Ocean DynamicsDOI 10.1007/s10236-011-0475-7

Scales and structure of frontal adjustment and freshwaterexport in a region of freshwater influence

Joanne Hopkins · Jeffrey A. Polton

Received: 14 October 2010 / Accepted: 12 July 2011© Springer-Verlag 2011

Abstract Sea surface temperature satellite imagery anda regional hydrodynamic model are used to investi-gate the variability and structure of the Liverpool Baythermohaline front. A statistically based water massclassification technique is used to locate the front inboth data sets. The front moves between 5 and 35 kmin response to spring–neap changes in tidal mixing, anadjustment that is much greater than at other shelf-seafronts. Superimposed on top of this fortnightly cycle aresemi-diurnal movements of 5–10 km driven by floodand ebb tidal currents. Seasonal variability in the fresh-water discharge and the density difference betweenbuoyant inflow and more saline Irish Sea water giverise to two different dynamical regimes. During winter,when cold inflow reduces the buoyancy of the plume,a bottom-advected front develops. Over the summer,when warm river water provides additional buoyancy,a surface-advected plume detaches from the bottomand propagates much larger distances across the bay.Decoupled from near-bed processes, the position of thesurface front is more variable. Fortnightly stratificationand re-mixing over large areas of Liverpool Bay is apotentially important mechanism by which freshwater,and its nutrient and pollutant loads, are exported from

Responsible Editor: Matthew Robert Palmer

This article is part of the Topical Collection on the UK NationalOceanography Centre’s Irish Sea Coastal Observatory

J. Hopkins (B) · J. A. PoltonNational Oceanography Centre, Joseph Proudman Building,6 Brownlow Street, Liverpool, L3 5DA, UKe-mail: jeh200@noc.ac.uk

the coastal plume system. Based on length scales es-timated from model and satellite data, the erosion ofpost-neap stratification is estimated to be responsiblefor exporting approximately 19% of the fresh estuarinedischarge annually entering the system. Although thebaroclinic residual circulation makes a more significantcontribution to freshwater fluxes, the episodic nature ofthe spring–neap cycle may have important implicationsfor biogeochemical cycles within the bay.

Keywords Spring–neap · Thermohaline front ·Freshwater export · Stratification · Coastal ·Shelf sea

1 Introduction

Liverpool Bay is a region of freshwater influence(ROFI). Located in the southeastern corner of theEastern Irish Sea (Fig. 1), the region receives on av-erage 200–300 m3 s−1 of freshwater from the Mersey,Dee, Ribble and Clwyd river catchments. This inputof buoyant river water creates an east–west densitygradient of the order 5×10−5 kg m−4 (Palmer 2009).Coupled with variable winds, a large tidal range andstrong currents (up to 10 m and 1 m s−1 at springtides, respectively), the dynamics of Liverpool Bay arecomplex (Polton et al. 2011). The strength and extent ofstratification is governed by the competition betweenthe stratifying influence of freshwater discharge inject-ing buoyancy into the system and the de-stratifyingeffect of tidal and wind mixing. The system oscillatesbetween episodes of well-mixed conditions and timesof periodic and enduring stratification (Sharples andSimpson 1993, 1995; Simpson et al. 1990). Based on a

Ocean Dynamics

Fig. 1 The Eastern Irish Seaand Liverpool Bay. Contoursare depth (metres). Blackcircle marks the location ofthe ISO main mooring site.CTD stations are indicated bysmall black crosses. Thedashed box shows the area ofeach SST image that wasanalysed. The horizontal lineextending from Formby Pointmarks the location of themodel transect

potential energy formulation, Simpson et al. (1990) ex-plore the conditions necessary to maintain stratificationagainst tidal mixing where stability is provided throughtwo main processes: (a) the estuarine circulation drivenby horizontal density gradients and (b) vertical tidalshear straining the density field. The term ROFI wassubsequently coined in a series of early 1990 papersby Simpson (e.g. Simpson et al. 1990, 1991). Burchard(2009) extends this analysis by including wind straining.The maximum extent of freshwater influence is markedby a thermohaline front running north–south across thebay, seaward of which the competition between surfaceheating and tidal stirring dominate the dynamics.

Most of the tidal variability in Liverpool Bay isaccounted for by the semi-diurnal lunar and solar tidalconstituents, M2 and S2, with 12.4- and 12-h periods,respectively. A fortnightly spring–neap cycle resultsfrom the difference in speeds between these two con-stituents. Every 2 weeks, the gravitational pull of thesun and moon is aligned and larger spring tides occur.In-between, during neap tides, the tidal range is smallerand currents are weaker. An elliptical semi-diurnallunar constituent, N2, with a 12.65-h period modulatesthe amplitude of consecutive spring and neap tides.

Enduring periods of stratification are observed tooccur on fortnightly timescales following neap tides.These episodes are triggered by a reduction in tidal

mixing energy coupled with an increase in stability anddampening of vertical mixing due to semi-diurnal tidalstraining. This allows the density-driven estuarine cir-culation to dominate and more permanent stratificationto develop (Linden and Simpson 1988b; Sharples andSimpson 1993, 1995; Simpson et al. 1990). A stratifiedregion, delimited by a strengthening surface frontpropagates westward, compensated at depth by on-shore flows (Czitrom and Simpson 1998; Sharples andSimpson 1993). Isopycnals on the eastern side of theexpanding stratified zone slope downwards forming abottom-attached front. Waters inshore of this reattach-ment tend to remain vertically well mixed. Stratificationmay persist for several days following neap tides un-til increases in vertical mixing with the approach-ing springs re-mixes the water column. In additionto this fortnightly cycle, frontal movement occurs onsemi-diurnal timescales; flood–ebb advection and tidalstraining both alter the structure of the water columnand position of the front.

Tidal variations in mixing intensity and stratificationand the associated changes in circulation modulate thehorizontal flux and export of freshwater, suspendedsediments, river pollutants and nutrients in estuarineand ROFI systems (Burchard et al. 2008; Jay andMusiak 1994; Monismith et al. 1996; Prandle 2004). It istherefore important to know the spatial and temporal

Ocean Dynamics

scales of these adjustments. Spring–neap changes intidal mixing, and the N2 modulation of this cycle, ebb–flood advection, tidal straining, the magnitude and di-rection of wind stress and the rate of freshwater inputall contribute to the stability of the water column andpropagation of the front. The strength of estuarinecirculation during neap tides has been seen to increasein response to reduced tidal mixing (Geyer and Cannon1982; Geyer et al. 2000; Nunes and Lennon 1987).Linden and Simpson (1988a) suggest that the salt fluxduring periods of prolonged stratification may be anorder of magnitude greater than when increased turbu-lence maintains a well-mixed water column. Addition-ally, semi-diurnal changes in stability caused by tidalstraining can enhance shoreward near-bottom residualflows (Scully and Friedrichs 2007). In a heavily popu-lated area that is under pressure from industry, shippingand tourism, understanding the export of freshwaterand its nutrient and pollutant loads is important in thedevelopment of predictive models and coastal manage-ment tools.

