# Detection of Chlorophyll a and CDOM Absorption Coefficient with a Dual-Wavelength Oceanic Lidar: Wavelength Optimization Method

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

_{1}and λ

_{2}are both random, the errors are relatively small when λ

_{1}is chosen between 420 and 560 nm and λ

_{2}is selected under 420 nm. For the case in which λ

_{1}is fixed at 532 nm, the errors generally decrease with decreasing λ

_{2}, with minimums around 300 and 356–360 nm under different water conditions. The wavelength optimization method discussed in this paper and the penetration depth criterion will be beneficial to the design of the dual-wavelength lidar.

## 1. Introduction

## 2. Method

#### 2.1. Inversion Formula

^{−1}. C is the concentration of chlorophyll a, and is expressed in μg L

^{−1}. $E(\lambda )$ is the index absorption coefficient of chlorophyll a. The data of $A(\lambda )$ and $E(\lambda )$ used in this paper comes from Ocean Optics Web Book [28]. ${a}_{\mathrm{g}}(\lambda )$ is the absorption coefficient of CDOM, which shows an exponential decay with λ increasing in the range of 200–800 nm, that is [29]

^{−1}, ${a}_{\mathrm{g}}({\lambda}_{0})$ is the absorption coefficient of CDOM at the reference wavelength λ

_{0}, which is a representation of the CDOM concentration [30]. It is worth noting that the absorption curves of all detritus and CDOM can be described by exponential absorption models [31], and the curves are very similar or even difficult to distinguish. Here we do simplification and express the absorption of both with ${a}_{\mathrm{g}}(\lambda )$, which will be meaningful when the absorption of detritus cannot be completely considered in ${a}_{\mathrm{p}}(\lambda )$.

_{0}is set at 532 nm, C is 20 μg L

^{−1}, ${a}_{\mathrm{g}}({\lambda}_{0})$ is 0.0772 m

^{−1}, and S is 0.014 nm

^{−1}. ${a}_{\mathrm{w}}(\lambda )$ is small if the wavelength is smaller than 550 nm but increases rapidly between 550 and 700 nm. For the particles, there is a primary peak at 440 nm, more significant than the secondary peak near 680 nm. Besides, particles have an elevated absorption near 310 nm, which is likely due to mycosporine-like amino acids (MAAs). MAAs are UV absorbing, compounds that contain either an aminocylcohexenone or aminocylcohexenimine unit. MAAs have been shown to be released from phytoplankton grown in cultures [32]. MAAs have also been observed in 83% of the samples analyzed with concentrations ranging from 0 to 2.75 μM in the particulate organic matter (POM) in ocean samples [33]. The CDOM absorption decreases exponentially with the increasing wavelength. The absorption trends of CDOM and particles were opposite between 360 and 440 nm and 550 and 680 nm but similar between 440 and 550 nm and 310 and 360 nm, respectively. The same trend was not conducive to distinguishing the 2 components. Figure 1b shows the total absorption curves under different C and ${a}_{\mathrm{g}}({\lambda}_{0})$. At shorter wavelengths, particles and CDOM contributed more to the absorption signal.

_{1}and λ

_{2}, which are,

#### 2.2. Error Analysis

_{1}and λ

_{2}were unavoidable. Therefore, it was necessary to evaluate the effects of these measured errors on the retrieval accuracy of C and ${a}_{\mathrm{g}}({\lambda}_{0})$. The classic error propagation law can be utilized here to study the chlorophyll error as follows

## 3. Results

_{2}and error was analyzed when λ

_{1}was fixed at 532 nm. Finally, the dual-wavelength lidar method was validated based on the in situ seawater absorption coefficients. Table 1 lists the input seawater optical properties in the following simulation. a

_{g}(532) was set at 0.01–0.05 m

^{−1}, C was set at 0.5–5.0 μg L

^{−1}and S was set at 0.011–0.019 nm

^{−1}. According to global CDOM (a

_{g}(443)) and chlorophyll distribution, 0.01–0.05 m

^{−1}for a

_{g}(532) and 0.5–5 μg L

^{−1}for C have covered a large dynamic range [29,36]. Studies have shown that the S value of coastal seawater is usually between 0.011 and 0.018 nm

^{−1}[37] and 0.014–0.019 nm

^{−}

^{1}[38].

