The Model-Space Spectral Gap: A Dynamical Criterion for Ensemble Averaging in Climate Projections

Equal-weight averaging of climate models treats every simulation as an independent, interchangeable sample of a common future. That assumption is rarely tested and often false. Models share code, parameterizations, and structural habits. When their internal dynamics belong to different regimes, the multi-model mean can be a state that no model, and no physical climate, ever occupies. The old parable of the drowning statisticians is the same error: three soundings of a river, averaged, produce a depth that is everywhere wadable and nowhere real. This paper proposes a test of whether averaging is even legitimate. Each model is treated as a high-dimensional dynamical system. From a pre-industrial control run, Dynamic Mode Decomposition extracts a short list of leading frequencies and decay rates: a spectral fingerprint of internal variability, read from unforced behavior rather than from the historical trend. The Model-Space Spectral Gap then measures how well those fingerprints stay apart at low resonant order. When the gap is large, the models share a commensurable dynamical skeleton and an equal-weight mean can be given a statistical bound. When the gap collapses, that bound fails and the ensemble should be split into coherent clusters and reported as discrete storylines rather than as a single central estimate. A permissive physical gate excludes fingerprints that fall outside observed bands for ENSO, the PDO, and the AMO, so uniqueness alone cannot reward an implausible model. A hybrid weight then multiplies historical skill by a discount for spectral redundancy. The paper also advances a testable claim: models whose control-run spectra are rigid tend to have lower equilibrium climate sensitivity than models whose spectra are crowded and floppy. That constraint, if it survives the data, would not use the forced warming period to filter the same forced warming period. The framework is offered as a protocol, not as a completed CMIP audit. DMD is a linear proxy for a nonlinear system, the resonance order must be chosen, control runs are only approximately stationary, and a large gap does not make a model true. The intended product is an honest report of how many independent dynamical families the ensemble actually contains, and a rule for when the mean should be retired.