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OverviewThis study establishes a framework for mapping carbon stocks at the level of individual trees at a sub-continental scale in semi-arid sub-Saharan Africa north of the Equator. We used satellite imagery from the early dry season (Extended Data Fig. 1). The deep learning method developed by a previous study1 allowed us to map billions of discrete tree crowns at the 50-cm scale from West Africa to the Red Sea. Then we used allometry to convert tree crown area into tree wood, foliage and root carbon for the 0–1,000 mm year−1 precipitation zone in which our allometry was collected (Extended Data Fig. 2). We introduce a viewer that enables the billions of trees to be viewed at different scales, with information on location, metadata of the Maxar satellite image used, tree crown area and the estimated wood, foliage and root carbon content based on our allometry (Fig. 4). We also make available our output data for the 1,000 mm year−1 precipitation zone southward to 9.5° N latitude with information on location, precipitation, metadata of the Maxar satellite image used, tree crown area, tree wood carbon, tree root carbon and tree leaf carbon.Satellite imageryWe used 326,523 Maxar multispectral images from the QuickBird-2, GeoEye-1, WorldView-2 and WorldView-3 satellites collected from 2002 to 2020 from November to March from 9.5° N to 24° N latitude within Universal Transverse Mercator (UTM) zones 28–37 for Africa (Extended Data Table 1a). These images were obtained by NASA through the NextView License from the National Geospatial-Intelligence Agency. Data were assembled over several years with a focus on later years to achieve a relatively recent and complete wall-to-wall coverage.When using satellite data from different satellites over several years, with varying sun–target–satellite angles, with varying radiometric calibration of satellite spectral bands and different atmospheric compositions through which the surface is imaged, there are two possibilities for using hundreds of thousands of satellite images together quantitatively. One approach, used extensively in NASA’s, NOAA’s and the European Space Agency’s Earth-viewing satellite programmes, is to quantitatively inter-calibrate radiometrically the satellite channels through time; correct these data for time-dependent atmospheric effects such as aerosols, clouds, haze, smoke, dust and other atmospheric constituent effects and then normalize the viewing perspective to the same sun–target–satellite angle38. Another approach is to use the satellite data as collected; assemble training data of trees viewed from different satellites under different sun–target–satellite angles, different times, different atmospheric conditions and use machine learning with high-performance computing to perform the tree mapping at the 50-cm scale. The key to successful machine learning is to account for all the sources of variation within the domain of study in the training data to ensure accurate identification of trees under all circumstances. We included trees viewed substantially off-nadir, trees collected under different aerosol optical thicknesses, trees collected under cirrus cloud conditions, trees viewed in the forward and backward scan directions, trees on sandy soils, trees on clay soils, trees on burn scars, trees in laterite areas and trees in riverine settings. Our training data were collected by one team member and are a carefully selected manual delineation of 89,899 individual trees under a range of atmospheric conditions, viewing perspectives and ecological settings.All multispectral and panchromatic bands associated with our Maxar images were orthorectified to a common mapping basis. We next pan-sharpened all multispectral bands to the 0.5-m scale with the associated panchromatic band. The absolute locational uncertainty of pixels at the 0.5-m scale from orbit is approximately ±11 m, considering the root-mean-square location errors among the QuickBird-2, GeoEye-1, WorldView-2 and WorldView-3 satellites (Extended Data Table 1). We formed the normalized difference vegetation index (NDVI)39 from every image in the traditional way from the pan-sharpened red and near-infrared bands. We also associated the panchromatic band with the NDVI band and ensured that the panchromatic and NDVI bands were highly co-registered. The NDVI was used