Transient Climate Response TCR Estimator
Evaluate one-box transient response at end of a linear forcing ramp (exponential CO2 growth under logarithmic forcing), with explicit restoring feedback/heat capacity/time and stable short-ramp limit; not observed TCR.
Description
Transient climate response differs from equilibrium warming because a climate system with heat capacity takes time to respond to changing forcing.
Transient climate response differs from equilibrium warming because a climate system with heat capacity takes time to respond to changing forcing. A one-box model represents this delay with a restoring parameter and one characteristic response time.1
Evaluate one-box transient response at end of a linear forcing ramp (exponential CO2 growth under logarithmic forcing), with explicit restoring feedback/heat capacity/time and stable short-ramp limit; not observed TCR.
When to use Transient Climate Response TCR Estimator
Use this tool to evaluate one-box transient response at end of a linear forcing ramp (exponential CO2 growth under logarithmic forcing), with explicit restoring feedback/heat capacity/time and stable short-ramp limit; not observed TCR.
Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.
How to use Transient Climate Response TCR Estimator and understand its results
- Prepare the climate observations and any independently chosen thresholds or model parameters. Confirm units, daily coverage, time order and the intended seasonal window.
- Enter doublingForcingWPerM2, restoringFeedbackWPerM2K, heatCapacityWYearPerM2K, co2DoublingTimeYears using the field table and calculation rules, then run the tool.
- Read oneBoxResponseTimeYears, equilibriumDoublingResponseK, oneBoxTransientDoublingResponseK. 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 |
|---|---|---|---|
| doublingForcingWPerM2 | Doubling forcing w per m2 | number | Required |
| restoringFeedbackWPerM2K | Restoring feedback w per m2 k | number | Required |
| heatCapacityWYearPerM2K | Heat capacity w year per m2 k | number | Required |
| co2DoublingTimeYears | Co2 doubling time years | number | Required |
Enter a positive restoring parameter λ in W/m²/K, positive heat capacity C in W·year/m²/K, positive forcing-ramp duration t in years and signed terminal forcing F in W/m². The tool computes τ = C/λ and the temperature reached at the end of a linear forcing ramp. For t/τ below 10⁻⁵ it evaluates the response factor as x/2 − x²/6 + x³/24 to avoid subtractive cancellation; otherwise it uses the displayed expm1 expression.
τ = C/λ; TCR = (F/λ)[1 + expm1(−t/τ)/(t/τ)] Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| oneBoxResponseTimeYears | One box response time years | number |
| equilibriumDoublingResponseK | Equilibrium doubling response k | number |
| oneBoxTransientDoublingResponseK | One box transient doubling response k | number |
{
"input": {
"doublingForcingWPerM2": 4,
"restoringFeedbackWPerM2K": 2,
"heatCapacityWYearPerM2K": 20,
"co2DoublingTimeYears": 10
},
"output": {
"oneBoxResponseTimeYears": 10,
"equilibriumDoublingResponseK": 2,
"oneBoxTransientDoublingResponseK": 0.7357588823428847
}
}Limitations and assumptions
This is a supplied-parameter, single-reservoir estimate. It does not infer climate sensitivity from observations, represent multiple ocean response times or validate an emissions pathway. A negative terminal forcing produces a negative temperature response; no positive-forcing assumption is enforced.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Radiative Forcing CO2 Logarithm: Calculate signed logarithmic CO2 radiative forcing change using caller concentration convention/coefficient; no warming, verified forcing or neglected gas/aerosol response is inferred. 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
-
Transient Climate Response TCR Estimator — tool.io
Similar or alternative tools
- Radiative Forcing CO2 Logarithm
Calculate signed logarithmic CO2 radiative forcing change using caller concentration convention/coefficient; no warming, verified forcing or neglected gas/aerosol response is inferred.
- 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.