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Abstract
The extraction of pigment characteristic spectra from the phytoplankton absorption spectrum has high application value in phytoplankton identification and classification and in quantitative extraction of pigment concentrations. Derivative analysis, which has been widely used in this field, is easily interfered with by noisy signals and the selection of the derivative step, resulting in the loss and distortion of the pigment characteristic spectra. In this study, a method based on the one-dimensional discrete wavelet transform (DWT) was proposed to extract the pigment characteristic spectra of phytoplankton. DWT and derivative analysis were applied simultaneously to the phytoplankton absorption spectra of 6 phyla (Dinophyta, Bacillariophyta, Haptophyta, Chlorophyta, Cyanophyta, and Prochlorophyta) to verify the effectiveness of DWT in the extraction of pigment characteristic spectra.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Phytoplankton, the primary producer in the marine ecosystem [1], the base and starting point of the food web, and an important food source for aquatic animals [2], play an important role in the marine biochemical cycle [3]. The study of phytoplankton is an important part of ecology, biology, oceanography, and other fields, and understanding the phytoplankton community structure and pigment concentration is fundamental work. The phytoplankton absorption spectrum contains information about pigment composition, pigment proportion, and community structure [4–6].
At present, there are well-developed measurement methods for phytoplankton absorption spectra, including laboratory measurement methods with spectrophotometers, remote sensing inversion [7–9], and underwater in situ measurement (AC-S) [10]. With the continuous development of marine observation platforms, hyperspectral technology, and marine hyperspectral satellites, it is possible to realize the quantitative observation of phytoplankton in large ranges at high frequencies [11,12]. There have been many studies on the extraction of phytoplankton pigment characteristic spectra from the absorption spectrum, and some effective inversion methods have been developed, such as derivative analysis [5,13–18], Gaussian decomposition [19,20], spectral reconstruction [21], linear regression [22,23], and neural networks [24,25], to quantitatively retrieve pigment concentrations. For example, derivative analysis was used to extract the characteristic spectra of different pigments, classify phytoplankton species and study the structure of pigments from the phytoplankton absorption spectrum [12–18]. By combining derivative analysis as a data preprocessing method with other mathematical methods, phytoplankton pigments concentration can also be quantitatively analyzed [5,6,18].
However, derivative analysis has some problems in practical applications. It is sensitive to noise, and the spectrum must be smooth-processed before the derivative analysis, but the processing will lead to spectral distortion and loss of some detail. The step size of the derivative operation needs to match the bandwidth of the characteristic peak, so it is difficult to extract a characteristic peak with too narrow or wide bandwidth at the same time. After derivative calculation, the range of spectral wavelengths is smaller than that of the original spectrum.
Wavelet transform is the inheritance and development of Fourier transform. It has the characteristic of multiresolution analysis, which can analyze the time/space frequency locally. Through expansion and translation, the signal is multiscale refined and ultimately achieves time/space subdivision at high frequency and frequency subdivision at low frequency. It makes the purpose of fully highlighting the characteristics and focusing on the details of the signal possible. In this study, discrete wavelet transform (DWT) was applied to the pretreatment of the phytoplankton absorption spectrum. The absorption characteristic spectra of the major pigments were extracted by multiresolution analysis of the DWT. Based on the width and height difference of different pigment absorption spectra, the pigment composition of phytoplankton was analyzed. Finally, the superiority of the wavelet analysis was illustrated by comparing it with derivative analysis.
2. Data and methods
2.1 Data
The data used in this study included the absorption spectra of phytoplankton cultured in the laboratory and collected in situ. The laboratory data is used to extract the characteristic spectra of major pigments and establish wavelet analysis method. The in situ measured data is used to preliminarily test the ability of DWT to quantitatively extract the concentration of major pigments. The following introduces these two types of data.
There are 40 absorption spectra of single species cultivated phytoplankton, which belong to 6 phyla and 27 species (as shown in Table 1). These 6 phyla include Dinophyta, Bacillariophyta, Haptophyta, Chlorophyta, Cyanophyta, and Prochlorophyta. The Chlorophyta absorption spectrum was collected from the literature [26], and the absorption spectra of other phyla were measured in our laboratory. The cultivation conditions were all at room temperature (20°C), with a light set of 60-80 µmol photon m-2 s-1 and a light-dark cycle ratio of 12 h to 12 h. The measurement period of absorption spectra is the stable growth period of phytoplankton. The quantitative filter membrane technology was used in the experiment, and the absorption spectra were measured with a dual-beam ultraviolet-visible photometer, with a resolution of 1 nm. The phytoplankton selected in this study are common phyla in the ocean or dominant phyla in red tide events.
