# Evaluating Traditional Empirical Models and BPNN Models in Monitoring the Concentrations of Chlorophyll-A and Total Suspended Particulate of Eutrophic and Turbid Waters

^{1}

^{2}

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## Abstract

**:**

^{−1}with an average of 39 µg·L

^{−1}while the TSP ranges from 8 to 162 mg·L

^{−1}and averages 42.5 mg·L

^{−1}. Ninety sets of 135 samples are used as training data to develop the retrieval models, and the remaining ones are used to validate the models. The results show that the proposed band ratio models, the three-band combination models, and the corresponding BPNN models are generally successful in estimating the Chl-a and the TSP, and the mean relative error (MRE) can be lower than 30% and 25%, respectively. However, the BPNN models have no better performance than the traditional empirical models, e.g., in the estimation of TSP on the basis of the reflectance at 555 and 750 nm (R555 and R750, respectively), the model of BPNN (R555, R750) has an MRE of 23.91%, larger than that of the R750/R555 model. These results suggest that these traditional empirical models are usable in monitoring the optically active water quality parameters of Chl-a and TSP for eutrophic and turbid waters, while the machine learning models have no significant advantages, especially when the cost of training samples is considered. To improve the performance of machine learning models in future applications on the basis of ground sensor networks, large datasets covering various water situations and optimization of input variables of band configuration should be strengthened.

## 1. Introduction

## 2. Data and Methods

#### 2.1. Study Area

#### 2.2. Data Acquisition and Preprocessing

#### 2.2.1. Data Acquisition

#### 2.2.2. Data Preprocessing

^{−1}), ${\mathsf{\rho}}_{\mathrm{p}}$ is the reflectance of the reference plaque with an approximate constant value of 0.25, r is the water surface Fresnel reflectance (0.028), ${\mathrm{L}}_{\mathrm{p}}$ represents the radiance received from the reference plaque, ${\mathrm{L}}_{\mathrm{s}}$ is the diffused radiation of the sky and ${\mathrm{L}}_{\mathrm{w}}$ is the water surface radiance.

#### 2.3. Method

#### 2.3.1. Retrieval Model of Chl-a

#### 2.3.2. Retrieval Model of TSP

#### 2.4. Model Training and Accuracy Verification

^{2}), root mean square error (RMSE) and mean relative error (MRE) were used to evaluate the model.

## 3. Results and Analysis

#### 3.1. Retrieval Results of the Chl-a Concentration

#### 3.1.1. Two-Band Ratio Models

^{−1}) were large, which led to a high RMSE. The linear model brought more negative values in the low-concentration samples (<10 µg·L

^{−1}), and the MRE was large. Among the five regression models, the retrieval accuracy of the logarithmic model was the lowest, and the quadratic polynomial model had the highest accuracy.

^{2}value increased from 0.81 to 0.86, while the RMSE decreased from 21.52 to 18.18 µg·L

^{−1}. This indicates that the BPNN model can also produce satisfactory retrieval results.

#### 3.1.2. T-Depth Models

^{2}= 0.83, RMSE = 20.4 µg·L

^{−1}, MRE = 28.01%). This case suggests that the machine learning approach of BPNN has the advantage in modeling in a non-linear way under certain conditions.

#### 3.1.3. Three-Band Models

^{2}of three-band BPNN model increased by 3.4% from 0.89 to 0.92, the RMSE decreased from 17.18 to 14.29 µg·L

^{−1}and the MRE decreased by 16.8% from 25.41% to 21.86%.

#### 3.1.4. Model Validation

^{2}increasing from 0.85 to 0.92, and with the MRE decreasing from 25.88% to 22.56%. The retrieval accuracy of the two-band BPNN model was improved, although in a small magnitude (Figure 3a,b). The validation results of the T-depth model are close to the training results (Figure 3d); however, the validation accuracy of the BPNN model was significantly improved (Figure 3e), which was consistent with the training set. The relative error distributions of the BPNN model and the corresponding empirical statistical model are shown in Figure 3c,f,i; the results show that the model with higher accuracy tends to present an error distribution with higher frequency at the middle and lower at two sides and that the error distribution of the three-band combination is close to a normal distribution with more bias values lower than 30%.

