The physics data were provided by the Global Ocean Physics Reanalysis (GLORYS12) , and the Global Ocean Color (GlobColour) dataset was used as the output target. GLORYS12 is a high-resolution reanalysis that provides daily and monthly data on the four predictors (MLD, SST, SSS, SSH), among other variables. It is based on the NEMO (Nucleus for European Modelling of the Ocean) platform and driven at the surface by ECMWF's ERA-Interim and ERA5 meteorological reanalyses. Satellite altimetry, SST, sea ice concentration, and in situ temperature and salinity vertical profiles are assimilated .

The GlobColour dataset provides a combination of gap-filled satellite observations of chl a from multiple remote sensors. Chl a concentrations are derived from reflectance using sensor-specific algorithm coefficients and then merged . Because the availability and quality of remotely sensed chl a degrade at high latitudes due to low solar elevation, persistent cloud cover, and sea-ice, we restrict the domain to a -60 to 80° latitude grid in order to ensure robust training targets.

Within the development dataset (January 1998–May 2017), the years 2001, 2005, 2010 and 2015 were used for validation, while the rest was used for training. The training set was used to fit the model, while the validation set served for hyperparameter optimization and selecting the most effective model architecture. After selecting the final parameters using the training and validation sets, the model is evaluated on an independent test set (2018–2023 for the 5 d model and 2020–2023 for the monthly model).

The physical ocean data were normalized using min-max scaling and the chl a data were log-transformed. Both datasets are available at a daily resolution, and the data were averaged to monthly and 5 d resolutions for training the respective versions of the model. The 1/12° GLORYS12 grid was coarsened using bicubic interpolation to match the observational grid resolution, which was obtained at 1/4°.

The proposed methodology reconstructs a six-month chl a grid (y^) given a corresponding six-month input grid of four physical variables (X={MLD,SST,SSS,SSH}). As mentioned above, the network operates on log-transformed chl a values, where pi=log⁡(y^i) denotes the predicted values for the ith grid point, and ri=log⁡(yi) denotes the corresponding log-transformed reference point. The training objective is defined as the mean squared error (MSE) between the network output and the reference: 1MSE=1N∑i=1N(ri-pi)2 where N is the total number predicted points in the training batch.

In spite of the log-transformation, initial assessments showed that the model had a tendency to underestimate chl a concentrations, so the standard MSE loss function was modified by adding a small penalty for underestimation. This adjustment was based on empirical testing and was implemented by applying a small weight w whenever the underestimation occurred: 2L=1N∑i=1N[(ri-pi)2+w⋅[max⁡(0,ri-pi)]2] where the second term applies an additional penalty w⋅(ri-pi)2 when pi<ri. While this approach was effective in reducing underestimation, more principled methods could provide a more robust solution.

The neural networks are based on the U-Net architecture , a convolutional neural network with an encoder-decoder structure that has been widely applied to Earth science forecasting tasks due to the grid-based nature of such data . The U-Net's skip connections enable it to combine low-level spatial details with high-level semantic information, allowing reconstruction of both large-scale patterns and fine-scale features simultaneously. Despite advances and increased complexity in more recent architectures, the U-Net's simplicity and efficiency make it an effective and resource-efficient choice for this task. To process both spatial and temporal dimensions simultaneously, we use 3D convolutions . To balance the additional computational cost of the 3D convolutions, the proposed architecture uses fewer layers and filters than the original U-Net.

The encoder consists of two blocks of convolutional and max-pooling layers, which downsample the input. Two additional convolutional layers refine feature extraction before transitioning to the decoder, which mirrors the encoder and upsamples the data back to the original resolution. Skip connections link matching layers of corresponding size in the encoder and decoder (see Table 1). A rectified linear unit (ReLU) activation function was used throughout the network, except in the output layer, where a Softplus activation function was empirically found to work best. The model architecture is summarized in Table 1.

All twelve models share a common architecture and hyperparameters (i.e. number and order of layers, number of convolutional filters and kernel size, learning rate, etc.), which were optimized empirically and using random search. The models were trained using the Adam optimizer and a learning rate of 0.001 for a maximum of 300 epochs. We used early stopping on the validation loss to prevent overfitting, but no explicit regularization methods were used. We also used transfer learning, where the training process of a model can be initialized with the pre-trained weights of another, to further optimize computational cost. The models were trained on a single GPU (NVIDIA A100, 40 GB).

