0–200 mWhite book v0.1 · Chapter 1

Research programme

The ocean is the largest active sink of anthropogenic carbon and the least observed component of the climate system. MOFOMO proposes to learn a single model of it from the complete observational record, to couple that model to the biology that mediates the carbon fluxes, and to validate the result where the predictions have direct users.

Nayat Sanchez-Pi and Luis MartíInria Chile Research Center
September 2026 · 9 min read
Full chapter in the white book (PDF)

1.1 An incomplete and incoherent record

The ocean absorbs about a quarter of anthropogenic CO₂ emissions: 3.4 ± 0.4 Pg C yr⁻¹ for 2024 in the latest global carbon budget [1]. This figure is well constrained; the rate at which the sink is changing is not. Over 2001–2018, estimates built on surface-CO₂ products give a strengthening of 0.61 ± 0.12 Pg C yr⁻¹ per decade, biogeochemical models give 0.34 ± 0.06 and inverse methods 0.41 ± 0.03 [2 , 3]. The three families of methods disagree by a factor of about 1.8 on a quantity that enters every mitigation pathway assessment.

At depth, the biological pumps that export on the order of 10 Pg C yr⁻¹ from the surface are even less well constrained, because the structure of the plankton community that governs export is almost never assimilated into flux estimates [4]. The disagreement originates less in the physics of the models than in the observational record to which they are fitted, which is incomplete and incoherent.

Incomplete: The ocean is undersampled by orders of magnitude: roughly 4,000 Argo floats, 1,000 biogeochemical floats, 1,000 moorings and 100 research vessels, against near-complete daily satellite coverage of the surface alone. Sampling density on its own biases the estimated decadal trend of the flux by 20–35% globally and by 50–130% in the Southern Ocean [5].
Incoherent: The modalities that could fill the gaps do not line up. Surface optics arrive daily at kilometre scale; interior profiles are sparse and irregular; imaging and genomic catalogues belong to a separate data culture. Each estimate is built within a single modality, and the results are compared only at the end, where disagreement is recorded rather than resolved.

They deliver better maps; they do not deliver counterfactuals.

On learned ocean emulators, white book §1.1

Two features of current modelling tools compound the problem. The learned emulators now replacing conventional ocean pipelines are trained on latitude–longitude grids whose polar distortion is worst where the sink uncertainty is largest, carry velocities as independent scalar channels, and conserve tracers only approximately. Budgets do not close, and residuals cannot be read as signal. And the ecosystem components of Earth system models still represent a few plankton functional types with fixed traits, which cannot acclimate, turn over or adapt.

1.2 A three-block system

MOFOMO responds with a single open, globally scoped system built in three linked blocks. Block A learns a model of the ocean from the complete record; block B couples that model to an adaptive, trait-based biology; block C validates the two together in two pilot regions.

Learning across the gaps
A multimodal world model of the ocean: a foundation model pre-trained on the heterogeneous record as a whole, fine-tuned for downstream tasks with little labelled data, and structured to respect the physics and the symmetries of the domain.
supplies the operator →
Projecting the living ocean
A coupled, multilevel, trait-based biogeochemical model that takes the ecosystem components of the PISCES-v2 class beyond fixed functional types, written differentiably so it trains together with block A.
supplies the mechanism, receives closures ↔
Validating where the impact is largest
Two contrasting pilots, the Patagonian inner sea of southern Chile and remote South Pacific island reefs, where the carbon signal is large, the in-situ record dense and each prediction has an immediate user.
evaluates on data excluded from training

The blocks are not independent deliverables. One constraint runs through all three: the observational record cannot be enlarged, so structure, meaning the symmetries and conservation laws of the domain, is the only remaining way to substitute assumptions for data. Those symmetries are only approximate, since the Coriolis parameter depends on latitude and coastlines break rotational symmetry, so they are treated as quantities to be discovered rather than imposed.

