David A. Griffin

The adjoint method of data assimilation used operationally for shelf circulation

A real-time shelf circulation model with data assimilation has been successfully used, possibly for the first time, on the outer Nova Scotian Shelf. The adjoint method was used to infer the time histories of flows across the four open boundaries of a 60 km × 60 km shallow-water equation model of Western Bank. The aim was to hindcast and nowcast currents over the bank so that a patch of water (initially 15 km in diameter) could be resampled over a 3-week period as part of a study of the early life history of Atlantic cod. Observations available in near real time for assimilation were from 14 drifting buoys, 2 telemetering moored current meters, the ships acoustic Doppler current profiler and the local wind. For the postcruise hindcasts presented here, data from two bottom pressure gauges and two more current meters are also available. The experiment was successful, and the patch was sampled over a 19-day period that included two intense storms. In this paper we (1) document the model and how the data are assimilated, (2) present and discuss the observations, (3) demonstrate that the interpolative skill of the model exceeds that of simpler schemes that use just the current velocity data, and (4) provide examples of how particle tracking with the model enables asynoptically acquired data to be displayed as synoptic maps, greatly facilitating both underway cruise planning and postcruise data analysis. An interesting feature of the circulation on the bank was a nearly stationary eddy atop the bank crest. Larvae within the eddy were retained on the bank in a favorable environment until the onset of the storms. The variable integrity of the eddy may contribute to fluctuations of year-class success.

Shipboard nowcasting of shelf circulation

Abstract A system has been developed which provides up-to-the-hour hindcasts and short term forecasts for the flow within the domain of a regional hydrodynamic model. The enabling technology is outlined here and principally includes: (i) a ship-board anemometer and Acoustic Doppler Current Profiler; (ii) telemetry systems for current meter moorings and LORAN-C drifters; (iii) an ethernet-linked network of PCs and workstations running data processing software; and (iv) an assimilative regional hydrodynamic model. The first operational application of the system has recently been completed on the outer Scotian Shelf where fisheries biologists needed to track a cohort of cod larvae ( Gadus morhua ) for 2–3 weeks. The cruise was successful: a patch of larvae initially 20 km across was found and tracked for 19 days despite the cruise being interrupted halfway through by storm force winds which forced the ship back to port for several days. Selected examples of data acquired on the cruise are presented to illustrate the usefulness of the system.

UPWELLING AND INTERNAL TIDES OVER THE INNER NEW SOUTH WALES CONTINENTAL SHELF

Nearshore variability of the thermocline depth and associated baroclinic currents at Sydney, New South Wales are analyzed for the locally and remotely forced components. Summer and winter data acquired in 65 m of water 3.5 km from the coast include thermistor string and current meter measurements. Cross-spectral analyses of the data are interpreted with reference to the free and forced modes of a simple two-layer frictional shelf model. Subinertial frequency (∼ 40 day-21 hour period) baroclinic variability appears to be locally forced, in contrast with the barotropic variability which is principally remotely forced and acts as one of the local forcing agents of the baroclinic variability through bottom Ekman layer dynamics. The local wind stress appears to be the more important forcing term, despite having less weather band variance than the bottom stress. Strong winds at Sydney are usually from the south and hence lead to downwelling, while bottom stress is responsible for the rarer upwelling events. Near-inertial variability is substantially inhibited at the study site except during winter when the internal Rossby radius becomes comparable to the distance from the coast. Superinertial frequency (to 6-hour period) baroclinic variability is dominated by standing internal Poincare waves, the principal energy source of which is presumed to be tidal currents over the outer shelf. The existence of a standing wave pattern implies that little dissipation occurs upon reflection at the coast.

Coastal-Trapped Waves behind a Large Continental Shelf Island, Southern Great Barrier Reef

Abstract The salient features of subinertial frequency fluctuations of current, sea level, temperature and wind stress observed within the Capricornia section of the Great Barrier Reef are interpreted by comparison with coastal-trapped wave (CTW) theories Near-coastal currents and sea levels are modeled with some success by a theory of first-mode wind-forced barotropic continental shelf waves with geographical origin at Fraser Island, the southern across-shelf boundary of the study region. However, current and temperature variations of period 8–10 days on the continental slope are observed to have energy far in excess of that generated by the local wind. Decomposition of the observed alongshore velocity field in terms of baroclinic CTW modes indicates the signal is predominantly a second- or third-mode wave propagating equatorward at 0.4–0.6 m s−1. These modes have most of their energy flux propagating along the continental slope, and the energy levels indicate that the source region lies to the south of ...

