EC-EarthFlow: Probabilistic emulation of daily transient global climate model simulations with flow matching
Authors: Kirien Whan, Nikolaj T. Mücke, Karin van der Wiel
Organizations: KNMI, Utrechtseweg 297, De Bilt, 3731GA, The Netherlands · Scientific Computing, Centrum Wiskunde & Informatica, Science Park 123, Amsterdam, 1098XG, The Netherlands · Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands · Faculty of Geosciences, Utrecht University, Utrecht, The Netherlands
We introduce EC-EarthFlow, a generative flow matching model that emulates simulations from the physical climate model EC-Earth3. The model is trained on transient simulations from EC-Earth3 (1950-2166, SSP2-4.5) to predict the day ahead temperature field from the previous days temperature as well as annual mean temperature. Predictions are made auto-regressively with rollout periods of between a month and an extended season. Using only this variable of interest, we are able to reproduce the daily variability, spatial patterns, annual cycle and long-term trend from EC-Earth3 at a substantially lower computational cost than the physical model. We demonstrate that EC-EarthFlow is stable for long inference periods, and that it can learn the physical relationships as simulated in EC-Earth3.
Figures & tables
Figure 1: The architecture of EC-EarthFlow showing that pseudo-time is concatenated with contextual inputs and fed into the neural network model to predict the flow matching vector field.
Figure 2: An illustration of the generative flow matching process. The process transforms noise to the target distribution by integrating an ODE over pseudo-time.
Figure 3: The auto-regressive rollout used at inference. The context information is combined with noise to produce a prediction for the next day. These predictions are then added to the context window for the following prediction. We produce an ensemble of predictions by using different noise samples.
Figure 4: Daily temperature at two locations (De Bilt, The Netherlands (top), and Sydney, Australia (bottom)) from May - November in 1950 (left), 2050 (middle) and 2150 (right). Predictions are made using a rollout length of 245 steps from only 5 EC-Earth member states at the end of April (member 16). For comparison the full EC-Earth simulation is shown in purple. The green shading indicates the ensemble range from nine EC-EarthFlow members, and the green line shows predictions from a single random EC-EarthFlow member. The gray line indicates a daily temperature value of 15 ∘ C as reference. The histograms show counts of the rank that the EC-Earth3 member is in the 10-member EC-EarthFlow ensemble.
Figure 5: Rank histograms of all grid points in 1950 (left), 2050 (middle) and 2150 (right). EC-EarthFlow predictions are made using the long (top) and short (bottom) rollout length from May in each year and inputs from a single EC-Earth member (member 16).
Figure 6: Global mean surface temperature with short rollout, starting in each month of the extended northern Hemisphere summer period (May - October). Each panel shows projections from a different year (1950, 2050, 2150). Inputs are from a single test member of EC-Earth3 (member 16, purple line). The green shading indicates the ensemble range from nine EC-EarthFlow members, and the green line shows predictions from a single random EC-EarthFlow member. The gray line indicates a GMST of 10 ∘ C as reference.
Figure 7: Global mean surface temperature (long rollout) (May - November). Columns show projections in select years (1950, 2050, 2150) made using EC-Earth3 members 16 and 15 as inputs (purple lines). The green shading indicates the ensemble range from all EC-EarthFlow members, and the green line shows predictions from a single random EC-EarthFlow member. The green dots show the EC-EarthFlow ensemble range from projections generated from EC-Earth3 member 16. The gray line indicates a GMST of 13 ∘ C as reference.
Figure 8: Global mean surface temperature projections from May - November with a short (top row, i.e., consecutive 30-day rollouts) and long (bottom row, i.e., a single rollout from May to November) lengths in 1950, 2050, and 2150. The black line is the ‘truth’ from EC-Earth3. The green lines are ensemble members created by the flow matching model. The red line indicates a GMST of 10 ∘ C as reference.
Figure 9: Box-plots of the grid point wise trajectory mean temperature differences between EC-Earth3 members (purple) and between predictions from EC-EarthFlow and the EC-Earth3 member used to generate them (green) in 2050. Similar results are seen for other years and other EC-EarthFlow members.