We evaluate our approach by using two distinct setups, each serving a different purpose. First, we perform a preliminary validation at a 5 d resolution using the GLORYS12 reanalysis as input. We generate a set of 5 d predictions covering the 2018–2023 period. This step isolates the model's ability to map physics to chl a when given accurate, observation-constrained physics, and serves to assess performance at a higher temporal resolution. We then validate seasonal forecast generation using 6 month forecasts from the ECMWF SEAS5 system as input. This is performed for the 2020–2023 period at a monthly temporal resolution to align with the available input data. This setup mimics the intended application of the model, where the chl a predictions would rely on predicted physics as opposed to a reanalysis. Both approaches use a spatial resultion of 1/4°. We describe the SEAS5 system in more detail below.

The forecast consists of an ensemble of 51 members, and it uses the IFS (Integrated Forecasting System) cycle 43r1 for the atmosphere, NEMO for the ocean, and LIM2 (Louvain-la-Neuve Sea Ice Model version 2) for sea ice. The system assimilates temperature, salinity, satellite altimetry, and snow cover . The forecasts are available free of charge on the Copernicus Climate Data Store at a monthly, one-degree resolution . A version of higher spatial resolution (1/4°) of the data was kindly provided by ECMWF, but it is possible to obtain similar results by downscaling with a simple interpolation method.

The SEAS5 forecast exhibits some biases relative to the reanalysis (see Fig. ), which is expected given their different sources and purposes. To account for this, we computed the difference between the monthly climatologies of both datasets over the training period (1998–2017), then subtracted this mean bias from the SEAS5 data before using it as model input. This offset is computed once, and can be applied to all forecasts, including future ones.

We used the first 10 (out of 51) ensemble members from SEAS5 as input for the neural network to generate six-month predictions at a monthly resolution (i.e. matching the available forecast resolution), using forecasts initialized from January 2020 to December2023. To evaluate performance across different lead times (i.e., the number of months after forecast initialization), we constructed six continuous time series by concatenating the corresponding month from each six-month forecast. Specifically, we extracted the first month from each forecast to create a one-month lead time series (January 2020–December 2023), the second month from each forecast for a two-month lead time series (February 2020–January 2024), and so on. This is illustrated in Fig.  for clarity. We compute SEAS5-based skill metrics over January 2020–December 2023 (i.e., truncating any lead time series months that extend into 2024).

We analyzed performance by zooming into some open-ocean regions of interest: the North Pacific (170° E–130° W, 25–45° N), Tropical Pacific (170° E–100° W, 10° S–10° N), South Pacific (170–100° W, 35–15° S), North Atlantic (70–20° W, 25–40° N), and Indian Ocean (55–95° E, 25–0° S), which are based on . We also examined model skill in the Equatorial Atlantic (35° W–5° E, 5° S–5° N) and in selected large coastal ecosystems, specifically the California Current (25–45° N, 130–113° W), Humboldt Current (50–5° S, 85–69° W), South China Sea (1–25° N, 105–119° E), Gulf of Mexico (18–30° N, 100–80° W), Benguela Current (35–12° S, 5–20° E), Bay of Bengal (5–25° N, 80–98° E), Celtic-Biscay Shelf (43–55° N, 15° W–0° E), and Northeast Australian Shelf (25–10° S, 140–155° E). These regions are illustrated in Fig. .

We evaluated our results against BIO4, a state-of-the-art global biogeochemical product from Mercator Océan International . BIO4 is based on the PISCES model (Pelagic Interactions Scheme for Carbon and Ecosystem Studies), the biogeochemical component of the NEMO platform . It simulates global cycles of carbon, oxygen, and key nutrients, includes two functional groups each of phytoplankton and zooplankton, and produces a 3D representation of nearly 30 biogeochemical variables. BIO4 provides both analyses and 10 d forecasts down to 5700 m depth. The model is driven by GLO12, a near-real-time physical reanalysis based on GLORYS12, the training input physics in our study, and it assimilates GlobColour observations on a weekly basis .

Our evaluation focused on the surface layer of the BIO4 analysis (rather than the forecast) due to differing forecast horizons. We note that BIO4 simulates a wide range of biogeochemical variables and processes beyond surface chl a, while our neural network is specifically optimized for chl a prediction and trained directly on observational data. We therefore use BIO4 as a contextual benchmark rather than a direct point of comparison.

