Ocean Dynamics (2011) 61:1421–1439DOI 10.1007/s10236-011-0431-6

Physical and dynamical oceanography of Liverpool Bay

Jeffrey A. Polton · Matthew Robert Palmer ·Michael John Howarth

Received: 2 December 2010 / Accepted: 28 April 2011 / Published online: 31 May 2011© Springer-Verlag 2011

Abstract The UK National Oceanography Centre hasmaintained an observatory in Liverpool Bay sinceAugust 2002. Over 8 years of observational measure-ments are used in conjunction with regional oceanmodelling data to describe the physical and dynam-ical oceanography of Liverpool Bay and to validatethe regional model, POLCOMS. Tidal dynamics andplume buoyancy govern the fate of the fresh wateras it enters the sea, as well as the fate of its sedi-ment, contaminants and nutrient loads. In this con-text, an overview and summary of Liverpool Bay tidaldynamics are presented. Freshwater forcing statisticsare presented showing that on average the bay re-ceives 233 m3 s−1. Though the region is salinity con-trolled, river input temperature is shown to significantlymodulate the plume buoyancy with a seasonal cycle.Stratification strongly influences the region’s dynamics.Data from long-term moored instrumentation are usedto analyse the stratification statistics that are represen-tative of the region. It is shown that for 65% of tidalcycles, the region alternates between being verticallymixed and stratified. Plume dynamics are diagnosedfrom the model and are presented for the region. Thespring–neap modulation of the plume’s westward ex-tent, between 3.5◦W and 4◦W, is highlighted. The rapid

Responsible Editor: Claire Mahaffey

This article is part of the Topical Collection on theUK National Oceanography Centre’s Irish Sea CoastalObservatory

J. A. Polton (B) · M. R. Palmer · M. J. HowarthNational Oceanography Centre, 6 Brownlow St.,Liverpool, L3 5DA, UKe-mail: jelt@noc.ac.uk

eastward erosion of the plume during spring tides isidentified as a potentially important freshwater mixingmechanism. Novel climatological maps of temperature,salinity and density from the CTD surveys are pre-sented and used to validate numerical simulations. Themodel is found to be sensitive to the freshwater forcingrates, temperature and salinities. The existing CTDsurvey grid is shown to not extend sufficiently near thecoast to capture the near coastal and vertically mixedcomponent the plume. Instead the survey grid capturesthe westward spreading, shallow and transient, portionof the plume. This transient plume feature is shown inboth the long-term averaged model and observationaldata as a band of stratified fluid stretching between themouth of the Mersey towards the Isle of Man. Finallythe residual circulation is discussed. Long-term mooredADCP data are favourably compared with model data,showing the general northward flow of surface waterand southward trajectory of bottom water.

Keywords Liverpool Bay · Climatology · ROFI ·Plume dynamics · Coastal dynamics · Coastaloceanography · Shelf sea · Model validation

1 Introduction

Liverpool Bay is a shallow subsection of the semi-enclosed Irish Sea (Fig. 1). The Proudman Oceano-graphic Laboratory and more recently the UK Na-tional Oceanography Centre (NOC) has maintainedan observatory in Liverpool Bay since August 2002.The observatory has evolved into a multiple platform,multidisciplinary ocean science undertaking with a highdensity and diverse range of partners and end-users.

1422 Ocean Dynamics (2011) 61:1421–1439

-3.8 -3.6 -3.4 -3.2 -3 -2.8 -2.6

53.2

53.3

53.4

53.5

53.6

53.7

53.8

53.9 10m interval

Clywd Dee

Mersey

Ribble

Site BSite A

10km

Longitude

Latit

ude

Conw

y

Liverpool

Fig. 1 Map showing the Liverpool Bay region, as part of the IrishSea, with major estuaries and long-term mooring sites A and B.The given location for site B was maintained from 5th April 2005until 26th January 2010. The major estuaries are labelled andthe tributaries are shown. The bathymetric contours are at 10-mintervals showing that site A is in about 20 m of water

While current plans are underway to extend the focusof the observatory to a wider Irish Sea perspective thereremains a requirement from the user community toprovide sustained monitoring of Liverpool Bay. Thispaper draws on over 8 years of measurements, in con-junction with model data, to describe the forcing mech-anisms and the physical oceanography of LiverpoolBay.

With a spring tidal range in excess of 10 m, theregion experiences one of the largest tidal ranges onEarth, only exceeded in the UK by the Bristol Channel.Subsequently, the bay experiences strong tidal cur-rents which interact with the seabed and horizontaldensity gradients to produce complex dynamics whichhave important consequences on the fate of freshwaterand biogeochemical pathways (Greenwood et al. (Spa-tial and temporal variability in nutrient concentrationsin Liverpool Bay, a temperate latitude region of fresh-water influence, submitted); Yamashita et al. 2011).Liverpool Bay is subject to many of the modern pres-sures on our coastal systems; it is in close proximity toa number of economically important cities and encom-passes the national boundaries of England, Wales andthe Isle of Man. The Bay receives freshwater input froma number of large English and Welsh rivers includ-ing the Mersey, Ribble and Dee (having large catch-ment areas covering heavily industrialised and highlypopulated regions) and the rivers Clwyd and Conwy(which have the comparatively pristine catchments of

rural North Wales and the Snowdownia National Park).Liverpool Bay is also important to the maritime energyindustry; the Irish Sea, and greater Liverpool Bay area,hosts numerous offshore oil and gas platforms, severalwind farms and has approved plans for significant fu-ture growth (The Crown Estate 2010). It is also thefocus of a number of proposed tidal barrier installations(Burrows et al. 2009; Walkington and Burrows 2009).Sediment dynamics are of primary concern for manyof the observatory stakeholders; much of the adjoiningcoast is protected by natural sand dune systems thatare actively accreting or eroding and yet which alsoprovide a major tourist attraction and income for thearea. The proximity of the historic, international portof Liverpool also provides a focus for research intosediment transport facilitating marine shipping chan-nel management. The intensity of human demand onLiverpool Bay combined with the complexity of thelocal dynamics provides the focus for coastal researchfrom both directive driven and blues skies researchersin order to better understand the coastal ocean.

In this article, data are presented from two fixedmooring sites (the full specifications are detailed inHowarth and Palmer (The Liverpool Bay CoastalObservatory, resubmitted)): (1) site A is located at53◦31.8′ N, 3◦21.6′ W at the Mersey Bar. The sitehas been maintained continuously since August 7th2002. The site is strongly influenced by the Merseyfreshwater outflow and to a lesser extent by the riverDee. (2) Site B is located 21 km to the west of siteA at 53◦27′ N, 3◦38.4′ W. The site was maintainedbetween 5th April 2005 and 26th January 2010, fol-lowing which the moored instrumentation was moved9 km north to the same latitude as site A. The newlocation of site B was chosen in order to better meetscientific demands and to avoid future wind farm de-velopment. In this paper only data from the originalsite B location is presented. Data from each moor-ing site and the other instrument platforms, whichcombine to make the Irish Sea Observatory, will becompared with the three-dimensional hydrodynamicalmodel, POLCOMS (Holt and James 2001; Holt et al.2005). The simulation data presented here are fromthe 1.8-km horizontal resolution configuration (Fig. 19shows this resolution in context with the LiverpoolBay subregion), with 32 evenly spaced vertical levelsat each location. The atmosphere is forced by 1◦ andsix hourly ECMWF winds and surface fluxes are com-puted using bulk formulae. The combination of ob-servational and simulation results are used to providea synoptic overview of the physical oceanography ofLiverpool Bay and to describe the fate of the riverinefreshwater. Following dynamical insights of Yankovsky

Ocean Dynamics (2011) 61:1421–1439 1423

and Chapman (1997), the freshwater, once it is in thebay, will be referred to as a plume.

The dynamics of Liverpool Bay are governed by thetides. The tides determine the fate of the fresh waterplume, the sediment, nutrient and contaminant riverineloads as they enter the sea. Therefore, to understandthe dynamical effects on chemical or biological cycles,it is necessary to understand the horizontal and verticalstructure of the tidal currents, how they vary in time,and to understand the associated mixing processes.Studying the dispersal of the fresh water plume as itenters the sea provides useful insight into how theriverine chemical, biological or sediment load mightalso disperse. In the following sections, we consider theinteractions between stratification, tidal currents andfreshwater forcing in order to identify key processesthat are dynamically important for Liverpool Bay.

