Can flow matching emulate daily global climate model simulations?

A day-ahead temperature field from six inputs

The paper asks whether a generative model can stand in for a physics-based global climate model at the daily scale, across a transient run that includes a forced warming trend. EC-EarthFlow targets one variable, the 2 m temperature field of EC-Earth3, and predicts the next day's field from a context made of the previous five days of gridded temperature plus the gridded annual mean temperature. That annual mean is the piece that fixes the mean climate state, so the same model can be asked for a day in 1950, 2050 or 2150.

The choice of a single variable is deliberate and framed as a proof of concept, for both computational and scientific reasons. The authors want to see how well a deep learning model handles one variable with a substantial trend, rather than the full atmosphere used in several earlier emulation studies. Because the annual mean temperature enters as an input, the emulator is expected to follow the warming level of whichever EC-Earth3 member supplies that input; the paper treats this dependence as a known characteristic rather than a surprise.

Flow matching transports noise into a temperature field

Flow matching generates a sample by starting from Gaussian noise and pushing it along an ordinary differential equation in an artificial integration time that runs from 0 to 1. A neural network predicts the vector field that defines this transport, conditioned on the context. Training uses conditional flow matching along an optimal transport path, which interpolates linearly between the noise sample and the real target field, so the network learns to reproduce the constant displacement between them.

Two implementation details matter for reading the results. The loss is weighted by latitude, because on a regular latitude-longitude grid an unweighted error over-represents the poles where grid cells are physically small. And the vector field is parameterised by a PDE-Transformer with 4×4 grid-cell patches. At inference, each ensemble member comes from an independent noise draw integrated through the same solver; the terminal state is appended to the context and the process repeats, which is how a one-day predictor becomes a rollout over a month or a season.

Long rollouts stay stable but accumulate small biases

The paper compares two rollout designs. In the short design, seven separate 30-day predictions are concatenated into an extended season, which re-injects the EC-Earth3 test member's daily temperatures at the start of each month and visibly pulls the trajectory back toward that member. In the long design, a single rollout runs from May to November with no such refresh. The long rollout's spread grows over the first few time steps and then stays consistent through the season, and the annual cycle and trend look similar in both designs.

That stability is the paper's central methodological claim: errors do not compound into instability over an extended season. But the comparison also exposes a cost. The longer rollout accumulates the model's deficiencies more than the shorter one, and the authors report a warm bias at the poles in the winter hemisphere. They tried per-grid-point normalization without much improvement and suggest the cause is likely the regular latitude-longitude grid, pointing to alternative projections such as HEALPix as future work.

The ensemble is realistic but under-dispersed

Rank histograms compare where the EC-Earth3 member falls within the EC-EarthFlow ensemble. A flat histogram would mean the physical member is statistically indistinguishable from the generated ensemble. Across all grid points the histograms are not flat: the EC-Earth3 member sits too often above the highest or below the lowest generated member, which the authors read as under-dispersion.

A second comparison sets the scale. Grid-point mean temperature differences between EC-EarthFlow and the EC-Earth3 member used to drive it are smaller than the differences between two EC-Earth3 members, again consistent with too little spread. The paper notes that tuning flow matching parameters during training could improve this. It also notes the opposite pressure: because the generated ensemble is strongly conditioned on the driving member, its ability to explore internal variability independently of that member may be limited.

Annual cycle and forced warming survive the emulation

Global mean surface temperature gives the clearest large-scale test. EC-EarthFlow reproduces the amplitude and phase of the annual cycle, including the stronger signal in northern hemisphere summer that the paper attributes to the larger land area there. It also reproduces the magnitude of the forced response, with northern hemisphere summer temperatures around 2.5°C warmer by 2150 in both EC-Earth3 and the emulator.

Inter-annual variability is preserved in a more conditional way. When EC-Earth3 member 16 is warmer than member 15 in 2150, the generated ensembles tend to follow the warming pattern of whichever member conditions them, which the authors expect given that annual mean temperature is an input. What they highlight as promising is that the ensembles generated from members 15 and 16 still overlap, so the emulator adds spread rather than simply copying its input.

Local variability and wave patterns are learned from temperature alone

At two locations, De Bilt in the Netherlands and Sydney in Australia, the emulator captures seasonally specific changes in daily variability. EC-Earth3 shows larger daily temperature variability in Sydney during October-December and in De Bilt from November onward, and EC-EarthFlow reflects both. The authors call this remarkable because the model receives only five days of temperature at the end of April plus the annual mean for those inference periods.

The spatial analysis goes further. After removing high-frequency variability, the paper correlates temperature at a central point with all other grid points. EC-EarthFlow reproduces the spatial autocorrelation and teleconnection-like wave patterns simulated by EC-Earth3, including the pattern around western Europe consistent with atmospheric blocking. The authors read this as evidence that the emulator learns multivariate physical processes from a single variable, while noting some smoothing at large distances, for example in the North Pacific in the Sydney-centred plots.

A cheap daily emulator, not yet a replacement for GCM ensembles

The paper's own framing sets the priority: this is the first emulation, to the authors' knowledge, of a transient GCM run at the daily scale including the forced trend over 1950-2166, with auto-regressive predictions for arbitrarily long periods, and it does so at substantially lower computational cost than the physical model. Training the final model took less than 28 hours in total. The authors also flag that their multi-stage training schedule, which changed batch size, loss and the number of EC-Earth3 members, was adopted because of compute availability, and that only the increase to five members almost certainly improved results.

The practical reading is therefore about which use case the evidence supports. For generating many daily temperature trajectories that follow a given warming level, the emulator reproduces the annual cycle, trend, local variability and large-scale correlation structure, with the caveats that its ensemble is under-dispersed and that polar winter temperatures carry a warm bias that grows with rollout length. For questions that require internal variability to be sampled independently of a driving member, the paper's own diagnosis points to a next step: sourcing the conditioning trend from greenhouse gas forcing, reduced-complexity climate models, or statistical emulators, so that a wider range of projections can feed the same generative model.

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