_{1}= 532 nm and λ

_{2}= 350 nm were selected to simulate all 7 cases in Table 1. The measurement error of b

_{bp}was 19.84%, and that of K

_{d}was 17.63% in [5]. Besides, the error of K

_{d}was 10.06% in [9]. Therefore, we set ${\mathsf{\Delta}}_{a({\lambda}_{1})}$ and ${\mathsf{\Delta}}_{a({\lambda}_{2})}$ at 20%. In Figure 2a,c, 500 MC results were plotted in red dots, the 3-σ results calculated by the theoretical model were plotted in the black dots, and the true values were plotted in the blue dots. Most of the MC results were within the 3-σ error range showing the great agreement between the theoretical model and the MC method. Notably, C

^{E}solved by Equation (5) contained negative numbers, resulting in the fact that C had an imaginary number solution, and thereby the red dots in Figure 2a cannot be exactly surrounded by 3-σ. In Figure 2b,d, the root mean squares of the relative errors of the MC results were plotted in red dots, and the theoretical errors were plotted in black dots. It shows that the MC results were very consistent with the theoretical results. Therefore, the theoretical model will be used for the following analysis, which largely decreases the computational costs.

#### 3.1. Dual-Wavelength Analysis

_{g}, M

_{C}, and M

_{E}in Equations (8) and (11) were related to both λ

_{1}and λ

_{2}. We set ${\mathsf{\Delta}}_{a({\lambda}_{1})}$ and ${\mathsf{\Delta}}_{a({\lambda}_{2})}$ at 20%, and other parameters as Case 1 in Table 1. The situation λ

_{1}> λ

_{2}instead of the situation λ

_{1}< λ

_{2}was considered to enhance the readability of Figure 3. The two situations were similar due to symmetry. Figure 3a,b show the effect of the dual-wavelength selection on C and a

_{g}(532). The black line indicates that inversion errors are 200%.

_{1}>560 nm or λ

_{1}<420 nm, the relative errors of C were greater than 200% no matter the value of λ

_{2}. However, for a

_{g}(532) in Figure 3b, the error was small when λ

_{2}was below 460 nm. Overall, the a

_{g}(532) relative error was smaller than that of C. Difference in contributions of chlorophyll and CDOM caused it. The absorption of CDOM increased exponentially with decreasing wavelength, contributing a large proportion of the total absorption and leading to small errors. When C = 2.0 μg L

^{−1}, chlorophyll absorption was small and similar to that of water, which caused large retrieval errors. When λ

_{1}>600 nm, the errors of C and a

_{g}(532) became significant because their absorptions became smaller than water. In Equation (7), the denominator will become larger, and the numerator will become smaller as C increases, causing smaller chlorophyll errors. That is to say, when the actual chlorophyll concentration was higher than the set value (C can reach 8.19 μg L

^{−1}at Ross Sea [39]), errors of C can be greatly reduced. Besides, there were many similarities between the two images: For example, when 420 nm < λ

_{1}< 560 nm and λ

_{2}<420 nm, the errors were both small; when the values of λ

_{1}and λ

_{2}were very close, the errors were large. Furthermore, a circular region with high errors appeared from 330 nm to 360 nm, because the M

_{C}× M

_{E}and M

_{g}values in Equations (8) and (11) were relatively close at this range.

_{1}to find corresponding λ

_{2}that can reach the minimum errors. Under different λ

_{1}in Table 2, the λ

_{2}that obtains the minimum errors were all at 300 and 358 nm. The results showed the smallest error of chlorophyll inversion can reach 112.06% when λ

_{1}= 500 nm and λ

_{2}= 300 nm, and for CDOM is 33.38% when λ

_{1}= 502 nm and λ

_{2}= 358 nm. The errors obtained when λ

_{2}= 358 nm and λ

_{2}= 300 nm were very close and both small. The results in Figure 3 and Table 2 provide references for the wavelength setting. Considering the inversion accuracy of CDOM only, λ

_{1}can be set in a wide range from 400 nm to 700 nm. Considering the accuracy of chlorophyll also, λ

_{1}should be set from 420 nm to 560 nm.

#### 3.2. One Fixed Wavelength at 532 nm

_{1}is determined, the error is only affected by λ

_{2}. With ${\mathsf{\Delta}}_{a({\lambda}_{1})}$ and ${\mathsf{\Delta}}_{a({\lambda}_{2})}$ to 20% and other parameters as Case 1 in Table 1, we found that the errors were large when λ

_{2}> 420 nm, which was more apparent when λ

_{2}was between 510 and 570 nm in Figure 4. This was consistent with the fact that the values of M

_{C}M

_{E}-M

_{g}in Equations (8) and (11) were small when the wavelengths were close. Besides, when both wavelengths were 532 nm, the dual-wavelength inversion model was not applicable, leading to the breakpoint at 532 nm in Figure 4. In other words, λ

_{2}should be set to a shorter wavelength than 420 nm. Therefore, the following analysis only considers the case when λ

_{2}is between 300 and 420 nm.