2 Dynamical overview

In this section, the tidal dynamics that are fundamentalto Liverpool Bay oceanography are investigated and re-viewed with a combination of observational and modeldata. For a detailed review of broader ranging Irish Seadynamics, refer to Bowden (1980).

2.1 Spring–neap and semi-diurnal tidal cycles

Gravitational forces of the Sun and Moon distort thesea surface and generate tidal waves. The rotation of

the earth, under the Sun and Moon, results in semi-diurnal components of the total tidal signal that explainmost of the Irish Sea’s tidal variability. These are theM2 and S2 constituents, with a 12.4- and 12.0-h period,and are associated with the gravitational pull of theMoon and Sun, respectively. Similarly, the orbit of theMoon around the Earth results in a twice monthlyalignment of the Earth, Moon and Sun. The alignmentof the gravitational pull between the bodies modulatesthe tidal amplitudes with a 2-week period. This cycleis known as the spring–neap cycle. Spring tides occuron the alternating weeks around the time when theMoon is either full or new, and are associated with thelarger tidal range. Neap tides have the smaller tidalrange and occur when the Moon is about half full,that is when the Sun, Moon and Earth are furthestfrom mutual alignment. Figure 2a shows the near bedpressure recorded at site A for a typical 4-week period.Measured in decibars, the pressure gives an accuraterepresentation of sea surface height (in m). The signalis dominated by two periods: the semi-diurnal tidalwave and the spring–neap cycle that gives rise to twospring tides and two neap tides per month. Notice thatthe consecutive spring tides have different amplitudes.These slowly evolving modulations can be representedwith additional tidal constituents that account for fac-tors such as the Earth’s tilt and orbit eccentricities. Thedifference between the successive spring tides shownis accounted for by the Moon’s elliptical orbit. Fora detailed description of tidal mechanics see Pugh(1987).

04/09/05 11/09/05 18/09/05 25/09/05

19

20

21

22

23

24

25

26

27

28

Date

Hei

ght a

bove

bed

(db

)

00h 06/05/04 12h 06/05/04 00h 07/05/04 12h 07/05/040

5

10

15

20

25

30velocity magnitude (m/s)

Date

Hei

ght a

bove

bed

(m

)

0.2

0.4

0.6

0.8

1

a b

Fig. 2 Tidal variations recorded at site A in Liverpool Bay.a Left panel, near-bed pressure showing the semi-diurnal tidevariation in sea surface height modulated by two spring–neap

cycles. b Right panel, ADCP east-west current data show themagnitude as a function of depth and time for four tidal periods

1424 Ocean Dynamics (2011) 61:1421–1439

Fig. 3 a Irish Sea co-tidalchart for semi-diurnal M2tide. Thick lines represent themaximum M2 tidal elevationin metres. Thin linesrepresent the relative phaselag of high tide (given inminutes with reference tohigh tide at Liverpool). Southof Liverpool the phases arenegative as the tidepropagates generallynorthwards. b The depthaveraged maximum currentsfor an average spring tide(in ms−1)

M2 Co-tidal chart

Longitude

Latit

ude

2.6

2.4

2.221.8

1.6

4.2

3.43

2.62.

21.8

1.4

1

1.4

1.2

1

0.8

1.2

0

20

40

-20-40

-80

-120

-180

-200

-220-240-260-280

-300

-320

400

–7 –6 –5 –4 –351

51.5

52

52.5

53

53.5

54

54.5

55

Longitude

Latit

ude

Spring tide max current amplitude chart

–4 –5 –6 –7 –851

51.5

52

52.5

53

53.5

54

54.5

55

55.5

56

0.001

0.25

0.5

0.75

1

1.25

1.5

2

2.5

a b

In addition to long period modulation, high-frequency corrections are also required to accuratelyrepresent the effects of shallow water on a propagatingtidal wave, since the wave is slowed by bed frictionand distorted by nonlinear effects. For example, Fig. 2bshows the magnitude of the depth-varying east-westcurrent at site A measured over four tidal periods.Here, the tidal currents are asymmetric with the great-est speeds on flood tide. For practical purposes, awayfrom the shore in Liverpool Bay, the tidal wave ele-vation can be reconstructed with the largest ten con-stituents. (At site A, 50% of the amplitude variabilityis described by M2 and S2 and 80% is described by thelargest ten constituents.)

Spring–neap and ebb-flood statistics can be obtainedfor site A. Observational data from May 2003 to May2005 give current statistics representative of the Bay.Comparing the depth mean maximum current magni-tudes for each tidal cycle, filtering out ebb-flood asym-metry, reveals that the average ratio of consecutivespring current to neap currents is 2, with a time averageneap flow of 0.4 ms−1 and a time average spring flow of0.7 ms−1. This is consistent with the amplitudes of theM2 constituent being about three times greater than theS2 constituent. The ratio of east-west depth averagedflood and ebb peak speeds is found to be 1.2.

In an area as large as the Irish Sea, the tides havespatial variability as well as the familiar temporal vari-ability. This is determined by complex interactions be-tween the tidal wave and the geometry of the coastlineand seabed. Both spatial and temporal information can

be simultaneously represented using a co-tidal chart. Aco-tidal chart contours the maximum tidal amplitudeand the time to high tide (or the phase) from a fixedreference point. Figure 3a shows the co-tidal chart forthe M2 tide (c.f. Kwong et al. 1997). In LiverpoolBay, the tide propagates as an east-west standing wave.More generally, the tide in the Irish Sea propagatesanticlockwise around the amphidromic point near thesoutheast coast of Ireland.

The magnitude of the tidal currents are determinedby the rate at which the sea water is moved aroundby the tidal forces with the rising and falling tides.Figure 3b shows the magnitude of the depth averagedmaximum tidal velocities associated with an averagespring tide.1 Maximum currents exceed 2 ms−1 aroundheadlands and are about 0.75 ms−1 in the LiverpoolBay. Current magnitudes are elevated in the SevernEstuary because the geometry of the Bristol Channelis resonant at the semi-diurnal frequency (Fong andHeaps 1978).

2.2 Vertical structure of momentum: tidal ellipses

Though the currents in Liverpool Bay are predomi-nantly orientated in the east-west direction, tidal cur-rents do not, in general, simply flow back and forth.

1Remarkably, the gross patterns in Fig. 3b can be derived fromthe co-tidal chart if the flow is assumed to be frictionless and thatthe acceleration is wholly forced by the barotropic tide.

Ocean Dynamics (2011) 61:1421–1439 1425

At a given location, a current metre would reveal thatthe two-dimensional horizontal currents rotate theirdirection through all points of the compass. Over atidal cycle, the horizontal current vector describes acomplete ellipse, which can be uniquely described bythe sum of two counter-rotating horizontal velocityvectors. Only in special cases does this elliptical pathhave a zero minor axis component such that the tidalcurrent does truly flow back and forth. It is the complexnature of the Irish Sea’s surrounding coastline that de-termines the shape and rotation direction of the depth-averaged tidal ellipses. The tidal ellipse structure alsovaries with depth. This is a result of the Earth’s rotationbiasing anticlockwise and clockwise rotary componentsof the tidal ellipses differently. For example, if at somedepth the superposition of clockwise and anticlockwiserotations cancel to produce back and forth tides, thenslightly deeper currents will have an anticlockwise ro-tation and slightly shallower will have a clockwise rota-tion. At site A, the tidal ellipse analysis shows the flowis rectilinear at 12 m above the bed (Fig. 4). Indeed,above this depth the ellipse rotates clockwise (red)and beneath anticlockwise (blue). For a more detailedanalysis of tidal ellipses, refer to Prandle (1982) andSoulsby (1983).

nort

hwar

d ve

loci

ty (

m s

–1)

M2 tidal ellipses: blue anti–clockwise, red clockwise

eastward velocity (m s–1)

