Lead 210 Sediment Dating
Evaluate unsupported Pb-210 constant-rate-of-supply inventory chronology and covariance-aware first-order age uncertainty; supply decay constant, supported-activity correction and complete inventory externally.
Description
Unsupported lead-210 inventory can date sediment under the constant-rate-of-supply model.
Unsupported lead-210 inventory can date sediment under the constant-rate-of-supply model. The fraction of inventory remaining below a depth determines its age relative to the sediment surface.1
The tool returns crsAgeYears, approximateAgeStandardErrorYears. The computation uses supplied observations and parameters rather than acquiring measurements.
When to use Lead 210 Sediment Dating
Use this for the following task: Evaluate unsupported Pb-210 constant-rate-of-supply inventory chronology and covariance-aware first-order age uncertainty; supply decay constant, supported-activity correction and complete inventory externally. Prepare observations and calibration parameters on the same unit and reporting basis.
How to use Lead 210 Sediment Dating and understand its results
- Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
- Enter totalUnsupportedInventory, unsupportedInventoryBelowDepth, decayConstantPerYear, totalInventoryVariance, remainingInventoryVariance, inventoryCovariance according to the field table, then run the tool.
- Read crsAgeYears, approximateAgeStandardErrorYears. 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 |
|---|---|---|---|
| totalUnsupportedInventory | Total unsupported inventory | number | Required |
| unsupportedInventoryBelowDepth | Unsupported inventory below depth | number | Required |
| decayConstantPerYear | Decay constant per year | number | Required |
| totalInventoryVariance | Total inventory variance | number | Required |
| remainingInventoryVariance | Remaining inventory variance | number | Required |
| inventoryCovariance | Inventory covariance | number | Required |
Supply positive inventories with remaining≤total and a positive annual decay constant. Use nonnegative variances and covariance satisfying covariance²≤varTotal×varRemaining.
age=ln(total/remaining)/decayConstant; SE=sqrt(max(0,varTotal/total²+varRemaining/remaining²−2×covariance/(total×remaining)))/decayConstant The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| crsAgeYears | Crs age years | number |
| approximateAgeStandardErrorYears | Approximate age standard error years | number |
{
"input": {
"totalUnsupportedInventory": 100,
"unsupportedInventoryBelowDepth": 25,
"decayConstantPerYear": 0.03465735902799726,
"totalInventoryVariance": 4,
"remainingInventoryVariance": 1,
"inventoryCovariance": 0
},
"output": {
"crsAgeYears": 40,
"approximateAgeStandardErrorYears": 1.2903856728918244
}
}Limitations and assumptions
The uncertainty is a first-order approximation. Supported-activity correction, complete inventory and CRS applicability must be established externally; the tool does not infer a decay constant or correct mixing and disturbed sediments.
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 Areal Hypolimnetic Oxygen Depletion for the complementary operation: Fit net hypolimnetic oxygen-inventory depletion and normalize by area; negative depletion records replenishment, and changing hypolimnetic boundaries or advective supply require separate correction.
Background reference: Bayesian analysis of 210Pb dating: CRS model background.
References
-
Bayesian analysis of 210Pb dating: CRS model background — Aquino-López and colleagues; arXiv
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.
- Areal Hypolimnetic Oxygen Depletion
Fit net hypolimnetic oxygen-inventory depletion and normalize by area; negative depletion records replenishment, and changing hypolimnetic boundaries or advective supply require separate correction.