# Remote Estimation of Water Quality Parameters of Medium- and Small-Sized Inland Rivers Using Sentinel-2 Imagery

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## Abstract

**:**

_{3}-N, the R

^{2}was 0.61, the root mean squared error (RMSE) was 0.177 and the mean absolute percentage error (MAPE) was 29.33%; for Chemical Oxygen Demand (COD), the R

^{2}was 0.26, the RMSE was 0.756 and the MAPE was 4.62%; for Total Phosphorus (TP), the R

^{2}was 0.69, the RMSE was 0.032 and the MAPE was 30.58%. After the application of the super-resolution algorithm, the inversion accuracy of water quality parameters in this study were as follows: for NH

_{3}-N, the R

^{2}was 0.67, the RMSE was 0.161 and the MAPE was 25.88%; for COD, the R

^{2}was 0.53, the RMSE was 0.546 and the MAPE was 3.36%; for TP, the R

^{2}was 0.60, the RMSE was 0.034 and the MAPE was 24.28%. Finally, the spatial distribution of NH

_{3}-N, COD and TP was obtained by using a machine learning model. The results showed that the application of the super-resolution algorithm can effectively improve the retrieval accuracy of NH

_{3}-N, COD and TP, which illustrates the application potential of the super-resolution algorithm in water quality remote sensing quantitative monitoring.

## 1. Introduction

_{3}-N, Chemical Oxygen Demand (COD) and Total Phosphorus (TP) are important reference indexes for water pollution prevention and control. Gong et al. found that nitrogen had the highest correlation coefficient for 404 nm and 447 nm [4]. Wang et al. found that NH

_{3}-N and COD have a high correlation with the SPOT5 satellite’s red band, green band and near infrared (NIR) band [5]. Chen et al. analyzed the COD standard solution with a certain ratio and found that COD has a significant spectral response characteristic at 550 nm, 565 nm, 1016 nm and 1047 nm [6]. Sun et al. estimated the concentration of TP in inland waters with complex optical turbidity based on the near-infrared and green bands of the HJ-1 satellite [7]. Previous studies have proven that there is a certain relationship between NH

_{3}-N, COD, TP and reflectance spectra [4,5,6,7,8,9], which lays a foundation for the use of remote sensing technology for water quality monitoring.

_{3}-N, COD and TP, which are three important parameters reflecting water quality, there is no corresponding inversion model for Sentinel-2 data. Therefore, the novelty of this paper is to apply super-resolution technology to water quality monitoring to weaken the impact of mixed pixels on water quality monitoring of small and medium-sized inland rivers and improve the utilization rate of multispectral bands of Sentinel-2 data. In addition, this paper focuses on establishing inversion models of NH

_{3}-N, COD and TP based on Sentinel-2.

