Description
Calculate a three-point elevation-profile second derivative at equal horizontal spacing.
Geomorphic measurements distinguish signed coordinates, grain-size scales, profile derivatives and transported-mass or cross-section bases. A supplied datum adjustment or threshold does not detect a landform or establish a process. Plan distance, profile second derivative and slope-normalized curvature are different quantities.
Calculate a three-point elevation-profile second derivative at equal horizontal spacing.
When to use this tool
Use Hillslope Profile Curvature Three Point Term when checking the stated local landform, sediment, profile or coordinate convention.
How to use the tool and how it works
- Enter leftElevation, centerElevation, rightElevation, equalHorizontalSpacing. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read secondDerivative. Use the output convention below.
Require equalHorizontalSpacing>0. Return (leftElevation-2*centerElevation+rightElevation)/spacing².1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| leftElevation | Left Elevation | Required. Finite number. |
| centerElevation | Center Elevation | Required. Finite number. |
| rightElevation | Right Elevation | Required. Finite number. |
| equalHorizontalSpacing | Equal Horizontal Spacing | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| secondDerivative | Centered elevation second difference/spacing²; inverse length for matching horizontal/vertical units, not slope-normalized curvature. | Required. Finite number. |
{
"input": {
"leftElevation": 1,
"centerElevation": 0,
"rightElevation": 1,
"equalHorizontalSpacing": 2
},
"output": {
"secondDerivative": 0.5
}
}Limitations and assumptions
- This centered second derivative has inverse-length units for matching elevation/distance units; it is not curvature normalized by profile slope or a fitted terrain model.
- 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
Use calibrated surveys, mapped geometry and suitable complete sediment/terrain models for trends, process interpretation, uncertainty or hazard assessment.
References
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