Table 1. Phytoplankton species belonging to six phyla used in this study
Dinophyta, Bacillariophyta, and Haptophyta are commonly dominant phytoplankton causing red tide. Bacillariophyta is one of the largest known phytoplankton phyla, is found in the world's oceans, and can adapt to different environmental conditions. The major pigments (Table 2 shows the information of relevant pigments) contained in Bacillariophyta are Chlorophyll a (Chl a), Chlorophyll c (Chl c), fucoxanthin, and diadinoxanthin. Dinophyta is widely distributed in the world's oceans and can take advantage of ocean mobility to cause red tide directly. The major pigments in Dinophyta are Chl a, Chl c, and Peridinin. Haptophyta is mainly composed of unicellular eukaryotic algae, which are widely distributed worldwide and highly adaptable to the temperature and salinity of the ocean. There are many species within Haptophyta [27]. In this study, Phaeocystis globosa was taken as the representative species to study the characteristic spectrum of the pigment Chl c3. Chlorophyta is rich in Chl a and Chlorophyll b (Chl b), with most members living in freshwater and a few living in the ocean. Dunaliella salina, which lives in seawater with high salinity, was taken as a representative of Chlorophyta to explore the spectral characteristics of Chl b.
Cyanophyta is the simplest and most primitive green autotrophic plant and is a kind of prokaryotic phytoplankton. Cyanophyta lives mainly in warm, well-lit, and oligotrophic waters in the tropics and subtropics. The photosynthetic pigments of Cyanophyta are mainly Chl a, phycobilin, and some carotenoids. To explore the spectral characteristics of phycobilin, we selected Synechococcus, which contains phycocyanin, as a representative of Cyanophyta [21]. Prochlorophyta is a prokaryotic autotrophic photosynthetic organism that is usually symbiotic with Cyanophyta. Prochlorophyta is the only phytoplankton that contains Dv-Chl a and Dv-Chl b.
Studies have found that the pigment composition and proportion of different phytoplankton species in the same phylum are similar [26,30], while those of different phytoplankton phyla are quite distinct. Fig. 1 shows the composition and proportions of pigments contained in the six phytoplankton phyla. The major pigments of Dinophyta, Bacillariophyta, and Haptophyta include Chl a, Chl c, PSC, and PPC, but the composition of Chl c is significantly different. Dinophyta and Bacillariophyta contain Chl c1 and Chl c2, while Haptophyta is dominated by Chl c3. In addition, compared with Bacillariophyta, Dinophyta, and Haptophyta contain a higher proportion of Chl c that is approximately 8 percentage points higher than the Chl c content of Bacillariophyta. Meanwhile, Dinophyta contains more PPC, with levels that can reach more than 20% of the total pigment content, while the PPC levels in Bacillariophyta and Haptophyta account for less than 10% of the total pigment content.
Fig. 1. Pigment composition of six phytoplankton phyla and their relative ratios to total pigments, Those for Bacillariophyta, Dinophyta, and Haptophyta were derived from the statistical average data of Ref. [30]. Pigment ratios for Chlorophyta and Cyanophyta were derived from Ref. [26] and that for Prochlorophyta was derived from Ref. [31].
Chlorophyta, Cyanophyta, and Prochlorophyta have relatively simple pigment compositions, which are composed of chlorophyll and PPC, and their Chl a accounts for more than 50% of total pigment content. The proportion of the characteristic pigment Chl b in Chlorophyta can also reach approximately 25%. Cyanophyta contains phycocyanin, which, together with chlorophyll, is responsible for photosynthesis. Therefore, PPC is the major carotenoid in Cyanophyta, reaching more than 30%. Prochlorococcus has the next highest proportion of PPC, while the PPC proportion in Chlorophyta is the lowest.
The phytoplankton absorption spectra and the corresponding pigment concentrations collected in the Yellow Sea and the Sea of Japan from May to June 2016 were obtained from SeaWiFS Bio-optical Archive and Storage System (SeaBASS) [32] as shown in Fig. 2. There were 64 sampling stations in total and sampling measurements were conducted at different layers in each station. The absorption spectra of phytoplankton were measured with quantitative filter technique, while major pigment concentrations were measured with high performance liquid chromatography (HPLC) method. The concentration of Chl a ranged roughly from 0.06 to 7.00 mg/m3. Finally, a total of 172 absorption spectra and the matched pigment concentrations were used for this study.