to distinguish tree crowns from non-vegetated background because the images were taken from a period when only woody plants were photosynthetically active in this area36. Our training data were labelled on images from the early dry season when only trees have green leaves. Because most semi-arid savannah trees continue to photosynthesize in the early dry season after herbaceous vegetation senesces, green leaf tree crowns are easily mapped because of their higher NDVI values than their senescent herbaceous vegetation surroundings. We substantiate this by analysis of 308 individual trees using NDVI time series with 4-m PlanetScope imagery that emphasized the importance of satellite data from the November, December and January early dry-season months (Extended Data Fig. 1).We next formed our data into mosaics by applying a set of decision rules, resulting in a collection of 16 × 16-km tiles within each UTM zone from 9.5° N to 24° N latitude for Africa. The initial round of scoring considered percentage cloud cover, sun elevation angle and sensor off-nadir angle: preference was given to imagery that had lower cloud cover, then higher sun elevation angle and finally view angles closest to nadir. In the second round of scoring, selections were assigned priority to favour early dry-season months and off-nadir view angles: preference was given to imagery from November, December and January with off-nadir angle less than ±15°; second to imagery from November to January with off-nadir angle between ±15° and ±30°; third to imagery from February or March with off-nadir angle less than ±15°; and finally to imagery from February or March with off-nadir angle between ±15° and ±30°. Image mosaics were necessary to eliminate multiple counting of trees. We formed mosaics using 94,502 images for tree segmentation, with 94% of these being from November, December and January. Ninety percent of our selected mosaic imagery was within ±15° of nadir, 87% were acquired between 2010 and 2020 and 94% were from the early dry season (Extended Data Fig. 7). A summary of month, year, solar elevation and off-nadir angle by UTM zone can be found in Supplemental Information Fig. 1.Possible obscuration of the surface by clouds totalled 4.1% of our input mosaic data area and aerosol optical depth >0.6 at 470-nm (ref. 40) areas totalled 3.4% of our input data. However, we mapped 691,477,772 trees in our possible cloud-cover-affected and aerosol-affected areas, indicating that cloud and aerosol effects were lower than these numbers. In addition, 0.9% of our input data did not process. We include a data layer in our viewer for these three conditions.Mapping tree crowns with deep learningWe used convolutional neural network models developed by a previous study1. The models were trained with manually delineated and annotated 89,899 individual trees along a north–south gradient from 0 to 1,000 mm year−1 rainfall1. Only features that showed a distinct crown area and associated shadow were included, which excluded small bushes, grass tussocks, rocks and other features that might have green leaves or cast a shadow from our classification. All training data and model training was done in UTM zones 28 and 29. Because tree floristic diversity in the 0–1,000 mm year−1 zone of our study is highly similar from the Atlantic Ocean to the Red Sea across Africa41,42,43, we added no further training data as our study moved further eastward. We used state-of-the-art deep learning to segment trees crowns at the 50-cm scale1. We used two different models based on a U-Net architecture, one for lower-rainfall desert regions with 150 mm year−1. Details about the network architecture, training process and hyperparameter choices can be found in ref. 1. Previous evaluation showed that early dry-season images performed better than late dry-season images, which was a limitation of our previous study. We reduced this error by using early dry-season images with only 6% of our area being covered by images from February and March. The models were also designed to separate clumped trees by highlighting spaces between different crowns during the learning process, similar to a strategy for separating touching cells in microscopic imagery22.AllometryVery-high-resolution satellite images and deep learning have achieved mapping of individual trees over large areas1. Each tree is georeferenced in the satellite