Formula used
How to use this calculator
- Enter wind stress components τx and τy in N/m².
- Provide seawater density ρ (kg/m³) and latitude magnitude (degrees).
- Select the hemisphere to set the sign of f.
- Optionally enter coastline length L to estimate volume transport.
- Press Calculate. Download CSV/PDF using the buttons in the results box.
Example data
| τx (N/m²) | τy (N/m²) | ρ (kg/m³) | Latitude | Hemisphere | L (m) | Expected |M| (m²/s) |
|---|---|---|---|---|---|---|
| 0.10 | 0.00 | 1025 | 30° | NH | 100000 | ~1.30 |
| 0.05 | 0.05 | 1027 | 45° | NH | 50000 | ~0.67 |
| 0.12 | -0.03 | 1024 | 20° | SH | 200000 | ~2.04 |
Professional notes on Ekman transport
1) What the calculator returns
This tool computes the depth-integrated Ekman transport per unit width, expressed in m²/s. It combines the wind stress vector (τx, τy), seawater density ρ, and the Coriolis parameter f. The outputs include components (Mx, My), magnitude |M|, and directions for both τ and M.
2) Typical wind stress ranges
Over the open ocean, daily wind stress commonly spans about 0.02–0.20 N/m², with stronger values in storms. Because |M| scales linearly with |τ|, doubling τ doubles the transport. For quick checks, τ = 0.10 N/m² often produces order‑one m²/s transport outside the tropics.
3) Latitude control through f
The Coriolis parameter f = 2Ω sin(φ) increases with latitude magnitude. For Earth, |f| is about 7.3×10⁻⁵ s⁻¹ at 30° and about 1.0×10⁻⁴ s⁻¹ at 45°. Smaller |f| yields larger transport for the same τ, which is why equatorial results are unstable.
4) Direction and the 90° relationship
In the ideal steady, homogeneous Ekman model, M is perpendicular to τ. The sign of f sets whether the transport is rotated to the right (Northern Hemisphere) or to the left (Southern Hemisphere). The calculator reports the relative angle between M and τ to help confirm the expected quadrant behavior.
5) Linking transport to coastal upwelling
Coastal upwelling potential is often inferred from the component of M directed offshore. When alongshore winds create an offshore Ekman transport, surface water is replaced by deeper, colder, nutrient‑rich water. Use the direction diagnostics to project M onto an “offshore” axis that matches your coastline orientation.
6) From m²/s to Sverdrups
The optional coastline length L converts |M| into a volume transport Q = |M|·L (m³/s). Reporting Q in Sverdrups is common for regional budgets: 1 Sv = 10⁶ m³/s. For example, |M| = 1.3 m²/s across L = 100 km gives Q ≈ 0.13 Sv.
7) Sensitivity and uncertainty
Results are most sensitive to τ and f. Wind stress depends on drag formulations, stability, and measurement height. Density varies with temperature and salinity, but typical ρ changes only slightly affect M. Consider using a range of τ values (e.g., ±20%) to bracket expected transport.
8) Model limits in real oceans
The classical Ekman solution assumes steady forcing, constant eddy viscosity, and negligible stratification effects on the depth integral. In practice, time variability, fronts, sea ice, and shallow shelves can modify transport. Treat this calculator as a first‑order diagnostic, then compare with observations or numerical model output.
FAQs
1) What is “transport per unit width”?
It is the depth‑integrated horizontal flow divided by the width of the current band. The unit m²/s can be multiplied by a coastline length to estimate a volume rate in m³/s.
2) Why does the calculator need hemisphere?
Hemisphere determines the sign of f, which sets whether the Ekman transport is rotated right or left of the wind stress. The magnitude depends on |f|, but the direction depends on the sign.
3) Why are equatorial results rejected?
Near the equator, f approaches zero, so the ideal formula predicts unrealistically large transport. Real dynamics there involve different balances and wave responses, so a simple Ekman estimate is not reliable.
4) How do I choose τx and τy?
Use wind stress from a reanalysis product, buoy estimates, or compute it from wind speed using a drag coefficient. Ensure your axes match the calculator: +x eastward and +y northward.
5) What density should I use?
A common default is 1025 kg/m³ for seawater. If you have local temperature and salinity, using 1020–1030 kg/m³ is usually sufficient for transport estimates.
6) Does this give Ekman layer depth?
No. This calculator returns the depth‑integrated transport. Ekman depth depends on vertical mixing and can vary widely; estimating it requires an eddy viscosity or turbulent scaling.
7) How do I estimate offshore transport for upwelling?
Compute M, then project its vector onto the direction normal to the coastline. That normal component is the offshore transport per unit width; multiply by coastline length to obtain a volume estimate.