DeepSeasons: Seasonal Forecasting Framework

• DeepSeasons is a transformer-based seasonal forecasting framework that predicts low-dimensional anomaly fields using EOF/PCA truncation to focus on predictable scales.
• It employs empirically optimized input lags and temporal averaging to capture dominant teleconnections such as ENSO, differing from full atmospheric state simulations.
• The approach achieves competitive skill against operational GCMs in global SST and European T2M forecasts while remaining computationally efficient.

DeepSeasons is a transformer-based, data-driven framework for seasonal forecasting that predicts low-dimensional representations of monthly or seasonal-mean anomaly fields rather than instantaneous atmospheric states. Its defining premise is that seasonal predictability is concentrated on selected spatial and temporal scales, so the forecasting system should target those scales directly through EOF/PCA truncation, empirically chosen lags, and anomaly or time-mean prediction, instead of attempting full atmosphere–ocean simulation as a general circulation model does (Navarra et al., 31 Aug 2025).

1. Concept and forecasting philosophy

DeepSeasons was introduced to address a standard constraint in seasonal prediction: beyond about two weeks, exact weather trajectories lose predictability, while useful signal survives primarily in averaged quantities such as monthly or seasonal means and in large-scale forced or slowly varying modes (Navarra et al., 31 Aug 2025). The framework is therefore explicitly not a full-state dynamical simulator. It is a targeted predictor for variables or regions such as global sea-surface temperature anomaly fields or regional 2-m temperature anomaly fields.

The paper defines this as a “scale-selecting” approach. Spatially, DeepSeasons retains only a chosen fraction of variance through EOF truncation; temporally, it uses monthly means or three-month rolling means rather than instantaneous fields; and in sequence design it selects input lags empirically. In the authors’ formulation, this means identifying and learning only the spatial modes and temporal averages that carry useful seasonal predictability (Navarra et al., 31 Aug 2025).

A plausible implication is that DeepSeasons occupies a distinct methodological niche within deep seasonal forecasting. It differs from one-month-ahead global temperature CNN systems trained on CMIP6 and ERA5 because it is centered on anomaly prediction in reduced EOF space rather than direct field regression at native grid resolution (Unal et al., 2023). It also differs from dual-branch seasonality-aware recurrent models such as the seasonally-integrated autoencoder for daily precipitation, where seasonality is represented as a separate latent branch rather than as explicit reduced-space target design and temporal averaging (Ponnoprat, 2021).

2. Reduced-space representation and target design

The training data are monthly mean anomalies from ERA5 over 1940–2022 (Navarra et al., 31 Aug 2025). Predictors and targets are projected onto EOF bases that are computed on the training period only, explicitly to avoid future-data leakage. DeepSeasons therefore predicts the principal components associated with the retained EOFs, and forecast fields are reconstructed back into physical space from the predicted PCs and the retained EOF basis.

Several target configurations are considered. In the global SST experiment, the target is the monthly mean SST anomaly field over $60^\circ\text{S}$–$60^\circ\text{N}$. In the regional land experiments, the target is monthly mean 2-m temperature anomaly over Europe or North America. In the seasonal-average experiment, the target is a three-month rolling mean anomaly of T2M over Europe, computed in a backward-looking operational way so that no future information enters preprocessing (Navarra et al., 31 Aug 2025).

The practical meaning of scale selection is visible in the truncation experiments. For global SST, the paper tests truncations retaining approximately 47%, 55%, 65%, and 76% of variance in SST, while U850 is fixed near 62%. Lower-order truncations preserve broad, dominant, low-frequency patterns and remove finer-scale variability; the paper reports that these larger-scale patterns are much more predictable, and that skill degrades as more EOFs are retained (Navarra et al., 31 Aug 2025).

Experiment	Predictand	Representative inputs and settings
Global SST	Monthly mean SST anomaly over $60^\circ\text{S}$–$60^\circ\text{N}$	Best results with SST+U850 or SST+SP; illustrative best figure uses 15 SST EOFs, 25 U850 EOFs, hidden dimension 256, and lags $[1,2,3,4]$
European monthly T2M	Monthly mean 2-m temperature anomaly over Europe	Preferred final configuration uses regional T2M plus T850, five EOFs each, hidden dimension 256, one transformer layer in encoder and decoder, and $\gamma=0.9$
European seasonal-mean T2M	Three-month rolling mean anomaly of T2M over Europe	Optimal setup uses an 18-time-step input sequence of three-month means, hidden dimension 256, one transformer layer, and enough EOFs to retain 90% variance

The predictor sets are task-dependent. For global monthly SST prediction, the paper tests combinations of SST, sea level pressure, zonal wind at 850 hPa, and top outgoing low-frequency radiation, finding the best results with SST+U850 or SST+SP. For European T2M, the tested inputs include T2M alone, SP+T2M, T850+T2M, U850+T2M, and $(U850,V850,T850,SST,T2M)$. For North American T2M, T850 is taken over the target region, while SST and pressure can be considered over the tropical belt $35^\circ\text{N}$–$35^\circ\text{S}$ to capture remote tropical influences (Navarra et al., 31 Aug 2025).