2.2 Methods
This section mainly introduces the wavelet analysis method adopted in this study. In addition, the derivative analysis used for comparison is briefly introduced for the completeness of this manuscript.
2.2.1 Wavelet analysis
Wavelet analysis is a kind of time-frequency local analysis based on Fourier analysis. By scaling and translating the wavelet function, the signal can be expressed as a series of wavelet function superpositions, to achieve the purpose of subtle observation of the original signal. Mathematically, it can be expressed as an inner basis of a finite-length sequence and wavelet function, and the specific expression is as follows:
In 1989, Mallat proposed multiresolution analysis, also known as multiscale analysis, based on the concept of function space and the corresponding fast algorithm called the Mallat algorithm [33]. In multiresolution analysis, the wavelet transform could be equivalent to a set of filtering processes. This means that the signal passes through a high-pass filter and a low-pass filter to obtain the high-frequency signal (detail signal) and low-frequency signal (approximate signal) respectively. The Mallat algorithm formula is as follows:
${D_j}$ is the detail coefficient of the jth layer of the signal, ${A_j}$ is the approximation coefficient of the jth layer, h(k) can be regarded as a low-pass filter, and g(k) can be regarded as a high-pass filter. The approximation coefficient of each layer is equal to the sum of the detail signal and the approximate signal of the next layer.
Different from the Fourier transform which is only expanded with trigonometric functions, the wavelet transform has many wavelet functions, and the results obtained by different wavelet functions are often distinct. The correct choice of wavelet function is the premise of achieving the wavelet transform. In previous studies, the performance of many wavelet functions such as Meyer, Haar, Db, and Coif had been evaluated and experiments showed that the compactly supported Meyer wavelet function performed best due to its symmetry, biorthogonality, infinitely differentiable, fast convergence speed, and good fluctuation [34]. Therefore, the Meyer wavelet function can reflect the discrepancy between different pigments, and the discrete form of Meyer (Dmeyer) was selected in this study. The scale ranges of detail signals at different layers are shown in Table 3.
Table 3. Scale ranges corresponding to different decomposition layers of the Dmeyer wavelet function
In this study, the phytoplankton absorption spectra were decomposed by the wavelet analysis, and 8 layers of wavelet detail signals were obtained for the analysis of the major pigment characteristic spectra.
2.2.2 Derivative analysis
Derivative analysis is one of the most widely used methods to extract the characteristics of major pigments from the absorption spectrum because of its excellent characteristic amplification ability. To illustrate the advantages of wavelet analysis, derivative analysis was applied to the characteristic extraction of the absorption spectrum to compare the performance of these two analytical methods.
The principle of derivative analysis is to extract the absorption peak or shoulder peak of the major pigments in the absorption spectrum through the operation of different order derivatives, to determine the composition of the major pigments in phytoplankton. Because there may be some noise interference in the absorption spectrum measurement process, the derivative transformation is particularly sensitive to noise. The higher the order of the derivative transformation is, the more noise interferes with the result. However, the traditional differential method more easily amplifies the high-frequency noise in the spectra [35]. In this study, the Savitzky–Golay method was used to smooth and derive the spectrum.
The Savitzky–Golay method was proposed by Savitzky and Golay in 1964 [36]. The principle of the S-G filter is to calculate the fitting of data in the smoothing window based on the least square method of polynomials. The S-G method, which can effectively maintain the peak height and shape of spectral signals while smoothing noise signals, is widely used in smoothing and denoising spectra.
However, the method proposed by Savitzky and Golay had the limitation of window selection. Madden improved the S-G method in 1978 to break the limit of the smoothing window of 25 [37]. Madden's formula for improvement is as follows:
where $P_i^{(0 )}$ is the coefficient of the ith point of the filter in the calculation of the zero-order derivative, $Y_j^\ast $ is the midpoint of the smooth window, n is the half-width of the window, and the width of the window is (2n + 1). According to Madden's formula, S-G smoothing is the 0th derivative of the spectrum. Similarly, the q-derivative formula of the spectrum is as follows:Although the S-G method has good performance, it cannot be effectively applied to the edges of the spectra. Therefore the wavelength range of the derivative spectrum is smaller than that of the original spectrum [38], which is also one of the limitations of the derivative method.
