run A (solid curve), run B (dotted curve), and run D (dash–dotted curve). White areas in (a) indicate missing data

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 7.
Fig. 7.

(a) Monthly averaged thermocline depth (m) for Aug, defined as the distance to the surface of the point where the temperature exceeds the bottom value by 0.5°C; (b) residual bottom stress (N m−2) for Aug; surface salinity distribution (psu) on (c) 7 Apr and (d) 5 Aug; and (e) daily averaged wind vectors at station BB.>

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 8.
Fig. 8.

Residual circulation fields for (a)–(c) Mar and (d)–(f) Aug: (a),(d) horizontal current at 15-m depth; (b),(e) circulation along a transect at 55°N; and (c),(f) northward current (m s−1) at the same transect; (c),(f) thick line represents zero current.>

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 9.
Fig. 9.

Monthly averaged values of the depth mean temperature (°C) obtained from the standard run A minus the corresponding value calculated from run D without temperature advection: (a) Mar and (b) Aug. Contour interval is (a) 0.25°C and (b) 0.5°C. White areas indicate negative temperature differences (advective cooling); gray and black areas represent positive values (advective warming). The plots show the effect of advective transport on the temperature distribution during typical winter and summer months

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 10.
Fig. 10.

Time series of depth mean temperatures at a number of selected stations as obtained from the observations (solid circles), run A (solid curves), run D (dash–dotted curves), and run E (dash and three-dotted curves).

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 10.
Fig. 10.

(Continued)

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 11.
Fig. 11.

Daily averaged temperature evolution (°C) at station DM for Jul and Aug according to (a) the observations, (b) run A, and (c) run B. Thick line represents 14.5°C contour. Time series of (d) the harmonically analyzed surface amplitude, (e) surface stress, and (f) the daily averaged downward surface heat flux

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 12.
Fig. 12.

(a) Bottom minus surface density difference (kg m−3) and circulation at 15-m depth on 7 Jul at neaps from run A; (b) as in (a) but for 26 Jul during spring tide; (c) neaps distribution of temperature (°C) along the 55°N transect on 7 Jul from run A; (d) as in (c) but for 26 Jul at spring; (e) as in (c) but for the northward current (m s−1); (f) as in (d) but for the northward current; (g) same as (c) but calculated from run B; (h) same as (f) but obtained from run E. Thick lines delineate the 14°C and zero current contours. The plots are obtained after removal of the M2 tide

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 12.
Fig. 12.

(Continued)

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 13.
Fig. 13.

Fraction of the total computational area where the surface minus bottom temperature difference exceeds 1°C as obtained from all model experiments: run A (solid line), run B (dotted line), run C (dashed line), run D (dash–dotted line), and run E (dash and three-dotted line)

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Fig. 14.
Fig. 14.

Time series (nonaveraged) at station DM from 28 Jul to 3 Aug: (a) observed temperature (°C), (b) modeled temperature, (c) northward current (m s−1), and (d) vertical velocity (10−4 m s−1) from run A. Thick lines represent the 15°C and zero current contours, dashed lines the 12°C contour. Depths below 30 m are omitted for clarity. (a) White areas represent missing data. Harmonically analyzed temperature amplitude at (e) 13-m and (f) 41-m depth for Jul and Aug: data (solid circles), run A (solid curve), and run B (dotted curve)

Citation: Journal of Physical Oceanography 33, 1; 10.1175/1520-0485(2003)033<0037:ANSOTL>2.0.CO;2

Table 1.

Setup of the model experiments

Table 1.
Table 2.

Start and end dates of the 1989 NSP cruises

Table 2.
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