3. Architecture and probabilistic objective

DeepSeasons is based on a transformer architecture inspired by Informer, although the paper states that in the experiments it is often used effectively as a standard transformer without Informer’s probabilistic attention or distillation because the reduced EOF-space problem is already computationally modest (Navarra et al., 31 Aug 2025). Each input time step contains the retained EOF coefficients for the selected variables together with temporal metadata such as year, month, and season. These inputs are embedded into a latent space, augmented with sinusoidal positional encodings, and processed through encoder layers with multi-head self-attention, residual connections, feedforward sublayers, and layer normalization. A decoder uses self-attention and cross-attention, and a final projection maps hidden states to parameters of the forecast probability distribution.

The model output at forecast step $t$ is written as

$60^\circ\text{N}$0

where $60^\circ\text{N}$1 is typically the retained EOF/PC dimension of the target field. Let $60^\circ\text{N}$2 denote the predicted conditional distribution and $60^\circ\text{N}$3 the target distribution. The per-time-step divergence is

$60^\circ\text{N}$4

With discount factor $60^\circ\text{N}$5, the training objective is

$60^\circ\text{N}$6

The paper states that the network is trained with negative log-likelihood under a Gaussian output distribution (Navarra et al., 31 Aug 2025).

This probabilistic formulation is nominal rather than fully exploited in the reported evaluation. The output layer predicts the parameters of a conditional probability distribution for the future sequence, and throughout the experiments this distribution is Gaussian. Ensembles are generated by sampling from this distribution autoregressively with greedy inference, with 50-member ensembles per start date, but the reported scores are primarily deterministic scores of the ensemble mean (Navarra et al., 31 Aug 2025). A common misconception is therefore that DeepSeasons is presented as a fully validated probabilistic seasonal forecast system; the paper explicitly defers ensemble properties and uncertainty diagnostics to future work.

4. Experimental design and verification protocol

The empirical study uses held-out recent periods drawn from the ERA5 anomaly record (Navarra et al., 31 Aug 2025). For SST, one boxplot summarizes initial dates from December 2019 to December 2021, yielding 28 forecasts. For European monthly T2M, the RMSE boxplot covers starts from 2017-06-01 to 2021-12-01, totaling 55 forecasts. For North American T2M, time-correlation diagnostics are based on 27 forecasts in some seasonal subsets. For seasonal European T2M, 61 forecast cases are produced on the same test period as the monthly-mean case.

The benchmark baselines are persistence and an operational CMCC GCM from the Copernicus seasonal forecasting service (Navarra et al., 31 Aug 2025). Evaluation is done mainly with spatial anomaly correlation coefficient, RMSE, and pointwise time-correlation maps. In the monthly-mean cases, forecasts extend from month 0 or month 1 out to month 12, although GCM comparisons are often limited to six months because the operational benchmark does not extend further.

Two details are methodologically important. First, EOFs are computed on the training period alone, which prevents future-data leakage in the reduced representation. Second, the lag structure is itself treated as a hyperparameter: the paper reports that short lag structures can improve short leads but degrade long leads, while in several experiments the best trade-off is four lags $60^\circ\text{N}$7 (Navarra et al., 31 Aug 2025). This makes the temporal memory scale part of the “scale-selecting” design rather than a fixed architectural constant.

A plausible interpretation is that DeepSeasons belongs to the same broad research family as spatio-temporal seasonal predictors trained on analysis-ready Earth-system datacubes, such as seasonal wildfire prediction models that vary temporal history length and spatial receptive field explicitly (Michail et al., 2024). The difference is that DeepSeasons pushes the reduction one step further by moving the target itself into EOF space before sequence modeling.

5. Reported forecast skill

Global SST

For global SST, DeepSeasons’ mean skill over leads 0–12 is reported as comparable to the operational GCM and always at least as good as persistence in the reported sensitivity plots (Navarra et al., 31 Aug 2025). The authors highlight particularly strong performance around months 4–5, where DeepSeasons surpasses the GCM. Boxplots of ACC over the test forecasts show median skill close to the GCM in the early forecast and superior around months four and five, while exhibiting fewer outliers and relatively stable performance.

The retained-variance analysis is one of the paper’s clearest results. With strong EOF truncation—47% or 55% retained variance—DeepSeasons clearly outperforms persistence and the GCM, while the advantage shrinks as more fine-scale variance is included (Navarra et al., 31 Aug 2025). This directly supports the claim that predictability is concentrated in dominant large-scale SST structures.

