Multimodal ENSO Forecast (MEF) Overview

• Multimodal ENSO Forecast (MEF) is a set of frameworks that integrate various data types and methodologies to predict the Niño 3.4 anomaly and ENSO phases.
• Key implementations include deep-learning models like 3D-CNNs combined with time-series modules and statistical syntheses using climate networks and complexity metrics.
• Ensemble distillation and weighted post-processing in MEF enhance forecast accuracy by selecting high-skill subsets based on lead time and seasonal dynamics.

Multimodal ENSO Forecast (MEF) denotes a family of ENSO prediction frameworks that combine heterogeneous predictors, model classes, or ensemble-processing layers to forecast the Niño 3.4 anomaly, ENSO phase, onset, or event magnitude. In the recent literature, the term refers both to a specific deep-learning system that fuses a 3D Convolutional Neural Network (3D-CNN) with a time-series module (Ganji et al., 10 Aug 2025) and to broader statistical or hybrid syntheses that combine climate-network precursors, complexity metrics, logistic probability models, or lead-specific ensemble distillation (Ludescher et al., 19 Jan 2025). Across these formulations, the principal target is usually the Niño 3.4 SST anomaly, commonly defined as the area-average SST anomaly over $5^\circ\mathrm{S}$–$5^\circ\mathrm{N}$ and $170^\circ\mathrm{W}$–$120^\circ\mathrm{W}$, for example

$$y(t)=\frac{1}{A}\iint_{\Omega}\left[\mathrm{SST}(x,y,t)-C(x,y,\mathrm{month}(t))\right]dx\,dy,$$

with $$\Omega=[5^\circ\mathrm{S},5^\circ\mathrm{N}]\times[170^\circ\mathrm{W},120^\circ\mathrm{W}]$$ (Ganji et al., 7 Sep 2025).

1. Scope and conceptual variants

MEF is not a single fixed architecture. The literature uses the term for at least three distinct but related design patterns. One is a genuinely multimodal deep-learning ensemble combining spatial fields and time-series indices. A second is a multimethod statistical synthesis in which different predictors target onset, magnitude, or phase probabilities separately and are then combined. A third is a post-processing layer that distills or reweights ensemble forecasts, including multimodal ensembles, after the underlying models have already produced member forecasts.

Formulation	Core inputs or mechanism	Representative papers
Deep ensemble MEF	3D-CNN spatial fields + time-series module	(Ganji et al., 10 Aug 2025)
Statistical-probabilistic MEF	Climate network + SysSampEn + ONI-conditioned logistic regression	(Ludescher et al., 19 Jan 2025, Ludescher et al., 16 Feb 2026)
Distilled or post-processed MEF	Skill-based subset selection, graph clustering, or entropic distillation	(Ganji et al., 7 Sep 2025, Groom et al., 15 Feb 2026)

This multiplicity of usage is important. Some MEF systems are multimodal in the input sense, using SST, upper-ocean heat content, winds, or pressure. Others are multimodal in the methodological sense, combining separate forecasting modalities such as teleconnection precursors, entropy-based diagnostics, and probability partitioning. A further distinction is that some studies evaluate explicitly multimodal predictors, whereas others develop model-agnostic aggregation rules that are proposed as drop-in layers for multimodal systems even when the reported experiments use a single-modal target or predictor set (Ganji et al., 7 Sep 2025).

Operational phase definitions are usually inherited from the Oceanic Niño Index (ONI). In the statistical-probabilistic MEF literature, El Niño is defined by $\mathrm{ONI}\ge 0.5^\circ\mathrm{C}$ for at least five consecutive overlapping months, La Niña by $\mathrm{ONI}\le -0.5^\circ\mathrm{C}$ for at least five consecutive overlapping months, and Neutral otherwise (Ludescher et al., 19 Jan 2025).

