Coupling ecological concepts with an ocean-colour model: inversion modelling

Abstract

Monitoring phytoplankton from space can help detect shifts in marine ecosystems, particularly under accelerating climate change. However, most existing ocean-colour chlorophyll-a (Chl-a) algorithms are empirical in nature, and do not explicitly consider any potential optical effects of shifts in phytoplankton community composition independent of a change in Chl-a. Similar ocean-colour signals may arise from different combinations of Chl-a and phytoplankton community composition. Revealing how phytoplankton are responding to environmental change using satellite data requires tackling this ambiguity. In previous work, we developed an Ocean Colour Modelling Framework (OCMF) to simulate ocean colour for varying Chl-a and phytoplankton size classes (PSCs). Here, we invert the OCMF to directly retrieve Chl-a, key inherent optical properties (IOPs), and PSCs, from satellite remote sensing reflectance and sea surface temperature (SST), accounting for deviations in non-algal particles (NAP) and coloured dissolved organic matter (CDOM) from assumed open ocean relationships with Chl-a. The model is validated using a global in situ dataset and shows stable performance across diverse oceanic conditions. Integrating ecological concepts into a bio-optical model may advance our ability to interpret long-term changes in phytoplankton community structure from space.

1 Introduction

Phytoplankton form the foundation of marine food webs and modulate planetary biogeochemical cycles, playing a key role in carbon sequestration (Longhurst et al., 1995; Field et al., 1998; Behrenfeld et al., 2006). In recent years, climate change has intensified (Terhaar et al., 2025), altering ocean temperature, stratification, and nutrient availability (Bindoff et al., 2019). Numerous studies have shown the sensitivity of phytoplankton to such environmental changes (Boyce et al., 2010; Thomas et al., 2012; Hutchins and Tagliabue, 2024; Viljoen et al., 2024), making accurate assessment of their biomass and community structure crucial for monitoring ocean ecosystems and understanding long-term changes (Sun et al., 2023, Sun et al., 2025).

Satellite ocean-colour observations are the only means of monitoring surface phytoplankton on a global scale and at high frequencies, providing synoptic and long-term data on their dynamics (McClain, 2009; Kavanaugh et al., 2021). With nearly 30 years of uninterrupted data, it is now possible to examine trends in phytoplankton at climatic scales, particularly in regions with sufficient temporal coverage (Henson et al., 2010; Hammond et al., 2020). Among the various ocean-colour products available, chlorophyll-a (Chl-a) is widely used as a proxy of phytoplankton biomass, community structure, and productivity (Platt and Sathyendranath, 2008; Sathyendranath et al., 2023). However, most standard Chl-a algorithms rely on empirical relationships (Hu et al., 2019; O’Reilly and Werdell, 2019), and do not explicitly account for influence of other optically active constituents such as non-algal particles (NAP) and coloured dissolved organic matter (CDOM). While some empirical relationships may implicitly capture changes in phytoplankton community structure (Sathyendranath et al., 2017), these assumptions may not apply across different environmental conditions (Sun et al., 2023). Other approaches, such as semi-analytical models (e.g., quasi-analytical algorithm (QAA), Garver-Siegel-Maritorena (GSM), generalized IOP (GIOP)) relate Chl-a to satellite-derived absorption and backscattering (Lee et al., 2002; Maritorena et al., 2002; Werdell et al., 2013), but they typically rely on globally tuned bio-optical parameters and rarely incorporate variability driven by phytoplankton composition or environmental factors such as sea surface temperature (SST). This can lead to ambiguity in interpretation (Defoin-Platel and Chami, 2007), since similar Chl-a concentrations can produce different ocean colours depending on the phytoplankton types present and the optical environment (Szeto et al., 2011; Alvain et al., 2012; Sauer et al., 2012), making it challenging to derive accurate phytoplankton information from ocean-colour data. Moreover, when investigating phytoplankton responses to climate change, changes in Chl-a alone can be hard to interpret, since it can vary with changes in physiology or the abundance of the cells (Siegel et al., 2013; Behrenfeld et al., 2015; Viljoen et al., 2024). A broader set of ecological and optical properties is therefore essential for understanding phytoplankton dynamics in a changing ocean (Uitz et al., 2010; Bellacicco et al., 2016; Sathyendranath et al., 2017).

With these considerations in mind, we developed the Ocean Colour Modelling Framework (OCMF), a forward ocean-colour modelling approach that simulates remote sensing reflectance based on ecological and bio-optical concepts (Sun et al., 2023; Sun et al., 2025). The OCMF explicitly accounts for size composition of phytoplankton by dividing the community into three size groups (Sieburth et al., 1978), i.e., picoplankton (m), nanoplankton (m), and microplankton (m), each of which is associated with different bio-optical properties (Alvain et al., 2012; Brewin et al., 2015a; Brewin et al., 2019). The OCMF also includes the contribution of an independent background component of NAP (Stramski et al., 2001; Zhang et al., 2020). A key option within the OCMF is to incorporate SST as an independent explanatory variable, which connects phytoplankton size structure to environmental variability (Ward, 2015; Brewin et al., 2017), improving the interpretation of ocean-colour data and helping mitigate ambiguity. Through forward modelling, the OCMF enables the estimation of from Chl-a and SST, capturing the interactions between biological composition, optical properties, and environmental variability.

The third paper in this series focuses on the inversion of the OCMF. The goal is to retrieve multiple ecological and optical variables, including Chl-a, phytoplankton size fractions, and absorption and backscattering properties, directly from satellite-derived and SST. While the forward OCMF was developed for Case-1 waters (Morel and Prieur, 1977), where variations in optical properties are closely linked to Chl-a (Morel and Maritorena, 2001), the inversion framework has been extended to accommodate more optically-complex environments. To support this, two additional wavelength-independent parameters are introduced to represent deviations in NAP and CDOM contributions, similar to the parameter proposed by Morel and Gentili (2009), allowing the model to account for an excess or a deficit in the inherent optical properties (IOPs) associated with these substances relative to what might be considered the norm in open ocean conditions, and retrieve them alongside Chl-a. While the OCMF inversion enables the retrieval of multiple variables, its application to large-scale or hyperspectral satellite data can be computationally demanding, due to the use of extensive parameters (Sun et al., 2025). Neural networks have been increasingly applied in ocean-colour studies due to their efficiency in handling large and complex datasets (Li et al., 2023; Zhang et al., 2024; Hammoud et al., 2025). Building on these developments, we present a neural network–based implementation of the OCMF inversion, designed to preserve ecological and optical consistency while improving computational efficiency.

