The two sampling sites, Station Gukdong and Station Gyedong, were located in the innermost areas of Gamak Bay and Yeosuhae Bay, South Korea, respectively (Figures 1A,B). These bays are located near the mouth of the Seomjin River, which is one of the largest rivers in Korea, from which freshwater runoff reaches the bays after heavy rainfall (Jeong et al., 2017). Twenty liters of seawater were collected below the water surface at St. Gukdong using a clean bucket, six times across May, July, and August 2019, and 20 L of seawater was gently collected below the surface at St. Gyedong, once in August 2019 (Table 1). The temperature, salinity, pH, and dissolved oxygen (DO) of the samples were measured using a YSI Professional Plus meter (YSI, Yellow Springs, OH, United States) immediately after collection. The seawater samples were gently filtered through a 100-μm Nitex mesh to minimize the effects of large detritus or solids in suspension on phytoplankton growth during the bottle incubation experiments (e.g., shading, flocculation, and nutrient adsorption) (Young and Barber, 1973; Sew and Todd, 2020). The collected seawater was then immediately transported to the laboratory and placed in culture chambers at the same temperature (±2°C) as the seawater temperature at collection. The amount of rainfall and the wind speed and path of Typhoon Danas during the sampling period were obtained from the Korea Meteorological Administration (2020)² and the Korea Hydrographic and Oceanographic Agency (2021).³

Seawater collected on each sampling date was gently mixed and evenly distributed into 2 L polystyrene bottles (JetBiofiltration Co., Ltd, Guangzhou, China). All bottles incubated under each condition were set up in triplicates and placed in temperature-controlled chambers set to the ambient water temperature (±2°C; Table 1). These bottles were capped loosely and then incubated for 10 days at 100 μmol photons m^–2 s^–1 under a 14 h:10 h light:dark cycle using light-emitting diodes (LEDs; FS-075MU, 6500K; Suram Inc., Suwon, South Korea). Based on the light intensity at which the maximum growth rates of many phytoplankton occurred and the effects of photoinhibition on phytoplankton growth were minimized, a light intensity of 100 μmol photons m^–2 s^–1 was used. This ensured that light was not a limiting factor in this study. For example, the light intensities at which the maximum growth rates were observed were >10 μmol photons m^–2 s^–1 for the dinoflagellate Paragymnodinium shiwhaense (Jeong et al., 2018), >58 μmol photons m^–2 s^–1 for the dinoflagellate Alexandrium pohangense (Lim et al., 2019), >70 μmol photons m^–2 s^–1 for the diatom Leptocylindrus danicus (Verity, 1982), >80 μmol photons m^–2 s^–1 for the diatoms Skeletonema costatum, Thalassiosira minima, and Thalassiosira eccentrica, and the dinoflagellates Protodinium simplex, Scrippsiella sweeneyae, and Prorocentrum micans (Chan, 1978), and >90 μmol photons m^–2 s^–1 for the dinoflagellate Margalefidinium polykrikoides (Kim et al., 2004). Moreover, the light intensities at which the negative growth rates of phytoplankton due to photoinhibition occurred were >123 μmol photons m^–2 s^–1 for the dinoflagellate Karenia brevis (Magaña and Villareal, 2006), >135 μmol photons m^–2 s^–1 for the dinoflagellate Tripos furca (Nordli, 1957), >247 μmol photons m^–2 s^–1 for the dinoflagellate Takayama helix (Ok et al., 2019), and >317 μmol photons m^–2 s^–1 for the diatoms Ditylum brightwellii and Thalassiosira sp. (Brand and Guillard, 1981). Daylength in the study area from May to August is approximately 13–14.5 h (Sunrise-Sunset, 2021).⁴ Thus, this light condition can simulate the natural environment in the study area.

Subsampling was conducted daily in all experimental seawaters except for the one collected on May 16, 2019 (every two days) to quantify the Chl-a and nutrient concentrations and the planktonic protist abundance.