data and defined by crown area. The challenge was to develop allometric equations for foliage, wood and root dry masses or carbon based on crown area regardless of species. This was met by reanalysing existing Sahelian and Sudanian woody plant data from destructive sampling. Overall, the seasonal maximum foliage, wood and root dry masses were measured on 900, 698 and 26 trees or shrubs from 27, 26 and 5 species, respectively, for which crown area was also measured. Several allometric regression models tested for foliage, wood or root masses are power functions and independent of species. All the regression outputs were inter-compared for fit indicators, by systematic estimates of prediction uncertainty and by root-to-wood ratios and foliage-to-wood ratios over the range of crown areas. This resulted in a set of ordinary least squares log–log equations with crown area as the independent variable. The Sahelian and Sudanian allometry equations were also compared with published allometry equations for tropical trees, primarily from more humid tropics, which are generally based on stem diameter, tree height and wood density. Our allometric predictions are within the range of other allometry predictions, reinforcing the confidence in their use beyond the Sahelian and Sudanian domains into sub-humid savannahs for discrete trees19.On the basis of ref. 19, we predicted the wood (w), foliage (f) and root (r) dry mass as functions of the crown area (A) of a single tree as:$$begin{array}{c}{text{mass}}_{{rm{w}}}(A)=3.9448times {A}^{1.1068},({N}_{{rm{w}}}=698)\ {text{mass}}_{{rm{f}}}(A)=0.2693times {A}^{0.9441},({N}_{{rm{f}}}=900)\ {text{mass}}_{{rm{r}}}(A)=0.8339times {A}^{1.1730},({N}_{{rm{r}}}=26)end{array}$$The tree mass components of wood, leaves and roots were combined to predict the total mass(A) in kg of a tree from its crown area A in m2:$$text{mass}left(Aright)={text{mass}}_{{rm{w}}}left(Aright)+{text{mass}}_{{rm{f}}}left(Aright)+{text{mass}}_{{rm{r}}}left(Aright)$$As in ref. 1, a crown area of size A  > 200 m2 was split into ({rm{lfloor }}A/100{rm{rfloor }}) areas of size 100 m2 and one area with the remaining m2 if necessary. We converted dry mass to carbon by multiplying with a factor of 0.47 (ref. 44).Uncertainty analysisWe evaluated the uncertainty of our tree crown area mapping and carbon estimation in two ways. First, we quantified our tree crown mapping omission and commission errors by inspecting randomly selected areas from UTM zones 28–37, validating that our neural network generalized over UTM zones consistently (Extended Data Fig. 8).Second, we quantified the relative error of our tree crown area estimation. We consider the uncertainty Δx of a quantity x and the corresponding relative uncertainty δx defined by the absolute and relative error, respectively45. To assess the relative error in crown area estimation resulting from errors by the neural network, we considered external validation data from ref. 1, which were not used in the model-building process. We considered expert-labelled tree crowns as well as the predicted tree crowns from 78 plots of 256 × 256 pixels. The hand-labelled set contained 5,925 trees and the system delineated 5,915 trees. The total hand-labelled tree crown area was 118,327 m2 and the neural network predicted 121,898 m2. This gave a relative error in crown area mapping of δarea = 3.3%. We matched expert-labelled and predicted tree crowns and computed the root-mean-square error (RMSE) per tree, taking overlapping areas and missed trees into account (see Extended Data Fig. 8). We estimated the allometric uncertainty (δallometric) using the data from ref. 19 (see below). The two relative errors δarea and δallometric were combined to an overall uncertainty estimate for the carbon prediction of ±19.8% (see below).Omission and commission errorsWe evaluated our tree crown mapping accuracy by analysis of 1,028 randomly selected 512 × 256-pixel areas over the 9.5° N to 24° N latitude within UTM zones 28–37. Because the drier 60% of our study area only contains 1% of the 9,947,310,221 trees we mapped in the 0–1,000 mm year−1 rainfall zone, we applied an 80% bias for selecting evaluation areas above the 200 mm year−1 precipitation line46, as >98% of tree identifications were above the 200 mm year−1 precipitation isoline. Identified tree polygons were further categorized into tree crown area classes from 