How Many Independent Models Does the World Really Have?
The world runs a fleet of global models — but a blend is only as strong as the number of independent information sources inside it. We measure independence directly: for every model pair, the correlation of their Day-5 500 hPa error fields against one common truth, reduced to Neff = k²/ΣR² — the effective number of independent models. When AI models train toward the same analyses, errors correlate, Neff falls, and consensus confidence becomes fake. Method ▸
The AI models (AIFS, the GraphCast family, WeatherNext) are trained toward ERA5 and the IFS analysis — ECMWF's own picture of the atmosphere. When the training target is wrong about a trough, the student is wrong the same way, at the same place, on the same day. And as physics agencies fold AI components into their own systems, even the "independent" dynamical models drift toward that shared error structure. The models still disagree on quiet details — but they increasingly bust together.
Every blend, every "8 of 9 models agree" headline, every ensemble-of-ensembles silently assumes the members are independent draws. They are not. If the fleet carries the information of only ~2 independent models, agreement among all of them is closer to one source repeating itself than to nine confirmations — the error bars you'd quote from the spread are too narrow, exactly when it matters most. That is why our House weights consume Neff as a diversity penalty rather than counting heads.
Neff = k means every model brings its own information; Neff → 1 means the fleet has collapsed onto a single shared view. The index is computed from the trailing archive each cycle (cos-lat-weighted spatial correlation of z500 error fields vs the ECMWF operational analysis, per region × lead), and the alert flags when the recent trend falls materially below its trailing norm.