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    Finite-difference grid and model bathymetry (m, dotted lines). Solid, bold lines represent open boundaries where M2 and S2 input were specified. Also shown are the locations of weather stations where meteorological forcing was obtained and current-meter rigs (numbered 1–4) where tidal validation was performed

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    Results from a diagnostic model run for an idealized shelf sea front, showing (a) density field (σt), which is uniform in the alongfront direction; (b) alongfront current (cm s−1) where isopleths denote flow into the page; and (c) cross-frontal circulation (bold arrows indicate u > 5 cm s−1). Note the different vertical and horizontal scales in (c)

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    (a) Model surface temperature (24-h mean) from 16 Aug. (b) Sea surface temperature (SST) from Advanced Very High Resolution Radiometer (AVHRR) satellite image at 1337 UTC 8 Aug 1995, with temperature scale along the left side of the image. The AVHRR image has been cropped to occupy the same geographical region as the model

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    Modeled temperatures from the stratification period during 1995: (a) 1 Jun, (b) 21 Jun, (c) 20 Jul, (d) 25 Jul, (e) 16 Aug, and (f) 30 Aug. Comparison can be made with the observations of Horsburgh et al. (2000), Fig. 8. From left to right the panels show (i) surface temperature, (ii) bottom temperature, and (iii) vertical temperature difference

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    (Continued)

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    Surface (solid line) and nearbed (dashed line) temperatures (°C, 24-h means) at the center of the stratified region (53.8°N, 5.5°W). Also shown are observed surface (solid squares) and nearbed (solid triangles) temperatures

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    Vertically well-mixed temperature conditions from the model at 31 Oct 1995. Note that the central region is now warmer and the existence of an east–west horizontal temperature gradient near the Irish coast

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    (a) Surface and (b) nearbed comparisons of observed with modeled temperatures at each station visited for cruises in 1995. The correlation coefficients, R2, and least squares fits are shown

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    Spatial pattern of top-to-bottom temperature differences at 16 Aug 1995 from (a) observations, (b) run SM1, (c) run SM2, and (d) the central difference run. Contours are in 0.5°C intervals

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    Residual circulation (over two M2 cycles) where depth-mean flows greater than 2 cm s−1 are shown and the tidal residual has been subtracted: (a) SM1, 25 Jul; (b) SM1, 16 Aug, (c) no heating, 25 Jul; and (d) no heating, 16 Aug. Note the distinct cyclonic gyre in (b) and its absence when heating was removed (d)

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    Density-driven circulation (greater than 2 cm s−1) obtained from a harmonic analysis of 14–16 Aug and subsequent subtraction of residual currents from a constant density run: (a) modeled currents averaged over σ levels 4–11, for consistency with the depth at which the drogues of drifters were placed, and (b) the low-pass filtered tracks of six Argos drifters deployed during Jul and Aug 1995

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    (a) Residual velocity vectors derived from the filtered tracks of 16 Argos drifters deployed in Jul/Aug 1995 and (b) residual currents at the same locations (four-cell averages) from levels 4–11 at 16 Aug. Apart from averaging over one tidal cycle, no other manipulation was performed on the modeled currents in (b)

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    Transverse sections (xz) of modeled temperature along model row corresponding to latitude 53°40′N on (b) 25 Jul, (d) 16 Aug, and (f) 21 Sep. Corresponding observations from CTD stations along this line are shown on the left in (a), (c), and (e).

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    (a) North–south component of residual velocity normal to the section shown in Fig. 12 on 16 Aug. Solid and dashed isotachs (cm s−1) indicate flow into and out of the page, respectively. The fainter dotted lines show the contours of temperature in 0.5°C intervals as previously, but for clarity the labels have been omitted. (b) East–west component of residual velocity normal to a meridional section through the model along longitude 5.4°W

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    North–south component of residual velocity normal to the section showing the response of the cold dome to a strong (17 m s−1) wind from (a) the north and (b) the south (isotachs: cm s−1, with solid lines depicting flow into the page and dashed lines indicating flow out of the page). The resulting temperature field (at 0.5°C contour intervals) after 36 h of wind is shown by the fainter dotted lines. The initial condition was the temperature field shown in Fig. 13a

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    Transverse sections (xz) of modeled temperature along model row corresponding to latitude 53°40′N at 2-day intervals beginning 1 Aug, showing modulation of the thermal structure by the tide. Meteorological forcing was turned off during this period

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    (a) Surface elevation at cell corresponding to the center of the stratified region (53.8°N, 5.5°W) over a 22-day period commencing 0000 UTC 1 Aug. (b) The 24-h mean kinetic energy of flow between σ levels 4–11, summed over the subdomain of the gyre (I = 10–35, J = 38–72). Solid line shows results from the baroclinic run used to produce Fig. 15, whereas the dashed line is from a run with tidal forcing only

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A Three-Dimensional Model of Density-Driven Circulation in the Irish Sea

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  • 1 School of Ocean Sciences, Marine Science Laboratories, Univesity of Wales Bangor, Menai Bridge, Ynys Môn, United Kingdom
  • | 2 Proudman Oceanographic Laboratory, Bidston Observatory, Birkenhead, Merseyside, United Kingdom
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Abstract

A semi-implicit version of the Princeton Ocean Model, ECOMsi, was used to simulate the cyclonic gyre that is found in the western Irish Sea during the spring and the summer. Mesoscale, seasonal, density-driven circulations such as this are an important component of the long-term flow in shelf seas, and they pose a challenge to coastal ocean models. Extensive comparisons are made here with observational data to assess model performance. The model successfully reproduced the development of the temperature field, and the associated density-driven currents, throughout seasonal simulations. The results demonstrate conclusively that the gyre is density-driven and reinforce the dynamical importance of strong nearbed horizontal density gradients. Maximum baroclinic currents of 0.14 m s−1 were obtained, and results showed that the regional kinetic energy due to the residual flow was 20%–25% of that due to tidal flow during periods in which density gradients were strongest. The model revealed important interactions between both wind and tide and the density structure; these interactions can direct and modulate density-driven flow.

Corresponding author address: Dr. Kevin J. Horsburgh, School of Ocean Sciences, Marine Science Laboratories, University of Wales Bangor, Menai Bridge, Ynys Môn LL59EY, United Kingdom. Email: oss110@bangor.ac.uk

Abstract

A semi-implicit version of the Princeton Ocean Model, ECOMsi, was used to simulate the cyclonic gyre that is found in the western Irish Sea during the spring and the summer. Mesoscale, seasonal, density-driven circulations such as this are an important component of the long-term flow in shelf seas, and they pose a challenge to coastal ocean models. Extensive comparisons are made here with observational data to assess model performance. The model successfully reproduced the development of the temperature field, and the associated density-driven currents, throughout seasonal simulations. The results demonstrate conclusively that the gyre is density-driven and reinforce the dynamical importance of strong nearbed horizontal density gradients. Maximum baroclinic currents of 0.14 m s−1 were obtained, and results showed that the regional kinetic energy due to the residual flow was 20%–25% of that due to tidal flow during periods in which density gradients were strongest. The model revealed important interactions between both wind and tide and the density structure; these interactions can direct and modulate density-driven flow.