0–15 m2, 15–50 m2, 50–200 m2 and >200 m2, with a total of 50,570 trees evaluated. Although a previous study reported greatest uncertainty in both the smallest and largest area classes1, our more expansive work found the greatest uncertainty in our smallest tree class. We excluded from evaluation any tiles that had annual precipitation46 >1,000 mm year−1 and all areas that were devoid of vegetation, leaving us with 850 areas.Seven members of our team evaluated the accuracy in terms of commission and omission by tree crown area classes for the 850 areas. Input data provided for every area were the NDVI layer, the panchromatic shadow layer and the neural net mapping results in each of the four crown area classes. Ancillary data available to evaluators included the centre coordinates for comparison with Google Earth data, the Funk et al.46 rainfall, the acquisition date of the area evaluated and the viewing perspective.We identified areas wrongly classified as tree crowns (commission errors), missed trees (omission errors) and crown areas corresponding to clumped trees (Extended Data Fig. 8). Clumped trees were most common for >200 m2 tree crown area. They were rare in the 3–15 m2 and 15–50 m2 tree classes, which comprise 88% of our tree crowns. In the 850 patches, the number of trees ranged from one tree to 326 trees, with a total of 50,570 trees evaluated and 3,765 errors identified. Overall, the commission and omission error rates were 4.9% and 2.7%, respectively, a net uncertainty of 2.2%.Allometric uncertainty estimationThe prediction of tree carbon from the crown area for a single tree based on crown area alone is inherently uncertain47,48. As the allometric equations are based on three different datasets, we compute their uncertainties independently, combine them and put them in relation to the total carbon measured in the three datasets.The allometric equations were established using an optimal least-squares fit of an affine linear model predicting the logarithmic carbon from the logarithmic tree crown area19. To estimate the uncertainty of the allometric equations, we repeated the fitting using random subsampling. The datasets were randomly split into training data (80%) for fitting the allometric equations and validation data (20%) for assessing the uncertainty. For example, from the root measurements, (({A}_{1},{y}_{1}),ldots ,({A}_{{N}_{{rm{r}}}},,{y}_{{N}_{{rm{r}}}})), we compute ({mu }_{{rm{r}}}=frac{1}{{N}_{{rm{r}}}}mathop{sum }limits_{i=1}^{{N}_{{rm{r}}}}{y}_{i}) and ({hat{mu }}_{{rm{r}}}=frac{1}{{N}_{{rm{r}}}}mathop{sum }limits_{i=1}^{{N}_{{rm{r}}}}{text{mass}}_{{rm{r}}}({A}_{i})). The corresponding error is ({varDelta }_{{rm{r}}}=|{mu }_{{rm{r}}}-{hat{mu }}_{{rm{r}}}|).Because the total carbon for a tree with a certain crown area is the sum of the three carbon components, we add the absolute uncertainties assuming independence45.$${varDelta }_{{rm{a}}{rm{l}}{rm{l}}{rm{o}}{rm{m}}{rm{e}}{rm{t}}{rm{r}}{rm{i}}{rm{c}}}simeq sqrt{{varDelta }_{{rm{f}}}^{2}+{varDelta }_{{rm{w}}}^{2}+{varDelta }_{{rm{r}}}^{2}}$$and compute the relative uncertainty as ({delta }_{text{allometric}}=frac{{varDelta }_{text{allometric}}}{{mu }_{text{mass}}}), in which the average mass μmass is given by the sum of the averages for wood (μw), leaves (μf) and root (μr). This process was repeated ten times, resulting in a mean relative uncertainty of$${bar{delta }}_{{rm{allometric}}}=19.5 % .$$Total carbon uncertaintyWe combine the uncertainties from the neural net mapping and our allometric equations, which can be viewed as considering (1 + A)·(1 + B) with A and B being random variables with standard deviations δarea and δallometric. Neglecting higher-order and interaction terms, we combine the two sources of uncertainty to (delta simeq sqrt{{delta }_{{rm{area}}}^{2}+{bar{delta }}_{{rm{allometric}}}^{2}}), resulting in an uncertainty in total tree carbon for our study of ±19.8%. See also Extended Data Fig. 9 for the RMSEs of our predicted crown areas calculated on external validation data from ref. 1, binned on the basis of the 50th quantiles of the hand-labelled crown areas and converted also into carbon. Extended Data Fig. 10 is a flow diagram summarizing our methods.Our viewerVisualizing our large tree-mapping dataset in an interactive format was essential for quality-control purposes, exploration of the data and hypothesis creation. Creating a