# Empirical Model for Phycocyanin Concentration Estimation as an Indicator of Cyanobacterial Bloom in the Optically Complex Coastal Waters of the Baltic Sea

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## Abstract

**:**

^{2}) 0.73. Moreover, no correlation with chlorophyll a concentration is observed, which makes it accurate in predicting cyanobacterial abundance in the presence of other chlorophyll-containing phytoplankton groups as well as for the waters with high colored dissolved organic matter (CDOM) concentration. The developed model was also adapted to spectral bands of the recently launched Sentinel-3 Ocean and Land Color Imager (OLCI) radiometer, and the estimation accuracy was comparable (RMSE = 0.28 and R

^{2}= 0.69). The presented model allows frequent, large-scale monitoring of cyanobacteria biomass and it can be an effective tool for the monitoring and management of coastal regions.

## 1. Introduction

_{u}to downwelling irradiance E

_{d}is the remote sensing reflectance R

_{rs}(here simply referred to as “reflectance”), which can be measured from a research vessel or from satellites. Since the reflectance spectra (i.e., spectral distribution of the reflectance) are affected by both fluorescence and absorption of phycocyanin, they can be used to study the extent of algal blooms, as well as for the estimation of phycocyanin concentration [18,19,20,21].

## 2. Materials and Methods

#### 2.1. Area of Investigation

_{rs}, and water samples were taken for laboratory analysis of pigment concentration and other parameters related to the optical properties of water (absorption coefficient of CDOM at 400 nm, Secchi depth and number of phytoplankton cells) using standard methods (described in [32]).

_{rs}spectra in Case 1 waters [25]. The studied area is a wide and relatively shallow water body, connected with the open sea and strongly influenced by riverine waters (Figure 1). It features many different hydro-geomorphological regimes, including lagoons, river mouths, and sheltered and open coastal areas, and it experiences strong anthropogenic pressure [34]. In the Gulf of Gdansk, the vegetation season usually starts with the bloom of diatoms and dinoflagellates in late March [35]. Cyanobacteria species able to fix atmospheric nitrogen start to dominate in summer, when dissolved nitrogen resources decrease and water temperature is the highest. During the same period, dinoflagellates or green algae can still dominate blooms in regions with higher inflow of nutrients from land. Summer algal blooms in the Gulf of Gdansk are dominated by cyanobacteria [32,35], primarily by the two filamentous, nitrogen-fixing species: Nodularia spumigena and Aphanizomenon flos−aquae [36]. Dolichospermum spp. also occurs in the summer algal blooms, but it is not the dominating species [37]. All these species are rich in phycocyanin [8].

#### 2.2. Radiometric Measurements

_{u}(0

^{−},λ) (W·m

^{−2}·nm

^{−1}·sr

^{−1}) just below the water surface was measured using the RAMSES−MRC TriOS hyperspectral radiance sensor. This radiometer is characterized by narrow detector and in-air nominal full-angle field-of-view of 20°, which helps to minimize the self-shading error during measurements. At the same time, downwelling irradiance E

_{d}(0

^{+},λ) (W·m

^{−2}·nm

^{−1}) above the water was measured using RAMSES−ACC−VIS TriOS hyperspectral irradiance sensor. In order to calculate the remote sensing reflectance, the upwelling radiance measured below the water surface L

_{u}(0

^{−},λ) was transferred into the air medium L

_{u}(0

^{+},λ) using the standard procedure, i.e., by applying the immersion factor I

_{f}[38,39]. On the basis of the received spectra, the remote sensing reflectance R

_{rs}(0

^{+},λ) was calculated using equation:

_{rs}

^{OLCI}) were created from the hyperspectral R

_{rs}data measured from the research vessel by averaging the data around the waveband centers used by the OLCI radiometer between 400 and 800 nm (400 nm, 412.5 nm, 442.5 nm, 490 nm, 510 nm, 560 nm, 620 nm, 665 nm, 673.75 nm, 681.25 nm, 708.75 nm, 753.75 nm, 761.25 nm, 764.375 nm, 767.5 nm, and 778.75 nm). A Gaussian curve was defined with a full width half maximum (FWHM) of the corresponding bandwidths and this was used to weigh R

_{rs}values on either side of the band center during averaging.

#### 2.3. Phycocyanin Measurement

#### 2.4. Model Development

_{rs}band ratio instead of singular R

_{rs}bands is popular in remote sensing models. The reflectance of a singular band can be influenced by more than one component, whereas the use of band ratios gives enhanced spectral signatures of different water constituents and reduced illumination effects. It is also less sensitive to the atmospheric correction errors when applied to satellite data.

_{rs}(λ

_{i}) and R

_{rs}(λ

_{j}) are the remote sensing reflectance at wavelengths λ

_{i}and λ

_{j}, respectively.

^{2}and root-mean-square error (RMSE). The ten best band ratios were selected for further analysis.

^{2}> 0.9), only the most physically meaningful terms were selected.

_{m}are the best fit coefficients.

