Stage Storage Volume Interpolation
Interpolate storage for measured monotone stage/storage calibration within its observed bounds; no extrapolation, contour integration or invented lake geometry.
Description
A stage-storage calibration records how lake volume changes with water level.
A stage-storage calibration records how lake volume changes with water level. Linear interpolation estimates storage between measured calibration points.1
The tool returns interpolatedStorageVolumesM3. The computation uses supplied observations and parameters rather than acquiring measurements.
When to use Stage Storage Volume Interpolation
Use this for the following task: Interpolate storage for measured monotone stage/storage calibration within its observed bounds; no extrapolation, contour integration or invented lake geometry. Prepare observations and calibration parameters on the same unit and reporting basis.
How to use Stage Storage Volume Interpolation and understand its results
- Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
- Enter stagesM, storageVolumesM3, queryStagesM according to the field table, then run the tool.
- Read interpolatedStorageVolumesM3. Use the calculation below to interpret the selected mean or the model’s signs, units and comparison flags.
- Review the supplied assumptions and calibration before comparing or reporting the result.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| stagesM | Stages m | list of number | Required |
| storageVolumesM3 | Storage volumes m3 | list of number | Required |
| queryStagesM | Query stages m | list of number | Required |
Supply aligned strictly increasing stages and nonnegative strictly increasing volumes, plus a nonempty query list. Interpolate each query within the measured range in its original order.
V(h) = piecewise-linear interpolation of measured stage/storage pairs The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| interpolatedStorageVolumesM3 | Interpolated storage volumes m3 | list of number |
{
"input": {
"stagesM": [
0,
1,
2
],
"storageVolumesM3": [
0,
100,
300
],
"queryStagesM": [
0.5,
1.5
]
},
"output": {
"interpolatedStorageVolumesM3": [
50,
200
]
}
}Limitations and assumptions
Stage may use a signed survey datum. Extrapolation is rejected, and geometry is not reconstructed from contours or invented outside the calibration.
Numerical inputs must be finite. Input-shape and calculation checks do not establish measurement quality or the validity of a supplied calibration.
Alternative or Complementary methods
Choose Hypsographic Curve Integration when you need its operation: Integrate observed hypsographic area-depth contours into a cumulative volume curve with trapezoids; contour geometry is supplied and only the measured depth range is represented. Choose Epilimnion Hypolimnion Volume Split for the complementary operation: Integrate a supplied piecewise-linear area-depth curve across thermal-layer boundaries including split contour intervals; geometry is supplied, not reconstructed from map coordinates.
Background reference: Digital Library of Mathematical Functions: Quadrature.
References
-
Digital Library of Mathematical Functions: Quadrature — National Institute of Standards and Technology
Similar or alternative tools
- Hypsographic Curve Integration
Integrate observed hypsographic area-depth contours into a cumulative volume curve with trapezoids; contour geometry is supplied and only the measured depth range is represented.
- Epilimnion Hypolimnion Volume Split
Integrate a supplied piecewise-linear area-depth curve across thermal-layer boundaries including split contour intervals; geometry is supplied, not reconstructed from map coordinates.