web-based viewer serves the purpose of being the initial point of interaction with our dataset for fellow researchers, local stakeholders or the general public. The visualization of more than 10 billion trees in a web browser required maintaining performance, interactivity and individual metadata for each polygon. Users should be able to zoom in to any area within the dataset to view individual tree polygons and query their statistics while at the same time accurately depicting the overall trends of the dataset at lower zoom levels. The visualization also needed to clearly denote where data were missing or possibly affected by clouds or aerosols. Finally, the extent and origin of the source imagery, its acquisition date and a preview of the imagery needed to be available. To accomplish these goals, a vector-tile-based approach was taken, with the data visualized in a Mapbox GL JS map within a React web application. To create vector tiles covering the entire study area, we developed a data-processing pipeline using high-performance computing resources to transform the data into compatible formats, as well as to package, optimize and combine the vector tiles themselves.We used two tracks to store and visualize the results of this study on the web: vector polygon data and generalized rasters representing tree crown density. At the native spatial resolution of 50 cm, the map shows the full-resolution tree polygon dataset. At lower-spatial-resolution zoom levels, rasterized representations of tree density are shown. Visualizing generalized rasters in place of vector polygons improves performance substantially. As users zoom in to higher spatial resolutions, the raster layer fades away and is replaced by the full-resolution polygon layer. Once zoomed far enough to resolve individual polygons, users can click to select a polygon to show a map overlay containing various properties of the tree, as well as the date on which the source imagery was acquired and a link to preview the source imagery.Rainfall dataWe used the rainfall data of Funk et al. to estimate annual rainfall at 5.6-m grids46. We averaged the available data from 1982 to 2017 and extracted the mean annual rainfall for each mapped tree and bilinearly interpolated it to 100 × 100-m resolution. The rainfall data were also used to classify the study area into mean annual precipitation zones: hyper-arid from 0–150 mm year−1, arid from 150–300 mm year−1, semi-arid from 300–600 mm year−1 and sub-humid from 600–1,000 mm year−1 zones. The rainfall data are found at https://data.chc.ucsb.edu/products/CHIRPS-2.0/africa_monthly/ (ref. 46). More

Data sourcesMODIS on the Aqua satellite provides a global coverage within 1–2 days. All images acquired by this satellite mission from January 2003 to December 2020 were used in our study to detect global coastal phytoplankton blooms, with a total of 0.76 million images. MODIS Level-1A images were downloaded from the Ocean Biology Distributed Active Archive Center (OB.DAAC) at NASA Goddard Space Flight Center (GSFC), and were subsequently processed with SeaDAS software (version 7.5) to obtain Rayleigh-corrected reflectance (Rrc (dimensionless), which was converted using the rhos (in sr−1) product (rhos × π) from SeaDAS)41, remote sensing reflectance (Rrs (sr−1)) and quality control flags (l2_flags). If a pixel was flagged by any of the following, it was then removed from phytoplankton bloom detection: straylight, cloud, land, high sunglint, high solar zenith angle and high sensor zenith angle (https://oceancolor.gsfc.nasa.gov/atbd/ocl2flags/). MODIS level-3 product for aerosol optical thicknesses (AOT) at 869 nm was also obtained from OB.DAAC NASA GSFC (version R2018.0), which was used to examine the impacts of aerosols on bloom trends.We examined the algal blooms in the EEZs of 153 ocean-bordering countries (excluding the EEZs in the Caspian Sea or around the Antarctic), 126 of which were found with at least one bloom in the past two decades. The EEZ dataset is available at https://www.marineregions.org/download_file.php?name=World_EEZ_v11_20191118.zip. The EEZs are up to 200 nautical miles (or 370 km) away from coastlines, which include all continental shelf areas and offer the majority of marine resources available for human use. Regional statistics of algal blooms were also performed for LMEs. LMEs encompass global coastal oceans and outer