Corresponding author address: Dr. Kevin J. Horsburgh, School of Ocean Sciences, Marine Science Laboratories, University of Wales Bangor, Menai Bridge, Ynys Môn LL59EY, United Kingdom. Email: oss110@bangor.ac.uk

1. Introduction

One of the most difficult challenges faced by coastal ocean numerical models is the accurate simulation of long-term regional circulation in order for model results to be used with confidence in water quality and marine ecosystem management. Long-term (subtidal) flow in shelf seas comprises wind-driven, tidally rectified and density-driven components. Historically, numerical models of the European shelf have assumed homogeneous (constant density) conditions because strong tides and winds ensure that large portions of the shelf are vertically well mixed. These models have demonstrated their ability to reproduce both wind-driven circulations (e.g., Davies and Jones 1992) and tidally rectified flows (Proctor 1981; Pingree and Maddock 1985). However, a series of recent observations have consistently shown the occurrence of significant, mesoscale, density-driven circulations in British shelf seas (Hill et al. 1997; Horsburgh et al. 1998; Brown et al. 1999; Horsburgh et al. 2000). The present generation of density-advecting models must simulate these baroclinic flows correctly if they are to supply a credible hydrodynamical framework for coupled physical–chemical–biological models (e.g., Skogen et al. 1995; Moll 1998). There is, therefore, a strong motivation to critically evaluate the present generation of coastal models against well-documented baroclinic features. A particularly useful test case is the seasonal, cyclonic gyre in the western Irish Sea (Hill et al. 1994; Horsburgh et al. 2000).

The Irish Sea (see Fig. 1) separates Ireland from mainland Britain, and is approximately 300 km long by 200 km wide. The topography is that of a channel with shelves on both sides; depths along the channel are 100–150 m in the south, reaching a maximum of 250 m in the north. Outside of the channel, most of the Irish Sea is between 50 and 100 m deep. The western Irish Sea gyre is present in spring and summer each year when stratification isolates a dome of cold, dense water beneath a strong thermocline. This localized stratification is possible because unlike most of the Irish Sea, where tidal currents are of the order 1 m s−1, currents to the west of the Isle of Man are less than 0.3 m s−1. Furthermore, this region coincides with the deep water channel (see Fig. 1). The transition from stratified to vertically well-mixed water takes place over a distance of approximately 10 km at tidal mixing fronts, which are located at critical contours of the hu−3 parameter (Simpson and Hunter 1974). Near the bed within this transition zone are strong horizontal density gradients, which can drive a geostrophic cyclonic circulation. Statistical analysis of drifter velocities (Horsburgh et al. 2000) and detided acoustic Doppler current profiler (ADCP) data (Fernand 1999) confirm that the baroclinic pressure gradient is the most likely forcing mechanism for the flow, and that speeds around the gyre are in good agreement with geostrophic calculations based on the thermal wind equation. Drifter speeds calculated by Horsburgh et al. (2000) suggest a mean speed for the gyre of 8 cm s−1 with a maximum of 20 cm s−1 in an intense, narrow jet at the depth of the thermocline. Dense water domes associated with cyclonic circulations can also be found in the Adriatic Sea (Henderschott and Rizzoli 1976; Rizzoli and Bergamasco 1983) and in the Yellow Sea (Hu et al. 1991). A well-documented and related feature is the anticyclonic circulation, due to tidal rectification, that occurs over Georges Bank; this circulation doubles in the summer months because of anticyclonic density-driven flow (Loder and Wright 1985). Baroclinic flows such as these have environmental implications, and the gyre in the western Irish Sea acts to retain the larvae of the commercially important Norway lobster, Nephrops norvegicus (Hill et al. 1996) and of pelagic juvenile fish (Dickey-Collas et al. 1997). A reliable circulation model of the region is, therefore, of obvious value to biologists and fisheries managers. The seasonal nature of most baroclinic flows, and their dependence on horizontal variations in density, also implies sensitivity to annual changes in climatic forcing. Models can provide a better understanding of these phenomena as possible indicators of the response of shelf seas to decadal climate change.

Over the past two decades constant density numerical models have improved our understanding of the physical oceanography of the Irish Sea, and in particular its response to storm surges (Davies and Jones 1992; Davies and Lawrence 1994). However, fine horizontal resolution (3–5 km) models of the Irish Sea (e.g., Proctor 1981; Davies and Aldridge 1993) do not predict the currents that make up the gyre. By conducting model runs with, and without, heating this paper provides final evidence that the gyre is density-driven. Density-advecting models have only recently been applied to European shelf seas. Proctor and James (1996) simulated the seasonal cycle of stratification in the southern North Sea with a fine-resolution (∼2.4 km), three-dimensional model and Schrum (1997) has modeled the density-driven flow due to prescribed initial salinity gradients in the German Bight using the model of Backhaus (1985). Skogen et al. (1995) coupled a version of the Princeton Ocean Model to the chemical–biological model described by Aksnes et al. (1995) in order to investigate the annual cycle of primary productivity in the North Sea. Xing and Davies (2001) used a sigma coordinate model to show qualitative agreement with observations of thermal stratification, frontal structure, and the cyclonic circulation in the western Irish Sea (obtaining maximum circulation speeds of 10 cm s−1). The same model confirmed the persistent nature of the gyre and suggested considerable interannual variability.

This paper presents a full seasonal simulation of the western Irish Sea gyre using a three-dimensional, density-advecting model and provides a detailed comparison of the model results with extensive observations made during 1995. The observational program, which combined the deployment of 55 satellite-tracked Argos drifters with repeated hydrographic measurements at 60 stations, is described fully in Horsburgh et al. (2000). Model results here are tested rigorously against both the observed three-dimensional temperature fields and the drifter-derived residual velocity measurements. The model was initialized with observational data and then forced with real winds and solar insolation from meteorological stations surrounding the region of interest. The model was used to reproduce the density structure and flow field over a spring-to-autumn simulation, and to investigate the effect of key parameterizations on the results. A further aim was that the model should provide new insights into the interaction between the density field and the wind and tide, as well as elucidating hitherto unobserved features of the gyre including the autumnal breakdown of stratification.

