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.

Description

Gradient wind balances pressure-gradient, Coriolis and curvature effects.

Gradient wind balances pressure-gradient, Coriolis and curvature effects. The normal branch approaches geostrophic wind as curvature weakens; some anticyclonic combinations have no real balance.^[1]

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.

When to use Gradient Wind Curvature Correction

Use this tool to 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.

Prepare the observed sounding, cloud records or forecast verification data. Check pressure and height coordinates, wind conventions and the stated units.

How to use Gradient Wind Curvature Correction and understand its results

Prepare the observed sounding, cloud records or forecast verification data. Check pressure and height coordinates, wind conventions and the stated units.
Enter signedCoriolisPerSecond, signedCurvatureRadiusM, geostrophicAlongFlowSpeedMPerSecond using the field table and calculation rules, then run the tool.
Read normalBranchGradientWindMPerSecond, gradientMinusGeostrophicMPerSecond. 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
signedCoriolisPerSecond	Signed coriolis per second	number	Required
signedCurvatureRadiusM	Signed curvature radius m	number	Required
geostrophicAlongFlowSpeedMPerSecond	Geostrophic along flow speed m per second	number	Required

Enter nonnegative geostrophic along-flow speed and signed Coriolis and radius with finite nonzero product fR. Reject a negative discriminant. Evaluate the stable normal-branch expression and report speed and signed difference from geostrophic speed.

V²/(fR) + V = Vg; V = 2Vg/[1 + sqrt(1 + 4Vg/(fR))]

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

Output field	Meaning	Value type
normalBranchGradientWindMPerSecond	Normal branch gradient wind m per second	number
gradientMinusGeostrophicMPerSecond	Gradient minus geostrophic m per second	number

json

{
  "input": {
    "signedCoriolisPerSecond": 0.0001,
    "signedCurvatureRadiusM": 100000,
    "geostrophicAlongFlowSpeedMPerSecond": 10
  },
  "output": {
    "normalBranchGradientWindMPerSecond": 6.180339887498948,
    "gradientMinusGeostrophicMPerSecond": -3.819660112501052
  }
}

Limitations and assumptions

The anomalous branch, friction and transient gust response are excluded. The signed curvature convention must match the supplied fR.

Numeric inputs and returned numeric values must be finite; an unrepresentable returned value 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 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. For a complementary task, use Ageostrophic Component Magnitude: Difference measured and independently supplied geostrophic wind vectors, not scalar speed subtraction or computed pressure-gradient wind.

References

Gradient Wind Curvature Correction — tool.io

Similar or alternative tools

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.
Ageostrophic Component Magnitude
Difference measured and independently supplied geostrophic wind vectors, not scalar speed subtraction or computed pressure-gradient wind.