Using a large dataset with global observations of Chl-a and IOPs gathered from previous studies (Sun et al., 2023; Sun et al., 2025), we conduct a comprehensive validation of the OCMF inversion model using multiple satellite datasets, including OC-CCI, GlobColour, MODIS, and Sentinel-3, as well as an independent synthetic dataset. The accuracy of the retrieval is assessed for both Chl-a and IOPs, and model sensitivity to seasonal changes is examined. We also demonstrate an application of the model using OC-CCI data for interpreting phytoplankton biomass, size structure, and optical properties from space.

2 Data

2.1 In-situ datasets

In total, 35,109 Chl-a measurements from the global surface ocean (20 m depth) were included in this study. This dataset was used to identify satellite match-ups and validate the inversion model (Figure 1). The dataset combines contributions from two earlier studies in this series of papers (Sun et al., 2023; Sun et al., 2025). These include publicly available data from multiple sources. Data portals include Australian Ocean Data Network (AODN), Biological and Chemical Oceanography Data Management Office (BCO-DMO), British Oceanographic Data Centre (BODC), Data Observation Network for Earth (DataONE), Environmental Data Initiative Data Portal (EDI), Government of Canada, NASA SeaBASS (SeaWiFS Bio-optical Archive and Storage System), and PANGAEA. Individual research programs and projects include Atlantic Meridional Transect (AMT), BOUSSOLE (Bouée pour l’acquisition de Séries Optiques à Long Terme) Project, NASA bio-Optical Marine Algorithm Dataset (NOMAD), Rothera Research Station, TARA Ocean, and Western Channel Observatory, as well as some published works. Some of these datasets were updated to include more recent measurements. Further details on the public data sources are provided in the Supplementary Section S1 and in Sun et al. (2023) and Sun et al. (2025).

FIGURE 1

The in-situ dataset was supplemented with additional Chl-a measurements, including those from: (1) the Atlantic Ocean (AMT cruises, Jordan et al., 2024a; Jordan et al., 2024b); (2) the Northwest Sargasso Sea [Bermuda Atlantic Time-series Study (BATS), Johnson et al., 2023]; (3) the North Pacific Ocean near Hawaii [Hawaii Ocean Time-series Data Organization and Graphical System (HOT-DOGS), HOT-DOGS, 2024]; (4) the Atlantic Southern Ocean (Viljoen and Fietz, 2021); and (5) the Chukchi Sea (Lomas, 2021).

Chl-a was measured either using the HPLC (High Performance Liquid Chromatography) method or the in-vitro fluorometric method. HPLC data were given the highest priority when multiple sources were available. Following earlier methodologies (Sun et al., 2023; 2025), we excluded data points where Chl-a concentrations were under 0.001 (Uitz et al., 2006) and retained only data collected from the uppermost 20 m that fall within the surface mixed layer (De Boyer Montégut et al., 2004). The dataset was split based on sampling date, using data collected before 2016 for training and after 2016 for validation to ensure independence in validation (Stock and Subramaniam, 2022), with consistent spatial coverage between the two periods (Supplementary Figure S1). Duplicate samples from different sources were removed. During validation, we retained only the shallowest sample from stations with multiple depth measurements, to best represent surface conditions.

2.2 Satellite datasets

The Ocean Colour Climate Change Initiative (OC-CCI) dataset (version 6.0, 4 km resolution, Sathyendranath et al., 2021) was used in this study (https://climate.esa.int/en/projects/ocean-colour/). For validation analyses, we used daily OC-CCI products, including optical properties at six wavelengths (412, 443, 490, 510, 560, and 665 nm) for , absorption of phytoplankton , absorption of NAP and CDOM , and backscattering of particles . We also included Chl-a concentrations, estimated using a blended combination of ocean-colour algorithms (e.g., OCI, OCI2, OC2, and OCx) on merged , for comparison with the OCMF retrievals. In addition, water class memberships (Jackson et al., 2017) were extracted for classifying water types, ranging from open ocean to coastal waters as the class number increases. We also used an 8-day composite OC-CCI for model application (see Section 4.3). A complete list of abbreviations and symbols can be found in Supplementary Table A1 of the Appendix.

To ensure a comprehensive validation, we also included other satellite datasets to test the model inversion performance. These include: the GlobColour dataset (daily, Level 3, 4 km resolution, European Union-Copernicus Marine Service, 2022), accessed from https://data.marine.copernicus.eu/product/OCEANCOLOUR_GLO_BGC_L3_MY_009_103, which provides at 412, 443, 490, 555, 670 nm, along with Chl-a products derived from the sensor-specific multi-algorithm blending approach (Garnesson et al., 2019); and the MODIS (Moderate Resolution Imaging Spectroradiometer) Aqua dataset (daily, Level 3, 4 km resolution, R2022), accessed from https://oceancolor.gsfc.nasa.gov/, which provides at 412, 443, 469, 488, 531, 547, 555, 645, 667, and 678 nm, as well as Chl-a products which use an ocean-colour band-ratio algorithm (OC3) and a colour index (CI) (Hu et al., 2019; O’Reilly and Werdell, 2019). Due to concerns about data quality from ageing sensors, only MODIS-Aqua data before 2020 were used in this study. The Sentinel-3 OLCI (Ocean and Land Colour Instrument) dataset (A&B, daily, Level 2, 300 m resolution, OL_L2M.003) was also used, providing at 400, 412, 443, 490, 510, 560, 620, 665, 673, 681 nm, along with Chl-a products which use OC4Me and CI (Morel et al., 2007). To extract match-ups between Sentinel-3 and in-situ measurements, we used the ThoMaS tool (https://gitlab.eumetsat.int/eumetlab/oceans/ocean-science-studies/ThoMaS), which applies spatial, temporal, and quality-control filters for accurate pixel-level extraction.