We evaluate model skill primarily using RMSE and Pearson correlation computed on the raw (non-log-transformed) chl a fields. All figures in this manuscript use non-log-transformed chl a. Because different diagnostics emphasize different aspects of performance, we report two complementary RMSE definitions. For the regional time series shown in Figs. –, we first spatially average each field over the region to obtain a region-mean time series, then compute RMSE between the ensemble-mean forecast and the GlobColour reference over 2020–2023 (with RMSE of the BIO4 analysis computed on the same dates). For the regional RMSE summaries (Figs. , , and ), we compute RMSE within each region using all valid grid-point samples over 2020–2023 either for a given calendar month (Figs.  and ) or averaged across months (Fig. ). For anomaly visualizations (Figs.  and ), anomalies are computed relative to a monthly historical climatology based on GlobColour (1998–2017). This provides a stable observation-based baseline while retaining systematic forecast biases.

To validate the neural network architecture and isolate model performance from forecast uncertainties, we first evaluated the model using GLORYS12 reanalysis as input physics. We generated predictions for 2018–2023 at a 5 d temporal resolution. Figure  shows that the globally averaged (spatial mean at each time step) time series of the neural network predictions exhibits good visual agreement with the observations. We also included outputs from the BIO4 analysis (dashed lines) for comparison. The neural network captures both the amplitude and phasing of the dominant signal. Although it slightly overshoots seasonal peaks, it represents seasonal lows more accurately than BIO4. This validates the model's ability to learn the relationship between the four physical variables and biological productivity.

To assess spatial skill, Fig.  presents a global map of Pearson correlation coefficients (r) computed at each grid point between the predictions and observations. Correlation values were computed for monthly-averaged data over the 2020–2023 period to facilitate comparison with the forecasting results, which have lower temporal resolution and only cover that temporal period. The correlation map shows strong spatial coherence, with positive correlation values across most of the global ocean. Regions of particularly high correlation are found in the Northern oceans, while the Tropical and South Pacific show less skill.

We next evaluated the model in a forecasting configuration by using SEAS5 seasonal forecasts as input physics. All results presented below use the monthly model and the SEAS5 ensemble (10 of 51 members) as input. We note here that the chl a reconstruction model is deterministic, and the ensemble spread arises solely from the SEAS5 physical ensemble.

We generated 6 month forecasts at monthly resolution for 2020–2023. Figure  displays the globally averaged time series for forecasts initialized in March, June, September and December, with individual ensemble member trajectories shown as thin lines and initializations indicated by colored markers. The ensemble forecasts are visually consistent with the observations, with individual member trajectories continuing to follow the observed chl a concentrations throughout the 6 month forecast horizon, indicating little skill degradation with increasing lead time.

Figure  illustrates spatial skill using the Pearson correlation coefficient between predictions and observations over the 2020–2023 period, shown for one and six-month lead times. Correlations remain spatially coherent but a small reduction in skill is observed relative to the GLORYS12 driven predictions (Fig. ). This slight decrease is expected from the transition to forecast inputs, since they can introduce a distributional shift relative to the training data (Fig. ) even after the bias correction applied to SEAS5 (see Methods). The discrepancies occur mostly in the tropical and southern Pacific, the Indian Ocean, and plume-influenced regions near Brazil and to the south of the Gulf of Guinea. We also note that the southern and tropical Pacific exhibit relatively modest skill even in the GLORYS12 validation, suggesting that our particular modeling framework might be suboptimal for these regions, irrespective of the physics being used as input. Nonetheless, skill remains high in the subtropical gyre regions, where correlations are strong and spatially consistent. Additionally, the large-scale correlation patterns show little degradation from lead time one to six-months, indicating that the spatial skill of the predictions is relatively stable over the forecast horizon.

Figure  summarizes skill within each region from Fig.  using Pearson's r computed against the GlobColour reference. For each region (and lead time), r is computed using all valid grid-point pairs in the ensemble-mean forecast within the region for each calendar month (pooling 2020–2023), and then averaged across months. In the open-ocean regions (Fig. , top), correlations are generally higher than 0.7. The neural-network forecasts outperform BIO4 in the northern basins, consistent with the strong performance visible in Fig. . They also outperform BIO4 in the Equatorial Atlantic, although skill there remains weak for the neural model too, as shown in Fig. . Performance is lower than BIO4 in the tropics and in the South Pacific and Indian Ocean, again consistent with the poor performance visible in Fig. .

In the coastal regions (Fig. , bottom), correlations are often higher (typically r≳0.8) and exceed BIO4 in all analysed regions, which is notable given the lack of explicit biogeochemical inputs and the challenges of coastal dynamics, although Fig.  shows that this performance is far from uniform. Across regions, correlations show limited sensitivity to lead time, with little degradation from lead times one to six-months.

