Stage Discharge Power Rating

Evaluate a caller stage/discharge power rating with zero-flow control stage; stages at/below control are modeled dry, while backwater, hysteresis and calibration range remain external.

Description

A power rating translates water level above a zero-flow control into discharge.

A power rating translates water level above a zero-flow control into discharge. Its coefficient and exponent come from a calibrated stage-discharge relationship.^[1]

The tool returns predictedDischargesM3PerSecond, atOrBelowControlFlags. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Stage Discharge Power Rating

Use this for the following task: Evaluate a caller stage/discharge power rating with zero-flow control stage; stages at/below control are modeled dry, while backwater, hysteresis and calibration range remain external. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Stage Discharge Power Rating and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter stagesM, zeroFlowStageM, calibratedCoefficient, ratingExponent according to the field table, then run the tool.
Read predictedDischargesM3PerSecond, atOrBelowControlFlags. 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
zeroFlowStageM	Zero flow stage m	number	Required
calibratedCoefficient	Calibrated coefficient	number	Required
ratingExponent	Rating exponent	number	Required

Provide a nonempty stage list, nonnegative coefficient and positive exponent. Return predicted discharge and numeric 1/0 flags for stages at or below control.

Q(h)=coefficient×max(0,h−zeroFlowStage)^exponent

The symbols and boundary conditions refer to the supplied fields and the implementation described above.

Output field	Meaning	Value type
predictedDischargesM3PerSecond	Predicted discharges m3 per second	list of number
atOrBelowControlFlags	At or below control flags	list of number

json

{
  "input": {
    "stagesM": [
      0,
      1,
      3
    ],
    "zeroFlowStageM": 1,
    "calibratedCoefficient": 2,
    "ratingExponent": 2
  },
  "output": {
    "predictedDischargesM3PerSecond": [
      0,
      0,
      8
    ],
    "atOrBelowControlFlags": [
      1,
      1,
      0
    ]
  }
}

Limitations and assumptions

This evaluates the supplied relation without fitting it or checking its calibration range. Backwater, rating hysteresis and changing channel controls are not modeled.

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 Stage Storage Volume Interpolation when you need its operation: Interpolate storage for measured monotone stage/storage calibration within its observed bounds; no extrapolation, contour integration or invented lake geometry. Choose Dilution Capacity Low Flow for the complementary operation: Invert ideal complete mixing for an effluent flow capacity when receiving concentration < target < effluent; not a legal discharge allowance, mixing-zone model or ecological guarantee.

Background reference: Generalization of the power-law rating curve using hydrodynamic theory and Bayesian hierarchical modeling.

References

Generalization of the power-law rating curve using hydrodynamic theory and Bayesian hierarchical modeling — Hrafnkelsson and colleagues; arXiv

Similar or alternative tools

Stage Storage Volume Interpolation
Interpolate storage for measured monotone stage/storage calibration within its observed bounds; no extrapolation, contour integration or invented lake geometry.
Dilution Capacity Low Flow
Invert ideal complete mixing for an effluent flow capacity when receiving concentration < target < effluent; not a legal discharge allowance, mixing-zone model or ecological guarantee.