For all satellite data sources, we followed the same procedures for match-up identification and data extraction: (1) satellite data were matched with in-situ measurements using a spatial window of 3 3 pixels and a daily temporal window; (2) the median of satellite-derived variables was calculated from nine pixels, and data were retained if at least five valid pixels were available; (3) for optical variables ( and IOPs), only wavelengths within the visible range (400–700 nm) were used; (4) since the OCMF does not simulate Raman scattering, a Raman scattering correction was applied to before model application, following the method of Lee et al. (2013); and (5) to assess the quality of , QA (quality assurance) scores were calculated (Wei et al., 2016; Wei and Aurin, 2020), with wavelengths selected individually for each satellite data source.

2.3 Auxiliary datasets

2.3.1 OISST SST

The OISST (Optimal Interpolation Sea Surface Temperature, version 2, 1/4° resolution, https://psl.noaa.gov/data/gridded/data.noaa.oisst.v2.highres.html) dataset was used as the input temperature for the OCMF inversion model, which demonstrated good agreement with in-situ measurements (Sun et al., 2023). The daily OISST data were applied in both validation and image mapping. For validation, each in-situ sample was matched with OISST data based on the nearest latitude and longitude (3 x 3 pixel window in space) and daily temporal resolution. For image mapping, the spatial resolution of OISST was resampled firstly to align with the resolution of the ocean-colour satellite dataset used in the analyses, maintaining compatibility across datasets.

2.3.2 A separate dataset for validation

To evaluate the performance of the OCMF inversion model, we also used an additional independent hyperspectral synthetic dataset generated through radiative transfer simulations, as described in Pitarch and Brando (2025). This dataset provides at a 1-nm spectral resolution in the visible range, which serves as input for the OCMF inversion model. For our analysis, we focused on simulations with a sun zenith angle of 0°, and radiance propagation in the nadir direction (zenith angle 0°), for which azimuth is undefined and not considered, ensuring consistency with the OCMF forward model setup (Lee et al., 2011; Sun et al., 2025). Following the methodology of Pitarch and Brando (2025), SST is fixed at 20 °C for this synthetic dataset. Chl-a values in this dataset were used to evaluate the OCMF inversion model outputs.

3 Ocean colour modelling framework inversion development

The OCMF (Sun et al., 2023; Sun et al., 2025) integrates the absorption and backscattering contributions of key optically active water constituents, including phytoplankton, NAP, CDOM, and pure seawater. Variations in these constituents (except for water itself) are controlled by phytoplankton, which are divided into three size classes using a phytoplankton size structure model that accounts for their dependence on temperature (see Section 2.4 in Sun et al., 2023). When integrating the size structure model with optical models, we assumed that each size class exists in its own unique optical environment (see Section 3 in Sun et al., 2025), characterised by its own set of chlorophyll-specific IOPs. The model also includes the contribution of a background of non-algal particles. The OCMF forward modelling enables the estimation of from Chl-a and SST.

Here, we implement an inversion of the OCMF. This inversion allows the estimation of Chl-a and associated optical parameters directly from observed and SST. The following sections describe the structure, components, and implementation of the OCMF inversion modelling.

3.1 Direct OCMF inversion approach

The OCMF inversion model retrieves Chl-a using and SST as inputs, which can be obtained from in-situ measurements or satellite observations. The direct inversion employs an optimisation approach, where the forward model is used to minimise the difference between modelled and measured (Figure 2a).

FIGURE 2

In the forward model (Sun et al., 2025), is computed from total absorption and total backscattering coefficients via a semi-analytical equation that incorporates the scattering phase functions of both particles and molecules (Lee et al., 2013), such that,where represents the sun-sensor angular geometry for , and . , , , and are 0.0604, 0.0406, 0.0402, and 0.1310 , respectively, for the observations made in the nadir direction and the sun at the zenith (Lee et al., 2011).

In Equation 1, is expressed as the sum of the pure water and its constituents, such that, , where is pure water absorption (Pope and Fry, 1997; Lee et al., 2015), and , , and represent phytoplankton, NAP, and CDOM absorption, respectively. Each component is represented as the sum of Chl-a for distinct size classes (, for pico-, nano-, and microplankton) scaled by their respective chlorophyll-specific absorption coefficients (, , and ), along with the background absorption coefficient of NAP , such that,and

Similarly, the total backscattering coefficient, , consists of contributions from both pure water and particles (phytoplankton and NAP), such that, , where is backscattering by pure water (Zhang and Hu, 2009; Zhang et al., 2009), assuming a constant salinity of 35 ppt for simplicity. Phytoplankton and NAP backscattering are represented as the sum of Chl-a in each PSC , each scaled by its corresponding chlorophyll-specific backscattering coefficient (, ), along with the contribution of a background of NAP , such that,and

In Equations 2–6, the chlorophyll-specific absorption and backscattering coefficients of different water constituents are adopted from Sun et al. (2025). The primary unknown is the total Chl-a, but it is represented here as the sum of the three size-fractionated components , through incorporating the SST-dependent three-component model (Sun et al., 2023), where the other input, SST, is introduced to determine the proportions of total Chl-a attributed to the three size classes.

The forward model (Sun et al., 2025) follows the classical Case-1 water assumption, which may limit its applicability in optically complex waters (e.g., coastal regions). To address this, the inversion model introduces two wavelength-independent parameters, and , which capture deviations from the Case-1 assumption, representing excesses or deficits of , , and relative to their assumed values of one, similar to the parameter proposed by Morel and Gentili (2009). For example, in coastal or high-CDOM environments, they may deviate from 1, reflecting variations in optical properties from standard global, open-ocean conditions. Given the similar spectral shapes of and , distinguishing between these two components using multispectral data is challenging. Therefore, is explicitly defined with reference to , and Equations 3, 4 are rewritten as,

Similarly, is a wavelength-independent factor that accounts for variations in , in a similar manner to for . Therefore, Equation 6 is rewritten as,

By introducing and in Equations 7, 8, the inversion model is taken forward to estimate three unknowns, Chl-a, , and (Figure 2a). These variables are retrieved by minimising the difference between observed and modelled using a minimisation method (‘lmfit’ package in Python).

