1. Introduction

The Irish Sea (Fig. 1) is the semienclosed body of water between Great Britain and Ireland, which has been the subject of intense physical oceanographic investigation because virtually all the important physical processes active in midlatitude shelf seas have a significant role in parts of this small region. Particularly important are tides, wind-driven currents, river plumes, thermal fronts, and density-driven currents (Heaps and Jones 1969). In common with many other shelf seas, this region is characterized by areas of seasonal temperature stratification separated by tidal mixing fronts from well-mixed areas. Hence studies here can provide insights for other shelf sea regions, such as Georges Bank (see for example Loder et al. 1993) and the Yellow Sea (for example Lee and Beardsley 1999) because the dynamics of stratification and frontal systems are central to our understanding of shelf sea ecosystems. The Irish Sea has a complicated coastline and rapidly varying bathymetry (compared with other parts of the northwest European continental shelf, such as the Celtic and North Seas), so it has long been realized that high spatial resolution is required to adequately model the tides and wind driven circulation here (for example Proctor 1981; Jones and Davies 1996; Young et al. 2000). However, limitations in computer power have generally restricted three-dimensional density evolving studies of this region to restricted areas, seasonal timescales, and resolutions of ∼3.5 km (e.g., the modeling studies of Horsburgh et al. 2000; Xing and Davies 2001b; Young et al. 2002; Horsburgh and Hill 2003). High-performance computing lifts many of these restrictions, and in this paper we investigate results from a 3-yr simulation of a high-resolution (∼1.8 km) model covering the whole of the Irish Sea, including both channels that connect it to rest of the northwest European continental shelf. This resolution is chosen because typically values of the internal Rossby radius R vary from R ∼ 1 km in spring to R ∼ 2 km in midsummer (based on a two-layer calculation in the western Irish Sea). The experiments of Griffiths and Linden (1982) show baroclinic eddies have a scale of l ∼ 2.2πR/D^0.25, where D is the ratio of upper to lower layer depths. For D = 0.3, l is in the range of 10–20 km, and so a resolution of 2 km should adequately resolve the baroclinic features.

The analysis presented here focuses on the temperature field in the Irish Sea and the extent to which it is controlled by horizontal advection. We focus on temperature rather than salinity because it is generally taken to dominate the density field away from the coastal regions, but salinity is included in the model, with some consequences that are discussed. The salinity structure in this region is primarily determined by a competition between river runoff and the inflow of more saline water from the Celtic Sea and Malin shelf. The survey presented by Horsburgh et al. (2000) shows a steady increase in salinity from the English coast across the eastern Irish Sea and also a wedge of fresher water against the Irish coast. They also identify temperature as the primary cause of density stratification in this region and show that in midsummer it accounts for more than 80% of the density stratification.

Investigations of the temperature structure on the northwest European continental shelf (including the Irish Sea) have in the most part focused on the vertical processes (e.g., Elliot and Clarke 1991; Pohlmann 1996; Warrach 1998; Holt and James 1999; Sharples et al. 2001). The surface heat flux is taken to determine the depth mean temperature and turbulent mixing determines the vertical structure; the mixing in turn depends on the vertical shear and the density stratification. The horizontal structure is then thought to be controlled by the relative strength of vertical mixing and buoyancy input from the surface heating [e.g., the H/u³ relation of Simpson and Hunter (1974)], and the resulting frontal structures primarily arise from horizontal variations in tidal currents and water depth. While criteria such as this are generally successful at predicting the gross frontal positions and the extent of stratified regions, a more complex viewpoint is required to examine the details and time evolution of the temperature distribution—for example, the shape of the fronts, their persistence and variability, and the evolution of temperature above and below the thermocline. This invariably requires the investigation of the details of the horizontal processes (advection and diffusion of temperature, salinity, and momentum), down to scales similar to the internal Rossby radius.

There has been much interest in recent years in the currents generated by horizontal variations in the density field at shelf sea fronts (often referred to as baroclinic jets; Hill et al. 1994; Horsburgh et al. 1998; Brown et al. 1999), particularly focusing on current measurements (from ADCPs and drifters) in comparison with estimates of geostrophic velocity from high-resolution density sections. However, these studies have not examined the adjustment of the density field to the baroclinic currents in detail and the relationship of variability in these density driven currents (for example due to eddies) to the large-scale temperature structure has yet to be investigated. It has been established that there is a complicated residual flow field in this region, [starting with the work of Heaps and Jones (1969)], driven by tides, winds, and density gradients, and this might be expected to have a significant effect on the temperature structure; this is almost certainly the case in the two channels (St. George's Channel and North Channel) connecting this sea with the wider continental shelf.