_{hyp}“ model). Next, the model was adapted to the multispectral case (“PC

_{OLCI}“ model) by selecting the nearest available OLCI bands. Then, multilinear regression was used to estimate model parameters. Both versions of the models were evaluated separately but in the same manner.

_{OLCI}in case of phytoplankton blooms in the Baltic Sea, data registered by MERIS (Envisat) radiometer were used as an example. All spectral bands of the MERIS radiometer will also be available in the OLCI radiometer on-board the Sentinel-3 satellite, so the model PC

_{OLCI}can be used with the data acquired with both radiometers. Remote sensing reflectances from MERIS data, atmospherically corrected using the Case−2 Regional (C2R) processor [41] recommended for Case 2 waters, were used to estimate PC and chl−a concentration. Chl−a concentration was calculated with equation C

_{a}(0)

_{MD}proposed in the DESAMBEM project (Equation AIII.3 in [42,43]) and evaluated as the most accurate model for chl−a surface concentration in the Baltic Sea [44]. The PC concentration was calculated with PC

_{OLCI}(described further in Section 3.4.2).

#### 2.5. Model Assessment

_{10}space, all statistics reported are based on log

_{10}transformed data [21,40]. These statistics are determination coefficient R

^{2}, systematic error (bias, log

_{10}(mg·m

^{−3})), and statistical error in terms of root-mean-square error (RMSE, log

_{10}(mg·m

^{−3})). Bias and RMSE were calculated using equations:

_{10}space) and expressed in percent:

_{10}space and not easily translated into absolute terms. Therefore, following [45,46], we calculated a dimensionless inverse transformed value for bias using:

_{med}is the median value of ratio ${x}_{\mathrm{i}}^{\text{mod}}$/${x}_{\mathrm{i}}^{obs}$. For instance if F

_{med}is 1, there is no model bias, if F

_{med}is 2, the model overestimates by a factor of 2; if F

_{med}is 0.5, the model underestimates by factor of 2. Median percent difference (MPD), a relative error was calculated using the formula:

^{2}were estimated using 70%, randomly chosen observations, using the MATLAB function randsample. The remaining 30% observations were used for validation, i.e., estimation of prediction bias and RMSE. Randsample function selects each data point with equal probability, and it is therefore expected that the test data typically included points spread uniformly in time. This makes it unlikely that the training dataset consisted entirely of points from one season. The procedure of randomly selecting training and validation subsets was repeated 5000 times to capture the distribution of the prediction errors, both in terms of the mean and standard deviation. For a robust and generalizable to other datasets model, cross-validation model skill should be reduced only slightly compared with the model derived from the full dataset.

## 3. Results and Discussion

#### 3.1. Field Measurements

^{−1}and 2.1 m

^{−1}(Table 1). In terms of the total number of phytoplankton cells, cyanobacteria contributed to at least 50% from the middle of June until the end of August [32,35]. The chl−a concentration measured in the Gulf of Gdansk varied between 0.93 mg·m

^{−3}and 30.91 mg·m

^{−3}(in log

_{10}space: −0.03 and 1.49, respectively), with a mean value of 7.3 mg·m

^{−3}(0.71 in log

_{10}space) and a median value of 4.6 mg·m

^{−3}(0.66 in log

_{10}space), see Figure 2. The measured values are in the range of chl−a concentration typical for the southern Baltic Sea with skewed distribution, where most values are low and around 2−3 mg·m

^{−3}, while high chl−a concentrations, even up to 100 mg·m

^{−3}, can occur during algal blooms [23,36]. Due to the occurrence of upwellings, riverine inflows, and the effect of algal blooms, the water composition in the Gulf of Gdansk shows high variability, which can cover the typical situation for the whole Baltic Sea waters.

^{−3}to 18.95 mg·m

^{−3}(in log

_{10}space: −1.29 and 1.28, respectively), with a mean value of 2.14 mg·m

^{−3}(0.02 in log

_{10}space) and a median value of 0.84 mg·m

^{−3}(−0.07 in log

_{10}space), see Figure 2. The minimal value was observed at the beginning of May, when the taxonomic composition of phytoplankton is typically dominated by diatoms and dinoflagellates, whereas the maximal value of PC concentration was observed in the last week of June, when cyanobacteria species typically start to dominate the phytoplankton composition [35].

^{−3}and concentration of phycocyanin was generally below 2.5 mg·m

^{−3}, which indicated relatively high biomass of phytoplankton but low contribution of cyanobacteria. In the later summer, when dissolved nitrogen resources decrease, cyanobacteria species able to fix atmospheric nitrogen start to dominate. For the same reason, the regions located further from the nutrient sources are more affected by cyanobacteria blooms. In such situation, high concentration of chlorophyll is expected to be accompanied by high concentration of phycocyanin, as observed in June at P110d and P115c (chl−a > 25 mg·m

^{−3}, PC > 15 mg·m

^{−3}). Samples from station P110c from each cruise represented waters relatively poor in phytoplankton (Figure 2).

