Algae (Microcystis and Scenedesmus) absorption spectra and its application on Chlorophyll a retrieval

Abstract

Blue algae and green algae are the dominant phytoplankton groups that contribute to the eutrophication and the water bloom in inland water of China. The absorption coefficients (spectra) of the algae, which do not change with its intrinsic optical characteristics and the observation geometry, are strictly additive quantities. The characteristics of the absorption spectra of the two algae are presented. The pure blue algae and the pure green algae cultured in the laboratory environment are diluted and mixed at ten volume ratios. The Quantitative Filter Technique was applied to measure their absorption spectra. The “hot-ethanol extraction” method was chosen to calculate their concentration of Chlorophyll a. The retrieval algorithm developed in this study extracts the mapping information between each individual alga and their Chlorophyll a concentration via Continuous Wavelet Transform, and retrieves the Chlorophyll a concentration of each alga in their mixture using a trust region optimizer. The results show that the retrieved and the measured Chlorophyll a concentrations of the blue algae and the green algae components in the ten mixture match well with the average relative error of 5.55%.

Keywords

algae / absorption coefficient spectra / Chlorophyll a / trust region / Continuous Wavelet Transform

Introduction

The outburst of water bloom occurs frequently in inland China in the past few years. Usually mixture of multiple types of algae together contributes to water bloom, although it may seem that there is only one dominant type. The algae composition in water bloom varies with time and place, therefore the comprehensive indicator, the total phytoplankton chlorophyll concentration, is ideal for monitoring the course and severity of water bloom (Kutser, 2004; Ahn et al., 2006). Chlorophyll is a common pigment in all types of phytoplankton, which reflects the overall biomass. The total chlorophyll concentration alone is not adequate to tell the composition of the phytoplankton types, let alone the biomass of each type. Since the total biomass is composed of various types of algae, the successful identification of a particular type relies on its distinctive biomass and optical characteristics (Cullen et al., 1997; Schofield et al., 1999). The composition of phytoplankton groups and the biomass of each group are two important subjects in the study of eutrophication and water bloom in inland water.

Each phytoplankton has its unique combination of pigments, which absorb incident lights with the strength varying with wavelength known as the pigments’ absorption spectra (Rowan, 1989; Bidigare et al., 1990). The absorption spectrum of a phytoplankton is the sum of the absorption spectra of its pigments. The optical characteristics of a phytoplankton such as the absorption and scattering of incidence can be used to identify the composition and the development of a mixed algae assemblage, retrieve the biomass of each individual alga, and contributes to the reveal of the mechanism of a water bloom outburst (Zhang et al., 2009). Numerous studies on the algae identification resort to their absorption features. Millie et al. (1997) utilized the photopigment (gyroxanthin-diester, carotenoid) and absorption signatures to detect and enumerate the red tide dinoflagellate, Gymnodinium breve (G. breve) in laboratory cultures and in natural assemblages. It is noted that the gyroxanthin-diester : Chlorophyll a ratio is relatively stable during bloom senescence and the stepwise discriminant analysis showed that the absorption spectra of accessory chlorophylls and carotenoids are good indicators of discerning the fucoxanthin-containing G. breve from peridinin-containing dinoflagellates, a diatom, a haptophyte, and a prasinophyte. Kirkpatrick et al. (2000) compared the fourth-derivative on the absorption spectra of the unknown sample and the standard sample of G. breve using a similarity index to detect the abundance of G. breve in natural, mixed phytoplankton communities. Moberg et al. (2002) applied the principal component analysis (PCA) model on the absorption spectra (350-770 nm) of phytoplankton samples and performed a partial least-squares regression on several independent variables to determine the relative abundance of nine individually cultured algae in the mixed assemblages. The average root mean square error of cross-validation was 8.6%, which implied that the minimum relative abundance of a species to be detected of this method is around 20%. Staehr and Cullen (2003) investigated the performance of the spectral similarity index method proposed by Millie and the multivariate partial least-squares regression technique for detecting algae; the methods were applied to fourth-derivative absorption spectra of Karenia mikimotoi mixed with the dinoflagellate Prorocentrum minimum, which are cultured under laboratory environment, to retrieve the abundance of K. mikimotoi and the concentration of some pigment; the result shows the partial least-squares regression method is more effective in optical discrimination of phytoplankton species from spectral absorption signatures. Zhang et al. (2006) measured the absorption spectra of nine typical phytoplankton species cultured under laboratory environment and used seven primary components of singular value decomposition to identify algae; the accuracy of this experiment is around 80%. Zhao and Qin (2008) measured and normalized the absorption spectra of five common algae in lab, Microcystis aeruginosa, Scenedesmus obliquus, Chlorella pyrenoidosa, Selenostrum capricornutum and Melosira granulate var angustissima, which were applied to partition the spectral absorption of mixed algae. Liu et al. (2002) obtained the quantitative characteristics of algae (reflectance) spectrum of Microcytis wesenbergii and Scenedesmus obliquus and retrieved the Chlorophyll a concentration of each alga in their mixture through the spectrum decomposition method, which fits the modes of Gaussian functions to the mixture spectrum at signature wavelengths. It is noted that the reflectance is one apparent optical property of water, which may vary with both its intrinsic optical characteristics and the observation geometry. Therefore, the reflectance spectra of algae mixtures are not strictly additive functions. In the contrast, the absorption coefficients are strictly additive quantities. This study presents the characteristics of the absorption spectra, extracts the mapping information between each individual alga and their Chlorophyll a concentration via Continuous Wavelet Transform (CWT), and retrieves the Chlorophyll a concentration of each alga in their mixture using a trust region optimizer.