Model studies have the advantage (over observations) of being able to explore all the terms in the governing equations independently, and this paper investigates the importance of advection, in comparison with the other terms in the transport equation, in determining the temperature distribution in the Irish Sea. To start with, we can identify four possibly important roles for advection in this context:

1. it determines the lateral heat and salt flux;

2. it allows the density field to adjust in response to the currents, which can lead to baroclinic instability;

3. it mediates shear-diffusion (in this process differential horizontal advection by vertically varying velocities accompanied by vertical mixing results in apparently enhanced horizontal diffusion); and

4. it results in upwelling and downwelling in convergent/divergent regions.

In order to put the model results in context and assess their applicability to the Irish Sea, we use three points of comparison with observations. First, we look at a number of CTD stations occupied in 1995. Figure 1 shows the location of about 300 CTD casts (many of which are repeat stations) held by the British Oceanographic Data Centre in this area for 1995, including a subset of the data analyzed by Horsburgh et al. (2000). Second, we consider Advanced Very High Resolution Radiometer (AVHRR) sea surface temperature data; some high-resolution (∼1.1 km) images are used for a qualitative comparison, but 9-km data (being easily accessible) are used for a model–data comparison of the full 3-yr model run. Since tidal mixing is central to our description of the temperature structure in this region, we also present a very brief comparison with tidal constituents from a subset of the current meter data analyzed by Kwong et al. (1997).

In the next section we describe the model setup and experiments, in section 3 we discuss the general circulation and temperature structure of the Irish Sea, and in section 4 we focus on the advective effects; conclusions are discussed in section 5.

2. Model setup and experiments

The Proudman Oceanographic Laboratory Coastal-Ocean Modelling System (POLCOMS) is used for this work. The hydrodynamic model at the heart of this system is the POL3DB model previously described by Holt and James (2001), and so we only give a brief summary of its features here. It is a finite-difference model solving for velocity (u, υ, w), (potential) temperature T, salinity S, surface elevation ζ, and turbulent kinetic energy q² on an Arakawa (1972) B grid in spherical-polar σ coordinates. For scalar and velocity advection it uses the Piecewise Parabolic Method (Colella and Woodward 1984; James 1996). This scheme assumes the variables vary parabolically across the grid boxes; after fitting these parabolas, they are integrated in an upwind sense to calculate the advective fluxes. This method ensures conservation and positivity, has excellent feature preserving properties (James 1996), and is not limited by a vertical Courant–Friedrichs–Lewy condition (James 2000). The Mellor–Yamada level-2.5 turbulence closure with an algebraic mixing length is used to determine vertical turbulent viscosity and diffusivity, and horizontal pressure gradients are calculated by interpolation of σ-level pressures onto horizontal planes. In regions of static instability a convective adjustment scheme is used to mix T and S in the vertical. With the high vertical resolution used in this model (see below) we found a tendency to produce spurious stratification, particularly in the St. George's Channel and southern Irish Sea. Therefore a a modification is made to the turbulence closure scheme of the standard model to produce a spatial distribution of T that agrees well with satellite observations. This is to require the buoyancy frequency N² to have values greater than 10⁻⁵ s⁻¹ (equivalent to a temperature gradient of ∼0.006 19°C m⁻¹ at 10°C) before it influences the vertical mixing (in the equations for q², mixing length and the stability functions):

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where b = g(ρ₀ − ρ)/ρ₀ is the buoyancy, ρ(T, S) is the (potential) density, and ρ₀ is a reference density. This prevents small fluctuations in ∂b/∂z growing to produce unrealistic stratification.

Much of the analysis in this paper arises from the transport equation for temperature, which can be written (in Cartesian coordinates for simplicity)

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with

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and the boundary conditions

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In the model we use σ coordinates, and so if H = h + ζ is the water depth, and z the vertical coordinate relative to a reference level, then σ is given by σ = (z − ζ)/H; h is the undisturbed water depth. Equations (2) and (4) include the surface heat flux: c_pρ₀q₊ is the incident radiation (W m⁻²) and c_pρ₀q₋ is the surface cooling (c_p is the specific heat capacity) calculated from bulk formulas including terms for sensible, latent, and longwave heat loss; see Holt and James (1999) for a description of these. Light penetration is governed by the attenuation coefficient λ. Vertical gradients of turbulent transport are here replaced by a diffusion term with a temporally and spatially varying diffusivity K_z evaluated by the turbulence closure scheme. As noted above, the model calculation also includes a convective adjustment, but for the purpose of the calculations described below this is included in the diffusion term, D(T). For reasons noted in section 1 a horizontal diffusion term is not included in the model formulation.

