Upwelling Velocity Calculator

Turn wind stress into a vertical velocity: coastal upwelling in m/day and Sverdrups, or open-ocean Ekman pumping from the wind stress curl.

⬆️ Upwelling Velocity Calculator
Wind stress source
Alongshore wind at 10 m (U10)
m/s
130
Drag coefficient CD
x 10⁻³
Alongshore wind stress (τ)
N/m²
Latitude (negative = south)
deg
-8080
Upwelling zone width (L)
km
5200
Source depth of upwelled water
m
10500
Air density
kg/m³
Seawater density
kg/m³
Curl input
Wind stress curl
x 10⁻⁷ N/m³
-1010
Change in τy (north-south stress)
N/m²
East-west distance for Δτy
km
Change in τx (east-west stress)
N/m²
North-south distance for Δτx
km
Latitude (negative = south)
deg
-8080
Seawater density
kg/m³
Upwelling velocity (w)
—
Velocity in m/s
—
Ekman transport (VE)
—
Wind stress (τ)
—
Coriolis parameter (f)
—
Flux per 100 km of coast
—
Time to rise from depth
—

Ekman pumping (w)
—
Velocity in m/s
—
Vertical displacement
—
Wind stress curl
—
Coriolis parameter (f)
—
Flux per million km²
—
Regime
—

⬆️ What is Upwelling Velocity?

Upwelling velocity is the speed at which water moves vertically toward the sea surface. It is tiny compared with horizontal currents, often only metres per day against metres per second, yet it is one of the most important motions in the ocean because it carries cold, nutrient-rich water into sunlit layers. Two different mechanisms drive it, and this calculator handles both. In coastal upwelling, wind blowing along a coast drives surface water offshore through Ekman transport, and deeper water rises to replace it. In Ekman pumping, the open-ocean wind field has a curl, so the Ekman transport diverges or converges and water is drawn up (Ekman suction) or pushed down (Ekman pumping).

Oceanographers, fisheries scientists and climate students use these numbers in many ways. Coastal upwelling velocity helps explain why the California, Humboldt (Peru and Chile), Canary and Benguela currents support some of the richest fisheries on Earth, and why summer monsoon winds cool the Arabian Sea off Somalia and Oman. Ekman pumping explains why the centres of subtropical gyres sit in a broad region of slow downwelling, which sets the depth of the thermocline, while the subpolar gyres and the equatorial belts show upwelling. Typical values are a few metres per day for the zone-mean coastal case and a few centimetres to a few decimetres per day for open-ocean pumping.

A few distinctions matter. The coastal calculation gives a mean over an upwelling zone of width L, but real upwelling is concentrated within a few kilometres of the shore and is much faster there. The width is also the least certain input: the first baroclinic Rossby radius, often roughly 10 to 50 km at mid latitudes, is a common guide but not a law. In pumping mode the calculator uses the simple form w = curl(τ)/(ρ f). It ignores the beta-term correction, which adds a contribution from the change of f with latitude and matters most at low latitudes, so results near the equator are not reliable. Positive w is upward in both modes.

For the horizontal transport itself, including direction and Sverdrups along a coast, see the related Ekman Transport Calculator. This page is about the vertical velocity that results.

📐 Formula

Coastal: w = τ ÷ (ρw |f| L)    Pumping: wE = curl(τ) ÷ (ρw f)
τ = alongshore wind stress (N/m²) = ρa CD U10², with ρa = 1.225 kg/m³ and CD = 1.3 × 10-3 by default
f = 2 Ω sin(φ), the Coriolis parameter (s-1), with Ω = 7.2921159 × 10-5 rad/s; latitudes within 1° of the equator are rejected
VE = τ ÷ (ρw |f|) = offshore Ekman transport per metre of coast (m²/s), ρw = 1025 kg/m³
L = width of the upwelling zone (m), often taken near the first baroclinic Rossby radius; w = VE ÷ L
Flux = VE × 100 km, in Sverdrups (1 Sv = 106 m³/s); rise time = depth ÷ w
curl(τ) = ∂τy/∂x − ∂τx/∂y (N/m³), x east and y north; positive w is upward
Sign convention: in the Northern Hemisphere (f > 0) a positive (cyclonic) curl gives upwelling, and a negative curl, as over subtropical gyres, gives downwelling. In the Southern Hemisphere f < 0, so the sign of w flips for the same curl.
Example: 8 m/s at 35°N with L = 30 km gives τ = 0.1019 N/m², VE = 1.189 m²/s and w = 3.96 × 10-5 m/s = 3.42 m/day.