Two SST-dependent phytoplankton size structure models (16- and 17-parameter approaches, Sun et al., 2023) are available to derive size-fractionated Chl-a for each pair of total Chl-a and SST, resulting in two corresponding sets of bio-optical parameters (Sun et al., 2025). To streamline the presentation and avoid redundancy, results from the 16-parameter model are shown in the main text, and those of the 17-parameter model in the Supplementary.

3.2 Accelerated OCMF inversion using neural network

The OCMF inversion model (Section 3.1) involves a large set of parameters (i.e., those in phytoplankton size structure model, size-fractionated chlorophyll-specific absorption and backscattering coefficients), which increases computational cost, especially for satellite applications. To address this, we implemented an acceleration method that replaces the minimisation process with a neural network-based trained model that is able to estimate results rapidly.

A multi-layer feed forward neural network (NN) was developed to retrieve Chl-a, , and , by learning their relationships with and SST. To train the NN, a large OCMF synthetic dataset was first generated to reflect realistic global-ocean conditions, with Chl-a, SST, , and as inputs. These inputs were introduced into the OCMF forward model (Sun et al., 2025) to compute the corresponding as output, forming a lookup table for NN training. During sampling, Chl-a was sampled randomly from a log-normal distribution spanning 0.001 to 100 , ensuring coverage of diverse oceanic conditions. SST values were uniformly sampled between −1.8 and 40 °C, capturing conditions from polar to tropical waters. Parameters and followed log-normal distributions, with values ranging from 0.001 to 12, a deliberately broad range that covers values derived from in-situ measurements and calculations. A total of 200 logarithmically (Chl-a, , ) or linearly (SST) spaced values were generated for each variable. Weighted random sampling was applied to Chl-a, , and , based on their probability distributions to better reflect their natural variability. Additionally, to generate a comprehensive dataset efficiently, 100 blocks of 4 million samples each were created and stored for further training processes.

The NN consists of four fully connected layers (Figure 2b), with an input layer of seven features: at the OC-CCI wavelengths (412, 443, 490, 510, 560, 665 nm) and SST, obtained from the OCMF synthetic dataset. Three hidden layers with 32, 16, and 8 neurons, respectively, use the ReLU (rectified linear unit) activation function (Kingma and Ba, 2014), while the output layer contains Chl-a, , and , corresponding to the input from the OCMF synthetic dataset. The input and output data were log-transformed and standardised before training. The model was trained using the Adam (adaptive moment estimation) optimizer (learning rate = 0.001, batch size = 10,240) for up to 12,000 epochs, with early stopping (patience = 1,000 epochs) to prevent overfitting (Prechelt, 1998; Nair and Hinton, 2010). During training, the synthetic dataset was randomly split into 80% for training and 20% for internal validation, and processed in batches. Each dataset block ( = 100) was processed separately, and the corresponding trained models and specific scalers were stored individually for further application. During internal validation, all 100 models achieved a coefficient of determination greater than 0.99 and a root mean squared difference below 0.04 for Chl-a in space.

Once trained, the NN was applied to and SST using the 100 trained models. The input data were standardised with the corresponding scalers, converted to PyTorch tensors, and processed with GPU acceleration to retrieve scaled Chl-a, , and , which were then inverse-transformed to their original units. The final retrievals across all blocks were aggregated, with the median computed and stored for further analysis. This accelerated approach, referred to as OCMF-NN, significantly reduces computational cost compared to the direct OCMF inversion method. For example, on a dataset of 20,000 samples, the direct OCMF inversion takes approximately 2,500 s, whereas the OCMF-NN approach reduces this to 30 s, enabling large-scale applications for global climate studies. In this study, the OCMF-NN was trained with OC-CCI wavelengths; however, it can be applied to other satellite sensors by retraining the model with inputs for the corresponding sensor-specific wavebands.

3.3 Statistical tests

Model performance was evaluated using several statistical metrics, including the Pearson correlation coefficient , significance level , bias , mean absolute difference (MAD, ), root mean squared difference (RMSD, ), centre-pattern root mean square difference , and regression slope , based on comparison between observed and estimated values. The , , , and were calculated following previous studies (Brewin et al., 2015b; Sun et al., 2023; Sun et al., 2025). The slope and intercept were determined through linear least-squares regression between estimated and measured values, , where is the variable of interest (e.g., Chl-a concentration, IOPs), and refer to estimated and measured variables, respectively. Given the log-normal distribution of bio-optical properties in the ocean (Campbell, 1995), statistical analysis for Chl-a and IOPs were calculated in space.

4 Results and discussion

4.1 Model validation

4.1.1 OC-CCI dataset

The OCMF was developed to retrieve Chl-a, PSCs and IOPs within a consistent framework that, unlike purely empirical algorithms, aligns with the characteristics needed for interpreting ocean-colour for climate-change studies (Sathyendranath et al., 2017). However, empirical algorithms are known to set the standard in performance when evaluated with discrete match-ups (Brewin et al., 2015b), and have consequently been adopted by space agencies when generating standard products of Chl-a. Therefore, a key step in evaluating our inversion of the OCMF is to compare performance in Chl-a retrievals with the empirical algorithms considered to be the gold standards, using a discrete match-up dataset.

Using the OC-CCI dataset, we present a global validation of Chl-a retrievals derived from OCMF, OCMF-NN, and compare them with the OC-CCI standard products (Figure 3). OCMF and OCMF-NN retrievals were obtained by applying the inversion model (direct or accelerated with NN) to the matched OC-CCI and OISST SST. To ensure data quality, measurements with a QA score below 0.8 were removed, and only the shallowest depth measurements were used when multiple depths were available. Retrievals with extreme and values were excluded (e.g., outside the range 0.1–10.0), retaining over 97.5% of the data. To avoid redundancy, results shown here are from the 16-parameter model, with the 17-parameter results available in the Supplementary. The two models show broadly comparable results at the global scale.

FIGURE 3

The OCMF inversion model shows a strong correlation with in-situ Chl-a, with = 0.857 for the full dataset and 0.826 for the independent dataset (Figures 3a,d). The OCMF-NN has similar performance ( = 0.877 and 0.849), demonstrating that the NN preserves the performance of the direct inversion model (Figures 3b,e). The OC-CCI standard products have slightly higher correlation ( = 0.896 and 0.898) and lower RMSD ( = 0.273 and 0.262), particularly in the independent dataset (Figures 3c,f). However, compared to OC-CCI, OCMF exhibits a lower bias and a regression slope closer to one, especially for the full dataset ( = 0.012, = 0.867).

