FISHERIES OCEANOGRAPHY Fish. Oceanogr. 2:2, 43-64, 1993

Influences of mean advection and simple behavior on the distribution of cod and haddock early life stages on Georges Bank

FRANCISCO E. WERNER,' FRED H. PAGE,' DANIEL R. LYNCH,3 JOHN W. LODER: R. GREGORY LOUGH,5 R. IAN PERRY,6 DAVID A. GREENBERG4 AND MICHAEL M. SINCLAIR4 'Skidaway Institute of Oceanography, P.O. Box 13687, Savannah, Georgia, U. S. A. 3 14 16 2Degartment of Fisheries and Oceans, Biological Station, St. Andrews, N. B., Canada EOG 2x0 'Dartmouth College, Hanouer, New Hampshire, U. S. A. 03755 4Department of Fisheries and Oceans, Bedford Znstitute of Oceanography, Dartmouth, N. S., Canada B2Y 4A2 'National Marine Fisheries Service, Northeast Fisheries Science Center, W o d Hole, Massachusetts, U. S.A. 02543 6Department of Fisheries and Oceans, Pacific Biological Station, Nanaimo, B. C., Canada V9R 5K6

ABSTRACT

Results of a modeling study designed to explore the influences of physical advection and certain biological mechanisms on the distribution of cod (Gadus morhua) and haddock (Melanogrammus aegkfinus) early life stages on Georges Bank are described. Using a late- wintedearly-spring 3-D circulation field driven by the Mz tidal current, mean wind stress and Scotian Shelf inflow, we examine the distribution of cod and haddock larvae spawned on the Northeast Peak of the Bank. The sensitivity to a March-April baroclinic field is also explored. Results indicate that larvae remaining in the surface Ekman layer are generally advected off-bank. However, downwelling associated with Ekman layer convergence near the shelf break provides a mechanism for larvae to exit from the off-bank surface drift. Larvae below the surface layer are transported south-westward along the southern flank of Georges Bank and are retained on the Bank if their position immediately upstream of the Great South Channel is shoalward of (roughly) the 70 m isobath. Within the Great South Channel region and between the 50 and 70 m isobaths,

Received for publication 27 October, 1992 Accepted for publication 20 January, 1993 @ 1993 Blackwell Scientific Publications, Znc

retention can depend on the phase of the tide. Spawn- ing shoalward of the 50 m isobath on the Northeast Peak greatly increases the chances of retention. These results apply to passive larvae and to those with specified vertical distributions and migration based on obser- vations. Directional on-bank swimming at rates of 0.5 to 1 body length per second would substantially enhance shoalward displacement, resulting in larval distributions during the first 2 months that are consist- ent with field observations.

Key words: circulation, eggs, cod, Georges Bank, gyre, haddock, larvae, models, NW Atlantic, retention

1 INTRODUCTION

It is generally recognized that the linkages between circulation and distributions of fish early life stages must be determined if marine fish population structure and dynamics are to be fully understood and the impacts of resource development and climatic change are to be assessed (e.g. Sinclair, 1988; GLOBEC, 1991).

On Georges Bank (Fig. 11, the link between the circulation and dispersal of the early life stages of cod (Gadus morhua) and haddock (Melanogrammus aegkfi- nus) has been studied for several decades. Plankton surveys between 1921 and 1987 showed that, although the distributions of cod and haddock eggs and larvae varied between months and years, the greatest concen- trations of eggs were consistently over the Northeast Peak. Haddock larval distributions were displaced very little from egg distributions in March, but by April the distributions of older eggs and larvae were shifted toward the south-west and dispersed over the southern flank of the Bank (Bigelow, 1926, 1927; Walford, 1938; Colton and Temple, 1961; Colton and St Onge, 1974; Sherman, 1980; Lough, 1984). The early life stages were distributed vertically throughout the water column, with maximum egg and larval concentrations often occurring near the surface and at mid-depths respectively (Walford, 1938; Miller et al., 1963; Col- ton, 1965).

Physical oceanographic measurements indicate that, although a mean gyral circulation is present on Georges

43

44 F. E. Wemer et al.

Figure 1. Topographic map of Georges Bank, Gulf of Maine, Scotian Shelf and adjacent regions corresponding to circulation model domain. Current meter stations A and M4 are indicated.

J

Bank, near-surface flows can be off-bank during the winterhpring period (Bigelow, 1927; Day, 1958; Col- ton and Temple, 1961; Bumpus, 1973; Butman and Beardsley, 1987a). Initially it was argued that the eggs and larvae remained in the surface mixed layer and were therefore susceptible to offshore drift (Colton and Tem- ple, 1961). This argument was supported by a signifi- cant correlation between an index of wind-induced near-surface circulation and haddock year-class size (Chase, 1955). However, this resulted in the enigma that the cod and haddock populations maintained themselves on the Bank despite an apparent offshore loss of progeny (Colton and Temple, 1961). More recent interpretations favor the concept that the eggs and larvae are substantially retained over the Bank, that offshore losses are relatively small, and that the south

westward rates of egg and larval displacement are con- sistent with mid-depth mean flows measured over the southern flank of the Bank (Smith and Morse, 1985). When these flow rates are anomalously large, as in 1987, the larval distributions extend further to the west and into the Middle Atlantic Bight (Polacheck et al., 1992).

The first attempts to model the distribution of cod and haddock early life stages on Georges Bank were to assess the potential impact of hydrocarbon exploitation (e.g. Spaulding et nl., 1983) and to investigate the influence of warm core rings on the distribution and recruitment of fish early life stages (Flier1 and Wrob- lewski, 1985). These studies used one- and two- dimensional circulation models and hence did not include organism vertical migration behavior, which

3-D modeling Georges Bank cod and haddock early life stages 45

can be important in determining the distribution of early life stages (e.g. Iles and Sinclair, 1982; Bartsch et al., 1989). Development of realistic 3-D models is now more plausible because of the availability of more com- plete descriptions of the circulation (e.g. Butman and Beardsley, 1987a; Loder et al., 1992), higher-resolution circulation models (e.g. Lynch et al., 1992), and improved descriptions of the vertical distributions of cod and haddock early life stages (e.g. Page et al., 1989; Lough and Potter, 1993).