2. Model description

The model used in this study was ECOMsi (Blumberg 1994), a semi-implicit version of the Princeton Ocean Model (Blumberg and Mellor 1987). It is a three-dimensional, sigma (σ) coordinate, coastal ocean circulation model. Whereas the original Blumberg and Mellor (1987) model uses time splitting (with different time steps for the free surface and internal modes), ECOMsi treats the free surface pressure gradient in the momentum equations and the velocity divergence in the continuity equation implicitly. Elevations at the forward time level are obtained by solving a linear, five diagonal system using a preconditioned conjugate gradient method (Casulli and Cheng 1992). Baroclinic velocities are then solved explicitly since they are subject to a less restrictive Courant–Friedrichs–Lewy (CFL) condition. Previous applications have demonstrated the model's ability to reproduce mesoscale gyres and long-term circulations; Chen and Beardsley (1995) used ECOMsi to investigate stratified tidal rectification over symmetrical banks, and the model was used by Wang et al. (1994) to simulate the climatological, summer circulation in Hudson Bay. A complete description of the model, including transformations to the governing equations and finite difference formulations, can be found in Blumberg and Mellor (1987) and Blumberg (1994), and therefore only a brief outline is given here. In Cartesian coordinates, with x increasing eastward, y increasing northward, and z increasing vertically upward, the primitive equations (with the Boussinesq and hydrostatic approximations) are
i1520-0485-33-2-343-e1
where (u, υ, w) are the (x, y, z) components of velocity vector v; g is acceleration due to gravity; f is the Coriolis parameter; p is the pressure; ρ0 is a reference density; KM is the vertical eddy viscosity; and Fx and Fy are horizontal diffusive mixing terms in the respective coordinate directions. Density is calculated through an equation of state, ρ = ρ(T, S). Horizontal derivatives of pressure which appear in the momentum equations (1) and (2) contain only horizontal gradients of surface elevation, η, and of the density departure, ρ′, from the reference state ρ0. Here, the time-varying spatial mean density is subtracted prior to the calculation of pressure and diffusion terms in order to reduce sigma error (Haney 1991). The summer time evolution of the density field in the western Irish Sea has been shown to be dominated by temperature (Horsburgh et al. 2000), so in this application salinity was held constant at a typical value of 34.0 psu. The model contains a prognostic equation for temperature,
i1520-0485-33-2-343-e5
where KM is a coefficient of eddy diffusivity and FT represents horizontal diffusion of temperature, as well as containing equations for turbulent kinetic energy and the master turbulent length scale. Vertical turbulent exchange coefficients are calculated using the level-2.5 turbulence closure model of Mellor and Yamada (1982):
i1520-0485-33-2-343-e6
where q2 is (twice the) turbulent kinetic energy, L is the turbulence macroscale, and SM and SH are the modified algebraic stability functions due to Galperin et al. (1988). The boundary layer approximations for the q2 and q2L equations are well-described components of the Mellor–Yamada turbulence closure scheme and are not repeated here. The interested reader is referred to Mellor and Yamada (1982), Blumberg and Mellor (1987), Galperin et al. (1988), and Deleersnijder and Luyten (1994) for details. The model also contains a background level of vertical mixing to parameterize unresolved shears, such as those due to breaking internal waves. In these numerical experiments the background diffusivity was set to 10−5 m2 s−1.
A Laplacian formulation for horizontal mixing was used with horizontal eddy viscosity, AM, being calculated through the grid-dependent formulation of Smagorinsky (1963):
i1520-0485-33-2-343-e9
where Δx and Δy are the local grid dimensions and α is a free parameter. Horizontal eddy diffusivity, AH, was specified via an eddy Prandtl number (AM/AH). To avoid unphysical temperature gradients developing in shallow parts of the model domain, and to ensure stability, the coefficient α in (9) was set equal to 0.1. The governing equations are transformed onto σ coordinates using σ = (zη)/(h + η) where h(x, y) is the depth, introducing a new velocity (ω) normal to σ surfaces. Once transformed, the flux-integrated momentum equations explicitly conserve volume in finite-difference form. The equations were solved on an Arakawa C grid using a time step of 372 s, subject to the following boundary conditions.
At the surface,
i1520-0485-33-2-343-eq1
where τsx and τsy are the surface wind stresses in the x and y directions respectively, calculated according to Large and Pond (1981); Q is the net surface heat flux (Reed 1976; Large and Pond 1982); u∗ is the friction velocity associated with the wind stress; and B1 is an empirical constant with the value 16.6 (Mellor and Yamada 1982). Boundary conditions at the bed are
i1520-0485-33-2-343-eq2
and heat flux at the bed is zero. Here, u∗ is the friction velocity associated with the bed stress; bed stresses, τbx and τby, are determined by matching a quadratic stress law at the nearest grid point to the bottom (zb) with the logarithmic wall profile:
i1520-0485-33-2-343-eq3
where κ is von Kármán's constant (0.40). The roughness length, z0, was set at 5 mm consistent with previous turbulence energy models of the Irish Sea (Xing and Davies 1996). In frontal simulations the choice of numerical advection scheme is crucial to the maintenance of sharp gradients in temperature (or salinity for river plume studies). It is well known that upwind schemes cause excessive numerical diffusion while, second-order methods are not positive definite (see James 1996). This model uses a recursive application of an upwind scheme (Smolarkiewicz 1984) that is positive definite and second-order accurate; numerical diffusion is corrected using an antidiffusion velocity based on the first-order truncation error.

The model grid and bathymetry are shown in Fig. 1. Cells were 120° of longitude (Δx = 3.3 km) by 130° of latitude (Δy = 3.7 km). The grid and bathymetry were identical to that used in the region by Xing and Davies (1996). Twenty-one irregularly spaced σ levels were used in the vertical to provide enhanced resolution in the high-shear surface and nearbed layers. The vertical levels were arranged as σ = (0, −0.02, −0.04, −0.07, −0.10, −0.15, −0.20, −0.30, −0.40, −0.50, −0.60, −0.70, −0.80, −0.85, −0.90, −0.93, −0.96, −0.98, −0.99, −0.995, −1.0). The model was forced along the open boundaries (shown by solid, bold lines in Fig. 1) with M2 and S2 tidal input, derived from a larger-scale shelf model (Flather 1976). Only the two most significant tidal constituents were used because the dynamically important horizontal density gradients are caused by spatial changes in available tidal mixing energy and the M2 and S2 constituents account for over 80% of tidal energy in the Irish Sea. In their model of the region, Xing and Davies (2001) found that the main features of the density distribution could be obtained with just M2, and that the use of six additional tidal constituents caused a change in frontal position of only a few kilometers. A radiation condition based on linearized, longwave propagation with an additional term allowing disturbances to relax over a prescribed timescale was applied at the open boundaries. The optimum relaxation timescale of 4 h, as found by Blumberg and Kantha (1985), was used in these simulations.

3. Validation

Extensive validation of model performance was carried out (Horsburgh 1999), a brief summary of which is presented here. In tidal validations this model was shown to be as accurate as previous models of the region using similar grids (Davies and Aldridge 1993) and turbulence closure schemes (Xing and Davies 1996). In these simulations temperature was held constant at 10°C, and the model was spun up for six days prior to a 30-day harmonic analysis. Computed M2 and S2 tides were in good agreement with observations (Robinson 1979) and with previous models of the area (Davies and Jones 1992; Davies and Aldridge 1993; Xing and Davies 1996). Amplitudes and phases of the modeled M2 elevation were compared with records from 33 coastal and offshore tide gauges around the Irish Sea, giving root-mean-squared errors of 9.4 cm in elevation and 5° of phase. These values compare favorably with other models of this region (e.g., Xing and Davies 1996). The distribution of signed elevation errors given in Table 1 shows a tendency for underprediction, which is typical of three-dimensional Irish Sea models and is discussed in detail by Davies and Aldridge (1993). Elevation errors were considered to be satisfactory and could reasonably be attributed to poor resolution of local, coastal features where most of the tide gauges used for comparison were located. In this work, it was desirable to model the vertical profile of tidal currents as accurately as possible, since they are responsible for the spatial pattern of mixing energy that controls the position of horizontal density gradients.