To evaluate further the OCMF and OCMF-NN models under varying environmental conditions, we assessed Chl-a retrieval performance across different Chl-a ranges (Figure 4), time periods, oceanic regions, and water classes (see Supplementary Section S4.1), using the same OC-CCI validation dataset. A key advantage of OCMF and OCMF-NN is their ability to provide consistent Chl-a estimates across both spatial and temporal scales (Figure 4; Supplementary Figure S8). Figure 4 shows the relative residuals between estimated and measured values for four Chl-a ranges (0.1, 0.1–1, 1–10, and 10 ). Medians and standard deviations of the residuals within each range are reported, where positive values indicate overestimation and negative values indicate underestimation. OC-CCI systematically overestimates Chl-a at low concentrations (median relative residual 0.105 and 0.147 for 0.1 and 0.1–1 , respectively) and underestimates at higher concentrations (−0.204 and −0.577 for 1–10 and 10 , respectively; Figure 4c), likely due to regional dependencies of the applied empirical algorithms (Sathyendranath et al., 2001; Brewin et al., 2015a; Lavigne et al., 2021; Dierssen and Smith, 2000). In contrast, both OCMF and OCMF-NN improve performance by reducing bias across a range of trophic regimes, providing more consistent estimates (Figures 4a,b), which is crucial for global studies requiring reliable Chl-a retrievals in diverse environments. Similarly, OCMF and OCMF-NN maintain a stable regression slope close to 1 across years (Supplementary Figure S8), whereas OC-CCI shows fluctuations in slope, indicating that the OCMF may provide a more stable representation of long-term changes, which is important for applications such as climate studies and trend analysis (Sathyendranath et al., 2017; Pauthenet et al., 2024).

FIGURE 4

However, regional and optical environment assessments reveal specific limitations of the OCMF inversion model (Supplementary Figures S10, S12). While all models perform well in the Atlantic, Pacific, and Indian Oceans, their accuracy decreases in polar regions (Supplementary Figure S10), likely due to under-representation of in-situ dataset during model development and the distinct optical properties of these waters (Babin et al., 2015). For example, in the Arctic, high CDOM and NAP absorption can lead to the overestimation of Chl-a (e.g., Lewis and Arrigo, 2020; Li J. et al., 2024), whereas in the Antarctica, differences in phytoplankton community structure and the optical properties of both phytoplankton and non-algal constituents introduce additional uncertainty (e.g., Robinson et al., 2021; Salyuk et al., 2025). In coastal waters, lower Chl-a accuracy may result from reduced reliability in satellite , as atmospheric correction is more challenging due to adjacency effects from land and variable aerosol conditions (e.g., Bulgarelli and Zibordi, 2018). Across different optical environments, OC-CCI shows slightly better performance in clear open-ocean waters, but all models exhibit higher uncertainties in optically complex regions (Supplementary Figure S12), consistent with previous studies (Jackson et al., 2017; Sathyendranath et al., 2019). This underlines the persistent difficulty of retrieving Chl-a in waters with NAP and CDOM that varies independently of Chl-a (Blondeau-Patissier et al., 2014).

In all assessments mentioned above, OCMF-NN achieves accuracy comparable to OCMF, despite relying on a simple machine learning approach without extensive parameter tuning. Its lightweight neural network architecture balances computational efficiency with reduced risk of overfitting. While more complex artificial intelligence models may improve accuracy (Pahlevan et al., 2022; Zhang Y. et al., 2023), our approach prioritises simplicity and strict alignment with the conceptual framework of the OCMF. The reliability of OCMF-NN stems from the theoretical rigour of the OCMF forward model, which ensures the training lookup table captures realistic optical variability.

The validation of IOPs (i.e., , , and ) between measured and OCMF-derived values further demonstrates the capability of the model (see Supplementary Section S4.2.1). While the OC-CCI standard IOP products generally show slightly lower RMSD and higher correlations, OCMF has comparable results and outperforms the OC-CCI in some cases (Supplementary Figures S14, S16, S18). In general, OCMF provides improved estimates of , comparable performance for , and shows slightly increased variability in the retrieval of . A key limitation of standard ocean-colour products is their reliance on separate algorithms for retrieving different variables, each based on distinct assumptions about water constituents and optical properties. For example, Chl-a is retrieved using OCx or CI algorithms (O’Reilly and Werdell, 2019; Hu et al., 2019), whereas IOPs are estimated using models such as QAA (Lee et al., 2002). This can lead to inconsistencies when combining outputs, as each algorithm has its own error characteristics (Brewin et al., 2015b; Zheng and DiGiacomo, 2017), potentially affecting further applications, for example, in biogeochemical modelling (Ciavatta et al., 2018; Ciavatta et al., 2019; Pradhan et al., 2020). Besides, the use of multiple algorithms requires users to be familiar with the parameter settings and limitations of each model.

In contrast, OCMF retrieves Chl-a and all key optical properties simultaneously within a single inversion framework, ensuring greater internal consistency and simplifying integration for applications. More importantly, OCMF explicitly incorporates chlorophyll-specific bio-optical properties and accounts for their variations with phytoplankton size structure and temperature, different from standard algorithms that often assume fixed relationships, limiting their reliability across spatial and temporal scales (Brown et al., 2008; Brewin et al., 2015a; Lee et al., 2020). This enables OCMF to address ambiguity in interpreting ocean colour related to differing combinations of phytoplankton sizes and Chl-a concentrations.

4.1.2 Other datasets

Beyond OC-CCI, validation of the OCMF inversion model using multiple satellite products demonstrates its broad applicability (see Supplementary Section S4.2.2; Supplementary Table S1). Comparisons with GlobColour, MODIS, and Sentinel-3 show that while standard products often achieve slightly better performance (e.g., higher correlation coefficient, lower bias) in estimating Chl-a, OCMF offers stable and consistent performance across different datasets.

