# Quantitative Inversion Method of Surface Suspended Sand Concentration in Yangtze Estuary Based on Selected Hyperspectral Remote Sensing Bands

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}of 0.9203, RPD of 4.5697, RMSE of 0.0339 kg/m

^{3}, and RMSE% of 8.55%, which are markedly higher than those of other framework combination forms, further verifying the effectiveness of the FD-CARS-BP framework in the quantitative inversion process of SSSC in the Yangtze estuary.

## 1. Introduction

^{11}m

^{3}of water and 3.76 × 10

^{8}t of sediment transported into the East China Sea by the South Channel, North Channel, North Port, and North Branch every year. The large amount of water and sand discharge has a significant impact on water temperature, sedimentation, and the ecological environment, not only in the Yangtze River estuary, but also in the adjacent shelf seas [7]. The Yangtze River estuary is one of the three major estuaries in China; it is a medium tidal estuary with branching estuaries and four mouths into the sea [8]. The complex topographic and hydrodynamic conditions cause a more complex distribution of suspended sand concentration. Therefore, the study of suspended sediment content and distribution in the Yangtze estuary has important scientific significance and application value.

^{2}, RPD, RMSE, and RMSE%, to determine the optimal spectral transformation form, feature band extraction, and inversion model building methods based on hyperspectral data in the inversion process of SSSC in the Yangtze estuary; and constructs the best framework combination form. The best framework combination was constructed by determining the optimal spectral transformation, feature band extraction method, and inversion model building method. Finally, the constructed framework was applied to the 2016 airborne hyperspectral simultaneous monitoring experiment in the Yangtze River estuary to further validate its effectiveness in the inversion process of the SSSC in the Yangtze River estuary, and to provide methodological support for the hyperspectral remote sensing inversion of the SSSC.

## 2. Materials

#### 2.1. Quantitative Experimental Data and Preprocessing

_{rs}is determined using Equation (1).

_{p}, S

_{sw}, and S

_{sky}are the average reflectance measurements of the standard plate, sand-bearing water body, and sky, respectively; ρ

_{p}is the reflectance of the standard plate; and r is the reflectance of the water–air interface. In this experiment, the wind speed was approximately 5 m/s and the value of r was determined to be 0.025 [49].

_{0}is the mass of the membrane before weighing, and V is the water sample volume.

#### 2.2. Airborne Hyperspectral Experiment Data and Preprocessing

## 3. Methods

#### 3.1. Spectral Transformation Methods

#### 3.2. Feature Band Extraction Methods

#### 3.2.1. Successive Projections Algorithm

#### 3.2.2. Competitive Adaptive Reweighted Sampling Algorithm

- (1)
- Random selection of n samples using a Monte Carlo algorithm and the development of a partial least squares regression (PLSR) model.
- (2)
- Selecting the variables by exponentially decreasing function (EDP) and adaptive weighted sampling algorithm (ARS), retaining those with high regression coefficients and removing those with low regression coefficients.
- (3)
- Create a PLSR model with the retained variables as a new subset of variables and calculate the root mean square error of cross-validation (RMSECV).
- (4)
- Repeat steps (1)–(3), and select N subsets of variables after N Monte Carlo sampling to obtain N RMSECVs, and select the subset of variables with the smallest RMSECV as the optimal band combination.

#### 3.3. BP Neural Network

#### 3.4. Model Evaluation Indices

^{2}), ratio of performance deviation (RPD), root mean square error (RMSE), and root mean square error percentage (RMSE%) were used to evaluate the performance of the inverse model of suspended sand concentration, and are calculated as follows:

^{2}indicates the strength of the correlation between measured and predicted values; RPD indicates the predictive ability of the model, and RPD less than 1.5 indicates very poor predictive ability of the model, between 1.5 and 2.0 indicates poor predictive ability of the model, and greater than 2.0 indicates good predictive ability of the model [57]. RMSE indicates the standard deviation of the prediction error, and RMSE% is the percentage of the standard deviation. Smaller RMSE and RMSE% values indicate a higher prediction accuracy of the model.

