Upper ocean currents, Coriolis force, and Ekman Transport Walfrid Ekman Gaspard-Gustave de Coriolis A theme running through the previous topic in vertical structure of the ocean was that the key to high biological productivity is the upwelling of new nutrients from deep waters into the euphotic zone by mixing, and that stratification acts to retain phytoplankton in the well-lighted mixed layer allowing phytoplankton to grow. Vertical mixing by convection (during the preceding winter, the fall transition, or episodic events) brings new nutrients upward where they can be transiently utilized by phytoplankton. In this next theme we consider regions where wind-induced horizontal currents lead to vertical upwelling of water that brings new nutrients into the surface waters. This can proceed almost continuously providing a steady supply of new nutrients and leading to sustained primary production over an entire season, or longer.

Upper ocean currents, Coriolis force, and Ekman Transport In the open ocean mixed layer: vertical structure was the key to biological productivity mixing, light, stratification, critical depth In coastal regions and the equator, wind-driven horizontal currents can cause upwelling of water with high nutrients leading to sustained production over a season, or longer Wind stress + Coriolis force give… Ekman currents and upwelling Seasonal input of new nutrients from winter convection A theme running through the previous topic in vertical structure of the ocean was that the key to high biological productivity is the upwelling of new nutrients from deep waters into the euphotic zone by mixing, and that stratification acts to retain phytoplankton in the well-lighted mixed layer allowing phytoplankton to grow. Vertical mixing by convection (during the preceding winter, the fall transition, or episodic events) brings new nutrients upward where they can be transiently utilized by phytoplankton. In this next theme we consider regions where wind-induced horizontal currents lead to vertical upwelling of water that brings new nutrients into the surface waters. This can proceed almost continuously providing a steady supply of new nutrients and leading to sustained primary production over an entire season, or longer. Sustained (or frequent) input of new nutrients

In the coastal ocean, variability in the currents arises through several different physical processes. Almost all of the processes depicted in this sketch occur on timescales greater than a day, and as a result the rotation of the Earth plays a role in the dynamics of the ocean currents. Time scales greater than a day introduce earth’s rotation in the dynamics – Coriolis force

From Lalli and Parson, “Biological Oceanography”

Some physics…

Coriolis force: In a fixed frame of reference the ball travels in a straight line (Newton’s laws) In a rotating frame of reference (on the table, or Earth), the ball appears to turn. In the example, the merry-go-round is turning clockwise and the ball turns toward the left. This is the Southern Hemisphere effect. In the Northern Hemisphere the local rotation is counter-clockwise, and Coriolis force deflects motion to the right. N S https://marine.rutgers.edu/dmcs/ms320/movies/coriolis-qt.mov

Figure 9.1 Inertial currents in the North Pacific in October 1987 (days 275-300) measured by holey-sock drifting buoys drogued at a depth of 15 meters. Positions were observed 10-12 times per day by the Argos system on NOAA polar-orbiting weather satellites and interpolated to positions every three hours. The largest currents were generated by a storm on day 277. Note: these are not individual eddies. The entire surface is rotating. A drogue placed anywhere in the region would have the same circular motion. From van Meurs (1998).

In the Northern hemisphere … Earth’s rotation is counter clockwise … direction of flow Coriolis force and Coriolis force is to the right … of the direction of movement In the absence of any other forces, Coriolis drives clockwise (NH) rotating inertial oscillations In the absence of any other forces, Coriolis drives clockwise (NH) rotating inertial oscillations

Suppose a balance of forces between wind stress and Coriolis Coriolis force is to right of the direction of movement So direction of movement is to the right of the wind (in the northern hemisphere) Wind force Coriolis force Current Current Current Wind force Current Wind force Wind force

Wind force Current

DE

V0 is 45° to the right of the wind (in the northern hemisphere) DE V0 is 45° to the right of the wind (in the northern hemisphere) V0 decreases exponentially with depth as it turns clockwise (NH) At depth z = -DE the flow speed falls to e-π = 0.04 times the surface current and is in the opposite direction (typical DE is 20 to 40 m)

Eastern Boundary Current program Progressive vector diagram Eastern Boundary Current program Progressive vector diagram. Apr-Oct 1993 water wind Progressive vector diagram, using daily averaged currents relative to the flow at 48 m, at a subset of depths from a moored ADCP at 37.1°N, 127.6°W in the California Current, deployed as part of the Eastern Boundary Currents experiment. Daily averaged wind vectors are plotted at midnight UT along the 8-m relative to 48-m displacement curve. Wind velocity scale is shown at bottom left. (From: Chereskin, T. K., 1995: Evidence for an Ekman balance in the California Current. J. Geophys. Res., 100, 12727-12748.)

