## 3 Simulation Results
### Multiple Scattering and Wind-Driven Roughened Sea Surface Effect  
Influences of multiple scattering and wind-driven roughened sea surface conditions on simulation results were then analyzed. We separated the first order of scattering, second order of scattering, third order of scattering, and more than third order of scattering parts in the total scattering signal, as shown in Figure 5a. The black line is the total signal, which is the sum of the single, double, triple and more than triple scattering event curves. Figure 5a shows that the single scattering signal decreases as depth increases, while multiple scattering signal increases first and then decreases. This is because, as the photon travels forward, multiple scattering occurs more frequently in water. Besides, the signal is the deepest depth the photon attained prior to scattering back to the surface and being detected. It also shows that the single, double, triple and greater than triple scattering events curves cross at about 20 m. The multiple scattering occurs more frequently as the water scattering coefficient becomes larger. When the water scattering coefficient is large, the depth of curves cross decreases, and the depth increases when the water scattering coefficient is small. The first order of scattering in logarithmic form decreases linearly with the increase of depth, which agrees with [PERSON]'s conclusion that light falls exponentially in water [1], and it indicates that our simulation method is correct and feasible. The contribution of high-order scattering signal increases with depth, until it dominates at a certain depth. Figure 5b shows the slope of return signal, namely, lidar effective attenuation coefficient (\(K_{\text{sys}}\)) falls between beam attenuation coefficient \(c\) and absorption coefficient \(\alpha\). The system attenuation coefficient, \(K_{\text{sys}}\), lies somewhere between \(\alpha\) and \(c\), and is dependent on the relative values of the transmitter beam spot size, transmitter divergence, receiver aperture, and receiver field of view. As Figure 5b shows, we can see that the cyan curve using a narrow FOV fits well with the blue curve of \(c\) and the black curve using a large FOV fits well with the dark green curve of \(\alpha\). It approaches \(c\) with a narrow FOV and approaches \(\alpha\) with a large FOV. \(K_{\text{sys}}\) approaches with a narrow field of view \(c\) since almost all of the light that had been scattered was not detected by the receiver; thus, the decay rate of the backscatter signal is the sum of \(\alpha\) and b. Since the field of view was large enough, \(K_{\text{sys}}\) approaches \(\alpha\) since the only light lost at the receiver was what had been absorbed. However, for a very large beam and large receiver aperture and field of view, \(K_{\text{sys}}\) approaches \(\alpha+b_{b}\) since almost all of the forward propagating photons remain in the receiver FOV until absorbed or scattered in the backward direction. However, when the field of view was large enough, \(K_{\text{sys}}\) approaches \(\alpha\), since the only light lost at the receiver was what had been absorbed. These results agree with previous studies [23; 24; 25]. They indicate that the configuration of multiple FOV applied for lidar system is useful for optical properties' inversion in various types of water. Figure 5c,d show the influence of wind-driven roughened sea surface on simulation signals. The incident angle in Figure 5c,d is the lidar incident angle. The reason why it spans to about 90 degrees in the \"From air to sea\" plot, but only to about 48 degrees in the \"From sea to air\" plot, is due to the critical angle for total internal reflection. We can see that the lidar transmittance coefficients remain unchanged when wind speed is less than 9 m/s, but it decreases significantly when the wind speed is greater than 9 m/s. It indicates that both wind-driven roughened sea surface and multiple scattering have significant effects on simulation results, which should not be ignored.