2. Deep-learning MEF architectures

The most explicit baseline labeled MEF uses two independent deep-learning modules and produces an ensemble of 80 forecasts for each lead/season pair (Ganji et al., 10 Aug 2025). The first module is a 3D-CNN operating on 12-frame tensors built from two spatial anomaly fields: sea surface temperature (SST) anomalies and vertically averaged temperature anomalies representing upper-300 m heat content (HC). These inputs span $0$–$360^\circ\mathrm{E}$ and $5^\circ\mathrm{N}$0–$5^\circ\mathrm{N}$1, regridded to $5^\circ\mathrm{N}$2, so that each sample is a $5^\circ\mathrm{N}$3 tensor. The 3D-CNN uses three 3D convolutional layers with $5^\circ\mathrm{N}$4 activation, 3D average pooling, 3D max pooling, and a dense layer that regresses a scalar Niño 3.4 anomaly; the first kernel is $5^\circ\mathrm{N}$5, later kernels are $5^\circ\mathrm{N}$6, and the implementation employs Xavier initialization, dropout, a learning rate of $5^\circ\mathrm{N}$7, and a mini-batch size optimized by ROA (Ganji et al., 10 Aug 2025).

The second module is a time-series model, termed the Adaptive Ensemble Module (AEM), which ingests ENSO-relevant indices and applies attention-based sequence modeling with multi-head attention and ProbSparse self-attention, described as Informer-style long-sequence transformers. This module uses standardization, seasonal encoding, and lagged inputs for multi-month leads, and outputs a predicted Niño 3.4 anomaly aligned with the 3D-CNN output (Ganji et al., 10 Aug 2025).

The baseline ensemble is constructed stochastically. The 3D-CNN contributes 40 members through variation in convolutional filter counts, fully connected neurons, random initializations, dropout masks, and ROA-driven mini-batch sizes. The time-series module contributes 40 members through variation in transformer hyperparameters, ProbSparse thresholds, dropout, lag windows, seasonal encodings, random seeds, and optimizer states. The original MEF fusion then averages within each module and combines the two module means with uncertainty-based weights, so that the globally lower-uncertainty module receives higher weight; no per-member weighting is performed in the baseline (Ganji et al., 10 Aug 2025).

Beyond this baseline, other deep-learning studies furnish blueprints for more general MEF systems. CTEFNet integrates CNNs and transformers over nine channels—SST, HC, MLD, SSS, SLP, UO, VO, TAUU, and TAUV—on a global $5^\circ\mathrm{N}$8–$5^\circ\mathrm{N}$9 domain regridded to $170^\circ\mathrm{W}$0, using a 12-month lookback and direct 24-month Niño 3.4 sequence prediction (Chen et al., 25 Mar 2025). ResoNet, although trained on global monthly SSTA only, uses a hybrid convolution–Transformer architecture over multiple basins and is explicitly presented as amenable to multimodal extension through channel stacking or modality-specific encoders with cross-attention (Lyu et al., 2023). This suggests that, within the MEF literature, multimodality is implemented either by direct channel-level fusion of heterogeneous geophysical fields or by parallel encoders followed by joint temporal integration.

3. Statistical, operator-theoretic, and reduced-state formulations

A second major meaning of MEF is a statistical synthesis of complementary predictors. In the 2025 probabilistic forecast framework, MEF combines a climate-network early-warning signal for El Niño onset, a complexity-based magnitude predictor derived from System Sample Entropy (SysSampEn), and a logistic regression conditioned on ONI to partition non–El Niño outcomes into neutral versus La Niña (Ludescher et al., 19 Jan 2025). The climate-network component is built from daily surface air temperature anomalies, with 14 “core” nodes in the central/eastern equatorial Pacific and 193 “periphery” nodes in the rest of the tropical Pacific; the early-warning statistic is the mean link strength

$170^\circ\mathrm{W}$1

and a threshold near $170^\circ\mathrm{W}$2 is used for onset alarms (Ludescher et al., 19 Jan 2025). The SysSampEn component uses daily near-surface air temperatures over 22 Niño 3.4 nodes, with parameters $170^\circ\mathrm{W}$3, $170^\circ\mathrm{W}$4, $170^\circ\mathrm{W}$5, and $170^\circ\mathrm{W}$6, and maps previous-year complexity to next-year El Niño magnitude via linear regression (Ludescher et al., 19 Jan 2025).