In situ observational data, much of which has beencollected as part of the Irish Sea Observatory (ISO),provides a rich time series of measurements allowingevolution of the water column structure at one pointto be studied. In this paper, we use both remotelysensed sea surface temperature (SST) observations andmodel data to examine the spatial scales over whichfrontal adjustment may occur. This contributes to ourunderstanding of Liverpool Bay by providing a moresynoptic picture of the dynamics. The location of thefront is estimated from satellite SST images using a sta-tistical classification technique tailored specifically forthis work. This analysis is supplemented and extendedby output from Proudman Oceanographic Labora-tory Coastal Ocean Modelling System (POLCOMS),a 3D hydrostatic sigma coordinate numerical modelspecifically designed to simulate macro-tidal regions,allowing changes in the vertical structure of the frontto be examined. We aim to address the following ques-tions: (1) What are the fortnightly and semi-diurnalscales of frontal movement caused by spring–neap andflood–ebb changes in tidal mixing? (2) What contribu-tion do enduring periods of stratification and re-mixingmake to the export of freshwater from the LiverpoolBay coastal plume system?

Sections 2 and 3 describe the data sets used in ouranalysis and the water mass classification techniquethat has been developed. Sections 4 and 5 present ouranalysis of satellite and model data. In Section 6, weestimate the potential equivalent freshwater flux drivenby the spring–neap tidal mixing cycle. Discussions andconclusions are presented in Section 7.

2 Data

Here we describe the data sets used in this study. Theposition of the front is estimated from both satelliteSST observations and from a regional model. Thisanalysis is supplemented and validated by in situ obser-vations collected as part of the Irish Sea Observatory.

2.1 Satellite sea surface temperature

Satellite images of SST between 2005 and 2009, at aspatial resolution of 1 km, from the advanced very highresolution radiometer have been used. Measurementsfrom each overpass, rather than composite images,were selected in order to maximise the size of the dataset and to ensure that any semi-diurnal frontal move-ment could be resolved. Data were provided by theNERC Earth Observation Data Acquisition and Anal-ysis Service, Plymouth (http://www.neodaas.ac.k/).

2.2 POLCOMS

The model is configured on a 1.8-km (1-nautical mile)B-grid that covers the whole of the Irish Sea with 32sigma depth levels. Temperature and salinity frontsare preserved using the Piecewise Parabolic Method(James 1996) advection scheme, and a quadratic dragmomentum boundary condition is used at the bed (im-plemented in Holt and James 1999). Following Ruddicket al. (1995), the bottom drag coefficient, Cd, is givenby Cd = (κ/ ln(z/z0))

2, where κ is the von Kármánconstant, z0 = 0.005 m is the bed roughness length andz is the height above the bed. If Cd is less than 0.005, itis assumed to be 0.005. Vertical mixing is parameterisedusing the Canuto et al. (2001) k-epsilon scheme. Thetuneable coefficients are presented in Holt and Umlauf(2008), wherein its performance against other turbu-lence closure schemes is also reported.

The model is forced by sea surface elevation anddepth varying tidal currents at the open boundaries.These data are taken from the Atlantic Margin Model(12-km resolution) which covers the North West Eu-ropean Shelf and encapsulates the shelf break. Thisin turn is forced by the UK Met. Office’s 1/3◦ Fore-cast Ocean Assimilation Model. The high-resolutionIrish Sea simulation, in this study, is forced withsix hourly, 1◦, European Centre for Medium-RangeWeather Forecasts winds and surface fluxes that arecomputed from meteorological bulk formulae. There-fore, mesoscale meteorological effects are excludedfrom these simulations.

River discharges, forcing the simulation, are com-puted from daily Environment Agency river gauge

Ocean Dynamics

measurements. Conversion factors to scale the riverflows into estuarine discharge fluxes come from theCentre for Ecology and Hydrology (CEH 2007; CEH,personal communications). Outside of Liverpool Bay,climatological daily values are used, though in the baythe actual daily river discharges are used. These arecomputed from the 13 gauges between the Clwyd andthe Ribble estuaries (Fig. 1).

River temperatures are set to vary with an annualsinusoidal cycle. This seasonal cycle is the first modeof variability from 3 years of SST data at the mouth ofthe Mersey. These data are measured by the LiverpoolViking Ferry as it passes through the Mersey Narrows(Balfour et al. 2007). Similarly, the freshwater dischargewas set to a constant value of 10 psu to better repre-sent the observed ferry-based salinities in the MerseyNarrows.

The model is spun up from a climatological statefor 2 years, and analysis is taken from 2007. For moredetails about the POLCOMS hydrodynamics refer toHolt and James (2001) and Holt et al. (2005). Forspecific examples of model configurations at this res-olution, see Holt and James (2006) and Holt andProctor (2008). Further model validation and compar-isons against observational data for Liverpool Bay canbe found in Polton et al. (2011) and Howarth andPalmer (2011).

2.3 Irish Sea Observatory time series

Fixed point time series measurements of temperature,salinity and vertical current structure were obtainedfrom the main ISO mooring site (Fig. 1) at the MerseyBar (53◦32′ N, 3◦21.8′ W). Conductivity and tempera-ture (CT) sensors are located in a frame on the seabedand at 5 and 10 m below the sea surface, logging10-min averages. CT sensors logging every 30 minare also located at 1 m below the sea surface on aCEFAS SmartBuoy. An upwards looking RDI 600-kHzacoustic Doppler current profiler (ADCP) mounted onthe bed frame records currents in 10-min ensemblesover 1 m depth bins. Every 4–6 weeks, these instru-ments are serviced and a CTD grid of 35 fixed stationsis completed. Density was calculated from practicalsalinity (PSS78) using the International Equation ofState of Sea Water, 1980 (Unesco 1981). Details on theIrish Sea Coastal Observatory and the above time seriesof measurements can be found in Howarth and Palmer(2011).

3 Methods: water mass classification

The river water that enters Liverpool Bay has differentthermohaline characteristics to the Irish Sea water fur-

Fig. 2 Satellite SST images ofthe thermohaline front andfreshwater plume at differenttimes of the year. Blackcontours mark the position ofthe front as estimated usingthe mixture modellingtechnique described inSection 3. All colourbars havea range of 3◦C

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ther offshore. The greater thermal inertia of the oceanensures that, aside from always being fresher, riverdischarge is warmer than seawater in the summer andcolder in the winter. As demonstrated in Fig. 2, thisallows the freshwater plume to be identified year-roundfrom satellite images of SST. Periods around the springand autumn equinoxes where ocean–estuarine temper-ature differences are the smallest are times when iden-tification of the front is more difficult (Fig. 2c).

Here, a statistical technique known as mixture mod-elling that enables a set of observed data to be di-vided into different subsamples is used to separateobservations of SST into two different surface watermasses. The division between them is assumed to bea reliable estimate of the position of the front. Thetechnique is also applied to modelled longitude-depthtransects of density extending westward from FormbyPoint (Fig. 1). In this way, our analysis is supplementedby information on the vertical structure of the plume.Statistical approaches to automated classification andedge discrimination have been explored in an oceano-graphic context by a number of authors: Cayula andCornillon (1992), Miller (2009) and Shimada et al.(2005) to name but a few. In the following sections,the statistical methodology and a validation of the tech-nique are presented.

