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Abstract
A laboratory experiment was conducted to obtain a floating algae index (FAI) of the floating macroalgae (Ulva prolifera), corresponding to various values of biomass per unit area (BPA). A piecewise empirical model was used to fit the statistical relationships between BPA and FAI, corresponding to FAI ≤ 0.2 (BPA ≤ 1.81kg/m2) and FAI ˃ 0.2 (BPA ˃ 1.81 kg/m2). Spectral mixing derived results show that a linear relationship between FAI and BPA is maintained when the BPA of endmembers is less than 1.81 kg/m2. However, when the BPA of the endmembers exceeds 1.81 kg/m2, there is substantial uncertainty in the optical remote estimation of biomass. Although the MODIS-derived FAI of Ulva prolifera is often less than 0.2, it is very difficult to determine whether the FAI results from low BPA (≤ 1.81kg/m2) of the endmembers, or from a low area ratio including high BPA (˃ 1.81 kg/m2), due to pixel mixing. If it is assumed that the unit biomass distribution of pure endmembers is a standard Gaussian distribution, then the uncertainty in the biomass estimation of Ulva prolifera from MODIS data can be expressed. This results in the uncertainty of ~36% in total biomass estimation, ~43% of which was contributed by a few pixels (10% of total pixels) with high FAI (˃ 0.05). The uncertainty in BPA caused by high FAI (˃ 0.05) pixels is about 7.2 times that for low FAI (≤ 0.05) pixels. In future research, the spatial distribution characteristics of the FAI of pure endmembers need to be considered in order to improve the accuracy of optical remote estimation of floating Ulva prolifera.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Although floating macroalgae (e.g., Ulva prolifera or Sargassum) is an important component of marine ecosystems, blooms of these species may adversely impact the marine environment in various ways [1–4]. Optical remote detection and quantification of algal blooms is a key research area in the monitoring of floating macroalgae [5–9].
A large-scale green tide caused by Ulva (U.) prolifera has occurred annually in the Yellow Sea (YS) since 2008 [6,8,10,11]. The green tide threatens marine ecosystems due to its role in promoting oxygen depletion of both the water column and the benthic environment, which may result in the death of fishes and shrimps offshore [12]. U. prolifera macroalgae floating on the ocean surface have spectral features which differ from those of the clear seawater background, or of other macroalgae (such as Sargassum), and can be observed using various optical sensors. The Space-borne Moderate Resolution Imaging Spectroradiometer (MODIS) provides observations twice daily and is widely used in mapping the spatio-temporal coverage of floating U. prolifera. According to the spectral features, various methods, such as the normalized difference vegetation index (NDVI) [13], floating algae index (FAI) [5], scaled algae index (SAI) [6], enhanced vegetation index (EVI) [14], and virtual-baseline floating macroalgae height (VB-FAH) [15], were designed to detect floating algae. FAI has been shown to have advantages over the traditional indexes because it is less sensitive to changes in environmental and observation conditions (such as aerosol type and thickness, viewing geometry, sunglint, and thin clouds) [5], and has thus been widely used in detecting floating algae in the global ocean [10,16,17]. Although the spatio-temporal coverage of floating U. prolifera over the YS can be determined from MODIS-derived FAI [8,15,17], knowledge of the total biomass is essential for salvaging and clean-up operations [13].
Based on a laboratory-derived statistical relationship between FAI and biomass (wet weight) per unit area (BPA) of floating U. prolifera, a linear unmixing model was employed to enable the estimation of total biomass from MODIS Rayleigh-corrected reflectance (Rrc) data [5]. Floating U. prolifera algae with FAI value ≤ 0.2 (corresponding to BPA ≤ 1.81 kg/m2) is an important boundary condition for application to MODIS-derived FAI [18]. However, thicker layers of floating algae, with FAI > 0.2 (corresponding to BPA > 1.81 kg/m2) have an uncertain impact on estimates of total biomass with MODIS-derived FAI imageries. In other words, it is difficult to identify whether the MODIS-derived FAI values are caused by the spatial distribution or by the thickness of floating U. prolifera.
In this study, laboratory measurements of FAI and BPA of floating U. prolifera were used to generate three models: ignoring the thickness of the algae (Fit I), a standard Gaussian distribution of the thickness of the floating algae (Fit II), and a thicker layer of floating algae (Fit III). Four MODIS-derived FAI imageries covering floating U. prolifera in the YS were used to determine the degree of uncertainty in optical remote estimation of the total biomass of the macroalgae using these three models. There is an uncertainty of ~36% in total biomass estimation, ~43% of which is produced by a few pixels (10% of total pixels) with high FAI (˃ 0.05). The uncertainty in BPA caused by a high FAI (˃ 0.05) pixel is about 7.2 times that of a low FAI (≤ 0.05) pixel. This means that the spatial distribution of floating algae thickness is as important as the spatial distribution of the coverage. If the thickness of macroalgae can first be established, the estimation accuracy of the total biomass of floating U. prolifera in the YS and the East China Sea would be greatly improved.