## 4. Results

#### 4.1. Quantitative Experimental Spectral Characteristic Curve

#### 4.2. Feature Band Extraction Results

#### 4.3. Construction of Inverse Model Results Based on Feature Bands

^{2}, RPD, RMSE, and RMSE%, as shown in Figure 9 and Figure 10. Figure 9 shows the results of inverse modeling based on SPA-extracted feature bands, and it was observed that the accuracies of the PLSR model and BP neural network model constructed based on different spectral transformation forms are different. Comparing the R

^{2}values, it was observed that the highest R

^{2}is 0.9927 for the FD-based SPA-BP model, and the lowest R

^{2}is 0.9119 for the SD-based SPA-PLSR model; comparing the RPD, it was observed that the highest accuracy is achieved for the FD-based SPA-BP model, with an RPD of 10.5649, and the lowest accuracy is achieved for the SD-based SPA-PLSR model, with an RPD of 3.0364; similarly, comparing RMSE and RMSE% shows that the SPA-BP model constructed based on FD has the highest accuracy, with 20.9943 mg/L RMSE and 9.92% RMSE%, and the SPA-PLSR model constructed based on SD has the lowest accuracy, with 69.8012 mg/L RMSE and 29.47% RMSE%.

^{2}values, it was observed that the highest R

^{2}is 0.9947 for the FD-based CARS-BP model, and the lowest R

^{2}is 0.9428 for the SQR-based CARS-PLSR model; comparing the RPD, it was observed that the highest accuracy is achieved by the FD-based CARS-BP model, with an RPD of 12.5453, and the lowest accuracy is achieved by the SQR-based CARS-PLSR model, with an RPD of 4.9796. The same comparison of RMSE and RMSE% shows that the CARS-BP model constructed based on FD has the highest accuracy, with an RMSE of 16.5801 mg/L and RMSE% of 8.08%, whereas the CARS-PLSR model constructed based on SQR had the lowest accuracy, with an RMSE of 52.1268 mg/L and RMSE% of 24.12%. Overall, FD is the best form of spectral transformation for both SPA and CARS to extract feature bands.

^{2}and RPD, and lower RMSE and RMSE%. For the same feature band extraction method, the accuracy of the BP neural network model is markedly higher than that of the PLSR model. Therefore, the best framework combination is FD-CARS-BP for the hyperspectral-based inversion of the SSSC in the Yangtze estuary.

#### 4.4. Validation of the Model Framework

^{2}, RPD, RMSE, and RMSE% were calculated to evaluate the model accuracy. The FD-SPA-PLSR, FD-SPA-BP, and FD-CARS-PLSR models were also established to compare their inversion accuracies, as shown in Figure 12. Compared with the other three models, the R

^{2}and RPD of the FD-CARS-BP model were the largest, 0.9203 and 4.5697, respectively, and the RMSE and RMSE% of the FD-CARS-BP model were the smallest (0.0339 kg/m

^{3}and 8.55%, respectively), indicating that FD-CARS-BP can be effectively used for the extraction and inversion of the characteristic waveband of SSSC in Yangtze River estuary modeling.

## 5. Discussion

#### 5.1. Construction of Inversion Model

^{2}, RPD, RMSE, and RMSE% were calculated to evaluate the accuracy of the inverse model and compare with the accuracy of the FD-CARS-BP model proposed in this paper, as shown in Table 6. Compared with the commonly used satellite visible and near-infrared wavelengths, where 655 nm and 870 nm are located in bands 4 and 5 of Landsat 8 OIL, respectively; 660 nm and 840 nm correspond to bands 3 and 4 of Landsat TM, respectively; 860 nm and 870 nm correspond to bands 2 and 16 of MODIS, respectively, which are the commonly used wavelengths for quantitative sand concentration inversion; 859 nm is the band with the largest correlation coefficient in hyperspectral images. It can be found that the accuracy of the FD-CARS-BP model has been significantly improved compared with the single-band model. Because the number of bands in multispectral remote sensing is small, the spectral resolution is low, and the spectral range of each band is long, which cannot express the changes in spectral information more finely, while the narrow bands in hyperspectral images can effectively solve this problem, and the BP neural network model constructed based on the feature bands extracted by CARS can derive quantitative estimations of the SSSC more accurately.