3.1 Statistical methodology

For a set of observations x = {x1, x2, . . . , xn}, which inour analysis are either temperature or density, supposethat there are K different water masses within thatset. For our purposes, K is set to either 1 or 2 (theselection of which will be discussed later), since weare either able to distinguish two water masses andtherefore a front (K = 2), or only one water mass andno front (K = 1). For each water mass, k = 1, . . . , K,the observations can be parameterised by a Gaussiandistribution with mean μk and covariance matrix �k.Note that alternative distributions could be used ifnecessary. The Gaussian probability density of watermass k is therefore:

fk(x) = φ(x|μk, �k)

= 1

(2π)12 |�k| 1

2

exp

(−1

2(x − μk)

t(�k)−1(x − μk)

),

(1)

where superscripts t and −1 denote the matrix trans-pose and inverse, respectively. The relative importanceof each water mass k within the set of observations asa whole is expressed by a prior probability or weightak, i.e. the proportion of the total number of observa-

tions assigned to each water mass. The k-componentGaussian mixture model is then a weighted linear com-bination of the K probability density functions:

f (x) =K∑

k=1

ak fk(x) =K∑

k=1

akφ(x|μk, �k). (2)

The log-likelihood of observations x given parame-ters θ = {ak, μk, �k} is expressed as:

L(x|θ) =n∑

i=1

log

(K∑

k=1

akφ(xi|μk, �k)

). (3)

The unknown parameters are estimated using theexpectation maximisation (EM) algorithm that aims tomaximise the log-likelihood L(x|θ). The weights ak andthe Gaussian parameters μk and �k can be optimizedseparately over four steps where parameters estimatedat the pth and (p + 1)th iterations are marked (p) and(p+1), respectively. These steps are as follows:

1. Select starting values for the iterations using ak-means clustering technique (discussed later).

2. Compute posterior probabilities, Pi,k, for all i =1, . . . , n and k = 1, . . . , K. The posterior probabil-ity is a revised probability that takes into accountthe most up-to-date information about ak, μk and�k calculated during the previous iteration. Whenp = 1, these will be the starting values from step 1.

Pi,k =a(p)

k φ(

xi|μ(p)

k , �(p)

k

)∑K

k=1 a(p)

k φ(

xi|μ(p)

k , �(p)

k

) . (4)

3. Optimize the Gaussian parameters, μk and �k, andprior probabilities ak using Pi,k.

a(p+1)

k =∑n

i=1 Pi,k

n, (5)

μ(p+1)

k =∑n

i=1 Pi,kxi∑ni=1 Pi,k

, (6)

�(p+1)

k =∑n

i=1 Pi,k

(xi − μ

(p+1)

k

) (xi − μ

(p+1)

k

)t

∑ni=1 Pi,k

. (7)

4. Compute the log-likelihood using the most up-to-date parameter estimates.

L(x|θ)(p+1) =n∑

i=1

K∑k=1

Pi,k log a(p+1)

k

+n∑

i=1

K∑k=1

Pi,k log φ(

xi|μ(p+1)

k ,�(p+1)

k

).

(8)

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Steps 2 and 3 are repeated until the parameter val-ues and likelihood have converged. The convergencetolerance for the log-likelihood function, L(x|θ), andparameter values θ , was set at 1×10−3. A maximumof 100 iterations was allowed. Each observation xi

is assigned to the water mass corresponding to thehighest posterior probability Pi,k. In the first instance,observations of surface water temperature from theCEFAS SmartBuoy are used to determine which clus-ter represents the fresher river discharge. If an in situmeasurement was not available within 12 h of the satel-lite overpass, then the expected seasonal horizontaltemperature gradient and location of each water masswas used to identify the plume. This was necessary for35 images between 28th October and 10th December2008 and for 26 images in September 2009 when noSmartBuoy data were available.

The EM algorithm is initiated (step 1 above) witha first guess at optimal parameter values generatedby a k-means clustering technique. This aims to parti-tion the n observations into k water masses such thateach observation belongs to the water mass with thenearest mean. For K water masses with means Z ={z1, . . . , zk}, the total mean squared error, denoted C,between the observation and the representative watermass mean is minimised.

C(Z , η) =n∑

i=1

‖xi − Zη(i)‖2, (9)

where η(i) = k denotes assignment of observation xi tothe kth water mass. The problem is solved iterativelyby assigning each observation to its closest water massusing Euclidean distance and then updating the meanby computing the average of all samples assigned to it.

The value of K, the optimal number of water massesor clusters that the set of observations x should bedivided into is itself an unknown quantity. It is deter-mined by a scoring system known as Akaike’s informa-tion criterion (AIC), a measure of statistical model fit(Hastie et al. 2001). It attempts to find the minimummodel fit that correctly explains the data by examiningthe complexity of the model, i.e. the number of watermasses, together with its goodness-of-fit to the data.AIC(K) = −2 log LK, where LK is the value of themaximum likelihood using K clusters. For each set ofobservations x, the AIC for K = 1 and K = 2 is calcu-lated. The value of K that generates the lowest AIC istaken as the optimal number of clusters with which tosubdivide x into. If K = 1, then only one water masscan be distinguished and the temperature histogramis described as unimodal (Fig. 3a). When K = 2, x isbest divided into two different populations and thedistribution of temperatures is bimodal (Fig. 3b).

Owing to variable cloud cover extent, not all avail-able SST images between 2005 and 2009 were analysed.Selection was based on the percentage and distributionof observations available within the area south of 54.42◦N and east of 4.9◦ W (marked in Fig. 1). A minimum

Fig. 3 The probability density functions of SST observations ona 7th April 2007 02:03:00 (Fig. 2c) where only one water mass canbe distinguished and b 22nd August 2007 20:45:00 (Fig. 2b) wherethe distribution is bimodal. The dashed line marks the 16.2◦C

isotherm optimally separating the two water masses. μ and � arethe means and variances of each water mass, respectively. a1 anda2 are proportions of the total number of observations assignedto each water mass

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requirement for 30% of the area to contain SST obser-vations and of these 15% to be east of 3.6◦ W was set.This was to ensure that enough measurements of bothoffshore and nearshore were available to estimate theposition of any front in the area. In total, 1,286 imagesbetween 2005 and 2009 met these criteria.

3.2 Quality control

To maintain only the highest quality results, clas-sifications were discarded if an optimization did notconverge, if only one water mass could be identified(minimum AIC(K) = 1) or if a water mass was assignedless than 5% of the available data. To further ensurethe identification of two well-defined watermasses, par-ticularly during equinox periods, and preserve only themost reliable estimates of frontal location, the internal(Vint) and external (Vext) variances of the two watermasses were calculated. Vint is the sum of the varianceswithin each of the watermasses. Vext is the contributionto the total variance (Vtot) of all the observations re-sulting from the separation, where Vtot = Vint + Vext, asthe proportion that Vext contributes to Vtot increasesso the definition between the two populations is en-hanced. Vext

Vtotis therefore used as an indicator of wa-

termass definition. If VextVtot

< 0.3, the two watermassesare considered to be weakly defined. Ninety-two imageclassifications were rejected on this basis, the majorityduring equinox periods (March–April and September–October), when estuarine and oceanic water temper-atures are most similar and there is an absence ofvertical temperature variations (Czitrom and Simpson1998). Additionally, six classifications were rejectedon account of the water mass temperature differences(|μ1 − μ2|) being 1.5◦C greater than the harmonicallyfitted seasonal value. Water mass statistics falling out-side reasonable bounds on the expected seasonal valuesare likely to result in unrealistic estimates of frontallocation.