## 2. Materials and Methods

#### 2.1. The Super-Resolution Algorithm

- (a)
- High-resolution, band-specific information S is separated from common-band information W. Firstly, the 10 m resolution band ${\mathrm{H}}^{\mathrm{o}}$ is subsampled to the 20 m version ${\mathrm{L}}^{\mathrm{d}}$. In this case, the optimal hybrid model is estimated by minimizing the difference between (a) the high-resolution observed pixel value ${\mathrm{H}}^{\mathrm{o}}$ and (b) the resolution enhancement value ${\mathrm{H}}^{\mathrm{r}}$ calculated from the subsampled data ${\mathrm{L}}^{\mathrm{d}}$ (Equation (2)). The initial weight ${\mathrm{W}}^{\mathrm{opt}}$ is set to 1/4. The initial shared value ${\mathrm{S}}^{\mathrm{opt}}$ is the mean value of ${\mathrm{H}}^{\mathrm{o}}$ of each high-resolution pixel it covers. The optimal weight value ${\mathrm{W}}^{\mathrm{opt}}$ and shared value ${\mathrm{S}}^{\mathrm{opt}}$ are solved iteratively.$$\left\{{\mathrm{S}}^{\mathrm{opt}},{\mathrm{W}}^{\mathrm{opt}}\right\}=\mathrm{argmin}{\sum}_{\mathsf{\beta}\in \mathcal{H}}{\sum}_{\mathrm{x},\mathrm{y}}{\Vert {\mathrm{H}}_{\mathsf{\beta},\mathrm{x},\mathrm{y}}^{\mathrm{o}}-{\mathrm{H}}_{\mathsf{\beta},\mathrm{x},\mathrm{y}}^{\mathrm{r}}\Vert}^{2},$$
- (b)
- Low-resolution, shared-value S is calculated.$$\mathrm{V}=\mathrm{argmin}{\sum}_{\mathsf{\beta}\in \mathcal{H}}{\sum}_{\mathrm{x},\mathrm{y}}{\Vert {\mathrm{S}}_{\mathsf{\beta},\mathrm{x},\mathrm{y}}^{\mathrm{opt}}-{\sum}_{\mathrm{n}\in \mathrm{N}\left(\mathrm{x},\mathrm{y}\right)}{\mathrm{v}}_{\mathrm{x},\mathrm{y},\mathrm{n}}{\mathrm{L}}_{\mathsf{\beta},\mathrm{n}}^{\mathrm{d}}\Vert}^{2},$$$${\mathrm{S}}_{\mathrm{b},\mathrm{x},\mathrm{y}}^{\mathrm{fit}}={\displaystyle \sum}_{\mathrm{n}\in \mathrm{N}\left(\mathrm{x},\mathrm{y}\right)}{\mathrm{v}}_{\mathrm{x},\mathrm{y},\mathrm{n}}{\mathrm{L}}_{\mathrm{b},\mathrm{n}},$$$${\mathrm{S}}_{\mathrm{b},\mathrm{x},\mathrm{y}}^{\mathrm{cor}}={\overline{\mathrm{q}}}_{\mathrm{b},\mathrm{x},\mathrm{y}}{\mathrm{S}}_{\mathrm{b},\mathrm{x},\mathrm{y}}^{\mathrm{fit}},$$
- (c)
- Super-resolution pixel values H are calculated.$${\mathrm{H}}_{\mathrm{b},\mathrm{x},\mathrm{y}}={\mathrm{W}}_{\mathrm{x},\mathrm{y},0}\times {\mathrm{S}}_{\mathrm{b},\mathrm{x},\mathrm{y}}^{\mathrm{cor}}+{\mathrm{W}}_{\mathrm{x},\mathrm{y},1}\times {\mathrm{S}}_{\mathrm{b},\mathrm{x}+1,\mathrm{y}}^{\mathrm{cor}}+{\mathrm{W}}_{\mathrm{x},\mathrm{y},1}\times {\mathrm{S}}_{\mathrm{b},\mathrm{x},\mathrm{y}+1}^{\mathrm{cor}}+{\mathrm{W}}_{\mathrm{x},\mathrm{y},3}\times {\mathrm{S}}_{\mathrm{b},\mathrm{x}+1,\mathrm{y}+1}^{\mathrm{cor}}$$

#### 2.2. The Inversion Models

^{2}), the mean absolute percentage error (MAPE) (Equation (9)) and the root mean squared error (RMSE).

_{3}-N, COD and TP) and selected the band or band combination with high correlation as parameters for modeling. For machine learning models, too many input variables may not necessarily improve the inversion accuracy [14,18,51]. After many attempts, 4~6 bands or band combinations with high correlation with NH

_{3}-N, COD and TP were selected as parameters for modeling.

#### 2.3. Study Area

_{3}-N, COD and TP of 41 water samples were collected in the study area. The distribution of the measured sampling points and the location of the study area are shown in Figure 3.

#### 2.4. Sentinel-2a Data

## 3. Experiments and Results

#### 3.1. Consistency Evaluation of the Super-Resolution Image and Original Image

#### 3.2. Correlation Analysis among NH_{3}-N, COD and TP with Sentinel-2

_{3}-N, COD and TP with 276 groups composed of a single band or a band combination was calculated. Four combination modes were adopted: (A/B), (A−B), (A+B) and (A−B)/(A+B), where A and B represent two different bands. The R value with the highest correlation coefficient among the four combinations was used as the R value between the two bands to draw the correlation matrix (Figure 6). From the statistical results of these three correlation coefficient matrices, it could be seen that the correlation coefficients of band combinations were quite different. We found that the correlation between reflectance and NH

_{3}-N, COD and TP increased after super-resolution enhancement. It also showed that the inversion accuracy of NH

_{3}-N, COD and TP could be improved by the enhancement of the Sentinel-2 image using the super-resolution algorithm.

_{3}-N, among which the combination of Band 5 and Band 8 has the highest correlation with NH

_{3}-N and has a correlation coefficient reaching 0.78. It is speculated that Band 2, Band 3, Band 4, Band 5, Band 6, Band 7, Band 8 and Band 8a are important bands for NH

_{3}-N inversion. The combination of the visible band and the red edge band has a high correlation with COD (Figure 6c). The combination of Band 4 and Band 5 can significantly improve the correlation between COD and spectral information, and its correlation coefficient can reach 0.53. It can be inferred that Band 2, Band 3, Band 4, Band 5, Band 6, Band 11 and Band 12 are important bands for COD inversion. The correlation coefficient between TP and spectral reflectance was generally high (Figure 6e). The correlation coefficient of TP with the combination of Band 1 and Band 4 was the highest, and the correlation coefficient was 0.81. It is speculated that Band 1, Band 2, Band 3, Band 4, Band 5, Band 7, Band 11 and Band 12 are important bands for TP inversion.