A detailed comparison of computed currents was carried out for three locations in the western Irish Sea and at one location in the shallower eastern part (see Fig. 1). Amplitudes and phases of M2 current components were calculated at those model cells corresponding to each current meter and at σ levels most closely matching the depths at which observations were made. Results are presented in Table 2 in tidal ellipse form so as not to exaggerate errors in phase, and in the smaller velocity component, that can occur when predominantly rectilinear tides are decomposed. Semimajor axes agreed to within 5.5 cm s−1, while the mean error in the semiminor axes was 1.3 cm s−1. The model reproduced the expected increase in ellipticity toward the seabed (Prandle 1982) and showed good predictive skill near the bed (particularly at locations 1 and 2). The mean error in orientation was 5° and ellipse phases agreed to within 4°. The model also predicted vertical current shear consistent with observations at all four locations. This property is a crucial test for three-dimensional models (Xing and Davies 1996) since shear is determined by the modelled distribution of stresses through the vertical and is not sensitive to input at the open boundary. Davies and Jones (1992) presented S2 ellipse properties for three of the current meter sites used here. S2 properties derived from this model agreed well with those observations, with mean errors of 1.8 cm s−1 for the semimajor axis and 4.5° for orientation. Depth-averaged (Eulerian) tidal residual currents obtained were consistent with a previous (5-km grid) model of the Irish Sea (Proctor 1981). Significant tidal rectification (of approximately 10 cm s−1) was predicted near Anglesey, the Isle of Man, and the North Channel (these residuals were subtracted from the time-averaged values presented in the next section, in order to eliminate tidal rectification and isolate the density-driven flow).

To test baroclinic performance, the model was run diagnostically (i.e., with density held constant) on a 2-km-square grid for the idealized frontal structure shown in Fig. 2a. This prescribed density field was uniform over the 200-km length of the domain, giving a pseudo two-dimensional arrangement. The strongest density gradients were 0.8 kg m−3 over 20 km. These values were chosen to emulate those described by James (1978) in a rigid-lid model of frontal circulation. The frontal structure is physically realistic although density gradients are somewhat higher than observed in the western Irish Sea. The model reached a steady state after 6 days of integration, and the resulting velocity field is shown in Fig. 2b and Fig. 2c. Peak alongfront flow (Fig. 2b) was 22 cm s−1 at σ-level 5 in the center of the front. The circulation induced by the unbalanced part of the cross-frontal pressure gradient is shown in Fig. 2c. Maximum cross-frontal flow (7 cm s−1) was found in the bottom boundary layer, and there were flows of 4 cm s−1 at the level of the pycnocline. The maximum vertical velocity of 1 mm s−1 was found immediately to the well-mixed side of the front. James (1978) obtained qualitatively similar results with slightly reduced magnitudes (alongfront flow of 12 cm s−1 and cross-frontal flows of 3–4 cm s−1). In a further series of numerical experiments [see Horsburgh (1999) for details] the vertical shears in both alongfront and cross-front currents agreed with the semianalytical model of Garrett and Loder (1981) to within 5%.

4. Seasonal simulation for 1995

The model was forced with observed hourly mean solar insolation from Dublin airport and hourly mean winds from 1995. Terrestrial weather stations surrounding the area can be sheltered from significant winds, so a hybrid wind field was synthesized from the higher value of the two weather stations on the Isle of Man shown in Fig. 1. It is known that winds over the sea surface are stronger than those on land because of reduced friction. Here, a factor of 1.3 was applied, consistent with calibrations of meteorological buoy data in the Irish Sea with terrestrial wind records (Lavin-Peregrina 1984). The model was initialized with temperatures of 7.5°C everywhere, which was the well-mixed value (±0.2°C) in the western Irish Sea during the 1995 and 1996 spring cruises (Horsburgh et al. 2000). Simulations began at the vernal equinox (day 80, 21 March) and were integrated forward in time until day 304 (31 October). A simple upwind advection scheme was introduced at the northern boundary:
i1520-0485-33-2-343-e10
where a temperature time series was synthesized from satellite imagery, calibrated against the most northerly station from the observations of Horsburgh et al. (2000). The model interpolated linearly between these values to obtain the boundary temperature. Observations show no significant north–south temperature gradient at the southern open boundary so a zero gradient boundary condition was used there. Air temperatures from Dublin airport (Fig. 1) were used in the calculation of longwave radiation losses from the sea surface. It was found that air temperatures needed to be modified from September onward to achieve an accurate breakdown of stratification, because marine air temperature is poorly specified from terrestrial weather stations. Lavin-Peregrina (1984) found that after 10 September 1981 the offshore air temperature exceeded that at Dublin airport by 0.5°–1.0°C and that there was no significant diurnal variation. Values of air temperature modified in this way were used in the seasonal model runs.

Most of the results presented here were obtained with an eddy Prandtl number of 1 and the Smolarkiewicz advection scheme (henceforth denoted SM1). For comparative purposes, some results are shown from a run using a central difference advection scheme, and from run SM2 with an eddy Prandtl number of 2 (i.e., horizontal diffusivity of temperature was half that of momentum). Temperature and velocity fields were extracted from the model at time steps corresponding to observational data.

a. Evolution of the temperature field

While these results focus on the western Irish Sea it is useful to examine briefly how well the model predicted surface temperature over the full domain. Satellite images of sea surface temperature (SST) in the Irish Sea, such as Fig. 3b (from 8 August 1995), consistently reveal three areas of relatively warm water, one of which is the stratified western Irish Sea. Modeled surface temperatures from SM1 (16 August) are shown in Fig. 3a. These agree well with the satellite image, predicting the same three regions of relatively high SST (with temperature approximately 18°C), and cooler water (∼14.5°C) in the central and southern Irish Sea. This is evidence that the modeled temperature predictions were accurate across the full range of mixing conditions.

The panels in Fig. 4 show (from left to right) daily mean surface temperature, bottom temperature and top-to-bottom temperature difference (the simplest measure of stratification in the constant salinity model) from June to August. The diagrams show qualitative agreement with contemporaneous observations (Fig. 8 of Horsburgh et al. 2000). Spatially complete observations beyond August 1995 were not available for comparison. Surface temperatures disagreed with observations by up to 1.5°C on occasion, whereas bottom temperatures were more accurately modeled. Discrepancies are partly due to the lack of spatial variability in solar heating and wind stress in the model. The observational data also contain temporal variability in surface temperature since cruise stations were visited over a period of 2–4 days. Bottom temperatures are less influenced by the direct effects of surface heating and cooling, which explains the better agreement. This is confirmed by Fig. 5 which shows daily mean surface and bottom temperatures for the full duration of SM1 from a model cell in the center of the stratified region at 53.8°N, 5.5°W. Throughout the simulation the modeled temperature stratification agreed well with the observations, which are depicted by solid squares (surface) and triangles (bed). The smooth rise in nearbed temperatures emphasizes the isolation of the cold, dense pool. In contrast, surface temperatures from the model showed greater variability while remaining physically realistic. The sharp rise in bottom temperature at day 240 lagged the rapid drop in surface temperature by a few days. This represents a significant mixing event due to increased winds (greater than 10 m s−1) after day 235.

