Seasonal forecasts months ahead rely on global climate models that require precise initialization of the ocean, atmosphere, and land. However, even the best systems suffer from initial-state drift, simplified parameterizations of subgrid processes, and a limited number of ensemble members. Existing approaches in this vein train neural networks on model data to forecast El Niño or specific regions, but they do not cover a quasi-global scale or provide rigorous uncertainty estimates. This work follows the same line but extends it to the entire globe and adds a probabilistic interpretation.
The authors build a conditional variational autoencoder (CVAE): an encoder compresses the predictor–predictand pair into a latent variable, and a decoder reconstructs the target field conditioned on that variable. The predictor is the ocean potential temperature profile at 15 depths from 5 to 300 meters in July; the predictand is the average precipitation and 2-meter temperature from October to March. The model is trained on 127,137 years of climate simulations from CMIP5 and CMIP6, including historical, pre-industrial, and scenario runs from 12 centers. The architecture uses convolutional layers to capture spatial structure, and a three-step training procedure first regresses the predictand on the predictor with zero latent variable, then trains the variational part, and finally fine-tunes all parameters. For practical forecasts over 1982–2018, the model is run on ORAS5 ocean reanalysis data, with verification against GPCP precipitation and ERA5 temperature.
Compared with four NMME models (CCSM4, CanCM3, CanCM4, FLOR-B01) and their multimodel ensemble, the CVAE shows higher correlation coefficients and areas under the ROC curve for precipitation and temperature on almost all continents. For temperature in the eastern tropical Pacific, the correlation exceeds 0.9 and the AUC is above 0.85. Using the Canadian CanESM model as an example, the authors separate the contributions of initialization errors and formulation: a CVAE forecast trained only on CanESM outperforms the dynamical CanCM4 system in Eurasia, the central United States, and mid-latitudes of the Southern Hemisphere. Comparing forecasts in the "model world" and real climate reveals regions where the model underestimates or overestimates the seasonal signal. Saliency maps show that the neural network relies on physically meaningful patterns: a negative relationship between Maritime Continent precipitation and east-central equatorial Pacific temperature, and a positive one with local warmth, consistent with the Walker circulation. The correlation of within-ensemble variance with the Niño3.4 index shows that forecasts starting in El Niño years have smaller spread in Southeast Asia, Australia, and southern Africa, whereas La Niña years yield greater uncertainty.
This work shows that a purely statistical model trained on model data can serve as a benchmark for diagnosing dynamical systems. Unlike neighboring studies that focus on specific regions or phenomena, this one covers a quasi-global scale and, for the first time, rigorously assesses the probabilistic nature of the forecast. This allows quantitatively separating the contributions of initialization, formulation, and internal variability to forecast errors, something previous approaches did not do.
The method can be extended to other predictors, such as snow cover or soil moisture anomalies, as well as to subseasonal horizons. A promising direction is training separate generative models for each GCM and then combining them into an ensemble, which would explicitly account for inter-model spread. It is also worth adapting convolutional architectures to spherical geometry to avoid distortions near the poles and discontinuities at projection boundaries.
The results directly relate to seasonal forecasting for agriculture, water resource management, and energy. The diagnostic tools will help climate model developers identify weaknesses more quickly.
The next step is to test the approach on independent periods and include additional predictors. It is also important to compare the model with new dynamical systems that have emerged since 2018.
This work links three unresolved problems in seasonal forecasting: how to initialize a model without state shocks, how to parameterize unresolved processes, and how to determine a sufficient ensemble size. The proposed probabilistic approach provides a tool for quantitatively assessing each of these problems, but does not fully solve them, since it relies on the same climate models whose defects it exposes.
Training used 127,137 years of model data: if a single computer generated it continuously, it would take over 127 millennia. Yet the model produces a one-season forecast in fractions of a second.
The idea of learning from a "model world" to predict the real one echoes Liu Cixin's novel "The Three-Body Problem," where a virtual simulation helps understand chaotic dynamics. Only here the simulation is used not for civilization's survival but for forecasting winter weather.