Figure 10: The correlation between temperature in De Bilt (left) or Sydney (right) and the rest of the world in EC-Earth3 (top) and EC-EarthFlow (bottom). We use a high-pass filter to remove variability and then take the correlation over all days.
Internal variability is a dominant contributor to the uncertainty of predictions at the interannual to decadal timescale. A typical approach to separating the internal variability from forced climate responses is to generate large ensembles of simulations under different initial conditions. Due to the complexity of Earth System Models, generating these large ensembles is computationally expensive. In this work, we present ArchesClimate, a deep learning-based climate model emulator designed to reduce the cost of exploring internal variability at timescales ranging from monthly to decadal. ArchesClimate is trained on decadal hindcasts of the IPSL-CM6A-LR climate model. We train a flow matching model following ArchesWeatherGen, which we adapt to predict near-term climate. Once trained, the model generates states at a one-month lead time from the states of the two preceding months, and can be used to auto-regressively emulate climate model simulations. We show that for up to 10 years, these generations are stable and physically consistent. We also show that for several important climate variables, ArchesClimate generates simulations that are interchangeable with the IPSL model. This work suggests that climate model emulators could reduce the cost of generating large ensembles with climate models.
Graham Clyne, Guillaume Couairon, Guillaume Gastineau +2
ARCHES, INRIA, Paris, France · UMR LOCEAN, IPSL, Sorbonne Universit´e, IRD, CNRS, MNHN, Paris, France · Department of Computer Science, University of Colorado Boulder, USA
We present a stochastic coupled emulator of E3SM version 3, built on the SamudrACE framework, which couples an atmosphere emulator (ACE2) with a full-depth ocean emulator (Samudra). We replace the deterministic atmosphere emulator with its stochastic counterpart, ACE2S, and fine-tune the coupled system with a probabilistic objective, so that the atmosphere acts as a source of internal variability for the ocean. Trained on 105 years of a pre-industrial control simulation and evaluated on an independent 400 years, the emulator reproduces E3SMv3's mean climate state with biases much smaller than existing model-to-observation differences. Relative to a deterministic baseline, stochastic training maintains internal variability across timescales, most notably in the ENSO power spectrum, eddy-rich SST anomalies, and sea ice variability in the marginal ice zone. The emulator captures daily precipitation accurately up to the 99.99th percentile, but underestimates the rarest tropical extremes. These results show that stochastic coupled emulators can reproduce long-timescale variability with high fidelity, while extrapolation to unseen extremes remains a key challenge.
Elynn Wu, James P. C. Duncan, Troy Arcomano +11
Allen Institute for Artificial Intelligence (Ai2), Seattle, WA, USA · Pacific Northwest National Laboratory, Richland, WA, USA · Los Alamos National Laboratory, Los Alamos, NM, USA +2
We evaluate the climate simulation capabilities of ArchesWeather and ArchesWeatherGen, two machine learning models originally trained for weather forecasting and evaluated up to a 10-day lead time. ArchesWeather is a deterministic model, while ArchesWeatherGen is a probabilistic flow-matching model leveraging ArchesWeather's forecasts, enabling ensemble-based uncertainty quantification. In this work, we adapt these models to act as forced atmospheric models by using additional conditioning on the monthly mean sea surface temperature (SST) and sea ice cover (SIC) as boundary conditions. In particular, we follow the AI Model Intercomparison Project (AIMIP) Phase 1 protocol, which, analogous to the Atmospheric Model Intercomparison Project (AMIP), proposes a standardized experimental setup to evaluate the climate skill of ML-based forced atmospheric models. We present a comprehensive evaluation of both models under these conditions, including comparison against numerical climate models, ablation studies that examine key design choices in the extension, and an analysis of forced versus unforced configurations. Despite being originally developed for weather forecasting, we demonstrate that forced configurations of ArchesWeather and ArchesWeatherGen produce stable long-term climate simulations, have a stable annual cycle, and capture the drift of many climate variables. The models faithfully reproduce ERA5's climatology, large-scale circulations and interannual variability, and they capture the tails of the distributions.
Renu Singh, Robert Brunstein, Antonia Jost +5
Google DeepMind, Paris, France · INRIA, Paris, France · Otto von Guericke University Magdeburg, Magdeburg, Germany +3