In general, GlobColour standard Chl-a products perform well (Supplementary Figure S20), as Chl-a is estimated separately for each sensor using its specific , accounting for sensor-specific spectral and spatial characteristics (Garnesson et al., 2019). This also supports good performance for single-sensor datasets such as MODIS and Sentinel-3 (Supplementary Figures S21, S22), which rely on empirical algorithms (e.g., OCx and CI) optimised using large in-situ datasets and calibrated for each sensor (O’Reilly and Werdell, 2019). In contrast, OCMF uses absolute values, making its performance highly sensitive to the quality of those inputs. For example, the slightly lower accuracy of OCMF-derived Chl-a from MODIS data, compared to the standard product, may result from the use of all visible wavebands of MODIS, some of which are known to be biased or less suitable for ocean-colour retrievals (Mélin et al., 2007; Hu et al., 2012; Bisson et al., 2021). This highlights the requirement of strict quality control of the input when applying OCMF to specific sensors, particularly for those with known degradation or spectral limitations. Additionally, non-ocean-colour satellite missions may offer complementary water-optical information and could be evaluated as supplementary data sources in future applications (Shi et al., 2021; Zhang X. et al., 2023).

Beyond satellite validation, good agreement was also observed between simulated and retrieved Chl-a using the synthetic dataset from Pitarch and Brando (2025), further supporting the reliability of the OCMF inversion model (see Supplementary Section S4.2.3). The Chl-a retrieval accuracy was higher than that in the satellite validation, likely due to the controlled optical conditions in the synthetic dataset (Supplementary Figure S23). Results also suggest that retrievals from hyperspectral (1-nm) data have slightly higher accuracy than those from multispectral (OLCI bands) retrievals (not shown). This aligns with previous studies that highlight the advantages of hyperspectral data for ocean-colour applications (Bracher et al., 2020; Dierssen et al., 2023), and demonstrates that OCMF can be easily applied to hyperspectral satellite observations (e.g., NASA PACE [Plankton, Aerosol, Cloud, ocean Ecosystem]), with the potential for improved performance.

4.2 Model sensitivity to seasonal changes: a case study at BOUSSOLE

We evaluated the sensitivity of the OCMF inversion model to seasonal changes using a long time series from the BOUSSOLE Project in Western Mediterranean Sea. By applying OCMF to OC-CCI daily products, we generated biweekly Chl-a climatologies and compared them with in-situ measurements (BOUSSOLE Project monthly cruise) and the OC-CCI standard Chl-a products (Figure 5a).

FIGURE 5

The in-situ Chl-a measurements exhibit clear seasonal patterns, characterised by a spring bloom between March and April (biweeks 6–8), followed by a post-bloom decline, low Chl-a concentrations throughout summer and autumn (biweeks 11–22), and a winter increase. Seasonal changes in physical and biogeochemical conditions are responsible for the observed variation in Chl-a (i.e., mixed layer depth dynamics, Marty et al., 2002; Volpe et al., 2012). Both satellite-derived Chl-a (OCMF and OC-CCI) capture these seasonal patterns but differ in their accuracy. A linear regression analysis between SST and -transformed Chl-a using the biweekly climatology dataset ( = 25, excluding the first and last biweeks due to a lack of in-situ data) showed that in-situ Chl-a decreases significantly with SST (slope = −0.0769, ). The OCMF-derived Chl-a (slope = −0.0505) exhibited a similar negative relationship, with the slope aligning more closely with the in-situ trend than that of the OC-CCI product (slope = −0.0361), though both slopes were statistically significant . This result suggests that OCMF has a slightly better representation of the seasonal variability in Chl-a at BOUSSOLE.

During winter and spring, both satellite products tend to underestimate Chl-a, with OCMF showing slightly lower values than OC-CCI. In summer and autumn, OC-CCI overestimates Chl-a significantly, especially at low concentrations, reflecting known biases in standard algorithms in this region (Bricaud et al., 2002; Volpe et al., 2007; Kournopoulou et al., 2024). OCMF, however, shows better agreement with in-situ measurements, particularly in capturing the lower values during these seasons. Although BOUSSOLE surface waters are classified as Case-1 water (Antoine et al., 2008), seasonal variations in parameter through OCMF inversion suggest that NAP backscattering does not follow a fixed covariation with Chl-a (Figure 5b), as assumed in standard Case-1 models. For example, during the bloom, reaches its lowest value (around 0.5), as phytoplankton dominate backscattering, reducing the relative contribution of NAP. Following the bloom, rises sharply over one, likely due to increased detrital material from grazing and cell degradation. In summer and autumn, remains high, which could result from the fragmented detritus from smaller phytoplankton. In winter, drops, possibly due to the dilution of particles in the mixed layer. This pattern aligns with previous observations that the ratio of and Chl-a is higher than expected in certain seasons, and its variability follows a strong seasonal cycle in this region (Antoine et al., 2011; Loisel et al., 2011). For the parameter, its relative stability throughout the year is consistent with previous observations that follows a similar seasonal pattern to Chl-a (Organelli et al., 2016; Álvarez et al., 2023). However, given that the region is thought to have systematically higher CDOM per unit Chl-a compared to standard Case-1 water, particularly in summers (Organelli et al., 2014), a higher derived from the inversion model would be expected. Instead, the model returns a value below one, suggesting that the maybe underestimated (seen in validation, not shown). This could explain the slight overestimation of Chl-a during summer, as the model may attribute more of the total absorption to phytoplankton.

Seasonal shifts in phytoplankton community structure is evident in OCMF-derived PSCs (Figure 5b), which are consistent with trends observed in HPLC-derived in-situ measurements (not shown). In winter and early spring, the violin plots (Figure 5a) show narrow peaks, suggesting a more consistent Chl-a concentrations inter-annually. Together with the PSCs, this suggests a relatively uniform phytoplankton community dominated by nano- and picoplankton. These patterns are likely driven by deep winter mixing and sufficient nutrient availability, which create uniform environmental conditions (Lavigne et al., 2013). Starting in spring, the Chl-a range becomes wider, indicating variability in phytoplankton growth intensity (Kheireddine and Antoine, 2014; Mayot et al., 2017). During this period, microplankton, such as diatoms, increase and contribute to the increased Chl-a concentrations. From late spring onward, the Chl-a concentration becomes more variable, as indicated by the broad range and dual peaks in the violin plots, potentially influenced by shifts in community structure, due to distinct responses of different phytoplankton classes to environmental conditions. PSCs derived from OCMF show that small phytoplankton (nano- and picoplankton) dominate throughout the year, with picoplankton peaking in summer (Figure 5b). This pattern is consistent with previous studies, where Synechococcus and Prochlorococcus thrive in summer under stratified, low-nutrient conditions (Navarro et al., 2017; El Hourany et al., 2019).

