Description
Divide apexElevation-toeElevation by that distance for gradient and take atan for angleRadians.
Geomorphic geometry uses lengths, areas, volumes, and dimensionless shape ratios to summarize a feature. Grain axes, channel dimensions, and angular units need explicit definitions because similar field names can describe different measurements.
Divide apexElevation-toeElevation by that distance for gradient and take atan for angleRadians.
When to use this tool
Use Alluvial Fan Radial Slope Term when you need a geometric summary of a supplied landform or sediment measurement.
How to use the tool and how it works
- Enter apexElevation, toeElevation, radialDistance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read gradient, angleRadians. Use the output convention below.
Require positive radialDistance. Divide apexElevation-toeElevation by that distance for gradient and take atan for angleRadians.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| apexElevation | Apex Elevation | Required. Finite number. |
| toeElevation | Toe Elevation | Required. Finite number. |
| radialDistance | Radial Distance | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| gradient | Gradient | Required. Finite number. |
| angleRadians | Angle Radians Unit: rad. | Required. Finite number. |
{
"input": {
"apexElevation": 100,
"toeElevation": 90,
"radialDistance": 100
},
"output": {
"gradient": 0.1,
"angleRadians": 0.09966865249116204
}
}Limitations and assumptions
- Elevations share a datum and lengths share units; signed slopes are allowed without identifying an alluvial fan, fitting its profile, or evaluating slope stability.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Inspect the measured feature and sampling method for the intended geometric definition. Use a spatial model or complete distribution when a single shape ratio or local term is insufficient.
References
Similar or alternative tools
- Slope Break Angle Difference
Convert each signed rise/run fraction using atan and return second angle minus first and its absolute magnitude in radians.
- Beach Profile Trapezoid Area Term
Return their width and width times the average endpoint height relative to referenceHeight as signedArea.