Climate Sensitivity Calculator

Formula Used

This calculator uses a simple global energy-balance relationship: ΔF = αΔT + N. Here, ΔF is radiative forcing change, ΔT is global mean temperature change, N is ocean heat uptake or energy imbalance, and α is the net feedback parameter.

• Feedback parameter: α = (ΔF − N) / ΔT (or α = ΔF / ΔT if N is not used)
• Sensitivity parameter: λ = 1 / α
• Equilibrium climate sensitivity: ECS = F2x / α

Sign conventions vary across literature. This tool assumes positive forcing warms and positive N reduces surface warming for a given forcing.

How to Use This Calculator

1. Enter ΔT as the temperature change over your chosen period.
2. Enter ΔF as the net forcing change for the same period.
3. Optionally enable N if you have an estimate of heat uptake.
4. Keep F2x at 3.7 W/m² unless your framework differs.
5. Press Calculate to view ECS, α, and λ above the form.
6. Use the export buttons to download your result summary.

Use consistent data sources and time windows for ΔT, ΔF, and N.

Example Data Table

Sample values below illustrate typical calculations.

Notes for Advanced Use

• For transient behavior, reported warming can lag forcing due to ocean heat uptake.
• Uncertainty propagation here assumes independent inputs and linearization.
• Different definitions exist for ECS and related metrics across models.
• Use a consistent baseline when computing ΔT and ΔF differences.

Climate Sensitivity in Practice

1) What the calculator estimates

Climate sensitivity links a sustained radiative forcing change (ΔF, W/m²) to the eventual global mean surface temperature response (ΔT, K). Using an energy-balance view, the tool derives the net feedback parameter α (W/m²/K), its inverse λ (K per W/m²), and equilibrium climate sensitivity (ECS, K).

2) Feedback parameter α and physical meaning

The feedback parameter summarizes combined processes that increase outgoing radiation as the planet warms, including water vapour, lapse-rate, cloud, and surface-albedo effects. Larger α means stronger stabilizing response per degree of warming; smaller α implies a larger temperature change for the same forcing.

3) Including ocean heat uptake (N)

When the ocean absorbs heat, less of the forcing immediately appears as surface warming. The calculator supports ΔF = αΔT + N, where N (W/m²) represents the net energy imbalance or ocean heat uptake. For recent decades, literature commonly reports N on the order of roughly 0.5–1.0 W/m², depending on period and dataset.

4) CO₂ doubling forcing (F2x)

To translate α into ECS, the tool uses an assumed forcing for CO₂ doubling, F2x. A widely used default is 3.7 W/m², which provides a consistent bridge between feedback strength and equilibrium warming. If your framework adopts a different value, you can enter it directly.

5) Example with realistic magnitudes

Suppose ΔT = 1.1 K, ΔF = 2.6 W/m², and N = 0.7 W/m². Then α = (2.6 − 0.7)/1.1 ≈ 1.727 W/m²/K. The implied λ ≈ 0.579 K per W/m², and ECS ≈ 3.7/1.727 ≈ 2.14 K. This illustrates how modest changes in N and α can shift ECS materially.

6) Why uncertainty matters

Small measurement differences in ΔT, ΔF, or N can meaningfully change α because the calculation divides by ΔT. The optional 1σ inputs estimate propagated uncertainty using first-order derivatives, assuming independent errors. This helps compare scenarios and document sensitivity to observational ranges.

7) Interpreting results responsibly

ECS is an equilibrium concept; it does not describe the pace of warming over coming decades. Short time windows, evolving aerosol forcing, and internal variability can bias inferred parameters. For robust analysis, pair consistent datasets, test multiple periods, and treat results as exploratory rather than definitive.

8) Best-practice workflow for analysts

Start by selecting a baseline and end period, then compute ΔT and ΔF from matched sources. Add N only when your imbalance estimate shares the same averaging window. Record inputs and outputs using the CSV or PDF export, and repeat with alternative forcing reconstructions to bracket outcomes.

FAQs

1) What is the difference between α and λ?

α is the feedback strength in W/m² per K. λ is its inverse in K per W/m², showing how much temperature changes for a unit forcing.

2) When should I enable the N term?

Enable N when you have an energy-imbalance or heat-uptake estimate for the same period as ΔT and ΔF. Otherwise, leave it off to avoid mixing inconsistent windows.

3) Why is F2x set to 3.7 W/m² by default?

3.7 W/m² is a commonly used estimate for effective radiative forcing from CO₂ doubling in many assessments, enabling consistent comparison of ECS across studies.

4) Can ECS be negative or extremely large here?

If α becomes negative or near zero, ECS can be negative or huge. That usually signals inconsistent inputs, sign conventions, or periods dominated by noise rather than a stable energy-balance signal.

5) Does this calculator replace comprehensive climate models?

No. It is a simplified diagnostic tool. Comprehensive models represent spatial patterns, feedbacks, and dynamics explicitly, while this approach compresses behaviour into a few global parameters.

6) What units should I use for ΔT?

Use temperature differences in K or °C; they are numerically identical for differences. Ensure the same baseline is used for the temperature and forcing changes.

7) How can I improve confidence in my estimate?

Use multiple forcing datasets, test different averaging windows, include uncertainty estimates, and compare inferred α against values reported in peer-reviewed assessments for similar periods.