Out of the 1,286 images analysed, 125 were rejectedaccording to the above criteria. Between 209 and 286images were available for each of the 5 years. An equalnumber of images were available during each season:579 in the summer (April–September) and 582 in thewinter (October–March). In general, observations arewell distributed between months. Figure 6 shows thetemporal spread of observations over each year.

3.3 Validation of technique

Irish Sea Observatory CTD surveys of Liverpool Bayallow the results of this technique to be validated.

Fig. 4 a Satellite image of SST (◦C) on 20th June 2007 at 21:40:00.The black contour marks the estimated position of the front(13.45◦C isotherm). Black dots are the locations of CTD casts.b Longitude-depth transects (marked A–D in a) of the tempera-ture taken between 20th and 21st June 2007. The 13.45◦C contouras estimated from a is marked

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Fig. 5 Model output on 20th June 2007 21:40:00. a Surface tem-perature field. The black contour (13.8◦C) marks the estimatedposition of the front using this SST field. Dashed line marks thelocation of the transect. b–d Temperature, salinity and densitytransects. The 13.8◦C contour in b marks the fronts’ location asestimated from the SST values in a and is a comparison to Fig. 4.The black contour in d shows the position of the front estimatedusing the depth-longitude density field

Figure 4 shows the position of the front estimated fromthe SST in a single overpass on 20th June 2007 at21:40:00 and CTD transects of the temperature takenbetween the 20th and 21st June 2007. The position ofeach CTD cast has been corrected for barotropic tidal

displacement relative to the time of the satellite imageusing POLCOMS. The position of the front estimatedfrom analysis of the SST image is not just a surfaceskin phenomenon but a genuine water mass boundary.The location of the front in Fig. 4a is comparable tothe surface outcropping of the 13.45◦C isotherm in theCTD transects (Fig. 4b).

Salinity rather than temperature, however, is theprimary control on density structures within LiverpoolBay (Palmer 2009). Consequently, model density ratherthan temperature is used to identify the location of thefront. Figure 5 shows model output of temperature,salinity and density corresponding to the same date andtime as Fig. 4. The freshwater signature of the plume, asshown by the salinity field in Fig. 5c, does not extend asfar offshore as suggested by analysis of the SST fieldalone (Fig. 5b). Therefore, estimating the position ofthe surface and bottom fronts using longitude-depthtransects of density provides more physically realisticresults (Fig. 5d).

4 Scales of frontal adjustment from SST images

In this section, analysis of the SST images is used toconsider both the spring–neap and semi-diurnal vari-ability of the Liverpool Bay front. The median position(longitude) of the front between 53.5◦ N and 54◦ N forall images analysed is presented in Fig. 6. There is alarge amount of variability within and between days,months and seasons. Estimates of the position rangefrom 3.15◦W to 4.5◦W.

Any spring–neap adjustment is difficult to distin-guish because of semi-diurnal flood–ebb advection, theimpact of variable wind stress and river discharge anda sparsity of data over individual fortnightly periods.Furthermore, as can be seen in Figs. 8 and 9, the fronttends to be orientated NW–SE such that if the northernhalf of the area were to be obscured by clouds, then themedian position of the front across the bay would bebiased towards the east and vice versa.

4.1 Spring–neap movement

To assess whether there is any spring–neap variability,a more composite presentation of results is necessarywhere semi-diurnal movement and the affects of windsand river input can be averaged out. Results are there-fore subdivided according to the 14-day spring–neapcycle. As clarification, Fig. 7 shows the median top-to-bottom density difference (�ρ kg m−3) at the main ob-servatory mooring site over 1 year, averaged accordingto the day of the spring–neap cycle, and the mean high

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Fig. 6 Median frontallocation (longitude) between53.5◦ and 54◦N estimatedfrom each SST image

−4.5 −4 −3.5 −3

25

50

75

100

125

150

175

200

225

250

275

300

325

350

2005

Yea

r D

ay

−4.5 −4 −3.5 −3

2006

−4.5 −4 −3.5 −3

2007

Longitude−4.5 −4 −3.5 −3

2008

−4.5 −4 −3.5 −3

2009

water level near the mouth of the Mersey calculatedfor the equivalent periods. The highest tidal range andtherefore the strongest spring currents occur on thethird day. Neap tides occur on day 10. Even from thislong-term mean, a fortnightly variation in the strengthof stratification can be seen. The median value of �ρ isthe weakest during spring tides (<0.2 kg m−3) and thestrongest (0.6 kg m−3) 1 day after neaps (day 11). Thewide range of values for each day highlights that eachevent will be different, but the overall trend demon-strates that the spring–neap cycle is persistent enoughto show up in long-term averages.

Using this approach, all the SST images are sortedaccording to their position in the spring–neap cycle andthe percentage of time that waters were classified as be-ing part of the coastal plume calculated. Subsequently,in the absence of any other statistics, we assume thatthere is a 50–50 chance (p ≥ 0.5) of any pixel beingclassified as either water mass and calculate confidenceintervals. Figure 8 summarizes the results for spring(days 3–4) and neap (days 10–11) periods. The thick

Fig. 7 Density anomaly between the bottom and 5 m at themain observatory mooring site (27th July 2006 to 27th July 2007),classified according to the day of the spring–neap cycle. Opencircles mark the median density anomaly. Filled boxes extendbetween the upper and lower quartile ranges. Whiskers extendto the most extreme values within 1.5 times the interquartilerange. The dashed black line is the mean high water level overthe same period at Gladstone Dock, Liverpool, relative to theLowest Astronomical Tide

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Fig. 8 The 99% (solid lines) and 1% (dashed lines) confidencecontours during neap (days 3–4) and spring (days 10–11) tides.The shaded and hashed areas in-between represent the most prob-able region for the front to be found in during neap and spring

periods, respectively. a Summer neaps (N = 76) and springs(N = 96). b Winter neaps (N = 100) and springs (N = 79). Nrefers to the number of SST images within each category

contours mark the 99% one-sided confidence intervalthat p ≥ 0.5 and represent the position shoreward ofwhich there is a significant bias towards plume waters.In contrast, the 1% contours (dashed lines) mark thelowest confidence level. The shaded areas in betweenrepresent the most probable region for the front to befound in during neap and spring periods.

During the summer, warmer surface waters are ob-served further west during periods of weaker neap tidalcurrents (Fig. 8a). The contrast is the strongest between53.5◦ N and 53.6◦ N where, based on the 99% contour,the front is located between 3.4 and 3.5◦ W during

springs and near 3.9◦ W at neaps. During the sum-mer, therefore 25–30 km of movement in the thermalsurface expression of the front can occur. Throughoutthe winter (Fig. 8b), the difference between the 99%spring and neap contours is greatly reduced to 5–10 km.Additionally, in contrast to the summer, the neap frontsare more likely to be observed further inshore. With theexception of summertime neaps, the front is orientatednorthwest–southeast.

The distance between the 99% and 1% contoursindicates the variability in position of the front owing toflood–ebb advection, wind mixing and river discharge.

Fig. 9 a Estimated positionof the front from individualSST images between the 17thand 18th February 2008.b Median frontal locationbetween 53.55◦ and 53.65◦W(dashed line and circles) anddepth mean east–westvelocity (±u m s−1) fromADCP measurements (solidblack line). Exact times ofeach estimate are indicatedby the horizontal lines

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These distances are of the same order of magnitude asany adjustments resulting from fortnightly variability intidal mixing energy. This variability is slightly higherduring the summer.