As part of the US Global Ocean Ecosystems Dy- namics program (GLOBEC, 1991) we are developing 3- D models for use in understanding the influence of physical and biological mechanisms on the distribution of the early life stages of marine fish populations. The objective of this paper is to examine the relative import- ance of the 3-D tidal and seasonal-mean circulations, and of specified biological behavior to the distributions of early life stages of cod and haddock on Georges Bank in late winter and early spring. We use a 3-D numerical model for the semidiurnal tidal current and the circu- lation associated with tidal rectification, mean winds, Scotian Shelf inflow and the seasonal density field, and a particle-tracking model which includes egg and larval behavior. The biological background, with respect to Georges Bank cod and haddock, is summarized in section 2 and the physical background and circulation model are described in section 3. The results of numeri- cal particle-tracking experiments are described in sec- tion 4 and they are discussed and summarized in section 5.

Figure 2. Schematic showing the distribution of haddock and cod eggs (gridded area), larvae 20-40 days post spawn (dotted area) and larvae 50-70 days post spawn (area with hatched lines). Two different grids are shown for the cod spawning (egg) region: the finer grid indicates the core spawning region and the coarser grid indicates the broader spawning area. This is a composite of data available from references given in the text. The generalized gyral pattern for the various life stages is best observed for haddock. The distribution pattern of cod is more widespread because their spawning is more protracted and occurs earlier in the winter, when there is more wind mixing and advection, and the mean circulation gyre is weaker (e.g. GLOBEC, 1992).

I . _-

,-- - _ _ Haddock -.. / -

--. - -

2 BIOLOGICAL BACKGROUND

2. J Egg and larval distributions: haddock Haddock spawn on Georges Bank from February through June, with peak spawning usually occurring during April and May (Walford, 1938; Colton and Temple, 1961; Marak and Livingstone, 1970; Colton and St Onge, 1974; Colton, 1978; Sherman et al., 1984; Smith and Morse, 1985). The timing of peak spawning has varied by several months in a manner consistent with interannual variations in water temperatures (Col- ton, 1968; Marak and Livingstone, 1970; Page and Frank, 1989). Early and late in the spawning season, haddock eggs are found almost exclusively over the Northeast Peak (Fig. 2) , whereas during peak spawning, eggs are more broadly distributed over the Northeast Peak and southem flank.

During the April-May period of peak larval abun- dance, the larvae are centered over the southern flank (Fig. 2 ) although they are distributed from the North-

east Peak to the Great South Channel (Walford, 1938; Colton and Temple, 1961; Colton, 1978; Smith and Morse, 1985; Morse et al., 1987). The pelagic juveniles are centered, during May-June, over western Georges Bank with their distribution extending over the southern flank and the Great South Channel (Lough and Bolz, 1989).

2.2 Egg and larval distributions: cod Cod on Georges Bank spawn throughout most of the year, with the majority of spawning occurring from November through May and peak spawning from Janu- ary through April (Colton, 1978). Eggs are released over most of the Bank, with the highest concentrations occurring on the eastern half (Fig. 2; Walford, 1938; Colton and St a g e , 1974).

Cod larvae are present on Georges Bank from November through June, with peak larval abundances

46 F.E. Werner et al.

in March and April. The larvae are distributed all over the Bank, with the highest concentrations over the southern flank. By early June, the pelagic juveniles are still broadly distributed across Georges Bank, with high abundances over the eastern spawning area, along the southern flank transit corridor between the 50 and 70 m isobaths, and extending into the western Georges Bank and Great South Channel region. Some surveys appear to show a resident larval-juvenile cod population on eastern Georges Bank (Fig. 2; Morse et al., 1987; Lough et al., 1992).

2.3 Vertical migration behavior The vertical distribution of cod and haddock eggs and larvae varies in space and time and is influenced by several processes. These include egg and larval buoyancy, which varies with egg development (Lough, 1984; Page et al., 1989), larval condition (Frank and McRuer, 1989), water column stratification (Perry and Neilson, 1988; Lough and Potter, 1993) and vertical turbulence (e.g. Page et al., 1989). However, consider- ing the relative scarcity of quantitative information on vertical distribution for Georges Bank, we assume a relatively simple vertical distribution for both species

(Fig. 3) which includes four egg stages and seven larval length intervals. Within each stage and length interval, the organisms are considered to be concentrated at a single depth that may vary with the day-night cycle as shown. When die1 migration begins, the shallow (deep) level is reached in 4 h, with the particles remaining fixed at that location for 8 h.

The specified egg distribution is primarily based on haddock egg profiles from MININESS tows in the Browns Bank region (Page et al., 1989). The distri- bution is consistent with that of haddock eggs on Georges Bank as reported by Walford (1938) and Col- ton (1965), and with observations of late-stage cod eggs by Lough (1984). Although laboratory estimates of stage-dependent cod egg buoyancy suggest that their vertical distribution may be somewhat different from that of haddock eggs (Sundnes et al., 1965), no field estimates for the stage-dependent vertical distribution of cod eggs over Georges Bank are available.

The vertical larval distribution is based on Miller-net and MOCNESS tows of cod and haddock made over Georges Bank and described in Miller et al. (1963), Perry and Neilson (1988), and Lough and Potter (1993).

Figure 3. Vertical distribution of cod and haddock egg (20 days) and larval stages (100 days). The egg-stage data (for stages I-IV) are from Page et al. (1989) and the larval data from Lough and Potter (1993). The larval size class for cod (from Lough and Potter, 1993) is indicated.

Size Class (mm) I 2-5 I 6-8 I $13 1 14-19 I 20-29 I 30-39 140-491

0

-80 0 20 40 60 80 100 120

Days

3-0 modeling Georges Bank cod and haddock early life stages 47

2.4 Horizontal migration behavior Lough and Bolz (1989) observed that larval haddock (and cod) that were spawned on north-eastern Georges Bank during spring of 1981 and 1983 were continuously recruited to the shoal.centra1 part of the Bank (<55 m) as they developed and were advected along the southern flank. They found a consistent cross-shelf age gradient, with older larvae nearer the shoals, and esti- mated their average rate of shoalward displacement to be 0.65 cm s-I. As larvae grow and develop into pelagic juveniles, their swimming capability attains speeds comparable to cross-bank residual current flows. A one- month-old larva can maintain a mean swimming speed of 1-3 body lengths per second (Blaxter, 1969), or 1-3 cm s-' in the case of cod and haddock larvae. External cues are needed for orientation which could be related, among others, to the flow, chemical signals, or the earth's magnetic field; migration of fish has been related to behavioral responses to these cues (McCleave et al., 1984). We will consider scenarios exploring the sensitivity to directed swimming (even if the mechan- isms involved are not fully understood) and its effect on distribution of cod and haddock larvae on Georges Bank.

