Internal Load Release Areal Rate
Infer signed internal phosphorus release as the residual of observed water inventory and external exchange, normalized by active sediment area/time; other missing processes can contribute to the residual.
Description
Internal phosphorus loading can be estimated as the residual of a matched water-column budget.
Internal phosphorus loading can be estimated as the residual of a matched water-column budget. Normalization by active sediment area and elapsed time expresses a signed areal release rate.1
The tool returns inferredInternalReleaseKg, signedArealReleaseGramsPerM2Day. The computation uses supplied observations and parameters rather than acquiring measurements.
When to use Internal Load Release Areal Rate
Use this for the following task: Infer signed internal phosphorus release as the residual of observed water inventory and external exchange, normalized by active sediment area/time; other missing processes can contribute to the residual. Prepare observations and calibration parameters on the same unit and reporting basis.
How to use Internal Load Release Areal Rate and understand its results
- Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
- Enter waterColumnStorageChangeKg, externalImportedPhosphorusKg, exportedPhosphorusKg, intervalDays, activeSedimentAreaM2 according to the field table, then run the tool.
- Read inferredInternalReleaseKg, signedArealReleaseGramsPerM2Day. 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 |
|---|---|---|---|
| waterColumnStorageChangeKg | Water column storage change kg | number | Required |
| externalImportedPhosphorusKg | External imported phosphorus kg | number | Required |
| exportedPhosphorusKg | Exported phosphorus kg | number | Required |
| intervalDays | Interval days | number | Required |
| activeSedimentAreaM2 | Active sediment area m2 | number | Required |
Supply signed storage change, nonnegative imported and exported masses and positive interval days and active sediment area. Preserve the residual’s sign.
internal kg=storageChange+exported−externalImported; g/(m²·day)=1000×internal/(area×days) The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| inferredInternalReleaseKg | Inferred internal release kg | number |
| signedArealReleaseGramsPerM2Day | Signed areal release grams per m2 day | number |
{
"input": {
"waterColumnStorageChangeKg": 10,
"externalImportedPhosphorusKg": 3,
"exportedPhosphorusKg": 5,
"intervalDays": 2,
"activeSedimentAreaM2": 100
},
"output": {
"inferredInternalReleaseKg": 12,
"signedArealReleaseGramsPerM2Day": 60
}
}Limitations and assumptions
Other missing processes can contribute to the inferred internal release. A negative result is retained, and the tool does not independently measure sediment flux.
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 Phosphorus Retention Coefficient when you need its operation: Close matched phosphorus inflow/outflow/storage budget to apparent retention; negative retention or ratios above one expose unmodeled exchange and are not clamped. Choose Vollenweider Phosphorus Load Limit for the complementary operation: Invert a caller Vollenweider-form steady retention relation for target areal external phosphorus load; not an authoritative load limit or site-specific ecological guarantee.
Background reference: Water Quality, Hydrology, and Response to Changes in Phosphorus Loading of Nagawicka Lake.
References
-
Water Quality, Hydrology, and Response to Changes in Phosphorus Loading of Nagawicka Lake — U.S. Geological Survey
Similar or alternative tools
- Phosphorus Retention Coefficient
Close matched phosphorus inflow/outflow/storage budget to apparent retention; negative retention or ratios above one expose unmodeled exchange and are not clamped.
- Vollenweider Phosphorus Load Limit
Invert a caller Vollenweider-form steady retention relation for target areal external phosphorus load; not an authoritative load limit or site-specific ecological guarantee.