# Retrieval of Suspended Sediment Concentration from Bathymetric Bias of Airborne LiDAR

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Waveform Decomposition Method

_{s}, t

_{s}, and σ

_{s}are the amplitude, peak position, and standard deviation of the AIR, respectively. Typically, the VBR is expressed as a triangular function:

_{c}, a, b, and c are the amplitude, start, peak, and end position of the VBR, respectively. BR is expressed as a Gaussian function if it exists in the raw waveform.

_{b}, t

_{b}, and σ

_{b}are the amplitude, peak position, and standard deviation of the BR, respectively. The constrained nonlinear optimization can be transformed into the following form:

_{C}and slope K = A

_{C}/(c − b) of the VBR can be obtained using constrained waveform decomposition and these can be used as indicators to retrieve the SSC. The waveform decomposition method has been verified as an effective method for SSC retrieval using airborne bathymetric LiDAR data [10]. However, full-waveform data are not always available for users; thus, this method is limited in its practical applications.

#### 2.2. Measurement Bias Method

_{0}obtained by single-beam or multibeam echo sounders as a reference, the depth bias Δh of the water bottom point derived by the green laser can be expressed as [26]:

_{ALB}represents the height of the water bottom point derived by the green laser. Previous studies have shown that the depth bias of ALB varies with water depth [28,29]. The rate of change in Δh with water depth is mainly affected by the SSC, beam scanning angle, and sensor height. Zhao et al. used the stepwise regression method to build a depth bias model considering SSC, which improved the ALB sounding accuracy [26] as follows:

_{1}–β

_{5}are the model coefficients, C is the SSC, θ is the beam scanning angle, and H is the sensor height. Conversely, the SSC can be estimated if Δh is known. Compared with SSC inversion using the NWSP derived by means of a green laser, this method does not require the water surface point to be derived using an infrared laser and can realize SSC inversion in a manner that is suitable for single- and dual-wavelength ALB systems.

## 3. Experiment and Results

#### 3.1. Research Area and Data Acquisition

_{1}, S

_{2}, and S

_{3}sampling stations were 315, 122, and 134 mg/L, respectively. Figure 3b presents an enlarged drawing of the red boxed area in Figure 3a. The blue, magenta, red, green, yellow, and cyan colors represent six strips of ALB measurements. The black curve represents Qinshan Island. The blue dotted lines represent the tracklines of single-beam echo sounding. Detailed descriptions of the experimental area and the Optech CZMIL system can be found in [26].

#### 3.2. Data Preparation

#### 3.3. SSC Modeling and Verification

^{2}θ, DH, and DH

^{2}. The hidden layer contains 20 neurons, and the output layer outputs the predicted value of the SSC. Neurons are connected in a feed-forward fashion with input neurons that are fully connected to neurons in the hidden layer and hidden neurons that are fully connected to neurons in the output layer [32]. The activation function, also called the transfer function, is used to transform the activation level of neuron x into an output signal [33]. The objective of the nonlinear activation function was to introduce non-linearity into the network. Without non-linearity, a neural net is unable to handle complex modeling problems [32]. The sigmoid symmetric function tansig is a commonly used activation function, and this was applied in our network as follows:

#### 3.4. SSC Inversion

## 4. Discussion

#### 4.1. Comparison Methods

#### 4.1.1. Exponential SSC Regression Model of Depth Bias

^{2}of the fitted exponential SSC model of ALB depth bias were 15.28 mg/L and 0.5116, respectively.

#### 4.1.2. Waveform Decomposition Method

- (1)
- Waveform extractionThe raw laser waveforms collected by ALB systems are usually stored in binary files to save storage space. The raw data files must be decoded according to the data file format to extract all useful parameters and raw waveform data.

- (2)
- Ocean-land waveform classificationALB systems can realize integrated ocean and land measurements based on the received laser pulse returns reflected from the ocean and land. Ocean-land waveform classification should be conducted to identify the ocean waveforms from the raw collected waveforms. Ocean-land waveform classification methods have been summarized and the dual-clustering method has been proposed as an effective method, with high accuracy for dual-wavelength ALB systems [35]. The dual-clustering method was used for ocean-land waveform classification in this study. The amplitudes of the IR waveforms were calculated and these are shown in Figure 8a. The yellow and blue colors in Figure 8b represent the spatial distributions of the obtained land and ocean waveforms, respectively.

- (3)
- Ocean waveform decompositionWaveform decomposition, which is achieved by fitting the mathematical waveform model to raw green waveforms using a nonlinear fitting approach, is a powerful tool to extract the VBR from raw bathymetric waveforms. An improved AVB decomposition method—setting reasonable lower and upper bounds of waveform parameters—has been proposed to guarantee the fidelity of the decomposed components [23]. The AVB decomposition method was performed on the ocean waveforms classified in step 2 to extract the VBR of each pulse waveform. Figure 9a shows the waveform decomposition results for a typical bathymetric waveform in the research area. The black discrete points represent the pulse return intensity with a sampling period of 1 ns. The magenta and blue curves represent the AIR and VBR, respectively. The green dotted line represents the sum of the AIR and VBR. The bottom return is missing in the raw waveform because of the high turbidity. The distribution of the amplitudes of the extracted VBRs for the entire research area is shown in Figure 9b. Although the AVB decomposition method has shown its effectiveness for VBR extraction [10], the decomposition accuracy of some waveforms was low and should be improved further, e.g., the amplitudes of VBRs at the edge of some strips shown in Figure 9b were significantly larger than those of the adjacent areas.

