1. Introduction
Airborne LiDAR bathymetry (ALB) is an accurate, cost-effective, and rapid technique for shallow water measurements [
1,
2,
3,
4,
5,
6]. Aside from its use in traditional nautical charting, ALB is also widely utilized to monitor engineering structures, sand movement, and environmental changes, as well as in resource management and exploitation [
7,
8,
9,
10]. ALB can also be used to produce environmental products, such as seafloor reflectance images, seafloor classification maps, and water column characterization maps [
11].
Figure 1 shows the principle of ALB measurements. Bathymetric accuracy is an essential requirement for a successful ALB system, and it is primarily affected by ALB measurement and ocean hydrological parameters. ALB bathymetric errors can be resolved by two components: depth bias and residuals [
12]. For an integrated infrared (IR) and green ALB system in which an additional IR laser is used to detect the water surface accurately, depth bias is mainly induced by pulse stretching of the green bottom return [
2,
13,
14]. Geometric dispersion and multiple scattering lead to temporal stretching of the received green bottom return, and this phenomenon is known as the pulse stretching effect [
1,
2,
3,
13,
14,
15,
16]. The pulse waveform is distorted (e.g., peak shifting) by the pulse stretching effect. Peak shifting induces bias in bathymetry estimates that is based on a peak detection of up to 92% of the true water depth [
14]. This depth bias is the largest source of error in ALB depth measurements. Water surface waves also affect depth bias. As energy is put into the water surface by wind, small capillary waves develop [
17]. As the water gains energy, the waves increase in height and length. When they exceed 0.0174 m in length, they take on the shape of the sine curve and become gravity waves [
17]. Increased energy increases the steepness of the waves [
17]. Different surface slope values may steer laser rays away from the original ray path, resulting in angle and depth biases. Depth bias can be corrected through theoretical analysis [
2,
14], empirical modeling [
12,
18,
19], and the error statistics method [
20,
21].
The Monte Carlo numerical method and the analytical approach are two classic theoretical analysis methods [
15]. A Monte Carlo simulation is used to estimate depth biases with the impulse response function (IRF), which is a function of the beam scanning angle, sea depth, phase function, optical depth, and single-scattering albedo [
2]. Single-scattering albedo is a main parameter in IRF and can be obtained by estimating the scattering coefficient. However, estimating scattering coefficients accurately and efficiently is difficult. Depth biases induced by peak shifting can be analyzed with the Water LiDAR (Wa-LID) simulator [
14]. Wa-LID was developed to simulate the reflection of LiDAR waveforms from water across visible wavelengths [
22]. The relationship among the time shifts of waveform peaks, bottom slope, water depth, and footprint size is modeled with the Wa-LID simulator [
14]. However, the model is based on the assumptions of a vertical incident beam and homogeneous water clarity, which are inconsistent with actual circumstances.
By combining bathymetric ALB and sonar data, an empirical model to depict ALB depth bias was established in a previous study through regression analysis; the model is a function of water depth only [
12,
18]. The ALB depth corrected by this model can meet the requirements of only several low-accuracy applications because the two parameters cannot fully reflect ALB depth bias. Wright et al. [
19] improved the depth bias model by adding a constant term. This model is also a function of water depth only and is simple to establish, but its adaptability to complex and variable ALB measurement and ocean hydrological parameters is weak. Therefore, an accurate model that considers all influencing factors must be built.
The error statistics method is often used to correct ALB depth biases in river measurements [
20,
21]. The magnitude and spatial variation of depth bias can be evaluated by referring to ground surveying results and can be obtained by subtracting ground surveying elevations from ALB-derived elevations. The error statistics shows that depth bias has low relevance with local topographic variance or flow depth and can be corrected by subtracting the mean bias from raw ALB-derived depths. This method is simple and efficient in correcting depth biases in water areas with small depth variations and has been applied successfully in rivers by Hilldale et al. [
20] and Skinner et al. [
21]. However, the method is difficult to apply in water areas with complicated depth variations.
All of these methods improve the ALB bathymetric accuracy to a certain extent. The error statistics method is simple and highly efficient, but its adaptability to complex ocean hydrological environments is weak. The theoretical analysis method provides an understanding of the physical processes involved, but it is limited by simplified assumptions that may be inconsistent with the actual ocean hydrological environment; therefore, it requires further improvement. The empirical modeling method can be used to establish a model of the relationship between ALB depth bias and influencing factors in a specific environment. This method is simple and easy to implement. However, in the empirical model, the parameters that influence depth bias should be completely identified, and their significance should be fully analyzed. Otherwise, the established empirical model may result in low-accuracy correction.
An improved model for ALB depth bias correction is developed in this study by analyzing ALB bathymetric mechanisms and the factors that influence ALB depth accuracy. The proposed model considers various parameters, such as the water depth, turbidity, beam scanning angle, and sensor height.
This paper is structured as follows.
Section 2 provides the detailed method of building the proposed depth bias model.
Section 3 presents the validation and analysis of the proposed method through experiments.
Section 4 provides the corresponding discussions.
Section 5 presents the conclusions and recommendations obtained from the experiments and discussions.
4. Discussion
The proposed method provides a good means to reduce depth bias and obtain an accurate water depth by ALB. The following factors influence the applications and accuracies of the proposed method.