2. Data and methods
2.1 Laboratory experiment
Details of water tank measurements of spectral reflectance of various floating U. prolifera with different values of BPA can be found in a previous study [18]. These data from the laboratory experiments were used to develop a piecewise empirical model to estimate BPA from FAI. Although the spectral reflectance of various floating U. prolifera increases with BPA (from 0 to 5.56 kg/m2), it is difficult to determine whether the contribution is from the spatial distribution of the coverage or its thickness. The FAI value of the joint point in this piecewise model was 2.0 (corresponding to BPA of 1.81 kg/m2, where U. prolifera covers the entire water surface), which indicated that FAI > 2.0 or BPA > 1.81 kg/m2 was caused by the effect of thickness (Fig. 1).
Fig. 1 (a) Spectral reflectances of floating U. prolifera macroalgae from a water tank experiment in Hu et al. [18]; the insert shows the spectral reflectance of algae-free seawater collected in the YS. (b) Piecewise model composed of linear and exponential functions; the inserted figures show the floating algae coverage and thickness in the water tank experiment.
2.2 MODIS data processing
MODIS Level-0 data of floating U. prolifera macroalgae in the YS on 20 June 2013 at 02:25 GMT, 12 June 2015 at 02:25 GMT, 21 June 2015 05:25 GMT, and 25 June 2016 at 05:10 GMT were obtained from NASA’s Goddard Space Flight Center. The data were processed using the NASA software package (version 7.4) which converts them to calibrated total radiance (Lt, in units of W·m−2·sr−1·nm−1). Rayleigh-corrected reflectance (Rrc, dimensionless) of the four MODIS images can be determined using Eq. (1):
Here, Lr is the Rayleigh scattering radiance calculated using the Geometrical optical feature and ozone characteristics, F0 is the extraterrestrial solar irradiance, and θ0 is the solar zenith angle. All of the MODIS Rrc images were resampled to 250-m resolution. Rrc data at 645, 555, and 469 nm were used as the Red, Green, and Blue channels to compose the four RGB images covering the floating macroalgae (Fig. 2).Fig. 2 MODIS Terra/Aqua RGB images of floating U. prolifera macroalgae in the YS and the East China Sea. Note that the observation times are all in June in order to minimize the seasonal effect of floating U. prolifera macroalgae.
2.3 FAI
FAI is a simple but very effective ocean color index which was developed to detect floating algae (i.e., U. prolifera and Sargassum) in the open ocean environment using MODIS data. It is superior to traditional indexes (i.e., NDVI and EVI) because it is less sensitive to changes in the background seawater environment and aerosol conditions [5]. Reflectance-based FAI can be defined using the following equation:
Here, R is the seawater reflectance (dimensionless); λ is the wavelength; and the subscripts RED, NIR, and SWIR represent the red, near infrared, and short-wave infrared wavelengths, respectively. FAI can be used to estimate the total biomass of floating algae using MODIS Rrc data (λRED = 645 nm, λNIR = 859 nm, λSWIR = 1240 nm) [5]. In this study, the laboratory-measured spectral reflectance data were averaged for MODIS bands using the spectral response functions of MODIS. It should be noted that the absolute accuracy of FAI is not critical and therefore we do not discuss it in depth.3. Spectral mixing effects
The BPA of floating U. prolifera macroalgae were collected from water tank measurements or field observations on 11 July 2013 and 16 July 2015 range from 0 to ~5.0 kg/m2 (corresponding to FAI values from 0 to 0.3) [18]. However, the FAI values of MODIS-derived results are generally less than 0.05 [5,7,18]. This is due to spectral mixing effects in different multi-band coarse spatial resolution sensors. Spectral mixing effects introduce a large amount of uncertainty into optical remote estimation of the biomass of floating U. prolifera macroalgae using MODIS data. The statistical relationship between FAI and BPA can be expressed using a piecewise model comprising linear and exponential functions, corresponding to FAI ≤2.0 (BPA ≤1.81 kg/m2) and FAI >2.0 (BPA >1.81 kg/m2) [18]. It is evident from Fig. 3 that if the BPA of a pure endmember (corresponding to 1/9 of a MODIS pixel) of floating U. prolifera macroalgae is less than 1.81 kg/m2 (BPA(A), corresponding to FAI(A) ≤2.0), the MODIS-derived FAI value (FAIMODIS(A)) is 1/9 of the pure endmember’s FAI(A), and the FAIMODIS(A)-derived BPA MODIS(A) is 1/9 of the pure endmember’s BPA (A), according to a linear mixing model. Moreover, when the BPA of a pure endmember (corresponding to 1/9 of a MODIS pixel) of floating U. prolifera macroalgae exceeds 1.81 kg/m2 (BPA(T) >1.81 kg/m2, corresponding to FAI(T) >2.0), the actual MODIS-observed value will be FAIMODIS(T), which corresponds to BPAMODIS(T). Due to spectral mixing, the FAIMODIS(T) would be less than 2.0 and equal to FAI′MODIS(T), which can be given a different BPA (BPA′MODIS(T)), according to a linear model (a part of the piecewise function). In other words, the uncertainty in the optical remote estimation of the biomass of U. prolifera macroalgae using MODIS imagery is mainly caused by their unknown spatial distribution and thickness.