The final breakdown of stratification in the model took place at day 300 (27 October), which was consistent with our observations and others presented for the same site (e.g., Gowen et al. 1998). By this time the model showed the region to be everywhere well-mixed in the vertical but that differential cooling had occurred leaving a relatively warm core in the deepest part of the region (Fig. 6). This is indicative of convective heat loss, with the most rapid cooling occurring in shallower areas. Geostrophic considerations would predict that the resultant weak horizontal density gradients along the east coast of Ireland could drive a northward flow along the Irish coast. If so, the density-driven circulation in the western Irish Sea may show a seasonal reversal. This could have implications for the dispersal of contaminants and for the biology of the region but it must be remembered that in winter months wind-driven currents will be a more dominant contributor and the predicted density-driven effect may not be significant. Also, lower salinities near the coast would act to reduce the density there (and therefore the east–west density gradient). A quantitative measure of the model's predictive skill was obtained by extracting surface and bottom temperatures at every location, and for each time, where a corresponding observation was made. Figure 7 shows surface and bottom temperatures from SM1 plotted against all corresponding observations. The agreement of both surface and bottom temperatures was good, with slightly better agreement for bottom temperatures. The R2 values (square of the correlation coefficient) and the least squares fits from three different model runs are given in Table 3; a regression line slope close to unity is a useful metric for gauging the predictive skill of a model.

All three model runs predicted the strength and spatial extent of thermal stratification with similar accuracy until late July 1995 (Figs. 8a–c), but by mid August the central difference advection scheme gave rise to spurious stratification in the southern part of the domain (see Fig. 8d). It is well known that central difference schemes are not positive definite and can give rise to numerical ripples. Here, deficiencies of the central difference advection scheme are exposed only after strong gradients of temperature have been formed; south of 53.4°N the tidal currents reach 1 m s−1 at spring tides, and from late July onward these currents are normal to the temperature gradient causing numerical error and erroneous stratification. Figure 8 also shows that run SM2 (with lower prescribed eddy diffusivity) overestimated the maximum vertical temperature difference by 1°C. The statistical approach of Table 3 identified run SM1 as having the best overall performance, however it should be noted that these statistics are somewhat biased by the spatial limitation of the observations. In Fig. 8b the stratification predicted by run SM1 agreed well with observations over most of the region but extended slightly too far south. This was due to colder deep water occupying a larger area in the model than was in fact the case [a similar tendency to overpredict the southern extent of stratification is evident in the results of Xing and Davies (2001)]. It may be possible to improve this aspect of model performance by the inclusion of additional tidal constituents (and thus better resolve the spatial variability in mixing energy) or by a more sophisticated parameterization of unresolved horizontal mixing processes. This simple comparison demonstrates the importance of numerical advection schemes to the accurate development of regional stratification in shelf seas.

b. Cyclonic circulation

A key objective of this study was to demonstrate that the model could reproduce the observed cyclonic circulation and show this circulation to be density-driven. Residual flows greater than 2 cm s−1 at 25 July and 16 August are shown in the upper two panels of Fig. 9. These depth-mean flow fields were obtained by averaging model velocities over two M2 cycles and then subtracting the depth-mean tidal residual. Consequently, the circulations seen in Fig. 9 contain wind-driven and density-driven contributions, and also a small S2 component. Even so, aspects of the familiar gyral pattern described by the drifter observations of Horsburgh et al. (2000) can be seen. By 16 August maximum depth-mean speeds of 8 cm s−1 were obtained on both sides of the gyre. The simplest way to investigate whether the flows were density-driven was to perform a repeat run with identical wind forcing but no heating. Depth-mean residual flow fields at the same times from the zero heating run are shown in the lower two panels of Fig. 9. The circulations are clearly different from the upper panels and the cyclonic gyre is absent once heating is removed, showing that the gyre is density-driven. The northward flow along the Irish coast on 25 July is present in both runs, which suggests that this is probably a wind-driven feature.

To isolate the density-driven component of the circulation a harmonic analysis was performed for the two day period 14–16 August. The results from an analysis of the same period obtained with a constant density model (i.e., forced only with wind and tide) were then subtracted from this. The residual flow thus obtained is due only to density forcing and any nonlinear interaction of the residual currents. This approach is a more realistic method of separating the baroclinic flow than either a diagnostic model run, or the calculation of geostrophic velocity from the modeled density field. The Eulerian tidal residual was again subtracted to give the density-driven circulation shown in Fig. 10a. For comparison, Fig. 10b shows the low-pass filtered trajectories of six satellite-tracked drifters deployed during July and August 1995 (Horsburgh et al. 2000), that define the extent of the gyre and its possible recirculations. The modeled flow pattern agrees well with the drifter tracks and also with the spatial arrangement of vertical temperature difference seen in Fig. 8b. To ensure a valid comparison with residual flows derived from the drifters, the currents in Fig. 10a were averaged over σ levels 4–11, spanning a depth range of 3–38 m on the western side of the gyre and 5–44 m on the eastern side. This extracts the modeled flow most closely corresponding to the depth at which drogues were deployed (24 m). Maximum speeds in Fig. 10a were 12 cm s−1 southward along the Irish coast and 14 cm s−1 northward to the west of the Isle of Man, with a mean modeled circulation speed of 8 cm s−1.

A map of the regional circulation during late July and August 1995 (Fig. 11a) was obtained by manipulating the low-pass-filtered data of all 16 drifters deployed at that time. Velocity components derived from the drifter tracks were averaged over a grid equivalent to four model cells. Figure 11b presents the currents from σ levels 4–11 averaged over one M2 cycle (this time without subtraction of wind-driven or tidal residual flow) grouped into correspondingly sized cells. The gridded model data are only presented for those cells where drifter data existed. A quantitative comparison was performed by correlating the u and υ components of the drifter and modeled velocities at each of these cells, in the same way as for temperatures in Table 3. Both components correlated significantly at the 99% confidence level (R2u = 0.47, R2υ = 0.55, n = 133). The significant correlation between the gridded drifter ensembles and corresponding model averages is evidence that the model results are physically realistic although the R2 values were lower than in the corresponding analysis of temperature. This was due to greater variability in both the modeled and observed velocity field, and the fact that comparisons were limited to those cells through which drifters had passed. The analysis can be extended if bivariate vector correlation is employed (Hanson et al. 1992); as well as characterizing the strength of the linear relationship between two vector fields this technique also accounts for rotational and reflectional relationships. When applied to the vectors in Fig. 11 the technique (see appendix) provided a significant overall correlation coefficient of ρ = 0.72. Rotational dependence indicates that the vector pairs rotate in the same sense, and is therefore an important test for a regional circulation. Hanson et al. (1992) define a rotation/reflection index, ξ, which here takes a value of 280. This confirms that covariance between like velocity components is dominant. The analysis also provided a phase angle of ϕ = 3° between the model and drifter vector orientations. The high rotational dependency and small value of phase angle obtained confirm that the model reproduces both the extent and the orientation of the gyre accurately.