Absorption spectra of algae

Algae culture experiment

Two algae, Microcystis (in Cyanophyta) and Scenedesmus (in Chlorophyta), are selected as our target algae. For convenience, Microcystis and Scenedesmus are called the blue algae and the green algae hereafter. They are the dominant species in inland China natural water (Zhang, 2007; Wu, 2000; Jiang et al., 2001). The algae for this experiment are purchased from Freshwater Algae Culture Collection of the Institute of Hydrobiology, Chinese Academy of Sciences (FACHB-Collection) and cultured at Nanjing Institute of Geography & Limnology, Chinese Academy of Sciences. Algae were first inoculated in a 150 mL Erlenmeyer flask, and cultured in the incubator with the BG-11 medium; the light cycle was controlled at 14-hour light︰10-hour dark; the relative light intensity is 20%; the temperature was 25°C. The absorption coefficients of the two algae were measured at 3:00 pm daily for thirteen days since day two; then the sampling rate was changed two days a time. At each time, the absorption coefficients of 50 mL pure Microcystis and 50mL pure Scenedesmus and their 1:1 mixture were measured. After the growth of algae entered the stable stage, the dilution and mixing experiments were conducted. The dilution experiment took 20mL of each alga, which were diluted with pure water to 24 mL, 30 mL, 40 mL, 60 mL, 100 mL, 200 mL, and 300 mL and their absorption coefficients were measured; the mixing experiment mixed the dilutions of the two alga at the ratios of 1∶9, 2∶8, 3∶7, 4∶6, 5∶5, 6∶4, 7∶3, 8∶2, and 9∶1, and the absorption coefficients of these mixtures were measured.