POLCOMS is applied to the region shown in Fig. 1 (to simulate the period 1995–97) on a 1/60° latitude × 1/40° longitude grid (∼1.8 km) nested within a northwest European continental shelf model (Holt and James 2001). The resulting grid of the Irish Sea is 173 × 301 × 34 vertical σ levels. The model uses domain decomposition for massively parallel computers (Ashworth et al. 2001) and scales efficiently on a large number of processors (up to ∼200); it takes about 12 h to run a model year on 128 SGI Origin 3000 processors. Forcing is by 6-hourly European Centre for Medium-Range Weather Forecasts (ECMWF) meteorological data through bulk formulas [see Holt and James (1999) for details of these], daily rainfall data from Bidston Observatory, monthly discharges from 4 major rivers, and annual means from 33 others. At the open boundaries of the Irish Sea model hourly depth mean currents and surface elevations are used in a flux/radiation boundary condition and daily temperatures and salinities are used in an advective boundary condition; these data are taken from the contemporary run of the shelfwide model (Holt and James 2001), which is forced with the same meteorological data (except rainfall) as the Irish Sea model. The boundaries of the shelfwide model are forced with 15 tidal constituents and monthly climatologies of temperature and salinity. In addition to this primary model run (referred to as expt 1), a second run (expt 2) is carried out for the year 1995, in which scalar advection [L(T) and L(S)] is omitted. In this case, temperature and salinity depend only on vertical processes, and so we can use this experiment to assess the overall importance of the advective term.

3. The Irish Sea temperature and current structure

Figure 2 shows the model surface temperature and the surface-to-bed temperature difference (ΔT) on a summer day near the height of the heating cycle (19 July 1995). The summer of 1995 was exceptionally hot (central England temperatures showed anomalies of +2.9°C in July and +3.9°C in August; Cullum 1996), and the calculated ΔT values show several stratified regions in the Irish Sea: a large region in the western Irish Sea has ΔT up to ∼6°C, a patch in the eastern Irish Sea has ΔT ≤ 3.5°C, and the strong stratification in the Celtic Sea extending northward into the St. George's Channel has ΔT ≤ 7°C. The surface temperature reflects some of this structure, but the surface fronts are generally not as well defined as the bottom fronts in this simulation. The shape and strength of the temperature stratification in the western Irish Sea are in reasonable agreement with the observations presented by Horsburgh et al. (2000) using the CTD stations shown in Fig. 1 and also Scanfish (towed-undulating-CTD) sections. These observations do not extend far enough into the North Channel to assess whether the northward extent of the stratification predicted by this model is realistic. The complicated horizontal structure seen in the stratification in this model is not apparent in these observations (resolution ∼20 km), although Scanfish data (Horsburgh et al. 2000, east–west resolution ∼1 km) from August 1995 along 53.667°N do show some variability. Similarly, high-resolution (∼1.1 km) AVHRR satellite images (such as Fig. 3) show complicated frontal structures in both the western Irish Sea and the St. George's Channel that are in good, if qualitative, agreement with our model results, both for the large-scale frontal positions and the scale of variability along the fronts. For example, the stratified waters in the Celtic Sea intrude into the Irish Sea on the east side of the St. George's Channel (Fig. 2b) in a shape that is very similar to that seen in Fig. 3. This structure, and the corresponding intrusion on the west side from the Irish into the Celtic Sea, has previously been observed by Horsburgh et al. (1998) and Carrillo (2002).