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

–0.5–1 0 0.5 1

Fig. 4 Tidal ellipse analysis at site A. Red ellipses denote clock-wise rotations at the semi-diurnal frequency and blue ellipsesrotate anticlockwise. Each ellipse is plotted on east-west andnorth-south velocity axes. Each ellipse is displaced on the y-axisby an amount corresponding to its bin height above the sea bed,such that all the crosses represent zero velocity. Near-bed ellipses(blue) are anticlockwise and orientated with the major axis in theeast-west direction. Surface ellipses are clockwise (red) with themajor axis orientated SE-NW. The data are from depths belowthe low tide level only. The vertical bin interval is 1 m

2.3 Vertical structure of heat: stratification

Taking the Irish Sea as a whole, the sea is warmedby solar heating in the summer and then cools inthe winter. Away from coastal regions, where thereare freshwater inputs, solar heating can control thelocal stratification unless the tidal mixing is sufficientlystrong to erode vertical density gradients. In re-gions like Liverpool Bay, the stratification is buoy-ancy controlled; freshwater continually replenishes thestratification that tidal mixing seeks to erode. To un-derstand the tidal mixing mechanism, consider the sit-uation shown in Fig. 2b. During this period, it is ap-parent that the current velocities diminish with depth.Though the fluid is evenly forced by horizontal pres-sure gradients, as a consequence of the gravitationallyinduced sea surface height gradients, the fluid nearestthe sea bed feels frictional forces exerted by the seabed on the flow. This retards the bottom flow andgenerates a vertical shear in the horizontal velocity.With typical magnitudes of tidal currents, these shearflows are generally unstable and easily turn turbulent.The resultant boundary layers grow in height (as long asthe tidal shear remains sufficiently strong relative to thestabilising effects of stratification) potentially envelop-ing the whole water column. The competition betweenthe turbulent boundary layer mixing and the stabilisingeffects of stratification are succinctly parameterised bya stability parameter, H/U3, where H is the waterdepth and U is the amplitude of the surface tidal ve-locity (Simpson and Hunter 1974). Taking velocitiesfrom a barotropic M2 tidal model and comparing themwith satellite observational data (Pingree and Griffiths1978) as well as top to bottom sea temperature (Bowersand Simpson 1987) a critical value for the stabilityparameter is obtained to predict the location of fronts.Though meteorological effects and seasonal variabilitycan affect the timing and location of surface temper-ature fronts the critical value of S = log10(H/U3) =2.7 ± 0.4 is generally accepted (Simpson and Sharples1994). The remarkable success of the parameter S inpredicting thermal front locations is evident in Fig. 5,showing a comparison between model stratification andS deduced from the POLCOMS shelf wide model. Innear coastal regions, like Liverpool Bay where salinityand not heat controls the density, this relationship thatpredicts fronts is not so robust (Fig. 5). In these regions,the freshwater forcing can not be neglected.

2.4 Freshwater forcing

Interactions between the fresh water discharge fromthe surrounding estuaries (the Clwyd, Dee, Mersey and

1426 Ocean Dynamics (2011) 61:1421–1439

Fig. 5 Figure showing top tobottom density difference, forJuly 07, compared withpredicted frontal locationbased on S = log10(H/U3)

parameter. The densitydifferences in (a) arecomputed from daily meansfor July 2007. The contourvalues are, with increasingbrightness, 0.1 and 0.4 kg m−3

(b) shows S = log10(H/|U |3),computed using the timeaverages of hourly barotropiccurrent magnitudes and waterdepths over the month of July2007. Contours that separateregimes are, with increasingbrightness, S={2.3,2.7,3.1,4}.These data are POLCOMSmodel output

lon

lat

–7 –6 –5 –4 –351

51.5

52

52.5

53

53.5

54

54.5

55ba

the Ribble) and tributaries with sea water result instrong horizontal density gradients that complicate thetidal forcing. Regions such as Liverpool Bay, where thedynamics are strongly influenced by estuarine outfloware called ROFIs, Regions of Freshwater Influence

(Simpson 1997). Data from the four catchment basinscome from historical Environment Agency river gauges(archived at the Centre for Ecology and Hydrology),these are scaled to represent downstream accumula-tion from unmeasured tributaries before reaching the

Fig. 6 River flux data forLiverpool Bay showing 7-dayrunning mean values for eachcatchment basin. The thickmonotonic increasing line isthe cumulative volume fluxfrom all the rivers in the Bay.The cumulative flux ofriverine water is 7.3 × 109 m3

for the year 2007

500 100 150 200 250 300 3500

50

100

150

200

250

300

350

Riv

er fl

ux (

m3 .

s–1 )

Julian days

0

2

4

6

8

Cu

mu

lati

ve r

iver

flu

x (x

109 m

3 )

ClwydDeeMerseyRibble

Ocean Dynamics (2011) 61:1421–1439 1427

estuary mouth. The Clwyd catchment includes mea-surements from the Clwyd2 and Elwy. The Dee catch-ment includes measurements from the Alyn and Dee.The Mersey catchment includes measurements fromthe Weaver, Dane, Wincham Brook, Irwell, Merseyand Sankey Brook. The Ribble catchment includesmeasurements from the Douglas, Lostock and the Rib-ble. Figure 1 shows the catchment mouth location. Noattempt is made in the model to represent ground waterseepage. Seven day running mean flow rates are givenin m3 s−1 and are presented for 2007 in Fig. 6. Actualdaily mean fluxes vary by over 300 m3 s−1/day makingthe rivers highly intermittent. There is no clear seasonalcycle to the flow data, though the river time series arehighly correlated. Table 1 gives the daily flow ratessorted by magnitude and binned by the percentage timefor which the value is the upper limit of the flow. Forexample, the sum of the rivers have a flow that is lessthan 61 m3 s−1 for 10% of days in the year and a flowthat is between 509 and 1,404 m3 s−1 also for 10% ofdays in the year. Cumulatively, over the year, the fourcatchment basins flux 7.3 × 109 m3 of water into theBay (Fig. 6), this yields an average flux of 233 m3 s−1.Therefore, a volume of sea bounded by the latitude andlongitude of the Ribble and Clwyd would take about3 years to fill at this rate. Notice that the mean daily fluxexceeds the daily average median value (143 m3 s−1)and the weekly average median value (161 m3 s−1,not shown). Thus on daily and weekly timescales thefreshwater forcing is characterised by high intensity andshort duration rainfall events. It is unknown how theepisodic nature of the freshwater modifies how rapidlythe plume mixes in Liverpool Bay. Similarly, work isunderway to improve the quality of the freshwater fluxfor use in high resolution hydrodynamics models. Inaddition to the estuarine flux volume varying through-out the year, the temperature and salinities also varyand both contribute to the buoyancy of the plume.3

Salinity and temperature are directly measured by aninstrumented ferry as it leaves the Mersey for Ireland(Fig. 7). There is a clear annual cycle in the temperaturefield but no annual cycle in salinity as this is determinedby episodic rain events. The temperature of the estuaryclosely matches the air temperature climatology, since

2The Conway contributes to the freshwater budget of LiverpoolBay but since data have been historically unavailable its contri-bution is incorporated by means of scaling the Clwyd.3At constant pressure and at typical salinities a change in tem-perature of 5◦C results in a change in density of about 1 kg m−3.Similarly, at constant pressure and at typical temperatures achange in salinity of 1 psu is required to change the density byabout 1 kg m−3.

Table 1 Volume flux statistics, by frequency, for estuariesflowing into Liverpool Bay

Estuary 10% 50% 90% 100%

Clwyd 12 31 121 407Dee 11 26 108 277Mersey 26 51 165 515Ribble 9 28 131 422Total 61 143 509 1404

Daily mean fluxes (m3 s−1) are sorted by magnitude. Tabularvalues represent the maximum flow rate for the associated timepercentage bin

the freshwater of the estuary is fed by a network ofshallow streams which are efficiently either heated orcooled by the atmosphere. Since the open sea hasgreater thermal inertia than the atmosphere, the seatemperatures lag the freshwater temperature. In winter,therefore, the sea is generally warmer than the estu-aries, whereas in summer the estuaries are generallywarmer than the sea. Figure 8 shows the temperaturedifference, along the ferry track, between the mouthof the Mersey and the Mersey Bar (near site A).The amplitude of the annual cycle in the temperaturedifference is much smaller than the amplitude of theabsolute temperature, and is about 2◦C. Though thefreshwater always make that estuaries plume positivelybuoyant, the 4◦C temperature variation means that inthe summer the stratification is enhanced. This will beaddressed in Section 2.6.