_{2}, but also by chlorophyll concentration(C), CDOM concentration (a

_{g}(532)), and spectral absorption slope S. To determine the impact of these parameters on the errors, an error analysis was performed under the parameter settings listed in Table 1. The effects of a

_{g}(532) (Cases 1–3 in Table 1), C (Cases 1, 4, 5 in Table 1) and S (Cases 1, 6, 7 in Table 1) are shown in Figure 5a–c, respectively.

_{2}, although there was a minimum at around 358 nm. Figure 5a shows the inversion errors of chlorophyll became larger with the increase of CDOM concentration, while those of CDOM became smaller. Similarly, the inversion errors of the chlorophyll become smaller as the chlorophyll concentration increases, while those of the CDOM are nearly unchanged, as shown in Figure 5b. Besides, in Figure 5c, both the errors became smaller as the spectral absorption slope S increased. S determined the wavelength at the minimum error and a larger S will lead to a smaller wavelength. When S was 0.011–0.019 nm

^{−1}, the minimum error was obtained when λ

_{2}was 356–360 nm.

_{2}and errors obtained in Figure 5.

#### 3.3. Real Water Simulation

_{1}and λ

_{2}are 532 nm and 412 nm in the first case and 532 nm and 440 nm in the second case, respectively. The data used here came from the field experiment in the Yellow Sea. In situ equipment was lowered into the seawater by a winch on the ship’s back deck to collect inherent optical properties. The absorption coefficients at different depths were collected using WET–Labs ac-9 at 532 nm, 412 nm, and 440 nm. The coincident temperature, salinity, and the data were provided by the SBE CTD. The scattering error in the particulate absorption was then corrected with the third method in [40]. S1 and S2 in Figure 7 represent different collection sites. The S1 collection site was located on Cold Water Mass of the Yellow Sea with a depth of 0–28 m; the S2 collection site was located near Pingshan Island with a depth of 0–16 m. The chlorophyll profile was measured by WET-Labs ECO fluorometer in the same cast of the ac-9 system.

^{−1}, and when the depth is greater than 10 m, set S to 0.015 nm

^{−1}; at the second station (Figure 8b), set S to 0.011 nm

^{−1}. The results showed that the two methods were consistent with the trend of true values with depth. The single-wavelength results were 2–10 μg L

^{−1}higher than the true value, and dual-wavelength were −2–3 μg L

^{−1}. Simultaneously, in dual-wavelength inversion, λ

_{2}= 412 nm performed better. This shows that the real water column simulation confirms that the proposed dual-wavelength model can improve accuracy. It is worth noting that there are many errors that may affect results, such as the assumed S.

## 4. Discussion

_{2}is, the smaller the inversion errors when λ

_{1}is fixed at 532 nm and λ

_{2}is between 300 and 336 nm or 358 and 420 nm when S = 0.015 nm

^{−1}. Notably, there is a minimum when λ

_{2}is at 300 and 358 nm. Mannino et al. have used a variety of inversion algorithms in ocean color remote sensing to conclude that the smaller the wavelength, the smaller the relative error of CDOM inversion [42], which is consistent with our conclusion between 300 and 336 nm or 358 and 420 nm. However, the penetration depth should be taken into account when using lidar. When only the penetration depth is considered, Liu et al. indicated 488 nm is the best detection wavelength for 70% of the world’s oceans. Therefore, 488 nm is the most suitable wavelength when considering the penetration depth of the global ocean [43]. Penetration depth probability, which is defined as the ratio of detection depth Z

_{max}to euphotic depth Z

_{eu}, is calculated at 412 and 443 nm by using the method of Liu et al. [43]. It can be seen from Figure 9 that the probability of penetration depth is determined by the laser wavelength.

_{d}are briefly described, but most methods can only be used under certain conditions. A more general method has not been proven, and this is one of the future directions of work.

## 5. Conclusions

_{1}is chosen between 420 and 560 nm. If considering the inversion accuracy of CDOM only, λ

_{1}should be set from 400 nm to 700 nm. At the same time, when the values of λ

_{1}and λ

_{2}are very close, the error value is enormous. For chlorophyll inversion, λ

_{1}= 500 nm and λ

_{2}= 300 nm will lead to the minimum error of 112.06%. For CDOM inversion, λ

_{1}= 502 nm and λ

_{2}= 358 nm will bring the smallest error of 33.38 %. If λ

_{1}is fixed at 532 nm, the errors generally increase with increasing λ

_{2}, with minimums around 300 and 356–360 nm. Actual data simulations show that the relative error of dual-wavelength inversion is smaller than that of single wavelength inversion.