The pumping formula ignores the beta term, so it is a first-order estimate. For the coastal mode the wind is assumed to be purely alongshore and upwelling-favourable.

📖 How to Use This Calculator

Steps

1
Choose a mode. Pick Coastal upwelling for a boundary where offshore Ekman transport is replaced from below, or Ekman pumping for the open-ocean response to the wind stress curl.
2
Enter the wind forcing. In coastal mode enter the alongshore wind speed and drag coefficient, or the stress directly. In pumping mode enter the stress curl, or two stress differences with the distances over which they occur.
3
Set latitude, width and depth. Enter the latitude (negative for the Southern Hemisphere), plus the upwelling zone width and the source depth in coastal mode.
4
Read the vertical velocity. Review w in m/day and m/s, the Sverdrup flux or yearly displacement, the time to rise, and the marked point on the chart.

💡 Example Calculations

Example 1 — California Coast in Summer

10 m/s equatorward wind at 37°N, constant CD = 1.3e-3, zone width 25 km, source depth 100 m

1
Wind stress: τ = 1.225 × 0.0013 × 10² = 0.1592 N/m²
2
Coriolis parameter: f = 2 Ω sin 37° = 0.8777 × 10-4 s-1
3
VE = 0.1592 / (1025 × 0.8777e-4) = 1.770 m²/s, and w = 1.770 / 25,000 = 7.08 × 10-5 m/s = 6.12 m/day
4
Flux per 100 km: 0.1770 Sv. Rise time from 100 m: 100 / 6.12 = 16.3 days
w = 6.12 m/day, flux = 0.1770 Sv per 100 km, rise time = 16.3 days
Try this example →

Example 2 — Peru and Humboldt Upwelling

6 m/s equatorward wind at 12°S, constant CD = 1.3e-3, zone width 40 km, source depth 80 m

1
Wind stress: τ = 1.225 × 0.0013 × 6² = 0.0573 N/m²
2
f = 2 Ω sin(-12°) = -0.3032 × 10-4 s-1. Only |f| enters the transport, so the sign does not change the magnitude.
3
VE = 1.845 m²/s, so w = 1.845 / 40,000 = 4.61 × 10-5 m/s = 3.98 m/day. A weak wind still lifts a lot of water because f is small at 12°.
4
Flux per 100 km: 0.1845 Sv. Rise time from 80 m: 80 / 3.98 = 20.1 days
w = 3.98 m/day, flux = 0.1845 Sv per 100 km, rise time = 20.1 days
Try this example →

Example 3 — Arabian Sea Summer Monsoon

Alongshore stress entered directly as 0.3 N/m² at 10°N, zone width 200 km, source depth 150 m

1
Stress is given directly: τ = 0.3 N/m², so no drag coefficient is needed
2
f = 2 Ω sin 10° = 0.2533 × 10-4 s-1
3
VE = 0.3 / (1025 × 0.2533e-4) = 11.557 m²/s, so w = 11.557 / 200,000 = 5.78 × 10-5 m/s = 4.99 m/day
4
Flux per 100 km: 1.1557 Sv. Rise time from 150 m: 150 / 4.99 = 30.0 days
w = 4.99 m/day, flux = 1.1557 Sv per 100 km, rise time = 30.0 days
Try this example →

Example 4 — Subtropical Gyre Ekman Pumping

Westerlies at 40°N (τx = +0.10) and trades at 20°N (τx = -0.05 N/m²) over 2200 km, evaluated at 30°N