For Chl-a analysis, a 20 mL aliquot taken from each bottle was filtered through a GF/F filter (Whatman Inc., Clifton, NJ, United States), and the filtered membrane was placed in a 15 mL conical tube and stored below −20°C. Then, 10 mL of 90% acetone was added to the conical tube containing the sample. The conical tubes were sonicated for 10 min, wrapped in aluminum foil to avoid light, stored in a 4°C chamber overnight, and centrifuged, and then 5 mL of the supernatant was taken from each tube and measured using a 10-AU Turner fluorometer (Turner Designs, Sunnyvale, CA, United States). For nutrient analysis, a 20 mL aliquot of the filtrate samples was stored in polyethylene vials below −20°C. The concentrations of nitrate plus nitrite (hereafter nitrate or NO₃), ammonium (NH₄), phosphate (PO₄), and silicate (SiO₂) in the seawater samples were measured using a 4-channel nutrient auto-analyzer (QuAAtro, SEAL Analytical GmbH, Norderstadt, Germany; Bran+Luebbe Analyzing Technologies, 2004a, b, 2005; SEAL Analytical GmbH, 2005).

To quantify the abundance of dominant planktonic protists, a 10 mL aliquot was taken from each bottle and fixed with 5% acidic Lugol’s solution (Sournia, 1978). Each dominant taxon was enumerated by counting >200 or all cells for each species in a Sedgewick-Rafter chamber using an inverted microscope (BX53, Olympus, Japan) at a magnification of ×100–200.

To convert the abundance (cells mL^–1) of dominant planktonic protists to biomass (ng C mL^–1), the cellular carbon content of each taxon was obtained from the literature or estimated from its biovolume according to Menden-Deuer and Lessard (2000). The biovolume of each taxon was calculated using Hillebrand et al. (1999) after measuring the cell length and width, or diameter and height of ≥5 cells of the taxon.

The concentrations of NO₃, NH₄, PO₄, SiO₂, and Chl-a were measured every sampling day and dissolved inorganic nitrogen (NO₃+NH₄; DIN) was calculated from these data. When Chl-a increased, the magnitude of the Chl-a peak (i.e., the maximum Chl-a) and the time elapsed until the Chl-a peak occurred (Day_peak) were determined. When Chl-a decreased, the initial Chl-a was regarded as the Chl-a peak. Using the data, the ratio of the initial NO₃ to Chl-a [μM (μg L^–1)^–1] was calculated by dividing the initial NO₃ by the initial Chl-a for each incubated seawater sample. This value was also calculated as a unitless ratio, multiplied by the molecular weight of N (=14 g mol^–1) to convert μmol L^–1 (=μM) to μg L^–1. The growth rate (μ, day^–1) of the phytoplankton community was calculated as follows:

When the Chl-a decreased, the growth rate was allocated to zero.

To develop equations for the magnitude of the Chl-a peak of the phytoplankton community, four different simple linear regressions were analyzed: the Chl-a peak versus the initial NO₃; the Chl-a peak versus the ratio of the initial NO₃ to Chl-a; the ratio of the peak-to-initial Chl-a versus the initial NO₃; and the ratio of the peak-to-initial Chl-a versus the ratio of the initial NO₃ to Chl-a. Furthermore, to develop an equation for Day_peak, four different simple linear regressions were also analyzed: Day_peak versus the natural log of the initial NO₃; Day_peak versus the natural log of the ratio of the initial NO₃ to Chl-a; the growth rate versus the natural log of the initial NO₃; and the growth rate versus the natural log of the ratio of the initial NO₃ to Chl-a. The growth rate was used as a variable because the growth rate equation itself includes time. Similar analyses were conducted using NH₄, DIN, PO₄ and SiO₂, as well as the ratio of the initial NO₃ to PO₄ and the ratio of the initial NO₃ to SiO₂. To apply this method at a species level, the peak abundance of Skeletonema costatum of each seawater sample during bottle incubation was determined. The goals were to develop equations for predicting bloom outbreaks of each species and to assess the contribution of each bloom species of interest to the phytoplankton community. The cellular chlorophyll-a content of S. costatum was obtained from Hitchcock (1980). The estimated Chl-a peak and Day_peak of S. costatum were determined using the analyses described above.

Linear regression equations were established by fitting the data using DeltaGraph (SPSS Inc., Chicago, IL, United States). These equations were solved to deduce the Chl-a peak and Day_peak.