Modeled time series of surface and near-bed temperature at a number of locations around the Irish Sea (Fig. 4) show seasonal heating/cooling cycles during the three years of this model run. Also shown on this figure are individual (nighttime) sea surface temperature measurements from the 9-km AVHRR pixel that includes the time series point. Surface and near-bed CTD measurements are shown for site F. While the model is seen to run stably over this period without any long term drift away from these observations (no restoring or relaxation to climatology or observations is included in the run), there are, however, a number of systematic discrepancies at some sites. Winter cooling generally occurs too late in the year and the winter temperatures (after the first winter) are too warm. This is particularly the case in the Celtic Sea, St. George's Channel, and Gyre sites (A, B, C, and F). Given the size of this discrepancy (∼2°C) it warrants investigation (and this will be reported on in the future). Agreement is best in the summer and improves on North Sea and shelfwide studies (Holt and James 1999, 2001), although the exceptionally high temperatures recorded around day 200 (1995) by the AVHRR are not reproduced by the model, or indeed by the CTD measurements at site F. This discrepancy is likely to result from the surface skin temperature measured by the AVHRR not being representative, under strong heating conditions, of the bulk temperature simulated by the model and measured by CTDs. If we calculate mean and RMS errors of the model SST averaged on to the 9-km AVHRR grid, the pattern seen in these individual locations is reflected over the whole domain. Table 1 gives the seasonally averaged rms errors for the 3 yr of this model run, and it demonstrates that there is no tendency for these to increase during this period. The largest errors are in the winter months (∼2°C), with a second smaller maximum in midsummer (∼1.4°C) when the model tends to systematically underestimate the surface temperatures. The smallest errors are in autumn and spring. The rms errors in the summer are comparable to a similar calculation for a single year (1989) presented by Holt and James (2001) (∼1.6°C over the whole continental shelf), although in that simulation there was a tendency to overestimate summer temperatures.

The vertical temperature and current structure across a section at 54°N on 19 July 1995 is shown in Fig. 5; the currents shown are 25-h means to include wind-driven, density driven, and some tidal residuals. This figure demonstrates the relationship between the current and the temperature fields that has been explored in many previous studies (Hill et al. 1994; Horsburgh et al. 2000; Xing and Davies 2001b) using satellite tracked drifters and models. For example, between −5.75° and −5°E (Fig. 5), the midwater jets can be interpreted as baroclinic currents encircling the cool bottom dome in the deeper water. In this section the midwater maximum in northward current is about 0.12 m s⁻¹ at −5.3°E and southward is about 0.06 m s⁻¹ at −5.7°E. The current structure is complicated, and there are a number of other features in this section. For example, the υ component transects a headland eddy from the surface to a depth of about 30 m between −4.8° and −5.2°E (around the south coast of the Isle of Man). West of the gyre circulation the u component shows a broad eastward, presumably wind-driven, flow.

The modeled temperature structure is in good agreement with CTD measurements along this section. For example, the tendency of the surface front to extend beyond the bottom front is well represented. In the vertical, the CTD observations show a gradual increase in temperature from the seabed to a broad thermocline at a depth of about 20 m, with a narrow mixed layer above this. The model is in good agreement with these observations, although the modeled mixed layer has more structure than can be observed with this spacing of CTD stations and the temperature of the cool water dome is underestimated and is too well mixed. Profiles of temperature at −5.5°E on the line used for Fig. 5 show (Fig. 6) the depth-mean temperature (T) is underestimated by ∼1°C, but when the mean is subtracted (the plots show T_r = T − T), the vertical structure is in good agreement; each of these days shows a qualitatively different structure, which the model reproduces reasonably well.

The depth-mean circulation for the summer of 1995 is shown in Fig. 7 and demonstrates the overall pattern that is expected from previous studies of this region (e.g., Xing and Davies 2001b). The gyre circulation in the western Irish Sea is visible in the depth mean currents, although the southward flow on the west side is better defined than the northward flow on the east. The residuals of a number of eddies between 53° and 54°N (also seen on Fig. 8) remain in this averaged flow, which makes identifying a continuous eastward and northward current difficult.

In the North Channel there is a complicated exchange flow generally with southward flow on the west side and (stronger) northward flow on the east, but with a number of recirculations. Currents measured by high-frequency radar at the southern entrance to the North Channel (Knight and Howarth 1999) show this pattern (with some evidence of recirculation) but do not extend far enough west to fully record the southward flow.

On the west side of the St. George's Channel there is a narrow but continuous southward flow from about 53°N around the south coast of Ireland, where it flows eastward and intensifies as it leaves the model domain. On the east side of St. George's Channel there is a broader northward flow associated with the intrusion of stratified water from the Celtic sea. The flow pattern in this channel is in general agreement with the drifter observations of Horsburgh et al. (1998).

