Methods

Technical details

Sources of the velocity fields and their limitations

1. Source for the velocity fields

   The velocity field is computed as the sum of 5 components: the long-term seasonal mean, the responses to along-shelf and cross-shelf wind stress and sea level forcing at the upstream boundary, and the M2 tidal currents. A detailed description of the procedure for calculating the composite fields is described by Hannah et al. (2000) for an application requiring estimating the monthly mean circulation in the vicinity of Browns Bank. A brief description is given here.

   For this application there are 4 seasons, spring, summer, fall and winter, representing the seasonal cycle. The velocity fields were computed for a model domain covering the Scotian Shelf and Gulf of Maine from Cape Breton Island to Cape Cod. Hannah et al. (2001) provide a description of the calculation procedure and a comparison with moored current observations. Shore et al. (2000) provide a description of the upper-ocean drift pathways in these circulation fields.

   The responses to the along- and cross-shelf stress were calculated using a linear 3-d barotropic model (Lynch et al. 1992) with specified vertical eddy viscosity and bottom friction coefficients. The boundary elevations were clamped at zero along the upstream and offshore boundary. The vertical mixing coefficients were based on a blending of an empirical upper-ocean profile and the vertical mixing coefficients taken from the spring solution (Hannah et al. 2000). The bottom friction coefficients were taken as the time-averaged coefficients from the spring solution plus the additional bottom friction due to 10 cm/s of unmodelled flow. The response patterns are similar to those described in Greenberg et al. (1997).

   The velocity response to boundary forcing was calculated using the same linear barotropic model, bottom friction coefficients and vertical eddy viscosities as used for the wind response. The upstream boundary forcing was specified as a linear elevation decrease from the coast to mid-shelf, with the rest of the upstream and offshore boundary clamped to zero. The user specified forcing for this component is the adjusted sea level anomaly at Halifax. The anomaly is with respect to the combination of the seasonal cycle and the effect of local wind forcing. There is further discussion of this forcing component below.

   The M2 tidal currents from Hannah et al. (2001) are included in the calculation of the velocity field.

   For the drift calculations all of the velocity fields have been vertically averaged. The available intervals are: 0-5 m (surface), 25-35 m (25 m), and 95-105 m (100 m). When the averaging interval intersects the bottom, the average over the bottom 10 m was used.

   When the tracking is being done in the surface layer, the user has the option to include an additional drift due to near-surface velocities that are not captured in the modelled fields and the direct effect of the wind on the object. The additional drift is specified in terms of a fraction of the user specified wind speed and a rotation.

   The tracking algorithm is based on the DROG3D program developed by Cisco Werner and Brian Blanton (Werner et al. 1993; Blanton 1995; www.opnml.unc.edu).

2. Limitations

   It is important to an understanding of the limitations of the circulation fields used to calculate the drift trajectories.

   • The seasonal mean circulation component

     The fields are a realistic representation of 3-d seasonal circulation on the western and central Scotian Shelf obtained from historical observations and a combination of diagnostic and prognostic numerical models with forcing by tides, wind stress and baroclinic and barotropic pressure gradients. The major current features - the southwestward Nova Scotian and shelf-edge currents, and partial gyres around Browns and Sable Island Banks - are found to persist year-round but with significant seasonal changes.

     The quality of the flow fields varies across the region. As described in Hannah et al. (2001), comparison with current meter observations shows good agreement for the Browns Bank, southwest Nova Scotia and inner-shelf regions, and poorer agreement in the Sable Island Bank and shelf-edge regions where current and density observations are sparser and tidal influences weaker. The agreement with observations on Georges Bank is also good. There has not been a systematic comparison with observations in the Gulf of Maine, primarily due to the limited number of multiyear observations.

     There is temporal variability on timescales from hourly to interannual and longer that is not captured by the climatological seasonal-mean calculation. For example, the circulation for any particular April or May will be different from each other and from the mean spring conditions.

   • The wind-driven flow

     The wind-driven flow has two components: the local response to wind and the response to the sea surface pressure field set-up by the large scale wind field. The spatially uniform winds give rise to errors in each. The wind stress near the drifter can be different in magnitude and direction from the nearest observation location and the winds away from the drifter play an important role in shaping the pressure field which is an important component of the velocity field near the drifter.

     The calculation also assumes a steady-state response to the wind. This can lead to errors in direction and magnitude. These errors depend on the space-time structure of the wind field and have not been quantified.