This statistical MEF yields coherent triplet probabilities by combining precursor-based exclusion of El Niño with ONI-conditioned logistic partitioning. For the 2025/26 target season, the reported probabilities are $170^\circ\mathrm{W}$7 Neutral, $170^\circ\mathrm{W}$8 La Niña, and $170^\circ\mathrm{W}$9 El Niño (Ludescher et al., 19 Jan 2025). A subsequent 2026 forecast applies the same multimodal logic to non-concurring onset signals from climate-network and complexity modalities, producing a combined forecast that favors Neutral over El Niño and reports, conditional on El Niño occurrence, a magnitude of $120^\circ\mathrm{W}$0 (Ludescher et al., 16 Feb 2026).

Operator-theoretic forecasting provides another route to MEF. Kernel Analog Forecasting (KAF) uses delay-embedded Indo-Pacific SST and nonlinear kernels to approximate conditional expectations of future observables under the Koopman operator. In the reported observational setting, KAF predicts Niño 3.4 out to a 10-month lead during 1998–2017 and extends useful lead time by 3–7 months over a linear inverse model; in CCSM4 control simulations, useful skill extends to 24 months versus 18 months for the benchmark LIM (Wang et al., 2019). The same source explicitly frames KAF as a basis for multimodal extension through concatenated delay embeddings or multimodal kernels.

Reduced-state, physics-guided MEF is exemplified by the Deep Echo State Network (DESN), which operates on interpretable climate modes selected from the extended recharge oscillator framework: Niño 3.4, warm water volume, NPMM, SPMM, IOB, IOD, SIOD, TNA, ATL3, SASD, and seasonal harmonic inputs. In out-of-sample validation over 2002–2023, DESN maintains ACC $120^\circ\mathrm{W}$1 up to 16 months and remains competitive to 20 months depending on initialization month; error-growth analysis in the same study suggests an ENSO predictability horizon of approximately 30 months (Zhang et al., 18 Jan 2026). In this line of work, multimodality is represented not by high-dimensional fields but by a compact index state vector spanning Pacific memory and inter-basin teleconnections.

4. Ensemble weighting, subset selection, and distillation

A central development in MEF research is the replacement of uniform ensemble averaging by lead- and season-dependent distillation. A model-independent post-processing study evaluates a 40-member ENSO ensemble verified against the observed Niño 3.4 index over 1986–2017 and shows that, for any large enough ensemble, there is a subset of members whose skill is substantially higher than that of the ensemble mean (Ganji et al., 7 Sep 2025). For each lead $120^\circ\mathrm{W}$2 and target season $120^\circ\mathrm{W}$3, the method forms a Top-5-by-RMSE subset and a Top-5-by-Correlation subset. Their union defines a Top-10 set with overlap-aware weights: members appearing in both Top-5 lists receive raw weight 2, members appearing in only one receive raw weight 1, and normalized weights sum to one. The resulting weighted forecast takes the generic form

$120^\circ\mathrm{W}$4

with comparison against the equal-weight All-40 mean (Ganji et al., 7 Sep 2025).

The reported gains are strongly lead dependent. At a 1-month lead, the distilled subset raises correlation by about $120^\circ\mathrm{W}$5 and reduces RMSE by about $120^\circ\mathrm{W}$6 relative to the All-40 mean. At a 23-month lead, correlation increases by about $120^\circ\mathrm{W}$7 and RMSE decreases by about $120^\circ\mathrm{W}$8 (Ganji et al., 7 Sep 2025). Improvements peak in transition seasons such as SON and DJF for correlation, and in mid-year seasons such as JJA and MJJ for RMSE. Paired $120^\circ\mathrm{W}$9-tests and bootstrap resampling indicate that, for leads greater than 12 months, over 85% of lead-season pairs show statistically significant correlation improvement at the 95% level, and RMSE reductions are significant for about 80% of long-lead cases (Ganji et al., 7 Sep 2025).