Individual plots of daily mean currents at 5-day intervals (Fig. 8) show that the surface currents are extremely variable over a short period of time. This degree of variability is not apparent in the below-thermocline currents (not shown). The surface currents are a combination of wind driven, density driven, and tidal residuals, but some of the currents do follow the temperature contours also shown on this figure. A feature present in all of the plots is the southward flow at about −5.6°E south of ∼54°N. Several branches appear to lead into this current from the north. The northward flow along the coast of Ireland (days 200 and 205) turns south to join this current at ∼54.25°N; a current from the North Channel follows the bathymetry southward to this point on days 200 and 215, and the northward current west of the Isle of Man recirculates at ∼54.25°N to join this current in days 205 and 210. The temperature contours indicate that this southward current brings cool water into the stratified region; this is particularly the case when it originates from the North Channel where the surface waters are significantly cooler (being well or partially mixed). This process is investigated further in section 4.

The surface signature of the northward component of the gyre circulation appears to be very variable as suggested above. It is best defined on day 215 but has a tendency to turn eastward at ∼53.8°N (days 200 and 205), which is reflected in the surface temperature structure. This surface variability is in contrast to drifter observations, drogued at 30 m, which show a narrow northward jet with no sign of eddies or wind-driven circulation (Hill et al. 1994; Horsburgh et al. 2000). There are some eddies at the surface apparent in the model in this region, but they do not appear to make up a particularly energetic component of the flow. This is in contrast to the Celtic Sea region of this model, where strong eddies are often seen.

To aid the interpretation of these results, and what follows, it is necessary to briefly discuss the tidal currents in this simulation [see, e.g., Davies and Jones (1992) for a detailed account of the tidal currents in the Irish Sea]. We use the data analyzed by Kwong et al. (1997) to estimate the uncertainties of the tidal currents in this model. The model tends to overestimate the anticyclonic component for M₂, and since this component is predominantly responsible for mixing the water column, this explains the tendency for the cool pool waters in Fig. 5 to be more well mixed than the observations would suggest. The cyclonic component shows a wide range of total rms errors, typically ∼0.03 m s⁻¹ but ranging from 0.007 to 0.122, and the M₂ constituent error has both positive and negative values. In contrast, the total error in the anticyclonic component shows little variability over the whole domain, having a value of about 0.06 m s⁻¹, and the M₂ constituent error is predominantly positive. The magnitude of these errors is similar to those presented by Kwong et al. (1997) for the whole shelf and by Young et al. (2002) and Horsburgh and Hill (2003) for the Irish Sea.

4. Advective effects on the temperature field

The effects of advection on the temperature structure of the Irish Sea are graphically demonstrated by the experiment in which advection is omitted (expt 2). This rather artificial experiment is equivalent to representing each model grid point as a one-dimensional model for temperature and salinity (as is often used to study vertical structure in isolation) but with currents from the three-dimensional model. Figure 9 shows the surface temperature and ΔT as in Fig. 2, and both are greatly changed from values seen in the standard model run (expt 1) throughout the domain. The high degree of small-scale variability in Fig. 9 reflects the bottom topography, while the effects on the stratification is one of the focii of this investigation. Comparing Figs. 2 and 9 shows that one effect of omitting advection is to significantly reduce the size of the stratified regions in both the Celtic Sea and western Irish Sea. This result is, however, strongly dependent on the imposition of a minimum value of N² for it to influence the mixing [Eq. (1)]. This has a moderate effect on experiment 1; for example, without it the frontal region in the St. George's Channel extends farther in the Irish Sea than Fig. 3 or Horsburgh et al. (1998) would suggest. In contrast it has a very significant effect on experiment 2; without it, most of the region from the Celtic Sea to the North Channel stratifies during the summer. Fig. 10 shows the surface and near-bed temperature at site F in the western Irish Sea for experiment 1 (a portion of the results are also shown in Fig. 4) and experiment 2 in 1995, along with CTD observations. The comparison with these CTD observations is significantly better for experiment 1 than experiment 2. This allows a number of effects of advection at this site to be immediately identified: it provides winter cooling and enhanced warming near the seabed during the summer. The onset of stratification occurs earlier in experiment 1 (about day 125) than experiment 2 (about day 153). This is due to salinity stratification reducing mixing in late spring. Figure 10 also shows the surface-to-bed salinity difference, which exhibits significant stable (and underestimated) salinity stratification from day 124 to 177 in experiment 1. This salinity stratification is not present in experiment 2, in which the salinity is only determined by surface fluxes and the onset of temperature stratification is delayed. Again this conclusion for experiment 2 is particularly dependent on Eq. (1); without this limit stratification occurs at about day 91 and surface temperatures grow to more than 20°C in the summer in experiment 2.

