Ice Out Date Trend Slope

Fit ice-out trend after fixed-reference circular phase unwrapping on a supplied standardized annual cycle; dates must be leap-normalized and anomalies must be interpretable within a half cycle.

Description

Ice-out dates are phases on an annual cycle, so dates near the cycle boundary need unwrapping before fitting a trend.

Ice-out dates are phases on an annual cycle, so dates near the cycle boundary need unwrapping before fitting a trend. A fixed reference defines which annual branch the observations occupy.^[1]

The tool returns trendDaysPerYear, fittedCycleDayAtPredictionYear, fitRSquared. The computation uses supplied observations and parameters rather than acquiring measurements.

When to use Ice Out Date Trend Slope

Use this for the following task: Fit ice-out trend after fixed-reference circular phase unwrapping on a supplied standardized annual cycle; dates must be leap-normalized and anomalies must be interpretable within a half cycle. Prepare observations and calibration parameters on the same unit and reporting basis.

How to use Ice Out Date Trend Slope and understand its results

Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
Enter observationYears, normalizedIceOutCycleDays, annualCycleDays, referenceUnwrapCycleDay, predictionYear according to the field table, then run the tool.
Read trendDaysPerYear, fittedCycleDayAtPredictionYear, fitRSquared. 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
observationYears	Observation years	list of number	Required
normalizedIceOutCycleDays	Normalized ice out cycle days	list of number	Required
annualCycleDays	Annual cycle days	number	Required
referenceUnwrapCycleDay	Reference unwrap cycle day	number	Required
predictionYear	Prediction year	number	Required

Supply increasing years, aligned cycle days and a positive cycle length. Normalize dates externally into [0,period), unwrap around the reference, fit least squares and wrap the fitted date back to the cycle.

anomaly=wrap(day−reference+period/2)−period/2; fit anomaly=intercept+slope×year

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

Output field	Meaning	Value type
trendDaysPerYear	Trend days per year	number
fittedCycleDayAtPredictionYear	Fitted cycle day at prediction year	number
fitRSquared	Fit r squared	number

json

{
  "input": {
    "observationYears": [
      2000,
      2001,
      2002
    ],
    "normalizedIceOutCycleDays": [
      120,
      118,
      116
    ],
    "annualCycleDays": 365,
    "referenceUnwrapCycleDay": 120,
    "predictionYear": 2001
  },
  "output": {
    "trendDaysPerYear": -2,
    "fittedCycleDayAtPredictionYear": 118,
    "fitRSquared": 1
  }
}

Limitations and assumptions

Prediction year must lie within observed years. Leap normalization and half-cycle interpretability are external; no calendar dates, extrapolated forecasts or causal climate attribution are produced.

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 Ice Thickness Stefan Law when you need its operation: Integrate a Stefan conductive growth model with fixed snow thermal resistance and initial ice; excludes melting, flowing water, radiation and evolving snowpack. 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: Least squares estimation.

References

Least squares estimation — NIST/SEMATECH

Similar or alternative tools

Ice Thickness Stefan Law
Integrate a Stefan conductive growth model with fixed snow thermal resistance and initial ice; excludes melting, flowing water, radiation and evolving snowpack.
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.