^{2}, RPD, RMSE, and RMSE% were calculated to evaluate the accuracy of each model, all of which were compared with the accuracy of FD-CARS-BP model, as shown in the table. It can be observed that the accuracy of the FD-CARS-BP model is still significantly higher than that of the combined two-band model.

^{2}, RPD, RMSE, and RMSE%, are calculated and compared with the PLSR model and BP neural network model for accuracy, and the results are shown in Table 6. It can be seen that the accuracy of the FD-CARS-BP model proposed in this study is still higher than that of other models, and its R

^{2}value is as high as 0.99, its RPD is greater than 12, its RMSE is less than 16 mg/L, and its RMSE% is only 8.08%, all of which have more obvious advantages.

#### 5.2. The Validation of the Model Framework

#### 5.3. The Limitations of the Model Framework

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Quantitative experimental scenes and main instrumentations. (

**a**) Quantitative experimental scenes. (

**b**) ASD Field Spec handheld hyperspectrometer. (

**c**) AQU Alogger 310TY turbidimeter with a range of 10,000 FTU.

**Figure 2.**Airborne hyperspectral experiment area. The green square on this figure is the location of Shanghai. The green line leads to a magnified view of the area. The blue square on this figure is the area covered by the airborne hyperspectral image. The blue line leads to the hyperspectral image map and the location map of the sampling points.

**Figure 5.**Spectral characteristic curves of 6 spectral transformation forms. (

**a**) The raw reflectance spectra (RS), (

**b**) the first derivative of the reflectance spectra (FD), (

**c**) the second derivative of the reflectance spectra (SD), (

**d**) the square root of the reflectance spectra (SQR), (

**e**) the reciprocal of logarithm of reflectance spectra (RLG), (

**f**) the mean center of the reflectance spectra (MC).

**Figure 6.**SPA−based feature bands extracted by different spectral transformation forms. (

**a**) The raw reflectance spectra (RS), (

**b**) the first derivative of the reflectance spectra (FD), (

**c**) the second derivative of the reflectance spectra (SD), (

**d**) the square root of the reflectance spectra (SQR), (

**e**) the reciprocal of logarithm of reflectance spectra (RLG), (

**f**) the mean center of the reflectance spectra (MC).

**Figure 7.**CARS feature band extraction process of FD. (

**a**) The number of sampled variables, (

**b**) 5-fold root mean squared error of cross−validation (RMSECV) values, and (

**c**) regression coefficient path of each spectral variable during the 50 iterations.

**Figure 13.**Correlation matrix. (

**a**) Correlation coefficient of DWI, (

**b**) correlation coefficient of RWI, (

**c**) correlation coefficient of AWI, (

**d**) correlation coefficient of NDWI. The small red squares in this figure refers to the band with the largest correlation coefficient, that is, the characteristic band.

