The drift-retention dichotomy on Browns Bank: a model study of interannual variability

The drift–retention dichotomy on Browns Bank:a model study of interannual variability

Charles G. Hannah, Jennifer A. Shore, and John W. Loder

Abstract: Interannual variability in drift and retention in the Browns Bank region in spring was investigated by track-ing particles in numerical-model estimates of the seasonal mean circulation and monthly mean flow anomalies com-puted using wind and sea-level data. The circulation changes associated with the variable forcing tend to reinforceeither drift to the Bay of Fundy or retention in the vicinity of Browns Bank. Regular spring spawning can lead towidely different distributions of 1-month-old larvae, supporting the concept of a drift–retention dichotomy for Atlanticcod (Gadus morhua) and haddock (Melanogrammus aeglefinus) larvae in the region. Analysis of interannual variabilityindicates that retention has bounded properties that must be accounted for when relating retention variability to forcingindices. As well, the nonlinearities associated with calculating particle trajectories from velocity fields contribute about10% of the variance in retention indices. Comparison with biologically based indices of haddock survival indicates thatcirculation variability alone is not the dominant influence on survival to ages 1 and 2 years. However, it can be ex-pected to have a significant influence in conjunction with biological factors such as the location and timing of peakspawning and the variable vertical position of eggs and larvae.

Résumé: Nous avons étudié la variabilité inter-annuelle de la dérive et de la rétention au printemps dans la région dubanc Browns, en faisant le suivi de particules à l’aide d’estimations des anomalies dans la circulation saisonnièremoyenne et le flux mensuel moyen provenant d’un modèle numérique basé sur les données de vent et de niveau de lamer. Les changements de circulation associés au forçage des variables tendaient à accentuer soit la dérive vers la baiede Fundy, soit la rétention dans les environs du banc. La fraye régulière du printemps peut donc résulter en des distri-butions très divergentes des larves de 1 mois, ce qui s’accorde avec la dichotomie entre la dérive des larves de morue(Gadus morhua) et la rétention des larves d’aiglefin (Melanogrammus aeglefinus) dans la région. L’analyse de la varia-bilité inter-annuelle montre que la rétention possède des propriétés bornées dont il faut tenir compte lorsqu’on relie lavariabilité de la rétention aux indices de forçage. De plus, l’absence de linéarité dans le calcul des trajectoires des par-ticules à partir des champs de vitesse explique environ 10% de la variance des indices de rétention. Une comparaisonavec des indices biologiques de la survie chez l’aiglefin montre que la variabilité de la circulation seule n’est pas lefacteur le plus important pour la survie aux âges d’un et 2 ans. Toutefois, cette variabilité peut vraisemblablement avoirun effet significatif si elle est associée à des facteurs biologiques, tels que le site et la date de la fraye maximale, ainsique la position verticale variable des oeufs et des larves.

[Traduit par la Rédaction] Hannah et al. 2518

Introduction

Physical drift and retention are important factors in vari-ous theories of marine population regulation, such as themember–vagrant and migration-triangle hypotheses (Sinclair1988; Harden-Jones 1968; Sinclair and 995). Potentialconsequences of variability in drift and retention include dif-ferences in food availability, ocean temperature, exposure topredators, and probability of recruitment to resident popula-tions. However, the pronounced spatial and temporal vari-ability in the physical and biological environment around

many spawning areas complicates the effects of drift and re-tention and confounds their explanation.

Browns Bank on the southwestern Scotian shelf (Fig. 1) isan important spawning area for Atlantic cod (Gadus morhua)and haddock (Melanogrammus aeglefinus) populations(Hurley and Campana 1989; Brander and Hurley 1992) thatwere the subject of the 1983–1985 Fisheries Ecology Pro-gram (FEP), an intensive field investigation of physics–plankton–fish dynamics. Results of the study included theidentification of both partial retention on Browns Bank and apreferred drift pathway towards the Bay of Fundy (Smith1989), spatial structure in prey fields and larval growth rates(Suthers et al. 1989), and evidence in fish-larva distributionsof both retention and drift influences, with differences be-tween cod and haddock (Campana et al. 1989a,1989b). Inparticular,Campana et al. (1989b) proposed a “drift–retentiondichotomy” for cod andhaddock larvae involving drift andretention processes acting in concert to split the larval popu-lations into varying portions retained in the Browns Bankspawning area or transported towards the Bay of Fundy. Fur-ther, Page and Smith (1989) pointed out the importance of

Can. J. Fish. Aquat. Sci.57: 2506–2518 (2000) © 2000 NRC Canada

2506

Received January 20, 2000. Accepted October 27, 2000. Publishedon the NRC Research Press web site on December 20, 2000.J15548

C.G. Hannah,1 J.A. Shore, and J.W. Loder. Fisheries andOceans Canada, Bedford Institute of Oceanography, Box 1006,Dartmouth, NS B2Y 4A2, Canada.

1Corresponding author (e-mail: [email protected]).

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tidally rectified and wind-driven flows to variable drift inthe region. However, many issues regarding the origin, vari-ability, and implications of the partitioning in larval distribu-tions have not been resolved.

One of the goals of the Global Ocean Ecosystem Dynam-ics (GLOBEC) Canada Program has been to examine furtherthe roles of physical and biological factors in the survivaland growth of gadoid early life stages on Browns Bank.Model fields for the seasonal mean circulation (Hannah et al.2001; Shore et al. 2000) show good agreement with observa-tions, providing a base-line representation of the Bank’s par-tial gyre and the major drift pathway along its southwesternflank towards the Bay of Fundy. Model fields for wind-driven flow provide 3-dimensional (3D) representations ofthe combined effects of local forcing (surface Ekman layer)and larger scale pressure-field variations (Greenberg et al.1997). Together with the FEP findings, the new model re-sults indicate that the Browns Bank retention area is leakybecause of its location in the equatorward throughflow onthe Scotian Shelf and its small size relative to low-frequencyand tidal water-parcel excursions.