4.2 Semi-diurnal movement

The movement resulting from flood–ebb advection isexplored in Fig. 9 where 14 clear overpasses wereavailable over a 48-h period in February 2008. Duringthe winter, there is minimal surface skin heating andno seasonal thermal stratification making this an idealperiod of time to resolve daily frontal adjustment. Thedepth-mean east–west flows (±u m s−1) have beencalculated from the ADCP at the main observatorymooring site and are representative of the rectilineartidal currents across Liverpool Bay. In this example,there is 5–10 km of movement over a flood–ebb cycleand offshore displacement of the front with increasinglatitude. Comparison of the fronts’ location to the stateof the tide shows the front moving shoreward duringflood and seaward during ebb. The greatest westwardand eastward positions tend to occur around high andlow water slack periods. Similar scales of adjustmentare seen at other times (e.g. 2nd May 2007 and 22nd–23rd January 2007) when enough cloud-free overpassesare available.

5 Modelled frontal movement and structures

In this section, we present an analysis of hourly modeldensity along an east–west transect extending offshore

from Formby Point (Fig. 1). This high-resolutionmodel data enable individual spring–neap events andsemi-diurnal movement to be better resolved. Depth-longitude transects also allow the vertical structure ofthe front to be considered. Satellite SST images onlypermit an estimate of the surface position of the front,whereas simultaneously locating the bottom reattach-ment from model transects enables an estimate of theextent of stratification. Furthermore, other importantfactors that complicate the control of tidal mixing canbe assessed: seasonal variations in horizontal and ver-tical temperature gradients, river discharge and windmixing.

There is a fortnightly cycle in the advance and retreatof the front (Fig. 10a) and in the extent of stratification(Fig. 10b). In general, the front is located furthestoffshore approximately 1–2 days after neap tides. Thebottom front is located around 3.3◦ W. It migrates nofurther east than 3.2◦ W and no further seaward of3.5◦ W. In contrast, the surface expression moves muchgreater distances. During periods of more enduringstratification, around neap tides, it is often found be-tween 3.5◦ W and 3.8◦ W. This translates to between 10and 35 km of fortnightly movement.

There is some evidence over the warmer months thatthe fronts’ development is influenced by N2 modulationof the spring–neap cycle. The maximum position of thesurface front on days 75, 88, 104, 119 and 149 (black cir-cles in Fig. 10a), when the range in tidal mixing betweenspring and neap tides is large, reaches or exceeds 3.55◦W (≥15 km stratified). In contrast, during the followingperiod where the tidal stirring during neap tides isgreater, frontal movement is reduced. On days 174, 193,

Fig. 10 a Location of thesurface front and bottomre-attachment over the modelyear (smoothed with a 25-hfilter to remove semi-diurnalvariability). Circles andtriangles indicate eventsreferred to in the text.b Distance (kilometres)between the surface andbottom fronts indicating theextent of stratification (blackline) and the tidal mixingpower (gray shading). Tidalmixing = εκb ρ〈u3〉 at 3.4◦ Wand is fully defined in the text

Ocean Dynamics

Fig. 11 a Top-bottom densitydifference (�ρ) at 3.4◦ W and3.65◦ W. b Tidal mixing(ϕtide) at 3.4◦ W. c Windmixing (ϕwind). d Total riverdischarge from the Merseyand Dee catchments (cubicmetres per second). e �t and�s at 3.4◦. f Horizontal�t, �s and �ρ between3.125◦ W and 4◦ W. Note thatthe series in a, e and f havebeen smoothed with a 25-hfilter window

206 and 221 (black triangles in Fig. 10a), the surfaceexpression outcrops closer to the shore and a reducedarea of the bay stratifies. The front reaches its furthestwestward extent (3.8◦ W) around day 236 following avery weak neap tide.

Fortnightly variation in tidal mixing is not the onlycontrol on frontogenesis in Liverpool Bay, and themagnitude of frontal adjustment varies throughout the

year. Figure 11 summarizes the horizontal and verti-cal anomalies in temperature, salinity and density; thevariation in tidal and wind mixing; and the dischargeof freshwater. The tidal mixing at 3.4◦ W (ϕtide) andthe wind mixing over the area (ϕwind) are calculatedfrom εκbρ〈u3〉 and δκsρaW3

s , respectively. 〈u3〉 is thedepth mean amplitude of the rectilinear tidal streamat 3.4◦ W, cubed and averaged over a tidal cycle. Ws

Ocean Dynamics

is the near surface wind speed. ε = 0.003 and δ = 0.023are the tidal and wind mixing efficiencies, respectively(Simpson and Bowers 1981). κb = 0.003 and κs = 6.4 ×10−5 are the bottom and surface drag coefficients as-sociated with u and Ws. ρa = 1.3 kg m−3 and ρ =1,025 kg m−3 are the approximate densities of air andseawater.

Based on this additional information, three different‘regimes’ are identified: (1) April to mid-September,(2) mid-September to mid-January and (3) mid-Januaryto March. The main features of each of these ‘regimes’will now be described and the details of specific fort-nightly events within them looked at more closely.

5.1 ‘Regime’ 1: surface-advected fronts

The greatest and most consistent frontal response toweak neap tidal mixing takes place between April andmid-September (‘regime’ 1). Over this period, windmixing is generally weak (Fig. 11c), and both the verti-cal and horizontal gradients in temperature (Fig. 11e, f)indicate that warm river discharge is providing positivebuoyancy to the freshwater plume. Coupled with alarge input of freshwater between days 160 and 210(Fig. 11d), all the important factors controlling fron-

togenesis are conducive to maximum surface advec-tion of the freshwater plume (Fig. 10) and the onsetof enduring stratification. At 3.4◦ W, the top-bottomdensity difference is frequently >2 kg m−3 (Fig. 11a).As discussed previously, it is during this period that theinfluence of N2 modulation on the spring–neap cyclecan be most clearly seen.

Over days 184–197, despite high river discharges(200–600 m3 s−1), the surface front does not progressfurther than 3.6◦ W (Fig. 12b), and the stratified zonebetween the top and bottom fronts does not exceed15 km. In contrast, over days 229–242, when dischargeis low (50 m3 s−1), the front moves beyond 3.8◦ Wand stratification develops over a distance of 35 km(Figs. 10b and 12a). The principal difference betweenthese two events is the tidal mixing; the range in mixingbetween spring and neaps tides is more than twice aslarge during event A (days 227–235), and the mixing en-ergy available during neaps is a factor of six smaller. Inaddition to westward progression of the front, the bot-tom attached front retreats shoreward approximately10 km during the neap period (Fig. 12a).

The scale of semi-diurnal frontal movement in re-sponse to flood–ebb tidal advection can be seen inFig. 12a, b. Excursions of the surface front (∼10 km) arelarger than the bottom reattachment (<10 km). During

Fig. 12 Location of surfaceand bottom fronts duringevents A to D (solid gray andblack lines, respectively) andthe tidal mixing power(dashed black line)

Ocean Dynamics

event B, this movement is comparable to the frontsspring–neap adjustment.