1
Stress differences: Δτx = 0.10 − (−0.05) = 0.15 N/m² over 2200 km north-south, and Δτy = 0
2
Curl = 0 − 0.15 / 2,200,000 m = -6.82 × 10-8 N/m³ (negative, anticyclonic)
3
f = 2 Ω sin 30° = 0.7292 × 10-4 s-1, so w = -6.82e-8 / (1025 × 0.7292e-4) = -9.12 × 10-7 m/s
4
In practical units: -0.0788 m/day, or -28.8 m/year (downward). Over one million km² this is -0.91 Sv.
w = -0.0788 m/day (-28.8 m/year), Ekman pumping (downwelling)
Try this example →

❓ Frequently Asked Questions

How do you calculate upwelling velocity from wind?+
Find the wind stress tau = rho_air Cd U10^2, divide by rho_w and |f| to get the offshore Ekman transport V = tau/(rho_w |f|) in m2/s, then divide by the upwelling zone width L. For 8 m/s at 35 degrees and L = 30 km this gives w = 3.96e-5 m/s, about 3.4 m/day.
What is a typical coastal upwelling velocity?+
Mean vertical velocities in coastal upwelling zones are commonly a few metres per day, with peaks of 10 to 20 m/day or more near the coast. The value depends on wind stress, latitude and how wide the upwelling zone is assumed to be.
What is Ekman pumping and how is it calculated?+
Ekman pumping is the vertical velocity at the base of the surface layer caused by divergence or convergence of wind-driven Ekman transport. It equals the wind stress curl divided by rho and f: w = curl(tau)/(rho f). Positive w is upward.
What is the difference between Ekman pumping and coastal upwelling?+
Coastal upwelling comes from offshore Ekman transport at a boundary that blocks the flow, concentrated within tens of kilometres of the coast. Ekman pumping comes from the curl of the wind stress over the open ocean, spread over thousands of kilometres and much slower.
Why does the sign of Ekman pumping differ between hemispheres?+
Because w = curl(tau)/(rho f) and f changes sign at the equator. In the Northern Hemisphere a positive, counterclockwise (cyclonic) curl gives upwelling. In the Southern Hemisphere f is negative, so the clockwise (cyclonic) negative curl gives upwelling.
Why is the subtropical gyre downwelling?+
Westerlies at about 40 degrees and trade winds at about 20 degrees give a negative stress curl over the subtropical gyres. With f positive in the north this gives negative w, so surface water converges and is pumped downward at roughly 0.05 to 0.1 m/day, or 20 to 40 m/year.
What width should I use for the upwelling zone?+
A common choice is the first baroclinic Rossby radius of deformation, roughly 10 to 50 km at mid latitudes depending on stratification. Observed upwelling zones range from a few kilometres to a few hundred kilometres, so try several values.
How long does it take water to rise from 100 m?+
Divide the depth by the vertical velocity. At w = 3.4 m/day the trip from 100 m takes about 29 days. Real water parcels also move alongshore and offshore, so this is a simple vertical-only time scale.
How much water does coastal upwelling lift in Sverdrups?+
The upwelled volume flux equals the offshore Ekman transport times the coast length. At V = 1.19 m2/s, each 100 km of coast lifts 1.19e5 m3/s, or 0.119 Sv. A 1000 km coast would lift about 1.2 Sv.
Why is the equator excluded?+
At the equator f is zero, so tau/f becomes infinite and the Ekman balance fails. The calculator rejects any latitude within 1 degree of the equator, and the open-ocean values are most reliable poleward of about 10 degrees.
What does this calculator ignore?+
It ignores the beta-term correction to Ekman pumping, geostrophic and pressure-gradient contributions, stratification, coastal geometry and the real offshore profile of upwelling. All results are first-order estimates for teaching and planning, not model output.
Tags: Upwelling Velocity Calculator Coastal Upwelling Velocity Ekman Pumping Calculator Wind Stress Curl Vertical Velocity Ocean Ekman Suction Upwelling Rate Calculator Formula Free

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How do you calculate upwelling velocity from wind?