3 CIRCULATION: OBSERVATIONS AND MODELING

3. I Observed circulation The currents on Georges Bank may be divided into a seasonally varying mean current, low-frequency current fluctuations (e.g. driven by winds and eddies), tidal currents, and higher-frequency fluctuations (e.g. associ- ated with internal waves) (Butman and Beardsley, 1987a).

The seasonal-mean current includes a persistent con- tribution from tidal rectification to the clockwise gyre (e.g. Loder, 1980; Butman et al., 1987). There are also seasonally varying contributions from the large-scale coastal current (Chapman and Beardsley, 1989) and mean wind stress (e.g. Greenberg, 1983) to through- flow in the region, and from the density field to the seasonal intensification of the gyre (Loder and Wright, 1985). During the March-April period of primary focus in this paper, the gyre strength on Georges Bank and the recirculating flow in Great South Channel are near their seasonal minima (e.g. Butman and Beardsley, 1987b; Butman et al., 1987). The mean flow in this period is strongest in the northeastward jet along the Bank's northern edge with peak speed near 20 cm s-', while the southwestward flow over the southern flank and into the Middle Atlantic Bight increases seaward from about 5 cm s-' in shallow water to near 10 cm s-I

over the shelf break (Fig. 4a). There is little stratifi- cation over the Bank in winter, except in the vicinity of the shelf-water/Slope-water front at the shelf break, while weak stratification develops over the Bank's outer flanks in early spring (Flagg, 1987). Quantitative infor- mation on the near-surface mean currents is limited, but drifter studies (Bumpus and Lauzier, 1965; Flagg et al., 1982) indicate an offshore component.

Moored current measurements indicate that there is also a seasonal minimum in the low-frequency current fluctuations in late winter and early spring, at least below the surface Ekman layer (Butman and Beardsley, 198713). Because the monthly low-frequency current standard deviations at mid-depths and deeper on the southern flank are of comparable magnitude to the mean flows, the latter should be the leading contributor to subsurface particle excursions (e.g. Loder et al., 1988). Wind-driven current fluctuations may be of increased importance in the surface layer however, particularly because the seasonal maximum in wind stress magnitude occurs in winter. Lagrangian drifters indicate that the average residence time of near-surface water on Georges Bank in December-April is 45 days (Flagg et al., 1982).

The most energetic flow component on Georges Bank is the barotropic semidiurnal tidal current, which has little seasonal variation. The rotary currents associ- ated with the M2 constituent are dominant, with maxi- mum current speeds (and tidal excursions) increasing from about 20 cm s-I (2.9 km) near the shelf break to about 100 cm s-' (14 km) near the northern edge (Moody et al., 1984). The horizontal particle excursions associated with higher-frequency motions are generally small, so that these flows are generally of lower import- ance to long-term drift.

3.2 Circulation model The circulation model (Appendix A) solves, using a harmonic finite element method, the 3-D nonlinear shallow-water equations with eddy viscosity closure in the vertical, and allows forcing by tides, surface stress and a prescribed density field (Lynch et al., 1992; Lynch and Naimie, 1993). The model mesh, extending from the Scotian Shelf into the Middle Atlantic Bight (Fig. 5), has 6756 nodes in the horizontal and 21 unequally spaced nodes in the vertical adding greater resolution in the surface and bottom Ekman layers. The horizontal resolution is variable, with grid size under 5 km over most of Georges Bank. The model bathymetry was specified using optimal linear interpolation (Bretherton et al., 1976) to smooth topographic variability on scales of the order 10 km and less, and is realistic to approxi- mately the 1000 m isobath.

48 F.E. Werner et al.

Figure 4. (a) Mean currents in March-April from moored measurements on Georges Bank described in Butman et al. (1987). Currents are shown for three depth ranges: near surface: within 15 m of surface; near bottom: between 4 and 15 m above bottom; intermediate: more than 15 m from surface and bottom. Each mean current is computed as the average of all monthly means for March and April for the site and depth interval. The stations are A, B, C, D, K, M, M1, M4, M5, M8, M9 and N; see Fig. 1 for locations of A and M4, and Moody et al. (1984) for remaining locations. (b) Vertical profile plots of predicted and observed mean currents at sites A and M4 in March-April. The base-case and baroclinic solutions are given by the solid and dashed lines respectively. The horizontal lines through the observed mean currents (crosses) represent the standard deviation of the monthly means about the seasonal means.

a I , ,_----__

I I \

,\ ‘I ., \ ‘.

\\ .J@-m, Meen currents m-lprls

Figure 5. Finite element mesh used in computation of the flow field. Darker regions correspond to higher resolution areas.

b Station A u (CWS) V (cmls)

8

Station M4 U (cmls) V (cmls)

Bo

Two cases of model forcing have been considered, each involving solutions at both the tidal and zero frequency. In the base case, the forcing was by Mz tidal elevations on the open boundaries as in Lynch and Naimie (1993), a spatially uniform mean wind stress, and a steady (barotropic) through-flow from the Scotian Shelf. The wind stress was taken as 0.1 Pa towards 137” (clockwise from true north), which is the average for the Georges Bank region in March-April computed from data provided by Bunker (1976). (Improved esti- mates of wind stress using the Comprehensive Ocean- Atmosphere Data Set (Woodruff et al., 1987) suggest that this magnitude of wind stress, i.e. 0.1 Pa, is near the high end of the interannual range of March-April averages. Thus, the model solutions used in this paper are probably more appropriate to years with above- average wind stress.) The through-flow in the base case was obtained through a 0.103 m mean set-up of the coastal node in Cabot Strait (upstream boundary) which, in combination with the tidal and wind forcing, yielded a south-westward mean transport of 0.56 x lo6 m3 s-’ between Halifax and Emerald Bank on the Scotian Shelf. This value approximates the observa- tional estimate for March-April for the same section

’

3-0 modeling Geurges Bank cod and haddock early life stages 49

obtained from the combined data of Drinkwater et al. (1979) and Anderson and Smith (1989).

The zero-frequency (mean) elevation in the base case was set to zero at other open boundaries, except on the cross-shelf boundary to the Middle Atlantic Bight where geostrophic flow was allowed. Zero normal flow was specified at solid boundaries for both frequencies and, for zero frequency, additionally at the truncated Bay of Fundy boundary. A full quadratic bottom stress law, and a vertically uniform but horizontally varying vertical eddy viscosity were used following the iterative method of Lynch and Naimie (1993). The Lynch and Naimie (1993) solution method was then used to obtain the tidal and mean flow solutions with full non-linear coupling, including tidally induced mean flow.