_{rs}) spectra collected in the field campaigns (Figure 3a). The collected R

_{rs}spectra represent quite typical spectral features consistent within optically complex waters [25]. The maximal value of R

_{rs}is found between 550 nm and 560 nm, and it shifts into the longer wavelength with increasing magnitude of the reflectance. There is a strong decrease and a small variability of the R

_{rs}values in the blue part of the spectrum due to high absorption of yellow substances and detritus in the studied area. The local minimum, near 660 nm, and the maximum, near 680 nm, correspond to the maximal absorption and fluorescence, respectively, of chl−a. In Figure 3a,b, two spectral bands are highlighted, one around 620 nm, where the maximal absorption of phycocyanin is observed, and one around 650 nm, where the maximum fluorescence of phycocyanin is observed. These features are clearly visible in the hyperspectral data in Figure 3a, but after converting the hyperspectral R

_{rs}data to the multispectral cases of the MERIS and OLCI sensors, they become less distinct (Figure 3b).

#### 3.2. Assessment of Known Models

_{rs}measured for different wavelengths, but also inherent optical properties. However, none of the models are developed to Baltic Sea waters. In our studies, we have examined the predictors used in those of the published models, which only use R

_{rs}spectra for PC concentration estimation, without any prior knowledge of inherent optical properties. Each one of the predictors summarized in Table 2 was used to estimate PC concentration for our dataset. The following linear model was used:

_{REF}is one of the predictors summarized in Table 2, and k and l are model parameters, estimated using linear regression.

^{2}below 0.5 and RMSE higher than 0.4. One major reason for the poor performance may be differences in the used data. The predictors in Table 2 were selected for datasets with PC concentration much higher than in the Baltic Sea waters. For example, the average value of PC was 419 mg·m

^{−3}in [48] and 68.9 mg·m

^{−3}in [31], whereas for the Gulf of Gdansk, it was 2.14 mg·m

^{−3}, and the maximum was 18.95 mg·m

^{−3}.

_{REF}was used in place of X. The use of logarithms instead of linear values improved the results. The greatest improvement was noted for SY00 and SP05, resulting in R

^{2}= 0.66, and RMSE = 0.29 for SY00 and R

^{2}= 0.63, and RMSE = 0.31 for SP05. MM09 and MS12 also showed significant improvement of R

^{2}to around 0.6 and RMSE to around 0.33, while the results for DA93 and HP10 were still poor, with R

^{2}below 0.3 and RMSE around 0.4. This analysis gave us motivation and suggestions for further model development for our study area.

#### 3.3. Optimal Band Ratio Selection

^{2}(Figure 4) were studied. It was observed that band ratios involving data from the two spectral ranges 640−660 nm and 600−620 nm show the highest R

^{2}values, over 0.6. Meanwhile, the values of R

^{2}for the band ratios commonly used in optical remote sensing methods (e.g., 440/555, 490/555 or 510/555) were low, around 0.3.

^{2}≥ 0.6, and p-value << 0.0001) are in the spectral range from 590 nm to 710 nm (Table 3 and Figure 4). Normalized RMSE for all chosen band ratios was around 11%, while bias was around 0 (F

_{med}was around 1), so on average the model was unbiased. The relative error MPD was around 45% for most of the models, with a minimum of 40% (for model #7) and a maximum of 59% (for model #1). In this spectral range, R

_{rs}values are influenced by absorption and fluorescence of phycocyanin and chlorophyll a, whereas the absorption of yellow substances has minimal effect on the R

_{rs}[49]. This is important in the waters of the Baltic Sea, where CDOM dominates the total absorption coefficient in the blue and green part of the spectrum [25,50]. For most of the ten chosen band ratios, the values of phycocyanin concentration decrease with increasing value of reflectance ratio (coefficient l < 0), see Table 3.

_{rs}spectrum close to 650 nm has stronger correlation with fluorescence of phycocyanin than 645 nm [8], while 625 nm has stronger correlation with absorption of phycocyanin than 630 nm [51]. Thus, as the second variable for further analysis, band ratio (625/650) was chosen. Studies presented by Schalles and Yacobi [47] also show the usefulness of this band ratio. The remaining three of the ten pre-selected band ratios use the band 710 nm, where the absorption coefficient is strongly dominated by water particles and the magnitude of R

_{rs}is increasing together with suspended particulate matter concentration. Thus, in the model created for Case 2 waters, where the magnitude of R

_{rs}spectra is increasing together with the concentration of suspended particulate matter due to high scattering, the inclusion of bands from the far red is reasonable and could help to minimize influence of suspended particles on model results. Taking into account their very high intercorrelation, only band ratio (620/710) was selected for the multilinear regression, as it also incorporates band of the maximal absorption of phycocyanin (620 nm), whereas in the range of 610−615 nm the optical properties of water in the Baltic Sea do not show any other characteristic features. Simis et al. [13] also used a similar band ratio in their semi-empirical model. All band ratios selected for multilinear model (Equation (3)) in relation to the phycocyanin concentration are shown in Figure 5.