3. Results and discussion
3.1 Absorption spectral wavelet analysis of 6 phytoplankton phyla
The Meyer wavelet function was used to decompose the phytoplankton absorption spectrum by eight layers of DWT. Eight detail signals D1-D8 and eight approximate signals A1-A8 were obtained. Fig. 3 shows the eight layers of wavelet detail coefficients D1, D2, D3, D4, D5, D6, D7, and D8. With the increase in the number of layers, the detail signal scale increased from small to large, and the signal intensity increased from low to high, with a difference of nearly 20 times.
Fig. 3. Detailed signal of phytoplankton absorption spectrum analyzed by Meyer discrete wavelet, (a)-(h) are the detail signals of layers 1-8 respectively.
Figure 4(a) shows the normalized phytoplankton absorption spectrum and Fig. 4(b)-(f) shows the approximate signal obtained after extracting the detail signal in the process of wavelet decomposition. ${a_{ph}}$ is the phytoplankton absorption spectrum. After the first level wavelet transform, the detail signal D1 was removed, and the approximate signal A1=${a_{ph}}$-D1, A2=${a_{ph}}$-(D1 + D2), and so on, A8=${a_{ph}}$-(D1 + D2 + D3 + D4 + D5 + D6 + D7 + D8). As shown in Fig. 4, with the increase in the approximate number of signal layers, the difference in absorption spectra between different phytoplankton phyla decreased. Thus, the information on pigment composition decreased, and there was almost no relevant information in A7.
Fig. 4. Phytoplankton absorption spectrum and the approximate signal after DWT. (a) is the normalized phytoplankton absorption spectrum, and (b)-(f) are the approximate signals of layers 3-7.
After wavelet multiscale decomposition of the phytoplankton absorption spectrum, the D1-D3 detail signals had a smaller scale and signal intensity. With significant randomness, different phytoplankton species of the same phylum had different characteristics. Therefore, this was regarded as a noise signal in the analysis process. Detail signals D4-D7 showed that the spectral characteristics of phytoplankton in the different phyla were significantly different, and the differences among different species of phytoplankton in the same phylum were very small. These detail signals reflected the information on pigment composition and were used as effective signals for subsequent analysis in this study. Due to the large decomposition scale and the similar details among different phyla, D8 contained little useful information about pigments and will not be considered in the subsequent analysis.
According to the experimental measurements of Bidigare et al. [39] (Table 4), the full width half maximum (FWHM) of peak absorption spectra of the six major pigments ranges approximately from 20 to 60 nm, which consists of the scale range of detail signals D4-D6 extracted by wavelet analysis (Table 3). The D7 signal extracts larger scale information, which is not the characteristic information of any certain pigment, but contains the superposition of residual characteristic information of multiple pigments (see later analysis).
Table 4. Absorption spectral characteristics of the six pigments [39]. λ is the peak center of pigment absorption spectra, FWHM is full width half maximum of each peak, and a* is the peak absorption of each pigment
3.2 Relationship between wavelet detail signals and absorption spectra of pigments
Intuitively, the wavelet decomposition coefficient represents the “similarity index” between the signal and the wavelet. If the degree of similarity is higher, the similarity index is larger. If the signals are similar at different scales, then the wavelet coefficients should also be similar at different scales. Therefore, the wavelet transform can be used to detect self-similarity, namely the fractal characteristic of a signal. In this study, the phytoplankton absorption spectra were decomposed at multiple scales by utilizing the characteristics of wavelet analysis. Due to the differences in the width and height of the absorption spectrum, the characteristics of pigments would be decomposed into detail signals at different scales. The pigment composition information of phytoplankton could be analyzed by using the characteristics of detail signals at different scales. In the following sub-sections, the details of signal characteristics similar to Table 4 extracted by DWT based on experimental measurements of major pigment absorption spectra [39] will be further analyzed.
Figure 3(d) shows the D4 wavelet detail signals of phytoplankton absorption spectra. It was the original signal that extracted D1, D2, and D3 detail signals and then further extracted larger scale detail signals. The corresponding scale range is 12-24 nm. The D4 signal extracted all peaks and shoulder peaks in the absorption spectra, and the positions of the extracted peaks were consistent with the positions of the pigment absorption peaks presented in Table 4. For example, there were five absorption peaks of Chl a (approximately 415 nm, 440 nm, 590 nm, 621 nm, and 675 nm). Chl b was located at absorption peaks of 470 nm and 650 nm, and Chl c was located at absorption peaks of approximately 465 nm and 640 nm. The central wavelength of some pigment absorption peaks might have been slightly shifted due to pigment proteins in different phytoplankton phyla or other uncontrollable factors.