#### 3.2. Retrieval Results of TSP Concentration

#### 3.2.1. Two-Band Ratio Models

^{2}up to 0.74. The retrieval accuracy of the red–green band ratio model (R670/R555) for TSP is low, with R

^{2}of 0.07. The retrieval accuracies of the BPNN model and the empirical model with the combination of (R555, R750) or (R555, R850) are very close to each other.

#### 3.2.2. Three-Band Models

#### 3.2.3. Model Validation

## 4. Discussion

^{−1}, TSP > 70 mg·L

^{−1}) are relatively few, which may lead to uncertainty in the retrieval accuracy when the models are applied to extremely turbid and eutrophic waters. Especially for the machine learning approaches without considering the characteristic bands of water quality parameters, a large dataset covering wide water conditions is necessary.

## 5. Summary

^{−1}) and high TSP concentration (8 to 162 mg·L

^{−1}). In this work, traditional empirical models and BPNN models with corresponding spectral bands were established to monitor the concentrations of Chl-a and TSP, and the models’ performances were evaluated. For the two optically active substances of Chl-a and TSP, both traditional empirical models and BPNN models work well to estimate their concentrations, although the accuracies of these models are highly dependent on the band selections. Optimized band selections can significantly improve models’ accuracies, and the corresponding BPNN models, on the basis of the characteristic bands used in the empirical models, may generally improve the retrieval accuracies. However, the BPNN models are not always better than the traditional models, e.g., in the estimation of TSP.

^{−1}, respectively, which means that a water body with Chl-a and TSP lower than the lowest values may not be monitored on the basis of the BPNN models. A hyperspectral reflectance sensor network is a good approach for monitoring water quality in a green way. To improve the performance of machine learning models in future applications on the basis of a ground reflectance sensor network, large datasets covering various water situations and optimization of the input variable of band configuration are still necessary.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Location of the study area; (

**b**) drainage distribution in the study area; (

**c**) field photos of some typical sampling points ((

**c1**–

**c4**), corresponding to the sampling point numbers in (

**b**).

**Figure 2.**Spectral reflectance. (

**a**) The training samples (N = 90) and (

**b**) the validation samples (N = 45).

**Figure 3.**Scatter plot (the dotted line is the 1:1 line) for (

**a**) The ratio model (R705/R670), (

**b**) The BPNN model (R705, R670), (

**d**) The t-depth statistical model, (

**e**) The BPNN model (R650, R675, R700), (

**g**) The three-band statistical model and (

**h**) The BPNN model (R670, R710, R750), and relative deviation distribution between the measured values and retrieval values for (

**c**) The two-band combination models, (

**f**) The T-depth statistical model and corresponding BPNN model and (

**i**) The three-band combination models for chlorophyll-a (Chl-a) concentration.

**Figure 4.**Scatter plot (the dotted line is the 1:1 line) for (

**a**) The ratio model (R750/R555), (

**b**) The BPNN model (R705, R670), (

**d**) The three-band statistical model, (

**e**) The BPNN model (R490, R555, R670) and relative deviation distribution between measured values and retrieval values for (

**c**) The two-band combination models, (

**f**) The three-band combination models for total suspended particulate (TSP) concentration.

**Figure 6.**Correlation coefficient matrix between TSP concentration and reflectance ratio combination (high-value area of correlation is enclosed by a black box).

Model | Equation | Band |
---|---|---|

Two-band | ${\mathrm{R}}_{\lambda 1}/{\mathrm{R}}_{\lambda 2}$ $\mathrm{B}\mathrm{P}\mathrm{N}\mathrm{N}\left({\lambda}_{1},{\lambda}_{2}\right)$ | ${\lambda}_{1}$ = 705 nm ${\lambda}_{2}$ = 670 nm |

T-depth | ${\mathrm{R}}_{\lambda 3}^{\mathrm{N}}-{\mathrm{R}}_{\lambda 1}^{\mathrm{N}}\times \frac{({\lambda}_{2}-{\lambda}_{1})}{({\lambda}_{3}-{\lambda}_{1})}+{\mathrm{R}}_{\lambda 1}^{\mathrm{N}}-{\mathrm{R}}_{\lambda 2}^{\mathrm{N}}$ $\mathrm{B}\mathrm{P}\mathrm{N}\mathrm{N}\left({\lambda}_{1},{\lambda}_{2},{\lambda}_{3}\right)$ | ${\lambda}_{1}$ = 650 nm, ${\lambda}_{2}$ = 675 nm ${\lambda}_{3}$ = 700 nm |