#### 3.4. Multilinear Model for PC Estimation

#### 3.4.1. Hyperspectral Data

_{3term}, with ${X}_{1}=\frac{{R}_{\text{rs}}(595)}{{R}_{\text{rs}}(660)}$, ${X}_{2}=\frac{{R}_{\text{rs}}(625)}{{R}_{\text{rs}}(650)}$, ${X}_{3}=\frac{{R}_{\text{rs}}(620)}{{R}_{\text{rs}}(710)}$, and the regression coefficients were estimated by fitting model to the data using multilinear regression (Table 5). The three-term model allows PC estimation with RMSE = 0.26 (NRMSE = 10%), MPD = 39% and R

^{2}= 0.74 (adjusted R

^{2}= 0.73, ANOVA statistic F = 63.19, significance level p-value << 0.0001, standard error of estimation: 0.27). Results of regression (Figure 6a,b) show improvement compared with the models with only one band ratio (Figure 5). For 73% of the cases, residuals of regression were in the range of ±0.26 (RMSE in log

_{10}space). This means that the three-term model biases the estimated PC by a factor between 0.55 and 1.82 in the most cases. Such range of residuals for single band ratio models were observed for less than 65% of cases.

_{3term}) is the component R

_{rs}(625)/R

_{rs}(650), which consists of a reflectance ratio for wavebands with the maximal absorption (625 nm) and maximal fluorescence (650 nm) of light by phycocyanin. Values of this band ratio vary in a relatively narrow range (Figure 5). However, the corresponding coefficient has an absolute value large enough to make the model sensitive to even small changes in the shape of R

_{rs}at this part of spectrum, reflecting changes in PC concentration, see Table 5. Similarly high contribution to PC estimation is given by the band ratio (620/710). The first term (595/660), despite its highest correlation with PC, is the least significant (p-value close to 0.2). Moreover, it is highly correlated with the two other band ratios (Table 4), which increases the risk of overfitting. Although the removal of the least significant band ratio gives a model with somewhat worse performance (R

^{2}= 0.73, adjusted R

^{2}= 0.72, RMSE = 0.2614, NRMSE = 10%, MPD = 38%), we chose to use the two-term model in the subsequent analysis, further briefly referred to as PC

_{hyp}(Table 5, Figure 6c,d):

_{hyp}model seems to be more stable in different conditions of water transparency (Figure 7). In the Baltic Sea, during cyanobacterial blooms Secchi depth can decrease to less than 4 m in the open sea and even to less than 2 m in coastal areas [52]. The coastal area is more problematic since the input of nutrients from rivers promotes and supports the growth of other phytoplankton groups, i.e., dinoflagellates and green algae. Thus, relatively high biomass of phytoplankton and chlorophyll a concentration occurs together with low contribution of cyanobacteria. In water with such low transparency, the one-term model overestimates PC if X = R

_{rs}(625)/R

_{rs}(650) and underestimated if X = R

_{rs}(620)/R

_{rs}(710) (Figure 7).

#### 3.4.2. Multispectral Data

_{hyp}(Equation (10)) can be adapted by using the nearest bands available for these spaceborne sensors, further briefly referred to as PC

_{OLCI}:

^{2}= 0.69, adjusted R

^{2}= 0.69, RMSE = 0.28, MPD = 37% NRMSE = 11%, ANOVA statistic F = 77.31, significance level p-value << 0.0001, standard error of estimation = 0.29, see Figure 8 and Table 6). For 70% of the cases, residuals of regression were in the range of ±0.28 (RMSE in log

_{10}space). This means that the estimated PC can be higher or lower in relation to measured value by a factor between 0.52 and 1.91. Therefore, PC

_{OLCI}(Equation (11)) can be used together with data acquired with the previous satellite radiometer MERIS, as well as the OLCI radiometer onboard the Sentinel-3 satellite, to monitor large-scale changes in PC concentration in the surface waters.

^{−3}in the eastern part of the sea) explains green patches which can be seen on RGB composite. However, temperature in spring is too low to trigger cyanobacteria bloom; instead, other species form the bloom. Therefore, phycocyanin concentration is expected to be below, or close to the limit of detection. Estimation using PC

_{OLCI}provides phycocyanin concentration less than 1 mg·m

^{−3}in the whole Baltic Sea, which is within the margin of the estimation error of this model.

#### 3.5. Model Robustness

_{hyp}(Equation (10)) and PC

_{OLCI}(Equation (11)) was based on all available data. To evaluate the robustness of the models, cross-validation was used. Table 7 and Figure 10 show the results of cross-validation analysis.

^{2}, RMSE and bias) in cross-validation analysis did not change significantly compared to the analysis based on the entire dataset, which suggests that both PC

_{hyp}and PC

_{OLCI}seem to be robust and stable. The regression coefficients did not change significantly either. For all statistical metrics, the range of the values from cross-validation was smaller for PC

_{hyp}than for PC

_{OLCI}, except for bias (Figure 10). For both models, average of bias is close to 0.0 (it means F

_{med}close to 1.0).

