Climate Zone Shift Velocity
Solve minimum-norm isotherm velocity from caller temporal tendency and planar measured temperature gradient; sign follows dT/dt+v·gradT=0, not mapped migration, species movement or a geodesy operation.
Description
Climate zone shift velocity translates a temperature trend into the speed and direction needed to follow an unchanged temperature.
Climate zone shift velocity translates a temperature trend into the speed and direction needed to follow an unchanged temperature. A local spatial gradient supplies the direction and strength of change across the map; this tool returns the smallest vector that cancels the supplied temporal trend.1
Solve minimum-norm isotherm velocity from caller temporal tendency and planar measured temperature gradient; sign follows dT/dt+v·gradT=0, not mapped migration, species movement or a geodesy operation.
When to use Climate Zone Shift Velocity
Use this tool to solve minimum-norm isotherm velocity from caller temporal tendency and planar measured temperature gradient; sign follows dT/dt+v·gradT=0, not mapped migration, species movement or a geodesy operation.
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 Climate Zone Shift Velocity 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 temporalClimateChangeCPerYear, spatialTemperatureGradientCPerKm using the field table and calculation rules, then run the tool.
- Read minimumNormClimateVelocityKmPerYear, climateVelocityMagnitudeKmPerYear. 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 |
|---|---|---|---|
| temporalClimateChangeCPerYear | Temporal climate change c per year | number | Required |
| spatialTemperatureGradientCPerKm | Spatial temperature gradient c per km | list of number | Required |
Supply exactly two east–north gradient components in °C/km and a signed temperature trend in °C/year. The gradient must be nonzero. The calculation normalizes the gradient and rescales by its magnitude to construct the minimum-length velocity vector in km/year. Its dot product with the spatial gradient equals the negative temporal trend; the reported magnitude is nonnegative.
v = −(dT/dt) ∇T / ||∇T||²; speed = ||v|| Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| minimumNormClimateVelocityKmPerYear | Minimum norm climate velocity km per year | list of number |
| climateVelocityMagnitudeKmPerYear | Climate velocity magnitude km per year | number |
{
"input": {
"temporalClimateChangeCPerYear": 0.02,
"spatialTemperatureGradientCPerKm": [
0.01,
0
]
},
"output": {
"minimumNormClimateVelocityKmPerYear": [
-2,
0
],
"climateVelocityMagnitudeKmPerYear": 2
}
}Limitations and assumptions
This is a local linear calculation, not a migration route or species dispersal prediction. A weak gradient can imply a large speed. The result does not account for terrain barriers, a changing gradient, seasonal patterns or uncertainty in either input.
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 Lapse Rate Environmental: Fit measured environmental temperature profile and expose extrapolated-height predictions, retaining inversion sign; not a prescribed constant atmosphere or pressure/altitude conversion. For a complementary task, 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.
References
-
Climate Zone Shift Velocity — tool.io
Similar or alternative tools
- Lapse Rate Environmental
Fit measured environmental temperature profile and expose extrapolated-height predictions, retaining inversion sign; not a prescribed constant atmosphere or pressure/altitude conversion.
- 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.