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 jmh@noc.ac.uk FASTNEt – Fluxes across sloping topography of the North East Atlantic – project deployments 2012 Bay of Biscay. Colour denotes date Faroe-Shetland Channel 2014. 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.

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

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.

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.

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

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)

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(80-100 km) especially for waters above ~ 150 m depth.

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. 2016. J. Mar. Systems 157, 65-74. (Biscay) Porter et al. 2018. Deep-Sea Research I, 140, 173-185. (Malin) Celtic Malin

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