To assess the significance of the difference between these two experiments we repeat the model–CTD comparison of Holt and James (1999) with the available CTD data from 1995 in the Irish Sea (Fig. 1); the CTD data are binned onto the model's vertical levels and compared with model results from the time and place of the observations. Table 2 lists the mean and rms errors in the total temperature T, and the depth-mean (T) and depth-varying (T_r = T − T) components of temperature from comparisons with experiments 1 and 2. In both experiments the depth-mean component provides the larger error, but all the rms errors are significantly increased in experiment 2 as compared with experiment 1. This particularly arises from an underestimation of the extent of the stratified region in experiment 2; Fig. 5 suggests this is reasonably well modeled in experiment 1. To put this increase in error in context Table 2 also shows values from the ∼12-km model used for boundary conditions, which produces rms errors that lie between experiments 1 and 2. So even at a resolution far too coarse to adequately model the Irish Sea, the full physics model gives significantly better results than experiment 2. Mechanisms whereby the horizontal advection can make such a marked difference on the temperature, particularly the vertical structure, are now investigated.

Time series at the locations shown in Fig. 1 are used to quantify the significance of the various terms in the temperature equation (2). Initially we consider the depth-mean equation because this removes the diffusion term, leaving the depth-mean advection L and the surface heat flux q = q₊ − q₋; that is, ∂T/∂t = L + q. For experiment 1, Fig. 11 shows these terms time-integrated and compared with the depth-mean temperature T, relative to the initial condition; it shows the two integrals and the left-hand side of

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Figure 11 shows the relative importance of advection and surface heating in determining the heat content of these water columns over the 3 yr of the model run, bearing in mind these are not independent; the currents respond to differences in heating and the surface heat flux responds to advective changes in the sea surface temperature. The integrated effect of advection at shallow-water sites in the western Irish Sea (E and G) is to significantly reduce the amplitude of the seasonal cycle by a net advection of warmer water in the winter and cooler water in the summer; simply from differences in heat capacity any advection from neighboring deeper water tends to reduce this amplitude. In contrast, at Liverpool Bay in the eastern Irish Sea (site D) the advective heat flux is limited to a short period of warming during the winter. However, this does have a significant effect on the temperature, since after three years T is ∼5°C warmer than the surface heat flux alone would suggest. In the western Irish Sea (site F) advection tends to enhance the seasonal cycle, particularly to increase the depth mean temperatures during the summer, although there is a weak cooling effect during the winter. This results in some warming over these 3 yr. In the Celtic Sea and St. George's Channel (sites A, B, and C) the advective cycle is again asymmetric, with much stronger warming in the summer than cooling in the winter.

To ascertain the relative importance of advection and diffusion in stratified waters we return to Eq. (2) and examine time integrals of L and D calculated during the model run. These are calculated for June–September 1995 at a stratified site in the western Irish Sea (site F; Fig. 12). This shows advection during the summer produces a warming below the thermocline, with a weaker net flux of cooler water above the thermocline and near the seabed. Below the thermocline, diffusion acts in the opposite sense (i.e., warms near the seabed and cools at middepth), indicating that the water being advected into this location has a vertical gradient in temperature that is being mixed here, presumably leading to the reasonably homogeneous cool dome seen in Fig. 5. The advective warming below the thermocline is, however, significantly greater (in vertical extent and magnitude) than cooling near the seabed. In contrast above the thermocline, there is continuous advective cooling and a diffusive (and convective) redistribution of the surface heat flux in this layer. This accounts for the warming in the near-bed temperatures seen in Fig. 10 and observed in these CTD measurements and also those of Lavin-Peregrina (1984, who speculated on the presence of near-bed advective warming in this region). Here we demonstrate that this arises from the advective flux below the thermocline in this experiment rather than being due to increased vertical mixing, since the diffusive flux across the thermocline shown in Fig. 12 is generally small.