Absorption spectra and calculation of Chlorophyll a

The Quantitative Filter Technique (QFT) was applied to measure the absorption spectra (Mitchell, 1990). Algae solution was obtained under sterile conditions; the organics in the supernatant, which was separated by a centrifuge, were removed; pure water was added into the residual; the solution was filtered by the Whatman GF/F glass microfiber filters with the diameter of 25 mm and the aperture of 0.7 µm. The reference filter was immersed in pure water to the same level as the sample filter. The optical density was measured by a Shimadzu UV-VIS spectrophotometer, which has a 1cm width Quartz cuvette, a 350-800 nm spectral range and a 1 nm spectral resolution. Each sample was measured three times and averaged to give its optical density. After the optical density of the pure and mixed algae was obtained, the absorption coefficient was calculated by the following steps:

First, the optical density at 750 nm was subtracted from the entire spectrum, and the light path amplification correction proposed by Cleveland and Weidemann (1993) was applied:

(1)\begin{array}{ll}O{D}_s=\mathrm{0.378}O{D}_f+\mathrm{0.523}O{D}_f^{\mathrm{2}}& O{D}_f\le \mathrm{0.4}\end{array},

where O{D}_fis the optical density to be corrected and O{D}_sis the optical density with the filter light path corrected. The absorption coefficient spectraa(\lambda )is calculated by:

(2)a(\lambda )=\mathrm{2.303}\times {\displaystyle \frac{S}{V}}O{D}_s(\lambda ),

where V is the volume filtered; S is the clearance area of the filter; \lambda is the wavelength.

There are several methods of determining the Chlorophyll concentration of phytoplankton (Lorenzen, 1967; Yentsch and Menzel, 1963; Schmid et al., 1998). We choose the “hot-ethanol extraction” method (Chen et al., 2006) to calculate the concentration of Chlorophyll a (Chl _a):

(3)Ch{l}_a=\mathrm{27.9}{V}_{ethanol}[(E_{\mathrm{665}}-E_{\mathrm{750}})-(A_{\mathrm{665}}-A_{\mathrm{750}})]/V_{sample},

where V_{ethanol} is the volume of ethanol; V_{sample} is the volume of the sample; E_{\mathrm{665}} and E_{\mathrm{750}} are the absorption of the ethanol extraction at wavelength 665 nm and 750 nm; and A_{\mathrm{665}} and A_{\mathrm{750}} are the absorption of the acidified ethanol extraction at the corresponding wavelengths.

Methodology

Continuous Wavelet Transform (CWT)

The CWT was used to map the one-dimension absorption spectrum to the two-dimension wavelength-scale matrix, which is capable of separating information from noise. Compared to the Discrete Wavelet Transform, CWT has the advantage of locating the spectral characteristics more accurately. It is noted that CWT will produce redundant coefficients which do not contribute to the signal reconstruction; however, it increases the quantity of samples, which makes the optimization more accurate and precise. CWT is expressed as:

(4)CWT(a,b)[f(t)]=\langle f,{\psi }_{a,b}\rangle ={\displaystyle {\int }_{-\infty }^{\infty }f(t)\cdot \overline{{\psi }_{a,b}(t)}dt},

where f(t) is the original 1 Dim signal; \psi denotes the wavelet functions, which is also known as the wavelet bases; and the subscripts a and b denote the scale parameter and the positioning parameter, respectively. The over-bar on \overline{{\psi }_{a,b}(t)} is the conjugate of a complex number. \langle f,{\psi }_{a,b}\rangle denotes the convolution operation; therefore, CWT can be interpreted as the projection of the original signal on wavelet bases at all the possible combinations of scale (a) and sampling position (b). The product of CWT is the wavelet coefficient matrix CWT(a,b). {\psi }_{a,b}(t) is generated via stretch and displacement of \psi. The choice of \psi is not unique as long as it meets the specific application requirements. Widely used \psi includes Morlet, Paul, and Gaussian. There is definite relationship between the scale and the period. For example, the period of Morlet wavelet functions is about 1.03 times that of its scale (Torrence and Compo, 1998). This study chooses the Morlet wavelet function as it is commonly used in the application of signature extraction.