- (4)
- Empirical model construction and SSC retrievalThe SSCs at the positions of the previously described point pairs and corresponding amplitudes of VBRs are shown in Figure 10a. The results showed that the SSCs and VBR amplitudes presented a positive correlation. A power function was used to build an SSC model of the VBR amplitude, similarly to Equation (10), based on the least-squares method. As indicated by the blue dotted line in Figure 10a, the fitted-power empirical SSC model of the VBR amplitude is expressed as follows:$$\mathrm{SSC}=-3564{\mu}^{\u20130.7687}+241.2$$
^{2}of the SSC retrieval model of VBR amplitude were 2.28 mg/L and 0.906, respectively. The distribution of the SSC of the entire research area could be retrieved by inputting the VBR amplitudes extracted via waveform decomposition (Figure 9b) into the SSC retrieval model (Equation (12)). Compared with exponential regression and ANN-based SSC models of ALB depth bias, the waveform decomposition method showed a higher SSC retrieval accuracy. The shortcomings of the waveform decomposition method are that it comprises complex waveform processing procedures and the laser waveforms are not always available for users.In summary, the MSEs of the exponential SSC regression model of depth bias, the power SSC regression model of VBR amplitude, and the proposed ANN-based SSC model of depth bias were 15.28, 2.28, and 2.564 mg/L, respectively. The waveform decomposition method presented the highest SSC retrieval accuracy among the three SSC models. The accuracy of the ANN-based SSC model of depth bias was higher than that of the exponential regression SSC model of depth bias because the neural network was able to build more precise connections between ALB depth bias and SSC than the traditional regression method.

#### 4.2. Advantages and Limitations

_{ALB}can be obtained is essential for the calculation of depth bias Δh. With the exception of extremely turbid water, ALB can realize water bottom detection and provide h

_{ALB}. (2) Single-beam echo sounding cannot realize full-coverage measurements but can only provide information on discrete points. ALB depth bias values calculated by taking single-beam echo sounding data as a reference can be obtained at those discrete points. Therefore, SSC inversion using depth bias cannot realize planar inversion but only discrete-point inversion, as shown in Figure 7b. This limitation can be overcome by taking multibeam sonar data as a reference in the future.

#### 4.3. Generalization Ability

## 5. Conclusions and Suggestions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A2.**Regression of SSC prediction results: (

**a**) regression of training data, (

**b**) regression of validation data, (

**c**) regression of test data, (

**d**) regression of all data.

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**Figure 3.**Locations of the ALB and sonar measurements. (

**a**) Locations and (

**b**) local enlarged view of the research area.

**Figure 4.**Probability density distribution of the model input and output data. (

**a**) Depth bias, (

**b**) depth, (

**c**) sensor height, (

**d**) beam scanning angle, and (

**e**) SSC.

**Figure 7.**Spatial distributions of depth bias and the retrieved SSC. (

**a**) Depth bias of ALB, and (

**b**) retrieved SSC.

**Figure 8.**Spatial distributions of ocean and land waveforms. (

**a**) Amplitudes of IR waveforms, and (

**b**) laser spot positions of corresponding separated ocean (blue) and land (yellow) waveforms.

**Figure 9.**Waveform decomposition of a typical waveform and the distribution of VBR amplitudes. (

**a**) Waveform decomposition, and (

**b**) VBR amplitude.

**Figure 10.**Distribution of VBR amplitude and retrieved SSC. (

**a**) Relationship between SSC and VBR amplitude, and (

**b**) retrieved SSC using the empirical model.

Parameter | Min | Max | Mean | Std |
---|---|---|---|---|

Depth bias (m) | −0.305 | 1.221 | 0.161 | 0.28 |

Depth (m) | 3.022 | 4.559 | 3.366 | 0.314 |

Scanning angle (degree) | 15.553 | 20.938 | 19.052 | 1.021 |

Sensor height (m) | 394.007 | 441.333 | 420.381 | 10.701 |

SSC (mg/L) | 164.087 | 193.044 | 176.591 | 5.587 |

Datasets | Samples | MSE (mg/L) | R |
---|---|---|---|

Training | 218 | 0.421 | 0.993 |

Validation | 72 | 1.248 | 0.985 |

Testing | 72 | 2.564 | 0.960 |

Model Number | MSE (mg/L) | R |
---|---|---|

1 | 2.564 | 0.960 |

2 | 2.026 | 0.976 |

3 | 2.548 | 0.954 |

4 | 1.750 | 0.971 |

5 | 2.080 | 0.969 |

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**MDPI and ACS Style**

Zhao, X.; Gao, J.; Xia, H.; Zhou, F.
Retrieval of Suspended Sediment Concentration from Bathymetric Bias of Airborne LiDAR. *Sensors* **2022**, *22*, 10005.
https://doi.org/10.3390/s222410005

**AMA Style**

Zhao X, Gao J, Xia H, Zhou F.
Retrieval of Suspended Sediment Concentration from Bathymetric Bias of Airborne LiDAR. *Sensors*. 2022; 22(24):10005.
https://doi.org/10.3390/s222410005

**Chicago/Turabian Style**

Zhao, Xinglei, Jianfei Gao, Hui Xia, and Fengnian Zhou.
2022. "Retrieval of Suspended Sediment Concentration from Bathymetric Bias of Airborne LiDAR" *Sensors* 22, no. 24: 10005.
https://doi.org/10.3390/s222410005