Mixing processes in the estuaries are subtle andthe circulation is complicated. These are beyond thescope of this article, where we restrict attention to thedynamics of fluid on leaving the estuary. However,for a contemporary review of estuarine processes seeMacCready and Geyer (2010).

2.5 Tidally induced periodic stratification

Near coastlines, with rivers and estuaries, freshwateringress can dominate the stratification. In these salin-ity dominated ROFIs stratification fronts cannot bereliably predicted using the H/U3 parameter (as inSection 2.3). This is because the freshwater distribution,unlike solar heating, is not spatially uniform. In theseregions, stratification modifies the vertical mixing rateon a tidal time scale. Then the variable mixing rate inturn modifies the tidal currents. In the following, weaddress the effects of tidally varying stratification onthe tidal dynamics.

The semi-diurnal tide in Liverpool Bay induces aperiodic stratification. If we consider that the freshwater plume, as it leaves the estuaries, is of one densityand that the salty sea water into which it flows is of a

1428 Ocean Dynamics (2011) 61:1421–1439

0 200 400 600 800 1000

16

18

20

22

24

26

28

30

32

Salinity at mouth of Mersey

days since 1 January 2008

salin

ty (

psu)

0 200 400 600 800 10000

2

4

6

8

10

12

14

16

18

20Temperature at mouth of Mersey

( ˚C)

days since 1 January 2008

Fig. 7 Mersey Ferry data for 3 years at mouth of Mersey (Mersey Narrows) showing salinity (left panel) and temperature (right panel).There is a clear annual cycle in temperature but not in salinity

greater density, then the semi-diurnal tide will advectthe plume bodily to the east on the rising tide, and tothe west on the falling tide. However, since the ebb andflood flow of the tide is always retarded by frictionaldrag at the sea bed, the flow at the bed always lags theflow higher up the water column. Thus, every ebb tidelight water is advected over heavy water. On the flood

Fig. 8 Temperature difference between the Mersey Bar (nearsite A) and the mouth of the Mersey (Mersey Narrows) showinga clear annual cycle. Grid lines show 1st January for years 2008,2009 and 2010. In the winter, the estuary is colder than the sea.In the summer, the estuary is warmer than the sea. The data arefrom the instrumented ferries

tide this transient stratification is undone as shownschematically in Fig. 10. This process is called StrainInduced Periodic Stratification (SIPS) after the phrasewas coined by Simpson et al. (1990).

The evolution of stratification can be examined interms of the potential energy anomaly, φ (Simpson andBowers 1981),

φ = 1

H

∫ 0

−H(ρ(z) − ρ)gz dz, (1)

where ρ = 1

H

∫ 0

−Hρ(z)dz. (2)

Here, H is the water column depth and ρ(z) is in situdensity. This parameter represents the work requiredto fully mix the water column. Therefore increasingstratification has a positive effect on φ whereas mixingreduces φ. Figure 9a shows the maximum (φmax) andminimum (φmin) value of φ over a tidal (M2) periodat site A for the year 2005. Positive φmax indicates thatstratification occurs at least once during the tidal cycle.It is clear that this is common throughout the year withonly a few instances of low φmax identified. Defining alimiting potential energy anomaly, φlim, correspondingto a top to bottom density difference of 0.05 kg m−3

(or an equivalent top to bottom temperature differenceof 0.25◦C) to classify a mixed water column (allowingfor pressure sensor error) we calculate stratificationstatistics for site A. It is found that the water columnis persistently mixed (that is, throughout a full tidalperiod) only 11% of the time and that the water columnis persistently stratified for 24% of the time. Periods

Ocean Dynamics (2011) 61:1421–1439 1429

Fig. 9 a Top panel:Maximum (black) andminimum (red) φ over a tidalperiod. The green lineindicates stratificationequivalent to 0.05 kg m−3 in25 m water depth. b Lowerpanel: Percentage of time permonth site A is mixed (red),periodically stratified (blue)and stratified for a full tidal(M2) period

that alternate between stratified and mixed conditionsduring a tidal period, i.e. φmax > φlim and φmin < φlim,occur for the remaining 65% of the time.

Sorting the occurrence of the three states (persis-tently mixed, temporary/periodic stratification and en-during stratification) into monthly averages (Fig. 9b)shows the likelihood of each state to be highly variable.

a)

b)

freshsalty

salty fresh

Fig. 10 Figure showing how periodic stratification is inducednear a strong source of freshwater when the current flows acrossthe density gradient. A horizontal density gradient is establishedby fresh water flowing into the saltier sea. a On the falling tidelight (fresher) water is advected over the ambient denser (saltier)water establishing a vertical density gradient. b On the rising tidethe flow is reversed and the stratification is removed

There is however some evidence of a seasonal cycle inenduring stratification, with a greater likelihood dur-ing summer months (when solar heating is greatest).Similarly intuitive is the greater likelihood of persis-tently mixed periods occurring during winter months(when solar heating is insufficient to restore thermalstratification following tidal, or wind, mixing). Otherprocesses, for example wind mixing (Burchard 2009;Verspecht et al. 2009a), can also modify the temporarystratification at the site. Additional processes will how-ever act within the context of the regions tidal dynamicsand will therefore have a periodic component due tothe tidal advection of water masses. These events arecombined under the SIPS process to allow for simpleclassification which the authors believe to be of greatestuse to the reader.

The occurrence of periodic stratification is impor-tant to the region’s dynamics. Stratification acts likea lubricant between horizontal layers of fluid, withstronger stratification tending to decouple the fluidlayers. The stratification controls the vertical distrib-ution of horizontal momentum throughout the watercolumn. Therefore, a time varying stratification canyield a time varying modification to tidal currents. Thisphenomena is observed at site A. Verspecht et al.(2010) report that the tidal ellipse structure indeedvaries with stratification on a semi-diurnal timescale.Similarly, analysing data from the Rhine region offreshwater influence, Visser et al. (1994) identifies thisphenomenon to explain how the stratification, whichvaries with the spring–neap cycle, modifies the surfacecurrent ellipses over the same time period.

In Liverpool Bay, Rippeth et al. (2001) report an ob-served periodic straining influence on dissipation. Over

1430 Ocean Dynamics (2011) 61:1421–1439

SIPS periods small scale vertical mixing is inhibited bythe increased stability. During the flood tide high levelsof dissipation penetrate from the sea floor to the sur-face. During the ebb tide, as the fluid stratifies, verticalmixing is inhibited and the high levels of dissipationare confined to the deepest fluid. At the end of theflood tide high levels of dissipation were also reported.These were inferred to be convective events as thedense water overtops the light fluid (Fig. 10) and werecorroborated by findings using a 1D model (Simpsonet al. 2002).

For flow that is elliptical, rather than rectilinear, theSIPS asymmetry can introduce a tidal modulation inthe layer coupling, or eddy viscosity, which can resultin a one way offshore pump of fresh water. In Liver-pool Bay, the major axis tidal current dominates thetidal ellipse and is predominantly east-west. Along thenorth-south English coastline in regions of freshwaterinfluence SIPS events are found as freshwater is ad-vected on and offshore by the major axis componentof the tide. Along the adjacent North Wales coastline,however, there is a haline stratification that runs nearparallel to the coastline. Here the minor axis tidalellipse component can induce a SIPS effect (Palmer2010). This differs from the Rhine effect (Visser et al.1994), where ellipses were modified over the springs,or neaps, period. Offshore of the north Wales coastobservations are of sufficiently high frequency that in-tertidal SIPS to mixed transitions are observed. Thisintroduces asymmetry such that there is net offshoremass flux of fresh water. When the minor axis flowis offshore at the surface SIPS is created. The surfaceand the bottom layers decouple and the top layer ispredominantly clockwise while the bottom layer is pre-dominantly anticlockwise. As the surface minor axisflow reverses and brings saline water onshore the fluidbecomes convectively unstable and vertically mixes.Since there can be no net mass flux onshore, because ofthe land barrier, the resultant surface mass flux onshoreis also zero. Hence, over a tidal period there is a netoffshore flux of surface fluid and a corresponding neton shore flux of saline fluid (Palmer 2010).