5.2 ‘Regime’ 2: bottom-advected fronts

Behaviour of the front between mid-September andmid-January (‘regime’ 2) is very different. In general,the top and bottom fronts remain locked together andrespond to changes in tidal mixing in tandem. Betweendays 313 and 321, they reach 3.45◦ W (Fig. 12c), but thewater column does not stratify. With the exception of aweak peak on day 325 of 0.5 kg m−3, �ρ remains below0.25 kg m−3 (Fig. 11a).

Over this autumn and winter period, wind mixingis moderate-strong and the temperature of the riverdischarge makes a negative contribution to the plumesbuoyancy. River water that is up to 4◦C colder thanthe seawater that it meets (Fig. 11f) reduces the netbuoyancy of the plume to the point where it becomesconvectively unstable (+�t in Fig. 11e). The result is abottom advected plume that tends to be well mixed, oroccasionally weakly stratified. The scale of flood–ebbadvection (5–10 km) during this period is of a similarmagnitude to spring–neap adjustments (Fig. 12c).

5.3 ‘Regime’ 3

‘Regime’ 3 is distinguished from the surface-advectedfronts in ‘regime’ 1 because the negative buoyancycontributions from the cold freshwater act to inhibitdecoupling of the top and bottom fronts. Progression ofthe surface front to 3.7◦ W over days 22–28 (Fig. 12d)is the result of a sudden decrease in wind mixing andthe preceding prolonged period of high discharge in-troducing sufficient volumes of freshwater to promotestratification, despite the destabilising temperature gra-

dients. The initial advance of the surface front coincideswith spring tidal currents. Large semi-diurnal move-ment of up to 20 km takes place over this period.

6 Equivalent freshwater ‘export’

The stratification of large areas in Liverpool Bay, fora number of days following neap tides, and the subse-quent erosion of this surface layer are a potential meansof removing freshwater and its nutrient and pollutantload from the coastal plume system. Here we make afirst attempt at estimating an equivalent freshwater fluxresulting from these events.

Consider an XY m2 surface area of water, h metresdeep, that stratifies during neap tides. The surface andbottom layers are h2 and h1 metres thick, respectively(Fig. 13). The bottom layer has the salinity of seawater,S1. The fresher top layer has a lower salinity of S2

which is considered to be a mixture of a volume Vf

of freshwater with salinity Sf and a volume Vsw ofseawater of salinity Ssw = S1 such that,

S2 = SswVsw + SfVf

Vsw + Vf, (10)

where V2 = Vsw + Vf. S1 and S2 are set at 34 and 32,respectively, based on observational and model data. Asalinity of 10 is chosen for the freshwater Sf since this isthe salinity of estuarine water input into the model. Weare interested in the volume of freshwater Vf requiredto freshen the top layer to S2. This can then be consid-ered as an equivalent volume flux of freshwater mixedout of the plume system when stratification is brokendown. If layers 1 and 2 mix and salt is conserved, then

Fig. 13 Schematic showingspring–neap adjustment of asurface advected plume

Ocean Dynamics

the total volume Vmix = XYh has a new salinity of Smix

where,

Smix = S1V1 + SswVsw + SfVf

Vmix. (11)

Knowing that Vsw = V2 − Vf, substituting intoEq. 11 and rearranging for Vf, the volume of freshwaterneeded to freshen the top layer is:

Vf = SmixVmix − S1V1 − SswV2

Sf − Ssw. (12)

Setting h2 = 5 m and h1 = 20 m, realistic values forthe top and bottom layer depths, respectively, andconsidering a conservative frontal adjustment of X =10 km (Fig. 10), over a length scale of Y = 20 km,8.3 × 107 m3 of fresh estuarine input (Sf = 10) is mixedout of the surface when this stratified zone is eroded.

Figure 10 shows that this fortnightly cycle takes placefor 2

3 of the year (∼17 events), predominantly duringthe spring and summer. Therefore, spring–neap frontaladjustments of this size account for an equivalent fresh-water export of 1.4 × 109 m3 year−1. Given that cumu-latively over the year POLCOMS injects 7.3 × 109 m3

of 10 psu water into the region from the four catchmentbasins, this export accounts for approximately 19% ofthe total estuarine discharge. Movement of up to 35 kmis possible so this fraction is a conservative estimate.

Within each estuary feeding into Liverpool Bay,the salinity field has a gradual along-channel gradient,from oceanic to fresh, as inflowing seawater at depth iscontinually freshened by vertical turbulent mixing withoutflowing freshwater above. The choice of Sf thereforedetermines what the equivalent volume flux Vf relatesto. Here, we have selected a salinity of 10, to allow acomparison with the model, and Vf relates to a volumeof estuarine discharge, with a salinity that is a mixtureof fresh river water and seawater. Recalculating usingSf = 0 results in an equivalent volume of 5.9 × 107 m3

of pure freshwater being exported during each event.Taking Sf up to a value of 20 does not change theorder of magnitude of Vf, and our overall conclusionthat spring–neap cycles of stratification and re-mixingcan remove significant volumes of freshwater from thecoastal plume remains the same.

7 Discussion and conclusions

Satellite SST images and model data reveal the posi-tion of the Liverpool Bay front to be highly variableacross a range of timescales. Over a spring–neap cy-

cle, it can move between 5 and 35 km. On shorter,semi-diurnal timescales, flood–ebb advection accountsfor 5–10 km of movement, which is comparable tothe lower range of spring–neap displacements. Thefortnightly adjustments shown here are much greaterthan those observed at other shelf-sea fronts on theUK continental shelf where the dynamics are prin-cipally controlled by the competition between tidalmixing and surface heating. Based on infrared satel-lite imagery of the Celtic Sea, Western Irish Sea andIslay fronts, where buoyancy added through surfaceheating is relatively constant throughout the summer,only a small ∼4 km adjustment in frontal position isattributed to the spring–neap stirring cycle (Simpsonand Bowers 1981). In contrast, episodic injections offreshwater into Liverpool Bay and seasonally varyingdensity anomalies introduce a high degree of variabilityto the buoyancy and subsequently to the fronts’ po-sition. Liverpool Bay is also a lot shallower (<50 m)than the Celtic and Western Irish Sea; consequently,as previously highlighted by other authors (Burchard2009; Verspecht et al. 2009a), wind mixing plays animportant role in controlling the strength, extent andtiming of stratification and can impose a more irregularbehaviour. Bottom up mixing from tidal currents thatcan reach the sea surface also becomes a considerationin shallower waters.

The N2 cycle can limit westward propagation ofthe front and the area of Liverpool Bay that stratifiesfollowing neap tides. Contrasting the fronts responseduring the strongest neap tide (Fig. 12b), with one ofthe weakest (Fig.12a), demonstrates that the surfaceexpression can move two to three times further dur-ing sufficiently weak tidal stirring. This is supportedby other observational and model data that show N2

modulation of the spring–neap cycle to have an impor-tant control on post-neap stratification (Sharples andSimpson 1995).

An estimate of the position of the Liverpool Bayfront can be found in Vincent et al. (2004) which isin broad agreement with the 99% confidence contoursof Fig. 8, particularly during the winter. The westwardincrease in position with distance north is also a fea-ture of Vincent et al. (2004) and is consistent withnorthwesterly advection by surface residual currents(Verspecht et al. 2009b).