To test whether the bloom prediction equations obtained from the present study (in sections “Correlations Between the Variables Related to the Chl-a Peak” and “Correlations Between Variables Related to the Timing of Chl-a Peaks”) can be used to predict bloom outbreaks in the field, in situ time-series data of the automated seawater quality monitoring system in the South Sea of Korea (St. Gwangyang and St. Masan; Figure 1) were obtained from the Marine Environment Information System (2021).⁵ Data from May to October in 2016–2019 were used because the water temperatures during this period were similar to those of our incubation experiments using the seawaters collected from St. Gukdong and St. Gyedong. The values of NO₃, Chl-a, salinity, and water temperature measured at five-minute intervals in a day were each averaged to obtain the mean value of the day (Supplementary Table 1). Based on these monitored data, the following steps were conducted (Supplementary Figure 1). First, the Chl-a peak was found when the Chl-a exceeded 5 μg L^–1 with an increasing trend, assuming the criterion of a phytoplankton bloom as 200 ng C mL^–1 and a carbon to Chl-a ratio of 40 (Peterson and Festa, 1984; Jeong et al., 2013). Second, Chl-a and NO₃ levels, prior to reaching the Chl-a peak, were selected. Third, the time elapsed until the Chl-a peak occurred (Day_peak) was counted. Fourth, using the selected NO₃ and Chl-a data and the equations developed in this study (in Sections “Correlations Between the Variables Related to the Chl-a Peak” and “Correlations Between Variables Related to the Timing of Chl-a Peaks”), the predicted values were calculated for each date and then compared with the actual Chl-a peak or Day_peak using linear regression analyses. Data were not used when the daily average salinity changed by >2 because it indicated seawater with different nutrient conditions introduced from the river or large streams.

Pearson’s correlation was used to examine the relationships between variables (Pearson, 1895). All statistical analyses were performed using SPSS (version 25.0; IBM Corp., Armonk, NY, United States). The significance criterion was set at 0.05.

During the study period in 2019, water temperature, precipitation, and salinity varied considerably whereas pH and dissolved oxygen (DO) did not (Figure 2): the water temperature ranged from 18.2°C on May 19 to 26.6°C on August 22 (Figure 2A); the precipitation summed for 7 days was 274.1 mm on July 22 and July 24 but <100 mm on the remaining dates (Figure 2B); the salinity was 24.36 and 29.10 on July 22 and July 24, respectively, but exceeded 29.9 on the remaining dates, with a maximum of 33.78 on May 16 (Figure 2C); the pH was 7.89 on July 22 but exceeded 7.90 on the remaining dates, with a maximum of 8.10 on August 22 (Figure 2D); and the DO was 5.01 mg L^–1 on July 24 but exceeded 5.4 mg L^–1 on the remaining dates with a maximum of 6.07 mg L^–1 on May 16 (Figure 2E).

There was 65.8 mm of rainfall between May 17 and May 18, 274.1 mm between July 17 and July 21, and 31.9 mm between August 21 and 22. Typhoon Danas passed through Korea and affected the study area on July 20 (Figure 1A). The maximum wind speed during the passage of the typhoon in the study area was 21.3 m s^–1.

At the beginning of each bottle incubation experiment, the most dominant planktonic protist species based on carbon biomass in chronological order was the diatom Cylindrotheca closterium on May 16, the photosynthetic dinoflagellate T. furca on May 19, the tintinnid ciliate Tintinnopsis sp. on July 17 and July 22, the diatoms Pseudo-nitzschia pungens on July 24 and Chaetoceros curvisetus on August 20, and the photosynthetic ciliate Mesodinium rubrum on August 22 (Figures 3A–G).

The initial concentrations of NO₃, NH₄, and DIN of the experimental seawater ranged from 0.6 μM (August 20) to 39.7 μM (July 22), from 0.1 μM (July 17) to 10.2 μM (July 22), and from 1.5 μM (July 17) to 49.9 μM (July 22), respectively (Figures 4A–C). The initial PO₄ concentrations ranged from 0.1 μM (July 24) to 1.1 μM (July 22; Figure 4D), while the initial SiO₂ concentrations varied from 4.4 μM (August 20) to 93.4 μM (July 22; Figure 4E). The initial Chl-a concentrations ranged from 0.8 μg L^–1 (May 19) to 24.5 μg L^–1 (July 24; Figure 4F).

Chl-a showed two different patterns as incubation time progressed (Figures 5A–G); first, it decreased in the seawater samples from May 16, July 17, and August 20 (Figures 5A–C); second, it increased to a peak, but then decreased later in the rest of the samples as NO₃, NH₄, DIN, PO₄, or SiO₂ became depleted (Figures 5D–G).

