Beta Plane Parameter Change Calculator
Local beta=df/dy spherical Earth approximation in m^-1 s^-1; no beta-plane validity guarantee.
Description
Calculate the local spherical-Earth northward gradient of the Coriolis parameter.
The beta parameter is the local northward gradient of the Coriolis parameter on a spherical Earth model. It depends on latitude, rotation rate and the chosen radius.
When to use this tool
Calculate the local spherical-Earth northward gradient of the Coriolis parameter. Use it when the input measurements and conventions below match the operation you need.
- Prepare latitudeDegrees, earthRadiusM, respecting the measurement basis and boundaries below.
- Compare the worked example with your intended operation before reusing its result.
How to use the tool and how it works
- Enter every field in the input table using the stated units and exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
For latitude from -90 to 90 degrees and positive radius, beta equals 2 times 7.292115e-5 times cos(latitude) divided by radius.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| latitudeDegrees | Latitude degrees. Degrees. | Finite number; from -90 to 90 inclusive |
| earthRadiusM | Earth radius m. Meters. | Finite number; greater than zero |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.betaPerMeterSecond | Beta per meter second; use the stated units and sign convention. |
{
"input": {
"latitudeDegrees": 0,
"earthRadiusM": 6371000
},
"output": {
"result": {
"betaPerMeterSecond": 2.2891586878041123e-11
}
}
}Limitations and assumptions
- The output is a local derivative in inverse meter-seconds when radius is in meters. It does not calculate a global current, wave dispersion relation or finite-distance change by itself.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Compare the result with independently checked observations or a model that covers the omitted dynamics. Use compatible frames, units and sampling conventions when carrying the value into another calculation. Compare the scope of the nearby tools below before substituting one.
References
Similar or alternative tools
- Coriolis Parameter F Latitude Calculator
Signed spherical-Earth Coriolis parameter using fixed rotation rate; zero at equator retained.
- haline contraction beta seawater
Haline contraction describes density's salinity derivative at fixed temperature and pressure.