At BOUSSOLE, the OCMF seems to capture seasonal variations, offering an improved representation of bio-optical dynamics by accounting for the influence of non-algal substances and improving Chl-a estimations relative to standard products. Additionally, OCMF provides information on PSCs, further enhancing its utility for biogeochemical studies. However, some discrepancies remain, such as potential biases in the parameter. It should be acknowledged that the OCMF was trained on a broad global dataset and was not specifically tailored for this region.

4.3 Model applications

We applied the OCMF-NN inversion model to the Southern Ocean, Atlantic section, using and SST from an 8-day composite OC-CCI product (17th to 24th January 2004) and a corresponding 8-day averaged OISST product, respectively. This region was selected because it represents an optically complex environment, spanning coastal and oceanic waters with diverse ecological and optical characteristics, with a wide range of temperature variations (i.e., −1.8–26 °C), and concurrent in-situ measurements are available for validation. Figure 6 shows the spatial distribution of model-derived Chl-a, , , fraction of microplankton to Chl-a , absorption properties (, , ), and backscattering properties (ratio of and ).

FIGURE 6

The OCMF-NN-derived Chl-a in January exhibits distinct latitudinal variations. On the Patagonian Shelf, microplankton dominates in areas with high Chl-a, consistent with previous studies showing that diatoms and dinoflagellates are the primary phytoplankton groups during bloom events (Garcia et al., 2008; Guinder et al., 2024). Some coastal patches exhibit a slightly higher fraction of nanoplankton (Supplementary Figure S6), which could be associated with the presence of coccolithophores during the season (Signorini et al., 2006). Without concurrent in-situ phytoplankton data, it is challenging to determine the exact community composition. However, bio-optical parameters such as and the ratio of and maps may provide insights into the types of phytoplankton present (Figures 6c,h). For example, areas dominated by coccolithophores are expected to show higher and lower and ratios, due to enhanced backscattering from inorganic particles (Balch et al., 2014).

Chl-a concentration decreases towards the Drake Passage, reaching low values around the Antarctic Polar Front region, before increasing again near the Antarctic shelf. This pattern is consistent with previous observations (Demidov et al., 2010). Across the Drake Passage, nanoplankton dominate the phytoplankton community (40%–50%), such as haptophytes (coccolithophores), which are characterised by higher values and lower and ratios. Microplankton also contribute significantly, with a clear gradient of increasing fraction toward the south (Figure 6d). This shift is probably associated with the Antarctic Polar Front, which acts as a biological boundary, with diatoms being more dominant in the colder and silicate-rich Antarctic waters (Hayward et al., 2024).

Previous studies of Chl-a distribution and phytoplankton communities in the western Antarctic Peninsula region during summer (Trimborn et al., 2015; Arrigo et al., 2017; Schofield et al., 2017; Biggs et al., 2019) are generally consistent with the results of this study. Coastal and shelf waters of the Antarctic Peninsula (e.g., Marguerite Bay) are known to exhibit phytoplankton blooms with high Chl-a concentrations, where large phytoplankton (e.g., diatoms) are dominant. In contrast, in the continental shelf and open waters, the contribution of microplankton generally decreases, but often remains significant, while nanoplankton (e.g., cryptophytes) also play an important role, with local variability in the region. This spatial distribution could be affected by sea-ice melt, which influences nutrient availability and water-column stratification (Ferreira et al., 2024).

The general pattern of OCMF-NN-derived Chl-a is consistent with the OC-CCI standard product, though the OCMF-NN model retrieves higher Chl-a values across most regions (Supplementary Figure S7). Previous studies found that standard Chl-a algorithms tend to overestimate low Chl-a concentrations and underestimate high concentrations in this region (e.g., Argentine Patagonian Shelf, Southern Ocean, Dogliotti et al., 2008; Johnson et al., 2013). A small amount of concurrent in-situ match-ups from the Antarctic Peninsula, collected during the period of the 8-day composite ( = 13), are overlaid on the satellite image (Supplementary Figure S7), showing that the OC-CCI standard product tends to underestimate Chl-a (bias = −0.349), whereas OCMF-NN shows much lower bias (0.040). This discrepancy is often linked to regional variations in bio-optical properties. For example, in the Southern Ocean, lower Chl-a-specific absorption results from a higher proportion of microplankton per unit Chl-a, combined with distinct CDOM absorption and particulate backscattering, contributing to an overall underestimation in Chl-a retrievals by global empirical algorithms (Ortega-Retuerta et al., 2010; Ferreira et al., 2018; Robinson et al., 2021). These bio-optical characteristics align with the predominance of large-celled phytoplankton in cold oceanic regions (Marañón et al., 2012; Ward, 2015). By explicitly incorporating PSCs, SST, and a full suite of bio-optical properties, the OCMF inversion model accounts for these factors. In particular, the SST-dependent PSC model increases the contribution of microplankton at low SST, improving representation in regions like the Southern Ocean.