A complementary component of the GLOBEC Canadaprogram has been the development (Shackell et al. 2000) ofa biologically based retention–survival index for early lifestages of haddock on Browns Bank, based on length-at-age 2(years) frequency distributions for each year class from 1968to 1993. In some years, length-at-age values show a distinctbimodal distribution that was interpreted as representing amixture of haddock which were retained on Browns Bankand grew slowly during early life, and others which wereadvected to the Bay of Fundy and grew more rapidly. Thisinterpretation is based on the observations that there is littlehaddock spawning in the Bay of Fundy, and that juvenilehaddock sampled there in July are generally larger thanthose found on the southwestern Scotian Shelf because of

higher growth rates (Hurley et al. 1997). Two intriguingsuggestions from Shackell et al.’s (2000) analysis are that(1) while haddock in the Bay of Fundy have higher growthrates, survival to age 1 is greater in years when there is in-creased retention on the offshore shelf; and (2) retention ofearly life stages in the lower growth offshore region is themost common condition, whereas the climatological circula-tion indicates a greater tendency for drift away from BrownsBank than for retention (Shore et al. 2000). These apparentdiscrepancies point to the need for further investigations ofdrift and retention in the region, and their implications forfish survival and recruitment.

We investigate interannual variability in drift and retentionon the southwestern Scotian Shelf, using particle tracking incomposite model flow fields that capture the salient featuresof spatial structure and temporal variability in the regionalcirculation. Our goals are to provide estimates of interannualvariability in retention and drift in the region, explore theirrelation to biologically based retention and survival indices,and illustrate aspects of the complexity of the retention con-cept from a physical perspective. We examine interannualvariability in wind-driven flow and throughflow using obser-vational data from 1975–1990 and the extent to which vari-ability in drift and retention indices in a simplified (butnonlinear) physical system can be predicted from forcing in-dices and velocity observations. This provides background tomore realistic model evaluations of the evolution of earlylife stages of haddock on Browns Bank that involve both bi-ological and physical factors (Brickman and Frank 2000;Brickman et al. 2000).

Methods

Circulation and drift were simulated for the individual monthsApril and May from 1975 to 1990. These months were chosen

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Hannah et al. 2507

Fig. 1. Map showing location and topography of the Scotian Shelf off Atlantic Canada, with the mean circulation shown schematically.The thick line on the eastern Scotian Shelf is the model boundary; the hatched portion of the line shows the active portion of theboundary for the boundary-forced anomalies.

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because peak haddock spawning occurs in spring (Hurley andCampana 1989) and the general decline in wind strength fromApril to May provides a contrast in forcing. During each month,particles were tracked in velocity fields representing flow in thesurface Ekman layer (the vertical average of the upper 5 m; “U5”or “near-surface”) and the velocity field at 20 m representing theflow below the Ekman layer. These vertical levels approximate thebasic modes in Frank et al.’s (1989) observations in which earlyegg stages were concentrated in the near-surface layer and lateregg stages and larvae were concentrated below it. Two adjoiningrelease areas were used (Fig. 2), one covering the western portionof Browns Bank (“west”), which is believed to be the primary had-dock spawning area (Shackell et al. 2000), and the other coveringthe outer-shelf portions of Browns and Baccaro banks (“east”),where important spawning also occurs (Hurley and Campana1989).

Flow fieldsThe estimated mean flow field (vT) for a given month (e.g.,

April 1982) comprises a linear combination of 4 components: theseasonal mean circulation (vm) and the responses to the along-shelf(τA) and cross-shelf (τC) monthly wind-stress anomalies and toanomalous monthly forcing at the upstream boundary (ςB). Thiscan be written as

(1) vT = vm + va τA/τa + vc τC /τc + vb ςB /ςb

whereva is the velocity response to a reference along-shelf windstress (τa), vc is the response to a reference cross-shelf wind stress(τc), vb is the response to a reference upstream boundary forcingwith coastal amplitude,ςb. These flow components were computedon a model domain extending from the eastern Scotian Shelf(Fig. 1) to the western Gulf of Maine and offshore into the sloperegion.

The seasonal mean component, the spring field described inHannah et al. (2001) and Shore et al. (2000), is constant acrossmonths and years. It was computed with a 3D prognosticadvanced-turbulence model (Lynch et al. 1996), initialized, andforced with observational data on M2 tides, and on seasonal mean

density gradients and wind stress. The flow field is in good quanti-tative agreement with the seasonal mean currents from mooredmeasurements at 46 (3D) positions on the southwestern ScotianShelf, the kinetic energy of the difference field being only 37% ofthat of the observed currents. The field at 10 m is also in approxi-mate agreement with the spring velocity pattern on Browns Bankestimated from a small drifter data set (Smith 1989), but there aredifferences along the northern edge and north of the Bank (Shoreet al. 2000).

The year-to-year variability comes from the wind- and boundary-forced components. The wind-forced component is based onmonthly anomalies of Sable Island wind stress, computed by sub-tracting the long-term April–May mean stress (0.0194 Pa at100°T (degrees True), which was included in the seasonal meanforcing) from each monthly mean. The responses to the along- andcross-shelf anomalies were calculated using a linear 3D barotropicmodel (Lynch et al. 1992; Greenberg et al. 1997) with specifiedvertical eddy viscosities and bottom friction coefficients. The latterwere taken as the time-averaged coefficients from the seasonalmean solution plus the additional bottom friction due to 0.1 m·s–1

of unmodelled flow.The specified vertical eddy viscosities were a combination of

those derived from the seasonal mean solution and an empiricalupper-ocean profile. The empirical eddy–viscosity profile (Fig. 3a),which is based on the work of Madsen (1977), Csanady (1984),and Craig et al. (1993), provides a high (vertical) resolution repre-sentation of some of the effects of processes such as storm-bandmixed-layer dynamics and surface waves that are not present in theseasonal mean solution. In the upper 2 m, the viscosity is definedas ν = –κ u*z, where the friction velocity,u* = 0.012 m·s–1, is com-puted using the rms (root mean squared) wind stress for April andMay (0.14 Pa; from hourly estimates),κ = 0.4 is the von Karmanconstant, andz is the vertical coordinate, positive upwards with or-igin at the sea surface. The viscosity is taken to beconstant atν =0.0094 m2·s–1 for z = –2 to –8 m (approximating the results inCsanady 1976) and to decrease linearly to a background value ofν = 0.001 m2·s–1 at z = –10 m.