edges of coastal currents areas, which are defined by various distinct features of the oceans, including hydrology, productivity, bathymetry and trophically dependent populations42. Of the 66 LMEs identified globally, we excluded the Arctic and Antarctic regions and examined 54 LMEs. The boundaries of LMEs were obtained from https://www.sciencebase.gov/catalog/item/55c77722e4b08400b1fd8244.We used HAEDAT to validate our satellite-detected phytoplankton blooms in terms of presence or absence. The HAEDAT dataset (http://haedat.iode.org) is a collection of records of HAB events, maintained under the UNESCO Intergovernmental Oceanographic Commission and with data archives since 1985. For each HAB event, the HAEDAT records its bloom period (ranging from days to months) and geolocation. We merged duplicate entries when both the recorded locations and times of the HAEDAT events were very similar to one another, and a total number of 2,609 HAEDAT events were ultimately selected between 2003 and 2020.We used the ¼° resolution National Oceanic and Atmospheric Administration Optimum Interpolated SST (v. 2.1) data to examine the potential simulating effects of warming on the global phytoplankton trends. We also estimated the SST gradients following the method of Martínez-Moreno33. As detailed in ref. 33, the SST gradient can be used as a proxy for the magnitude of oceanic mesoscale currents (EKE). We used the SST gradient to explore the effects of ocean circulation dynamics on algal blooms.Fertilizer uses and aquaculture production for different countries was used to examine the potential effects of nutrient enrichment from humans on global phytoplankton bloom trends. Annual data between 2003 and 2019 on synthetic fertilizer use, including nitrogen and phosphorus, are available from https://ourworldindata.org/fertilizers. Annual aquaculture production includes cultivated fish and crustaceans in marine and inland waters, and sea tanks, and the data between 2003 and 2018 are available from https://ourworldindata.org/grapher/aquaculture-farmed-fish-production.The MEI, which combines various oceanic and atmospheric variables36, was used to examine the connections between El Niño–Southern Oscillation activities and marine phytoplankton blooms. The dataset is available from https://psl.noaa.gov/enso/mei/.Development of an automated bloom detection methodA recent study by the UNESCO Intergovernmental Oceanographic Commission revealed that globally reported HAB events have increased6. However, such an overall increasing trend was found to be highly correlated with recently intensified sampling efforts6. Once this potential bias was accounted for by examining the ratio between HAB events to the number of samplings5, there was no significant global trend in HAB incidence, though there were increases in certain regions. With synoptic, frequent, and large-scale observations, satellite remote sensing has been extensively used to monitor algal blooms in oceanic environments17,18,19. For example, chlorophyll a (Chla) concentrations, a proxy for phytoplankton biomass, has been provided as a standard product by NASA since the proof-of-concept Coastal Zone Color Scanner (1978–1986) era43,44. The current default algorithm used to retrieve Chla products is based on the high absorption of Chla at the blue band45,46, which often shows high accuracy in the clear open oceans but high uncertainties in coastal waters. This is because, in productive and dynamic coastal oceans, the absorption of Chla in the blue band can be obscured by the presence of suspended sediments and/or coloured dissolved organic matter (CDOM)47. To address this problem, various regionalized Chla algorithms have been developed48. Unfortunately, the concentrations of the water constituents (CDOM, sediment and Chla) can vary substantially across different coastal oceans. As a result, a universal Chla algorithm that can accurately estimate Chla concentrations in global coastal oceans is not currently available.Alternatively, many spectral indices have been developed to identify phytoplankton blooms instead of quantifying their bloom biomass, including the normalized fluorescence line height21 (nFLH), red tide index49 (RI), algal bloom index47 (ABI), red–blue difference (RBD)50, Karenia brevis bloom index50 (KBBI) and red tide detection index51 (RDI). In practice, the most important task for these