Trust Region algorithm

Because of its good properties of reliability, robustness, and convergence, the trust region algorithm is widely used in solving non-linear optimization problems. Iterations are necessary in solving non-linear optimization numerically. The methods of updating the status vector at step k+1 from step k are not unique. The iterations are finished as certain stop criteria are met. The solution of the approximation model, usually linear or quadratic, at the current point is taken as the initial point for the next iteration. Only the region of the approximation model near the current point, which is called the trust region, fits the original function locally. The location and the radius of the trust region are adjusted at every step. Generally, the trust region algorithm determines whether and how the location and radius should vary at each trial step. For example, if the indicator suggests that the current approximate model fits the original function well, the radius can be enlarged; otherwise, the radius should be reduced (Coleman and Li, 1994; Coleman and Li, 1996; Dennis, 1977).

Chlorophyll a retrieval

Ideally, the absorption coefficient spectrum of the mixed algae (c) is the linear addition of those of the blue algae (a) and those of the green algae (b): a+b=c. If the property of being additive is still valid after applying CWT on these absorption coefficient spectra, then CWT(a)+CWT(b)=CWT(c), and the retrieval of the blue and green algae Chlorophyll a can be performed in the wavelet domain. The absorption coefficient spectra of the blue algae and the green algae are denoted by a and b, respectively; the absorption coefficient spectrum of the mixed algae is denoted by c; the abbreviation CWT denotes both the continuous wavelet transform and the corresponding two dimensional wavelet coefficient matrix.

The absorption coefficient spectra of the pure algae (the blue or green algae) at multiple Chlorophyll a levels covering a wide range are measured through the dilution experiment. CWT is performed on these spectra and the fitting parameters of the wavelet coefficients (the dependent variables) and the Chlorophyll a concentrations (the independent variables) at each qualified point in the wavelet domain are calculated and stored in a three dimensional space, where the first two dimensions represent the wavelet domain and the third dimension is related to the fitting parameters. Let C₁ denote the fitting parameters matrix of the blue algae, C₂ the fitting parameters matrix of the green algae, i the point in the wavelet domain that has a significant fitting result, X₁ the blue algae Chlorophyll a concentration in the target mixture, and X₂ the green algae Chlorophyll a concentration in the target mixture. Under the assumptions of the property of addition on both the absorption coefficient spectra and their wavelet transform, the estimate of X₁ and X₂ is obtained when the sum of the squared residuals between the corresponding absorption coefficients spectra of the pure algae and the target mixture in wavelet domain is minimized. The objective function for the trust region algorithm is expressed as:

(5)\underset{X_{\mathrm{1}},X_{\mathrm{2}}}{\min }{\displaystyle \sum _i{(CW{T}_{mixed}(i)-(C_{\mathrm{1},i}(X_{\mathrm{1}})+C_{\mathrm{2},i}(X_{\mathrm{2}})))}^{\mathrm{2}}},

where C_{\mathrm{1},i}(X_{\mathrm{1}}) represents the wavelet coefficient at location i given the blue algae Chlorophyll a concentration in the target mixture, X₁; C_{\mathrm{2},i}(X_{\mathrm{2}}) represents the wavelet coefficient at location i given the green algae Chlorophyll a concentration in the target mixture, and X₂; CW{T}_{mixed}(i) represents the wavelet coefficient of the target mixture at location i. The trust region algorithm, implemented in Matlab, is chosen to solve X₁ and X₂. Since X₁ and X₂ are concentrations, their physical lower limits are zero. Since the reliability of extrapolation is much less than that of interpolation, the upper limits of X₁ and X₂ are set at the highest concentrations of the blue algae and the green algae in the dilution experiment.