Tracking of the surface and bottom fronts inPOLCOMS has revealed the Liverpool Bay freshwa-ter plume to have two different dynamical regimes.During the winter, a bottom-advected plume is mostcommon (‘regime’ 2), where buoyant inflow is well

Ocean Dynamics

mixed throughout the water column and the surfaceand bottom fronts lie on top of one another. Dur-ing the summer (‘regime’ 1), river discharge initiallyspreads offshore maintaining contact with the bottomout to approximately 3.3◦ W, beyond which point theupper part of the plume detaches from the bottom andspreads seaward as a surface advected front. The vol-ume of river discharge and seasonal density anomaliesappear to be the primary controls on plume structure.This is supported by Yankovsky and Chapman (1997)who predict the vertical structure and offshore spread-ing of buoyant plumes based solely on inflow para-meters (including inflow velocity and density anom-aly). Surface-advected plumes and the development ofstratification are not strictly a summer regime. Wherethe volume of freshwater input is sufficient to offsetthe negative buoyancy contribution from the temper-ature a surface-advected plume may develop in thewinter. Further evidence for winter stratification, inspite of destabilising temperature gradients, is found inSharples and Simpson (1995) and Czitrom and Simpson(1998).

Yankovsky and Chapman (1997), and referencestherein, help explain some of the features of resultspresented here. The front of a bottom-advected plumeis established by offshore advection of buoyancy in thebottom boundary layer and continues to be pushedseaward as it moves downstream along the coast(Chapman and Lentz 1994). This offshore progressionwith increasing latitude is evident in Figs. 8 and 9aand is a feature of the majority of images analysed.During the summer, the dynamics of the bottom partof the plume will be most strongly influenced by near-bed processes, while the surface-advected part, decou-pled from the bottom, is affected by surface processessuch as Coriolis and wind stress. Once released fromthe influence of bottom stress, the surface front canprogress much further offshore and occupies a widerrange of positions. Evidence of the surface and bottomfronts behaving in different ways is found in Fig. 12awhere the bottom front moves shoreward and the sur-face front advances offshore. This is likely the result ofenhanced estuarine circulation that can occur duringneap tides (Geyer et al. 2000). Intensified westwardsurface residuals are compensated at depth by eastwardnear-bed flows that subsequently drive the shorewardretreat of the bottom front.

Salinity, rather than temperature, is the primary con-trol on stratification in Liverpool Bay (Palmer 2009).The limitations of using SST as an indicator of thefronts’ position should therefore be considered. Be-tween May and August, the salinity and temperaturestructures contribute equally to the vertical density

distribution (Czitrom and Simpson 1998), and CEFASSmartBuoy data show temperature and salinity to besignificantly negatively correlated during the summermonths. For example, during July 2007, the correla-tion coefficient for the raw 30-min time series is −0.8,significant at the 99% level. From this perspective,satellite SST images during the summer should be rep-resentative of the fronts location. Conversely, at theinterface between the ROFI and the wider Irish Sea,where salinities are higher, the water column may sea-sonally stratify if currents are weak enough (Howarthand Palmer 2011). This makes the separation of warm,fresh plume water from warm, saline Irish Seawater lessreliable and introduces a westward bias to the estimatedposition of the surface front. It is difficult to know whatcontribution any seasonal thermal stratification may bemaking to the summertime neap position in Fig. 8a.Analysis of model density does not suffer from thiscomplication.

Sea surface temperatures during the winter revealedless spring–neap movement (5–10 km) than duringthe summer (25–30 km). This is supported by themodel and explained by increased summer buoyancyand decoupling of the surface and bottom fronts.The higher probability of finding winter spring frontsfurther offshore, however, cannot be fully explained(Fig. 8b). It is unclear whether this unexpected findingis the result of dynamically different regimes, or simplya consequence of the composite presentation of results.Larger and more frequent periods of stratification andfrontal movement take place during the summer whichare more readily identified against shorter timescalevariability. Over the winter, flood–ebb advection andthe irregular response to wind stress and river dis-charge may mask more subtle fortnightly adjustmentsto tidal mixing energy when 5 years worth of data arecombined.

Fortnightly stratification and remixing over largeareas of Liverpool Bay is one of a number of processesresponsible for the redistribution of freshwater, therelative importance of each requiring consideration.A weak, but continual background residual circulationcomprising northwesterly surface flow and southeast-erly near-bed currents (Heaps 1972) may be enhancedby semi-diurnal tidal straining (Simpson et al. 1990;Verspecht et al. 2009b) and therefore make a significantcontribution to the horizontal mass flux of freshwater(Jay and Musiak 1994; Prandle 2004). Based on 5 yearsof observational data, Verspecht et al. (2009b) estimatethe long-term mean surface residual at the main obser-vatory mooring site to be 0.025 m s−1 (northwesterly).Palmer (2009) reports comparable northward residualsof 0.036 m s−1, 20 km further west.

Ocean Dynamics

Using the estimate of Verspecht et al. (2009b) andthe approach introduced in Section 6, we can ap-proximate the contribution that this baroclinic resid-ual may make to the annual export of freshwater outof Liverpool Bay. Considering a 0.025 m s−1 residualflow across a 5-m-deep surface layer, over a 10-kmeast–west section, then 3.9×1010 m3 year−1 is advectednorthwards through this layer. If 8% of this total vol-ume is considered to be fresh (where Sf = 10), then3.15×109 m3 year−1 of estuarine discharge is exportedby the residual flow. This accounts for approximately43% of the total model estuarine inflow. In comparisonto the 19% from post-neap stratification and springremixing, the residual circulation makes the more sub-stantial contribution towards freshwater export.

Although the slow residual circulation may be re-sponsible for the majority of freshwater export, spring–neap tidal mixing and the associated frontal movementcan influence biogeochemical cycles within Liver-pool Bay. During the winter, between December andFebruary, there is a strong linear relationship be-tween the primary nutrient concentrations and salinity(Greenwood et al. 2011). The main source of nutri-ents is from river inputs, and during the winter, theirdistribution is principally controlled by the physicalmixing of fresh and saline waters within the ROFI.Greenwood et al. (2011) show that the mean (±1 stan-dard error) monthly concentration of TOxN (nitrite+ nitrate) across the observatory survey grid is thehighest in February (18±1 μmol l−1). This is coinci-dent with a regime of surface-advected plumes andenduring stratification (Fig. 10). Taking a TOxN con-centration within the surface plume to be 18 μmol l−1

(252 mg m−3), over a depth of 5 m, when stratificationis eroded 1,260 mg m−2 TOxN is lost from the plume.Over the 7 days between neap and spring tides, this isan irreversible export rate of 180 mg m−2 day−1. For a20-km stretch of front, adjusting by 10 km, 252 tonnesTOxN (or 36 tonnes day−1) is mixed out of the plume.During late winter therefore when a wide area of thebay stratifies, for example between days 20 and 30 in2007 (Fig. 10), large amounts of nutrients can be mixedout of surface waters.

Over the summer months, nutrient concentrationsare much lower and the salinity–nutrient relationshipis not so conservative. Following wintertime accumula-tion, rapid biological uptake during the spring bloomdepletes the nutrient pool, and the system becomesnet autotrophic (Greenwood et al. 2011; Panton et al.2011). Fortnightly cycles in chlorophyll-a concentrationand dissolved oxygen saturation suggest that spring–neap variability in tidal mixing has a role to play incontrolling biological cycles through its influence on

sediment and nutrient resuspension from the bed andthe associated impact on light penetration (Panton et al.2011). The area over which this takes place, i.e. the scaleof frontal adjustment, will be reflected in the scale ofany phytoplankton blooms, which are visible in oceancolour satellite imagery.