In the second case, baroclinic forcing was included through pressure gradients computed from a seasonal- mean density field obtained from historical temperature and salinity data for the region. The input database comprised about 15 000 different stations (profiles) for February-May obtained from national archives and recent cruises. A 3-D density field centered on 1 April was estimated using four-dimensional optimal linear interpolation (Bretherton et al., 1976). Correlation scales were taken as 45 days for time, 15 (30) m above (below) 75 m for the vertical coordinate on the shelf, and 40 km for the horizontal coordinates on the shelf except for 20 km and 60-100 km for the cross- and along-isobath directions respectively in the Georges Bank region. The resulting pressure gradients were specified as forcing in a zero-frequency solution with boundary conditions as in the base case except on the upstream cross-shelf boundary: elevations computed to give zero geostrophic bottom flow normal to this bound- ary were specified, with set-down on the Cabot Strait coastal node modified to yield the observed transport on the Halifax section (after addition to the base case). Friction parameters were taken from the base case. The final ‘baroclinic’ flow field for the second case was a linear superposition of the base-case tidal and mean flow fields, and the additional zero-frequency baroclinic solution.

3.3 Predicted circulation and comparison with observations 3.3.1 Model flow fields The tidal ellipses (Fig. 6a) show the well-known strong amplification over Georges Bank and adjacent shallow areas (for additional dis- cussion of the M2 tidal solution and its residual, see Lynch and Naimie, 1993). The tidal current magnitude largely determines the eddy viscosity (N) magnitude and hence the vertical current structure in the Georges Bank portion of our solutions. The eddy viscosity vari- ation is illustrated by the distribution of Ekman layer

Figure 6. (a) Depth-averaged model Mz tidal ellipses; the ellipses are scaled to indicate approximate particle excursions. Only every sixth ellipse is shown. The 60 m, 100 m and 200 m depth contours are indicated. (b) The Ekman depth; the dashed line is the 100 m bathymetric contour.

depth (Fig. 6b), taken as V(2Nlf), where f is the Coriolis parameter, which shows values ranging from about 10 m in deep water to over 40 m (exceeding the water depth) on the central Bank.

Horizontal and vertical sections of the base-case zero- frequency flow field driven by the M2 tide, wind and Scotian Shelf inflow are shown in Figs 7 and 8 respect- ively. The tidal residual jets on the Bank’s northern flank and on the western side of the Great South Channel are apparent throughout the water column in

50 F.E. Wemer et al.

Figure 7. Horizontal sections of the zero-frequencyhesidual flow on Georges Bank 1, 10,30 and 50 m below the surface. The 60 m and 100 m depth contours are shown. The blank regions in the 30 m and 50 m sections indicate locations shallower than the depth of the section.

the horizontal sections. Away from shallow areas and regions of strong tidal residuals, the near-surface current is southward, consistent with simple Ekman dynamics. The veering with depth of the surface Ekman layer is generally apparent, particularly in deep areas.

Starting on the Northeast Peak and proceeding along the southern flank, the currents below the surface Ekman layer are generally southwestward, with peak

magnitude in the vicinity of the shelf break. On the southern flank, the cross-bank component of subsurface current is generally weak, with on-bank flow inside the 60 m isobath and at mid-depth over the shelf break, and off-bank flow in the lower water column seaward of the 60 m isobath. Approaching the Great South Channel, the currents seaward of roughly the 60 m isobath continue southwestward with the near-surface currents

3 - 0 modeling Gemges Bank cod and haddock early life stanes 5 1

Figure 8. Vertical sections of zero-frequency or residual flow on Georges Bank (a) on Northeast Peak zonally along 41.87"N, between 66.03"W and 67.20"W (maximum depth is 98 m); (b) across the southern flank between (40.67"N, 67.28"W) and (41.32"N, 67.78"W) (maximum depth is 106 m); (c) zonally across the Great South Channel along 40.89"N, between 69.33"W and 68.36"W (maximum depth is 77 m); and (d) meridionally along the Great South Channel on 68.84"W, between 40.29"N and 41.32"N (maximum depth is 114 m). Refer to Fig. 10 for the location of the sections. Contours of currents (cm s-I) normal to the section are positive into the figure.

b

having an off-bank component from the wind forcing. Below the surface layer in the Channel, there is a saddlepoint in the flow with generally weak currents: southwestward in the south, northward along the Channel's eastern side, eastward along the 100 m isobath to the north, and southward along the western

side (see Ridderinkhof and Loder, 1993 for further discussion).

The computed baroclinic flow field over Georges Bank (Fig. 9) is qualitatively similar to the barotropic base case (Fig. 7). This is expected as, during spring, there is little stratification over the Bank. Differences in

52 F.E. Werner et al.

Figure 9. Horizontal section 30 m below the surface on Georges Bank of the zero-fiequencyhesidual flow with baro- clinic forcing. The 60 rn and 100 m depth contours are shown. The blank regions indicate locations shallower than the depth of the section.

the baroclinic case are stronger along-bank currents near the shelf break (consistent with the circulation along the shelf-water/slope-water front), stronger in- flow to the Great South Channel from the Cape Cod region, a weakening in the current 'connecting' the Great South Channel and the northern flank of the Bank, and increased small-scale structure near the Bank edge. These differences receive contributions from both the local baroclinic pressure gradients and changes in the spatial structure of the through-flow associated with the different upstream conditions.

3.3.2 Comparison with observations A comprehensive comparison of the model's M2 tidal solution with field data (Lynch and Naimie, 1993) has shown that tidal velocities agree to within 6.4 (4.8) cm s-' for the major (minor) axis (average value of 44 cm s-') and 10 (7) degrees for phase (orientation). We discuss next a comparison of the mean currents with moored measure- ments.

Moored current measurements of at least half-month duration in March-April are available for 12 sites in the Georges Bank region (Butman eta!., 1987). The long- term mean currents at these sites in March-April (Fig. 4a) show substantial qualitative and quantitative simi- larity to both the base-case and baroclinic model solu- tions, although measurements are available at only a

single depth in many cases. Furthermore, the along- bank transport inside the 200 m isobath on the southern flank in both the base-case (0.375 X lo6 m3 s-') and baroclinic (0.383 x lo6 m3 s-') solutions is in good agreement with previous observational estimates (0.33- 0.43 X lo6 m3 s-') for winter (Flaggetal., 1982). Over the shelf break, the alongshelf flows in the baroclinic case are closer to those observed while, in the Great South Channel, the barotropic case has greater north- ward flow, as observed.