#### 3.6. Sensitivity for High chl−a Concentration

_{hyp}and PC

_{OLCI}models in order to verify that the models are robust and not biased by high chl−a concentration. Additionally, PC concentration was estimated from the empirical relation between PC and chl−a, derived from the analyzed dataset (Figure 11):

_{hyp}is robust and does not overestimate PC concentration when chl−a concentration is high and cyanobacteria biomass is low. This is due to the fact that model PC

_{hyp}uses the spectral bands related to the maximum of phycocyanin absorption and to fluorescence, which determine the shapes of the reflectance spectra (Figure 3a). In addition, PC

_{hyp}utilizes band 710 nm, which is outside the range of spectrum influenced by chlorophyll a and other pigments. Such combination makes residuals of PC

_{hyp}model not correlated with chl-a concentration (correlation coefficient for PC

_{hyp}residuals vs. log

_{10}(chl-a) is r = 0.15, p-value = 0.21). Absolute estimation errors for PC

_{OLCI}are similar to the absolute estimation errors for PC

_{hyp}, but its residuals are slightly correlated with chl-a concentration (correlation coefficient for PC

_{OLCI}residuals vs. log

_{10}(chl-a) is r = 0.25, p-value = 0.035). This is because the spectral bands of MERIS and OLCI radiometers do not exactly fit to the spectral band responsive to the phycocyanin fluorescence (650 nm) and the nearest channel used in the PC

_{OLCI}model was more related to chl−a absorption (665 nm). The model PC

_{OLCI}works well for situations when cyanobacteria are dominant (both PC and chl−a concentration are high) but it is less accurate in cases when other species form blooms. It can explain why the spatial distribution of PC concentration evaluated on the basis of MERIS data for April (Figure 9a) shows similar spatial distribution like chl−a concentration.

_{OLCI}values are more reliable. When different dominating groups of phytoplankton can occur in different regions of the bloom, like in the example from July (Figure 9b), PC

_{OLCI}helps to distinguish these regions.

## 4. Summary and Conclusions

_{hyp}version) and later adapted to existing multispectral data from satellite radiometer (PC

_{OLCI}version). Depending on version, it uses four (PC

_{hyp}) or three (PC

_{OLCI}) different spectral bands that cover ranges of spectrum related to: the maximal absorption (620–625 nm) and the maximal fluorescence (close to 650 nm) of phycocyanin, and the absorption strongly dominated by water particles where the magnitude of R

_{rs}is increasing together with suspended particulate matter concentration (close to 710 nm).

_{OLCI}can be used with the data acquired from both radiometers. This allows frequent, large-scale monitoring of cyanobacteria biomass, which may find its applications in both climate related research, weather forecasting, coastal management, and risk assessment. Archived MERIS data acquired during its 10 years of operation can also be used in such monitoring for long-term analysis.

_{hyp}(Equation (10)) proposed here. The advantage of the presented solution is that it takes into account the statistical distribution of PC concentration characteristic for the Baltic Sea (e.g., through the use of logarithmic transformation). Moreover, it uses a combination of band ratios, which both emphasizes the response of reflectance spectra to changes in phycocyanin concentration and minimizes their response to uncorrelated changes related to other optically significant constituents.

_{hyp}model were chosen based on both statistical analysis and interpretation of physical properties of the selected bands, which makes PC estimation robust and gives an effective tool for monitoring of the occurrence of cyanobacteria filamentous species. As was expected, the best results were achieved using expressions utilizing spectral bands of reflectance determined by the optical properties of phycocyanin (625 and 650 nm). Schalles and Yacobi [47] present a model with a single band ratio (650/625) which is also used in the PC

_{hyp}model (Equation (10)) proposed in this work. However, as shown in our analysis, the additional (620/710) band ratio of model PC

_{hyp}increases accuracy and stability of the model, as they also account for the influence of other optically significant components in water. Moreover, in water with low transparency, the one-term models overestimate or underestimate phycocyanin concentration.

_{3term}model showed somewhat better results of estimation than the PC

_{hyp}model. However, statistical analysis leads us to exclude the band ratio 595/660 as redundant. In the future, additional analysis of a larger dataset from different areas of the Baltic Sea could confirm or totally reject the importance of the 595/660 band ratio.

_{OLCI}and PC

_{hyp}models shows that worse performance for PC concentration estimation is obtained if fluorescence of PC is neglected. If replaced by nearest channel of MERIS or OLCI radiometer, results are more dependent on spatial distribution of chl−a concentration, which can be associated with other phytoplankton groups besides cyanobacteria. It suggests the need for new spectral bands in satellite radiometers.

