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.
Description
Stefan conductive ice growth balances heat removal with latent heat of freezing.
Stefan conductive ice growth balances heat removal with latent heat of freezing. Fixed snow thermal resistance reduces growth compared with bare ice under the same accumulated freezing temperatures.1
The tool returns predictedIceThicknessM. The computation uses supplied observations and parameters rather than acquiring measurements.
When to use Ice Thickness Stefan Law
Use this for the following task: Integrate a Stefan conductive growth model with fixed snow thermal resistance and initial ice; excludes melting, flowing water, radiation and evolving snowpack. Prepare observations and calibration parameters on the same unit and reporting basis.
How to use Ice Thickness Stefan Law and understand its results
- Prepare the measured quantities and supplied model parameters. Match the units and align paired lists before calculating.
- Enter initialIceThicknessM, snowThermalResistanceM2KPerW, iceConductivityWPerMK, iceDensityKgPerM3, latentHeatJPerKg, freezingDegreeDays, secondsPerDay according to the field table, then run the tool.
- Read predictedIceThicknessM. 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 |
|---|---|---|---|
| initialIceThicknessM | Initial ice thickness m | number | Required |
| snowThermalResistanceM2KPerW | Snow thermal resistance m2 k per w | number | Required |
| iceConductivityWPerMK | Ice conductivity w per m k | number | Required |
| iceDensityKgPerM3 | Ice density kg per m3 | number | Required |
| latentHeatJPerKg | Latent heat j per kg | number | Required |
| freezingDegreeDays | Freezing degree days | number | Required |
| secondsPerDay | Seconds per day | number | Required |
Supply nonnegative initial thickness, snow resistance and freezing-degree days, with positive conductivity, density, latent heat and day length. Evaluate the increment with a numerically stable rationalized expression.
r=conductivity×snowResistance; F=2×conductivity×freezingDegreeDays×secondsPerDay/(iceDensity×latentHeat); h=sqrt((initialThickness+r)²+F)−r The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| predictedIceThicknessM | Predicted ice thickness m | number |
{
"input": {
"initialIceThicknessM": 0.1,
"snowThermalResistanceM2KPerW": 0.1,
"iceConductivityWPerMK": 2,
"iceDensityKgPerM3": 900,
"latentHeatJPerKg": 300000,
"freezingDegreeDays": 10,
"secondsPerDay": 86400
},
"output": {
"predictedIceThicknessM": 0.12062439083762795
}
}Limitations and assumptions
This is a growth-only model with fixed snow resistance. Melting, flowing water, solar radiation and changing snow are excluded; predicted thickness does not establish bearing safety.
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 Snow Load On Ice Bearing Checker when you need its operation: Screen layered ice/snow hydrostatic freeboard for potential snow flooding; this is buoyancy only, not bearing strength or permission to walk, drive or work on ice. Choose Ice Out Date Trend Slope for the complementary operation: 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.
Background reference: Temperature and Dissolved Oxygen Simulations for a Lake with Ice Cover.
References
-
Temperature and Dissolved Oxygen Simulations for a Lake with Ice Cover — Fang and Stefan, University of Minnesota
Similar or alternative tools
- Snow Load On Ice Bearing Checker
Screen layered ice/snow hydrostatic freeboard for potential snow flooding; this is buoyancy only, not bearing strength or permission to walk, drive or work on ice.
- 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.