To resolve the near-surface velocity structure, additional verticalnodes were added to the linear model (yielding 6 in the upper 1 mand 5 in the next 5 m). The wind-driven velocity profile (Ekman-layer response) derived from the empirical profile is shown inFig. 3b. Flow is largely at a 90° angle to the right of the wind stressin the upper 10 m, with enhanced downwind drift in the upper 1 mand Ekman spiral effects penetrating to 30 m, providing a reason-able representation of near-surface wind-forced current structureunder typical conditions. In locations where the seasonal mean

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2508 Can. J. Fish. Aquat. Sci. Vol. 57, 2000

Fig. 2. The particle-release areas on Browns Bank east (E) andwest (W) and the particle-counting zones on the Scotian Shelf(SS) and Bay of Fundy (BoF). The Browns Bank particle-counting zone is the union of the east and west release areas.

Fig. 3. (a) The empirical vertical viscosity profile for the surfaceEkman layer, based on Madsen (1977) and others. (b) The veloc-ity profile for a 0.1-Pa wind stress towards the north (the solidline shows eastward velocity and the broken line shows north-ward velocity).



solution gives viscosities greater than the empirical profile, the lat-ter is used forz ≥ –1 m and the profile makes a smooth transitionto the eddy viscosities from the seasonal mean solution (with aminimum value ofν = 0.001 m2·s–1 imposed forz ≤ –1 m).

For calculating the wind-forced anomaly, the reference along-shelf andcross-shelf wind stress in (1) was 0.1 Pa at 56°T and 0.1 Paat 326°T, respectively. The elevations were clamped at zero alongthe upstream and offshore boundary; thus, any non-zero interior el-evations are due to the wind forcing over the model domain. Theresponse patterns are similar to those described in Greenberg et al.(1997).

The boundary-forced component is based on the monthly meanadjusted sea level (ASL) at Halifax. An anomaly time series forApril was computed by subtracting the average April ASL for1970–1993 from the April time series. Then for each April, thecomponent (ζHw) of ASL due to the anomalous wind stress over themodel domain was computed from

(2) ζHw = ζHa τA / τa + ζHc τC / τc

whereζ Ha andζ Hc are the model elevation responses at Halifax dueto the reference along-shelf and cross-shelf wind stresses, respec-tively; ζ Hw was then subtracted from the Halifax ASL anomaly toyield the de-winded ASL anomaly (that component due to forcingfrom outside the model domain). A similar calculation was donefor May. This approach assumes that the Halifax elevation associ-ated with the seasonal mean circulation field is a good approxima-tion of the long-term average ASL for April and May.

The velocity response to boundary forcing was calculated usingthe same linear model, bottom friction coefficients, and verticaleddy viscosities used for the wind response. The upstream bound-ary forcing was specified as a linear decrease in elevation from thecoast to midshelf (Fig. 1), with the rest of the upstream and off-shore boundary clamped to zero. The boundary-forcing anomalyζBwas chosen to give an elevation magnitude at Halifax that matchedthe de-winded ASL anomaly.

The time series of anomalous wind stress (τA, τC) and boundary(ζ B) forcing are shown in Fig. 4. Both the stress and boundaryanomalies are generally largest in April, with peak stress anomaliesthat are an order of magnitude larger than the long-term seasonalaverage, and ASL anomalies that are of comparable magnitude tothe seasonal range.

In addition to the monthly mean flow fields, the M2 tidal cur-rents (the most energetic current component in the region) from theprognostic model (Hannah et al. 2001) were included in the simu-lations. The Stokes drift (the difference between mean velocitymeasured at a point and mean velocity of a drifter) associated with

large spatial variations in the tidal currents across the edges ofbanks can make important contributions to residual drift (e.g.,Loder 1980; Page and Smith 1989; Ridderinkhof and Loder 1994).

Particle trackingParticles were tracked in the monthly mean (vT) and tidal (M2)

velocity fields using a fourth-order Runge–Kutta method (Werneret al. 1993) and a time step∆t = 357.7 s. Additional random hori-zontal kicks were added that correspond to a horizontal eddydiffusivity of 50 m2·s–1, comparable to that estimated by Smith

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Hannah et al. 2509

Fig. 4. (a and b) Monthly wind-stress anomalies for April andMay, respectively; the solid lines are the along-shelf anomalies(positive northeastward) and the broken lines are the cross-shelfanomalies (positive northwestward). (c and d) Monthly boundary-forcing anomaly for April and May, respectively. The wind-stressanomalies are with respect to the April–May mean of 0.0194 Paat 100°T. The boundary anomalies are with respect to themonthly means for the period 1970–1993. (e and f) Monthlymean eastward component of the near-surface currents at C2 forApril and May, respectively. The observed currents (*) are be-tween 15 and 30 m below the surface and the modelled currents(solid line with solid triangles) are 20 m below the surface. (g–j)Retention indices for Browns Bank;g and h are the ScotianShelf (SS) retention indices for the west release for April andMay, respectively, computed as the average of the near-surfaceand 20 m depth results;i and j are the retention–survival andsurvival indices, respectively, from Shackell et al. (2000).



(1989) from drifter measurements. These random kicks approxi-mate the effects of unmodelled motions such as eddies and storm-driven currents. Nevertheless, the flow fields and particle trajecto-ries are only an approximation of reality because the spatial andtemporal structures of such motions and their influence on verticalmixing are not fully represented.

In total, 128 different particle-tracking experiments of 30 days’duration were conducted: 16 years, 2 months per year, two verticallevels per month, and two release areas per level. The west andeast release areas (Fig. 2) had 2737 and 4501 particles, respec-tively, spaced at 850-m intervals. To describe the overall spatialpattern of particle dispersal, the particles were counted at the endof each simulation using a regular 50 × 50 km grid covering theentire domain. Interannual variability in retention and drift wasquantified using retention and drift indices computed as the per-centage of total particles in specified zones after 30 days in eachsimulation. Particles were fixed at one of the vertical levels to ex-amine sensitivity extremes in physical retention and drift.

Results

Circulation variabilityThe basic flow fields used to construct the monthly mean

circulation fields are shown in Fig. 5. The forcing magni-tudes of the wind- and boundary-forced components werechosen to represent very large positive anomalies (Fig. 4) inorder to illustrate the spatial structure. Note that negativeanomalies simply reverse the directions of the flows, owingto linearity.