Find the wind stress tau = rho_air Cd U10^2, divide by rho_w and |f| to get the offshore Ekman transport V = tau/(rho_w |f|) in m2/s, then divide by the upwelling zone width L. For 8 m/s at 35 degrees and L = 30 km this gives w = 3.96e-5 m/s, about 3.4 m/day.

What is a typical coastal upwelling velocity?

Mean vertical velocities in coastal upwelling zones are commonly a few metres per day, with peaks of 10 to 20 m/day or more near the coast. The value depends on wind stress, latitude and how wide the upwelling zone is assumed to be.

What is Ekman pumping and how is it calculated?

Ekman pumping is the vertical velocity at the base of the surface layer caused by divergence or convergence of wind-driven Ekman transport. It equals the wind stress curl divided by rho and f: w = curl(tau)/(rho f). Positive w is upward.

What is the difference between Ekman pumping and coastal upwelling?

Coastal upwelling comes from offshore Ekman transport at a boundary that blocks the flow, concentrated within tens of kilometres of the coast. Ekman pumping comes from the curl of the wind stress over the open ocean, spread over thousands of kilometres and much slower.

Why does the sign of Ekman pumping differ between hemispheres?

Because w = curl(tau)/(rho f) and f changes sign at the equator. In the Northern Hemisphere a positive, counterclockwise (cyclonic) curl gives upwelling. In the Southern Hemisphere f is negative, so the clockwise (cyclonic) negative curl gives upwelling.

Why is the subtropical gyre downwelling?

Westerlies at about 40 degrees and trade winds at about 20 degrees give a negative stress curl over the subtropical gyres. With f positive in the north this gives negative w, so surface water converges and is pumped downward at roughly 0.05 to 0.1 m/day, or 20 to 40 m/year.

What width should I use for the upwelling zone?

A common choice is the first baroclinic Rossby radius of deformation, roughly 10 to 50 km at mid latitudes depending on stratification. Observed upwelling zones range from a few kilometres to a few hundred kilometres, so try several values.

How long does it take water to rise from 100 m?

Divide the depth by the vertical velocity. At w = 3.4 m/day the trip from 100 m takes about 29 days. Real water parcels also move alongshore and offshore, so this is a simple vertical-only time scale.

How much water does coastal upwelling lift in Sverdrups?

The upwelled volume flux equals the offshore Ekman transport times the coast length. At V = 1.19 m2/s, each 100 km of coast lifts 1.19e5 m3/s, or 0.119 Sv. A 1000 km coast would lift about 1.2 Sv.

Why is the equator excluded?

At the equator f is zero, so tau/f becomes infinite and the Ekman balance fails. The calculator rejects any latitude within 1 degree of the equator, and the open-ocean values are most reliable poleward of about 10 degrees.

What does this calculator ignore?

It ignores the beta-term correction to Ekman pumping, geostrophic and pressure-gradient contributions, stratification, coastal geometry and the real offshore profile of upwelling. All results are first-order estimates for teaching and planning, not model output.

📌 Quick Tips

💡Coastal upwelling velocity depends strongly on the width you assume. Halving the upwelling zone from 30 km to 15 km doubles the mean w, so quote the width next to any velocity.
💡The first baroclinic Rossby radius, often roughly 10 to 50 km at mid latitudes and smaller at high latitudes, is a common width scale for the upwelling zone. Treat it as a guide, not a fixed law.
💡Wind stress grows with the square of wind speed, so a 10 m/s alongshore wind drives about 56 percent more upwelling than an 8 m/s wind at the same latitude.
💡Ekman pumping is tiny compared with coastal upwelling, typically 0.01 to 0.2 m/day, but it acts over millions of square kilometres and sets the depth of the thermocline.
💡The calculator ignores the beta-term correction for Ekman pumping. This matters close to the equator, so keep latitudes above roughly 10 degrees for reliable open-ocean values.