Frontal Slope Margules Formula
Evaluate signed Margules temperature-weighted along-front geostrophic-wind slope under declared uniform two-air-mass convention; not frontal motion or an observed frontal elevation map.
Description
Margules balance relates frontal slope to temperature contrast and geostrophic winds in two idealized air masses.
Margules balance relates frontal slope to temperature contrast and geostrophic winds in two idealized air masses. A declared along-front and Coriolis convention determines the slope sign.1
Evaluate signed Margules temperature-weighted along-front geostrophic-wind slope under declared uniform two-air-mass convention; not frontal motion or an observed frontal elevation map.
When to use Frontal Slope Margules Formula
Use this tool to evaluate signed Margules temperature-weighted along-front geostrophic-wind slope under declared uniform two-air-mass convention; not frontal motion or an observed frontal elevation map.
Prepare the observed sounding, cloud records or forecast verification data. Check pressure and height coordinates, wind conventions and the stated units.
How to use Frontal Slope Margules Formula 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 coldAirTemperatureK, warmAirTemperatureK, coldAirAlongFrontWindMPerSecond, warmAirAlongFrontWindMPerSecond, coriolisPerSecond, gravityMPerSecondSquared using the field table and calculation rules, then run the tool.
- Read signedMargulesFrontalSlope. 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 |
|---|---|---|---|
| coldAirTemperatureK | Cold air temperature k | number | Required |
| warmAirTemperatureK | Warm air temperature k | number | Required |
| coldAirAlongFrontWindMPerSecond | Cold air along front wind m per second | number | Required |
| warmAirAlongFrontWindMPerSecond | Warm air along front wind m per second | number | Required |
| coriolisPerSecond | Coriolis per second | number | Required |
| gravityMPerSecondSquared | Gravity m per second squared | number | Required |
Use positive Kelvin temperatures with warm greater than cold, positive gravity and nonzero signed Coriolis. Enter both along-front winds in m/s; return the signed dimensionless slope with temperature weighting intact.
slope = f(Tcold × Vwarm − Twarm × Vcold)/[g(Twarm−Tcold)] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| signedMargulesFrontalSlope | Signed margules frontal slope | number |
{
"input": {
"coldAirTemperatureK": 280,
"warmAirTemperatureK": 300,
"coldAirAlongFrontWindMPerSecond": 5,
"warmAirAlongFrontWindMPerSecond": 10,
"coriolisPerSecond": 0.0001,
"gravityMPerSecondSquared": 10
},
"output": {
"signedMargulesFrontalSlope": 0.00065
}
}Limitations and assumptions
The uniform two-air-mass approximation does not infer frontal motion or a spatial elevation map.
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 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. For a complementary task, use Frontogenesis Function 2D: Compute 2D adiabatic kinematic material growth of temperature-gradient magnitude from caller local velocity-gradient tensor; no vertical tilting/diabatic term, coordinates or front forecast.
References
-
Frontal Slope Margules Formula — tool.io
Similar or alternative tools
- 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.
- Frontogenesis Function 2D
Compute 2D adiabatic kinematic material growth of temperature-gradient magnitude from caller local velocity-gradient tensor; no vertical tilting/diabatic term, coordinates or front forecast.