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Upwelling Index Calculator

Calculate coastal upwelling index from wind stress, latitude, and water density using Ekman transport theory.

About this calculator

This calculator applies the Ekman transport model oceanographers use to explain coastal upwelling -- the process by which nutrient-rich deep water rises to the surface along eastern boundary coastlines such as California, Peru, and northwest Africa. Wind Stress drags the surface layer, and Earth's rotation (through the Coriolis effect) deflects that wind-driven flow 90° to the wind, pushing surface water offshore and drawing colder water up from below to replace it -- this is Ekman Transport. Upwelling Index simply rescales Ekman Transport to a standard coastline length (per 100 meters) so results from different scenarios are directly comparable.

Because both Wind Stress and Latitude are restricted here to positive, upwelling-favorable values (this calculator's Latitude range is 5° to 70°, deliberately excluding the equator where the Coriolis effect vanishes and the Ekman framework breaks down), Direction will always read "Upwelling" rather than "Downwelling" -- this calculator does not model poleward, downwelling-favorable alongshore winds. Ekman Pumping Velocity estimates the vertical rise speed over a fixed 10 km offshore length scale rather than one measured for a real coastline, and Ekman Layer Depth uses a fixed representative eddy viscosity rather than a site-specific value, so both should be read as order-of-magnitude estimates rather than precise local forecasts.

Inputs

Pa
°
kg/m³

Results

Upwelling Index

116.63 m³/s/100m

Ekman Transport1.17 m³/s/m
Ekman Pumping Velocity10.08 m/day
Ekman Layer Depth48.6 m
Upwelling StrengthStrong
DirectionUpwelling
How to Use This Calculator
  1. Enter Wind Stress, Latitude, and Water Density.
  2. Review the Upwelling Index (m³/s/100m) result.
  3. Use Ekman Transport (m³/s/m) and Ekman Pumping Velocity (m/day) to inform your decision.

How the result changes with Water Density

Water DensityUpwelling Index
1,022116.97 m³/s/100m
1,025116.63 m³/s/100m
1,030116.06 m³/s/100m
1,034115.61 m³/s/100m

What each input means

Wind Stress
Alongshore wind stress in Pascals. Typical values range from 0.01 (light) to 0.5 (strong) Pa.
Latitude
Geographic latitude in degrees. Must be non-zero; Coriolis effect vanishes at the equator.
Water Density
Seawater density in kg/m³. Typical surface ocean values are 1024-1028 kg/m³.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    Wind Stress = 0.1, Latitude = 35, Water Density = 1025 = 3 input(s) provided
  2. Calculate Upwelling Index
    Upwelling Index
    116.63 = 116.63
  3. Calculate Ekman Transport
    Ekman Transport
    1.1663 = 1.1663
  4. Calculate Ekman Pumping Velocity
    Ekman Pumping Velocity
    10.077 = 10.077

Engine last updated . Checked against 4 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

Why does Direction always read "Upwelling" and never "Downwelling"?

Both inputs this calculator accepts are restricted to physically upwelling-favorable values -- Wind Stress only accepts positive alongshore stress, and Latitude only accepts 5° to 70° in a convention where the resulting Ekman transport always points offshore. The underlying math for downwelling exists inside the formula, but this calculator's input ranges never reach it, so every combination of allowed inputs produces a positive Upwelling Index and the "Upwelling" label.

What input moves the Upwelling Index result the most?

Wind Stress, by the widest margin among the three inputs -- across its full 0.001 to 1 Pa range it swings Upwelling Index roughly a thousandfold, more than Latitude's roughly tenfold swing across 5° to 70° and far more than Water Density's sub-2% influence across its realistic seawater range. Stronger alongshore wind is the dominant driver of how much water gets pushed offshore.

Why does Upwelling Index fall as Latitude increases toward 70°?

The Coriolis Parameter grows with sin(latitude), and Ekman Transport is inversely proportional to it, so the same Wind Stress produces progressively weaker offshore transport at higher latitudes, where Earth's rotation more strongly deflects the flow. This is part of why classic upwelling systems like the California and Peru currents sit in the mid-latitude range this calculator covers, rather than near the poles.

Do Wind Stress and Water Density affect the Ekman Layer Depth output?

No -- Ekman Layer Depth depends only on Latitude, through the Coriolis Parameter, and a fixed representative eddy viscosity value. Wind Stress and Water Density both move Upwelling Index and Ekman Transport, but they leave Ekman Layer Depth completely unchanged in this calculator's formula.

How should I interpret the Upwelling Strength label?

Strength is a simple magnitude bucket applied to Upwelling Index -- None below 10, Weak from 10 to 50, Moderate from 50 to 100, Strong from 100 to 200, and Very Strong at 200 or above, all in m³/s per 100 m of coastline. These thresholds are a convenience scale built into this calculator rather than a formal oceanographic standard, so use them to compare scenarios relative to each other rather than as an official classification.

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