# Reflection Spectra Coupling Analysis and Polarized Modeling of Optically Active Particles in Lakes

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}) of 0.91, root mean square error (RMSE) 0.035, and a verification accuracy of 0.959. This shows that the model has better prediction ability for the coupling characteristics of water particles by the polarization reflection spectra and provides good support for mixed spectral unmixing of class II water.

## 1. Introduction

_{11D}[16]. Polarized scattered light was used to analyze the change in the physiological state of marine microalgae [17]. Furthermore, polarized light scattering data were used to analyze microalgae and early warning of cyanobacterial blooms based on machine learning methods [18]. These studies show the unique role of polarization information in the detection of algae particles.

## 2. Materials and Methods

#### 2.1. Materials

#### 2.1.1. Laboratory Samples

#### 2.1.2. Lake Water Samples

#### 2.2. Instruments

^{2}was 0.99998. When the spectrum was measured, the experimental stainless steel cylindrical iron pool was used to hold water samples. The inside and outside of the pool were sprayed with black matte paint, and two stirring pumps were placed at the bottom of the pool to prevent particles precipitation.

#### 2.3. Methods

#### 2.3.1. The Degree of Linear Polarization (DOLP)

#### 2.3.2. Construction and Verification of Estimation Models

_{d}are the regression coefficients and the residual matrices, respectively. Equations (5) and (6) can be combined to obtain Equation (7). For prediction, the scoring matrix T of the input spectral matrix X is calculated according to the load matrix P of X, and then the predicted value of the pending sample can be calculated using Equation (7) [38].

^{2}) and the correlation coefficient represents the main index of the degree of correlation between different variables. The larger the correlation coefficient is, the higher the correlation. The accuracy is tested by the root mean square error (RMSE), which can evaluate the correlation between different variables after fitting. The smaller the RMSE, the higher the correlation. The RMSE formula is as follows:

## 3. Results and Discussion

#### 3.1. Coupled Analysis of the Polarization Intensity Spectrum and DOLP Spectrum Characteristics of Lake Water

#### 3.1.1. Spectral Variation

#### 3.1.2. Angle Variation

#### 3.1.3. Mixing Spectral Analysis

#### 3.2. Coupling Modeling of Polarized Reflection between the Particles

#### 3.2.1. Polarized Reflection Spectra of Chaohu Lake

#### 3.2.2. PLSR Modeling of the Particle Concentration in Lake Water

_{chl-a}), inorganic suspended solids (C

_{TSS}) were selected as independent variables (x), the reflectance and DOLP as dependent variables (y), and PLSR algorithms were selected to establish the coupling model of the particles, respectively. The accuracy of the model was determined by R

^{2}and RMSE, as shown in Table 2.

^{2}0.74, RMSE 0.063, but the correlation between DOLP ratio and the concentration of algae particles was almost the same in Figure 7a,b. For algae particles, because chlorophyl-a fluorescence in algae cells was excited at 705 nm, the fluorescence was obviously unpolarized. For inorganic suspended solids, the single scattering in the low concentration and the multiple scattering in the high concentration both had a strong correlation with their concentration. This indicates that DOLP is more sensitive to inorganic particle scattering than inelastic algae particle scattering, and it is helpful to improve the precision of the model [41].

_{chl-a}, C

_{TSS}), and the reflectance and DOLP could be taken as dependent variables (y). Accordingly, PLSR on multiple regression analysis was generated, and the fitting results were shown in Table 3. Compared to Table 2, the coupled model of DOLP had a good significant level with R

^{2}0.91, RMSE 0.035, 9.6% higher than that of reflectance, 22.9% higher than that of the single component optimal model, and RMSE 63.5% and 44.4% higher.

^{2}of the reflectance and DOLP is 0.925 and 0.959. Therefore, the coupling model of two types of particles significantly improved the prediction ability of the model [42].