Some pigment peaks could not be fully reflected, such as the absorption peak of PPC at 490 nm. Due to the absorption of pigments overlapping each other, the peak position was also related to the proportion of relevant pigments. In addition, at 510-600 nm, the large noise also led to too small an extraction of the PSC absorption peak at 521 nm. To a certain extent, the detail signals of D4 showed the differences in pigments contained in different phyla, reflecting certain information about pigment composition. For example, near 440 nm, the D4 detail signal showed the difference between the characteristic pigment Dv-Chl a in Prochlorococcus and Chl a in the other phytoplankton [40].
Figure 3(e) shows the extracted D5 detail signal, which was the further larger scale detail signal extracted from the original signal after the D1, D2, D3, and D4 detail signals. The corresponding scale range is 24-48 nm. As shown in Fig. 3(e), the D5 detail signals showed significant differences between phytoplankton of different phyla but small differences between the same phyla. The D5 detail signals contain rich information about phytoplankton pigment composition.
The characteristic peaks of pigments extracted by D5 in the range of 400-450 nm were different in height and central wavelength. The central wavelength of Dinophyta, Bacillariophyta, and Haptophyta was approximately 430 nm, and that of Chlorophyta and Cyanophyta was approximately 437 nm, which reflected the pigment characteristics of Chl a. There were two adjacent and overlapping absorption peaks in Prochlorophyta in this wavelength range, both of which belonged to the pigment characteristics of Dv-Chl a. The center of the main peak was located at 445 nm, and the center of the secondary peak was located at 420 nm, which fully showed the difference from Chl a and the obvious characteristics of Dv-Chl a in Prochlorophyta. The relative proportions of Chl a in Dinophyta, Bacillariophyta, and Haptophyta were similar but significantly lower than those in the other three phyla (see Fig. 1). This characteristic pigment composition was reflected in the relative height of the characteristic peak of pigment in layer D5.
Within the range of 460-540 nm, the information of the absorption spectra of the six phytoplankton phyla was very rich. There were great differences in the height and location of the peaks, which mainly reflected the characteristics of Chl c, Chl b, and carotenoids. In the range of 460-480 nm, Chl c, Chl b, and PPC all had absorption peaks. Dinophyta and Bacillariophyta contain Chl c1 and Chl c2, but the content of the former is significantly higher than that of the latter. Therefore, after D4 extraction, there was no obvious Chl c peak of Bacillariophyta in the D5 signal. Haptophyta contains Chl c2 and Chl c3, and studies have shown that the absorption peak of Chl c3 is shifted approximately 5-6 nm to the right of Chl c1 [41]. Therefore, Dinophyta and Haptophyta also had obvious differences. Because there is no Chl c and Chl b in Cyanophyta, there was no absorption peak in this band range. For Prochlorophyta and Chlorophyta, although both contain Dv-Chl b/Chl b, the D5 signal no longer had characteristic peaks after D4 extraction because of the small absorption spectrum scale and weak intensity.
The range of 480-540 nm was the absorption band of PPC and PSC. The absorption spectra of Dinophyta and Bacillariophyta were very different from those of Haptophyta, which was caused by the different relative contents of PPC and Chl c3. The peak of Chl c3 in Haptophyta was too close to PPC, so the two peaks were combined into one. In addition, Cyanophyta, Chlorophyta, and Prochlorophyta had high PPC contents, so the peak value near 490 nm was high. Cyanophyta had a significant absorption peak near 550 nm, which was the characteristic peak of PE. However, Prochlorophyta also had an absorption peak at this position, which was caused by the characteristics of DWT, rather than the actual characteristic absorption of Prochlorophyta.
At approximately 585 nm, Dinophyta, Bacillariophyta, and Haptophyta coexisted in a small peak, while the other three phyla did not, with these three phyla belonging to the absorption peak of Chl c. The absorption peak between 620 nm and 640 nm was influenced by both Chl a and Chl c or Chl b. Finally, 675 nm was the absorption peak of Chl a.
Figure 3(f-g) shows the D6 and D7 detail signals, and their extracted signal scales were approximately 48-96 nm and 96-192 nm, respectively. With the increase in the wavelet decomposition series, the width of the extracted characteristic peaks increased, and the number of characteristic peaks decreased. After D1-D5 detail extraction, smaller absorption peaks and shoulder peaks in the original signal no longer existed, as shown in Fig. 4(d). The extracted D6 and D7 detail signals were the detail signals with a large scale among the remaining signals, a phenomenon that is usually the result of a superposition of absorption of different adjacent pigments.