_{hyp}was based on R

_{rs}spectra typical for Case 2 waters of the Baltic Sea, which covered wide range of situations. For the other areas, characterized by similar optical properties and similar range of phycocyanin concentration (up to 20 mg·m

^{−3}), the model parameters may need to be estimated from reference data. In the future, model PC

_{OLCI}also needs to be validated against satellite data and atmospheric corrections should be taken into account in such validation as well.

## Acknowledgements

## Author Contributions

## Conflicts of Interest

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**Figure 2.**Spatial and temporal distribution of PC (left axis, gray) and chl−a (right axis, green) measured during our studies (in mg·m

^{−3}). The same scale is used for each type of axis in all six diagrams. Red points on simplified maps show location of sampling stations in relation to the coastline and rivers.

**Figure 3.**The variance of the studied R

_{rs}spectra for the (

**a**) hyperspectral and (

**b**) multispectral cases. Narrow spectral bands around the maximum of absorption and fluorescence of phycocyanin are highlighted in light and dark grey, respectively.

**Figure 4.**Determination coefficient R

^{2}for Equation (2) for all possible band ratios R

_{rs}(λ

_{i})/R

_{rs}(λ

_{j}) in the spectral range 400–750 nm.

**Figure 5.**The dependence between the logarithm of PC concentration and the logarithm of the selected remote sensing reflectance band ratio (

**a**) and distribution of the regression residuals (

**b**). Also shown are: regression line with 95% confidence interval, best fit coefficients, the number of observations (N), the coefficient of determination (R

^{2}), and the root-mean-square error (RMSE).

**Figure 6.**Scatter plots showing comparison between the PC concentrations measured in situ and estimated using the three-term model (PC

_{3term}) shown in Equation (3) with: X

_{1}= R

_{rs}(595)/R

_{rs}(660), X

_{2}= R

_{rs}(625)/R

_{rs}(650), X

_{3}= R

_{rs}(620)/R

_{rs}(710) (

**a**); distribution of the PC

_{3term}regression residuals (

**b**); two-term model (PC

_{hyp}) with: X

_{1}= R

_{rs}(625)/R

_{rs}(650), X

_{2}= R

_{rs}(620)/R

_{rs}(710) (

**c**); and distribution of the PC

_{hyp}regression residuals (

**d**).

**Figure 7.**Distribution of regression residuals for different PC models (two one-term models according to Equation (2) and one two-term model PC

_{hyp}according to Equation (10)) for different water transparency conditions (Secchi depth as an indicator for transparency).

**Figure 8.**Scatter plots showing the correlation between the PC concentrations measured in situ and estimated using the PC

_{OLCI}model shown in Equation (11) (

**a**) and distribution of the regression residuals (

**b**).

**Figure 9.**(

**Left**) RGB image; (

**center**) spatial distribution of PC concentration; and (

**right**) spatial distribution of chl−a concentration for sample scenes from spring (

**a**) and summer (

**b**,

**c**), recorded during blooms of different phytoplankton composition. Satellite data were acquired by the MERIS sensor onboard the Envisat satellite.

**Figure 10.**Box plots showing statistics of: the coefficient of determination (

**a**); RMSE (

**b**); and bias (

**c**) obtained during cross-validation of the selected models.

**Figure 11.**PC versus chl−a concentration, both measured in situ. Cases (#1–#5, red dots) when chl−a concentration was high and PC was low, are marked in red.

**Table 1.**Water transparency (Secchi depth) during sampling and statistical characteristics of environmental parameters measured in the same water samples: a

_{CDOM}(400 nm): CDOM absorption at 400 nm, PC: phycocyanin concentration, chl−a: chlorophyll a concentration, PC/chl−a: ratio of phycocyanin to chlorophyll a concentration, phytoplankton biomass, cyanobacteria biomass content: content of cyanobacteria in total mass of phytoplankton, phytoplankton cells number, cyanobacteria cells content: content of cyanobacteria cells in total number of phytoplankton cells. Min.: minimum, Max.: maximum values; Q: quantiles.

Parameter | Min. | Q_{25%} | Q_{50%} | Q_{75%} | Max. |
---|---|---|---|---|---|

Secchi depth (m) | 1.5 | 3.0 | 3.5 | 4.5 | 7.0 |

a_{CDOM}(400 nm) (m^{-1}) | 0.72 | 0.83 | 1.05 | 1.42 | 2.1 |

PC (mg·m^{−3}) | 0.05 | 0.5 | 0.84 | 3.00 | 18.95 |

chl-a (mg·m^{−3}) | 0.93 | 2.87 | 4.60 | 8.73 | 30.91 |

PC/chl−a (-) | 0.02 | 0.12 | 0.20 | 0.37 | 0.73 |

phytoplankton biomass (µg·dm^{−3}) | 30 | 495 | 1118 | 2831 | 8928 |

cyanobacteria biomass content (%) | 0.5 | 17.8 | 37.7 | 68.9 | 95.4 |

phytoplankton cells number (×10^{3}·dm^{−3}) | 119 | 1429 | 5929 | 10704 | 19165 |