The primary features in the seasonal mean fields(Figs. 5a, 5e) are strong northwestward and northward ve-locities along the southwestern side of Browns Bank and ex-tending northwards to the mouth of the Bay of Fundy; asouthwestward flow on the western Scotian Shelf with asmall nearshore branch following the 100-m isobath aroundCape Sable and a large branch going to the shelf break andthen along the southwestern side of Browns Bank; someeastward flow on the northern flank of Browns; and onlysmall differences between the near-surface and 20-m levels.The circulation associated with upstream inflow (positiveASL anomaly; Fig. 5d) shows similarity to the seasonalmean in having a southwestward flow on the inner and outerScotian Shelf, a northward flow towards the Bay of Fundy,and little vertical structure. However, it differs from the sea-sonal mean in being weak along the western side of BrownsBank, with the flow towards the Bay of Fundy primarilysupplied from the inner Scotian Shelf.

The wind-forced components (Figs. 5b, 5c, 5f) differ fromthe others in that they introduce substantial vertical structureassociated with the surface Ekman layer. Northeastwardalong-shelf wind stress gives rise to a generally southeast-ward near-surface flow (i.e., 90° to the right of the stress di-rection), modified in some areas by the associated barotropicpressure-field response. At 20 m, the pressure-field contribu-tion dominates the wind-forced component, and primarilyinvolves flow on the inner shelf around Cape Sable (and on-shelf flow in the Northeast Channel) supplying the Ekmandivergence on the Scotian Shelf. Similarly, northwestwardcross-shelf wind stress gives rise to a generally northeast-ward near-surface flow, but in this case there is only a weakpressure-field response.

At both levels, along-shelf stress and boundary-forcinganomalies provide the potential to either offset or reinforcekey pathways in the seasonal mean flow, particularly the

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Fig. 5. The current components used to construct the monthlymean flow fields: the near-surface currents (upper 5 m) offsouthwestern Nova Scotia for the seasonal mean solution (a); thealong-shelf wind solution forτA = 0.1 Pa (b); the cross-shelfwind solution forτC = 0.1 Pa (c); and the boundary-forced solu-tion for ζ B = 0.1 m (d). (e and f) The 20-m currents for the sea-sonal mean solution and the along-shelf wind solution forτA =0.1 Pa, respectively. The cross-shelf wind solution at 20 m (notshown) is small, and the boundary-forced solution is very similarto the near-surface solution (d).



westward drift on the inner shelf off Cape Sable and thenorthward drift towards the Bay of Fundy. The effect shouldbe largest in the near-surface layer, where the Ekman trans-port and pressure-field contributions can be reinforcing, butcould also be important below the Ekman layer, especiallywhen along-shelf stress and boundary-forcing anomalieshave opposite signs.

The most extreme events in the anomaly forcing occur inApril 1982, when the along-shelf stress anomaly is stronglypositive (northeastward) and the boundary-forcing anomalyis strongly negative (coastal set-down), and in April 1984,when the opposite occurs. In April 1982, the wind- andboundary-forcing components dramatically change the circu-lation pattern at both depths (Figs. 6a, 6c). The northwardflow off western Nova Scotia has been eliminated in thenear-surface and substantially reduced at 20 m, and there isa broad gyre around Browns Bank. This expanded gyre, withcontributions from tidal rectification, density gradients, andwind and boundary forcing, contrasts with the small topo-graphic-scale gyre due to tidal and density forcing in theseasonal-mean flow. In April 1984, the anomalous forcingslargely reinforce the seasonal mean, and there is enhancedthroughflow in the region, with only a small recirculationarea on the cap of Browns Bank (Figs. 6b, 6d).

Examples of the 30-day particle distributions that resultfrom the different circulation fields are shown in Fig. 7. For

the near-surface seasonal-mean flow (Figs. 7a, 7b), the west-release particles are spread out between Browns Bank andthe Bay of Fundy, with some turning west around GeorgesBasin and some remaining on Browns Bank. The case of theeast release is similar, but there are almost no particles re-maining near Browns Bank because the release grid lies onthe main artery of the seasonal mean flow, which sweeps theparticles around Browns Bank into the Gulf of Maine. Theseparticles tend to move into the Gulf in deeper water thanthose from the west release, but many eventually move to-wards the Bay of Fundy.

Figures 7c and 7d show the dramatic difference in particledistributions for the near-surface flows in April of 1982 and1984. In April 1982 most particles are retained near BrownsBank in the expanded gyre, while in April 1984 all particles

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Hannah et al. 2511

Fig. 6. Near-surface (a and b) and 20-m (c and d) currents offsouthwestern Nova Scotia for April 1982 (a and c) and April1984 (b and d).

Fig. 7. Particle distributions after 30 days for the west releasewith the near-surface seasonal mean currents (a), the east releasewith the near-surface seasonal mean currents (b), the west re-lease with the April 1982 near-surface currents (c), the west re-lease with the April 1984 near-surface currents (d), the westrelease with the April 1982 20-m currents (e), and the west re-lease with the April 1984 20-m currents (f). For clarity, only50% of particles are shown.



are swept to the western Gulf of Maine. The effects of theextreme wind events are not as great at 20 m (Figs. 7e, 7f),and the particle distributions are generally intermediate be-tween the individual year and seasonal mean distributionsfor the near-surface cases.

Validation of interannual variability in the modelled circu-lation is difficult because of the paucity of multiyear current-meter observations. We focus on site C2 (Smith 1989) on the110-m isobath south of Cape Sable (Fig. 1), where 6 yearsof data are available for each of April and May. The mod-elled and observed monthly mean currents at 20 m at site C2are compared in Figs. 4e and 4f. Both the model and obser-vations show much more year-to-year variability in Aprilthan in May, which is consistent with the larger forcinganomalies. The time series shows very good agreement for1983–1985 but poorer agreement for 1979–1982. In particu-lar, the largest westward current anomaly was observed inApril 1984, with magnitude in agreement with the modelprediction, while April 1982 was one of two months withthe largest eastward anomaly, although it was smaller thanpredicted. It is not clear whether the discrepancies in 1979–1982 reflect a spatial shift in the currents or a broader scaledeficiency in the model fields associated with interannualvariability in baroclinic circulation or with the estimation ofthe forcing anomalies.

