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.

Description

Offshore upwelling indices project Ekman transport onto a coastline normal.

Offshore upwelling indices project Ekman transport onto a coastline normal. That normal defines what positive offshore means.

Project signed Ekman transport onto an explicitly supplied offshore normal and coast length; no shoreline coordinate construction, latitude conversion or Bakun alias.

When to use Ekman Offshore Upwelling Index

Use this tool to project signed Ekman transport onto an explicitly supplied offshore normal and coast length; no shoreline coordinate construction, latitude conversion or Bakun alias.

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 Offshore Upwelling Index 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 eastwardWindStressNPerM2, northwardWindStressNPerM2, offshoreUnitNormal, waterDensityKgPerM3, signedCoriolisPerSecond, coastLengthM using the field table and calculation rules, then run the tool.
Read signedOffshoreEkmanTransportM2PerSecond, coastIntegratedOffshoreTransportM3PerSecond. 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
eastwardWindStressNPerM2	Eastward wind stress n per m2	number	Required
northwardWindStressNPerM2	Northward wind stress n per m2	number	Required
offshoreUnitNormal	Offshore unit normal	list of number	Required
waterDensityKgPerM3	Water density kg per m3	number	Required
signedCoriolisPerSecond	Signed coriolis per second	number	Required
coastLengthM	Coast length m	number	Required

Use positive density, nonzero signed f and a two-component unit normal within 1e−10 norm tolerance. Multiply signed transport per width by nonnegative coast length for integrated m³/s.^[1]

offshore transport = (north stress × east normal − east stress × north normal)/(ρf)

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

Output field	Meaning	Value type
signedOffshoreEkmanTransportM2PerSecond	Signed offshore ekman transport m2 per second	number
coastIntegratedOffshoreTransportM3PerSecond	Coast integrated offshore transport m3 per second	number

json

{
  "input": {
    "eastwardWindStressNPerM2": 1,
    "northwardWindStressNPerM2": 2,
    "offshoreUnitNormal": [
      1,
      0
    ],
    "waterDensityKgPerM3": 1000,
    "signedCoriolisPerSecond": 0.01,
    "coastLengthM": 10
  },
  "output": {
    "signedOffshoreEkmanTransportM2PerSecond": 0.2,
    "coastIntegratedOffshoreTransportM3PerSecond": 2
  }
}

Limitations and assumptions

No coastline geometry or latitude-derived Coriolis is constructed.

Numbers and computed results must be finite; overflow produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use 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. For a complementary task, use Ekman Spiral Surface Deflection Angle: Calculate a constant-viscosity steady Ekman current vector at depth, including hemisphere-dependent rotation and exponential decay; not a universal observed 45-degree surface rule.

References

Ekman Offshore Upwelling Index — tool.io

Similar or alternative tools

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.
Ekman Spiral Surface Deflection Angle
Calculate a constant-viscosity steady Ekman current vector at depth, including hemisphere-dependent rotation and exponential decay; not a universal observed 45-degree surface rule.