Figure  summarizes regional RMSE for the chl a fields. For each region and lead time, similarly to r, the RMSE is computed over all valid grid cells of the ensemble-mean for each calendar month, and then averaged to obtain a single regional RMSE per lead time. The neural model exhibits lower RMSE than BIO4 across all regions considered, including regions where its correlation is lower (see Fig. ). This indicates that, in those regions, the neural model is closer to the reference in absolute value even if it might be missing specific patterns (such as spatial shifts in mesoscale features), which can penalize correlation more strongly than RMSE. This is consistent with Fig. , where the neural predictions generally match the mean level and broad seasonal evolution of GlobColour but can show small timing/position offsets in bloom development. Conversely, although correlations are often higher in coastal regions, RMSE is also higher on average (note the larger y axis scale), consistent with the larger variability and dynamic range of coastal chl a.

Having assessed global-average skill, we now examine performance in the specific regions highlighted in Fig.  more in detail.

Figures  and show regional time series for forecasts, this time initialized in January, April, July, and October. For each region, we compare the neural network predictions, the GlobColour reference observations, and the BIO4 analysis. Figures  and show the corresponding anomalies, computed by subtracting a monthly GlobColour climatology (computed over 1998–2017) from each region to assess the ability to predict deviations from the seasonal cycle. We report the RMSE for each regional (and corresponding anomaly) time series, computed between the ensemble-mean forecast and the regional GlobColour time series over 2020–2023 (with BIO4 RMSE computed on the same dates). These time-series RMSE values quantify errors in the integrated regional signal after spatial averaging and thus complement the gridpoint-based RMSE reported in Fig. .

Across regions, the seasonal predictions generally reproduce the observed seasonal cycle and often track GlobColour more closely than BIO4 in terms of magnitude and amplitude. Nonetheless, skill is not uniform and performance varies by region and initialization month, with larger discrepancies often occurring during the peak of the bloom. Note that the RMSE displayed in Figs.  and is identical to that of the raw-value figures (Figs.  and ) because the anomalies are computed by subtracting the same monthly GlobColour climatology from both the forecasts and the reference.

The anomaly plots reveal which deviations from the seasonal cycle the model successfully reproduces. The time series demonstrate that forecasts capture departures from the seasonal cycle with varying skill across initialization months and regions, and some cases exhibit consistent offsets or systematic biases. For example, in the South Pacific, predicted anomalies align more closely with BIO4 than with observations, suggesting that shared errors may tied to limitations in the physical input set, or may be predominantly driven by processes that we are either not modeling or struggling to represent.

Notably, in coastal regions such as the Celtic-Biscay Shelf, the South China Sea, the California Current, and the Bay of Bengal, the forecasts capture the overall trend and temporal evolution of the observed anomalies, despite not always matching absolute magnitudes.

Figure  shows Hovmöller diagrams, which visualize the evolution of the field as a function of time and one spatial dimension (latitude in this case). The plots summarize the spatiotemporal evolution of surface chl a, making it easier to compare bloom timing, propagation, and amplitude across models. The SEAS5- and GLORYS12-driven neural-network predictions are broadly similar across regions, but the Hovmöller format makes it possible to identify subtle shifts in the timing, latitude/extent, and amplitude of peak concentrations that are likely to contribute to the regional skill degradation highlighted in Fig. . BIO4's tendency to overestimate chl a magnitude, is apparent as systematically elevated values relative to GlobColour. These diagrams also highlight interannual variability: despite the dominant seasonal cycle, year-to-year differences in the timing and intensity of blooms are visible. The neural-network predictions exhibit variation across years rather than repeating a purely climatological seasonal pattern, even though these do not always align with the observed deviations from the seasonal cycle.

To investigate how error evolves through the seasonal cycle, Figs.  and show RMSE as a function of calendar month for each region. Here, RMSE is computed separately for each calendar month using all valid grid points within the region over 2020–2023 (i.e. not averaged across months like we do in Fig. ).