Composite particle distributionsComposite monthly particle distributions were created by

combining individual-month results over all years for eachof the two release grids (Fig. 8). Overall, most of the parti-cles end up in the northeastern Gulf of Maine (approachingthe mouth of the Bay of Fundy) after 30 days. This is similarto the distributions computed using only the seasonal meancirculation (Figs. 7a, 7b), although there is broad scatter andsensitivity to depth, month, and release location. The Apriland near-surface composites show the most scatter, whichreflects the importance of temporal variability in the circula-tion to overall larval dispersal. There is also increased over-all retention on Browns Bank (especially for the near-surfacewest releases) associated with the expanded gyre in someyears.

Most of the near-surface particles for the April east re-lease (Fig. 8e) are found in the northeastern Gulf, but somehave drifted off-shelf south of Georges Bank. Near-surfaceparticles from the west release have spread over a large areaof the Gulf, with maximum concentrations on the cap ofBrowns Bank and in the Gulf’s northern coastal region(Figs. 8a, 8b). The reduced year-to-year variability in theMay currents (compared with April) results in tighter distri-butions with larger peaks. For example, the near-surfaceApril west release shows two peaks surrounded by a largeregion of low particle concentration, whereas the May re-lease shows the same peak on Browns Bank but tighter clus-tering of particles in the northeastern Gulf (Figs. 8a, 8b).

The 20-m east releases (April and May) show most of theparticles clustered together between western Nova Scotiaand Jordan Basin, with relatively few in the Browns Bankregion. On the other hand, the 20-m April west releaseshows that upwards of 15% remain on the Bank after30 days. For the 20-m May west release, upwards of 25%remain on Browns Bank, while the rest have spread into the

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Fig. 8. Particle-concentration maps for the composite of the simula-tions over the period 1975–1990. The symbols represent the per-centages of the total number released that were in each 50 × 50 kmcell: r, >15%; ., 10–15%;d, 5–10%; •, 1–5%. (a) April west0–5 m. (b) May west 0–5 m. (c) April west 20 m. (d) May west20 m. (e) April east 0–5 m. (f) May east 0–5 m. (g) April east20 m. (h) May east 20 m.



northeastern Gulf of Maine or have crossed the NortheastChannel heading southwestward out of the domain. For bothrelease grids the April and May 20-m distributions are simi-lar, the east release resulting in a large concentration nearthe mouth of the Bay of Fundy and the west release showingtwo peaks in concentration (near the mouth of the Bay ofFundy and on Browns Bank). However, the east-release dis-tributions are shifted into deeper water in the northeasternGulf.

The west-release results reflect known drift behaviouraround Browns Bank. Smith (1989) and Loder et al. (1988)computed average residence times of 14 days (± 9 days(SD)) for drifters drogued at 10 m and released on the Bank’scap during May–October (1983–1985), and 5 (± 4) days forreleases in April and November. Model experiments in the

seasonal mean circulation indicate that about 70% of theparticles released at 10 m on the west grid leave within 5–25 days depending on season and background diffusivity,which is consistent with the observational estimates (Shoreet al. 2000). Some near-surface particles from the west gridcross the Northeast Channel to the eastern flank of GeorgesBank, which is consistent with the pathways identified in theseasonal mean circulation by Shore et al. (2000).

Retention and drift indicesTo quantify interannual variability in drift and retention,

we computed the percentage of particles in three zones after30 days (Fig. 2). Two of the zones, the Scotian Shelf poly-gon (SS) and the Browns Bank polygon (BB), include therelease grids, so percentages can be interpreted as retentionindices. BB corresponds to the primary haddock spawningarea (the union of the west and east release areas) and SScorresponds to the broader offshore shelf region (groundfishsurvey strata), for which Shackell et al. (2000) infer thathigher retention leads to higher survival. The Bay of Fundy(BoF) zone corresponds to the region (survey strata) withhigher growth rates for juvenile, and possibly larval, had-dock. It is located away from the release areas, so we referto its particle percentages as drift indices.

The retention indices (Fig. 9) show large year-to-yearvariability for SS, with greater retention for the west releasesthan for the east releases (cf. Fig. 8). The April near-surfacereleases show large variability in the number of particles de-livered to BoF but the other releases show much weakervariability. The May releases at 20 m show almost constantdelivery of particles to BoF, which is consistent with the20-m composite particle-concentration maps (Fig. 8), whichshow a narrow distribution of particles between Browns Bankand the Bay of Fundy. In many of the near-surface cases thesum of particle concentrations for SS and BoF is less than100%, since some particles go elsewhere (e.g., 1984). In thecomposite distributions, this shows up in the broad distribu-tion of the low percentages. Retention in BB is generallyless than in SS but has the same overall features.

The circulation fields suggest that retention of particles inthe vicinity of Browns Bank should be increased for bothpositive τA anomalies and negativeζB anomalies becausethey both induce circulation that reduces the (northward)seasonal mean flow from Browns Bank to the Bay of Fundy.Table 1 shows the linear correlations between various mea-sures of retention in the vicinity of Browns Bank and theforcing functions. In each case the retention values for Apriland May have been grouped together in order to look for ageneral relationship between retention measures and forcingindices. The results generally show highly significant (p <0.05) correlations between retention values and bothτA andζB (with opposite signs, as expected) and poor correlationswith τC. Of the forcing functions,ζB is the best overall pre-dictor of retention. The correlations for BB, the smaller re-tention zone, are generally weaker than for SS, but notdramatically so. This indicates that for this system, the 30-day retention variability in the vicinity of Browns Bank isnot a strong function of retention-zone size.

Table 1 also shows that the retention indices for SS andBB are significantly correlated with the eastward currents atC2 (C2U) in the model (r ≥ 0.67, p < 0.05). This is due to

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Hannah et al. 2513

Fig. 9. Interannual variability in particle retention in the ScotianShelf zone (solid bars) and drift into the Bay of Fundy zone(open bars). (a) April west 0–5 m. (b) May west 0–5 m.(c) April west 20 m. (d) May west 20 m. (e) April east 0–5 m.(f) May east 0–5 m. (g) April east 20 m. (h) May east 20 m.