European monthly T2M

For European monthly T2M, the paper treats the regional, tailored use of DeepSeasons as a major operational advantage. RMSE is emphasized because regional ACC can be sensitive to spatial details over a small domain. With T850+T2M as predictors, the reported RMSE values are 0.62 at M1, 0.73 at M2, 0.75 at M3, 0.74 at M4, 0.77 at M5, 0.76 at M6, and remain around 0.70 down to 0.63–0.70 through M12. The corresponding persistence values are 0.89, 1.32, 1.30, 1.34, 1.48, 1.42, and the GCM values are 0.86, 0.99, 0.91, 0.81, 0.86, 0.84 up to M6 (Navarra et al., 31 Aug 2025). Some other DeepSeasons variable sets achieve the minimum RMSE at particular leads, but all DeepSeasons configurations outperform persistence, and several beat the GCM.

North American monthly T2M

For North American monthly T2M, the results are explicitly less favorable. DeepSeasons beats persistence at all leads beyond month one, but compared with the GCM it performs better only through about month two and is consistently worse afterward according to the RMSE boxplot analysis (Navarra et al., 31 Aug 2025). This negative result is central to the paper’s argument: the framework is not presented as uniformly superior to operational dynamical systems.

Seasonal three-month-average European T2M

The seasonal-average European experiment is the strongest validation of the temporal-scale argument. After preprocessing monthly anomalies into backward-looking rolling 3-month means and training the same architecture on these smoothed targets, the paper reports that DeepSeasons outperforms both persistence and the GCM in RMSE at all evaluated leads (Navarra et al., 31 Aug 2025). The associated time-correlation maps show broader and more organized regions of significant correlation than in the monthly-mean case, particularly in winter, and in summer at six-month lead DeepSeasons shows considerably larger areas of positive temporal correlation than the GCM.

Forecast problem	Reported comparative outcome	Noted caveat
Global SST	Comparable to the operational GCM on mean skill over leads 0–12; stronger around months 4–5; always at least as good as persistence in reported sensitivity plots	Skill degrades as more EOFs are retained
European monthly T2M	Better than persistence at every lead; lower than the GCM where GCM results are available for several leads	Tends to smooth temporal evolution
North American monthly T2M	Better than persistence beyond month one	Better than the GCM only through about month two
European seasonal-mean T2M	Outperforms both persistence and the GCM in RMSE at all evaluated leads	Still based on monthly mean analysis data and rolling-window smoothing

6. Scientific interpretation, operational significance, and limitations

The paper argues that DeepSeasons works because it captures dominant teleconnections and nonlinear dependencies in historical data without integrating the governing equations (Navarra et al., 31 Aug 2025). In the SST application, its strongest skill is tied to large-scale tropical Pacific and Indian Ocean structures; the authors explicitly mention ENSO-related patterns, persistence of La Niña, and an Indian Ocean dipole-like signal. In regional T2M prediction, the inclusion of global SST for Europe and tropical SST for North America is motivated by remote teleconnections from the tropics.

The empirical support for this interpretation comes primarily from sensitivity experiments. As more EOFs are included, skill declines; as lags are shortened, short-term skill rises but long-lead skill worsens; and as model depth increases, performance often declines, especially in regional T2M, suggesting that the useful predictive structure in these reduced spaces may not require deep architectures and that shallower networks generalize better with the available data (Navarra et al., 31 Aug 2025).

Operationally, the framework is presented as much cheaper than running coupled seasonal GCM ensembles. The paper notes that all computations were performed on Apple M1/M2 laptop or desktop machines (Navarra et al., 31 Aug 2025). It can be trained for targeted applications—global SST anomalies, European T2M, North American T2M, or seasonal means—rather than for full-system prediction, and it predicts anomalies directly from observed historical anomalies, bypassing some of the drift-correction and hindcast-climatology procedures required in dynamical systems.

Several limitations are stressed. DeepSeasons tends to smooth variability and evolve anomalies too slowly, which can cause it to miss abrupt month-to-month changes and sharp anomaly gradients (Navarra et al., 31 Aug 2025). Skill is not uniformly better than GCMs, as shown by the North American T2M case. Spatial skill can collapse outside “islands of predictability,” especially in higher latitudes and over regions such as the North Pacific and North Atlantic for SST. Despite the probabilistic formulation and 50-member ensembles, the paper does not present CRPS, Brier score, reliability diagrams, or spread-skill relationships, and it does not provide a fully detailed optimization recipe.

In the broader landscape of deep seasonal forecasting, this suggests a specific interpretation of DeepSeasons. It is best understood not as a replacement for full climate modeling, but as a reduced-space transformer for variables and regions whose predictability is demonstrably concentrated in low-order, time-averaged modes (Navarra et al., 31 Aug 2025). A plausible implication is that its most durable contribution is methodological: it formalizes the idea that seasonal deep learning should forecast the scales that remain predictable, rather than the full atmospheric state.