The same study explicitly generalizes this logic to multimodal systems. It proposes per-modality selection of high-skill members and a second-stage fusion

$$y(t)=\frac{1}{A}\iint_{\Omega}\left[\mathrm{SST}(x,y,t)-C(x,y,\mathrm{month}(t))\right]dx\,dy,$$0

where $$y(t)=\frac{1}{A}\iint_{\Omega}\left[\mathrm{SST}(x,y,t)-C(x,y,\mathrm{month}(t))\right]dx\,dy,$$1 indexes modalities such as SST, subsurface temperature, and winds, and the modality weights $$y(t)=\frac{1}{A}\iint_{\Omega}\left[\mathrm{SST}(x,y,t)-C(x,y,\mathrm{month}(t))\right]dx\,dy,$$2 are lead- and season-dependent (Ganji et al., 7 Sep 2025). In that sense, the distillation layer is not itself a multimodal forecast model; rather, it is a multimodal ensemble-combination rule.

Graph-based refinement extends this idea. The GNN-enhanced MEF study treats the 80 ensemble members of the baseline deep MEF as nodes in an undirected weighted graph, constructs edge weights from RMSE and correlation similarities, applies Louvain community detection, and selects an optimized subset of 20 members whose final forecast is the simple mean of the selected subset (Ganji et al., 10 Aug 2025). The authors report that this graph-based selection does not always outperform the baseline under every scenario, but does produce more stable and consistent outputs, particularly in compound long-lead situations (Ganji et al., 10 Aug 2025).

A more abstract distillation strategy appears in the entropic-learning framework based on ensembles of entropy-optimal Sparse Probabilistic Approximation (eSPA) models. There, 50 lead-specific probabilistic models are distilled into $$y(t)=\frac{1}{A}\iint_{\Omega}\left[\mathrm{SST}(x,y,t)-C(x,y,\mathrm{month}(t))\right]dx\,dy,$$3 “superclusters” per lead by aggregating only those ensemble members that make correct predictions. The distilled model preserves forecast performance while exposing lead-specific feature-importance vectors, regime transitions, and canonical cross-lead pathways that are impractical to extract from the full ensemble (Groom et al., 15 Feb 2026). This work shifts MEF from weighted averaging of members toward compression of ensemble structure.

5. Interpretability and precursor diagnostics

Interpretability is a defining concern in MEF because long-lead skill is often coupled to high-dimensional or ensemble-based models. CTEFNet applies gradient-based sensitivity analysis to a multivariate CNN–Transformer and reports physically meaningful and statistically significant precursor structures spanning the Pacific, Atlantic, and Indian Oceans (Chen et al., 25 Mar 2025). Approximately 11 months before El Niño peak, the model emphasizes positive heat-content sensitivity in the equatorial western Pacific and negative mixed-layer-depth sensitivity in the tropical Pacific; by about 8 months before peak, sensitivity extends into the central and eastern Pacific and the eastern Indian Ocean, while North Tropical Atlantic cooling appears as a significant precursor (Chen et al., 25 Mar 2025). These diagnostics align with recharge-oscillator and Bjerknes-feedback interpretations, while also emphasizing inter-basin coupling.

ResoNet uses Integrated Gradients to interpret a hybrid convolution–Transformer trained on global SSTA. The study identifies attributions consistent with the Recharge Oscillator, the Seasonal Footprint Mechanism, and the Indian Ocean capacitor effect, and further argues that the model captures asymmetry between El Niño and La Niña development: El Niño at 18-month lead shows strong sensitivity in the South Pacific, whereas La Niña is more sensitive to the eastern equatorial Pacific (Lyu et al., 2023). Although ResoNet itself is SSTA-only, its interpretability framework is directly relevant to MEF because it shows how long-range inter-basin signals can be diagnosed even before additional modalities are introduced.