The spatial distribution of advective and diffusive heating below the thermocline can be seen through time averages of L(T) and D(T) for July 1995 (Fig. 13). For this calculation we take the water to be stratified when ΔT > 0.5°C and the thermocline is defined to be at the nearest grid point to

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Here this criterion for stratification is applied to the monthly mean temperatures and the thermocline depth [Eq. (6)] is calculated using these. We then average L and D from the sea-bed to this depth throughout July. The criterion of ΔT > 0.5°C is chosen so as to include weakly stratified regions; also shown on Fig. 13 is the ΔT = 2°C contour (dashed line) to indicate more strongly stratified regions. Figure 13 shows that the largest continuous region of advective heating below the thermocline stretches from the north entrance of the North Channel (with the highest values at the sides of the channel) and encompasses a large portion of the deeper water of the western Irish Sea. This shows that the warming of the cool dome water is due to advection of weakly stratified (and hence warmer at depth) water from the north by the persistent southward current from the west side of the entrance to the North Channel (shown in Figs. 7 and 8). The contribution to this flow from the North Channel is strongly affected by the northward current on the Malin shelf (Xing and Davies 2001a; Holt et al. 2001) outside the model boundaries, so this demonstrates an important far-field effect on conditions in the Irish Sea. In contrast, the Celtic Sea and St. George's Channel shows weaker advective warming/cooling. A particular feature here, however, is the band of advective warming that follows the ΔT = 0.5°C contour (i.e., the edge of the region where this is calculated) in a loop around the entrance to the Irish Sea. This is closely mirrored by below-thermocline diffusive heating, but since diffusion and advection have the same sign here this is not a tidal straining phenomenon (as discussed below) but rather advection of weakly stratified water northward, where it is mixed by stronger tides.

Apart from in the St. George's Channel, diffusive effects are generally limited to frontal and coastal regions as might be expected: in strongly stratified regions the suppression of turbulence by density gradients prevents significant diapycnal mixing (at least in this model), whereas in weakly stratified regions, the gradients of temperature are too small for D(T) to have a significant value. The localized regions of advective cooling generally correspond to regions of high diffusive warming. At the coast this is likely to be an upwelling processes, whereby cool water is advected up into the coastal regions and then quickly mixed by the tidal currents. On the other hand, near-bed diffusive cooling (usually associated with convection) always occurs in regions of strong near-bed advective warming, for example in Liverpool Bay. In this region this process has previously been attributed to tidal straining (Sharples and Simpson 1995; Rippeth et al. 2001), where vertical variations in advection due to vertical changes in tidal currents periodically destabilize the water column.

5. Discussion

Results from these numerical experiments demonstrate that the horizontal and vertical temperature structure in the Irish Sea arises from a complex interaction of advective, diffusive, and dynamical processes. All of the processes listed in section 1 appear to play a significant role in parts of this region, along with the heating–stirring process that is ubiquitous throughout the continental shelf. Comparisons of summertime below-thermocline advective and diffusive heating show that they are of similar importance in frontal/weakly stratified regions but advective heating dominates in strongly stratified areas. This conclusion is likely to be sensitive to the details of the turbulence closure scheme, particularly because it does not explicitly include sporadic diapycnal mixing processes such as breaking internal waves and Kelvin–Helmholz instability. However, our ability to accurately reproduce the bottom warming at site F (Fig. 10) and the accuracy of the modeled depth-varying component of temperature (∼0.66°C) lend weight to this conclusion. Shear-diffusion tends to blur the distinction between advective and diffusive processes. From Fig. 13 we can identify the regions where it might be important, as far as it affects the below-thermocline temperatures, since it appears as a coincident horizontal advective and vertical diffusive flux. From Fig. 13 we can see its effects are concentrated in frontal regions and in the eastern Irish Sea, rather than the main stratified areas of the western Irish Sea and the Celtic Sea. However, we cannot distinguish here between this process and the mesoscale variability of the front discussed below, which will also increase the apparent horizontal diffusion.

The comparison between the experiments with and without T and S advection (expts 1 and 2) shows a marked increase in errors against the CTD survey in experiment 2. However, this is difficult to interpret because the omission of advection also eliminates salinity stratification from experiment 2, which tends to counteract the increased stratification due to the lack of temperature advection. A comparison of the size of the stratified patch in the western Irish Sea in experiments 1 and 2 suggests that it is entraining well- or partially mixed water in Exp. 1. Further analysis allows us to identify the current from the entrance of the North Channel as the primary source of this entrainment, although surface current fields (Fig. 8) show this water can originate both from the North Channel and from recirculation within the western Irish Sea. The southward current on the west side of the North Channel is a frequently reported feature (Howarth 1982; Brown and Gmitrowicz 1995; Knight and Howarth 1999) but has yet to be the subject of systematic observations; in our model it results from both local and nonlocal (through the open boundary conditions) wind forcing and density gradients.