For example, the absorption peak of the D6 detail signal was the contribution of pigments Chl a, Chl b, Chl c, PPC, and PSC from 410-500 nm. There was only one peak in this band, and the distribution characteristics were significantly different (except that those for Dinophyta and Bacillariophyta were similar). At 520-570 nm, Cyanophyta had an absorption peak contributed by PE. In addition, the absorption peak at 640-700 nm was obtained by the contribution of Chl a.
D7 was the detail signal of a larger scale. In terms of signal characteristics, Dinophyta, Bacillariophyta, and Haptophyta had similar signals, Prochlorophyta and Chlorophyta had similar signals, and Cyanophyta was significantly different from the other phytoplankton in its signal. These phytoplankton had only two peaks for the whole spectrum, one of which was in the red light region, while the distribution of the other was different. For example, Chlorophyta and Prochlorophyta were in the blue light region center at 440 nm, Dinophyta, Bacillariophyta, and Haptophyta at 480 nm, and Cyanophyta at approximately 530 nm. This also reflected the differences in the composition of the major pigments of the six phytoplankton phyla.
The detail signals D4, D5, D6, and D7 represented the absorption spectrum characteristics of pigments at different scales and revealed the pigment composition of different phytoplankton phyla from different levels. The combination of detail signals of different scales could reflect more comprehensive characteristics different from those of a single scale. The following three combinations (D4 + D5, D4 + D5 + D6, and D4 + D5 + D6 + D7) were taken as examples (as shown in Fig. 5).
Fig. 5. Superposition of detail signals at various levels. (a) Detail signal D4 + D5. (b) Detail signal D4 + D5 + D6. (c) Detail signal D4 + D5 + D6 + D7.
From the D4 + D5 combined signal shown in Fig. 5(a), it could be seen that the characteristics of the combined signal were similar to those of the D5 signal with little difference due to the small intensity of the D4 signal. Fig. 5(b) and 5(c) represent the combined signals of D4 + D5 + D6 and D4 + D5 + D6 + D7. Because these two combined signals contained large-scale detail signals, the pigment spectral characteristics of each phytoplankton phylum were, relatively speaking, completely extracted and can reflect information on pigment composition.
The relationship between the wavelet details of different scales and the absorption spectral characteristics of pigments in the six phytoplankton phyla was analyzed. The results showed that the detail signals of different scales (including D4, D5, D6, and D7) and their combined signals revealed information on the spectral characteristics of pigments contained in different phytoplankton phyla. The D4 signal of a smaller scale showed the absorption peak position information of almost all pigments, but there was no significant difference in characteristics. The large-scale D5 signal showed very strong characteristic information for the pigment absorption spectra contained in the six phyla, especially in the range of 420-540 nm. D6 and D7 were larger detail and spectral signals of overlapping absorption for adjacent pigments, showing differences between phytoplankton phyla with very different pigment compositions. Dinophyta and Bacillariophyta had little difference in pigment composition, so in the D6 and D7 details, their spectra did not show any difference. However, they were different from other phytoplankton in the D6 detail signal. For the same reason, only Cyanophyta showed characteristic information about PE in the D7 detail signal.
In addition, the combination of different detail signals (the combination of detail signals at different scales) also showed relatively comprehensive information on the pigment composition of different phytoplankton phyla. Therefore, when the wavelet analysis method is applied, the detail signal or the combined signal can be selected flexibly according to what is needed.
3.3 Comparison with the derivative analysis method
To evaluate the performance of DWT, the characteristic spectra of major pigments extracted by DWT were compared with those extracted by derivative analysis. The correlation of spectral characteristics and major pigment concentrations was also analyzed to demonstrate the potential of DWT in quantitatively extracting major pigment concentrations. Before applying derivative analysis method, the appropriate smoothing window and derivative transform step size which both directly affect the results of derivative analysis have to be carefully selected. In this study, the absorption spectra of Bacillariophyta and Prochroophyta were used to analyze the effects of smoothing window size and derivative step size on the 2nd and the 4th derivatives. The results showed that the optimal smoothing window size was 9 while the optimal derivative step sizes were 9 and 15 on the 2nd and 4th derivatives, which is consistent with previous studies [12]. Finally, the value of 9 was selected for smoothing window size. The step size in the 2nd derivative analysis is 9 and in the 4th derivative analysis is 15.