c. Vertical structure

In order to examine qualitative features of the vertical temperature structure (e.g., position and strength of the thermocline, location of bottom fronts), Fig. 12 presents transverse (xz) sections from the model (SM1) and from a line of corresponding observations at latitude 53°40′N at three times. The model reproduced the domelike temperature (and therefore density) structure throughout the stratification period, predicting horizontal gradients on both flanks of the cold pool. The strongest gradients of density near the bed in the model were located between 5.25° and 5.4°W, as were the observed bottom fronts. The modeled temperature gradient for 25 July and 16 August was 2°C over a horizontal distance of 10 km, slightly less than that observed. The center of the fully developed model thermocline was located at approximately 18 m, which is consistent with the observations from July and August 1995. In oceanic situations, turbulence closure schemes often underpredict mixed layer depths due to spatial and temporal smoothing of wind stress (Martin 1985). There did not appear to be any significant underprediction of the thermocline depth in these results, which may be due to the fact that the seasonal thermocline in shelf seas remains shallow.

The vertical structure of density-driven flow at 16 August can be seen in Fig. 13a, which shows contours of the north–south component of residual current (derived from the subtraction of harmonic analyses) for the same xz section as in Fig. 12. Solid lines indicate flow into the page and reveal a broad current toward the north, with maximum speeds of 10.5 cm s−1 in a narrow core at 20-m depth. On the western side of the section (Irish coast) there was a weaker (7 cm s−1) and deeper (30 m) southward flow. A meridional (yz) section along longitude 5.4°W showing the east–west component of residual current is given in Fig. 13b. The residual component normal to this section was concentrated in near-surface jets at the northern and southern limits of stratification. Maximum residual flows at the northern limit were 11 cm s−1 toward the west, and at the southern end of the gyre currents were 7.5 cm s−1 toward the east. The jetlike nature of the strongest flow was consistent with the geostrophic calculations and detided ADCP sections presented in the observations of Horsburgh et al. (2000). It should be noted that the strongest flows normal to both the east–west and north–south sections were associated with the sharpest horizontal density gradients in the bottom part of the water column which reinforces the dynamical significance of bottom fronts and lends further support to a thermal wind-based account of these currents.

d. Effect of winds and of spring–neap cycles on the density structure

The observations of Horsburgh et al. (2000) show that the cold pool density structure and the associated circulation persist beyond the autumnal equinox (this is confirmed by the timing of stratification breakdown in Fig. 5). There is potential for the onset of stronger winds to interact with the isopycnal structure so as to temporarily intensify horizontal density gradients, resulting in stronger baroclinic currents. The warmest lens of water above the thermocline could be advected into a regime where it rapidly becomes vertically mixed. The now warmer, well-mixed water would create a stronger density contrast with the coldest water beneath the thermocline (whose temperature remains unchanged). This mechanism is not amenable to direct observation but is explored in the following numerical experiments that take their initial conditions from the temperature (density) structure of 16 August (an east–west section of which was shown in Fig. 12d and again by the dotted lines in Fig. 13a). Gale-force winds of 17 m s−1 were prescribed for 36 h, first from the north and then (in a second experiment) from the south. The model response was analyzed by the behavior of the temperature field along the section and by the vertical structure of residual currents; in order to eliminate the direct influence of the wind, these were obtained by running the model without wind for a further two M2 cycles and analyzing over the last of these. The adjusted temperature field and meridional component of residual current following 36 h of northerly winds are shown in Fig. 14a. The horizontal gradients of temperature on the dome's eastern side were not significantly changed, but nearbed gradients on the western flank (at 5.75°W) were much stronger. This is consistent with warm surface water moving toward the west and downwelling along the Irish coast, advecting isotherms toward the center of the cold pool. The residual flow pattern now shows the strongest southward flow increasing to 11 cm s−1 in a strong band of currents near the surface. Northward flow was now weaker (in comparison with Fig. 13a) and more diffuse with maximum flows of 8 cm s−1.

The model response to strong winds from the south is shown in Fig. 14b. After 36 h the bottom front on the eastern flank of the cold pool had intensified and the northward flowing component of the residual currents had increased (again in comparison with Fig. 13a). Maximum surface currents of 13 cm s−1 marked the center of an intense band of near-surface flow at 5.3°W, concentrated above the strongest horizontal density gradients. In contrast, the nearbed density gradients to the west weakened and southward flow diminished to 4 cm s−1. Ekman transport to the right of the southerly winds caused the warmest water above the thermocline to be advected eastward. A surface front marking the western limit of the warm water persisted but as the warm lens was advected into the well-mixed area (at 5.1°W) the front was eroded. In this example, the density-driven flows were only 20% of the magnitude of the direct wind-driven currents (not shown) caused by the preceding wind. Nevertheless, the simulations identify an important interaction between the wind and density field that could modulate the cyclonic flow around the gyre during the heating season. As long as the wind regime does not completely dominate the nontidal flow, the wind direction can determine the location of the strongest horizontal density gradients, and therefore can determine where in the gyre the fastest baroclinic currents are found. Thus the potential energy in the density field is directed by the wind into releasing differing amounts of kinetic energy at varying locations.

In a semidiurnal regime the density field can also be modulated by the spring–neap cycle as shown in Fig. 15, which is a series of east–west temperature sections along 53°40′N at 2-day intervals throughout a 22-day period beginning on 1 August. To obtain these results the model was integrated normally until 1 August and then run forward with no wind or thermal forcing (so that changes in the thermal structure cannot be due to wind events here). The stage in the spring–neap cycle can be deduced from the free surface elevation at the center of the stratified region (53.8°N, 5.5°W) shown in Fig. 16a. The strongest horizontal temperature gradients in Fig. 15 occur approximately on day 4 and then again on day 18. This suggests that the response of the density field lags the strongest tidal mixing (which occurs at spring tides) by about a day. The weakest gradients in Fig. 15 occur around days 10–12, on or slightly after neap tides. It appears that as tidal currents increase, increased density gradients develop along with associated baroclinic flow. Figure 16b shows a time series of the daily mean kinetic energy (per unit area) of flow between σ levels 4–11, summed over the subdomain containing the western Irish Sea gyre (i.e., the region defined in Fig. 10). The solid line is from the tidal modulation run described here, while the dashed line shows the results from a purely tidal simulation of the same period. Maximum kinetic energy for the baroclinic run is seen shortly after days 4 and 18, consistent with the strongest horizontal nearbed density gradients in Fig. 15 and lagging the largest tides by about one day. The barotropic kinetic energy of the subdomain during this period, shown by the dashed line, confirms this lag. Figure 16b also suggests that the contribution to regional kinetic energy of the residual flow may be as large as 20%–25% of that due to the M2 and S2 tidal currents, during the presence of strong density gradients like those seen in Fig. 15.

