Simple Energy Balance Model Equilibrium Temp Solver

Solve bounded monotone nonlinear emissive-plus-linear-cooling energy balance with residual; extra cooling differs from blackbody solar equilibrium, assumptions are caller supplied and not a validated climate forecast.

Description

An energy-balance equilibrium can include thermal emission and an additional linear cooling term.

An energy-balance equilibrium can include thermal emission and an additional linear cooling term. A bracketed monotone model allows the temperature to be solved while exposing the remaining energy imbalance.^[1]

When to use Simple Energy Balance Model Equilibrium Temp Solver

Use this tool to solve bounded monotone nonlinear emissive-plus-linear-cooling energy balance with residual; extra cooling differs from blackbody solar equilibrium, assumptions are caller supplied and not a validated climate forecast.

Prepare the climate observations and independently chosen model parameters. Confirm units, daily coverage, chronological order and the intended seasonal window.

How to use Simple Energy Balance Model Equilibrium Temp Solver and understand its results

Prepare the climate observations and independently chosen model parameters. Confirm units, daily coverage, chronological order and the intended seasonal window.
Enter absorbedMeanRadiationWPerM2, effectiveThermalEmissivity, stefanBoltzmannWPerM2K4, linearCoolingWPerM2K, minimumTemperatureK, maximumTemperatureK using the field table and calculation rules, then run the tool.
Read equilibriumModelTemperatureK, energyBalanceResidualWPerM2. 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
absorbedMeanRadiationWPerM2	Absorbed mean radiation w per m2	number	Required
effectiveThermalEmissivity	Effective thermal emissivity	number	Required
stefanBoltzmannWPerM2K4	Stefan boltzmann w per m2 k4	number	Required
linearCoolingWPerM2K	Linear cooling w per m2 k	number	Required
minimumTemperatureK	Minimum temperature k	number	Required
maximumTemperatureK	Maximum temperature k	number	Required

Supply nonnegative absorbed radiation and linear cooling coefficient, positive emissivity at most one, positive Stefan–Boltzmann constant, and increasing positive temperature bounds. Both endpoint balances must be finite and enclose the root. The tool performs 80 bisection iterations and returns equilibrium temperature in kelvin and its signed residual in W/m².

emissivity σT⁴ + coolingCoefficient T − absorbedMeanRadiation = 0

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

Output field	Meaning	Value type
equilibriumModelTemperatureK	Equilibrium model temperature k	number
energyBalanceResidualWPerM2	Energy balance residual w per m2	number

json

{
  "input": {
    "absorbedMeanRadiationWPerM2": 16,
    "effectiveThermalEmissivity": 1,
    "stefanBoltzmannWPerM2K4": 1,
    "linearCoolingWPerM2K": 0,
    "minimumTemperatureK": 1,
    "maximumTemperatureK": 3
  },
  "output": {
    "equilibriumModelTemperatureK": 2,
    "energyBalanceResidualWPerM2": 0
  }
}

Limitations and assumptions

The cooling term and coefficients are supplied model assumptions, not fitted climate feedbacks. A small energy residual does not certify model accuracy. A bracket that fails to enclose the root is an input error.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Effective Radiating Temperature: Invert a spherical mean absorbed-solar equilibrium to effective radiating temperature with caller emissivity/Stefan constant; not actual surface temperature or existing forward thermal-flux calculation. For a complementary task, use Albedo Forcing Delta Temperature: Apply caller area-weighted albedo perturbation to incident solar absorption and supplied equilibrium response; local/global incident-energy conventions must match and no climate feedbacks are inferred.

References

Simple Energy Balance Model Equilibrium Temp Solver — tool.io

Similar or alternative tools

Effective Radiating Temperature
Invert a spherical mean absorbed-solar equilibrium to effective radiating temperature with caller emissivity/Stefan constant; not actual surface temperature or existing forward thermal-flux calculation.
Albedo Forcing Delta Temperature
Apply caller area-weighted albedo perturbation to incident solar absorption and supplied equilibrium response; local/global incident-energy conventions must match and no climate feedbacks are inferred.