The 2nd and 4th derivatives were applied to the absorption spectra of all phytoplankton phyla. On the basis of the above analysis, for the 2nd derivative, the smoothing window 9 nm and the derivative step 9 nm were used, and the analysis results are shown in Fig. 6(a). For the 4th derivative, the smoothing window 9 nm and the derivative step 15 nm were selected, and the analysis results are shown in Fig. 6(b). Then, the 2nd and 4th derivative results were compared with the wavelet analysis results (single-scale and multiscale combined signals).
Fig. 6. Derivative transformation of the phytoplankton absorption spectrum. (a) 2nd derivatives with the smoothing window of 9 nm and derivative step of 9 nm, (b) 4th derivatives with the smoothing window of 9 nm and derivative step of 15 nm.
The 2nd derivative transformation was able to effectively extract the characteristic peaks in the phytoplankton absorption spectrum. The absorption peaks of Chl a at 418 nm, 440 nm, and 675 nm, Chl c at 585 nm, Chl b at 650 nm, and PE at 550 nm were still present. The different characteristics of Chl c among Dinophyta, Bacillariophyta, and Haptophyta were similar to the results of the wavelet transform, which reflected the shift of Chl c3 in Haptophyta and the characteristics of Chl c content in the three phytoplankton phyla. Because the characteristic peaks of Chl c and PPC were similar and the two characteristic peaks merged, the characteristic peaks of PPC in Haptophyta at 490 nm did not appear. However, other phytoplankton had obvious characteristic peaks of the PPC and PSC combination at this position.
For Dinophyta and Bacillariophyta, the relative size of the Chl c peak contained in the D5 detail signal of wavelet analysis was very clear, while the 2nd derivative showed little difference. In addition, the absorption characteristics of Chl a and Chl c pigments within the band range of 600-640 nm were not extracted from the 2nd derivative spectrum (as shown in Fig. 6(a)). In general, the 2nd derivative spectrum was similar to the sum of the detailed coefficients of the D4, D5, and D6 layers of the wavelet decomposition, and the extracted pigment absorption characteristics were the same. However, the wavelet transform had a stronger ability to extract smaller absorption characteristics.
The 4th derivative has a more powerful detail-focusing ability than the 2nd derivative, but it is also more susceptible to noise interference. Therefore, the choice of the tradeoff between the smoothing window and the derivative step is more important. In Fig. 6(b), although the smoothing window and derivative step were large enough, the 4th derivative spectrum for Prochlorophyta still had some noise. The position of the single peak of pigment in the 4th derivative spectrum did not change. Chl a at 621 nm and Chl c at 638 nm that were not extracted in the 2nd derivative spectrum were able to be extracted separately in the 4th derivative spectrum. The Dv-Chl a of Prochlorophyta and the PE of Cyanophyta were still present. However, the differences in Chl c content and composition between Dinophyta, Bacillariophyta, and Haptophyta were not reflected in the 4th derivative transformation.
Another limitation of the 4th derivative spectrum was that to avoid noise interference, the large derivative step led to the loss of the edge part of the derivative spectrum over a wider range, causing the Chl a shoulder peak that was located at 418 nm to disappear in the 4th derivative spectrum. The 4th derivative spectrum was closer to the detail coefficient of the 4th layer of the wavelet transform. Therefore, it could only capture the information on phytoplankton pigment composition but could not reflect more information about the proportion of pigment content.
Since the characteristic wavelengths where peak absorption occurred varied for different pigments, the following analyses were focused on the correlations between DWT signals at characteristic wavelengths and the corresponding pigment concentrations. The performance of DWT and derivative analysis were comparable for Chl a and PSC pigment with high determination coefficients > 0.85 (data not shown). For simplicity, we only compared the DWT and derivative analysis for pigments of Chl b, Chl c, and PPC. The characteristic wavelengths of Chl b, Chl c, and PPC are 650, 585, and 495 nm, respectively. The layer signal of DWT and the order of derivative also varied with the characteristic wavelength of each pigment. For example, D4 and the 4th derivative were used for Chl b while D5 and the 2nd derivative were used for Chl c. Note that, the signal of D5 at 495 nm was influenced by other pigments such as PSC, the difference of D5 between 495 and 460 nm was used to minimize the influence of other pigments. The same procedure was applied to derivative analysis for PPC pigment. Fig. 7 shows the analysis results. Clearly, the signal of DWT highly correlated with concentration of Chl b, Chl c, and PPC with determination coefficients of 0.80, 0.90, and 0.77, respectively. The relatively lower correlation was found between derivative analysis and pigment concentration, particularly for Chl b where the determination coefficient was < 0.1. These comparison results mentioned above largely demonstrate the good performance of wavelet analysis method in quantitative analysis of pigment concentration. To obtain better inversion results, it is necessary to select more characteristic wavelengths and use complex inversion algorithms, which will be systematically studied in future work.