2.6 Plume dynamics

The riverine water enters the bay as a body of fresh-water that flows northwards, along the English coast,and is eroded by tidal processes (Section 2.5). Thisbody of freshwater, while it is distinguishable fromthe ambient saline water, is referred it as a plume.During spring tides, when tidal mixing is most vigorous,the plume is vertically mixed with an eastward frontalboundary near 3.5◦W. During neap tides, when the

mixing is weaker, a shallow surface layer can extendwestward from the main body of the plume out as faras 4◦W, (Hopkins and Polton (Scales and structure offrontal adjustment and freshwater export in a region offresh water influence, resubmitted), see also Simpsonet al. 1991; Sharples and Simpson 1993). Simpson andBowers (1981) predict that the spring–neap frontalmigration would be small for a system with constantwind and buoyancy forcing. However, simulations sug-gest that the forcing in Liverpool Bay is sufficientlyimportant and variable to permit the front to migrate.Figure 11 illustrates the spring and neap frontal mi-gration of the plume. The figure shows east-west crosssections of temperature, salinity and density throughLiverpool Bay for a neap high tide (panel a) and theprevious spring high tide (panel b). During the neaptide there is insufficient energy in the tidal flow to erodethe stratification of the buoyant plume all the way tothe surface. In this situation persistent, or runaway,stratification can prevail over multiple tidal cycles andthe shallow surface stratified layer extends to 4◦W.During spring tides, however, the plume is eroded, frombelow, and the front retreats back to around 3.3◦W. Notall neap tide produce runaway stratification. Through-out the spring and summer the temperature of the estu-arine outflow gives additional buoyancy to the fresh-water plume. Following the autumn equinox, for thewinter months, the estuarine temperatures are colderthan the ambient sea temperature (Fig. 8). During thesemonths, the temperature of the freshwater reduces thenet buoyancy of the plume to the extent that it istemperature controlled. Figure 11c shows a winter crosssection at low tide following a neap tide event. Atthis phase of the tide, a surface plume would be at itsmost westward extent. However, during winter monthsair–sea fluxes regularly render the fluid convectivelyunstable and vertically homogenise the fluid. Addi-tionally, cooler winter estuarine temperatures reducethe strength of the, salinity controlled, lateral densitygradient. Consequently, persistent winter stratificationevents that endure multiple tidal cycles rarely occur.

Figure 12 shows the spring–neap modulation of den-sity diagnostics throughout 2007. The spring–neap cycleis manifest in sea surface height variability, shown inpanel (a). Events when the stratification, shown inpanel (d), are maximal correspond to neap tides. Panels(b) and (c) show the bottom and surface densities forthe 22, 23, 24, and 25 kg m−3 potential density contours.(The 21 kg m−3 contour does periodically appear in thisdomain, though for figure clarity it is masked.) Sincethe time axis spans an entire year, the comparativelyrapid semi-diurnal front variability makes the contoursappear as shaded bands. During neap tides runaway

Ocean Dynamics (2011) 61:1421–1439 1431

dept

h (m

)

–3.7

–10

0

–30

–20

–40

–10

0

–30

–20

–40

–10

0

–30

–20

–40

–10

–30

–20

–40

–10

–30

–20

–40

–10

–30

–20

–40

–10

0

–30

–20

–10

0

–30

–20

–10

0

–30

–20

–3.6 –3.5 –3.4 –3.3 –3.2

–3.7 –3.6 –3.5 –3.4 –3.3 –3.2

–3.7 –3.6 –3.5 –3.4 –3.3 –3.2

–3.7 –3.6 –3.5 –3.4 –3.3 –3.2

–3.7 –3.6 –3.5 –3.4 –3.3 –3.2

–3.7 –3.6 –3.5 –3.4 –3.3 –3.2

–3.7 –3.6 –3.5 –3.4 –3.3 –3.2

–3.7 –3.6 –3.5 –3.4 –3.3 –3.2

–3.7 –3.6 –3.5 –3.4 –3.3 –3.2

dept

h (m

)de

pth

(m)

22

24

23

21

25

Longitude

Temperature

Salinity

Density

dept

h (m

)

9

10

11

12

dept

h (m

)

29

30

31

32

33

Longitude

dept

h (m

)

22

24

23

25

Temperature

Salinity

Density

dept

h (m

)de

pth

(m)

29

14

13

12

33

32

31

30

dept

h (m

)

22

24

23

Longitude

Temperature

Salinity

Density

c) Day 295

a) Day 147 b) Day 13613

12

11

10

32

33

31

30

29

Fig. 11 East-west cross section of model temperature (◦C), salin-ity (in psu) and density (in kg m−3) through Liverpool Bay (andthrough site A) from 2007. a During neap tides, the plume has athin surface layer that is not mixed by the low energy tide. This

allows the plume to extend westward. b During spring tides theplume is well mixed back to 3.3 W. c A winter section during aneap low tide. In the winter, the temperature gradient acts againstthe freshwater buoyancy preventing run away stratification

stratification occurs when the tide no longer verticallymixes the entire water column and a thin light layerdecouples from the bed fluid. During spring tides sur-face intertidal excursion of density contours can exceed10 km making the interpretation of fixed point timeseries more challenging. Figure 12d confirms that fewerstratification events persist over complete tidal cyclesduring winter months. Tidal mixing is not required tolimit the westward extent of fresh and shallow surfacewaters during these times as the region is convectivelyunstable due to radiative heat loss.

As well as poleward freshwater export by the resid-ual circulation we see that lateral dispersal of freshwa-ter is modulated by the spring–neap cycle. The exis-

tence of a broad horizontal density gradient beneaththe low salinity surface layer (Figs. 11a and 12b) re-minds us that SIPS induced convection is mixing fluidon a semi-diurnal timescale (Simpson et al. 1990).

2.7 The role of wind and waves

Synoptic scale weather patterns induce changes in sealevel that, in conjunction with spring tides, can causecoastal flooding. While these events can have hugeeconomic impact on coastal communities the actualimpact of the storm surge on the dynamics is to simplyincrease the short-term average fluid depth. The wind

1432 Ocean Dynamics (2011) 61:1421–1439

Fig. 12 East-west crosssection of density throughLiverpool Bay from FormbyPoint, through site A, varyingwith time for 2007. a Seasurface height (in m). b, c Thetop and bottom densitycontours. The darkestcontour shows the 22 kg m−3

locus. Intervals of 1 kg m−3

up to 25 kg m−3 are shownwith lightening shades of grey.d Threshold stratification(kg m−3): |�ρ| < 0.05 (white),0.05 ≤ |�ρ| ≤ 1 (grey) and|�ρ| > 1 (black). Circlemarkers on the time axiscorrespond to snap shotsin Fig. 11

ρ

and the waves that are generated, however, have a fargreater effect on the dynamics. The strongest winds atmid-latitudes are associated with depressions that trackfrom west across of the British Isles. These depressionsare accompanied by winds which veer from south-westto north-west, generally lasting one to2 days at anylocation. These winds have been measured at HilbreIsland, in the mouth of the Dee, since April 2004. Thestrongest wind recorded in the 6 1

2 -year period being31.4 ms−1. This is equivalent to a Beaufort Force 11

(exerting a surface stress in excess of 3 Pa on the oceansurface), though 134 passing gale systems have beenrecorded (that is with winds in excess of 17.2 ms−1).Any shore-based wind measurement will be influencedby the local topography. In the case of Hilbre, strongwinds from the south-west are moderated by the Welshhills. In addition, winds from between east and south,which are common although usually less than galeforce, are channelled by the Dee. Offshore measure-ments are scarce but a 2-year record at the site of the

Fig. 13 Histograms of a windspeed at Hilbre measuredevery 10 min since April2004 in the left panel andb significant wave height atsite A sampling every 30 minsince November 2002 in theright panel. (Wave data fromCEFAS WaveNet waveriderbuoy)

ba

Ocean Dynamics (2011) 61:1421–1439 1433

proposed Gwynt y Môr wind farm, operated by nPowerRenewables, shows that the topographic influence onHilbre winds is limited and that wind speeds recordedat Hilbre are representative of the wider area. For acomparison between Hilbre and offshore winds, seeWolf et al. (2011). Figure 13a shows a histogram of windspeeds from the 10 m mast at Hilbre.