cyanobacteria cells content(%) | 0.1 | 15.4 | 40.6 | 69.5 | 89.4 |

Model Symbol | Proposed Predictor X_{REF} | Reference |
---|---|---|

SY00 | R_{rs}(650)/R_{rs}(625) | Schalles and Yacobi 2000 [47] |

DA93 | 0.5·(R_{rs}(600) + R_{rs}(648)) − R_{rs}(624) | Dekker 1993 [15] |

MM09 | R_{rs}(700)/R_{rs}(600) | Mishra et al. 2009 [11] |

MS12 | R_{rs}(709)/R_{rs}(600) | Mishra 2012 [48] |

HP10 | (R_{rs}^{−1}(615) − R_{rs}^{−1}(600))·R_{rs}(725) | Hunter et al. 2010 [31] |

SP05 | R_{rs}(709)/R_{rs}(620) | Simis et al. 2005 [13] |

**Table 3.**Estimated coefficients and basic regression statistics for the ten best band ratios used with one-term model (Equation (2)).

No. | Band Ratio R_{rs}(λ_{i})/R_{rs}(λ_{j}) | Coefficients | R^{2} | RMSE | MPD (%) | |
---|---|---|---|---|---|---|

k | l | |||||

#1 | R_{rs}(595)/R_{rs}(660) | 2.4952 | −7.8331 | 0.6734 | 0.2889 | 59 |

#2 | R_{rs}(625)/R_{rs}(645) | 0.7659 | −20.5767 | 0.6728 | 0.2891 | 42 |

#3 | R_{rs}(660)/R_{rs}(600) | 2.4564 | 8.9935 | 0.6699 | 0.2904 | 46 |

#4 | R_{rs}(625)/R_{rs}(650) | 0.7263 | −16.6351 | 0.6636 | 0.2932 | 42 |

#5 | R_{rs}(630)/R_{rs}(645) | 0.6032 | −21.6371 | 0.6597 | 0.2949 | 41 |

#6 | R_{rs}(600)/R_{rs}(655) | 2.1574 | −8.9421 | 0.6581 | 0.2956 | 49 |

#7 | R_{rs}(660)/R_{rs}(590) | 2.4100 | 6.0379 | 0.6418 | 0.3032 | 40 |

#8 | R_{rs}(610)/R_{rs}(710) | 1.1968 | −3.5895 | 0.6342 | 0.3057 | 43 |

#9 | R_{rs}(615)/R_{rs}(710) | 1.0850 | −3.5850 | 0.6349 | 0.3055 | 45 |

#10 | R_{rs}(620)/R_{rs}(710) | 1.0330 | −3.5534 | 0.6330 | 0.3064 | 45 |

**Table 4.**Correlation matrix for logarithmic transformation of the ten best band ratios used with one-term model (Equation (2)). #x is a number of model from Table 3; correlation coefficients over 0.95 are highlighted (all correlations are statistically significant at the p-level < 0.01).

#1 | #2 | #3 | #4 | #5 | #6 | #7 | #8 | #9 | #10 | |
---|---|---|---|---|---|---|---|---|---|---|

#1 | 1.00 | 0.91 | −0.99 | 0.88 | 0.89 | 0.99 | −0.98 | 0.86 | 0.86 | 0.85 |

#2 | 1.00 | −0.94 | 0.99 | 0.99 | 0.93 | −0.85 | 0.77 | 0.77 | 0.77 | |

#3 | 1.00 | −0.92 | −0.93 | −0.99 | 0.96 | −0.82 | −0.81 | −0.81 | ||

#4 | 1.00 | 0.99 | 0.90 | −0.82 | 0.77 | 0.77 | 0.77 | |||

#5 | 1.00 | 0.92 | −0.84 | 0.77 | 0.77 | 0.77 | ||||

#6 | 1.00 | −0.97 | 0.84 | 0.84 | 0.83 | |||||

#7 | 1.00 | −0.88 | −0.88 | −0.87 | ||||||

#8 | 1.00 | 1.00 | 0.99 | |||||||

#9 | 1.00 | 1.00 | ||||||||

#10 | 1.00 |

**Table 5.**Statistical characteristics of multilinear regression coefficients for multilinear model shown in Equation (3) utilizing three or two predictors (coefficients marked by * refer to factors after standardization).