5. Concluding remarks

The model described here presents an accurate picture of seasonal circulation in the Irish Sea throughout the stratified period. The agreement between model predictions and hydrographic and drifter observations during 1995 was good, although better quantitative skill could doubtless be obtained with a finer grid and spatially varying wind and heat fluxes. As discussed by Xing and Davies (2001), the present grid cannot resolve small-scale baroclinic instabilities, internal inertial-gravity waves, and coastal boundary flows generated by wind events (e.g., Allen and Newberger 1996). Nevertheless, all of the characteristic features of the western Irish Sea cold pool and its associated cyclonic near-surface circulation were reproduced because the grid used here does resolve the structure of the jetlike flows and the horizontal density gradients that cause them. Characteristic features of the cyclonic gyre were visible in the circulation pattern even before the wind-driven and baroclinic flows were separated. All of these features were absent when no seasonal heating was applied which shows conclusively that the gyre is indeed a density-driven phenomenon. The choice of constant salinity in the model was based on the observations of Horsburgh et al. (2000), which showed temperature to have the primary influence on density from late June onward. The fact that good predictions of the cyclonic pattern of circulation and associated speeds were obtained with the model is because salinity has only a second-order influence on the density field over most of the heating season. This work also shows that modeling the main features of this mesoscale density-driven feature does not depend critically on spatially varying winds (although in any model intended for management applications one would obviously use interpolated winds from a mesoscale meteorological model).

The best picture of the modeled residual circulation comes from the separated baroclinic flow shown in Fig. 10a. The multiple possible recirculation paths, shown by the drifter tracks in Fig. 10b and described in detail by Horsburgh et al. (2000), were seen in the predicted flow field. The spatial extent of the modeled stratification and gyral circulation also agreed well with those observations. Modeled maximum speeds along the northward flowing arm of the gyre to the west of the Isle of Man were 14 cm s−1, lower than the mean value of 18 cm s−1 obtained from drifters over this segment (Horsburgh et al. 2000). This was largely due to the subtraction of the tidally rectified component, which is in the same direction at this location and has a magnitude of approximately 5 cm s−1. The spatial resolution of the model will affect the accuracy of density-driven flows: the horizontal resolution (and choice of advection scheme) determines those density gradients that can be maintained, and the vertical resolution affects the level at which maximum flows will be found. In this study, diffusion of momentum in the model (both prescribed and numerical) tended to result in broader, weaker flows than those observed. Even so, the scalar average of currents at σ levels 4–11 (Fig. 10a) gave a mean circulation speed of 8 cm s−1, the same as that calculated from the complete drifter dataset. Sufficient confidence can be placed in the flow fields to include chemical and biological tracers, or to use the model to provide a database of regional circulation maps for use with biological transport models. With the inclusion of spatially variable wind forcing, accurate maps of residual currents at monthly intervals could be produced operationally during the period of larval release for commercially important species such as Nephrops norvegicus. The seasonal pattern of stratification and residual flow in the western Irish Sea and in the North Channel of the Irish Sea also affects the relationship between phytoplankton production and copepod abundance (Gowen et al. 1998). It would be a useful future exercise to compare predictions of advective transport from the western Irish Sea with the observed appearance of copepods in the North Channel prior to the summer peak in primary production (Gowen et al. 1998).

In these simulations a small amount of horizontal eddy diffusivity was required to avoid unphysical temperature gradients developing in shallow parts of the domain. Even with this relatively high resolution grid, there are subgrid-scale physical processes that demand parameterization. In a sensitivity study of the Smagorinsky (1963) formulation, Oey (1996) found that only at horizontal grid scales of 0.5 km was the coefficient successfully put at zero. The best results here were obtained with the coefficient α = 0.1 and an eddy Prandtl number of 1 which, on this grid, gave values of eddy diffusivity between 50 and 130 m2 s−1 over a tidal cycle. These values are consistent with observational estimates of 100 m2 s−1 for the region (Lavin-Peregrina 1984; Durazo-Arvizu 1993). It may well be the case that diffusive processes (in reality, small-scale eddies) are different in the surface and nearbed layers. Bottom fronts are known to be more stable to baroclinic instability than surface fronts (Flagg and Beardsley 1978; James 1989) and global model skill may be improved if horizontal diffusivity were related to some combination of horizontal density gradient and height above the bed. The fact that bottom temperatures in the cold pool could be reliably predicted by the numerical model, but showed a sensitivity to change in the horizontal Prandtl number, implies that lateral processes (both diffusive and advective) may be as important as vertical processes in the slow warming of the deep water.

These results provide useful knowledge about long-term (subtidal) processes at shelf sea fronts and cold pool systems. The frontal validation simulations here (Fig. 2) suggest that cross-frontal flow from the mixed to the stratified side is concentrated at the level of the pycnocline. Previous two-dimensional (James 1978) and diagnostic (Garrett and Loder 1981) models employed simpler closure schemes for vertical mixing and predicted instead a surface convergence. If the secondary circulation is indeed focused at the pycnocline then it could act as a conveyor belt for the supply of nutrients to phytoplankton throughout the stratified period. Further model studies of cross-frontal transfer are under way as are dye release experiments to verify the existence and location of cross-frontal flows. The stability and persistence of bottom fronts to strong winds was demonstrated by the numerical experiment whose results are shown in Fig. 14. The rapid erosion of surface structure was seen for both wind directions. When the wind was from the north, water from the east of the section was advected over the warmer water. This created convective instability in the upper 20 m as was found by Wang et al. (1990). When the wind was from the south, a lens of water with the highest temperatures moved toward the east where it encountered progressively stronger tidal mixing. In both cases the dome of cold water near the bed remained intact and the horizontal temperature gradients intensified, causing corresponding increases in the density-driven residual flow. Modulation of the density field is also brought about by the spring–neap cycle where horizontal gradients of temperature and maximum residual current kinetic energy in the gyre are strongest shortly after spring tides. These simple numerical experiments illustrate a transfer of energy between the baroclinicity contained in the density field and the residual currents of the gyre. Potential energy in the isopycnal structure can be increased both by strong wind events and by increased vertical mixing during the neap to spring phase of the semidiurnal tide. These important interactions between wind, tide, and density structure reinforce the need for well-resolved, full physics, three-dimensional models if all aspects of the seasonal variability in shelf sea circulation are to be properly simulated.

Acknowledgments

This work was funded by an award, GR3/9601, from the U.K. Natural Environmental Research Council. We are grateful to Alan Blumberg for providing the original code for ECOMsi. Thanks are also due to Jiuxing Xing and Alan Davies for supplying the bathymetry and for useful discussions. Wind data for the seasonal model runs were provided by the U.K. Met Office, while solar data and air temperatures were courtesy of the Irish Meteorological Service. The satellite image in Fig. 3b was processed by the NERC Remote Sensing Data Analysis Service (RSDAS). We are grateful to Dr. Emma Young for comments on the draft manuscript and also to two referees for their very helpful suggestions.