A model of the circulation on the outer Scotian Shelf with open boundary conditions inferred by data assimilation

The circulation on Western Bank is described using data collected in spring 1991 and 1992 as part of an interdisciplinary study of the early life history of Atlantic cod (Gadus morhua). The mean circulation over the crest of the bank is weak, of the order of a few centimeters per second, and is flanked to the south and west by an anticyclonic flow with a speed of about 10 cm s−1. A thermal wind calculation shows the mean circulation is due primarily to horizontal variations in the density field. The M2 tidal constituent is dominant and reaches speeds of about 20 cm s−1. The tidal residuals have a standard deviation of about 10 cm s−1 and characteristic time and length scales of several days and tens of kilometers, respectively. In order to help collect and interpret biological data from Western Bank, we developed a hydrodynamic model of the near-surface flow that could be used operationally. The model is based on a decomposition of the flow into components driven by (1) local wind stress, (2) horizontal density gradients, and (3) flows through the open boundaries of the model. The wind-driven component is calculated using a simple slab model driven by the observed wind. The other two components are estimated through the assimilation of observed bottom pressures, dynamic heights, and currents into the hydrodynamic model. The hindcast skill of the model is quantified by cross validation and shown to be higher than that of four simple, statistically based schemes.

Oceanic circulation and turbulence in the coastal zone

Abstract Measurements of turbulent eddy viscosities within 1 km of Bass Point (a 4 km wide headland near Sydney, Australia) indicate the presence of a relatively high level of turbulent energy, apparently caused by the complex subsurface topography near the point. This energy has typical length scale ∼300 m, typical time scale ∼100 min and an eddy viscosity of ∼15 m2 s−1, one to two orders of magnitude greater than that due to mixed layer turbulence alone. Despite the fact that the headland protrudes well out onto the continental shelf where strong longshore (∼0.2–0.5 m s−1) currents often exist, large-scale recirculation in the lee of the headland is rarely observed. The turbulence near the tip of the point prevents the formation of a single narrow shear layer (caused by separation at the point), and instead provides a much wider turbulent shear layer where the non-linear terms are apparently ineffective at driving a large-scale recirculation. The overall effect appears to be analogous to a “trip wire” or “vortex generator” whereby the enhanced generation of turbulence acts to alter the overall pressure field and pushes the separation point far downstream (or eliminates it entirely). The result is that the large scale flow appears often to be almost laminar, and somewhat analogous to that which is expected from a truly low Reynolds number flow.

Surface salinity variations in the Juan de Fuca Strait: test of a predictive model

Abstract We present a predictive scheme for surface salinity variations in the Juan de Fuca Strait. The scheme is based on a two-layer box-model which incorporates the combined effects of freshwater runoff, tidal mixing and wind forcing. Estuarine outflow into the Juan de Fuca Strait encounters two sills on its way seawards: the key parameters of our model represent entrainment and mixing at those sills. The parameters are tuned to a best fit of years (1967–1972) of summertime surface salinity variations at the east end of the Juan de Fuca Strait (Race Rocks light station). Surface salinites are then predicted for the 12 years 1973–1984 and 1988 using fitted parameter values. Model results follow observations closely and fit best in years of high salinity variance. The model predicts particularly well fortnightly and monthly changes in salinity as well as freshening events associated with certain wind conditions. For the year 1988, current and water property data were also available at the seaward end of the Juan de Fuca Strait. Although our model was again successful at forecasting conditions in the eastern Strait, the link with property variations at the western entrance of the Strait was not very clear, suggesting the influence of other causes.

Mooring design to minimize savonius rotor overspeeding due to wave action

Abstract A theoretical formula providing an estimate of the surface wave induced overspeeding of non-vector-averaging recording current meters is derived for shallow water (continental shelf) single meter moorings having subsurface buoyancy directly above the meter. It is shown that the common practice of placing meters close to the bottom in an attempt to escape wave action can result in greater overspeeding, even though the wave induced currents are weaker at depth. In cases where a variety of meters are available to be used at various depths, it is therefore recommended that the newer vector-averaging meters be used near the bottom as well as near the surface, with non-vector-averaging meters being used only at mid-depth on moorings whose uppermost buoyancy is also at mid-depth.

Steady wind-driven flow in long channels or lakes

Abstract The steady, wind-driven, barotropic circulation in an infinitely long frictional channel of parabolic depth profile is examined. The flow is forced by an along-channel wind-stress which varies sinusoidally in the along-channel direction with wavenumberk. A constant Coriolis parameterf is chosen and bottom friction is assumed to be proportional to the along-channel component of depth-averaged velocity with coefficientr. Polynomial series solutions are found for the case of a parabolic depth profile having, in general, a non-zero depth at the coasts. The nature of the response is determined by the dimensionless coastal wall depth γ and by the dimensionless channel widthδ = b/L, where the coastal trapping distanceL = (rb/2Dk |f|)1/2. The major effect of γ is on the spatial phase of the coastal response relative to the forcing, while δ determines whether the circulation is double-cellular (small δ) with no flow across mid-channel or single-cellular (large δ) with streamlines crossing mid-channel diagonally. The results are made applicable to long homogeneous “narrow” lakes (δ small) with steady uniform wind-forcing by observing that the normal transport at the lake ends is automatically (approximately) zero of the lake length isnπ/k,n integral and small. By summing solutions, a constant wind-stress may hence be approximated. For “wider” lakes such as Lake Ontario (δ ∼ 14) the results are less directly applicable but indicate that the flow should be diagonally symmetrical such that an easterly wind stress produces westward coastal jets along the northern and southern shores and northeastward return flow at mid-lake, in agreement with various other barotropic lake models.