Results and discussion

Absorption coefficient spectra of the two algae and their mixture

The absorption coefficient spectra are mainly influenced by the pigment composition and concentrations in algae cells (Bricaud et al., 1988; Roesler et al., 1989). As the pigment concentration increases, the absorption coefficients also increase with similar spectral shapes over the 350-750 nm range (figure 1). Since the pigment composition in blue algae is different from green algae, the two algae have very distinctive shapes of absorption coefficient spectra. To extract the characteristic spectra of the two algae, the envelopes of the spectra are removed. It is seen that both the green and blue algae have strong absorption peaks near 675 nm and 440 nm due to the existence of Chlorophyll a in both algae. In contrast with the green algae, the blue algae have a relatively strong absorption peak around 620 nm due to the pigment phycocyanin. There are two weak absorption peaks near 470 nm and 665 nm in the green algae spectra due to Chlorophyll b; the blue algae do not contain Chlorophyll b, therefore these two weak peaks cannot be found in the blue algae spectra. Both of the algae have an absorption shoulder near 490 nm due to carotenoids. Because the concentration of carotenoids in the green algae is higher than in the blue algae, the shoulder is more apparent in the green algae spectra.

Figure 2 shows the absorption coefficient spectra of the mixed algae at ten mixing ratios described in the previous section — Algae Culture Experiment (Section 2.1). It is seen that the spectra of the mixed algae have the characteristics of pure blue algae and pure green algae simultaneously. As the proportion of the blue algae increases, the absorption peak near 620 nm becomes more prominent. In contrast, the blue algae spectra at low proportions have no apparent absorption peak near 620 nm, which resembles the pure green algae spectra. The spectra of the mixed algae with a low proportion of green algae barely have absorption peak at 650 nm, which also resembles the pure green algae spectra. The spectra beyond 660 nm do not vary much with the ratio between the green algae and the blue algae. Figure 2 is based on the mixture experiment at one time. A similar behavior of the two algae over the entire growth period is also found. However, the proportion of blue algae and green algae without dilution at any time during growth does not change dramatically. In order to test the retrieval algorithm under more proportional conditions, the data of the dilution experiment are used. If the algorithm is successful on the dilution data, it should also apply to the Chlorophyll a retrieval on the mixed algae at any given time during growth, although this algorithm is not verified in this paper.

Preprocessing the absorption coefficient spectra

In order to reduce the edge effect during CWT, each absorption coefficient spectrum is mirrored at both ends, which makes the new data has three times elements as the original one. CWT is performed on those mirrored data and the two dimensional wavelet coefficients are obtained (Figure 3). The x-axis indicates the wavelength and the y-axis indicates the scale. The Cone of Influence (COI) area is given by determining the scale range at each wavelength where the convolution between stretched and translated wavelet function and the input data is not influenced by the edge effect. In our example, the shape of COI is a truncated inverted isosceles triangle. We observe that the area where scales are small is less influenced by the edge effect; in contrast, the area where scales are large and close to the edge is more influenced by the edge effect.

Figure 4 displays the difference of the wavelet coefficient matrixes of the absorption coefficient spectra between the undiluted pure blue algae and the undiluted pure green algae in the dilution experiment. The magnitude of the difference is around 10^-12, which is significantly less than the magnitude of the wavelet coefficients (around 10¹). It suggests that the wavelet coefficients of absorption coefficient spectra have the property of being additive.

Figure 5 shows the concentrations of Chlorophyll a versus the corresponding absorption coefficients at 622 nm where the Phycocyanin absorption peaks before and after the adjustment. The blue “+” symbols represent the absorption coefficients of the blue algae before adjustment. The blue line that goes through the origin is the linear fitting of those points. The dashed vertical line that passes the three red symbols “*” indicate the concentration of Chlorophyll a (299.7 mg/L) of the mixed algae whose volume ratio of the blue algae and the green algae is 20:0. The “*” red near the blue fitting line indicates the approximate absorption coefficient of the blue algae at 622 nm if the concentration of Chlorophyll a is 299.7 mg/L in the dilution experiment. The red “*” above indicates the absorption coefficient of the mixed algae whose volume ratio of the blue algae and the green algae is 20:0 under the same concentration of Chlorophyll a (299.7 mg/L). The gap between these two red “*” symbols reflects the growth status difference of the blue algae between the dilution experiment and the growth experiment. Applying the absorption coefficient ratio at the two “*” symbols to the blue algae in each dilution pair makes the concentration of Chlorophyll a at 622 nm comparable between the two experiments. This ratio also ensures the additivity of the wavelet coefficients at this wavelength. The red “+” symbols are the adjusted pairs of the absorption coefficients and the concentrations of Chlorophyll a. The red origin-passing line is the fitting line of the red “+” symbols.