The best vertical resolution is available at two sites (stations A and M4) on the outer southern flank, for which the observed and predicted currents are com- pared in Fig. 4(b). Both solutions are in rough agree- ment with the observed currents at mid-depth at A and near-bottom at M4, while there is poorer agreement at the other positions, particularly those at M4. Interan- nual variability in the observed currents and/or wind stress may be a significant factor to the discrepancies. We conclude that the barotropic solution is most appro- priate as the base case because its flow components are more firmly established (except for the frontal circu- lation at the shelf break) and it is in approximate agreement with the most extensive set of current measurements (station A). We will also, however, use the baroclinic flow field in an initial exploration of the influence of baroclinicity, recognizing that further effort is required to fully resolve the circulation associated with baroclinicity over variable topography.

4 RESULTS

We describe in this section the fate of passive and active particles on Georges Bank in the flow fields described above. Information on the particle tracking model is given in Appendix B. In brief, particles are released in different horizontal layers within a 62.5 km square located over the Northeast Peak of Georges Bank (Fig. 10). The standard release per horizontal layer is of 121 particles, the standard length of the simulations is 93 days and the displays are at multiples of the M2 period. We refer to 'retained' particles as those within the Georges Bank region, east of 68.96"W and shoalward of the 100 m isobath. All cases are run in the base-case flow field; we explore the sensitivity to the addition of a baroclinic flow component using passive particles.

4.1 Fixed-depth partick trajectories Considering the possibility of eggs and larvae remaining at particular depths through some combination of bio- logical and physical processes, we start with a set of particle releases in which the vertical position is fixed. The monthly position of particles released at 1 m, 30 m

3-D modeling Gemges Bunk cod and haddock early life stages 53

Figure 10. The model spawning grid for cod and haddock (stars). The southern limit of the grid is 41.57'" and the northern limit is 42.03"N; the western boundary is at 67.18"W and the eastern boundary at 66.42"W. The locations of the vertical sections shown in Fig. 8 are indicated (thin solid lines). Also shown is the meridional section on the western edge of the southern flank, from which particles are released to study the sensitivity to the location upstream of the Great South Channel (thick solid line).

Figure 11. at 15 and 31 days.

Horizontal location of 1 m fixed-depth particles

and 50 m in the base-case flow field with the vertical velocity flow components 'turned off is shown in Figs 11, 12 and 13 respectively. In each case, the trajectories may be interpreted in relation to the Eulerian velocity fields (Fig. 7).

The 1 m fixed-depth release, in the wind-driven surface Ekman layer, resulted in all particles lost south- ward to the deep ocean after 31 days (Fig. 11). The particles at 30 m stay on the shelf, reaching the Great South Channel (GSC) by 62-93 days (Fig. 12). Although particles do enter the GSC they eventually re-enter the southwestward flow to the New England Shelf and leave the Bank. Particles fixed at a depth of 50 m (Fig. 13) separate into two groups by day 3 1 , a small cluster released in the northernmost row of the spawn- ing grid moving along the 100 m isobath of the North- east Peak, and the remaining particles straddling the 60

Figure 12. Monthly horizontal location of 30 m fixed-depth particles at 3 1, 62 and 93 days.

54 F.E. Werner et al.

Figure 13. particles at 31, 62 and 93 days.

Monthly horizontal location of 50 m fixed-depth

I. \ .

....................

m isobath. Between days 62 and 93, the latter particles reach the GSC and most continue their circuit around Georges Bank. The effect of the on-bank displacement of the particles released at 50 m relative to those released at 30 m, and the resulting on-bank retention of the particles released at 50 m is clear.

A 10 m fixed-depth release (trajectories not shown) resulted in all particles leaving southwestward along the Bank’s edge. While at 1 m the particles are in the dominantly wind-driven layer, at 10 m their trajectories are a combination of the wind-driven currents moving the particles off-bank and the general southwestward subsurface flow field along the Bank‘s southern flank.

4.2 Passive particle trajectories We next consider the passive case (including the verti- cal velocity component) in which particles are advected by the 3-D base-case velocity field. A release of 1210

particles in horizontal layers at 5 m intervals between 5 and 50 m tracked over a 93 day period is shown in Fig. 14(a). The particles released in the top layers, at depths of 5, 10 and 15 m, leave the Bank, with some moving to the deep ocean, and the majority to the Middle Atlantic Bight. O f the particles released in the top 25 m, 77% were still on the Bank after 31 days, 25% after 62 days and 7% after 93 days. O f those released at 30 m or deeper, all remained on the Bank after 31 days, 94% after 62 days and 73% after 93 days. After 93 days, 95% of those released at 45 m and 50 m were still on the Bank.

The mean depth and the number of particles over the Bank are shown in Fig. 14(b) for the 93 day period. The mean depth of the retained particles released at 25 m or shallower increases over the first 62 days from a starting mean depth of 15 m to a mean depth of approximately 35 m. Those retained particles that were released at 30 m or deeper maintain their depth on average at roughly 35 m. These results suggest that the observed deepening with age of the larvae (Fig. 3) may be explained in part by hydrodynamic processes acting on passive particles.

Figures 15-17 show monthly snapshots of the par- ticles released at 10 m, 30 m, and 50 m respectively. The initial trajectories of the 10 m released particles are off-bank owing to the surface Ekman transport. After 3 1 days, when they reach the shelf edge, they are down- welled and exit the surface off-bank flow and continue southwestward along the edge of the Bank. These particles continue to be downwelled, and at 93 days (at which time they have left the Bank) they are deeper than 50 m. The particles released at 30 m straddle the 60 m isobath, with the more southerly ones continuing their southwestward trajectory. Those nearest the 60 m isobath move into the GSC circulation; some of these are recirculated towards the northern flank, but others exit southwestward. The particles released at 50 m move similarly to those released at 30 m, with the difference that a larger number of particles move in- itially in an on-bank direction and thus more are retained. Some particles released at 50 m are caught in the off-bank flow at depth and are lost to the continen- tal slope.