#### 3.3. Accuracy Comparison of Inversion Models

_{3}-N, COD and TP were constructed. Twenty-three samples were used to train the models, and the remaining eighteen samples were selected for verification. The accuracy of each model method was evaluated by comparing the measured values with the estimated values. The detailed information on the optimal model inversion results is shown in Figure 7. For the super-resolution images, the optimal results obtained by the statistical regression method are shown in Figure 7a–c. The R

^{2}between the measured NH

_{3}-N and the estimated NH

_{3}-N using Band 5 and Band 8 was 0.67, the RMSE was 0.161 and the MAPE was 25.88%. The R

^{2}between the measured COD and the estimated COD using Band 4 and Band 5 was 0.53, the RMSE was 0.546 and the MAPE was 3.36%. The R

^{2}between the measured TP and the estimated TP using Band 1 and Band 4 was 0.60, the RMSE was 0.034, and the MAPE was 24.28%. For the original image, the optimal results based on statistical regression method are shown in Figure 7d–f. The R

^{2}of measured NH

_{3}-N and estimated NH

_{3}-N using Band 2 and Band 4 was 0.61, the RMSE was 0.177, and the MAPE was 29.33%. The R

^{2}of measured COD and estimated COD using Band 2 and Band 8a was 0.26, the RMSE was 0.756 and the MAPE was 4.62%. The R

^{2}of measured TP and estimated TP using Band 4 and Band 11 was 0.69, the RMSE was 0.032 and the MAPE was 30.58%. We found that when using the same inversion method, the accuracy of COD and NH

_{3}-N retrieved from the super-resolution image was higher than from the original image. Although the coefficient of determination R

^{2}between the measured TP and the estimated TP was reduced, the average relative percentage error MAPE was significantly reduced by 6.3%. In general, the super-resolution image is better for water quality inversion than the original Sentinel-2 image. In addition, it was found that in the process of constructing the statistical regression model, the correlation coefficient between the TP concentration value retrieved from the reciprocal model and the measured value data was higher, the error was smaller and the cubic function model was more suitable for the inversion of NH

_{3}-N and COD.

_{3}-N, COD and TP was constructed based on super-resolution images. The optimal inversion results based on the machine learning method are shown in Figure 8. The R

^{2}between the measured NH

_{3}-N and estimated NH

_{3}-N using Band 2, Band 3, Band 4, Band 5 and Band 8 was 0.74, the RMSE was 0.149 and the MAPE was 22.68%. The R

^{2}between the measured COD and estimated COD values using Band 2, Band 3, Band 4, Band 5, Band 6 and Band 7 was 0.60, RMSE was 0.476 and MAPE was 2.99%. The R

^{2}between measured TP and estimated TP using Band 1, Band 3, Band 4, Band 5, Band 11 and Band 12 was 0.81, the RMSE was 0.028 and the MAPE was 21.93%. The results showed that the machine learning method has greater advantages in estimating the concentration of water quality parameters of complex inland rivers.

#### 3.4. Spatial Distribution of Water Quality Parameters

_{3}-N, COD and TP in the Xinyang section of Huaihe River Basin is shown in Figure 9. Most of the water bodies in the study area were in a healthy state, which is consistent with the results of the local water resources bulletin. It can be seen that most of the ammonia nitrogen concentrations in the study area were within the limits of the three indicators (Figure 9a), and only the southeast part of the study area had mild COD pollution (Figure 9b). In addition, the concentration of total phosphorus in some sections of the Huanghe River was relatively high, and the pollution was serious (Figure 9c). The nutrient C:N:P required for the growth and reproduction of microorganisms is 100:5:1, and microorganisms can obtain C and N from nature, while P is almost completely supplied by human beings (there is no urban sewage with phosphorus removal or poor phosphorus removal and irrigation water flowing into water body on the land with phosphate fertilizer). It can be seen from the geographical location of the river section that the river passes through residential areas and that the discharge of domestic sewage directly affects the water quality of the river section, resulting in a TP concentration of the river section higher than that of other areas.