Parameters | Value |
---|---|

Wavelength Range | 325–1075 nm |

Sampling Interval | 1 nm |

Spectral Resolution | 3 nm |

Integration time | ≥8.5 ms |

Field of view | 25° |

Parameters | Value |
---|---|

Wavelength Range | 300–1000 nm |

Number of Channels | 270 |

Spectral Resolution | 2.6 nm |

Flight altitude | 1000 m |

Spatial resolution | 1.2 m |

ID | SSSC (mg/L) | ID | SSSC (mg/L) |
---|---|---|---|

1 | 554.5 | 10 | 197.6 |

2 | 451.5 | 11 | 259.6 |

3 | 809.8 | 12 | 420.3 |

4 | 843.6 | 13 | 476.6 |

5 | 968.8 | 14 | 439.5 |

6 | 729.5 | Max | 968.8 |

7 | 357.8 | Min | 197.6 |

8 | 345.3 | Mean | 511.8 |

9 | 310.9 | SD | 288.3 |

Name | Method or Formula | Abbreviation |
---|---|---|

First Derivative | Savitzky–Golay method | FD |

Second Derivative | Savitzky–Golay method | SD |

Square Root | ${x}_{sqrt}=\sqrt{{x}_{i}}$ | SQR |

Mean Centering | ${\mathrm{x}}_{\mathrm{mcenter}}=\mathrm{x}-\overline{\mathrm{X}}$ | MC |

Reciprocal of Logarithmic | ${\mathrm{x}}_{1}/\mathrm{lg}=1/{\mathrm{log}}_{10}{(\mathrm{x}}_{\mathrm{i}}$) | RLG |

Datasets | No. | Minimum (mg/L) | Maximum (mg/L) | Average (mg/L) |
---|---|---|---|---|

training | 30 | 3.64 | 654.39 | 200.39 |

validation | 11 | 3.62 | 682.06 | 210.40 |

Variable | Model | R^{2} | RPD | RMSE (mg/L) | RMSE% | |
---|---|---|---|---|---|---|