index-based algorithms is to determine their optimal thresholds for bloom classification. However, such optimal thresholds can be regional-or image-specific20, due to the complexity of optical features in coastal waters and/or the contamination of unfavourable observational conditions (such as thick aerosols, thin clouds, and so on), making it difficult to apply spectral-index-based algorithms at a global scale.To circumvent the difficulty in determining unified thresholds for various spectral indices across global coastal oceans, an approach from a recent study to classify algal blooms in freshwater lakes52 was adopted and modified here. In that study, the remotely sensed reflectance data in three visible bands (red, green and blue) were converted into two-dimensional colour space created by the Commission Internationale del’éclairage (CIE), in which the position on the CIE chromaticity diagram represented the colour perceived by human eyes (Extended Data Fig. 1a). As the algal blooms in freshwater lakes were manifested as greenish colours, the reflectance of bloom-containing pixels was expected to be distributed in the green gamut of the CIE chromaticity diagram; the stronger the bloom, the closer the distance to the upper border of the diagram (the greener the water).Here, the colour of phytoplankton blooms in the coastal oceans can be greenish, yellowish, brownish, or even reddish53, owing to the compositions of bloom species (diatoms or dinoflagellates) and the concentrations of different water constituents. Furthermore, the Chla concentrations of the coastal blooms are typically lower than those in inland waters, thus demanding more accurate classification algorithms. Thus, the algorithm proposed by Hou et al.52 was modified when using the CIE chromaticity space for bloom detection in marine environments. Specifically, we used the following coordinate conversion formulas to obtain the xy coordinate values in the CIE colour space:$$begin{array}{c}x=X/(X+Y+Z)\ y=Y/(X+Y+Z)\ X=2.7689R+1.7517G+1.1302B\ Y=1.0000R+4.5907G+0.0601B\ Z=0.0000R+0.0565G+5.5943Bend{array}$$
(1)
where R, G and B represent the Rrc at 748 nm, 678 nm (fluorescence band) and 667 nm in the MODIS Aqua data, respectively. By contrast, the R, G and B channels used in Hou et al.52 were the red, green and blue bands. We used the fluorescence band for the G channel because, for a given region, the 678 nm signal increases monotonically with the Chla concentration for blooms of moderate intensity21, which is similar to the response of greenness to freshwater algal blooms. Thus, the converted y value in the CIE coordinate system represents the strength of the fluorescence. In practice, for pixels with phytoplankton blooms, the converted colours in the chromaticity diagram will be located within the green, yellow or orange–red gamut (see Extended Data Fig. 1a); the stronger the fluorescence signal is, the closer the distance to the upper border of the CIE diagram (larger y value). By contrast, for bloom-free pixels without a fluorescence signal, their converted xy coordinates will be located in the blue or purple gamut. Therefore, we can determine a lower boundary in the CIE two-dimensional coordinate system to separate bloom and non-bloom pixels, similar to the method proposed by Hou et al.52.We selected 53,820 bloom-containing pixels from the MODIS Rrc data as training samples to determine the boundary of the CIE colour space. These sample points were selected from nearshore waters worldwide where frequent phytoplankton blooms have been reported (Extended Data Fig. 2); the algal species included various species of dinoflagellates and diatoms20. A total of 80 images was used, which were acquired from different seasons and across various bloom magnitudes, to ensure that the samples used could almost exhaustively represent the different bloom conditions in the coastal oceans.We combined the MODIS FLHRrc (fluorescence line height based on Rrc) and enhanced red–green–blue composite (ERGB) to delineate bloom pixels manually. The FLHRrc image was calculated as:$$begin{array}{c}{{rm{FLH}}}_{{rm{Rrc}}}={R}_{{rm{rc}}678}times {F}_{678}-[{R}_{{rm{rc}}667}times {F}_{667}+({R}_{{rm{rc}}748}times {F}_{748}\ ,,-,{R}_{{rm{rc}}667}times {F}_{667})times (678-667)/(748-667)]end{array}$$
(2)
