Description
Return exact circular basal-area change and its linear approximation.
Botanical measurements use explicit specimen geometry, pixel scales, length origins and angular direction. A projected-area ratio or geometric contribution summarizes supplied measurements without identifying a species, recovering an actual shape or establishing biological health.
Return exact circular basal-area change and its linear approximation.
When to use this tool
Use Tree Basal Area Diameter Sensitivity when checking the stated plant-measurement, geometry or angular convention.
How to use the tool and how it works
- Enter diameter, diameterIncrement. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read initialArea, finalArea, areaIncrement, linearApproximation. Use the output convention below.
Return exact circular basal-area change and its linear approximation. Require diameter and diameter+increment nonnegative; areas = pi*d²/4, areaIncrement = pi*(2*d*increment+increment²)/4, linearApproximation = pi*d*increment/2.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| diameter | Diameter | Required. Finite number; minimum 0. |
| diameterIncrement | Diameter Increment | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| initialArea | Initial Area | Required. Finite number. |
| finalArea | Final Area | Required. Finite number. |
| areaIncrement | Area Increment | Required. Finite number. |
| linearApproximation | Linear Approximation | Required. Finite number. |
{
"input": {
"diameter": 10,
"diameterIncrement": 2
},
"output": {
"initialArea": 78.53981633974483,
"finalArea": 113.09733552923255,
"areaIncrement": 34.55751918948772,
"linearApproximation": 31.41592653589793
}
}Limitations and assumptions
- Use matching length units; circular cross sections and measurement consistency are assumed rather than observed.
- 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 specimen and measurement protocol, apply verified calibration and use an appropriate biological or geometric model for substantive interpretation.
References
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