As well-mixed or weakly stratified water is advected into the stratified region of the western Irish Sea (from whichever route) its stratification increases because of the ambient conditions, and so the front remains in approximately the same location, but the resulting stratified water has a lower near-surface temperature and a higher near-bottom temperature (than the ambient), and hence advection by these large-scale currents tends to reduce the stratification in the western Irish Sea (in comparison with the predictions of a local heating–stirring model). This advection of weakly stratified water is demonstrated to be the cause of the warming of the cool pool waters in the western Irish Sea observed by Lavin-Peregrina (1984) and Horsburgh et al. (2000, Fig. 9). This process has wider implications since the well-mixed water might be expected to have significantly higher surface nutrient concentrations than the stratified regions into which it is being advected, suggesting this as a mechanism for fuelling intermittent primary production throughout the summer. An alternative mechanism is that small-scale eddies, resulting from baroclinic instability, mediate cross-frontal transfer of well-mixed water. While eddies are seen in this region, they are generally weak surface features and are prevalent only in the region between Angelsey and the Isle of Man where below-thermocline advective warming is not strong.

In either of the processes described above, the frontal region develops “mesoscale” variability (as seen on Fig. 3), while the small-scale variability due to the bathymetry (e.g., in Fig. 9) is smoothed out and the overall extent of the stratified region expands somewhat. This develops the concept of the isolated cool water dome (Hill 1996) to include a weak “leakage” significant on seasonal timescales. This is a concept that has previously been suggested by Hill et al. (1997) on the basis of drifter paths in this region. The increase in spatial extent of the stratified region can be reconciled with the criteria of Simpson and Hunter (1974) by noting that this criterion assumes a constant mixing efficiency and so is most appropriate for describing well-mixed water becoming stratified, rather than mixing already stratified water, where the mixing efficiency is significantly reduced.

This work suggests that while a one-dimensional (vertical) description can explain some aspects of the large-scale structure it is not adequate to explain the details of the observed spatial distribution and time evolution. This is particularly apparent in the western Irish Sea where the stratified region is not large when compared with the characteristic eddy size (∼2πR), and so cross-frontal exchanges might be expected to affect most of this area. It may be possible to account for some of the observed phenomena (such as the warming of the cool dome) if we are simultaneously overestimating the advective temperature fluxes and underestimating the diapycnal mixing (to some extent the former is probably true because we tend to underestimate the strength of surface fronts). To address this issue it is useful to draw a comparison between the Irish Sea and the North Sea. The vertical mixing scheme included in this model is similar to that used in many other modeling studies, and particularly it has been used with some success in predicting temperatures in the North Sea in both one and three dimensions (e.g., Warrach 1998; Luyten et al. 2003). At the resolution (vertical and horizontal) of the present model a minor modification of this scheme is required to prevent noise in the buoyancy frequency leading to spurious stratification (see section 2), and so the scheme used here is not identical to that used by Holt and James (2001); nonetheless, a heating–stirring model tuned to reproduce Fig. 10 is unlikely to give good results in the North Sea or similar areas. The North Sea is a region where there have been notable successes in one-dimensional temperature modeling (Elliot and Clarke 1991; Sharples and Tett 1994; Warrach 1998); it differs significantly from the Irish Sea in that the stratified region in the central and northern North Sea extends for many hundreds of Rossby radii, and so one-dimensional point models well isolated from frontal regions are possible; these are not possible in the Irish Sea. This work has focused on the effects of advective heat flux on the temperature using temperature observations as the primary guide, but a critical assessment of the residual currents in the model against drifter and moored observations would add further weight to these results. Of particular interest in such a comparison is whether the (lack of) variability in the drifter tracks at 30-m depth is reproduced by the model. Chapman and Lentz (1994) identify advection in the bottom boundary layer as being responsible for trapping coastal fronts to topography. It may the case that there is an analogous process at work here and near-bed advection, seen in this work, has a role in the observed stability of the bottom fronts.

The analysis has primarily concentrated on the first year of this simulation, because this corresponds to the time of most of the observations, but by continuing the simulation for two further years we gain some insight into the relative importance of the surface heating and advective terms on longer timescales. There is a general tendency toward advective warming for most of the sites in Fig. 11, which is in agreement with a net northward transport of water since the Celtic Sea is usually warmer than the Irish Sea. However, there is a tendency for the model to significantly underestimate winter cooling, giving increased errors against AVHRR observations in the winter. Whether this increase arises from either the northward transport or the boundary condition temperatures being overestimates or is a product of the surface heat flux has yet to be established. What these results do show is that the SST errors recover in both subsequent summers, to give better results than 1995, which was something of an anomalous year.