Climate science faces a unique epistemological challenge: the Earth's climate system cannot be experimentally manipulated, observational records are short relative to the timescales of interest, and predictions must extend decades to centuries into the future. Bayesian inference provides the framework for integrating diverse evidence — instrumental temperature records, paleoclimate proxies, physical constraints, and climate model simulations — into coherent probabilistic assessments of climate change and its causes.
Equilibrium Climate Sensitivity
The equilibrium climate sensitivity (ECS) — the long-run warming from a doubling of atmospheric CO₂ — is perhaps the most consequential uncertain parameter in climate science. Its value determines whether future warming will be merely disruptive or catastrophic. Bayesian estimation of ECS combines multiple lines of evidence: the instrumental warming record, volcanic eruption responses, paleoclimate constraints from ice ages, and the output of general circulation models.
where F₂ₓ is the forcing from CO₂ doubling (~3.7 W/m²), ΔT is observed warming,
F is total radiative forcing, and ΔQ is ocean heat uptake.
Each quantity has a Bayesian posterior distribution; ECS inherits their combined uncertainty.
The IPCC's assessed likely range for ECS (2.5 to 4.0 °C in the Sixth Assessment Report) was derived through a Bayesian synthesis of multiple evidence lines, each contributing a likelihood function. The prior on ECS — particularly whether it should have a heavy upper tail — has been extensively debated, as it strongly influences the probability assigned to catastrophic warming scenarios.
Paleoclimate Reconstruction
Reconstructing past temperatures from proxy data — tree rings, ice cores, coral records, sediment cores — is a Bayesian inverse problem. The relationship between a proxy and the climate variable of interest is uncertain and must be calibrated. Bayesian hierarchical models treat the true climate as a latent process, proxy observations as noisy indicators, and use priors informed by the physics of proxy formation. This approach naturally handles missing data, varying proxy networks through time, and age model uncertainty.
Paleoclimate records from sediment cores and speleothems require a chronology — mapping depth to age. Bayesian age-depth models like Bacon and OxCal combine radiometric dates (with measurement uncertainty), stratigraphic ordering constraints (superposition), and prior assumptions about sedimentation rates to produce posterior age-depth relationships with full uncertainty. This transforms a set of dates with error bars into a continuous probabilistic chronology.
Detection and Attribution
Detection and attribution (D&A) asks whether observed climate changes are distinguishable from natural variability (detection) and what fraction can be attributed to specific causes — greenhouse gases, aerosols, solar variability, volcanic eruptions (attribution). Bayesian D&A methods regress observed spatial-temporal patterns of climate change onto fingerprints predicted by climate models for each forcing agent, with priors on the scaling factors and the observational noise structure informed by climate model control runs.
Climate Model Evaluation and Weighting
With dozens of climate models (GCMs) contributing to international assessments like CMIP6, Bayesian model averaging provides a principled framework for combining their projections. Rather than giving each model equal weight, Bayesian methods weight models by their posterior probability given historical performance, while accounting for model interdependence. This produces probability distributions for future climate that are better calibrated than simple multi-model ensembles.
"Climate projections are inherently probabilistic. The question is not whether to use Bayesian methods, but whether to use them honestly and transparently." — James Annan and Julia Hargreaves, pioneers of Bayesian climate sensitivity estimation
Current Frontiers
Bayesian emulators — Gaussian process surrogates for computationally expensive climate models — enable uncertainty quantification across high-dimensional parameter spaces. Bayesian causal inference is being applied to extreme event attribution. And the integration of process-based models with statistical learning through Bayesian calibration promises more physically consistent climate projections.