Interpretable-by-design analog forecasting provides a different perspective. The optimized model-analog framework uses a U-Net to estimate spatially varying weights over SST, SSH, and zonal wind stress, and these weights directly determine analog selection (Toride et al., 2024). The resulting maps emphasize NPMM in boreal spring, SPMM in boreal winter, equatorial SSH as a recharge–discharge memory channel, and western-to-central tropical Pacific wind stress in boreal summer. The same study reports a phase asymmetry in sensitivity: El Niño forecasts are more sensitive to initial SST uncertainty in boreal winter, whereas La Niña forecasts are more sensitive to initial zonal wind stress uncertainty in boreal summer (Toride et al., 2024).

The entropic distillation framework adds lead-specific feature complexity diagnostics. By aggregating the feature-importance vectors of correct eSPA ensemble members, it defines an effective dimension of the input space and shows that this complexity peaks when forecasts must cross the boreal spring predictability barrier (Groom et al., 15 Feb 2026). Spatial importance maps derived from SSA modes and their feature weights identify NPMM-like northeastern Pacific patterns, tropical Atlantic signals, wind-stress hotspots near the Warm Pool and Maritime Continent associated with westerly wind bursts, and an eastward-shifting upper-thermocline signal as lead time shortens (Groom et al., 15 Feb 2026). Taken together, these interpretability studies indicate that MEF is not only a fusion problem; it is also a framework for diagnosing where predictive information resides in each field and at each lead.

6. Skill regimes, predictability limits, and methodological caveats

Across recent studies, MEF is primarily motivated by the spring predictability barrier and the difficulty of maintaining skill beyond about half a year. Multivariate deep architectures report some of the strongest lead times. CTEFNet maintains correlation greater than 0.7 up to 12 months and effective skill, defined as correlation greater than 0.5, up to about 20 months, while showing ACC greater than 0.5 for leads greater than 20 months from June to December and about 16 months during boreal spring (Chen et al., 25 Mar 2025). The baseline deep MEF maintains correlation skill of at least 0.4 across all lead months in post-2000 validation and outperforms a CNN baseline especially beyond 17 months; the GNN-enhanced version further improves stability at extended leads (Ganji et al., 10 Aug 2025). DESN reaches similar lead ranges with far lower computational cost, while its error-growth analysis argues that the intrinsic predictability horizon is near 30 months rather than the 15–20 month ceilings seen in many empirical systems (Zhang et al., 18 Jan 2026).

At the same time, MEF studies repeatedly stress that skill depends on how multimodality is operationalized. Some systems are trained on CMIP or control simulations and validated on post-2000 reanalyses, so domain shift remains a central concern (Ganji et al., 10 Aug 2025). Distillation studies warn against look-ahead bias, overfitting to very small subsets, and double counting of correlated modalities or datasets when probabilities are combined (Ganji et al., 7 Sep 2025, Ludescher et al., 16 Feb 2026). The GNN-enhanced MEF work notes that formal significance tests were not reported, even though qualitative stability improvements were emphasized (Ganji et al., 10 Aug 2025). The entropic-distillation study obtains strong distilled skill, but its filtering of correct ensemble members is verification-based, so a fully real-time analogue requires an additional model-selection mechanism (Groom et al., 15 Feb 2026).

A common misconception is that multimodality by itself guarantees superior ENSO forecasts. The literature instead suggests a more conditional picture. Multimodality is most effective when the fusion mechanism is lead-aware, season-aware, and physically selective: WWV-mediated coupling is critical in DESN (Zhang et al., 18 Jan 2026); phase and amplitude skills must be separated through correlation and RMSE in ensemble distillation (Ganji et al., 7 Sep 2025); and precursor complexity rises sharply when the forecast trajectory must traverse boreal spring (Groom et al., 15 Feb 2026). A plausible implication is that MEF should be viewed less as a single algorithmic template than as a structured design principle: combine complementary predictors or model outputs, preserve dynamical diversity, and then apply diagnostically transparent weighting or distillation at the lead and season where each information source is most informative.