Wind-driven currents and upwelling On timescales longer than a few days: Earth’s rotation introduces Coriolis force flow turns to the right (northern hemisphere) or left (southern hemisphere) wind stress balances Coriolis force = Ekman transport Oceanographer’s rule: Ekman transport is toward the right of the wind stress (in northern hemisphere) Adjacent to a coast… Alongshore wind produces Ekman transport across-shore … causes upwelling or downwelling of a few meters per day

Equator-ward winds on ocean eastern boundaries Pole-ward wind on ocean western boundaries Pole-ward winds on ocean eastern boundaries Equator-ward wind on ocean western boundaries

Current Wind force http://marine.rutgers.edu/cool/research/upwelling.html

The magnitude of the Ekman transport is m2 s-1 τ = wind stress (Pascals or N m-2) = water density (1027 kg m-3) f = Coriolis parameter = 2 Ω sin φ Ω = 2π/(24 hours) = 2 x Earth rotation rate x sin(latitude) A balance between wind forcing and Coriolis force leads to Ekman currents. The Ekman transport is given by the equation M=T/rho.f where f is the local Coriolis parameter Why does Coriolis parameter f vary with latitude? Consequences: At LOW latitudes (nearer to the equator) f is smaller so the same wind stress produces stronger upwelling (the Ekman physics works up to within about 2 degree latitude of the equator – any closer and we need a more complicated dynamical theory that involves other aspects of the momentum conservation law. ME can be though of as an average horizontal velocity times a depth of the Ekman layer. Typical transports are 0.1 Pa / 1000 /1e-4 = 1 m2s-1 For a Ekman layer depth of about 20 meters this means an average velocity of about 5 cm/s or about 4.3 km/day

Estimating the upwelling velocity from NJ coast data Wind data show southerly of 6 m s-1 over a few days To balance mass transport in a 2-dimensional (across-shelf/vertical) process, the average upwelling velocity (w) times the width of the upwelling zone must balance the Ekman transport. Over 1 day (86400 sec) this is 4.32 m day-1

Depth (z)

uE Depth (z) Depth (z)

m2 s-1 Notice how this changes with f (i.e. latitude) when the wind stress stays the same uE Depth (z) The Ekman transport can be thought of as some average velocity acting over a layer. At lower latitudes the Ekman transport becomes larger, yet the Ekman depth also becomes larger. What about the average Ekman current? Ue becomes larger at LOW latitudes because its inversely proportional to the square root of f Northwest Africa values: Typical τ = 0.1 Pa f = 5x10-5 at 20N typical DE ~ 30 m uE ~ 0.1 / 1027 / 5x10-5 / 30 = 6.5 cm s-1

Wind speed m s-1 Wind speed and along-shelf currents at various depths along the continental shelf off northwest Africa

Strong wind toward south Weak or no wind Strong wind toward south Weak or no wind

typical τ = 0.1 Pa 50/8 = 6.25 km day-1 f = 5x10-5 at 20N, DE ~ 30 m Why do we care about the speed: Consider upwelling events – the speed at which water moves offshore will be related to the Ekman current. Once transported away from the upwelling region, the supply of nutrients ceases. So the primary production that results will have to be sustained with the transient input of nutrient, not from a continuous source. This has consequences for successions of trophic levels, nutrient recycling, and export. typical τ = 0.1 Pa f = 5x10-5 at 20N, DE ~ 30 m 50/8 = 6.25 km day-1 = 5.6 km/day

Wind-driven currents and upwelling On timescales longer than a few days: Earth’s rotation introduces Coriolis force flow turns to the right (northern hemisphere) or left (southern hemisphere) wind stress balances Coriolis force = Ekman transport Oceanographer’s rule: Ekman transport is toward the right of the wind stress (in northern hemisphere) Adjacent to a coast… Alongshore wind produces Ekman transport across-shore … causes upwelling or downwelling of a few meters per day