Figure 1.1. Architecture of the MOFOMO foundation modela world model, not a map

Observations, each with its encoder

Sentinel-3 ocean colour0 m · km-scale, dailySpherical / ViT encoder
Argo, WOD, CMEMS, WOA230–2,000 m · profiles, reanalysisInterpolation-free profile encoder
Passive acoustics~1,000 m · continuous, at pointsAcoustic encoder
Plankton images, OBIS0–200 m · Planktonzilla, surveysImage encoder (Planktonzilla CLIP init.)
Tara Oceans, BIO-GO-SHIP0–1,000 m · multi-omicsGenomic encoder
Scientific publicationsthe written recordText encoder

Structured latent space

Shared subspace · cross-modal alignment (contrastive stage)
Modality-unique subspaces · masked reconstruction
Latent dynamics operator · latent-predictive loss, score-based conditioning
Interventions · counterfactual forcings, hypothetical observations

Outputs

Physical decoders (T, S, currents)
Biogeochemical decoders
Biodiversity and community heads
Symbolic regression + causal discovery · closed-form closures
NPZ-T layer · Floquet persistence thresholds
Downstream modules · HAB risk, reef bleaching

Figure 1.1. Modality-specific encoders consume each observation type at its native location, time and resolution, with no destructive regridding, and map it into a structured latent space: a cross-modal shared subspace plus per-modality unique subspaces. What makes the model interventional is the explicit latent dynamics operator: score-based conditioning lets counterfactual forcings and hypothetical observations be supplied at inference time without retraining. Symbolic regression paired with causal discovery reads the operator back out in closed form and hands it to the NPZ-T layer as an explicit closure. Deep ensembles and conformal prediction put calibrated uncertainty on every output.Redrawn from the MOFOMO white book v0.1, Figure 1.1

1.3 Three methodological commitments

Block A names five architectural ingredients. Three of them are commitments in the strong sense: choices that could be wrong, that determine what the project builds, and that the evaluation plan is designed to test. Table 1.1 sums them up; each is argued below.

**Table 1.1.**The three commitments and the observation that would count against each.
Commitment	What it changes	What would falsify it
World model	The model predicts its own next latent state and accepts hypothetical observations; it is not an observation-to-field regressor.	Conditioning on hypothetical observation sets yields trajectories no better than the nowcast baseline.
Geometric deep learning	State lives on the sphere and on bathymetry-conforming meshes rather than on a rectangular grid.	A gridded transformer of matched capacity equals or beats the geometric backbone at equal data.
Symbolic regression	What the model learned can be written down, criticised and inserted into the mechanistic layer.	Recovered expressions do not hold out of sample, or survive only as correlations that causal tests reject.

1.3.1 A world model, not a map

The learned emulators now displacing conventional ocean pipelines are input–output maps: given the present state, return the next one. The questions posed by the pilots are interventional: how a bloom would have developed had river discharge held up, or whether a reef would have bleached under the previous decade's thermal history. A world model in the sense used here has two parts that an emulator collapses into one: a latent state inferred from whatever observations exist, and a dynamics operator that advances that state and can be conditioned, perturbed and queried [6].

1.3.2 Geometric deep learning as the structural prior

State on the sphere and on bathymetry-conforming meshes, vector fields under operators independent of the local frame, equivariant message passing where the domain is a mesh rather than a grid, and tendencies in flux form so that budgets close identically [7]. On a record this sparse, structure is what substitutes for the data that cannot be collected.

1.3.3 Symbolic regression: reading the model back out

Symbolic regression applied to the trained operator, not to the raw data, converts it into closed-form expressions that an oceanographer can evaluate and that block B can incorporate as explicit closures. Paired with causal representation learning, it separates the relations that carry causal content from those that are only predictive.

References

Friedlingstein, P., O'Sullivan, M., Jones, M. W., et al. (2026). Global Carbon Budget 2025. Earth System Science Data, 18(5), 3211–3288.
Gruber, N., Bakker, D. C. E., DeVries, T., et al. (2023). Trends and variability in the ocean carbon sink. Nature Reviews Earth & Environment, 4(2), 119–134.
DeVries, T., Yamamoto, K., Wanninkhof, R., et al. (2023). Magnitude, trends, and variability of the global ocean carbon sink from 1985 to 2018. Global Biogeochemical Cycles, 37(10), e2023GB007780.
Boyd, P. W., Claustre, H., Levy, M., Siegel, D. A., & Weber, T. (2019). Multi-faceted particle pumps drive carbon sequestration in the ocean. Nature, 568(7752), 327–335.
Hauck, J., Nissen, C., Landschützer, P., et al. (2023). Sparse observations induce large biases in estimates of the global ocean CO₂ sink. Phil. Trans. R. Soc. A, 381(2249), 20220063.
Ha, D., & Schmidhuber, J. (2018). World models.
Bronstein, M. M., Bruna, J., Cohen, T., & Veličković, P. (2021). Geometric deep learning: grids, groups, graphs, geodesics, and gauges.