Waves also impact the local dynamics of LiverpoolBay. Principally, waves generated by the wind affectthe degree of mixing within the water column andin shallow water this is especially important for sedi-ment resuspension. In Liverpool Bay the largest wavescome from the west through to the north, maximis-ing the input of momentum by strong winds over along fetch. The waves are locally generated withinthe Irish Sea with the impact of swell being minimal,Wolf et al. (2011). Waves have been measured at theMersey Bar, site A, site since November 2002; thelargest significant wave height is 5.4 m, with a cor-responding peak period of 12 s. The significant waveheight is less than 2 m for 93% and less than 1 m for68% of the time. Figure 13b shows significant waveheight data at site A using the CEFAS WaveNet wa-verider buoy. Both winds and waves vary from yearto year and seasonally. In general, both are weakestbetween April and August but of course in the UKstorms (or calm periods) can occur at any time ofthe year.

3 Liverpool Bay climatology

In this section, long-term average properties of temper-ature, salinity and currents are presented. Combining

observational and model data allows us to validate themodels (and see where improvements need to be made)and also to infer from the model the climatologicalpicture for variables that are beyond the scope of theobservational campaign.

3.1 Temperature and salinity

Following 8 years of sustained CTD observations (on a9 × 9-km grid of 34 stations) in Liverpool Bay compos-ite spatial maps of the temperature and salinity struc-ture are constructed. The model statistics are compiledfrom a 2007 run. The model means are computed fromcontinuous data (down to the timestep discretisation)whereas the CTD observational means are a compositeof stations visited on 68 cruises (not all of the stationswere visited on each cruise). Given that the errorsin the model are principally attributed to inaccuratefreshwater forcing (discussed below) only model datafrom 2007 are used in these statistics as this year hadthe most reliable freshwater forcing data.

Figure 14 shows the time and depth averaged densityfrom the observations and the model. The density fieldis characterised by a broad east-west gradient, with thelightest fluid being found near the coast and estuarymouths. The model over estimates the east-west densitygradient across Liverpool Bay, by almost a factor of 2.(This is shown to be due to freshwater flux errors in themodel.) The horizontal variations in density over thescale of the Liverpool Bay greatly exceed the verticaldensity variations.

Figure 15 shows the top to bottom density difference,again calculated from the CTD survey array and bythe model. The observations show a maximum top

Fig. 14 Depth-averageddensity (in kg m−3) fromobservations (left) and model(right). Red arrows show thespatially varying meansurface current, and blackarrows show the mean nearbed current

53.3

53.4

53.5

53.6

53.7

53.8

53.9

0.1 m/s

–3 –3 –3 –3.8 .6 .4 .2 –3

53.3

53.4

53.5

53.6

53.7

53.8

53.9

20.5

21

21.5

22

22.5

23

23.5

24

24.5

25

25.5

1434 Ocean Dynamics (2011) 61:1421–1439

Fig. 15 Top minus bottomdensity differences(in kg m−3). Left panel: 8-yearmean values taken fromobservations. Right panel:2007 simulation values

to bottom density difference of about 0.5 kg m−3,which is one contour interval in the horizontal densitygradient map. Consequently climatological spatialmaps of Liverpool Bay depth averaged quantities andtheir equivalent surface quantities are very similar andthe character is determined by the horizontal variabil-ity. Conversely, because the sea is so shallow, verticalgradients greatly exceed the horizontal gradients. Thisresults in phenomena like tidal ellipses where, com-paring metre for metre in the horizontal and verticaldirections, the current structure varies so much morerapidly in the vertical direction that horizontal variabil-ity can be neglected when describing the structure. Thetime-averaged survey data show an area of enhancedstratification that runs from the south-east corner tothe north-west corner of the grid. The model supportsthis and extends the area to show that there is a bandof stratified band that emerges from the Mersey region

and extends out towards the Isle of Man. This is the re-sult of the tidally induced periodic stratification by themajor axis tidal flow. Though the model does appearto overestimate the stratification towards the northernextent of the survey area, it is likely that some sortof stratification signature would exist there in the realworld. The model’s over prediction of the stratificationis suggestive that the vertical mixing scheme is notsufficiently energetic. In this model, configuration theCanuto et al. (2001) k − ε turbulence scheme is used,which is generally thought to be the most cost effectiveocean mixed layer turbulence scheme (Burchard andBolding 2001; Holt and Umlauf 2008). It could perhapsbe better tuned for ROFI dynamics.

The density distribution (Fig. 14) is highly correlatedwith salinity. Figure 16 compares near surface salinity.Again the model over estimates the east-west salinitygradient. Extrapolating the observations we see that

Fig. 16 Near-surface salinity(in psu). Left panel: 8 yearmeans values taken fromobservations. Right panel:2007 simulation values

Ocean Dynamics (2011) 61:1421–1439 1435

Fig. 17 Comparison ofnear-surface temperatures(in ◦C) in summer betweenthe model and observations.The left panel showsobservations and the rightpanel shows model data.Here, summer corresponds tobeginning of April untilmid-August

53.3

53.4

53.5

53.6

53.7

53.8

53.9

–3.8 –3.6 –3.4 –3.2 –3

53.3

53.4

53.5

53.6

53.7

53.8

53.9

11

11.5

12

12.5

13

13.5

14

there is an east-west salinity and density differencesof approximately 3 psu and 2.5 kg m−3. It is clear,therefore, that the density gradient is controlled bythe salinity difference (as an equivalent difference intemperature across Liverpool Bay of 11◦C would berequired to generate such a large density gradient). Thefigures of surface salinity and depth averaged densityare nearly identical in form, supporting the argumentthat climatological spatial maps are dominated by thehorizontal structure.

The mean temperature contributes little to the meandensity, though it is well simulated by the model.Unlike salinity, temperature has a strong annual cy-cle with the east-west temperature gradient switchingdirection from summer to winter. Figures 17 and 18shows that the river outflow is warmer than the ambientsea temperatures in the summer months, making the

freshwater more buoyant, but also that in the winter thefreshwater is colder than the ambient sea temperatures.The reversal occurs because the river temperatures aremore tightly coupled to the atmospheric temperaturethan the sea temperature, which has greater thermalinertia.

The depth-averaged density gradients (Fig. 14) aremaintained over time, against the eroding influence ofthe tides and slumping under gravity, by the continualreplenishing of freshwater from the estuaries and alsoby the action of the Coriolis force. A significant sourceof error in the model density structure results fromuncertainty in the freshwater forcing at the estuaries.Nevertheless the balance of forces between pressuregradients and the Coriolis force lie at the heart ofa seminal work by Heaps (1972) that describes thelong-term mean depth-varying circulation observed in

Fig. 18 Comparison ofnear-surface temperatures inwinter between the modeland observations. The leftpanel shows observations andthe right panel shows modeldata. Here, wintercorresponds to middle ofAugust until the end ofMarch

1436 Ocean Dynamics (2011) 61:1421–1439

Liverpool Bay. The nature the long-term averagedcurrent structure of Liverpool Bay is explored in thenext section.

3.2 The residual circulation

In environments like Liverpool Bay, the time meancirculation is of great interest to particular applications.For example, in the study of sediment dynamics ortracer dispersal the long-term mean flow, in addition tothe tidal oscillations, determine the sediment pathwaysor dispersion timescales. This can be critical in assess-ing the impact of, for example, anthropogenic nutrientloading of the freshwater estuarine outflows.

The residual circulation is driven by the resultantof competing forces. In a seminal work, Heaps (1972)devised a simple model to describe the time-averagedflow whereby horizontal pressure gradient forces arebalanced by the Coriolis force and frictional effects.The pressure gradient force includes the combinedeffect of long-term average sea surface height varia-tions, such as are sustained by wind setup, and long-term average lateral density gradients, caused by thesalinity gradient in the offshore direction. The Coriolisforce is associated with the residual flow itself (notthe semi-diurnal tidal ellipse velocity). The frictionalterms include a bottom drag and a viscosity term thatrepresent the vertical mixing of horizontal momentum.