## 4. Discussion

_{3}-N (Figure 6a). Among them, the sensitivity of NH

_{3}-N to the near-infrared band shows the frequency-doubled or combined frequency characteristics of nitrogen-containing functional groups. In addition, COD has a high correlation with Band 2, Band 3, Band 4, Band 5 and Band 8a (Figure 6b). The sensitivity of COD to Band 3 and Band 8a shows the combined frequency of the vibrations of hydrogen-containing groups (O–H, C–H) in organic molecules and their frequency-doubled absorption characteristics. The red band and the red edge band are the sensitive bands of Chl-a [20], and the metabolism of phytoplankton in the water body will also release organic matter. Chl-a can reflect the level of phytoplankton inventory. From this process, COD is the passive factor of Chl-a. TP affects and controls the growth and reproduction of planktonic algae to different degrees, and some studies have shown that it is closely related to chlorophyll content [7]. In this paper, Band 1, Band 4 and Band 11 were used to estimate TP concentration in both the statistical regression method and the machine learning method, which provides a useful reference for monitoring TP concentration with band data of the multi-spectral imager. The rivers in the study area belong to a flowing water body, and the water composition is not uniform. Therefore, some sensitive bands of NH

_{3}-N, COD and TP in Sentinel-2 satellite are slightly different from those of previous studies.

_{3}-N, COD and TP) was calculated (Figure 10). The central wavelength and bandwidth of the same band of different data sources were different, so for different satellite images, the correlation between the same band or band combination and water quality parameters is different. Compared with other medium and high-resolution satellite data (GF-1 and Landsat 8), the band combination of Sentinel-2 data shows a relatively high correlation with water quality parameters (NH

_{3}-N, COD, TP) and has great potential in water quality parameter inversion.

## 5. Conclusions

_{3}-N, COD and TP) were estimated from Sentinel-2 data. It can be concluded from the present study that Sentinel-2 is an effective tool to establish a cheap and effective routine monitoring method for inland river water quality. The super-resolution algorithm can effectively improve the quality of Sentinel-2 data, weaken the negative impact of mixed pixels on water quality monitoring, and improve the accuracy of water quality prediction, which has great application potential in quantitative remote sensing of water quality. The machine learning model constructed in this paper can be used as the best method to predict water quality in the Xinyang section of Huaihe River Basin and can provides data support for water quality monitoring and water pollution prevention and control in Huaihe River Basin. Agencies can combine super-resolution technology with remote sensing data as an alternative to collecting and processing information on inland surface water quality. In the future, the super-resolution algorithm can be extended to other satellite remote sensing images with multispectral bands and different spatial resolutions. In terms of long-term dynamic water quality monitoring, multiple data sources can be combined.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Values (S) are shared between neighbor pixels and combined by weights (W) to form the high-resolution pixels. The black solid line represents the distribution of high-resolution pixels, and the gray dotted line represents the distribution of shared values across pixels.

**Figure 2.**Estimation of water quality parameters of inland medium and small rivers based on the super-resolution algorithm.

**Figure 4.**Comparison of the enhanced image and original image. (

**a**) RGB true-color image, R/G/B = Band4/Band3/Band2; (

**b**) Band 8a (20 m) of the original image; (

**c**) Band 8a (10 m) of the resampling image by nearest neighbor method; (

**d**) Band 8a (10 m) of the enhanced image by super-resolution algorithm; (

**e**) Band 9 (60 m) of the original image; (

**f**) Band 9 (10 m) of the resampling image by nearest neighbor method; (

**g**) Band 9 (10 m) of the enhanced image by super-resolution algorithm.

**Figure 5.**Reflectance consistency analysis of the super-resolution image and the original image. The X-axis is the original image reflectivity value, and the Y-axis is the super-resolution image reflectivity value.

**Figure 6.**The correlation coefficient matrix of water quality parameters with bands and band combinations. The X and Y axes are the respective bands of the image: (

**a**,

**c**,

**e**) super-resolution image; (

**b**,

**d**,

**f**) resampling image by nearest-neighbor method. (

**a**,

**b**) NH

_{3}-N; (

**c**,

**d**) Chemical Oxygen Demand (COD); (

**e**,

**f**) Total Phosphorus (TP). Relation of 0.6 > R > 0.4 is significant at the 0.05 level, and the relation of R > 0.6 is significant at the 0.01 level.