Three-band | $(1/{\mathrm{R}}_{\lambda 1}-1/{\mathrm{R}}_{\lambda 2})\times {\mathrm{R}}_{\lambda 3}$ $\mathrm{B}\mathrm{P}\mathrm{N}\mathrm{N}({\lambda}_{1},{\lambda}_{2},{\lambda}_{3})$ | ${\lambda}_{1}$ = 670 nm, ${\lambda}_{2}$ = 710 nm ${\lambda}_{3}$ = 750 nm |

Model | Equation | Band |
---|---|---|

Two-band | ${\mathrm{R}}_{\lambda 1}/{\mathrm{R}}_{\lambda 2}$ $\mathrm{B}\mathrm{P}\mathrm{N}\mathrm{N}\left({\lambda}_{1},{\lambda}_{2}\right)$ | ${\lambda}_{1}$ = 670 nm or 750 nm or 850 nm, ${\lambda}_{2}$ = 555 nm |

Three-band | $10\u02c6[\mathrm{a}+\mathrm{b}({\mathrm{R}}_{\lambda 2}^{\mathrm{N}}+{\mathrm{R}}_{\lambda 3}^{\mathrm{N}})+\mathrm{c}({\mathrm{R}}_{\lambda 1}^{\mathrm{N}}/{\mathrm{R}}_{\lambda 2}^{\mathrm{N}}\left)\right]$ $\mathrm{B}\mathrm{P}\mathrm{N}\mathrm{N}({\lambda}_{1},{\lambda}_{2},{\lambda}_{3})$ | ${\lambda}_{1}$ = 490 nm, ${\lambda}_{2}$ = 555 nm ${\lambda}_{3}$ = 670 nm |

Parameter | Dataset | Minimum | Maximum | Average | Standard Deviation |
---|---|---|---|---|---|

Chl-a (µg·L ^{−1}) | Training set | 3 | 258 | 38.53 | 40.92 |

Validation set | 3 | 202 | 39.80 | 41.30 | |

TSP (mg·L ^{−1}) | Training set | 8 | 162 | 42.39 | 28.54 |

Validation set | 11 | 162 | 42.84 | 28.83 |

Input | Regression Model | Equation | R^{2} | RMSE (µg·L ^{−1}) | MRE (%) |
---|---|---|---|---|---|

Logarithmic | Y = 156.19ln(x) + 2.03 | 0.62 | 29.90 | 89.44 | |

Linear | Y = 111.43x − 106.7 | 0.70 | 26.93 | 63.06 | |

R705/R670 | Exponential | $\mathrm{y}={1.28\mathrm{e}}^{2.26\mathrm{x}}$ | 0.73 | 71.99 | 43.93 |

Power | $\mathrm{y}={10.66\mathrm{x}}^{3.51}$ | 0.81 | 34.40 | 34.13 | |

Quadratic polynomial | $\mathrm{y}=36.99{\mathrm{x}}^{2}-16.19\mathrm{x}-11.5$ | 0.81 | 21.52 | 27.93 | |

R670, R705 | BPNN | -- | 0.86 | 18.18 | 28.26 |

**Table 5.**The T-depth and back-propagation neural network (BPNN) (R650, R675, R700) models for Chl-a concentration.

Input | Equation | R^{2} | RMSE (µg·L ^{−1}) | MRE (%) |
---|---|---|---|---|

T-depth (${\mathrm{R}}_{\lambda \mathrm{i}}$) | $\mathrm{y}={8.71\mathrm{e}}^{219.54\mathrm{x}}$ | 0.39 | 45.01 | 60.59 |

T-depth (${\mathrm{R}}_{\lambda \mathrm{i}}^{\mathrm{N}}$) | $\mathrm{y}={6.41\mathrm{e}}^{4.62\mathrm{x}}$ | 0.61 | 39.36 | 44.72 |