_{2}for the dual-wavelength lidar, it is necessary to consider the influence of wavelength change on inversion accuracy and penetration depth. In addition, more accurate particles and CDOM absorption models will help improve the inversion accuracy.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**C and a

_{g}(532) retrieved by the theoretical model and Monte Carlo (MC) method under 7 cases in Table 1. (

**a**) C; (

**b**) relative error of C; (

**c**) a

_{g}(532); (

**d**) relative error of a

_{g}(532).

**Figure 3.**Dual-wavelength inversion error under Case 1 in Table 1 of (

**a**) C and (

**b**) a

_{g}(532). The black line indicates that the inversion error is 200%.

**Figure 6.**Relative errors of chlorophyll (red lines) and CDOM absorption (blue lines) in different Δ.

**Figure 8.**Simulated comparison of the retrieval and true results at (

**a**) S1 and (

**b**) S2. Three kinds of retrieval methods are utilized, including (1) dual-wavelengths at 532 and 412 nm, (2) dual-wavelengths at 532 and 440 nm and (3) single wavelength at 532 nm.

Case | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

a_{g}(532) (m^{−1}) | 0.03 | 0.01 | 0.05 | 0.03 | 0.03 | 0.03 | 0.03 |

C (μg L^{−1}) | 2.00 | 2.00 | 2.00 | 0.50 | 5.00 | 2.00 | 2.00 |

S (nm^{−1}) | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.011 | 0.019 |

Retrieval | λ_{1} | λ_{2} | Relative Errors |
---|---|---|---|

C | 412 nm | 300 nm | 230.84% |

440 nm | 140.80% | ||

500 nm | 111.76% | ||

532 nm | 127.16% | ||

672 nm | 325.96% | ||

C | 412 nm | 358 nm | 233.66% |

440 nm | 141.42% | ||

500 nm | 112.06% | ||

532 nm | 127.62% | ||

672 nm | 326.10% | ||

a_{g}(532) | 412 nm | 300 nm | 47.64% |

440 nm | 37.58% | ||

502 nm | 33.64% | ||

532 nm | 33.60% | ||

672 nm | 45.98% | ||

a_{g}(532) | 412 nm | 358 nm | 48.08% |

440 nm | 37.46% | ||

502 nm | 33.38% | ||

532 nm | 33.52% | ||

672 nm | 47.28% |

**Table 3.**Inversion error of chlorophyll with single-wavelength lidar under Cases 1–7 and different Δ.

Case | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

Relative error (Δ = 10 %) | 168.27% | 66.13% | 282.32% | 569.08% | 79.63% | 168.27% | 168.27% |

Relative error (Δ = 20 %) | 203.37% | 102.12% | 318.17% | 660.92% | 100.48% | 203.37% | 203.37% |

Relative error (Δ = 30 %) | 243.39% | 142.93% | 360.77% | 793.77% | 126.38% | 243.39% | 243.39% |

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## Share and Cite

**MDPI and ACS Style**

Liu, R.; Ling, Q.; Zhang, Q.; Zhou, Y.; Le, C.; Chen, Y.; Liu, Q.; Chen, W.; Tang, J.; Liu, D.
Detection of Chlorophyll *a* and CDOM Absorption Coefficient with a Dual-Wavelength Oceanic Lidar: Wavelength Optimization Method. *Remote Sens.* **2020**, *12*, 3021.
https://doi.org/10.3390/rs12183021

**AMA Style**

Liu R, Ling Q, Zhang Q, Zhou Y, Le C, Chen Y, Liu Q, Chen W, Tang J, Liu D.
Detection of Chlorophyll *a* and CDOM Absorption Coefficient with a Dual-Wavelength Oceanic Lidar: Wavelength Optimization Method. *Remote Sensing*. 2020; 12(18):3021.
https://doi.org/10.3390/rs12183021

**Chicago/Turabian Style**

Liu, Ruoran, Qiaolv Ling, Qiangbo Zhang, Yudi Zhou, Chengfeng Le, Yatong Chen, Qun Liu, Weibiao Chen, Junwu Tang, and Dong Liu.
2020. "Detection of Chlorophyll *a* and CDOM Absorption Coefficient with a Dual-Wavelength Oceanic Lidar: Wavelength Optimization Method" *Remote Sensing* 12, no. 18: 3021.
https://doi.org/10.3390/rs12183021