Fig. 7. Comparison of the statistical relationship between characteristic spectra extracted by DWT and derivative analysis and the concentration of pigments. The first row shows the results of DWT, and the second row shows the results of derivative analysis.
In general, the characteristics of pigment absorption derived from the wavelet analysis are consistent with those from the 2nd and 4th derivatives, but the wavelet analysis had a stronger ability to obtain smaller and richer absorption characteristics. In addition, wavelet analysis can also make it possible to overcome some of the limitations of derivative analysis, such as smooth denoising and improper selection of the derivative step, resulting in information loss and spectral distortion. DWT also performed well in quantitatively extracting pigment concentrations.
4. Conclusion
The positions and widths of absorption peaks of different pigments in phytoplankton were significantly different. The advantage of wavelet analysis was that after the decomposition of the absorption spectrum, the pigment of different absorption peak widths could be extracted into the detail signals of different decomposition layers. To achieve the effective extraction of the major phytoplankton pigment characteristics, the multilayer decomposition of absorption spectra by wavelet transform provided a variety of possibilities for analyzing the pigment composition. Compared with the derivative analysis method, wavelet analysis had a similar performance in extracting the major pigment characteristics. However, wavelet analysis could extract smaller pigment difference information and the extracted pigment characteristic spectrum has a better correlation with pigment concentration. In addition, wavelet analysis could overcome some of the shortcomings of the derivative method, such as information loss caused by smoothing and spectral distortion caused by improper step selection in derivative transformation.
The wavelet transform method also had some limitations. Due to the limitations of the mechanism of the wavelet transform, there might be peaks with no physical meaning in the middle of the spectrum. In addition, the wavelet analysis could not extract the absorption peaks of different pigments when there were overlapping or close absorption peaks, which was similar to the limitations of the derivative analysis method. The extracted absorption peaks were the combined absorption peaks. The location of the peaks was related to the degree of absorption of related pigments, and the peaks were closer to the pigment with larger absorption.
In this study, different phytoplankton phyla with known pigment compositions were taken as examples to study the ability of wavelet analysis to extract pigment compositions from absorption spectra. The results showed that DWT could obtain information on pigment composition differences among phytoplankton of different phyla, but it could not be effectively applied to the analysis of pigment differences among different phytoplankton species in the same phylum. In addition, the present work only qualitatively studies the ability of wavelet transforms to extract phytoplankton pigment characteristics. The next step is to apply this method in the quantitative analysis of pigments from absorption spectra, especially as a pretreatment technique in satellite remote sensing inversion application research on phytoplankton pigment content. The proposed method in this study requires hyperspectral absorption data of phytoplankton as input. In addition to laboratory measurements with spectrophotometers and underwater in situ measurements with hyperspectral absorption meters, hyperspectral satellite remote sensing is also a measurement method. Using hyperspectral remote sensing data to retrieve the absorption spectrum of phytoplankton [7], and then using this proposed method, combined with the pigment retrieval algorithm, the spatial and temporal distribution information of the major pigments concentration in a large area of marine water can be obtained, which has significant application value in marine ecological environment monitoring, biogeochemistry cycle, and other aspects. Yet, the operational hyperspectral ocean color satellites are currently not available, but some missions such as Plankton, Aerosol, Cloud, and ocean Ecosystem (PACE) and Environmental Mapping and Analysis Program (EnMAP) are scheduled to be launched in the near future. When they become operational, we believe that our proposed method can be applied to hyperspectral remote sensing data to map global pigment concentrations.
Funding
National Natural Science Foundation of China (41276041, T2222010); National Natural Science Foundation of China-Shandong Joint Fund (U1406405).
Acknowledgments
The authors are grateful to everyone who worked hard collecting the in situ data, and to those who maintained and contributed data to the NASA SeaBASS data archive. Thanks to Dr. Tiezhu Mi from the Ocean University of China for his assistance in the cultivation process of phytoplankton. We truly appreciate the anonymous reviewers who provided constructive suggestions to improve the quality of this manuscript.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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