R650, R675, R700 | BPNN | 0.83 | 20.40 | 28.01 |

Input | Equation | R^{2} | RMSE (µg·L ^{−1}) | MRE (%) |
---|---|---|---|---|

${\mathrm{R}}_{670}^{-1}-{\mathrm{R}}_{710}^{-1}$ | Y = 158.07x + 15 | 0.89 | 17.18 | 25.41 |

R670, R710, R750 | BPNN | 0.92 | 14.29 | 21.86 |

Input | Equation | R^{2} | RMSE (mg·L ^{−1}) | MRE (%) |
---|---|---|---|---|

R670/R555 | Y = 42.14x + 7.16 | 0.07 | 27.54 | 58.44 |

R750/R555 | Y = 101.9x − 1.44 | 0.74 | 14.81 | 23.05 |

R850/R555 | Y = 116.43x | 0.67 | 17.09 | 28.10 |

R555, R670 | BPNN | 0.12 | 28.43 | 45.48 |

R555, R750 | BPNN | 0.76 | 14.99 | 23.91 |

R555, R850 | BPNN | 0.68 | 16.33 | 27.89 |

Input | Equation | R^{2} | RMSE (mg·L ^{−1}) | MRE (%) |
---|---|---|---|---|

$\mathrm{x}1:\mathrm{R}555+\mathrm{R}670$ $\mathrm{x}1:\mathrm{R}490/\mathrm{R}555$ | $\mathrm{y}={10}^{1.38+1.07\mathrm{x}1+0.2\mathrm{x}2}$ | 0.01 | 29.19 | 48.10 |

$\mathrm{x}1:{\mathrm{R}}_{555}^{\mathrm{N}}+{\mathrm{R}}_{670}^{\mathrm{N}}$ $\mathrm{x}2:{\mathrm{R}}_{490}^{\mathrm{N}}+{\mathrm{R}}_{555}^{\mathrm{N}}$ | $\mathrm{y}={10}^{2.89-0.48\mathrm{x}1+0.1\mathrm{x}2}$ | 0.42 | 21.89 | 32.60 |

R490, R555, R670 | BPNN | 0.25 | 24.09 | 49.09 |

Model | Sample Number | TSP (mg·L ^{−1}) | Chl-a (µg·L ^{−1}) | R^{2} |
---|---|---|---|---|

$({\mathrm{R}}_{684}^{-1}-{\mathrm{R}}_{690}^{-1})\times \mathrm{R}718$ (Chen et al., 2011 [31]) | 32 | 40.8 | 17.6 | 0.81 |

$({\mathrm{R}}_{671}^{-1}-{\mathrm{R}}_{710}^{-1})\times \mathrm{R}740$ (Dall’Olmo et al., 2005 [32]) | 86 | 18.9 | 46.50 | 0.94 |

$({\mathrm{R}}_{670}^{-1}-{\mathrm{R}}_{710}^{-1})\times \mathrm{R}750$ (this paper) | 90 | 42.39 | 38.53 | 0.89 |

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**MDPI and ACS Style**

Jiang, B.; Liu, H.; Xing, Q.; Cai, J.; Zheng, X.; Li, L.; Liu, S.; Zheng, Z.; Xu, H.; Meng, L. Evaluating Traditional Empirical Models and BPNN Models in Monitoring the Concentrations of Chlorophyll-A and Total Suspended Particulate of Eutrophic and Turbid Waters. *Water* **2021**, *13*, 650.
https://doi.org/10.3390/w13050650

**AMA Style**

Jiang B, Liu H, Xing Q, Cai J, Zheng X, Li L, Liu S, Zheng Z, Xu H, Meng L. Evaluating Traditional Empirical Models and BPNN Models in Monitoring the Concentrations of Chlorophyll-A and Total Suspended Particulate of Eutrophic and Turbid Waters. *Water*. 2021; 13(5):650.
https://doi.org/10.3390/w13050650

**Chicago/Turabian Style**

Jiang, Bo, Hailong Liu, Qianguo Xing, Jiannan Cai, Xiangyang Zheng, Lin Li, Sisi Liu, Zhiming Zheng, Huiyan Xu, and Ling Meng. 2021. "Evaluating Traditional Empirical Models and BPNN Models in Monitoring the Concentrations of Chlorophyll-A and Total Suspended Particulate of Eutrophic and Turbid Waters" *Water* 13, no. 5: 650.
https://doi.org/10.3390/w13050650