C2’s location on the main artery of the flows induced byτAandζB. Large retention values generally correspond to east-ward (positive) or slightly westward currents at C2, and zeroretention often corresponds to large westward (negative)currents (Fig. 10). Figure 10 shows that the linear relation-ship between retention (SS west U5) and C2U is good butbreaks down for strong westward currents. This breakdownis an example of the nonlinearity associated with retentionbeing a bounded function; extremes in forcing cannot reduceretention below 0% or increase it above 100%. In Fig. 10,the linear region is roughly –0.1 < C2U < 0.1 m·s–1.

To determine how much of the variability in retention inthis system can be predicted by linear functions of the forc-ing anomalies, we conducted a multiple (linear) regressionanalysis (Table 2). To account for the boundedness of reten-tion, C2U was used to determine the linear regime for eachretention time series. Mean retention was computed for0.02 m·s–1 bins of C2U and the data points were retained foranalysis if they fell in a bin with mean retention in the range1–95% (the retention thresholds). The number of samplesremoved in each case was small, between 1 and 8. Forexample, in Fig. 10 (SS west U5) the five points with C2U <– 0.1 m·s–1 were removed, as were the two points withC2U ≥ 0.07 m·s–1. Removing these seven points increasesthe r2 value of the correlation with C2U from 0.77 to 0.84.

Table 2 shows that when all the data are used, 60–84% ofthe variance in retention is linearly related to the forcinganomalies. When the analysis is repeated for the linear re-gime, the explained variance (r2) increases to 78–97%. Thebounded properties of retention account for 5–27% of thevariance, which is generally more than 50% of the unex-plained variance in the “all data” regression model. Ther2

value for each case of BB retention is less than for the re-spective SS case, and the effects of zone size are largest forthe near-surface cases using the linear regime.

Cross-shelf wind stress (τC) is poorly correlated with re-tention (Table 1), and its contribution to the regression mod-els is limited to the two cases with a significant linearcorrelation (SS/BB east U5). The generally good correla-tions with τA imply dependence on wind-stress direction,which results in weak correlations between retention and the

magnitude of the wind-stress anomaly (|τ|), generally with|r| < 0.2 andp > 0.1. There is one marginally significant cor-relationbetween BB west U5 retention and |τ | (r = –0.29,p = 0.1), which is consistent with Shackell et al.’s (2000)finding that survival and wind-stress magnitude are nega-tively correlated. However, this correlation disappears whenthe analysis is restricted to the linear regime. There is also anegative correlation (r = –0.46, p < 0.05) between wind-stress magnitude and the residuals from the multiple regres-sion for BB west U5 retention (linear regime), indicatingthat wind-stress magnitude can account for about 5% of theretention variance for this case.

Relation to biological indicesRetention–survival indices and a survival (to age 1 year)

index described by Shackell et al. (2000) are shown inFigs. 4i and 4j. For comparison, the SS retention for thewest releases is shown in Figs. 4g and 4h. The correlationbetween the biological indices and the various model-basedretention indices is very weak in all cases (|r| < 0.28,p > 0.1,n = 16). The survival index is dominated by the steady de-crease from 1975 to 1985, which is not present in our indi-ces. There is also no relationship between the observedcurrents at C2 and the biological indices.

Discussion

Circulation and retention variabilityThe spatial structures of the seasonal mean and anomaly

currents provide basic explanations for most of the featuresof the retention time series shown in Fig. 9. Consider theeast release at 20 m, which exhibits almost constant deliveryof particles to BoF. The drift pathway in the seasonal-meanflow follows the core of strong currents between the 100-and 200-m isobaths from the release site to the entrance tothe Bay of Fundy and is only weakly influenced by theanomaly currents at that depth. In contrast, there is enor-mous variability in the transport of particles to BoF for thewest near-surface releases because all the anomaly compo-nents have an influence on the primary drift pathway to thenorthwest of Browns Bank.

© 2000 NRC Canada


Fig. 10. Particle retention in the Scotian Shelf zone (zone SS)for the near-surface west release as a function of eastward modelcurrents at C2. April (×) and May (s) are indicated but the solidline is the best fit (r2 = 0.77) for the two months together. Thebroken line is the best fit (r2 = 0.84) through the data points inthe linear regime described in the text.

τA τC ζ B C2U

SS west U5 0.69* 0.22 –0.67* 0.87*SS west 20 m 0.48* 0.22 –0.86* 0.90*SS east U5 0.31† 0.49* –0.76* 0.67*SS east 20 m 0.50* 0.19 –0.81* 0.87*BB west U5 0.69* 0.15 –0.63* 0.83*BB west 20 m 0.40* 0.29 –0.87* 0.87*BB east U5 0.35† 0.41* –0.74* 0.68*BB east 20 m 0.43* 0.23 –0.82* 0.84*

Note: The name of each retention measure contains the retention zone(Scotian Shelf, SS) or Browns Bank (BB)), the release grid (east or west),and the flow field (near-surface (U5) or 20 m). The forcing indices arethe along- and cross-shelf wind-stress anomalies (τA and τC), theboundary-forcing anomaly (ζB), and the model eastward velocity at mooringlocation C2 (C2U). *, correlation is significant at the 0.05 level (two-tailed); †, correlation is significant at the 0.1 level (two-tailed); df = 30.

Table 1. Linear correlations (r) between retention measures andother indices, with April and May grouped together.



Comparison of the average retention indices with theirvalues in the seasonal mean flow confirm that the inclusionof wind- and boundary-forced flow anomalies can result inincreased overall retention in SS, in spite of broader overallscatter. Average values of retention (over all years) for thenear-surface and 20-m levels increase to 20 and 15% from10 and 6%, respectively, in the seasonal mean circulation.This reflects the significant occurrence of wind and sea-levelanomalies that act in concert with the seasonal mean flow toenhance retention, such as through the expanded BrownsBank gyre. Retention percentages should not be interpretedas percentages of larvae retained, since the larger influencesof predation and mortality are not included here.