Chlorophyll-a decreased during incubation when the initial NO₃ concentrations were ≤2.4 μM (Figures 5A–C,H–J and Supplementary Figure 2A). In contrast, Chl-a increased when the initial NO₃ concentrations were ≥3.5 μM (Figures 5D–G,K–N and Supplementary Figure 2B). Chl-a decreased when the initial NH₄ concentrations were ≤1.0 μM, while Chl-a increased when the concentrations were ≥2.1 μM (Figures 5O–Q,R–U). Furthermore, Chl-a decreased when the initial DIN concentrations were ≤3 μM but increased when the concentrations were ≥6.4 μM (Figure 5V–X,Y–AB). Chl-a decreased during incubation when the initial PO₄ concentrations were ≤0.3 μM (Figures 5A–C,AC–AE) with one exception: Chl-a increased when the initial PO₄ concentration was 0.1 μM in the seawater on July 24 (Figures 5F,AH). Chl-a also decreased when the initial SiO₂ concentrations were ≤24.5 μM (Figures 5A–C,AJ–AL) with one exception: Chl-a increased when the initial SiO₂ concentration was 18.7 μM in the seawater of May 19 (Figures 5D,AM).

The Chl-a peak of the phytoplankton community was in between 4.6 and 114 μg L^–1 (Figures 6A,B). The ratio of the peak-to-initial Chl-a of the phytoplankton community varied from 1.0 to 61.4 (Figures 6C,D). The ratio of the initial NO₃ to Chl-a of the phytoplankton community ranged from 0.1 to 24.2 μM (μg L^–1)^–1 (equivalent to 0.8–339 in a unitless ratio, respectively; Figures 6B,D).

To develop equations for the magnitude of the Chl-a peak using the initial NO₃ or the ratio of the initial NO₃ to Chl-a, four different linear regressions between two variables were analyzed (see section “Data Analysis and Equation Development”). The Chl-a peak of the phytoplankton community was significantly correlated with the initial NO₃ concentration and the ratio of the initial NO₃ to Chl-a (Figures 6A,B). The ratio of peak-to-initial Chl-a of the phytoplankton community was also significantly correlated with the initial NO₃ and with the ratio of initial NO₃ to Chl-a (Figures 6C,D). Equations (Eqs 1–4 in Table 2) for calculating the Chl-a peak of the phytoplankton community were obtained from linear regressions in Figure 6.

These types of correlations were significant when NH₄, DIN, PO₄, and SiO₂ were used (Supplementary Figures 3, 4). However, the Chl-a peak or the ratio of the peak-to-initial Chl-a of the phytoplankton community was not significantly correlated with the ratio of the initial NO₃ to PO₄ and the ratio of the initial NO₃ to SiO₂ (Supplementary Figure 5).

In these incubation experiments, the elapsed day until the Chl-a peak of the phytoplankton community occurred (Day_peak) ranged from days 0 to 4, (Figures 7A,B). Furthermore, the growth rates of the phytoplankton community ranged from 0.0 to 1.4 day^–1 (Figures 7C,D).

To develop equations for determining Day_peak using the natural log of the initial NO₃ or the natural log of the ratio of initial NO₃ to Chl-a, four different linear regressions between two variables were analyzed (see section “Data Analysis and Equation Development”). Day_peak of the phytoplankton community was significantly correlated with the natural log of the initial NO₃ and with the natural log of the ratio of the initial NO₃ to Chl-a (Figures 7A,B). The growth rate of the phytoplankton community was also significantly correlated with the natural log of the initial NO₃ and with the natural log of the ratio of the initial NO₃ to Chl-a (Figures 7C,D). Equations (Eqs 5–8 in Table 2) for calculating Day_peak were obtained from the equations of linear regressions in Figure 7.

These types of correlations were significant when NH₄, DIN, and SiO₂ were used, however, this was not always the case when PO₄ was used (Supplementary Figures 6, 7). Moreover, Day_peak or growth rate of the phytoplankton community was significantly correlated with the natural log of the ratio of initial NO₃ to PO₄ but not with the ratio of the initial NO₃ to SiO₂ (Supplementary Figure 8).