The downwelling of particles from the Ekman layer on the outer southern flank, or their increased deepen- ing with age, points to an important secondary aspect of surface Ekman dynamics on Georges Bank. Examin- ation of model solutions for the individual forcings in the present base case indicates that the shelf-break downwelling (Fig. 8b) includes significant contri- butions from both the wind-driven flow in the upper 2C- 30 m and the through-flow in the middle and lower water column. Idealized model solutions indicate that

3-D modeling Geurges Bank cod and haddock early life stages 55

Figure 14. (a) Monthly horizontal passive particle locations at 31, 62 and 93 days. The horizontal release locations are as in Fig. 10. In the vertical the releases occurred simultaneously at 10 layers from 5 to 50 m. (b) Mean depth of the retained particles over 93 days. The solid line shows the mean depth of the particles released at 25 m or shallower, the dashed line shows the mean depth of the particles released at 30 rn or deeper. Also shown is the time-history of the percentage of particles retained on the Bank for particles released at 25 rn or shallower (open bars), and for particles released at 30 m or deeper (solid bars).

a

1 Day 931

b 0

31 62

Time (days) 93

the wind-driven contribution results from a horizontal convergence driven by the offshore/off-bank wind stress in combination with the tidally imposed cross-shelf variation in eddy viscosity, as essentially proposed by

Heaps (1980). Thus, while the offshore winter-spring wind stress on Georges Bank results in off-bank near- surface transport, Ekman dynamics also provides a mechanism for the 'escape' of passive particles to the

56 F.E. Werner et al.

Figure 15. Monthly horizontal passive particle locations released at 10 m at 31 and 62 days.

primarily alongbank (and sometimes on-bank) flow regime below.

As in the fixed-depth trajectories, the transit time to the GSC is approximately 60 days. Particles reaching the GSC region can either continue their trajectory to the New England shelf (these are generally furthest south) or veer northward. The ones veering north at times re-enter the south-westward branch of flow out of the Georges Bank region or they get caught in a branch of the flow that continues clockwise around the Bank.

The stragglers in Figs 16 and 17 are particles that were advected to depths greater than 50 m over certain areas of the Northeast Peak where they encounter a sluggish residual flow (Figs 7 and 8a). Once these particles exit the Northeast Peak, they continue their south- westward flow along the Bank's southern flank.

A key area in determining whether a particle will be retained is the region immediately upstream of the GSC, roughly between the 70 m and the 50 m isobaths. To examine this region in greater detail, we released passive particles spaced every 500 m horizontally and every 10 m vertically along the meridional section shown in Fig. 10 and ran three 60 day simulations: two cases to examine the effect of the initial tidal phase which differed only in a 6 h shift in start-time, and a third case where the M2-period current was removed

Figure 16. released at 30 m at 3 1, 62 and 93 days.

Monthly horizontal passive particle locations

Day 31

entirely. From the composite starting locations of retained particles (Fig. 18) we see that seaward of roughly the 65 m isobath no particles are retained, that particles below 30 m and inside the 50 m isobath are retained, and that particles in the top 25 m are lost from the Bank unless they start shoalward of the 50 m isobath. The differences between the runs revealed that retention in the region between the 50 and the 65 m isobath is affected by the phase of the tide.

In a passive-particle release in the baroclinic flow field we found small quantitative differences over the first 2 months (not shown) from the base-case particle distributions (Fig. 14). The southwestward drift of particles on the outer southern flank is somewhat faster, with particles reaching the Middle Atlantic Bight after 60 days. The downwelling at the shelf break is still observed. Thus, over the southern flank and southern

3-0 modeling Georges Bank cod and haddock early life stages 57

Figure 17. released at 50 rn at 3 1, 62 and 93 days.

Monthly horizontal passive particle locations

* ..-- >-' *',- - ,--,- -.

- - a / -

Day 31

Day 9

GSC, particle trajectories are not significantly affected by this additional flow component. After 93 days, the main difference is that the particles in the baroclinic field - once they reached the GSC - showed a weaker tendency to recirculate around the Bank. Only a small number of the deepest (50 m) released particles recircu- lated through the GSC, with the remaining particles continuing southwestward to the Middle Atlantic Bight. This is clearly related to the missing branch of the flow connecting the GSC and the flow along the Bank's northern flank (Fig. 9), which may be due to unresolved baroclinic features in view of drifter obser- vations from the region (Beardsley et al., 1991).

4.3 Trajectories of vertically active particles The monthly trajectories obtained with the vertical behavior function shown in Fig. 3 and with horizontal displacements as determined from the base-case flow

field are shown in Fig. 19. The particles spend the first 60-70 days at depths of 35 m and shallower and thus move primarily along-bank to the south-west, with a small off-bank displacement associated with the surface wind-driven layer. A comparison of the particles' posi- tions at 3 1 and 62 days with the fixed-depth 30 m case (Fig. 12) shows the active particles moving further off- bank and southwestward during the first 31 days, con- sistent with their spending more time in the upper water column. By day 62, some particles have entered the GSC, and by day 93 almost all have continued to the New England shelf. Those in the GSC remain trapped near the saddlepoint.

From these results it appears that imposing vertical behavior on the particles decreased their retention. However, the reason for the weaker retention is related to their residing in the upper layers of the water column in the early (egg) stages. To test the effect of the prescribed die1 migration during the later larval stages, we examined a case where only the mean vertical position of the particles was specified. The results were indistinguishable from those in Fig. 19, indicating that the mean (24 h averaged) vertical position is the dominant effect.

4.4 Comparison with observations: horizontal distribution and shoaling The results described in the preceding section are based on our best estimates of the spawning location and vertical behavior of cod and haddock early life stages. After 31 days the model distribution forms an elongated patch centered over the southern flank of Georges Bank, similar to the 20-40 day observed distribution of haddock larvae (Figs 2 and 19). It is, however, much smaller than the idealized 20-40 day distribution of cod larvae (Fig. 2), which is as expected given the broader spawning area of cod. After 62 days, larger discrepancies between modeled and idealized distributions for both cod and haddock become apparent. The modeled distri- bution is centered over the south-west quadrant of Georges Bank, and particles are not found shoalward of the 60 m isobath (Fig. 19). By contrast, the observed distributions of cod and haddock are both broader and centered shoalward of the 60 m isobath, covering the western half of Georges Bank.

The same may be said about the passive and fixed- depth results: in general the positions of the modeled and the observed horizontal distributions are in approxi- mate agreement after 31 days, with increasing discrep- ancy in cross-shelf position at 62 and 93 days.

