1. Estimating ocean-shelf flux and exchange with drifters
John Huthnance1, Marie Porter2,
1National Oceanography Centre, UK, 2Scottish Association for Marine Science
Ocean-shelf exchanges influence global climate and regional resources
FASTNEt – Fluxes across sloping topography of the North East Atlantic – project deployments
2012 Bay of Biscay. Colour denotes date
Faroe-Shetland Channel Colour denotes temperature (°C)
2013 Malin shelf. Colour denotes date
Complex topography: difficult to define “along-slope” or “cross-slope” direction.
Transport estimates from mooring data are sensitive to these definitions.
Drifter positions and corresponding water depths recorded every three hours. Hence we know to what extent depth contours were crossed by the drifters.

2. Drifter crossings of depth contours between position fixes
analysed ~ month by month.
Relevant water-depth changes Δh regressed on displacements
(Δx, Δy), i.e. (east, north)
→ “slope” (magnitude dependent on direction).
(Displacement mean and departures from mean) / (“slope” x 3 hours)
→ cross-slope flux û and exchange |u'| (velocities)
For all three areas, |u'| typically > |û|.
Transport estimates hû and ½h|u'| comparable in more cases.
Cross-slope exchange estimates across 200 m depth contour:
2.8 m2/s (Faroe-Shetland Channel)
2.3 m2/s (Malin shelf)
2.8 m2/s (Celtic Sea)
from daily positions

3. Relating Δh to (Δx, Δy) for “slope” and Δh → u (cross-slope)
To estimate cross-slope flow, avoiding assumption that “along-slope” ↔ current direction
(which could “define” some aspects of cross-slope flow to be zero)
Even with defined directions at mooring, flow angle to depth contours may differ elsewhere
Obvious estimate of “slope”: multiple regression of Δh on Δx, Δy (east, north displacements).
But this averages out irregular steep slopes (e.g. Biscay) to a much smaller mean.
Hence modified multiple regression based on
|slope along direction θ| = |s cos(θ-θ0)|.
Square both sides writing l2 = (Δx)2 + (Δy)2 :
|Δh/l|2 = a + b[(Δx)2-(Δy)2]/l2 + cΔxΔy/l2
or |Δh/l| = {a + b[(Δx)2-(Δy)2]/l2 + cΔxΔy/l2}/|Δh/l|
to avoid over-weighting crossings with steep slopes – subjective!
|Δh/l| and RHS Δx, Δy known; multiple regression → a, b, c → maximum slope (↔ θ=θ0).
Complex topography weakens slope dependence on θ
but typical slope steepness is retained via a.

4. Bias from analysing only contour-crossing intervals
Bias not expected from choice of depth contours;
some depth contour is crossed in any three-hour interval;
chosen contours 500 m, 200 m, 150 m are “conventional”,
should be representative
Analysing only occasions of contour crossing may introduce bias
Estimate from mean l = [(Δx)2+(Δy)2]1/2 in crossings
c.f. mean l for all intervals
Done for daily positions
The bias factor in all cases is between 0.96 and 1.46 (i.e. not large),
typically less at 500 m than at 200 m or 150 m.

5. Bias from initial deployment location
500 m drifter crossings bias (majority to shallower water)
influenced by the initial locations of drifter deployments.
Susceptibility to “events”
Initial off-shelf crossings to deeper Biscay waters 2012 (Celtic Sea)
show the influence of a storm at the time of deployment.
The drifters never really returned to FASTNEt observations area

6. Daily 24-hour-mean positions to filter out most of tidal contribution
Estimates based on 3-hourly positions include tidal displacements.
Semi-diurnal tides reverse every 6.2 hours reducing impact of exchange.
To remove most of tidal contribution,
also used daily 24-hour-mean positions
Exchange ½h|u'| is increased by (partial) inclusion of tidal excursions
in 3-hourly positions
c.f. daily positions
but increase << mooring comparison (l.f. << total currents)

7. Combined with salinity → Atlantic water transport onto the Malin shelf
2013 Malin deployment
Estimate integrated transport 0.2 Sv on to the shelf:
(speed of drifters) × (estimated cross-sectional area with high salinity)*
*from glider transect across shelf (Porter et al. 2018)
0.2 Sv is only O(10%) of typical O(2 Sv) in poleward along-slope current
but is substantial diversion in an along-slope sector O( km)
especially for waters above ~ 150 m depth.

8. Discussion Along-shelf flow >> cross-shelf flow;
mooring estimates uncertain, maybe unrepresentative
Partition between “Flux” and “Exchange” depends on averaging period.
Short-period averaging favours a time-varying flux and small exchange.
Long-period averaging implies a slowly-varying and usually smaller flux
but large exchange as deviations from the longer-term average
We have to assume that drifters follow the water
(not quite true: windage, “stuck” at constant depth)
Drifters also disperse
→ estimates of effective diffusivity:
Porter et al J. Mar. Systems 157, (Biscay)
Porter et al Deep-Sea Research I, 140, (Malin)
Celtic
Malin

9. Conclusions
Useful complement to mooring estimates; sure contour crossing, poor control of location
Large cross-slope exchange estimates across 200 m depth contour:
2.8 m2/s (Faroe-Shetland Channel)
2.3 m2/s (Malin shelf)
2.8 m2/s (Celtic Sea)
from daily positions; comparable with mooring and model estimates.
Comparisons seem to reflect
slope steepness (less at 150 m depth allowing freer cross-contour flow)
strong Biscay tides and eddies in deeper water
meanders of strong slope current in Faroe-Shetland Channel and beyond