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.
Description
An effective radiating temperature balances absorbed solar energy with emitted thermal energy in a simplified planetary model.
An effective radiating temperature balances absorbed solar energy with emitted thermal energy in a simplified planetary model. Averaging incident sunlight over a sphere introduces the factor of four between intercepted and emitting areas.1
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.
When to use Effective Radiating Temperature
Use this tool to 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.
Prepare the climate observations and independently chosen model parameters. Confirm units, daily coverage, chronological order and the intended seasonal window.
How to use Effective Radiating Temperature 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 solarConstantWPerM2, planetaryAlbedo, thermalEmissivity, stefanBoltzmannWPerM2K4 using the field table and calculation rules, then run the tool.
- Read effectiveRadiatingTemperatureK, globalMeanAbsorbedSolarWPerM2. 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 |
|---|---|---|---|
| solarConstantWPerM2 | Solar constant w per m2 | number | Required |
| planetaryAlbedo | Planetary albedo | number | Required |
| thermalEmissivity | Thermal emissivity | number | Required |
| stefanBoltzmannWPerM2K4 | Stefan boltzmann w per m2 k4 | number | Required |
Supply positive solar constant and Stefan–Boltzmann constant, albedo from zero to one and emissivity greater than zero and at most one. The tool computes globally averaged absorbed energy in W/m² and inverts the thermal-emission relation to kelvin. Albedo one gives zero absorbed energy and zero modeled radiating temperature.
absorbed mean = S(1−albedo)/4; Te = [absorbed mean/(emissivity σ)]^0.25 Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| effectiveRadiatingTemperatureK | Effective radiating temperature k | number |
| globalMeanAbsorbedSolarWPerM2 | Global mean absorbed solar w per m2 | number |
{
"input": {
"solarConstantWPerM2": 1360,
"planetaryAlbedo": 0.3,
"thermalEmissivity": 1,
"stefanBoltzmannWPerM2K4": 5.670374419e-8
},
"output": {
"effectiveRadiatingTemperatureK": 254.5313641586735,
"globalMeanAbsorbedSolarWPerM2": 237.99999999999997
}
}Limitations and assumptions
This model assumes spherical averaging and radiative equilibrium. Its temperature is not the actual surface temperature; atmospheric structure, greenhouse transfer, spatial contrasts and transient heat storage are absent.
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 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. For a complementary task, use Greenhouse Effect Enhancement Delta: Compare actual supplied surface temperature against measured outgoing-longwave blackbody-equivalent emission temperature; unlike solar equilibrium temperature, no absorbed/OLR equality or causal greenhouse attribution is assumed.
References
-
Effective Radiating Temperature — tool.io
Similar or alternative tools
- 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.
- Greenhouse Effect Enhancement Delta
Compare actual supplied surface temperature against measured outgoing-longwave blackbody-equivalent emission temperature; unlike solar equilibrium temperature, no absorbed/OLR equality or causal greenhouse attribution is assumed.