Optimal fingerprinting studies regress observed temperature changes on simulated response patterns of greenhouse-gas (G) and other-anthropogenic (OA, mainly aerosol) forcing to estimate attributable-warming trends. Jones, Stott & Mitchell (2016) showed that this framework cannot reconcile the diversity of spatio-temporal response patterns across CMIP5 models: depending on which detector model is used, the model-scaled G and OA trends over the twentieth century differ widely, and the derived observational constraints on transient climate response remain correspondingly uncertain. The challenge that paper poses to the detection-and-attribution community is to make the partition of observed warming between greenhouse gases and other anthropogenic influences robust to the choice of detector model, by (1) establishing a formally justified treatment of inter-model pattern uncertainty in the optimal detection framework that does not treat the multi-model 'ensemble of opportunity' as a representative sample; (2) designing feasible coordinated single-forcing experiments with adequate signal-to-noise for weak forcings; (3) explaining why pre-CMIP5 detection studies reported more consistent model-scaled trends than CMIP5-based analyses; and (4) standardizing per-model effective-radiative-forcing diagnostics so multi-model fingerprints are comparable. The problem remains open: components (2) and (4) have been substantially addressed institutionally by CMIP6's Detection and Attribution Model Intercomparison Project (DAMIP) and Radiative Forcing Model Intercomparison Project (RFMIP), but the core statistical treatment of inter-model pattern uncertainty (1) is still unresolved and under active methodological development through 2021-2025, and the pre-CMIP5/CMIP5 consistency discrepancy (3) remains unexplained.

Background

Detection and attribution (D&A) is the branch of climate science that formally decides whether observed climate changes are inconsistent with natural internal variability ('detection') and how much of them is explained by individual external forcings such as well-mixed greenhouse gases (G: CO2, CH4, N2O and other long-lived gases) and other anthropogenic influences (OA: chiefly aerosol particles from combustion and land-use change, plus ozone) ('attribution'). The standard tool is optimal fingerprinting: a regression, usually by total least squares (TLS, a regression variant in which noise in both the predictand and the predictors is accounted for), of the observed spatio-temporal temperature record onto simulated response patterns ('fingerprints') taken from climate-model experiments run with individual forcings. The regression returns scaling factors that rescale each simulated pattern to best match the observations; a forcing is 'detected' when its scaling factor's confidence interval excludes zero and the simulation is judged consistent with the observations when the interval includes unity. The fingerprints come from coordinated model intercomparison projects (CMIP5, CMIP6), in which modeling centers run a shared protocol: all-forcing 'historical' simulations, single-forcing experiments such as well-mixed greenhouse-gas-only or natural-only (solar and volcanic), and long unforced 'piControl' simulations used to estimate internal climate variability. Where a single-forcing experiment is absent, its response is estimated by differencing two experiments, which inflates noise. The signal-to-noise ratio (SNR) of a fingerprint - the magnitude of its forced response relative to internal variability - determines how precisely its scaling factor can be estimated. Two further quantities matter here: effective radiative forcing (ERF), the change in Earth's net energy flux caused by a forcing agent after rapid atmospheric adjustments, which varies substantially across models (especially for aerosols); and the transient climate response (TCR), the warming at the time of CO2 doubling in a 1%-per-year increasing-CO2 experiment, which observational attribution of G and OA warming can constrain and which feeds directly into near-term climate projection. Jones, Stott & Mitchell (2016, J. Geophys. Res. Atmos. 121, 6969-6992, doi:10.1002/2015JD024337) applied optimal detection to fifteen CMIP5 models. In the standard experimental design (G, OA, natural fingerprints, with OA obtained by differencing), only eight of fifteen models detected a separate greenhouse-gas signal and only five also detected the other-anthropogenic signal; the model-scaled G warming trends (0.86-1.22 K per century against an observed twentieth-century warming of about 0.65 K per century, with cooling from other anthropogenic and natural influences of -0.54 to -0.21 K per century in the multi-model-mean analysis) differed widely across detector models. They attributed the inconsistency to two factors: regression predictors with low SNR inject noise, and the spatio-temporal response patterns - especially for the non-greenhouse anthropogenic (aerosol-dominated) forcings - differ across models in ways the standard analysis cannot reconcile. Because CMIP-type archives are an 'ensemble of opportunity' (models that happened to be submitted, not a sample designed to span uncertainty), this pattern diversity cannot simply be averaged away. Earlier attempts to include model uncertainty in the regression include the error-in-variables treatment of Huntingford et al. (2006) and the multiple-uncertainty formulation of Hannart, Ribes & Naveau (2014), but no agreed practical implementation existed. Alongside this methodological gap, the paper raised three linked issues: how to design future coordinated experiments (Ribes, Gillett & Zwiers (2015) had recommended, from a perfect-model study, order ten natural-only ensemble members, more than any institution provided for CMIP5, and designs that avoid low-SNR predictors and differencing); why pre-CMIP5 detection studies (as assessed in the IPCC Fourth Assessment Report) had given more consistent scaled G and OA trends than CMIP5-based analyses - candidate explanations including solar forcing datasets with larger historical trends before CMIP5, simpler experimental designs with higher SNR, and less diverse model responses; and the need for routine per-model ERF estimates per forcing agent and consistent treatment of forcing components (aerosol indirect effects, ozone, land use) across models.

Problem Statement

Jones, Stott & Mitchell (2016) pose the following challenge. Standard optimal fingerprinting cannot reconcile the diversity of simulated spatio-temporal response patterns across CMIP5 models, so the model-scaled attributable warming trends for well-mixed greenhouse gases (G) and other anthropogenic factors (OA) over the twentieth century depend strongly on which detector model is used. The problem is to make the attribution of observed warming to G versus OA model-robust, together with the linked supporting issues the source raises, namely: (1) establish a formally justified treatment of inter-model pattern uncertainty in the optimal detection framework that does not rely on treating the CMIP 'ensemble of opportunity' as a representative sample of model uncertainty, and determine whether, under such a treatment, the G and OA attributable trends and the observationally derived constraint on transient climate response become consistent across detector models, or whether no such consistent treatment exists; (2) determine a feasible, near-optimal coordinated experimental design - which single-forcing experiments to run directly rather than obtain by differencing, and how many initial-condition ensemble members per experiment (for example, how many natural-only members are needed in practice) - that achieves adequate signal-to-noise for weak forcings under real institutional computational constraints; (3) explain why pre-CMIP5 detection studies (such as those assessed in the IPCC Fourth Assessment Report) reported more consistent model-scaled G and OA trends than CMIP5-based analyses - in particular how much of the difference is attributable to changed external forcing datasets (larger pre-CMIP5 historical solar trends), simpler experimental designs with higher signal-to-noise, lesser inter-model process diversity, or other factors; and (4) establish routine per-model diagnostics - standardized effective radiative forcing estimates per forcing agent and consistent inclusion of forcing components such as aerosol indirect effects, ozone and land use - that make multi-model fingerprint comparisons interpretable. Post-2016 work has institutionally addressed component (2) through the CMIP6 DAMIP single-forcing experiments and substantially progressed component (4) through RFMIP effective-radiative-forcing diagnostics. The scientific target is the justified method and the demonstrated (or refuted) model-robustness of the partition (component (1)) together with the explanation of the pre-CMIP5/CMIP5 consistency difference (component (3)).

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