4.4 Model implications and future directions

Ocean-colour research has been advancing beyond a sole focus on Chl-a, increasingly embracing phytoplankton community structure, its dynamics, and interactions with other components of the marine ecosystem. Many recent studies have emphasised the importance of retrieving phytoplankton community structure and IOPs to better characterise biogeochemical processes and ecosystem functions (Nair et al., 2008; IOCCG, 2014; Bracher et al., 2017; Mouw et al., 2017; Cetinić et al., 2024). The OCMF has been developed to further this goal, by simultaneously retrieving phytoplankton size structure, absorption coefficients, and backscattering properties from satellite remote sensing, expanding its applications beyond Chl-a estimation. For example, phytoplankton size affects nutrient uptake, light absorption, sinking rates, and interactions with grazers (Finkel et al., 2009). By incorporating phytoplankton size structure, the model provides insights into community composition, which is important for understanding carbon cycling and energy flow in marine ecosystems (Guidi et al., 2009; Atkinson et al., 2024). A validation of the retrieved PSCs is provided in the Supplementary Section S4.2.4, demonstrating the model’s simultaneous inversion capability and showing that the satellite-derived PSCs are consistent with in-situ measurements. Meanwhile, understanding IOP variability facilitates in classifying pigment and phytoplankton community composition (Chase et al., 2013; Sun et al., 2022), assessing carbon pools (Evers-King et al., 2017; Fox et al., 2022; Li M. et al., 2024), and improving ecosystem models (Ciavatta et al., 2014; Dutkiewicz et al., 2015). These advancements highlight the value of multi-variable satellite retrievals. Unlike traditional empirical algorithms, the OCMF is also able to account for some level of regional variability in phytoplankton community composition, which has been shown to affect optical properties and ocean colour (Bracher and Tilzer, 2001; Mouw et al., 2012; Barrón et al., 2014). Moreover, the OCMF allows uncertainty propagation from input (e.g., OC-CCI products) to retrieved variables, such as Chl-a, using a Monte Carlo approach with perturbed inputs (see Supplementary Section S4.3). This provides not only concentration estimates but also uncertainties, which are important for climate studies and ecosystem models (Jackson et al., 2017). Despite these advantages, some limitations remain. For example, lower accuracies are observed in specific areas (Section 4.1; Supplementary Section S4.1), likely due to regional optical properties of phytoplankton assemblages and non-algal components not being captured by the model. In addition, the OCMF relies on Chl-a specific absorption and backscattering coefficients derived from previous parameterisation. However, these properties can vary with phytoplankton community composition and change with space and time (e.g., Kheireddine et al., 2018; Bellacicco et al., 2019). This limitation is further influenced by the uneven distribution of in-situ measurements (Figure 1), with the some regions being more densely sampled (e.g., the Atlantic Ocean), while some regions remaining under-sampled. Future efforts could focus on refining the bio-optical parameterisation and collecting high-quality optical data to improve performance in these regions.

The application of ocean-colour remote sensing in climate studies has been increasing with the availability of datasets that are sufficient in length to detect trends (e.g., Kulk et al., 2020; Thomalla et al., 2023). Satellite-derived Chl-a trends have been widely used to study phytoplankton responses to climate change, with some studies reporting Chl-a declines in warming waters and others showing regional increases (Antoine et al., 2005; Martinez et al., 2009; Vantrepotte and Mélin, 2011; Gregg and Rousseaux, 2014). Beyond global trends, spatial-temporal changes in phytoplankton dynamics under climate forcing, such as shifts in distribution, bloom timing and intensity, and the structure of productivity zones, have also been investigated (Polovina et al., 2008; Salgado-Hernanz et al., 2019; Turner et al., 2024; Peng et al., 2025). However, differences in dataset length, sensor calibration, and algorithm selection have led to both consistent and contradictory trends across studies (Gregg et al., 2017; Hammond et al., 2017), highlighting the need to re-evaluate long-term changes using consistent models and harmonised datasets (Dierssen, 2010). While most satellite-based climate studies focus solely on Chl-a, a few have investigated shifts in phytoplankton size structure (Montes-Hugo et al., 2009; Polovina and Woodworth, 2012; Lamont et al., 2019; Sun et al., 2019), which can respond differently to environmental and climate-driven changes compared to total Chl-a (Mouw et al., 2019). Accounting for size-fractionated information is therefore important for understanding shifts in ecological function and biogeochemical cycling (Rousseaux and Gregg, 2015). In this context, incorporating SST as an independent variable alongside ocean-colour data is particularly valuable for long-term analyses, as it provides complementary environmental information linked to phytoplankton community structure and helps capture their climate-driven shifts (Ward, 2015; Sun et al., 2023). Furthermore, the complexity of the ocean environment cannot be adequately captured by a single index such as Chl-a. Although widely used, Chl-a may not always reflect phytoplankton carbon biomass due to physiological variability, such as photoacclimation (Siegel et al., 2013; Leonelli et al., 2022). Multi-variable approaches that account for IOPs, including contributions from NAP and CDOM, are necessary for a more comprehensive understanding. Future work will focus on applying OCMF to long-term climate datasets (e.g., OC-CCI) to track changes in Chl-a, phytoplankton size structure, and optical properties over time, providing deeper insights into how phytoplankton respond to global change.

5 Summary

To address the ambiguity in interpreting ocean-colour data, an OCMF was developed, designed to be suitable for constructing long-term records of Chl-a concentration (Sun et al., 2023; Sun et al., 2025). The OCMF explicitly incorporates phytoplankton size structure and IOPs, along with their temperature-dependent variability, ensuring both biological and optical interpretation. In this third paper of the series, we present an inversion of the OCMF, which retrieves Chl-a and two wavelength-independent parameters ( and ) accounting for deviations in contributions of non-algal substances from standard global conditions. These parameters are retrieved directly from and SST, with information on phytoplankton size structure and optical properties derived simultaneously.

Using a large global dataset of in-situ Chl-a and IOPs collected from the surface ocean (20 m depth), we conducted a comprehensive validation of the inversion model. Chl-a retrievals were compared across multiple satellite and synthetic datasets, showing consistency with standard products while achieving more stable retrievals, with slopes closer to one across a wide range of Chl-a concentrations, regions, water types, and time periods. This indicates that the OCMF can represent Chl-a variability well, which is particularly important for climate trend analyses. In addition, the model demonstrated good performance for all IOPs, making it suitable for broader ecological and biogeochemical applications. The sensitivity of the OCMF to environmental variability supports its use in the detection of change in phytoplankton community composition. With sound performance and a strong foundation in ecological principles and optical theory, the OCMF provides a valuable tool for understanding long-term changes in phytoplankton in the surface ocean. Its compatibility with hyperspectral observations and neural-network implementation also offer potential for applications in hyperspectral satellite missions and biogeochemical model data assimilation. Future studies will focus on applying the model to long-term satellite datasets to investigate how phytoplankton biomass and community structure evolve under climate change.

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