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APPENDIX

Vector Correlation Measures

Two-dimensional vector correlation is described in detail by Hanson et al. (1992). Their approach is similar to that of Kundu (1976) but develops the range of correlation measures to distinguish between rotational and reflectional relationships between vector fields. Here we confine ourselves to the correlation measures described in this paper; for a complete exposition see Hanson et al. (1992).

Corresponding two-dimensional vectors can be represented as N pairs of complex numbers, z = x + iy and w = u + where i = √−1. Variance and covariance can then be defined as
i1520-0485-33-2-343-ea1
where (zz)* denotes the complex conjugate of the residual. The vector correlation measure,
i1520-0485-33-2-343-ea3
relates the vector magnitudes, just as in scalar correlations. Additionally, a rotation/reflection index can be defined as follows:
ξσxuσyvσxvσyu
which yields a positive (negative) number for rotational (reflectional) relationships between the vector series. A reflectional dependency implies a twisting of components between vector pairs and is not detectable in scalar covariance. Rotational dependence implies a correlation between the angular progression of the two vector fields and yields an angle, ϕ, between corresponding vectors, where
i1520-0485-33-2-343-ea5

Fig. 1.
Fig. 1.

Finite-difference grid and model bathymetry (m, dotted lines). Solid, bold lines represent open boundaries where M2 and S2 input were specified. Also shown are the locations of weather stations where meteorological forcing was obtained and current-meter rigs (numbered 1–4) where tidal validation was performed

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 2.
Fig. 2.

Results from a diagnostic model run for an idealized shelf sea front, showing (a) density field (σt), which is uniform in the alongfront direction; (b) alongfront current (cm s−1) where isopleths denote flow into the page; and (c) cross-frontal circulation (bold arrows indicate u > 5 cm s−1). Note the different vertical and horizontal scales in (c)

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 3.
Fig. 3.

(a) Model surface temperature (24-h mean) from 16 Aug. (b) Sea surface temperature (SST) from Advanced Very High Resolution Radiometer (AVHRR) satellite image at 1337 UTC 8 Aug 1995, with temperature scale along the left side of the image. The AVHRR image has been cropped to occupy the same geographical region as the model

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 4.
Fig. 4.

Modeled temperatures from the stratification period during 1995: (a) 1 Jun, (b) 21 Jun, (c) 20 Jul, (d) 25 Jul, (e) 16 Aug, and (f) 30 Aug. Comparison can be made with the observations of Horsburgh et al. (2000), Fig. 8. From left to right the panels show (i) surface temperature, (ii) bottom temperature, and (iii) vertical temperature difference

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 4.
Fig. 4.

(Continued)

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 5.
Fig. 5.

Surface (solid line) and nearbed (dashed line) temperatures (°C, 24-h means) at the center of the stratified region (53.8°N, 5.5°W). Also shown are observed surface (solid squares) and nearbed (solid triangles) temperatures

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 6.
Fig. 6.

Vertically well-mixed temperature conditions from the model at 31 Oct 1995. Note that the central region is now warmer and the existence of an east–west horizontal temperature gradient near the Irish coast

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 7.
Fig. 7.

(a) Surface and (b) nearbed comparisons of observed with modeled temperatures at each station visited for cruises in 1995. The correlation coefficients, R2, and least squares fits are shown

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 8.
Fig. 8.

Spatial pattern of top-to-bottom temperature differences at 16 Aug 1995 from (a) observations, (b) run SM1, (c) run SM2, and (d) the central difference run. Contours are in 0.5°C intervals

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 9.
Fig. 9.

Residual circulation (over two M2 cycles) where depth-mean flows greater than 2 cm s−1 are shown and the tidal residual has been subtracted: (a) SM1, 25 Jul; (b) SM1, 16 Aug, (c) no heating, 25 Jul; and (d) no heating, 16 Aug. Note the distinct cyclonic gyre in (b) and its absence when heating was removed (d)

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 10.
Fig. 10.

Density-driven circulation (greater than 2 cm s−1) obtained from a harmonic analysis of 14–16 Aug and subsequent subtraction of residual currents from a constant density run: (a) modeled currents averaged over σ levels 4–11, for consistency with the depth at which the drogues of drifters were placed, and (b) the low-pass filtered tracks of six Argos drifters deployed during Jul and Aug 1995

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 11.
Fig. 11.

(a) Residual velocity vectors derived from the filtered tracks of 16 Argos drifters deployed in Jul/Aug 1995 and (b) residual currents at the same locations (four-cell averages) from levels 4–11 at 16 Aug. Apart from averaging over one tidal cycle, no other manipulation was performed on the modeled currents in (b)

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 12.
Fig. 12.

Transverse sections (xz) of modeled temperature along model row corresponding to latitude 53°40′N on (b) 25 Jul, (d) 16 Aug, and (f) 21 Sep. Corresponding observations from CTD stations along this line are shown on the left in (a), (c), and (e).

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 13.
Fig. 13.

(a) North–south component of residual velocity normal to the section shown in Fig. 12 on 16 Aug. Solid and dashed isotachs (cm s−1) indicate flow into and out of the page, respectively. The fainter dotted lines show the contours of temperature in 0.5°C intervals as previously, but for clarity the labels have been omitted. (b) East–west component of residual velocity normal to a meridional section through the model along longitude 5.4°W

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 14.
Fig. 14.

North–south component of residual velocity normal to the section showing the response of the cold dome to a strong (17 m s−1) wind from (a) the north and (b) the south (isotachs: cm s−1, with solid lines depicting flow into the page and dashed lines indicating flow out of the page). The resulting temperature field (at 0.5°C contour intervals) after 36 h of wind is shown by the fainter dotted lines. The initial condition was the temperature field shown in Fig. 13a

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 15.
Fig. 15.

Transverse sections (xz) of modeled temperature along model row corresponding to latitude 53°40′N at 2-day intervals beginning 1 Aug, showing modulation of the thermal structure by the tide. Meteorological forcing was turned off during this period

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Fig. 16.
Fig. 16.

(a) Surface elevation at cell corresponding to the center of the stratified region (53.8°N, 5.5°W) over a 22-day period commencing 0000 UTC 1 Aug. (b) The 24-h mean kinetic energy of flow between σ levels 4–11, summed over the subdomain of the gyre (I = 10–35, J = 38–72). Solid line shows results from the baroclinic run used to produce Fig. 15, whereas the dashed line is from a run with tidal forcing only

Citation: Journal of Physical Oceanography 33, 2; 10.1175/1520-0485(2003)033<0343:ATDMOD>2.0.CO;2

Table 1.

Distribution of signed elevation errors for the M2 tidal constituent

Table 1.
Table 2.

Observed and computed M2 tidal ellipses for locations 1–4 in Fig. 1. Here M and m, are, respectively, the semimajor and semiminor axes (cm s−1). +θ- is the orientation (°) counterclockwise from east and +ϕ- is phase (°) of the semimajor axis

Table 2.
Table 3.

Regression coefficients, R2, and least squares fits for three different model runs

Table 3.
Save