Acknowledgements All remote sensing data were providedcourtesy of the NERC Earth Observation Data Acquisitionand Analysis Service, Plymouth (http://www.neodaas.ac.uk/). Wethank all those involved with the Irish Sea Observatory who havecollected and processed the data sets used in this study. Theauthors are grateful for the constructive comments and sugges-tions made by two anonymous reviewers that have improved thismanuscript.

References

Balfour C, Howarth MJ, Smithson M, Jones D, Pugh J (2007) Theuse of ships of opportunity for Irish Sea based oceanographicmeasurements. In: Marine challenges: coastline to deep sea,Aberdeen, Scotland, Oceans ‘07. IEEE Aberdeen, p 6

Burchard H (2009) Combined effects of wind, tide, and horizon-tal density gradients on stratification in estuaries and coastalseas. J Phys Oceanogr 39(9):2117–2136

Burchard H, Flöser G, Staneva J, Riethmuller R, Badewien T(2008) Impact of density gradients on net sediment transportinto the Wadden Sea. J Phys Oceanogr 38:566–587

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

Cayula JF, Cornillon P (1992) Edge-detection algorithm for SSTimages. J Atmos Ocean Technol 9(1):67–80

CEH (2007) Derivation of daily outflows from hydrometric areas.Internal report, CEH Wallingford, July 2003

Chapman DC, Lentz S (1994) Trapping of a coastal density frontby the bottom boundary layer. J Phys Oceanogr 24:1464–1479

Czitrom SPR, Simpson JH (1998) Intermittent stability and fron-togenesis in an area influenced by land runoff. J GeophysRes Oceans 103(C5):10369–10376

Geyer W, Cannon G (1982) Sill processes related to deep waterrenewal in a Fjord. J Geophys Res Oceans 87(C10):7985–7996

Geyer W, Trowbridge J, Bowen M (2000) The dynamics of apartially mixed estuary. J Phys Oceanogr 30:2035–2048

Greenwood N, Hydes D, Mahaffey C, Wither A, Barry J, SivyerD, Pearce D, Hartman S, Andres O, Lees H (2011) Spa-tial and temporal variability in nutrient concentrations inLiverpool Bay, a temperate latitude region of freshwaterinfluence. Ocean Dyn. doi:10.1007/s10236-011-0463-y

Hastie T, Tibshirani R, Friedman J (2001) The elements ofstatistical learning: data mining, inference, and prediction.Springer Series In Statistics. Springer, New York

Heaps N (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 (1999) A simulation of the Southern NorthSea in comparison with measurements from the North SeaProject. Part I: temperature. Cont Shelf Res 19:1087–1112

Holt J, James ID (2001) An s-coordinate density evolving modelof the north west European continental shelf. Part 1. Model

Ocean Dynamics

description and density structure. J Geophys Res Oceans106(C7):14,015–14,034

Holt J, James ID (2006) An assessment of the fine-scale eddiesin a high-resolution model of the shelf seas west of GreatBritain. Ocean Mod 13:271–291

Holt J, Proctor R (2008) The seasonal circulation and volumetransport on the northwest European continental shelf: afine-resolution model study. J Geophys Res 113:C06021.doi:10.1029/2006JC004034

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

Howarth MJ, Palmer MR (2011) The Liverpool Bay CoastalObservatory. Ocean Dyn. doi:10.1007/s10236-011-0458-8

James ID (1996) Advection schemes for shelf-sea models. J MarSyst 8:237–254

Jay D, Musiak J (1994) Particle trapping in estuarine tidal flows.J Geophys Res Oceans 99(C10):20445–20461

Linden PF, Simpson JE (1988a) Gravity-driven flows in a turbu-lent fluid. J Fluid Mech 172:481–497

Linden PF, Simpson JE (1988b) Modulated mixing and fron-togenesis in shallow seas and estuaries. Cont Shelf Res8(10):1107–1127

Miller P (2009) Composite front maps for improved visibilityof dynamic sea-surface features on cloudy SeaWiFS andAVHRR data. J Mar Syst 78:327–336

Monismith S, Burau J, Stacey M (1996) Stratification dynamicsand gravitational circulation in northern San Francisco Bay.In: Hollibaugh T (ed) San Francisco Bay: the ecosystem.Pacific Division, Amer. Assoc. Adv. Sci., San Francisco,pp 123–153

Nunes R, Lennon G (1987) Episodic stratification and gravitycurrents in a marine environment of modulated turbulence.J Geophys Res 92(C5):5465–5480

Palmer MR (2009) The modification of current ellipses bystratification in the Liverpool Bay ROFI. Ocean Dyn60(2):219–226

Panton A, Montagnes D, Sharples J, Hopkins J, Mahaffey C(2011) Short-term and seasonal variation in metabolic bal-ance in Liverpool Bay. Ocean Dyn. Accepted with revisions

Polton J, Palmer MR, Howarth MJ (2011) Physical and dy-namical oceanography of Liverpool Bay. Ocean Dyn.doi:10.1007/s10236-011-0431-6

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

Ruddick K, Deleersnijder E, Luyten P, Ozer J (1995) Halinestratification in the Rhine–Meuse fresh water plume: athree-dimensional model sensitivity analysis. Cont Shelf Res15:12507–12630

Scully M, Friedrichs C (2007) The importance of tidal and lateralasymmetries in stratification to residual circulation in par-tially mixed estuaries. J Phys Oceanogr 37:1496–1511

Sharples J, Simpson JH (1993) Periodic frontogenesis in a regionof fresh-water influence. Estuaries 16(1):74–82

Sharples J, Simpson JH (1995) Semi-diurnal and longer pe-riod stability cycles in the Liverpool region of freshwaterinfluence. Cont Shelf Res 15(2–3):295–313

Shimada T, Sakaida F, Kawamura H, Okumura T (2005) Ap-plication of an edge detection method to satellite imagesfor distinguishing sea surface temperature fronts near theJapanese coast. Remote Sens Environ 98(1):21–34

Simpson JH, Bowers D (1981) Models of stratification andfrontal movement in shelf seas. Deep-Sea Res Part AOceanogr Res Pap 28(7):727–738

Simpson JH, Brown J, Matthews J, Allen G (1990) Tidal strain-ing, density currents, and stirring in the control of estuarinestratification. Estuaries 13(2):125–132

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

Unesco (1981) The practical salinity scale 1978 and the interna-tional equation of state of seawater 1980. Tenth report of thejoint panel on oceanographic tables and standards. Unescotechnical papers in marine science 36. Tech. rep., Sponsoredby UNESCO, ICES, SCOR, IAPSO

Verspecht F, Rippeth TP, Howarth MJ, Souza AJ, Simpson JH,Burchard H (2009a) Processes impacting on stratificationin a region of freshwater influence: application to Liver-pool Bay. J Geophys Res Oceans 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(5):765–779

Vincent M, Atkins S, Lumb C, Golding N, Lieberknecht L, Web-ster M (2004) Marine nature conservation development—the Irish sea pilot. Report to Defra by the Joint NatureConservation Committee, Peterborough

Yankovsky AE, Chapman DC (1997) A simple theory for the fateof buoyant coastal discharges. J Phys Oceanogr 27(7):1386–1401