Ekman Pumping Wind Curl

Compute vertical curl of stress/(rho f), including the supplied beta correction for eastward stress; positive is upward and no coordinate-derived Coriolis values are inferred.

Description

Ekman pumping is the curl of stress divided by density and Coriolis.

Ekman pumping is the curl of stress divided by density and Coriolis. Spatial change in Coriolis adds a beta correction.

Compute vertical curl of stress/(rho f), including the supplied beta correction for eastward stress; positive is upward and no coordinate-derived Coriolis values are inferred.

When to use Ekman Pumping Wind Curl

Use this tool to compute vertical curl of stress/(rho f), including the supplied beta correction for eastward stress; positive is upward and no coordinate-derived Coriolis values are inferred.

Gather the water, wave, current or profile observations and any supplied calibration constants. Confirm units and the stated coordinate and pressure conventions.

How to use Ekman Pumping Wind Curl and understand its results

Gather the water, wave, current or profile observations and any supplied calibration constants. Confirm units and the stated coordinate and pressure conventions.
Enter windStressCurlNPerM3, eastwardWindStressNPerM2, signedCoriolisPerSecond, coriolisNorthGradientPerMeterSecond, waterDensityKgPerM3 using the field table and calculation rules, then run the tool.
Read verticalEkmanPumpingMPerSecond. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
windStressCurlNPerM3	Wind stress curl n per m3	number	Required
eastwardWindStressNPerM2	Eastward wind stress n per m2	number	Required
signedCoriolisPerSecond	Signed coriolis per second	number	Required
coriolisNorthGradientPerMeterSecond	Coriolis north gradient per meter second	number	Required
waterDensityKgPerM3	Water density kg per m3	number	Required

Use positive density and nonzero signed f with signed supplied curl, eastward stress and beta. Return m/s, with positive upward and negative downward.^[1]

upward velocity = curl/(ρf) + eastward stress × beta/(ρf²)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
verticalEkmanPumpingMPerSecond	Vertical ekman pumping m per second	number

json

{
  "input": {
    "windStressCurlNPerM3": 0.01,
    "eastwardWindStressNPerM2": 0.1,
    "signedCoriolisPerSecond": 0.01,
    "coriolisNorthGradientPerMeterSecond": 0.001,
    "waterDensityKgPerM3": 1000
  },
  "output": {
    "verticalEkmanPumpingMPerSecond": 0.002
  }
}

Limitations and assumptions

No coordinates, latitude conversion or measured gradients are inferred.

Numbers and computed results must be finite; overflow produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Ekman Offshore Upwelling Index: Project signed Ekman transport onto an explicitly supplied offshore normal and coast length; no shoreline coordinate construction, latitude conversion or Bakun alias. For a complementary task, use Sverdrup Interior Transport: Compute signed Sverdrup interior transport per width and supplied strip transport; assumes steady linear vorticity balance, not a western boundary current or global circulation prediction.

References

Ekman Pumping Wind Curl — tool.io

Similar or alternative tools

Ekman Offshore Upwelling Index
Project signed Ekman transport onto an explicitly supplied offshore normal and coast length; no shoreline coordinate construction, latitude conversion or Bakun alias.
Sverdrup Interior Transport
Compute signed Sverdrup interior transport per width and supplied strip transport; assumes steady linear vorticity balance, not a western boundary current or global circulation prediction.