Fig. 3 Schematic graph showing the origin of the uncertainty in the optical remote estimation of the BPA of U. prolifera macroalgae using MODIS imagery. Note that FAI(A) and FAI(T) of pure endmembers in a mixed pixel.
4. Results and discussion
4.1 Uncertainty in FAI-derived BPA estimates
The laboratory-based piecewise model shows that FAI = 2.0 is an important cut-off point (corresponding to BPA = 1.81kg/m2) for a pure pixel with floating U. prolifera macroalgae. In order to evaluate the effects of mixed pixels on estimates of the biomass of floating U. prolifera macroalgae with MODIS data, laboratory-based values of spectral reflectance and BPA of floating U. prolifera macroalgae were divided into two groups: BPA ≤1.81 kg/m2 and BPA >1.81 kg/m2. An in situ measured spectral reflectance of algae-free seawater in the YS was used as the background spectrum of seawater to produce various mixing spectra. For such mixed pixels, the spectral reflectance is given by:
where RUlva represents the laboratory-based spectral reflectance of floating U. prolifera macroalgae with different values of BPA, RSeawater represents the in situ measured seawater spectral reflectance in the YS (Fig. 1(a)), and α and (1-α) represent the proportions of floating U. prolifera macroalgae and seawater within a pixel. Mixed spectral reflectances (R’Ulva) will be given by changing α from 100% to 0 with decrements of 5%. The biomass of floating U. prolifera macroalgae of a mixed pixel (BPA’Ulva) can be estimated using Eq. (4) (BPAUlva is the laboratory-measured BPA). Therefore, the FAI values of mixed pixels can be determined from the simulated spectras.The statistical relationship between R’Ulva-derived FAI and BPA’Ulva for a simulated mixed spectral reflectance of floating U. prolifera macroalgae can be divided into two groups: BPA ≤1.81kg/m2 and BPA >1.81kg/m2. If the thickness of floating U. prolifera macroalgae is within a certain range (corresponding to BPA ≤1.81kg/m2 or FAI ≤2.0 of pure pixels), then the R’Ulva-derived FAI and BPA’Ulva have a good linear statistical relationship (Fig. 4(a)). Even if the floating U. prolifera macroalgae have a greater thickness (corresponding to BPA ≥1.81 kg/m2 or FAI ≥2.0 of pure pixels), the R’Ulva-derived FAI value of the most mixed pixels will fall within the range of 0~2.0 (Fig. 4(b)). This also indicates that the effect of thickness on the estimation of the biomass of floating U. prolifera macroalgae cannot be ignored. Therefore, the actual estimated biomass of the floating U. prolifera macroalgae from MODIS imagery is neither lower than the results derived from Fit I, nor higher than the results derived from Fit III. If the thickness distribution of the algae conforms to a standard Gaussian normal distribution, the results derived from Fit II (average of Fit I and Fit III) will approach the true value (Fig. 4(c)).
Fig. 4 Statistical relationship between FAI and BPA of simulated mixed pixels of floating U. prolifera macroalgae. (a) Mixed spectral reflectance produced by laboratory measurements where BPA ≤1.81 kg/m2 (corresponding to FAI ≤2.0). (b) Mixed spectral reflectance produced by laboratory measurements where BPA >1.81kg/m2 (corresponding to FAI >2.0). (c) Three statistical models (Fits I, II, and III) can be determined. It should be noted that: Fit I is the same as Fit I in Fig. 1 which was used as an estimate without considering thickness effects; Fit III considers the thickest layer of floating algae; and Fit II is based on the standard Gaussian distribution of algae thickness. Fit I and III are the minimum and maximum boundaries of the estimation, respectively.