We show in Fig. 20 the monthly abundance of particles versus bottom depth for the passive particle releases at 30 m and 50 m for the first 62 days and the

58 F. E. W e m et al.

Figure 18. Vertical and meridional dependence of particle retention upstream of the Great South Channel (Fig. 10; section indicated by thick line). Particles throughout this section were released every 10 m vertically and every 500 m horizontally. Particles released within the diagonally hatched area were retained; those within the vertically hatched area were lost from the Bank. Black region indicates the Bank's bottom topography.

I Section along MSOW -1 0

-20

-30 h

E d n

-40

f3 -50

-60

-70

40.6"N 40.93"N

biologically active case. No indication of shoaling is apparent in the passive 30 m or the vertically active cases. The passive 50 m case does show monotonic shoaling, but it is not sufficient (Fig. 17) to account for the observed shoalward displacement of cod and had- dock larvae.

One of the hypotheses proposed by Lough and Bolz (1989) to explain the cross-bank age gradient they found with older larvae nearer the shoals is directed swimming ability. To further evaluate the significance of such a capability, we released particles at 30 m on the Northeast Peak spawning grid and allowed them to drift passively except for an active post-hatch on-bank swim- ming component directed toward a fixed point on top of the Bank. Their swimming speed over the first 40 post- hatch days increased from 0.3 cm s-' at the time of hatch to just over 1 cm s-' for 40 day-old larvae, consistent with a cruising speed of 1 body length per second and the Bolz and Lough (1988) growth function. The horizontal distribution of particles including the active on-bank swimming component is shown in Fig. 21. The shoaling results for the first 60 days, shown in Fig. 20(d), indicate that if directional swimming ability occurs, the shoalward displacements can be significant over time scales of 60 days. Halving the on-bank

swimming component to 0.5 body length s-' generated distributions after 31 and 62 days (not shown) closer to those of the completely passive 30 m released particles (Fig. 16). However, by 93 days, continued on-bank swimming at 0.5 body length s-' resulted in a separ- ation of the horizontal distribution of particles, with roughly half of the particles over the shoal-central portion of Georges Bank and the other half located over Nantucket Shoals. These results suggest that direc- tional swimming at plausible speeds would be significant to the fate of larvae on Georges Bank, if a directional capability were possible.

5 DISCUSSION AND CONCLUSIONS

The model results presented here help to clarify the influences of circulation and simple behavior on the distribution of cod and haddock early life stages on Georges Bank. On the physics side, the circulation model confirms the importance of tidal currents, tidal residual currents, wind-driven flow and Scotian Shelf inflow to the mean drift of particles on Georges Bank in winter-spring. It also points to the importance of wind- driven downwelling on the outer southern flank and a critical branch point in the horizontal circulation in the

3-D modeling Georges Bank cod and haddock early life stages 59

Figure 19. 3 1 ,62 and 93 days.

Monthly location of vertically active particles at

Great South Channel. The baroclinic flow case indi- cates that the influence of local density gradients on the Bank-scale circulation is largely confined to the shelf- break region, but that smaller scale flow-structures can arise around the Bank edge in general. Further investi- gation is required to determine whether the latter are artificial structures associated with the limited density data and the joint effect of baroclinicity and relief (JEBAR, e.g. Huthnance, 1984), or realistic structures. Nevertheless, relevant to the fate of the early life stages of cod and haddock, the predicted currents on the southern flank and the subsurface transit times between the Northwest Peak and Great South Channel are in approximate agreement with observations.

On the biological side, we summarize the model results for passive, fixed-depth and vertically active particles released on the Northeast Peak as follows:

1. The geographic location and depth of spawning has an important influence on whether eggs and larvae will be retained on the Bank. 2. Progeny released in the upper 10 m of the water column (whether passive or maintained at a fixed depth) are lost from the Bank within 30-60 days (Figs 11 and 15). 3. The relative importance of the two principal loss routes from the southern flank (off-bank surface drift versus along-bank subsurface flow into the Middle Atlantic Bight) depend on the particles’ vertical posi- tion in the water column: eggs and larvae remaining in the surface Ekman layer are lost off-bank to the North Atlantic, whereas passive eggs and larvae downwelled from the surface layer near the shelf break are generally lost into the Middle Atlantic Bight.

4. Progeny given egg depth-distributions and larval behavior that are consistent with the literature, are not retained on the Bank (Fig. 19). This loss is primarily due to the hypothesized surface-layer egg distribution during the first 20 days. 5. Progeny released deeper than 30 m have a higher probability of being retained (whether maintained at a fixed depth or passive, Figs 13 and 17). 6. Larvae at 50 m depth along the southern flank are advected shoalward, even with passive behavior (Fig. 20b), owing to the on-bank flow in deeper water in this area (Figs 7 and 8). 7. With realistic swimming speeds towards the Bank’s crest, the shoalward displacement with age is substan- tially enhanced (Fig. 20d). With this behavioral characteristic, the larval distributions during the first 2 months would be consistent with field observations. 8. The depth and horizontal distributions of larvae along the southem flank have an important influence on whether larvae are retained on the bank or advected towards the Middle Atlantic Bight, suggesting that interannual changes in larval distribution along the southern flank and in the circulation result in variable losses of larvae from the Bank.

The model results also clarify conceptual issues in the recruitment literature for Georges Bank, and identify important issues that need further investigation. The approximate 60 day transit time required for eggs and larvae to be advected from the Northeast Peak to the Great South Channel, and the need for progeny to be shoalward of (or near) the 50 m isobath in the vicinity of the Great South Channel if they are to be retained, constrain the location of spawning. Eggs spawned on the south-western part of the Bank would be transported either offshore or to the Middle Atlantic Bight. If these

60 F.E. Wemer et al.

\ . ' _ - _ _ _ ,',/:,c.r.:----- \ - ... . ' , , .?' ; . ' \ \

; . ** 'I I ,,.it :.- ,;

.p' '.,\, ,' ,.:

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I : I :

., ., : . . . '/ . .

I '/ . ...' . . . . .' T . : . ..-

. . . .. ... ... . - - - >'- 1

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Figure 20. (c) the vertically migrating case, and (d) with active on-bank swimming. Curves are plotted for 0, 31 and 62 days,

Particle abundance versus bottom depth for the first 62 days for the passive particle releases at (a) 30 m and (b) 50 m,

vagrants in the sense of Sinclair (1988). In a more general sense, the model results indicate that advection off the Bank at both egg and larval stages is substantial for the upper layer. If these progeny are lost to the Georges Bank populations, the vagrancy rate (and its dependence on circulation and mixing processes) is inferred to be an important component of population regulation (both density dependent and density inde- pendent).