     Another limitation on the wind-driven flow is that the vertical structure of the wind-driven flow is fixed. The vertical eddy viscosities are based on the spring model solutions. Thus the surface wind-mixed layer will be too deep in summer and too shallow in winter. There may also be a systematic underestimation of the mixed layer depths because storm effects were not included on the seasonal-mean simulations. In addition events such as the deepening of the mixed layer due to a particular storm is not included.

   • The boundary forced flow

     Knowing the correct amplitude for this forcing term is difficult. Adjusted Halifax sea level (sea level plus air pressure) contains contributions from the wind over the Scotian shelf, from the wind over the shelf regions to the north and east, changes in the density field over the Scotian Shelf, changes in the density field on the shelf regions to the north and east and changes in the density field over the Scotian Slope. The required components are those due to changes in the wind and density fields on the shelf regions to the north and east, and only the part that deviates from the seasonal cycle. In addition, the spatial structure of the boundary forced flow component is fixed, and the specified spatial structure of the boundary forcing will not be correct for all situations. There are large uncertainties associated with this component.

   • Tidal currents

     For studies of the small-scale structure of the trajectories, there are limitations associated with only having a single tidal component. In the Gulf of Maine the other semi-diurnal components contribute to both the phase and amplitude of the tidal currents and on the Scotian Shelf the diurnal tidal components can be important.

Details of the Seasonal Mean Wind Effects:

In its present configuration, WebDrogue subtracts the seasonal mean wind stress from the User Specified Wind Stress when calculating the velocity response associated with the oceanic response to wind stress (the Ekman response and the currents associated with the surface-pressure gradients that arise as the ocean responds to the wind). This is the response to along and cross-shelf winds that is discussed in the documentation here.

If the 'User-Specified Wind Stress' is zero (the default) and the seasonal mean wind stress is non-zero (more below) then WebDrogue calculates the velocity response associated with the negative of the seasonal mean wind stress and adds that to the mean currents. Thus one does not get the seasonal mean circulation when tracking with a zero wind stress. This is a bit annoying but not necessarily wrong.

Of the four data sets currently available, only the Scotian Shelf, Gulf of Maine set (also called cg1) has non-zero values for the seasonal mean wind stresses.

To eliminate the seasonal mean wind stresses from the drogue calculation in the Scotian Shelf, Gulf of Maine domain the user has two choices:

1. Add a wind forcing that will (approximately) cancel the seasonal mean wind stress. The appropriate values for the wind speed and direction are given below.

   Season	Wind Speed (m/s)	Wind Direction (deg CW from N)
   Winter	4.91	291
   Spring	2.84	280
   Summer	2.87	212
   Fall	3.22	278

2. Edit the data file and set the wind stresses to zero. The file to edit is <WebTide Home Directory>/data/cg1/vel_data.txt. The lines to edit are the ones below labels of the form <SEASON>STRESSX and <SEASON>STRESSY, where <SEASON> is one of WINTER, SPRING, SUMMER or FALL. Set the numbers below each label to "0.0".

References

Blanton, B. 1995. DROG3D: User's Manual for 3-Dimensional Drogue Tracking on a Finite Element Grid with Linear Finite Elements. Program in Marine Sciences, University of North Carolina, Chapel Hill, NC, 13 pp.

Greenberg, D. A., Loder, J. W, Shen, Y, Lynch, D. R, and Naimie, C. E. 1997. Spatial and temporal structure of the barotropic response of the Scotian Shelf and Gulf of Maine to surface wind stress: a model based study. J. Geophys. Res. 102: 20897-20915.

Hannah, C. G., J. A. Shore and J. W. Loder. 2000. The retention-drift dichotomy on Browns Bank: a model study of interannual variability. Can. J. Fish. Aquat. Sci. 57: 2506-2518.

Hannah, C. G., J. Shore, J. W. Loder, and C. E. Naimie. 2001. Seasonal circulation on the western and central Scotian Shelf. J. Physical Oceanography. 31:591-615.

Lynch, D. R., Werner, F. E, Greenberg, D. A, and Loder, J. W. 1992. Diagnostic model for baroclinic, wind-driven and tidal circulation in shallow seas. Cont. Shelf Res. 12:37-64.

Shore, J. A., C. G. Hannah and J. W. Loder. 2000. Drift pathways on the western Scotian shelf and its evirons. Can. J. Fish. Aquat. Sci. 57: 2488-2505.

Werner, F., Page, F., Lynch, D., Loder, J., Lough, R., Perry, R., Greenberg, D., and Sinclair, M. 1993. Influence of mean advection and simple behavior on the distribution of cod and haddock early life stages on Georges Bank. Fish. Oceanogr. 2: 43-64.