4.2 MODIS-derived FAI estimates
MODIS Rrc derived FAI is an important process parameter for estimating the biomass of floating U. prolifera macroalgae. It should be noted that an initial FAI value (T0) is needed to determine the floating macroalgae from algae-free seawater with MODIS imagery [13]. In this study, T0 = 0.004 was applied to four MODIS-derived FAI imageries (its absolute accuracy is not critical and therefore it is not discussed in depth). Four MODIS-derived FAI images of floating U. prolifera macroalgae in the YS and East China Sea are shown in Fig. 5. A histogram and a cumulative curve of the MODIS-derived FAI of each image are given to show the distribution of FAI values (Fig. 5(a1)-5(d1)). A second-order differential curve of the cumulative distribution of FAI was used to divide the pixels of floating U. prolifera macroalgae into two groups with low and high FAI values, respectively (Fig. 5(a2)-5(d2)). The cut-off value of the four images is FAI = 0.05. The pixels of floating U. prolifera macroalgae with high FAI values are all located in the center of the area of floating algae coverage. These different groups are used to assess the contribution of uncertainty in estimating the biomass of floating U. prolifera macroalgae using statistical models.
Fig. 5 Spatial distributions of FAI of floating U. prolifera macroalgae from four MODIS imageries. The insert images (a1, b1, c1, and d1) show the statistical histogram and summation curve of the FAI values. Other insert images (a2, b2, c2, and d2) indicate the rate of change of FAI based on the second derivative of the cumulative curve. Note that FAI = 0.05 is an important value for assessing the uncertainty in the optical estimation of the biomass of floating U. prolifera macroalgae from MODIS imagery.
4.3 Uncertainty in MODIS-estimated total biomass
It is difficult to estimate biomass accurately due to the lack of information on the spatial distribution of the thickness of floating U. prolifera macroalgae. An important assumption is that the spatial distribution of thickness conforms to the standard Gaussian distribution, which also means that field observations of the BPA of floating U. prolifera macroalgae should range from 0 to ~5.5 kg/m2. In this case, the biomass estimated by the model of Fit II would be accurate. Therefore, models of Fits I, II, and III were applied to the MODIS-derived FAI data to assess the uncertainty in the optical estimation of the biomass of floating U. prolifera macroalgae. The three MODIS-derived biomass estimates for the same day (21 June 2015) show significant differences, especially in the center of the aggregation of floating U. prolifera macroalgae (Fig. 6(a)-6(c), corresponding respectively to the modeled biomass with Fits I, II, and III). There is an uncertainty of ~36% in the optical estimation of the total biomass of floating U. prolifera macroalgae.
Fig. 6 Optical remote estimates of the biomass of floating U. prolifera macroalgae obtained using three models ((a), (b), and (c), corresponding respectively to the results derived from Fits I, II, and III). Note the substantial difference in the estimated BPA located in the center of the floating macroalgae.
In order to further assess the contribution of pixels with various FAI values to the uncertainty in estimating the total biomass of floating U. prolifera macroalgae, statistical parameters of two groups (corresponding to FAI ≤0.05 and FAI >0.05) are given in Table 1. The average uncertainty of the optical estimation of the total biomass for the four MODIS images is ~36%, ~43% of which is contributed by pixels with high FAI (FAI >0.05), which is only ~10% of the total pixels covering the area of floating U. prolifera macroalgae. This also means that the precise estimation of pixels with high FAI values will greatly reduce the uncertainty in the optical estimation of the biomass of floating U. prolifera macroalgae.
Table 1. Statistical parameters (pixel number, total biomass (TB), and uncertainty) for two groups corresponding to FAI ≤ 0.05 and FAI >0.05 for the four MODIS data sets.
5. Conclusions
The optical remote detection and quantification of floating macroalgae is a key research area in the monitoring and management of the marine environment. FAI is an effective parameter for detecting floating U. prolifera macroalgae in the YS, and for estimating its biomass using MODIS images. However, the degree of uncertainty in the optical remote estimation of the biomass of floating U. prolifera macroalgae with MODIS data has yet to be determined. In this study, laboratory-based measurements of floating U. prolifera macroalgae with various values of BPA were used to simulate mixed spectral reflectance. The statistical relationship between the FAI and BPA values of mixed pixels indicates that the thickness of floating U. prolifera macroalgae is the main source of uncertainty in the optical estimation of biomass (corresponding to BPA >1.81 kg/m2 or FAI >2.0 of pure pixels). Three statistical models were applied to the FAI of four MODIS images to assess the degree of uncertainty in the optical estimation of biomass. There is an uncertainty of ~36% in the optical estimation of biomass due to thickness effects, and ~43% of the total uncertainty is caused by a few pixels with high MODIS-derived FAI values (FAI >0.05, ~10% of the total pixels with floating macroalgae in four images). Continued investigation of the spatial distribution of the thickness of floating U. prolifera macroalgae will further improve the accuracy of estimates of algal biomass in the YS and East China Sea.
Funding
National Natural Science Foundation of China (Grant No. 41771376, 61675187 and 41371014), the Fundamental Research Funds for the Central Universities (090414380023).
Acknowledgments
We thank the NASA/GSFC for providing MODIS data and SeaDAS software.
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