## 4. Conclusions

^{2}0.91, RMSE 0.035, and effectively improved the low accuracy of the model in the high concentration region.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**(

**a**) BRDF spectrum measurement system; (

**b**) SVC HR1024; (

**c**) results of the calibration for polarization at 600 nm; (

**d**) geometric coordinate system observed by BRDF.

**Figure 3.**Reflectance spectra (

**a**) and DOLP (

**b**) of the underwater upwelling radiance dominated by single algae particles; reflectance spectra (

**c**) and DOLP (

**d**) of the underwater upwelling radiance dominated by single inorganic suspended solids.

**Figure 4.**Angular distributions of the underwater upwelling radiance signals at 685 nm with a solar zenith angle of 45°. Concentric circles correspond to the sensor zenith angle, and the plane of the azimuth angle of 0° and 180° is the solar meridian plane. Distribution of reflectance spectrum (

**a**) and DOLP (

**b**) dominated by single algal particles in 2π space; distribution of reflectance spectrum (

**c**) and DOLP (

**d**) dominated by single inorganic suspended solids in 2π space.

**Figure 5.**Reflectance spectra (

**a**) and DOLP (

**b**) of laboratory mixed water samples; reflectance spectra (

**c**) and DOLP (

**d**) of natural water samples in the pond.

**Figure 6.**Reflectance spectra (

**a**) and DOLP (

**b**) of water samples in Chaohu Lake. The curves of different colors represent the measured spectra of the different water samples.

**Figure 7.**Analysis of regression between the reflectance (

**a**), DOLP (

**b**), and algae particle concentration, and between the reflectance (

**c**), DOLP (

**d**) and inorganic suspended solid concentration.

**Figure 8.**Comparison between the measured and predicted values of the reflectance (

**a**) and DOLP (

**b**) coupling model. The black line shows the 1:1 relationship and the red dotted line shows the model trend. The coupling model falls within the largest number of points within the 95% confidence band.

Sample Set | Number | Algae Particles (μg/L) | Inorganic Suspended Solids (mg/L) | ||||||
---|---|---|---|---|---|---|---|---|---|

Min | Max | Mean | Standard Deviation | Min | Max | Mean | Standard Deviation | ||

Train set | 24 | 11.81 | 76.51 | 24.81 | 16.48 | 14.77 | 54.67 | 28.08 | 12.52 |

Validation set | 12 | 13.43 | 50.76 | 26.13 | 12.44 | 15.6 | 53.92 | 27.21 | 12.8 |

**Table 2.**Analysis of the model on the relationship between particle concentration and the reflectance, DOLP in lake water.

Type | Reflectance | DOLP | ||||
---|---|---|---|---|---|---|

Model | R^{2} | RMSE | Model | R^{2} | RMSE | |

Algal particles | R (705)/R (675) = 0.0117C_{chl-a} + 0.9245 | 0.71 | 0.126 | P (705)/P (675) = −0.0061C_{chl-a} + 1.0007 | 0.7 | 0.068 |

Inorganic suspension solids | R (705)/R (675) = 0.0145C_{TSS} + 0.786 | 0.63 | 0.142 | P (705)/P (675) = −0.0083C_{TSS} + 1.0081 | 0.74 | 0.063 |

**Table 3.**PLSR coupling model and precision analysis of the relationship between particle concentration and reflectance, DOLP in lake water.

Type | Reflectance | DOLP | ||||||
---|---|---|---|---|---|---|---|---|

Model | R^{2} | RMSE | Verified R^{2} | Model | R^{2} | RMSE | Verified R^{2} | |

Coupling model | R (570)/R (675) = 0.8116 + 0.0078C_{chl-a} + 0.0067C_{TSS} | 0.83 | 0.096 | 0.925 | P (570)/P (675) = 1.0716 − 0.0038C_{chl-a} − 0.0047C_{TSS} | 0.91 | 0.035 | 0.959 |

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## Share and Cite

**MDPI and ACS Style**

Pan, B.; Cheng, H.; Du, S.; Yu, H.; Tang, Y.; Shu, Y.; Du, J.; Xie, H.
Reflection Spectra Coupling Analysis and Polarized Modeling of Optically Active Particles in Lakes. *Water* **2023**, *15*, 1706.
https://doi.org/10.3390/w15091706

**AMA Style**

Pan B, Cheng H, Du S, Yu H, Tang Y, Shu Y, Du J, Xie H.
Reflection Spectra Coupling Analysis and Polarized Modeling of Optically Active Particles in Lakes. *Water*. 2023; 15(9):1706.
https://doi.org/10.3390/w15091706

**Chicago/Turabian Style**

Pan, Banglong, Hongwei Cheng, Shuhua Du, Hanming Yu, Yi Tang, Ying Shu, Juan Du, and Huaming Xie.
2023. "Reflection Spectra Coupling Analysis and Polarized Modeling of Optically Active Particles in Lakes" *Water* 15, no. 9: 1706.
https://doi.org/10.3390/w15091706