655 nm | y = 10093x − 115.67 | 0.7930 | 1.9634 | 96.6928 | 47.71% | |

y = 8.8443e^{78.31x} | 0.9821 | 3.4376 | 81.8898 | 33.37% | ||

y = 126.13ln(x) + 677.1 | 0.3965 | 0.9219 | 169.7026 | 98.12% | ||

y = 280010x^{2} − 6409.2x + 43.773 | 0.9665 | 5.3117 | 39.9233 | 18.21% | ||

660 nm | y = 10173x − 113.17 | 0.7969 | 1.9876 | 95.7472 | 47.14% | |

y = 9.1108e^{78.596x} | 0.9828 | 3.3746 | 84.1994 | 34.16% | ||

y = 124.38ln(x) + 673.57 | 0.3937 | 0.9883 | 170.6553 | 93.01% | ||

y = 279307x^{2} − 6112.1x + 41.65 | 0.9682 | 5.4470 | 38.9028 | 17.74% | ||

840 nm | y = 22336x − 28.066 | 0.9703 | 5.3603 | 37.8763 | 17.35% | |

y = 24.442e^{140.37x} | 0.8748 | 1.7822 | 232.9018 | 84.36% | ||

y = 160.08ln(x) + 1004.9 | 0.7059 | 1.5699 | 115.0457 | 56.19% | ||

y = 202027x^{2} + 16921x−8.335 | 0.9870 | 7.8004 | 26.3551 | 12.01% | ||

860 nm | y = 25350x − 13.708 | 0.9836 | 6.84 | 29.4738 | 13.55% | |

y = 27.664e^{155.33x} | 0.8621 | 1.7759 | 232.1537 | 86.01% | ||

y = 153.96ln(x) + 1011.2 | 0.7574 | 1.6222 | 105.2444 | 49.97% | ||

y = 105858x^{2} + 22906x − 6.5177 | 0.9885 | 8.0156 | 25.3042 | 11.61% | ||

870 nm | y = 27158x − 7.3402 | 0.9776 | 6.1185 | 33.267 | 15.25% | |

y = 32.182e^{158.01x} | 0.8496 | 1.735 | 242.3157 | 89.10% | ||

y = 162.45ln(x) + 1071.2 | 0.6016 | 1.5411 | 161.5067 | 92.94% | ||

y = 91181x^{2} + 25205x − 2.011 | 0.9823 | 6.8874 | 29.7421 | 13.64% | ||

859 nm | y = 24537x − 12.381 | 0.9792 | 6.1074 | 34.7046 | 16.16% | |

y = 26.63e^{160.09x} | 0.8569 | 0.8011 | 264.5516 | 92.54% | ||

y = 146.04ln(x) + 957.7 | 0.7286 | 1.8937 | 111.9162 | 56.06% | ||

y = 30674x^{2} + 23845x − 10.34 | 0.9812 | 6.3617 | 33.3162 | 15.50% | ||

689 nm/737 nm | y = − 312.32x + 909.04 | 0.6771 | 1.7564 | 120.6730 | 55.11% | |

y = 15515e^{−2.181x} | 0.9811 | 6.3245 | 33.5115 | 15.42% | ||

y = − 740.5ln(x) + 785.62 | 0.7872 | 2.1519 | 98.4939 | 44.54% | ||

y = 189.27x^{2} − 1213.6x + 1923.7 | 0.9091 | 3.1233 | 67.8582 | 30.19% | ||

717 nm − 400 nm | y = 19738x − 31.298 | 0.9453 | 4.2041 | 50.4119 | 23.78% | |

y = 24.99e^{120.42x} | 0.9650 | 2.3001 | 92.1450 | 39.64% | ||

y = 195.92ln(x) + 1144.6 | 0.7858 | 2.1578 | 98.2221 | 47.83% | ||

y = 291334x^{2} + 10938x + 5.2895 | 0.9727 | 5.7809 | 36.6645 | 17.19% | ||

859 nm + 859 nm | y = 12795x − 17.05 | 0.9792 | 6.1712 | 32.8574 | 14.95% | |

y = 26.932e^{78.775x} | 0.8610 | 1.7498 | 240.0633 | 87.32% | ||

y = 156.48ln(x) + 912.48 | 0.7286 | 1.6072 | 110.4144 | 52.91% | ||

y = 35185x^{2} + 11178x−7.4145 | 0.9868 | 7.5416 | 27.1006 | 12.30% | ||

$\frac{689\mathrm{nm}-737\mathrm{nm}}{689\mathrm{nm}+737\mathrm{nm}}$ | y = − 1758.5x + 847.52 | 0.8232 | 2.0634 | 89.6017 | 41.44% | |

y = 6866e^{−11.42x} | 0.9740 | 5.4736 | 42.9276 | 19.95% | ||

y = − 601ln(x) − 426.44 | 0.9192 | 3.0110 | 62.5053 | 28.79% | ||

y = 4534.4x^{2} − 4988.2x + 1375.2 | 0.9647 | 4.0573 | 46.0922 | 21.07% | ||

MLR | 0.9788 | 6.8815 | 30.8272 | 15.12% | ||

PLSR | 0.9697 | 5.6096 | 37.7826 | 17.71% | ||

FD−CARS−BP | 0.9947 | 12.5453 | 16.5801 | 8.08% | ||

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## Share and Cite

**MDPI and ACS Style**

Luan, K.; Li, H.; Wang, J.; Gao, C.; Pan, Y.; Zhu, W.; Xu, H.; Qiu, Z.; Qiu, C.
Quantitative Inversion Method of Surface Suspended Sand Concentration in Yangtze Estuary Based on Selected Hyperspectral Remote Sensing Bands. *Sustainability* **2022**, *14*, 13076.
https://doi.org/10.3390/su142013076

**AMA Style**

Luan K, Li H, Wang J, Gao C, Pan Y, Zhu W, Xu H, Qiu Z, Qiu C.
Quantitative Inversion Method of Surface Suspended Sand Concentration in Yangtze Estuary Based on Selected Hyperspectral Remote Sensing Bands. *Sustainability*. 2022; 14(20):13076.
https://doi.org/10.3390/su142013076

**Chicago/Turabian Style**

Luan, Kuifeng, Hui Li, Jie Wang, Chunmei Gao, Yujia Pan, Weidong Zhu, Hang Xu, Zhenge Qiu, and Cheng Qiu.
2022. "Quantitative Inversion Method of Surface Suspended Sand Concentration in Yangtze Estuary Based on Selected Hyperspectral Remote Sensing Bands" *Sustainability* 14, no. 20: 13076.
https://doi.org/10.3390/su142013076