Ekman Transport Calculator
Find the wind-driven Ekman transport per metre of width, its direction and the total volume moved along a coast, with the upwelling or downwelling it causes.
🧭 What is Ekman Transport?
Ekman transport is the net movement of water in the upper ocean that is driven by the wind and turned by the rotation of the Earth. When wind blows over the sea it drags the surface along by friction. Because the Earth rotates, each layer of water is deflected by the Coriolis force, and each layer drags the one below it, so the current turns with depth in the famous Ekman spiral. Added up over the whole wind-driven layer, the water flows at exactly 90 degrees to the wind: to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. The idea was worked out by Vagn Walfrid Ekman in 1905 after Fridtjof Nansen noticed that Arctic ice drifted to the right of the wind.
The size of the transport is set by only three things: the wind stress, the Coriolis parameter and the water density. This calculator finds the wind stress from the wind speed at 10 m, then returns the mass transport in kilograms per metre of width per second and the volume transport in cubic metres per second per metre of width. Oceanographers use it to estimate how much surface water the wind pushes toward or away from a coast, to explain the cold, productive water of the California, Peru, Benguela and Canary upwelling systems, to interpret upwelling indices from fisheries agencies, and to size the wind-driven part of ocean circulation in textbook exercises.
Two common misconceptions are worth clearing up. First, the surface current is not at 90 degrees to the wind; it is only about 45 degrees from it, and the full 90 degrees applies to the depth-integrated flow. Second, the transport does not depend on the viscosity or the thickness of the Ekman layer, because those factors cancel when the stress is integrated over depth. Also keep in mind that the formula is not valid at the equator, where the Coriolis parameter vanishes, and that it describes only the steady, open-ocean balance. Near a real coast, tides, pressure gradients and eddies all modify the response.
This calculator also adds a practical coastal layer. You can choose a coastline length to convert the transport into Sverdrups (1 Sv = 1,000,000 m³/s), choose whether the ocean lies west or east of the coast, and select an equatorward or poleward alongshore wind to see at once whether the result is coastal upwelling or downwelling. Ekman pumping, the vertical velocity set by the curl of the wind, is a separate topic and is not computed here.
📐 Formula
Direction rule: the transport vector points at +90° (clockwise) from the wind where f > 0 and at -90° where f < 0. For coastal upwelling, only the component of the wind stress parallel to the coast matters, so the calculator assumes a purely alongshore wind.
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — California Coast Upwelling
8 m/s equatorward wind at 35°N, ocean to the west, 1000 km of coast, constant CD = 1.3e-3
Example 2 — Trade Winds at 20°N
7 m/s equatorward wind at 20°N, ocean to the west, 500 km of coast, constant CD = 1.3e-3
Example 3 — Strong Storm at 55°N
25 m/s wind at 55°N, Large and Pond CD, 300 km of coast, equatorward wind, ocean to the west
Example 4 — Southern Hemisphere Westerlies at 45°S
12 m/s poleward wind at 45°S, Large and Pond CD, ocean to the west, 800 km of coast
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate Ekman transport from wind speed?
First find the wind stress tau = rho_air Cd U10^2 with rho_air = 1.225 kg/m3 and Cd about 1.3e-3. Then divide by the Coriolis parameter f = 2 Omega sin(latitude). Mass transport is M = tau/|f| in kg per metre per second and volume transport is V = M/rho_w in m2/s.
In which direction does Ekman transport flow?
The net transport of the wind-driven layer points 90 degrees to the right of the wind in the Northern Hemisphere and 90 degrees to the left in the Southern Hemisphere. This is a depth-integrated result, not the direction of the surface current, which is only about 45 degrees from the wind.
What is a typical Ekman transport value?
At 35 degrees latitude, an 8 m/s wind with Cd = 1.3e-3 gives a wind stress of 0.102 N/m2 and a volume transport of about 1.19 m2/s, or roughly 1,190 cubic metres per second for every kilometre of coast.
What is a Sverdrup and why use it for Ekman transport?
One Sverdrup (Sv) equals 1 million cubic metres per second. Multiplying the transport per metre by a coastline length gives a total flow, and for long coasts it lands in the range of fractions of a Sverdrup to a few Sverdrups, easy to compare with ocean currents.
How does Ekman transport cause coastal upwelling?
When the wind blows along a coast so that the Ekman transport points away from the shore, surface water leaves and colder, nutrient-rich water rises from below to replace it. In the Northern Hemisphere that needs a wind with the coast on its left, for example a southward wind off California.
Why is the equator excluded from the calculation?
At the equator the Coriolis parameter f is zero, so tau/f becomes infinite and the Ekman balance breaks down. The calculator requires an absolute latitude of at least 1 degree. Near the equator the transport result should be treated as an upper bound only.
What drag coefficient should I use?
A constant Cd of about 1.3e-3 is a good default for moderate winds. The Large and Pond (1981) formula uses 1.2e-3 below 11 m/s and (0.49 + 0.065 U10)e-3 above that, which reaches about 2.1e-3 at 25 m/s. The calculator offers both options.
What is the Ekman upwelling index?
The coastal upwelling index of Bakun (1973) is the offshore Ekman transport per unit length of coast, computed from the alongshore wind stress. Positive values mean upwelling. It is commonly quoted in m3/s per 100 m of coastline, which equals 100 times the value of V in m2/s.
Is Ekman transport the same as Ekman pumping?
No. Ekman transport is the horizontal volume flux driven by the wind stress. Ekman pumping is the vertical velocity caused by the curl of that stress or by horizontal divergence of the transport. This calculator covers transport only.
What are the main assumptions behind Ekman transport?
The theory assumes a steady wind, a balance between the Coriolis force and friction in the upper layer, no horizontal pressure gradients and a deep ocean. Real coasts, tides and eddies alter the flow, so the result is a first estimate.
Does transport depend on the Ekman layer depth or viscosity?
No. The depth-integrated Ekman transport depends only on the wind stress, the Coriolis parameter and the density. Viscosity and the layer depth set the spiral shape and the thickness of the layer but cancel out of the total transport.