Geostrophic Wind Speed

Compute signed east/north geostrophic vector under caller horizontal pressure gradients, density and Coriolis, not true terrain wind or a pressure-force magnitude alias.

Description

Geostrophic wind balances horizontal pressure-gradient acceleration against Coriolis acceleration.

Geostrophic wind balances horizontal pressure-gradient acceleration against Coriolis acceleration. The balance gives a wind perpendicular to the pressure gradient; its direction reverses with the sign of the Coriolis parameter.^[1]

Compute signed east/north geostrophic vector under caller horizontal pressure gradients, density and Coriolis, not true terrain wind or a pressure-force magnitude alias.

When to use Geostrophic Wind Speed

Use this tool to compute signed east/north geostrophic vector under caller horizontal pressure gradients, density and Coriolis, not true terrain wind or a pressure-force magnitude alias.

Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.

How to use Geostrophic Wind Speed and understand its results

Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.
Enter pressureGradientPaPerM, airDensityKgPerM3, coriolisPerSecond using the field table and calculation rules, then run the tool.
Read geostrophicWindComponentsMPerSecond, geostrophicWindSpeedMPerSecond. 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
pressureGradientPaPerM	Pressure gradient Pa per m	list of number	Required
airDensityKgPerM3	Air density kg per m3	number	Required
coriolisPerSecond	Coriolis per second	number	Required

Supply exactly two east–north pressure-gradient components in Pa/m, positive density in kg/m³ and a finite nonzero signed Coriolis parameter in s⁻¹. The tool evaluates the displayed components in m/s and returns their magnitude. The Coriolis sign must match the intended hemisphere and coordinate convention.

u = −(∂p/∂north)/(ρf); v = (∂p/∂east)/(ρf); speed = sqrt(u² + v²)

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

Output field	Meaning	Value type
geostrophicWindComponentsMPerSecond	Geostrophic wind components m per second	list of number
geostrophicWindSpeedMPerSecond	Geostrophic wind speed m per second	number

json

{
  "input": {
    "pressureGradientPaPerM": [
      0.001,
      0.002
    ],
    "airDensityKgPerM3": 1,
    "coriolisPerSecond": 0.0001
  },
  "output": {
    "geostrophicWindComponentsMPerSecond": [
      -20,
      10
    ],
    "geostrophicWindSpeedMPerSecond": 22.360679774997898
  }
}

Limitations and assumptions

This balance approximation omits friction, curvature, acceleration and vertical motion. It becomes unsuitable near the equator where the Coriolis parameter approaches zero. The output is not a terrain-level observed wind or a complete atmospheric flow solution.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value 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 Pressure Gradient Force per Mass: Convert measured three-dimensional Cartesian pressure gradient to signed per-mass acceleration; no Coriolis balance, coordinates or hydrostatic-gravity cancellation inferred. For a complementary task, use Gradient Wind Curvature Correction: Solve continuous geostrophic-limit normal branch of V²/(fR)+V=Vg with signed curvature, rejecting no-real anticyclonic balance; no anomalous branch, surface gusts or safe-flight inference.

References

Geostrophic Wind Speed — tool.io

Similar or alternative tools

Pressure Gradient Force per Mass
Convert measured three-dimensional Cartesian pressure gradient to signed per-mass acceleration; no Coriolis balance, coordinates or hydrostatic-gravity cancellation inferred.
Gradient Wind Curvature Correction
Solve continuous geostrophic-limit normal branch of V²/(fR)+V=Vg with signed curvature, rejecting no-real anticyclonic balance; no anomalous branch, surface gusts or safe-flight inference.