where Rrc667, Rrc678 and Rrc748 are the Rrc at 667, 678 and 748 nm, respectively, and F667, F678 and F748 are the corresponding extraterrestrial solar irradiance. ERGB composite images were generated using Rrc of three bands at 555 (R), 488 (G) and 443 nm (B). Although phytoplankton-rich and sediment-rich waters have high FLHRrc values, they appear as darkish and bright features in the ERGB images (Extended Data Fig. 3), respectively21. In fact, visual examination with fluorescence signals and ERGB has been widely accepted as a practical way to delineate coastal algal blooms on a limited number of images21,54,55. Note that the FLHRrc here was slightly different from the NASA standard nFLH product56, as the latter is generated using Rrs (corrected for both Rayleigh and aerosol scattering) instead of Rrc (with residual effects of aerosols). However, when using the NASA standard algorithm to further perform aerosol scattering correction over Rrc, 20.7% of our selected bloom-containing pixels failed to obtain valid Rrs (without retrievals or flagged as low quality), especially for those with strong blooms (see examples in Extended Data Fig. 4). Likewise, we also found various nearshore regions with invalid Rrs retrievals. By contrast, Rrc had valid data for all selected samples and showed more coverage in nearshore coastal waters. The differences between Rrs and Rrc were because the assumptions for the standard atmospheric correction algorithm do not hold for bloom pixels or nearshore waters with complex optical properties57. In fact, Rrc has been used as an alternative to Rrs in various applications in complex waters58,59.We converted the Rrc data of 53,820 selected sample pixels into the xy coordinates in the CIE colour space (Extended Data Fig. 1a). As expected, these samples of bloom-containing pixels were located in the upper half of the chromaticity diagram (the green, yellow and orange–red gamut) (Extended Data Fig. 1a). We determined the lower boundary of these sample points in the chromaticity diagram, which represents the lightest colour and thus the weakest phytoplankton blooms; any point that falls above this boundary represents stronger blooms. The method to determine the boundary was similar to Hou et al.52: we first binned the sample points according to the x value in the chromaticity diagram and estimated the 1st percentile (Q1%) of the corresponding Y for each bin; then, we fit the Q1% using two-order polynomial regression. Sensitivity analysis with Q0.3% (the three-sigma value) resulted in minor changes ( 1/3 AND y  > y2), it is classified as a ‘bloom’ pixel.Depending on the local region and application purpose, the meaning of ‘phytoplankton bloom’ may differ. Here, for a global application, the pixelwise bloom classification is based on the relationship (represented using the CIE colour space) between Rrc in the 667-, 678- and 754-nm bands derived from visual interpretation of the 80 pairs of FLHRrc and ERGB imagery. Instead of a simple threshold, we used a lower boundary of the sample points in the chromaticity diagram to define a bloom. In simple words, a pixel is classified as a bloom if its fluorescence signal is detectable (the associated xy coordinate in the CIE colour space located above the lower boundary). Histogram of the nFLH values from the 53,820 training pixels demonstrated the minimum value of ~0.02 mW cm−2 μm−1 (Extended Data Fig. 1a), which is in line with the lower-bound signal of K. brevis blooms on the West Florida shelf21,47. Note that, such a minimum nFLH is determined from the global training pixels, and it does not necessarily represent a unified lower bound for phytoplankton blooms across the entire globe, especially considering that fluorescence efficiency may be a large variable across different regions. Different regions may have different lower bounds of nFLH to define a bloom, and such variability is represented by the predefined boundary in the CIE chromaticity diagram in our study. Correspondingly, although the accuracy of Chla retrievals may have large uncertainties in coastal waters, the histogram of the 53,820 training pixels shows a lower bound of ~1 mg m−3 (Extended Data Fig. 1a). Similarly to nFLH, such a lower bound may not be applicable to all coastal regions, as different regions may have different lower bounds of Chla for bloom definition.Although the MODIS cloud (generated by SeaDAS with Rrc869 0.12) and Index2 ( More

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