**Figure 7.**Accuracy assessment results of NH

_{3}-N, COD and TP estimated by the statistical regression models using super-resolution images (

**a**–

**c**) and original images (

**d**–

**f**). The X-axis is measured data, and the Y-axis is estimated data. (

**a**,

**b**,

**d**,

**f**) used the cubic function model; (

**c**,

**f**) used the reciprocal model.

**Figure 8.**Accuracy assessment results of NH

_{3}-N, COD and TP estimated based on the machine learning model. The X-axis is the measured data, and the Y-axis is the estimated data. (

**a**) Comparison of measured and estimated NH

_{3}-N; (

**b**) comparison of measured and estimated COD; (

**c**) comparison of measured and estimated TP.

**Figure 9.**The spatial distribution of NH

_{3}-N, COD and TP in the Xinyang section of Huaihe River Basin;

**1**is part of the Huanghe River;

**2**is part of the Nianyushan reservoir. (

**a**) The spatial distribution of NH

_{3}-N; (

**b**) the spatial distribution of COD; (

**c**) the spatial distribution of TP.

**Figure 10.**Distribution of the correlation coefficient between different band combinations and water quality parameters (NH

_{3}-N, COD and TP). The X-axis is the number of single bands and band combinations. G001, G002, ⋯, G028 and G029 are the numbers of the four multispectral bands and band combinations of the GF-1 satellite. L001, L002, ⋯, L090 and L091 are the numbers of the seven multispectral bands and band combinations of the Landsat 8 satellite. S001, S002, ⋯, S275 and S276 are the numbers of the seven multispectral bands and band combinations of Sentinel-2 satellite. The Y-axis is the R value. The labels in the figure are the band combination numbers and R values of the highest correlation between different satellite sensors and NH

_{3}-N, COD and TP. (

**a**) NH

_{3}-N; (

**b**) COD; (

**c**) TP.

TSR Models | Mathematical Expression (a, b, c and d Are Undetermined Parameters) |
---|---|

linear model | $\mathrm{y}=\mathrm{a}+\mathrm{b}\times {\mathrm{x}}^{1}$ |

quadratic model | $\mathrm{y}=\mathrm{a}+\mathrm{b}\times {\mathrm{x}}^{1}+\mathrm{c}\times {\mathrm{x}}^{2}$ |

cubic model | $\mathrm{y}=\mathrm{a}+\mathrm{b}\times {\mathrm{x}}^{1}+\mathrm{c}\times {\mathrm{x}}^{2}+\mathrm{d}\times {\mathrm{x}}^{3}$ |

exponential model | $\mathrm{y}=\mathrm{a}\times {\mathrm{e}}^{\mathrm{bx}}$ |

logarithmic model | $\mathrm{y}=\mathrm{a}+\mathrm{b}\times \mathrm{log}\left(\mathrm{x}\right)$ |

reciprocal model | $\mathrm{y}=\mathrm{a}+\frac{\mathrm{b}}{\mathrm{x}}$ |

power model | $\mathrm{y}=\mathrm{a}\times {\mathrm{x}}^{\mathrm{b}}$ |

Band | Wavelength Range (nm) | Spatial Resolution (m) |
---|---|---|

Band1—Coastal aerosol | 430.4~457.4 | 60 |

Band2—Blue | 447.6~545.6 | 10 |

Band3—Green | 537.5~582.5 | 10 |

Band4—Red | 645.5~683.5 | 10 |

Band5—Vegetation Red edge | 694.4~713.5 | 20 |

Band6—Vegetation Red edge | 731.2~749.2 | 20 |

Band7—Vegetation Red edge | 768.2~796.5 | 20 |

Band8—NIR | 762.6~907.6 | 10 |

Band8a—Vegetation Red edge | 848.3~881.3 | 20 |

Band9—water vapour | 932.0~958.0 | 60 |

Band11—SWIR | 1542.2~1756.7 | 20 |

Band12—SWIR | 2081.4~2323.4 | 20 |

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## Share and Cite

**MDPI and ACS Style**

Huangfu, K.; Li, J.; Zhang, X.; Zhang, J.; Cui, H.; Sun, Q.
Remote Estimation of Water Quality Parameters of Medium- and Small-Sized Inland Rivers Using Sentinel-2 Imagery. *Water* **2020**, *12*, 3124.
https://doi.org/10.3390/w12113124

**AMA Style**

Huangfu K, Li J, Zhang X, Zhang J, Cui H, Sun Q.
Remote Estimation of Water Quality Parameters of Medium- and Small-Sized Inland Rivers Using Sentinel-2 Imagery. *Water*. 2020; 12(11):3124.
https://doi.org/10.3390/w12113124

**Chicago/Turabian Style**

Huangfu, Kuan, Jian Li, Xinjia Zhang, Jinping Zhang, Hao Cui, and Quan Sun.
2020. "Remote Estimation of Water Quality Parameters of Medium- and Small-Sized Inland Rivers Using Sentinel-2 Imagery" *Water* 12, no. 11: 3124.
https://doi.org/10.3390/w12113124