Nonlinear tidal effects (e.g. ebb-flood asymmetry)where they produce a nonzero mean flow are dis-counted. However there is corroborating observation(Rippeth et al. 2001) and model data to suggest thatstrain induced periodic convection (Simpson et al.1990) is important in controlling the time mean salinitystructure (Sharples and Simpson 1995; Prandle 2004).Nevertheless these effects are not considered in theHeaps (1972) model.

The Heaps (1972) model predicts northward nearsurface flows and southward near bed flows, consis-tent with the sparse data that were then available, e.g.Bowden and Din (1966). More recently Verspecht et al.(2009b) has revisited this problem analysing 5 years ofcontinuous acoustic doppler current profiler data fromsite A. Verspecht et al. (2009b) demonstrate that theHeaps solution is in qualitative agreement with the timeaverage observational data and demonstrate how themissing nonlinear tidal effects could be partially re-sponsible for the disparity. Similar findings are reportedfrom northern San Francisco Bay (Stacey et al. 2001).

Figure 14b shows the mean density structure andtop and bottom model velocity vectors (red vectorsare time mean surface velocities and black vectors aretime mean bed velocities). There is a clear northward

trend in the surface currents that is partially balancedby a southward flow in the bottom velocities. Figure 19shows long-term mean currents at sites A and B takenfrom (a) observational data and (b) model data. InFig. 19, the red vectors are near-surface mean currents

Fig. 19 Long-term time-averaged depth-varying horizontal ve-locities at sites A and B. Vectors denote velocity directions thatare binned at 1-m depth intervals. Colours denote bin depth withblue being nearest the bed. Data are binned up to the low tideextrema such that bins are continually wet. a Top panel: Datafrom site A that spans the period August 2002–August 2010 anddata from site B that spans the period April 2005–January 2010.b Lower panel: The same diagnostics using model data from2007. Generally, the surface residual flow is northward and thenear bed flow is southward, though the model over estimates theshallower velocities. In b the unlabelled bathymetry shaded in thebackground as a reminder of the 1.8-km grid resolution

Ocean Dynamics (2011) 61:1421–1439 1437

that flow northward and the blue vectors are the bedcurrents that flow southward. Intermediate depths arealso shown at 1-m intervals with depth-varying charac-teristics that are qualitatively expressed in the Heaps(1972) solution. The numerical model captures the formof the observed spirals, including the retroflection atsite A. The magnitudes favourably compare in the bot-tom half of the water columns, though in the upper binsthe magnitudes are overestimated by an average factorof 2. The most likely candidate for this error is theover estimation of vertical stratification. Overestimatesin the horizontal density gradients and uncertaintiesin the bed roughness will also contribute to the resul-tant residual circulation. These modelling challengesare currently under investigation and will be reportedelsewhere. It is worth noting, however, that the errorshere are of the order of a couple of cm s−1 in a resolvedbackground tidal flow that is of the order 50 cm s−1.

4 Summary and discussion

Following an overview of the physical processes thatgovern the dynamics we have presented climatologicalmaps of temperature, salinity and density for Liver-pool Bay. These data are compiled from 8 years ofCTD survey cruises that are part of the NOC (for-merly the Proudman Oceanographic Laboratory) IrishSea Observatory. These data, for the first time, allowus to validate the 1.8-km resolution numerical modelPOLCOMS (which is simulating the whole of the IrishSea) in the challenging region of Liverpool Bay. Inparticular, the observations show that the model’s hor-izontal salinity, and consequently density, gradient istoo strong because the freshwater entering the sea fromthe estuaries is not sufficiently well known. In regionalmodels of this scale care needs to be taken to correctlyforce the model not only with the appropriate fresh-water fluxes, but also their appropriate temperatureand salinity. Simulations of Liverpool Bay (not shown)reveal that the fate of the freshwater plume (primarilyin terms of its stratification) is sensitive to the fresh-water temperature and salinity as it enters the Bay.Setting the freshwater to have a temperature seasonalcycle that matches the Mersey Narrows annual cycle, asmeasured by the ferry, produces qualitatively improvedplumes compared with setting the estuarine water tosimply match the ambient sea water temperature. Forcoarser resolution models, e.g. 7-km Atlantic MarginModel, one could speculate that the fractional volumecontribution of freshwater entering a coastal grid boxis sufficiently small that the estuarine temperature andsalinity can be neglected. However, for finer resolution

models, this effect will be more pertinent. Comparisonsbetween the model and observational data also revealthat the vertical stratification in the model is slightlytoo strong. This may be a repercussion of errors in thefreshwater forcing, though more likely it is a result ofthe turbulent kinetic energy closure scheme’s inabilityto adequately erode stratification. This is an area ofongoing research.

In addition to the CTD array, the Observatory hastwo long-term moored ADCPs. Both tidal ellipse andlong-term residual currents are calculated in LiverpoolBay and compared against the model. The tidal ellipsedata show that near the surface the currents rotateclockwise and near the bed they rotate anticlockwise.Also, we have shown that the residual flow, which isof special significance to tracer transport, is reasonablyrepresented in the model. It is worth clarifying thatestuarine loads are not carried through Liverpool Bayon the estuary momentum. This can be established byestimating the speed of freshwater ingress and compar-ing it with the residual circulation flow speed. Takingthe plume width as extending out from the coast to3.4 W, then if all the Liverpool Bay rivers fed thisplume it would extend about 27 km per year, whichis less than 1 mm s−1. This is an order of magnitudesmaller than the residual current speed, which is cen-timetres per second (Fig. 19). These velocities representa minimum speed at which quantities suspended in thewater column will move. In addition to these advectivevelocities, mixing processes (e.g. SIPS, which is shownhere to occur for 65% of tidal cycles) may dispersetracers at a faster rate than they are advected. Thoughdispersion rates are beyond the scope of this article, itis work ongoing. Given the model’s ability to capturethe spatially varying horizontal structure of the residualcirculation at sites A and B, one could confidently usemodel data to compute volume fluxes and transportsin this neighbourhood. The alternative of obtainingthese calculations from a more extensive mooring arraywould be logistically impossible, with so much shippingactivity, or prohibitively expensive.

In this paper, we have seen that the freshwaterfluxes which control the climatology of Liverpool Bayoceanography have a clear annual cycle in temperaturebut not in salinity and that the density in the Bayis determined by the salinity distribution. The riversannually contribute 7.3 × 109 m3, at a rate of 233 m3 s−1,of water into the Bay.4

The body of riverine freshwater, referred to asa plume, predominantly follows the English coast

4with unknown error estimates

1438 Ocean Dynamics (2011) 61:1421–1439

northwards. It has a vertically well-mixed near-coastalportion but on the seaward side the front character vac-illates with the strength of the tide. The existing CTDsurvey grid is shown to not extend sufficiently near thecoast to capture the near coastal and vertically mixedcomponent the plume. Instead the survey grid capturesthe westward spreading, shallow and transient, portionof the plume. On neap tides the plume has a shallowsurface layer that can extend, from the vertically mixedbody of the plume, as far westward as 4◦W. Whereason spring tides there is little or no vertical stratificationas the tidal mixing is strong. Collapse of the plumestratification during spring tides is identified as a po-tentially important mixing mechanism in the freshwaterbudget (Hopkins and Polton (Scales and structure offrontal adjustment and freshwater export in a regionof fresh water influence, resubmitted)). The portion ofthe bay into which the plume advances and retreatsis identified in both the long-term mean observationsand the model data as a band of stratified fluid thatextends from the mouth of the Mersey towards the Isleof Man. One might speculate that this band would bebiologically different to the neighbouring persistentlymixed nutrient-rich plume water and more saline shelfwater.

The Observatory is focused on the Liverpool Bayarea. This is an exceptionally interesting region asthe interaction between fresh water river input andthe effects of strong tidal forcing give rise to com-plex dynamics. Though the freshwater volume enteringLiverpool Bay is small on global standards, the tidaldynamics and plume buoyancy govern the fate of thefresh water as it enters the sea, as well as the fate of itssediment, contaminants and nutrient loads and, there-fore, mediate any biological interactions. Simplifiedmodelling studies (e.g. Prandle 2004) can demonstratethe sensitivity of the plume structure to the non-linear effects of strain induced periodic stratification(Simpson et al. 1990). Accurately simulating coastalmixing is a challenge (Burchard et al. 2008) and in par-ticular difficulties in sourcing appropriate freshwaterforcing data make it difficult to quantify the level ofskill in the numerical model has in this area. Neverthe-less the model is an excellent process study laboratorythat complements direct observational campaigns tohelp us better understand the governing physics. Cer-tainly dynamical models are an essential tool for marinemanagement and for marine forecasting.