(a) Different ALB systems
ALB systems are categorized as integrated IR and green ALB systems and green ALB systems according to the lasers used [
36,
37,
38,
39]. For integrated IR and green ALB systems in which an additional IR laser is used to detect the water surface accurately, the improved depth bias model can be used directly to correct the ALB-derived depth. However, for green ALB systems, the primary IR laser is no longer used, and the green surface return cannot accurately represent the water surface [
1,
38,
39]. The height models of green ALB systems proposed by Jianhu Zhao et al. [
38] that consider near water surface penetration (NWSP) of the green laser should be used to correct the green water surface and water bottom heights. Then, the improved depth bias model can be used to correct the ALB-derived depth bias.
(b) Effects of surface wave and bottom slope
Surface wave and bottom slope affect ALB depth. As mentioned previously, the surface wave affects depth bias and is difficult to characterize and incorporate within a model [
18]. The effect is not considered in the improved depth bias model but is weakened during data preprocessing. During data preprocessing, the slope of gravity waves can be estimated by referring to wave height and wavelength caused by wind speed, and its effect can be compensated for by adding the surface wave slope to the beam scanning angle when the laser beam footprint is incident on a single water surface facet or a single slope value. Capillary waves are small. Water surface with small capillary waves can be regarded as flat. The bottom slope can change the bottom incident angle of the laser beam and affect the pulse stretching of the green bottom return [
14]. The larger the bottom slope is, the more the peak of the bottom return shifts to the surface return and the larger the depth bias is [
14]. In reference [
14], a model was proposed to estimate the effect of the bottom slope on ALB depth, and the effect varying with the bottom slope is shown in
Figure 7. The effect intensifies with the increase in the bottom slope. If the limitation is set to 0.05 m, then the effect of the bottom slope less than 7° can be ignored when the beam footprint radius is less than 2 m and the water depth is less than 10 m; otherwise, the effect should be considered. By using the model proposed in reference [
14], the effect can be estimated by integrating the beam footprint size, water depth, and bottom slope for the compensation of ALB depth. The residual of the compensation remains in the depth bias and should be further corrected by the improved model proposed in this study.
(c) Effects of flight directions
As shown in
Figure 2, the flight directions of the six lines are different. Different flight directions change the relative location of the sensor to the sun, introduce various background noises in the pulse waveform, and affect the ALB depth measurements. The effect can be filtered before using a pulse detection algorithm [
40]. Moreover, the effect of the surface wave on depth bias varies with flight directions [
16]. The asymmetry of surface waves also plays an important role, affecting the return signal. It distorts the signal by altering the downwelling light field, complicating the comparison of the bottom return signals from two different flightlines. The asymmetry effects are less pronounced in strongly scattering environments making the effect less important in turbid waters or at greater depths [
16].
Figure 8 shows the residual depth biases of the six flight lines in the red rectangular area in
Figure 2. With the sounding result as a reference, the residual depth biases of different-direction flight lines were calculated by subtracting the reference from the ALB depth compensated for by the improved depth bias model. Standard deviations of 0.059 and 0.042 m were obtained by the northwest–southeast flight lines (lines 1, 2, and 5 in
Figure 2) and the southeast–northwest flight lines (lines 3, 4, and 6), respectively. The residual of the northwest–southeast flight direction was slightly larger than that of the southeast–northwest flight direction. Large background noise may be introduced to the northwest–southeast direction ALB measurements because this direction is facing sunlight.
(d) Applications
The current experiment was conducted in a shallow water area with a water depth range of 3 to 4.5 m and SSC variation of 164 mg/L to 193 mg/L. The proposed improved model can correct the depth bias in this area. In other water areas with different water depths and turbidity, the depth bias model needs to be built according to the corresponding parameters of the measurement area used in Equation (6). The established depth bias model may be different from the above model in terms of model coefficients, but the modeling process and model form are the same as those depicted above.
5. Conclusions and Suggestions
An improved model for ALB depth bias correction was developed by considering ALB measurement and ocean hydrological parameters. The t-test of the model coefficient showed that all of the parameters in the improved model are significant and should be included, which indicates that the proposed improved model is reasonable. The traditional model and the proposed improved model were used to correct raw ALB-derived depth bias. The accuracies of ALB-derived depths corrected by the two models meet the “Order-1” specification of the IHO and have standard deviations of 0.086 and 0.055 m, respectively. The improved model is better than the traditional model.
In the application of the improved model, various factors, such as different ALB systems, surface waves, seabed slopes, and measurement areas, should be considered. The process of depth bias correction depicted in this study is appropriate for integrated IR and green ALB systems, but can be used for green ALB systems after calculating the water surface and water bottom heights considering the NWSP of the green laser. The surface wave effect can be estimated by referring to the wave height and can be compensated for by adding the surface wave slope to the beam scanning angle. The effect of the bottom slope can be estimated and compensated for by an approximation model. Although the modeling process and model form are suitable for other water areas, the depth bias model must be re-established by the local modeling parameters. The authors recommend using the traditional model in water areas with approximately the same turbidity and using the improved model in water areas with varying turbidity. In addition, density and representativeness should be considered in setting SSC sampling stations based on the measured water area to guarantee the accuracy of the proposed method.