XBT Fall Rate Equation Depth

Evaluate a caller-calibrated XBT quadratic fall-rate relation only within the supplied valid time horizon; no probe model coefficients or universal depth accuracy embedded.

Description

XBT probes estimate depth from elapsed fall time through a calibrated relation.

XBT probes estimate depth from elapsed fall time through a calibrated relation. Probe-specific fall coefficients determine that conversion.

Evaluate a caller-calibrated XBT quadratic fall-rate relation only within the supplied valid time horizon; no probe model coefficients or universal depth accuracy embedded.

When to use XBT Fall Rate Equation Depth

Use this tool to evaluate a caller-calibrated XBT quadratic fall-rate relation only within the supplied valid time horizon; no probe model coefficients or universal depth accuracy embedded.

Gather the water, wave, current or profile observations and any supplied calibration constants. Confirm units and the stated coordinate and pressure conventions.

How to use XBT Fall Rate Equation Depth and understand its results

Gather the water, wave, current or profile observations and any supplied calibration constants. Confirm units and the stated coordinate and pressure conventions.
Enter elapsedSeconds, linearFallCoefficientMPerSecond, quadraticFallCoefficientMPerSecondSquared, maximumCalibrationTimeSeconds using the field table and calculation rules, then run the tool.
Read estimatedDepthsM, instantaneousDescentRatesMPerSecond. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
elapsedSeconds	Elapsed seconds	list of number	Required
linearFallCoefficientMPerSecond	Linear fall coefficient m per second	number	Required
quadraticFallCoefficientMPerSecondSquared	Quadratic fall coefficient m per second squared	number	Required
maximumCalibrationTimeSeconds	Maximum calibration time seconds	number	Required

Use positive linear coefficient and calibration horizon, nonnegative quadratic coefficient and times within the horizon. With a nonzero quadratic term, require the horizon strictly before zero descent speed. Return depths and instantaneous rates.^[1]

depth = linear coefficient × time − quadratic coefficient × time²

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
estimatedDepthsM	Estimated depths m	list of number
instantaneousDescentRatesMPerSecond	Instantaneous descent rates m per second	list of number

json

{
  "input": {
    "elapsedSeconds": [
      0,
      1,
      2
    ],
    "linearFallCoefficientMPerSecond": 6,
    "quadraticFallCoefficientMPerSecondSquared": 0.1,
    "maximumCalibrationTimeSeconds": 10
  },
  "output": {
    "estimatedDepthsM": [
      0,
      5.9,
      11.6
    ],
    "instantaneousDescentRatesMPerSecond": [
      6,
      5.8,
      5.6
    ]
  }
}

Limitations and assumptions

No probe coefficients or universal accuracy are embedded.

Numbers and computed results must be finite; overflow produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use CTD Descend Rate Consistency Checker: Audit observed CTD signed descent rates and adjacent speed jumps against caller acquisition policy; flags do not automatically identify sensor lag or discard data. For a complementary task, use ADCP Bin Depth Transducer Offset: Compute ADCP beam-range bin centers on positive-down depths and caller bottom-clearance screen for a vertical instrument; side-lobe contamination and attitude corrections are not modeled.

References

XBT Fall Rate Equation Depth — tool.io

Similar or alternative tools

CTD Descend Rate Consistency Checker
Audit observed CTD signed descent rates and adjacent speed jumps against caller acquisition policy; flags do not automatically identify sensor lag or discard data.
ADCP Bin Depth Transducer Offset
Compute ADCP beam-range bin centers on positive-down depths and caller bottom-clearance screen for a vertical instrument; side-lobe contamination and attitude corrections are not modeled.