The close correlation between SS retention and both theτA and ζB anomalies is due to the spatial relationship be-tween the induced flows and the seasonal mean flow. Along-shelf wind stress towards the northeast (positiveτA) reducesthe northward mean flow from Browns Bank to the Bay ofthe Fundy (through an ocean pressure-field response) and re-duces the westward flow off Cape Sable (through bothEkman transport and a pressure-field response). A negativesea-level anomaly has a similar effect. Extreme combina-tions of positiveτA and negativeζB have the potential to cre-ate an expanded gyre in the Browns Bank region (e.g., April1982). In less extreme years the combination reduces themagnitude of the currents that carry particles away fromBrowns Bank. For the most part, the currents that determinethe magnitude of retention in SS are not the currents onBrowns Bank but those in the deep water around the edgesof the Bank and along the pathways from the Bank to theBay of Fundy. For example, the circulation associated withζB has no signature inside the 100-m isobath on BrownsBank but has the greatest impact on retention variability.

The currents at each point are completely determined aslinear functions of the forcing terms (in the present ap-proach), thus any unexplained variance in the linear-regression analysis of retention variability must arise fromeither the process of computing particle trajectories from ve-locity fields or the process of computing retention from par-ticle positions. The regression analysis showed that thebounded properties of retention are important when relatingretention variability to the forcing anomalies. When thebounded properties are accounted for, the unexplained vari-ance substantially decreases: to 3 and 5% for SS and BBwest 20-m cases, respectively, and to the 10–22% range forthe other cases. The linear-regime analysis is crude and it islikely that some of the unexplained variance is still due tothe boundedness of retention. For example, the retentionthresholds could be set on a case-by-case basis.

There are also nonlinearities associated with calculatingparticle trajectories (or displacements) from velocity fields,the Eulerian-to-Lagrangian transformation, which is nonlin-ear (even for steady flows) when there is spatial structure inthe velocity fields. This is why it is important to have a goodrepresentation of the spatial structure of all the flow compo-nents. There are further nonlinearities in the Eulerian-to-Lagrangian transformation associated with the interactionbetween spatial structure and the temporal variability pro-vided by the tidal currents and unmodelled flows such asthose associated with storm-band wind forcing. These areexpected to become important as the size of the retention

zone is reduced to the order of the excursion scale of thetemporal perturbations (e.g., the tidal excursion). We notethat the width of the western portion of BB is about 20 km,roughly two M2 tidal excursions. The strong influence of thespatial structure in the flow components on the particle tra-jectories, and the greater unexplained variability in BB casesthan in SS cases, suggest that the nonlinearities of theEulerian-to-Lagrangian transformation are an importantsource of unexplained variance. For the present set of simu-lations, the maximum contribution of these nonlinearities tothe retention variance is of the order of 5–20%, which placesan upper bound (80–95%) on the predictability of retentionbased on linear functions of the forcing anomalies or veloc-ity fields. Furthermore, Ridderinkhof and Loder (1994)showed that storm-intensity wind stress can cause chaoticmotion in the Browns Bank region, which would further re-duce the predictability of drift and retention from the forcinganomalies.

For each release scenario the retention statistics for SSand BB have a very similar relationship with the forcinganomalies, although the smaller BB has lower overall reten-tion. Thus, we conclude that the results (for the present flowfields) are robust to the details of the retention zone; in par-ticular, retention in SS is not dominated by particles leavingBB but not quite leaving SS in 30 days. However, for reten-tion zones on Browns Bank smaller than BB, the resultswould be expected to become sensitive to the details of theretention calculation, as well as to increased resolution ofsmall-scale flow features. For example, a more sophisticated

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Hannah et al. 2515

n R0 R3 r2

All dataSS east U5 32 14 8.5 0.63SS east 20 m 32 10 4.8 0.78SS west U5 32 31 15 0.76SS west 20 m 32 28 11 0.84BB east U5 32 5.5 3.5 0.60BB east 20 m 32 4.0 2.1 0.73BB west U5 32 17 9.1 0.70BB west 20 m 32 14 6.4 0.80

Linear regimeSS east U5 24 15 5.5 0.87SS east 20 m 31 10 4.2 0.83SS west U5 25 27 8.6 0.90SS west 20 m 28 28 5.2 0.97BB east U5 24 6.0 2.7 0.80BB east 20 m 31 4.0 1.9 0.78BB west U5 27 16 7.5 0.79BB west 20 m 28 15 3.4 0.95

Note: For each retention measure,R0 is the rms value of the retentiontime series with the mean removed (%),R3 is the rms values of theresidual (%) after the contribution of three forcing anomalies (τA, τC, ζB)is removed, andr2 = 1 – (R3 /R0)

2 is the variance explained. The resultsshown under “all data” use all the data and the results under “linearregime” use the data in the linear regime as described in the text. Thename of each retention measure contains the retention zone (Scotian Shelf(SS) or Browns Bank (BB)), the release grid (east or west), and the flowfield (near-surface (U5) or 20 m). All regressions are significant at the0.05 level (two-tailed).

Table 2. Results of the multiple linear regression analysis be-tween the retention indices and forcing anomalies.



definition of retention would be required to account for par-ticles repeatedly moving into and out of the retention zonebecause of the tidal currents.

The strong correlations between retention in both SS andBB and the eastward currents at C2 are due to C2’s locationon one of the main flow arteries for bothτA andζB and thespatial coherence of the model responses to sea-level and(spatially uniform) wind-stress anomalies. For each flowcomponent the spatial structure is fixed and its magnitude atany location reflects the value of the forcing anomaly. How-ever, Smith et al. (2001) show that the monthly anomalies involume transport in the upper ocean (<75 m) over the 200-misobath on the western flank of Browns Bank are poorly cor-related with the monthly transport anomalies at C2. There-fore, while the currents at C2 are likely a good measure ofthe currents along the 100-m isobath west of Cape Sable,they are probably not a good measure of the currents in thedeeper water to the west and north of Browns Bank. Thisspatial incoherence, which is probably associated withbaroclinic flow variability not addressed here, places an im-portant limitation on the use of C2 as a measure of circula-tion for the purpose of estimating retention.