Figure 6 (a) illustrates the ratio spectra of the absorption coefficients of the blue algae between the dilution experiment and the growth experiment at the same concentration of Chlorophyll a. Figure 6 (b) illustrates the ratio spectra of the absorption coefficients of the green algae between the dilution experiment and the mixture experiment at the same concentration of Chlorophyll a. For the Phycocyanin absorption peak of the blue algae, the absorption coefficients of the blue algae in the growth experiment are about 1.1 to 1.2 times higher than those in the dilution experiment. The ratio is close to 1.0 near the Chlorophyll a absorption peak. The large values of the ratio beyond 700 nm reflect higher uncertainty in the small absorption coefficients. Similar trend is seen in the green algae but with less variation.

Results of Chlorophyll a retrieval

Applying the spline fitting on the wavelet coefficients and the corresponding concentrations of Chlorophyll a on each point (the wavelength – scale point), the fitting parameter matrixes for the blue algae and the green algae, C₁ and C₂, are obtained. Note that only the points with R²>0.9995 in both C₁ and C₂ are used in the Chlorophyll a retrieval. Figure 7 gives some examples of such fitting.

The non-linear least square function in Matlab, lsqnonlin, the core of lsqnonlin is the trust region algorithm, is chosen to solve the Eq. (5) on the qualified 5595 points (R²>0.9995 in both C₁ and C₂, and not influenced by the edge effect of CWT). Table 1 lists the retrieval of the Chlorophyll a of the blue algae and the green algae in the ten mixed algae. It is seen that the least square residuals for all volume ratios are close, most of which are between 10 and 40. The retrieved total Chlorophyll a is close to that measured with an average relative error of 5.55%.

In order to illustrate the performance of the Chlorophyll a retrieval algorithm, the absorption coefficient spectra of the pure blue algae and the pure green algae at the retrieved Chlorophyll a concentrations of each pair are calculated and the combined spectrum of each pair is compared with the corresponding measured mixed spectrum. The results of all 11 pairs have an R² greater than 0.99, which suggests the retrieval algorithm is accurate and reliable. Figure 8 shows an example of the pair of the 10:10 blue:green volume ratio. It is seen that the retrieved and the measured mixed absorption coefficient spectra match well with each other. This algorithm also gives the seperated blue and green absorption coefficient spectra of any mixed absorption spectrum of these two algae.

Conclusions

The eutrophication and the outburst of water bloom has been occuring frequently in inland China in the past few years. The mixture of multiple types of algae together, especially blue algae and green algae, is the main cause of these phenomena. The absorption coefficient (spectrum), which does not change with its intrinsic optical characteristics and the observation geometry, is a better quantity than the reflectance in revealing the nature of the algae. The characteristics of the absorption spectra of the two algae are presented. The pure blue algae and the pure green algae cultured in a laboratory environment are diluted and mixed at ten volume ratios. The Quantitative Filter Technique (QFT) was applied to measure their absorption spectra. The “hot-ethanol extraction” method was chosen to calculate their concentration of Chlorophyll a. The retrieval algorithm developed in this study extracts the mapping information between each individual alga and their Chlorophyll a concentration via Continuous Wavelet Transform (CWT), and retrieves the Chlorophyll a concentration of each alga in their mixture using a trust region optimizer. The results show that the retrieved and the measured Chlorophyll a concentrations of the blue algae and the green algae components in the ten mixtures match well with an average relative error of 5.55%. The algorithm also gives the seperated blue and green absorption coefficient spectra of any mixed absorption spectrum of these two algae.

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