Both the neural network and BIO4 exhibit increased errors during bloom peaks. Northern-hemisphere regions show larger RMSE in the first half of the year, while southern-hemisphere regions peak later, consistent with hemispheric seasonality. This behavior is expected because bloom peaks concentrate the largest amplitudes and strongest spatiotemporal gradients, in RMSE these timing offsets or amplitude damping near the peak translate into large squared errors. The fact that both the neural and process-based models show similar seasonality in error suggests that peak-bloom conditions may be intrinsically harder to predict, potentially reflecting sensitivity to rapidly evolving states and/or drivers that are not explicitly represented, rather than model class alone. However, this seasonal structure is not uniform across regions or between the two models. For example, in the Tropical Pacific the neural-network RMSE shows little seasonal variation compared to BIO4, while in the Humboldt Current BIO4 error has a secondary late-year peak that is not mirrored by the neural model, and the Benguela Current shows a different seasonal pattern. These differences suggest different sources of uncertainty and region-specific dynamics, and that accuracy might be constrained by different representations (or omission) of key drivers.

Our framework is intentionally minimalist, and this design choice implies several limitations. First, stricter diagnostics that emphasize interannual variability and small departures from the climatological seasonal cycle are highly phase-sensitive and can penalize even modest changes in timing or small spatial shifts in bloom features. This is expected because removing the seasonal cycle isolates a weaker, noisier signal, and because the monthly evaluation record, with only 48 time steps, is relatively short. In addition, limited predictability in the forecast physical anomalies can further constrain skill. We therefore emphasize metrics (RMSE and Pearson correlation on the raw fields) that better reflect our main objective, which was reproducing realistic magnitudes and large-scale spatiotemporal evolution of surface chl a in a resource-efficient manner. Performance in more complex scenarios where accurate reproduction of anomalies and outliers is crucial would likely require enhancements beyond the minimalist setup presented here. A more systematic treatment of interannual skill would also require a more methodological assessment of SEAS5 skill with respect to anomalies, in order to evaluate how forecast errors might propagate into the chl a reconstruction. A similar decomposition of skill for the process-based benchmark would enable a more principled comparison of performance between approaches

Second, we deliberately restrict predictors to four variables (MLD, SSH, SSS, and SST) that are available in both reanalyses and seasonal forecasts, and in order to keep the framework lightweight and readily deployable, but by doing so, we neglect drivers that can be crucial. These include irradiance (PAR), a key driver in light-limited regimes, winds and mixing variability not fully summarized by monthly MLD, and biogeochemical state variables (e.g. nutrients). As a result, forecast errors will increase in regimes where chl a variability is strongly controlled by factors not captured in the input set, such as light limitation and nutrient supply. Several studies suggest that interannual predictability in chl a is closely linked to biogeochemical drivers, which can exhibit longer predictability than physical variables alone . As with any modeling approach, trade-offs are inevitable. While biogeochemical variables can carry higher uncertainties, they may also capture important feedbacks not fully represented by physical drivers. Future versions of this approach could therefore benefit from a more principled investigation of predictor uncertainty and sensitivity analyses to systematically incorporate any additional relevant physical and biogeochemical inputs.

Third, the neural network design is intentionally lightweight, but this comes at the cost of potentially failing to capture the full intricacy of the underlying processes. We used a simplified U-Net architecture and a month-conditioned strategy implemented as twelve separately trained networks (one per initialization month) rather than a single unified model. While this choice simplifies training across the seasonal cycle, it increases system complexity and can introduce month-to-month inconsistencies because the mapping from physics to chl a is learned independently for each network. A natural extension would be to adopt a more robust architecture that explicitly conditions on month and lead time through a shared-backbone design.

Furthermore, while MSE is a standard choice for regressive neural networks such as this one, its focus on minimizing error can lead to overly smooth predictions that tend toward the mean. This can result in the loss of fine-scale detail in regions with high variability, and an overall impact on the realism of the model's predictions. Future work could mitigate this by adopting more robust learning objectives and/or by increasing architectural capacity. In addition, the forecast “ensemble” presented here is derived from the propagation of uncertainty from the SEAS5 physical ensemble through a deterministic chl a reconstruction. It does not explicitly represent chl a uncertainties, and it inherits any shared biases and limits in the physical forecast. A more complete approach would require the inclusion of more comprehensive sources of uncertainty and the perturbation of these within the predictive framework.

Finally, data-driven methods like ours, which learn directly from observations, can better reproduce observed chl a magnitudes and avoid some of the systematic biases that arise from uncertain parameterizations in process-based models (manifested as systematic overestimations relative to GlobColour in the case of BIO4). Nonetheless, this same minimalistic design, which emphasizes good skill in the raw fields in its current form, may also limit performance. Mechanistic biogeochemical models, by enforcing dynamical and biogeochemical consistency across variables, may be more robust for extrapolation beyond the observational regime, whereas purely data-driven approaches may degrade under distribution shift or in regimes that are poorly represented in the training data.