The circulation due to boundary forcing is a crucial partof drift and retention dynamics, but there are a number ofapproximations in the transformation of Halifax sea-leveldata into boundary forcing. One issue is the averaging pe-riod used to provide the mean wind stress and mean Halifaxsea level used in calculatingζB. We estimate that the choiceof averaging period introduces uncertainty of the order of 1–2 cm·s–1 into the mean value of the modelled currents at C2,the present value probably having an eastward bias. Forcomparison the rms difference between the observed andmodelled currents is 5 and 3 cm·s–1 for April and May, re-spectively. A second issue is the distribution of elevationsacross the upstream boundary. While the flow patternsaround Browns Bank are quite robust to changes in the de-tails of the upstream boundary, there is some sensitivity towhether the flow is concentrated over the inner shelf or theshelf break. There are also issues regarding mean and trendremoval in the Halifax ASL and the relative contributions ofbarotropic and baroclinic flows to the ASL anomalies (wehave assumed that the anomalies are 100% barotropic). Allof these issues can affect the magnitude ofζB and its impor-tance relative to the wind-stress anomalies and the seasonalmean circulation.

Relation to biological indicesThe comparison of the circulation-based retention indices

with the biological indices indicates that circulation variabil-ity alone is not the predominant influence on regulation ofthe Browns Bank haddock population. This is not unex-pected for a nonlinear ecosystem comprising many interact-ing biological components with their own spatial andtemporal variability. Whereas Shackell et al. (2000) found anegative correlation between survival and wind-stress mag-nitude, the one marginally significant correlation between re-tention and wind-stress magnitude in our results (near-surface BB west) disappears when the analysis is restrictedto the estimated linear regime. However, the negative corre-lation between wind-stress magnitude and the regression re-siduals for this case indicates that wind-stress magnitude can

account for about 5% of the retention variance. The varianceexplained (25%) by Shackell et al.’s result is at the level ofthe uncertainty in our calculations, so a relationship betweenretention and wind-stress magnitude cannot be ruled out. Inparticular, if life-history processes favour survival of larvaeretained on Browns Bank (perhaps in a region even smallerthan our BB), then the influence of wind-stress magnitudecould be magnified.

The spatial structures in the flow fields and the weak cor-relation between the forcing anomalies in April and May ofa given year mean that the timing and location of spawningare likely very important to the drift/retention fate of the lar-vae. This raises two important points with respect to retro-spective studies of early life stages: (1) since the timing andlocation of peak spawning are poorly known, they will besignificant sources of uncertainty and possible tuning param-eters; and (2) the circulation may have to be resolved ontime scales of less than 1 month in order to match the peakspawning period. In addition, the dominant drift pathwaysare narrow relative to the station spacing in typicalichthyoplankton surveys (e.g., FEP), and the exit pathwaysfor drifters from Browns Bank are not stationary (Shore etal. 2000; Smith 1989). Thus, it is likely that the spatial struc-ture of fish-larva distributions are not fully resolved in exist-ing data sets for the region. These points are consistent withthe findings on Western Bank (Scotian Shelf), where thespatial distributions of a wide variety of fish larvae and otherplanktonic species are consistent with the circulation onlywhen both the circulation and the plankton distributions aresampled in order to resolve the relevant spatial and temporalscales (Reiss et al. 2000).

Brickman et al. (2000) and Brickman and Frank (2000)have developed an early life history model for Browns Bankhaddock that uses the flow fields described here and includesan egg-production model, vertical motions, and temperature-dependent growth and survival rates. They found that com-bining biological and circulation variability provides a bettermodel-based estimate of retention–survival indices than thatprovided by the drift indices given herein. Their model, to-gether with our findings, provides a potential basis for deter-mining the relative contribution of the different physical andbiological processes to the overall survival of early life stages.

In conclusion, the model evaluations of circulation anddrift variability support the concept of a drift–retention di-chotomy (Campana et al. 1989b) for cod and haddock larvaein the Browns Bank region; there is both retention on theBank and drift away from it. They also point to aspects ofcirculation variability that can amplify, as well as compli-cate, the roles of drift and retention in larval survival ratesand in marine population regulation in the region. The spa-tially structured circulation, with persistent retention featuresand drift pathways, provides the potential for current fluctu-ations to have important influences on population dynamicsand recruitment variability. The present results show that thecirculation changes associated with variable wind stress andupstream inflows tend to reinforce either drift to the high-growth Bay of Fundy region or retention in the high-survivaloffshore shelf region, but they can also introduce additionalloss pathways from the overall region. The computed indicesindicate that the reinforcing tendencies are not infrequent, sup-porting a potentially important role in population dynamics.

© 2000 NRC Canada




The results also show how spatial and temporal structurein the circulation can contribute to complexity in populationregulation, both through direct drift or retention effects andthrough effects in combination with biological factors. Had-dock spawning in the Browns Bank region has been distrib-uted in time across a period with a seasonal change in theintensity of circulation anomalies (e.g., the contrasts in esti-mated retention indices between April and May), and inspace across an area with different retention–drift responsesto circulation anomalies (e.g., the limited correlation be-tween the west and east retention indices). Further, the de-pendence of drift and retention on depth introduced by theEkman-layer component of the response to wind forcing re-sults in well-known sensitivities to the timing of wind influ-ences in relation to egg and larval development. With suchspatial and temporal structure in the circulation on biologi-cally important scales, the effects of circulation variabilityon population regulation can be expected to be complicated.

It should be emphasized that the circulation variabilityprovided by the model solutions used here is simplified andapproximate. The use of monthly mean fields for wind andboundary influences illustrates potential effects but does notfully represent associated circulation variability. As well,baroclinic flow variations associated with density-gradientfluctuations are not represented and may contribute to thediscrepancies with observed currents, add additional com-plexity, or modify the effects in the present simulations.

The combination of multiple forcings and associated spa-tial and temporal complexity in an apparently simple andpersistent circulation system like that in the Browns Bankregion may help explain the difficulty in unravelling the en-vironmental influences on recruitment variability in manymarine populations.

Acknowledgements

We thank Dan Lynch, Chris Naimie, and Cisco Werner forproviding the circulation and particle-tracking models, BrianPetrie for assistance with the sea-level and wind-stress data,Nancy Shackell for providing the biological indices and fordiscussions, Dave Brickman and Peter Smith for discussionsand internal reviews, and two anonymous reviewers for con-structive comments. This is a contribution of the GLOBECCanada Program, jointly funded by Fisheries and OceansCanada and the Natural Sciences and Engineering ResearchCouncil of Canada.

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The drift-retention dichotomy on Browns Bank: a model study of interannual variability

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