Acknowledgements Wave data were provided by CEFASas part of the WaveNet project and distributed underthe Open Government Licence (http://reference.data.gov.uk/id/open-government-licence). This work was supported by NERCNational Oceanography Centre national capability modelling

and was partially funded under a NERC New InvestigatorAward. The authors are grateful for the constructive comments,received through the review processes, which have resulted in animproved manuscript.

References

Bowden KF (1980) The north west European shelf seas: the seabed and sea in motion II: Physical and chemical oceanog-raphy, and physical resources. In: Banner FT, Collins MB,Massie KS (eds), vol 2, Elsevier, Amsterdam, pp 391–413.doi:10.1016/j.physletb.2003.10.071

Bowden KF, Sharaf El Din SH (1966) Circulation and mix-ing processes in the Liverpool Bay area of the Irish Sea.Geophys J R Astron Soc 11:279–292

Bowers DG, Simpson JH (1987) Mean position of tidal fronts inEuropean-shelf seas. Cont Shelf Res 7(1):35–44

Burchard H (2009) Combined effects of wind, tide, and horizon-tal density gradients on stratification in estuaries and coastalseas. J Phys Oceanogr 39:2117–2136

Burchard H, Karsten B (2001) Comparitive analysis of foursecond-moment turbulence closure models for the oceanicmixed layer. J Phys Oceanogr 31: 1943–1968

Burchard H, Craig PD, Gemmrich JR, van Haren H, MathieuP-P, Meier HEM, Nimmo Smith WAM, Prandke H, RippethTP, Skyllingstad ED, Smyth WD, Welsh DJS, WijesekeraHW (2008) Observational and numerical modeling methodsfor quantifying coastal ocean turbulence and mixing. ProgOceanogr 76:399–442

Burrows R, Walkington IA, Yates NC, Hedges TS, Wolf J, HoltJ (2009) The tidal range energy potential of the west coast ofthe United Kingdom. Appl Ocean Res 31:229–238

Canuto VM, Howard A, Cheng Y, Dubovikov MS (2001) Oceanturbulence. Part I: one-point closure model—momentum andheat vertical diffusivities. J Phys Oceanogr 31(6):1413–1426

Fong FW, Heaps NS (1978) Note on quarter wave tidal reso-nance in the Bristol Channel. Technical report, Bidston Ob-servatory, Birkenhead, Institute of Oceanographic Sciences,11 pp. I.O.S. Report no. 63 (unpublished)

Heaps NS (1972) Estimation of density currents in the LiverpoolBay area of the Irish Sea. Geophys J R Astron Soc 30:415–432

Holt J, James ID (2001) An s-coordinate model of the northwestEuropean continental shelf. Part I: model description anddensity structure. J Geophys Res 106(C7):14015–14034

Holt J, Umlauf L (2008) Modelling the tidal mixing fronts andseasonal stratification of the Northwest European Continen-tal shelf. Cont Shelf Res 28:887–903

Holt JT, Allen JI, Proctor R, Gilbert F (2005) Error quan-tification of a high-resolution coupled hydrodynamic-ecosystem coastal-ocean model: part 1 model overview andassessment of the hydrodynamics. J Mar Syst 57:167–188

Kwong SCM, Davies AM, Flather RA (1997) A three-dimensional model of the principal tides on the Europeanshelf. Prog Oceanogr 39:205–262

MacCready P, Geyer WR (2010) Advances in estuarine physics.Annu Rev Marine Sci 2:35–58

Palmer MR (2010) The modification of current ellipses bystratification in the Liverpool Bay ROFI. Ocean Dyn60:219–226. doi:10.1007/s10236-009-0246-x

Pingree RD, Griffiths DK (1978) Tidal fronts on the shelf seasaround the British Isles. J Geophys Res 83(C9):4615–4622.doi:10.1029/JC083iC09p04615

Prandle D (1982) The vertical structure of tidal currents.Geophys Astrophys Fluid Dyn 22:29–49

Ocean Dynamics (2011) 61:1421–1439 1439

Prandle D (2004) Saline intrusion in partially mixed estuaries.Estuar Coast Shelf Sci 59:385–397

Pugh DT (1987) Tides, surges and mean sea-level. Wiley,New York

Rippeth TP, Fisher NR, Simpson JH (2001) The cycle of tur-bulent dissipation in the presence of tidal straining. J PhysOceanogr 31:2458–2471

Sharples J, Simpson JH (1993) Periodic frontogenesis in a regionof freshwater influence. Estuaries 16:74–82

Sharples J, Simpson JH (1995) Semi-diurnal and longer periodstability cycles in the Liverpool Bay region of freshwaterinfluence. Cont Shelf Res 15:295–313

Simpson JH (1997) Physical processes in the ROFI regime. J MarSyst 12:3–15

Simpson JH, Bowers D (1981) Models of stratification and fron-tal movement in shelf seas. Deep-Sea Res 28A(7):727–738

Simpson JH, Hunter JR (1974) Fronts in the Irish Sea. Nature250:404–406

Simpson JH, Sharples J (1994) Does the earth’s rotationinfluence the location of the shelf sea fronts? J Geophys Res99(C2):3315–3319

Simpson JH, Brown J, Matthews J, Allen G (1990) Tidal strain-ing, density currents, and stirring in the control of estuarinestratification. Estuaries 13:125–132

Simpson JH, Sharples J, Rippeth TP (1991) A prescriptive modelof stratification induced by freshwater runoff. Estuar CoastShelf Sci 33(1):23–35

Simpson JH, Burchard H, Fisher NR, Rippeth TP (2002)The semi-diurnal cycle of dissipation in a ROFI: model-measurement comparisons. Cont Shelf Res 22:1615–1628

Soulsby RL (1983) The bottom boundary layer of shelf seas.In: Johns B (ed) Physical oceanography of coastal and shelfseas. Elsevier, Amsterdam, pp 189–266

Stacey MT, Burau JR, Monismith SG (2001) Creation of resid-ual flows in a partially stratified estuary. J Geophys Res106:17013–17037

The Crown Estate (2010) The UK offshore wind report 2010.http://www.thecrownestate.co.uk/uk_offshore_wind_report_2010.pdf

Verspecht F, Simpson JH, Rippeth TP (2010) Semi-diurnaltidal ellipse variability in a region of freshwater influence.Geophys Res Lett 37(L18602). doi:10.1029/2010GL044470

Verspecht F, Rippeth TP, Howarth MJ, Souza AJ, Simpson JH,Burchard H (2009a) Processes impacting on stratification ina region of freshwater influence: application to LiverpoolBay. J Geophys Res 114(C11022). doi:10.1029/2009JC005475

Verspecht F, Rippeth TP, Simpson JH, Souza AJ, Burchard H,Howarth MJ (2009b) Residual circulation and stratificationin the Liverpool Bay region of freshwater influence. OceanDyn 59:765–779. doi:10.1007/s10236-009-0233-2

Visser AW, Souza AJ, Hessner K, Simpson JH (1994) The effectof stratification on tidal current profiles in a region of fresh-water influence. Oceanol Acta 17(4):369–381

Walkington I, Burrows R (2009) Modelling tidal stream powerpotential. Appl Ocean Res 31:239–245

Wolf J, Brown JM, Howarth MJ (2011) The wave climate ofLiverpool Bay—observations and modelling. Ocean Dyn61(5):639–655. doi:10.1007/s10236-011-0376-9

Yamashita Y, Panton A, Mahaffey C, Jaffé R (2011) Assess-ing the spatial and temporal variability of dissolved or-ganic matter in Liverpool Bay using excitation–emissionmatrix fluorescence and parallel factor analysis. Ocean Dyn.doi:10.1007/s10236-010-0365-4

Yankovsky AE, Chapman DC (1997) A simple theory forthe fate of buoyant coastal discharges. J Phys Oceanogr27:1386–1401