Factors | Partial Correlation | Coefficients | Standard Error | Significance p−value | |
---|---|---|---|---|---|

three-term model (PC_{3term}) | intercept | k = 1.39 | 0.34 | 0.0001 | |

${\mathrm{log}}_{10}\left(\frac{{R}_{\text{rs}}(595)}{{R}_{\text{rs}}(660)}\right)$ | −0.15 | l_{1} = −1.97 | 1.55 | 0.2095 | |

l_{1}*= −0.21 | 0.16 | ||||

${\mathrm{log}}_{10}\left(\frac{{R}_{\text{rs}}(625)}{{R}_{\text{rs}}(650)}\right)$ | −0.32 | l_{2} = −7.75 | 2.75 | 0.0064 | |

l_{2}*= −0.38 | 0.13 | ||||

${\mathrm{log}}_{10}\left(\frac{{R}_{\text{rs}}(620)}{{R}_{\text{rs}}(710)}\right)$ | −0.32 | l_{3} = −1.46 | 0.53 | 0.0075 | |

l_{3}*= −0.33 | 0.12 | ||||

two-term model (PC_{hyp}) | intercept | k = 0.98 | 0.09 | <<0.0001 | |

${\mathrm{log}}_{10}\left(\frac{{R}_{\text{rs}}(625)}{{R}_{\text{rs}}(650)}\right)$ | −0.52 | l_{1} = −10.14 | 2.01 | <<0.0001 | |

l_{1}*= −0.50 | 0.10 | ||||

${\mathrm{log}}_{10}\left(\frac{{R}_{\text{rs}}(620)}{{R}_{\text{rs}}(710)}\right)$ | −0.45 | l_{2} = −1.84 | 0.44 | <<0.0001 | |

l_{2}*= −0.35 | 0.10 |

**Table 6.**Statistical characteristics of multilinear regression coefficients for PC

_{OLCI}model shown in Equation (11) (coefficients marked by * refers to factors after standardization).

Factors | Partial Correlation | Coefficients | Standard Error | Significance p−level |
---|---|---|---|---|

intercept | − | k= 1.71 | 0.17 | <<0.0001 |

${\mathrm{log}}_{10}\left(\frac{{R}_{\text{rs}}(620)}{{R}_{\text{rs}}(665)}\right)$ | −0.48 | l_{1}= −5.47 | 1.23 | <<0.0001 |

l_{1}*= −0.35 | 0.08 | |||

${\mathrm{log}}_{10}\left(\frac{{R}_{\text{rs}}(620)}{{R}_{\text{rs}}(708.25)}\right)$ | −0.68 | l_{2}= −3.13l _{2}*= −0.60 | 0.41 0.08 | <<0.0001 |

Model | Cross-Validation | |||||||
---|---|---|---|---|---|---|---|---|

Coefficients | R^{2} | RMSE | Bias | |||||

Mean | SD | Mean | SD | Mean | SD | Mean | SD | |

PC_{hyp} | k = 0.98 l _{1} = −10.27l _{2} = −1.82 | ±0.05 ±1.35 ±0.25 | 0.73 | ±0.11 | 0.27 | ±0.05 | −5 × 10^{−4} | ±0.08 |

PC_{OLCI} | k = 1.72 l _{1} = −5.56l _{2} = −3.11 | ±0.11 ±0.81 ±0.22 | 0.69 | ±0.13 | 0.29 | ±0.05 | −2 × 10^{−3} | ±0.08 |

**Table 8.**PC concentration (mg·m

^{−3}) calculated using the two models PC

_{hyp}and PC

_{OLCI}for the cases when chl−a concentration (mg·m

^{−3}) was high (points #1–#5 highlighted in the Figure 11).

#1 | #2 | #3 | #4 | #5 | RMSE | bias | |
---|---|---|---|---|---|---|---|

Measured Values: | |||||||

PC _{in situ} | 0.42 | 1.51 | 3.46 | 3.01 | 3.09 | − | |

chl−a_{in situ} | 22.27 | 20.01 | 30.91 | 26.55 | 24.85 | − | |

Estimated Values: | |||||||

PC_{hyp} (Equation (10)) | 0.30 | 2.71 | 2.22 | 4.25 | 3.50 | 0.17 | 0.02 |

PC_{OLCI} (Equation (11)) | 0.27 | 2.80 | 2.36 | 3.32 | 2.49 | 0.17 | -0.03 |

PC (Equation (12)) | 4.44 | 3.99 | 6.19 | 5.31 | 4.97 | 0.53 | 0.43 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Woźniak, M.; Bradtke, K.M.; Darecki, M.; Krężel, A.
Empirical Model for Phycocyanin Concentration Estimation as an Indicator of Cyanobacterial Bloom in the Optically Complex Coastal Waters of the Baltic Sea. *Remote Sens.* **2016**, *8*, 212.
https://doi.org/10.3390/rs8030212

**AMA Style**

Woźniak M, Bradtke KM, Darecki M, Krężel A.
Empirical Model for Phycocyanin Concentration Estimation as an Indicator of Cyanobacterial Bloom in the Optically Complex Coastal Waters of the Baltic Sea. *Remote Sensing*. 2016; 8(3):212.
https://doi.org/10.3390/rs8030212

**Chicago/Turabian Style**

Woźniak, Monika, Katarzyna M. Bradtke, Miroslaw Darecki, and Adam Krężel.
2016. "Empirical Model for Phycocyanin Concentration Estimation as an Indicator of Cyanobacterial Bloom in the Optically Complex Coastal Waters of the Baltic Sea" *Remote Sensing* 8, no. 3: 212.
https://doi.org/10.3390/rs8030212