The model results clarify the 'enigma' of Georges Bank spawning (Colton and Temple, 1961) in the sense that, although eggs and larvae that remain in the surface layer are advected off-bank, those progeny in the deeper water remain on the Bank. An important aspect of Ekman dynamics on the outer southern flank is the downwelling ftom the surface layer, providing a path- way for passive eggs and larvae to exit from the off-bank surface drift and a possible explanation for the observed deepening of larvae with age. Although progeny affec-

1 I I I l l 1 1 1 1

-20 -30 -40 -50 -60 -70 40 -90 -100 -110

Water Column Depth (m) Water Column Depth (m)

3-D modeling Georges Bank cod and haddock early life stages 61

ted by this downwelling still tend to drift south- westward from the Georges Bank region, their retention on the shelf may enhance their potential for displace- ment back onto the Bank during unmodeled time- dependent (e.g. wind-driven) flow events. With the enigma of Georges Bank spawning resolved, the results provide support for the possibility that the specific location of spawning for cod and haddock on Georges Bank is determined by circulation and mixing charac- teristics that influence egg and larval distributions.

The comparison between observed and predicted distributions over the first 60 days is encouraging. Unfortunately, the idealized nature of the initial and subsequent egg and larval distributions, and the limited available observational data, preclude a detailed com- parison between model and observed distributions. Nevertheless, the study suggests that eggs and larvae below the surface Ekman layer can maintain an on-bank distribution which is not significantly affected by the die1 vertical migration shown in Fig. 3.

After 60 days a conspicuous discrepancy between predicted and observed distributions is that model par- ticles do not move shoalward towards the crest of the Bank, as indicated by the idealized distributions of Fig. 2. Our results suggest the potential significance of a directional swimming capability, in that with realistic swimming speeds, if directional, the shoalward dis- placement with age is significantly enhanced and the resulting larval distributions during the first 2 months are consistent with field observations. Alternately, the observed discrepancy may reflect unmodeled physical processes that could contribute to a weak cross-bank circulation on the southern flank.

Despite the complexities encountered, the physical regime we considered was somewhat simplistic. We did not consider low-frequency current fluctuations driven by winds and warm-core rings, nor any stochastic move- ments of either water or the organisms. Future modeling should progress toward resolving events, including low- frequency current fluctuations, the vertical mixing of the particles, and the temporal evolution of stratifi- cation and associated frontal circulation. Future efforts also need to examine more quantitatively existing egg and larval data for cod and haddock on Georges Bank, and to include more realistic initial distributions differ- entiating the two species.

ACKNOWLEDGMENTS

We thank Brian Blanton for his invaluable help with the particle simulations, Christopher E. Naimie for computing the velocity fields, Mary Jo GraGa for pro- cessing the density field and current observations, and

Y ingshuo Shen and Randy Losier for programming help associated with the model and data analysis. Insightful comments from Drs H. Ridderinkhof, P. Smith and M. J. Tremblay, and critical reviews from Drs K. Drink- water, K. Frank, J. Rice, R. Stephenson and three anonymous reviewers are greatly appreciated. Dr B. Butman kindly provided the observed monthly mean currents. We thank W.G. Smith for providing access to unpublished MARMAP egg and larval data. This proj- ect was funded in part by NSF grants OCE-9012612, OCE-9016921, OCE-9018388 and OCE-9013887 and the Canadian Panel on Energy, Research and Develop- ment.

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24:1-13.

APPENDIX A: THE CIRCULATION MODEL

The circulation model is an extension of Lynch et al. (1992) [detailed in Lynch and Naimie (1993)l to in- clude nonlinearities. We solve the 3-D shallow water equations with conventional hydrostatic and Boussi- nesq assumptions, eddy viscosity closure in the vertical and prescribed density/baroclinic forcing. They are the 3-D continuity equation

v * v = o (Al) its 2-D vertical average

and the horizontal components of the 3-D momentum equation

where using conventional notation: r(x,y,t) is the free surface elevation; v(x,y,z,t) is the fluid velocity; S(x,y,t) is the vertical average of v; R(x,y,z) = (g/po) Jf V pdz is the baroclinic pressure gradient (assumed known); h(x,y) is the bathymetric depth; N(x,y,z,t) is the verti- cal eddy viscosity; g is gravity; f is the Coriolis vector; V,, is the horizontal gradient operator (a/ax,a/ay); (x,y,z) are Cartesian coordinates where z is positive upward; and t is time.

The surface and bottom boundary conditions are

av a4

N-=hW (z = 0)

av az

N- = C~JVIV + 0.00035~ ( Z = -h) (A5)

where hW is the atmospheric forcing and C d the bottom drag cofficient taken as 0.005. The bottom stress follows a quadratic drag law and also inclOudes a (linear) background contribution (value of 0.00035 in m s-I) from unmodeled flows. The vertical eddy viscosity N is horizontally variable but constant vertically and con- sists of a contribution from the modeled currents NT plus a background value (0.002 m2 s-'), i.e.

N(x,y,) = NT + 0.002 = NolVI2 + 0.002 (A6)

with No = 0.2 s as in Davies and Fumes (1980). Following Synder et al. (1979), a harmonic expan-

sion in time of the free-surface and velocity components of eqns Al-A6 is used, providing equations at zero and the Mz tidal frequency but neglecting higher har- monics. Non-linear contributions arising from the advective terms, the bottom stress and the eddy visco-

64 F.E. Werner et al.

sity term are kept. The computational task is the solution of non-linear eqns A2-A5, in the frequency domain for a two-constituent spectrum; additional de- tails of the computation are given in Lynch and Naimie (1993).

APPENDIX B: PARTICLE TRACKING MODEL

The drift of particles in a specified flow field is obtained by solving for the position of the particles x(t) from

where the 3-D position vector xi+ at time ti+ depends on the velocity vi(xi,t) at a previous time ti. We used a standard fourth-order Runge-Kutta integration with adaptive step-size control, also referred to at times as fifth-order Runge-Kutta scheme (Press et al., 1986; Foreman et al., 1992). Active-particle tracking is op- tional with full flexibility in prescribing desired be- haviors, e.g. age-dependent vertical or horizontal mirations. A complete description of the tracking code is given in Blanton (1992).