The ranges of the daily average values of the water temperature, salinity, NO₃, and Chl-a in St. Gwangyang and St. Masan at the selected dates in 2016–2019 were different from those of St. Gukdong and St. Gyedong (Table 3 and Supplementary Table 1). The daily average water temperature ranges at St. Gwangyang (17.9–31.2°C) and St. Masan (16.5–30.6°C) were greater than those at St. Gukdong and St. Gyedong (18.2–26.6°C). The maximum values of the daily average salinity at each station were slightly different, but the minimum values at St. Gwangyang (5.1) and St. Masan (19.1) were much lower than those at St. Gukdong and St. Gyedong (24.4). The ranges of the daily average NO₃ concentration at St. Gukdong and St. Gyedong (0.6–39.7 μM) were much greater than those at St. Gwangyang (0.6–16.1 μM) and St. Masan (0.1–7.7 μM). However, the ranges of the daily average Chl-a concentration at St. Gwangyang (1.1–49.5 μg L^–1) and St. Masan (0.3–36.8 μg L^–1) were much wider than those at St. Gukdong and St. Gyedong (0.8–24.5 μg L^–1).

Applying Eqs 1–3 from Table 2, the actual peak Chl-a value measured at St. Gwangyang or St. Masan and the combined actual Chl-a peak values from both stations were not always significantly correlated with the predicted peak Chl-a value (Figures 8A–I). By contrast, using Eq. 4, the predicted values of Chl-a peak showed significant correlations with the actual Chl-a peak (Figures 8J–L). The root mean square errors (RMSE) were 10.6, 9.2, and 11.6 μg L^–1 for St. Gwangyang, St. Masan, and the combined data of the two stations, respectively. Thus, Eq. 4 was chosen as a best-fit equation to predict the Chl-a peak in the field.

Based on Eqs 5, 7, and 8 from Table 2, the actual Day_peak data obtained from St. Gwangyang or St. Masan and the combined data of the two stations were not always significantly correlated with the predicted Day_peak (Figures 9A–C,G–L). On the other hand, with Eq. 6, the actual Day_peak data were significantly correlated with the predicted Day_peak (Figures 9D–F). The RMSE was all 1 day for St. Gwangyang, St. Masan, and the combined data of the two stations. Thus, Eq. 6 was selected as a best-fit equation to predict Day_peak in the field.

These comparisons were also made on Eqs 9–16 for in situ NH₄ data and Eqs 17–24 for in situ DIN data (Supplementary Tables 1–3). The actual peak Chl-a values measured at St. Gwangyang or St. Masan and the combined actual peak Chl-a values from both stations were significantly correlated with the predicted values calculated using Eq. 11, 19, and 20 (Supplementary Figures 9, 10). The predicted Day_peak values were significantly correlated with the actual values when Eqs. 13 or 14 and Eqs. 21 or 22 were used (Supplementary Figures 11, 12). Therefore, any type of nitrogen data (NO₃, NH₄, or DIN concentrations) can be implemented to predict Day_peak values at St. Gwangyang or St. Masan.

The Chl-a peak estimated for Skeletonema costatum ranged from 0.02 to 12.2 μg L^–1 (Supplementary Figure 13A,B). The ratio of the peak-to-initial Chl-a estimated for S. costatum showed a spectrum of 1.0–90.4 (Supplementary Figures 13C,D). The ratio of the initial NO₃ to Chl-a estimated for S. costatum had values in the range 2.7–1225.6 μM (μg L^–1)^–1 (equivalent to 38 and 17,158, in a unitless ratio, respectively; Supplementary Figures 13B,D).

Among the four types of linear regression (see section “Data Analysis and Equation Development”), there were significant correlations between the Chl-a peak estimated for S. costatum against the initial NO₃ concentration and the ratio of the latter to the Chl-a concentration estimated for S. costatum against the ratio of the peak-to-initial Chl-a concentration estimated for S. costatum (Supplementary Figures 13A–D). These two correlations were always significant when NH₄, DIN, PO₄, or SiO₂ were used (Supplementary Table 4). However, the Chl-a peak or the ratio of the peak-to-initial Chl-a concentration estimated for S. costatum was not significantly correlated with the ratio of initial NO₃ to PO₄ concentrations nor the ratio of initial NO₃ to SiO₂ concentrations (Supplementary Table 4).

In these incubation experiments, it took 0–4 days to reach the Chl-a peak (Supplementary Figures 13E,F). The growth rates of S. costatum ranged from 0.0 to 2.3 day^–1 (Supplementary Figures 13G,H). Four different linear regressions between two variables were all significant when NO₃, NH₄, and DIN were applied (Supplementary Table 5 and Figures 13E–H). However, when PO₄ was used, there were no significant correlations (Supplementary Table 5). Moreover, Day_peak or the growth rate of S. costatum was not always significantly correlated with the natural log of the ratio of initial NO₃ to PO₄ or initial NO₃ to SiO₂ (Supplementary Table 5).